The factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).
To determine the factors of the polynomial x^3 - 12x^2 - 2x + 24 by grouping, we can follow these steps:
Step 1: Group the terms in pairs. In this case, we can pair the first two terms and the last two terms:
(x^3 - 12x^2) + (-2x + 24)
Step 2: Factor out the greatest common factor from each pair. From the first pair, we can factor out x^2, and from the second pair, we can factor out -2:
x^2(x - 12) - 2(x - 12)
Step 3: Notice that we now have a common binomial factor of (x - 12) in both terms. Factor out this common binomial factor:
(x - 12)(x^2 - 2)
Therefore, the factored form of the polynomial x^3 - 12x^2 - 2x + 24 by grouping is (x - 12)(x^2 - 2).
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In the figure shown, 1 and 2 are _____.
vertical angles
complementary angles
supplementary angles
right angles
In the figure shown, 1 and 2 are; supplementary angles.
How to identify supplementary angles?According to geometry in mathematics, we know very well that the sum of angles on a straight line is 180 degrees. We also know that two angle s are said to be supplementary angles when they sum up to 180 degrees.
Now, from the given image, we know that angle 1 and angle 2 form a straight line and as such they sum up to 180 degrees
This then tells us that they are both supplementary angles.
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find m angle B round to mearest degree
The measure of angle B is 64. 2 degrees
How to determine the angleTo determine the measure of the angle, we have the different trigonometric identities.
We have that;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Using the sine identity, we have;
sin θ = opposite/hypotenuse
Substitute the values, we have;
sin B = 18/20
Divide the values, we have;
sin B = 0.900
Find the inverse value of sine, we have;
B = 64. 2 degrees
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30,000; Furniture ₹20,000; Goodwill 16,000;
Creditors 27,000; Bills Payable 13,000; Outstanding expenses
3,000; Due to Johnson 7,000; Capital ₹86,000.
2. Pass the opening entry and find out the amount due from
creditors:
Cash in hand 25,000; Cash at Bank 15,000; Machinery
*50,000; Furniture ₹20,000; Debtors 10,000; Bills payable
10,000; Bank loan ₹15,000; Salary Outstanding 8,000; Capital
*69,000.
3. Journalise the following transactions:
(i) Paid 2,000 in cash as wages on installation of a machine.
(ii) Sold goods toMr. Chopra at a list price of ₹4,000. Sales
subject to 10% Trade Discount and 5% Cash discount if payment
is made immediately, Mr. Chopra availed of cash discount.
(iii) Supplied goods costing ₹600 to Gopi& Sons. Issued invoice
at 10% above cost less 5% trade discount. (iv) Paid Custom Duty
10,000 in cash on import of a new machinery.
(v) Goods sold costing 10,000 to M/s Abbas & Sons at a invoice
price 10% above cost less 10% Trade Discount.
(vi) Purchased goods on credit ₹5,000
(vil) Sold goods on credit 1,000
4. Journalise the following transactions:
(a) Started business with Cash 1,50,000 and goods worth
10,000
(b) Goods purchased from M/S Garg& Sons 4,000 and from
Peterson 1,000.
(c) Goods worth 300 used by the proprietor for personal use.
(d) Goods uninsured worth 2,000 were destroyed by fire.
(e) Supplied goods costing 1,000 to Gavaskar issued at 10%
above cost less 5% Trade discount.
(f) Issued a cheque in favour of M/s Garg& Sons on account of
purchase of goods worth &*4,000.
(g) Outstanding salary at the end of the year ₹650.
(h) Interest charged on drawings 5% p.a.
(i) Paid to Peterson ₹990 in full settlement of 1,000.
The amount due from creditors is ₹17,000.
Opening Entry:The opening entry is a term used to describe the initial journal entry of a company's financial transactions in its general ledger. To begin the accounting process, an opening entry is made that records the beginning account balances for all accounts in the ledger.
The opening entry is an important component of the accounting cycle, as it establishes the starting point of all transactions and provides a basis for future analysis and reporting.
The opening entry for the above transactions is:
Particulars Amount Particulars Amount Cash in hand 25,000 Capital 86,000Cash at bank 15,000 Furniture 20,000Machinery 50,000 Debtors 10,000Bills payable 10,000 Bills payable 13,000Bank loan 15,000 Salary Outstanding 8,000Total 1,50,000 Total 1,50,000
Amount due from creditors:
Creditors refer to an individual or organization that a company owes money to for goods or services that it has received. The amount owed to creditors by the company can be calculated by subtracting the amount of bills payable from the total of all accounts payable. Creditors' amount is ₹14,000. Transactions:1. Paid 2,000 in cash as wages on installation of a machine. Particulars Amount Particulars Amount Wages 2,000 Cash 2,0002. Sold goods to Mr. Chopra at a list price of ₹4,000. Sales subject to 10% Trade Discount and 5% Cash discount if payment is made immediately, Mr. Chopra availed of a cash discount. Particulars Amount Particulars AmountSales 3,600 Mr. Chopra 3,600Trade discount 400 Cash 3,420Bank charges 1803. Supplied goods costing ₹600 to Gopi& Sons. Issued invoice at 10% above cost less 5% trade discount. Particulars Amount Particulars AmountGopi& Sons 660 Sales 660Trade discount 30 Cost of goods sold 6004. Paid Custom Duty 10,000 in cash on import of a new machine. Particulars Amount Particulars AmountCustom Duty 10,000 Cash 10,0005. Goods sold costing 10,000 to M/s Abbas & Sons at an invoice price 10% above cost less 10% Trade Discount. Particulars Amount Particulars AmountSales 9,000 M/s Abbas & Sons 9,000Trade discount 1,000Cost of goods sold 10,0006. Purchased goods on credit ₹5,000. Particulars Amount Particulars AmountPurchase 5,000 Creditors 5,0007. Sold goods on credit 1,000. Particulars Amount Particulars AmountDebtors 1,000Sales 1,0008. Started business with Cash 1,50,000 and goods worth 10,000. Particulars Amount Particulars AmountCash 1,50,000 Goods 10,0009. Goods purchased from M/S Garg& Sons 4,000 and from Peterson 1,000. Particulars Amount Particulars AmountPurchase 5,000 M/S Garg& Sons 4,000Purchase 1,000 Peterson 1,00010. Goods worth 300 used by the proprietor for personal use. Particulars Amount Particulars AmountDrawings 300 Goods 30011. Goods uninsured worth 2,000 were destroyed by fire. Particulars Amount Particulars AmountLoss by fire 2,000 Goods 2,00012. Supplied goods costing 1,000 to Gavaskar issued at 10% above cost less 5% Trade discount. Particulars Amount Particulars AmountGavaskar 1,050 Sales 1,050Trade discount 50Cost of goods sold 1,00013. Issued a cheque in favour of M/s Garg& Sons on account of purchase of goods worth 4,000. Particulars Amount Particulars AmountM/s Garg& Sons 4,000 Bank 4,00014. Outstanding salary at the end of the year ₹650. Particulars Amount Particulars AmountSalary 650 Salary Outstanding 65015. Interest charged on drawings 5% p.a. Particulars Amount Particulars AmountDrawings Interest on Drawings Total Drawings*5%/12 Total Drawings/12 0.00 0.00*5% = 3,25016. Paid to Peterson ₹990 in full settlement of 1,000. Particulars Amount Particulars AmountPeterson 990 Discount 10 Cash 1,000Total 1,000 Total 1,000.
Therefore, the solution is:The opening entry for the given transaction is: Particulars Amount Particulars AmountCash in hand 25,000 Capital 86,000Cash at bank 15,000 Furniture 20,000Machinery 50,000 Debtors 10,000Bills payable 10,000 Bills payable 13,000Bank loan 15,000 Salary Outstanding 8,000Total 1,50,000 Total 1,50,000
Calculation of Amount due from creditors:
Creditors = Total of all accounts payable - Bills payable
Creditors = ₹30,000 - ₹13,000Creditors = ₹17,000.
Therefore, the amount due from creditors is ₹17,000.
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Thomas is on a road trip to San Francisco. At this point, he is already 140 miles away from his house. He continues driving at a rate of 65 miles every hour. Which equation represents the number of hours, h, it takes Thomas to be 500 miles away from his house. Based on the given information, how many hours will it take Thomas to be exactly 335 miles away from his house?
A. 1 hour
B. 2 hours
C. 3 hours
D. 4 hours
Mr. Ahamad's science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type.
The probability that the three randomly selected students will have blood types A, B and AB is given as follows:
0.00164 = 0.164%.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Hence the probability for this problem is calculated as follows:
41/100 x 1/10 x 1/25 = 0.00164 = 0.164%.
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HELPPP!! I'LL MARK U
The area of the figure is ______ square units.
Answer:
8 units
Step-by-step explanation:
Area of square:
length * width
2 * 3
= 6 units
Area of triangle:
1/2 * base * height
1/2 * 2 * 2
= 2 units
Area of entire shape:
6 + 2
= 8 units
So, the area of the shape is 8 units.
If this answer helped you, please leave a thanks!
Have a GREAT day!!!
what is 7 (y+4.5) =?
Answer:
7y+31.5
Step-by-step explanation:
your distributing the 7 to the y and the 4.5
Answer:
7y + 31.5
Step-by-step explanation:
7(y+4.5)
7y + 31.5
So, the answer is 7y + 31.5
PLSS HELP
GIVING 36 POINTS
Answer:
a
Step-by-step explanation:
the data is represented in the dot plot
Answer:
answer is 77.67
Step-by-step explanation:
explain by the x axis is 68 to y axis is 84 so the median is 77.67
WHen it means units does it mean spaces or ????
The solutions to the equation |2x - 11| = 7 are x = 2 and x = 9. Option D
To find the numbers that satisfy the given condition, we can set up an equation based on the information provided.
Let's assume the number we're looking for is x. According to the problem, twice the number is 7 units from 11. Mathematically, we can represent this as:
|2x - 11| = 7
To find the possible values of x, we need to solve this equation. We can split it into two cases:
Case 1: 2x - 11 = 7
In this case, we have:
2x = 7 + 11
2x = 18
x = 18/2
x = 9
Case 2: -(2x - 11) = 7
In this case, we have:
-2x + 11 = 7
-2x = 7 - 11
-2x = -4
x = -4/-2
x = 2
Therefore, the solutions to the equation |2x - 11| = 7 are x = 2 and x = 9. These are the numbers that satisfy the condition where twice the number is 7 units from 11.
The correct answer is:
x = 2, 9 Option D
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Looking at the table above ,
A. What would you consider as the independent variable in this situation ? Introduce the symbol/ name (x,t,...) you will use to represent this variable . Remember to include the units.
B. What is the dependent variable ? Introduce the symbol /name for this variable . Remember the units .
The independent Variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).
The table above illustrates the relationship between the temperature of a substance and its volume. The independent variable is the temperature of the substance and the dependent variable is the volume of the substance.
The symbol or name used to represent the independent variable is "T" for temperature and its units are given as degrees Celsius or °C.The symbol or name used to represent the dependent variable is "V" for volume, and its units are given as milliliters or mL.
The temperature is the independent variable as it is being manipulated in the experiment while the volume is dependent on the temperature as it is changing based on the temperature.
An independent variable is a variable in an experiment that is being manipulated by the experimenter, while the dependent variable is the variable that is being measured in response to changes in the independent variable.
In summary, the independent variable in the situation presented in the table is the temperature (T), which is measured in degrees Celsius (°C), and the dependent variable is the volume (V), which is measured in milliliters (mL).
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enter the number that belongs in the green box 7 4 10
Answer:
Step-by-step explanation:
Khoi has a total of $600 invested in two accounts. The accounts earn 5% and 10% simple interest. The interest due to Khoi after one year is $49. How many dollars are in each account?
Khoi invested $220 in the account that earns 5% interest and $380 in the account that earns 10% interest.
Khoi has a total of $600 invested in two accounts. The accounts earn 5% and 10% simple interest. The interest due to Khoi after one year is $49.Let x be the amount of money invested in the account that earns 5% interest and y be the amount of money invested in the account that earns 10% interest.
As per the problem statement, the sum of the two investments equals $600.
Therefore,x + y = 600orx = 600 - y
Also, the interest earned on the first account is given by,0.05xAnd, the interest earned on the second account is given by,0.10yThe total interest earned is $49.
Thus, we can write,0.05x + 0.10y = 49
Substituting the value of x from the first equation, we get,
0.05(600 - y) + 0.10y = 49
Simplifying this equation, we get,30 - 0.05y + 0.10y = 49Or,0.05y = 19
Therefore,y = 380
Plugging this value of y back into the first equation, we get,x + 380 = 600orx = 220.
Therefore, Khoi invested $220 in the account that earns 5% interest and $380 in the account that earns 10% interest.
Hence, the solution is as follows:Khoi invested $220 in the account that earns 5% interest and $380 in the account that earns 10% interest.
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What is the equation of the line that passes through the point (-1, 5) and has a slope of −3?
The answer is:
In point slope:
[tex]\rm{y-5=-3(x+1)}[/tex]
In slope intercept:
[tex]\rm{y=-3x+2}[/tex]
Work/explanation:
Given:
point : (-1, 5)slope : -3To find the equation of the line, I'm going to use point slope:
[tex]\sf{y-y_1=m(x-x_1)}[/tex]
Where the slope is m and the point is (x₁, y₁).
So our point-slope is:
[tex]\rm{y-5=-3(x-(-1)}[/tex]
Let's simplify.
[tex]\rm{y-5=-3(x+1)}[/tex]
That's our equation in point slope.
__________________________
We might want to write the equation in slope intercept (y = mx + b).
We can do that, too, but let's simplify first.
We take our point slope equation.
We simplify the right side.
[tex]\rm{y-5=-3x-3}[/tex]
Add 5 on both sides
[tex]\rm{y=-3x+2}[/tex]
This is our equation in slope intercept.Question 1 1. Weight Loss X runs a number of weight reduction centers within a large city. From the historical data it was found that the weight of the participants is normally distributed with a mean of 175 lbs and a standard deviation of 35 lbs. Calculate the standard error of the average sample weight when 15 participants are randomly selected for the sample? Enter your answer rounded to two decimal places. For example, if your answer is 12.345 then enter as 12.35 in the answer box. 9.05 Question 2 5 pts Question 3 5 pts 2. Continuing with problem 1. calculate the probability that the average sample weight is greater than 185 lbs when 15 participants are randomly selected for the sample? Enter your answer rounded to two decimal places. Do not enter % in the answer box. For example, if your answer is 0.12345 or 12.345% then enter as 12.35 in the answer box. 5 pts
Q1. The standard error of the average sample weight when 15 participants are randomly selected for the sample is approximately 9.05 lbs.
Q2. the probability that the average sample weight is greater than 185 lbs when 15 participants are randomly selected for the sample is approximately 0.8643, or 86.43%
Question 1:
To calculate the standard error of the average sample weight, we can use the formula:
Standard Error = Standard Deviation / √(Sample Size)
In this case, the standard deviation is given as 35 lbs and the sample size is 15 participants. Plugging in these values into the formula, we get:
Standard Error = 35 / √(15) ≈ 9.05 (rounded to two decimal places)
Therefore, the standard error of the average sample weight when 15 participants are randomly selected for the sample is approximately 9.05 lbs.
Question 2:
To calculate the probability that the average sample weight is greater than 185 lbs, we need to standardize the average sample weight using the standard error.
First, we calculate the z-score using the formula:
z = (Sample Mean - Population Mean) / Standard Error
The population mean is given as 175 lbs, the sample mean is 185 lbs, and the standard error is 9.05 lbs. Plugging in these values, we get:
z = (185 - 175) / 9.05 ≈ 1.10 (rounded to two decimal places)
Next, we use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 1.10. From the table, we find that the probability is approximately 0.8643.
Therefore, the probability that the average sample weight is greater than 185 lbs when 15 participants are randomly selected for the sample is approximately 0.8643, or 86.43% (rounded to two decimal places).
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What is the measure of the unknown angle? A straight angle divided into a thirty-seven-degree angle and an unknown angle. 123° 127° 143° 147°
The measure of the unknown angle is 143 degrees.
To find the measure of the unknown angle, we need to use the properties of straight angles. A straight angle is a line, and it measures 180 degrees.
In this case, we have a straight angle divided into a 37-degree angle and an unknown angle. So, we can set up the equation:
37° + unknown angle = 180°
To solve for the unknown angle, we need to isolate it on one side of the equation.
Subtracting 37° from both sides of the equation:
unknown angle = 180° - 37°
Simplifying:
unknown angle = 143°
As a result, the unknown angle is 143 degrees in length.
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7/8 X 2/7 = ________ reduce your answer to the lowest terms
The product of 7/8 and 2/7, reduced to the Lowest terms, is 1/4.
To find the product of the fractions 7/8 and 2/7, we multiply the numerators together and the denominators together:
(7/8) * (2/7) = (7 * 2) / (8 * 7) = 14/56
To reduce this fraction to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 14 and 56 is 14. We can divide both the numerator and denominator by 14:
14/56 = (14/14) / (56/14) = 1/4
Therefore, the product of 7/8 and 2/7, reduced to the lowest terms, is 1/4.
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solve for x and y in the equation shown
Answer:
x = 13 and y = (7 - 3x) / (-2)
Step-by-step explanation:
Solving for X
The given equation is:
3x - 7 = 2x + 6
To solve for x, we can simplify and rearrange the equation as follows:
3x - 2x = 6 + 7 (subtracting 2x and adding 7 to both sides)
x = 13 (combining like terms)
Therefore, the solution to the given equation is x = 13.
Thus, the correct answer is 13.
The given equation is:
3x - 2y = 7
solving for y
To solve for y, we need to isolate y on one side of the equation.
First, we can subtract 3x from both sides of the equation:
3x - 3x - 2y = 7 - 3x
Simplifying, we get:
-2y = 7 - 3x
Next, we can divide both sides by -2 to get y by itself:
y = (7 - 3x) / (-2)
Therefore, the solution for y is y = (7 - 3x) / (-2).
Thus, the above is the solution for y.
What is the y-intercept of f(x) = (1/2)^x?
The y-intercept of [tex]f(x) = (1/2)^x[/tex] is option d D. (0, 1)
To find the y-intercept of a function, we need to evaluate the function when x = 0. In the given function f(x) = (1/2)^x, we substitute x = 0 and calculate the corresponding y-value.
f(0) = [tex](1/2)^0[/tex] = 1
Therefore, the y-intercept of the function is the point (0, 1). This means that when x is 0, the function has a y-value of 1.
The y-intercept represents the point where the function intersects the y-axis, which corresponds to the value of the function when x is 0. In this case, as x approaches 0, the value of [tex](1/2)^x[/tex] approaches 1. This is because any number raised to the power of 0 is equal to 1.
Option D. (0, 1) correctly represents the y-intercept of the function f(x) = [tex](1/2)^x[/tex]. The point (0, 1) indicates that when no units of the base (1/2) are multiplied together, the result is 1.
The other options (A. (0, 0), B. (1, 1/2), and C. (1, 0)) do not correctly represent the y-intercept because they either have incorrect y-values or are not on the y-axis (x ≠ 0). The y-intercept specifically refers to the point where the function crosses the y-axis, which occurs when x = 0.
The complete question is:
What is the y-intercept of[tex]f(x) = (1/2)^x[/tex]?
A. (0, 0)
B. (1, 1/2)
C. (1, 0)
D. (0, 1)
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Enter the number that belongs in the green box 7 4 8
Answer:
61.03°
Step-by-step explanation:
You want the angle opposite the side of length 7 in the triangle with other sides of lengths 4 and 8.
Law of CosinesThe law of cosines relates the angles of a triangle to the side lengths. For triangle ABC with opposite sides a, b, c, the relation is ...
c² = a² +b² -2ab·cos(C)
ApplicationSolving for angle C, we have ...
cos(C) = (a² +b² -c²)/(2ab)
C = arccos((a² +b² -c²)/(2ab))
In this triangle, that means ...
C = arccos((4² +8² -7²)/(2·4·8)) = arccos(31/64)
C ≈ 61.03°
The angle of interest is about 61.03°.
__
Additional comment
We get the same result from a triangle solver. See the second attachment. (The angle we want is angle B in that attachment.)
<95141404393>
6. Use Structure Point B has coordinates (-4,-2). The x coordinate of point A is 5. The distance between point A and point B is 15 units.
a. What are the possible coordinates of
point A?
b. Find the possible coordinates of point A
if point B were moved to (-7, -2).
ei Olog bris 9.3
4mb ST
a. To find the possible coordinates of point A, we know that the x-coordinate of point A is 5 and the distance between point A and point B is 15 units. Since the x-coordinate of point B is -4, we can calculate the difference between the x-coordinates of point A and point B:
x-coordinate of point A - x-coordinate of point B = 5 - (-4) = 9
So, the possible x-coordinate of point A is 9.
Now, we can use the distance formula to find the possible y-coordinate of point A. The distance between point A (5, y) and point B (-4, -2) is given as 15 units:
√[(x2 - x1)^2 + (y2 - y1)^2] = 15
Plugging in the coordinates of the points:
√[(5 - (-4))^2 + (y - (-2))^2] = 15
Simplifying:
√[9^2 + (y + 2)^2] = 15
Squaring both sides:
81 + (y + 2)^2 = 225
Solving for (y + 2)^2:
(y + 2)^2 = 225 - 81
(y + 2)^2 = 144
Taking the square root:
y + 2 = ±12
Solving for y:
y = -2 ± 12
This gives us two possible y-coordinates:
y = -2 + 12 = 10
y = -2 - 12 = -14
Therefore, the possible coordinates of point A are (9, 10) and (9, -14).
b. If point B were moved to (-7, -2), we follow the same process as above.
The x-coordinate of point A is 5, and the x-coordinate of point B is -7. The difference in x-coordinates is:
x-coordinate of point A - x-coordinate of point B = 5 - (-7) = 12
So, the possible x-coordinate of point A is 12.
Using the distance formula, we have:
√[(12 - (-7))^2 + (y - (-2))^2] = 15
Simplifying:
√[19^2 + (y + 2)^2] = 15
Squaring both sides:
361 + (y + 2)^2 = 225
Solving for (y + 2)^2:
(y + 2)^2 = 225 - 361
(y + 2)^2 = -136
Since the square of a real number cannot be negative, there are no real solutions for (y + 2)^2. Therefore, there are no possible coordinates for point A if point B is moved to (-7, -2).
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NO LINKS!! URGENT HELP PLEASE!!
Answer:
a. My quadrilateral has four equal sides.
Must be: Rhombus.
Could be: Square.
b. My quadrilateral has two sets of parallel sides.
Must be: Parallelogram.
Could be: Rectangle, Rhombus, Square
c. My quadrilateral has four right angles.
Must be: Rectangle.
Could be: Square.
Explanation:
a. A quadrilateral with four equal sides must be a rhombus. It could also be a square, but a square is a special type of rhombus, so a rhombus is the "must be" shape.b. A quadrilateral with two sets of parallel sides must be a parallelogram. It could also be a rectangle, a rhombus, or a square. However, a rectangle, rhombus, or square is also a parallelogram, so a parallelogram is the "must be" shape.
c. A quadrilateral with four right angles must be a rectangle. It could also be a square, but a square is a special type of rectangle, so a rectangle is the "must be" shape.
Answer:
a) Must be a rhombus.
Could be a square, a rectangle, a parallelogram, a trapezoid, or a kite.
b) Must be a parallelogram.
Could be a square, a rectangle, a kite, or a rhombus.
c) Must be a rectangle.
Could be a square, a kite, a rhombus or a parallelogram.
Step-by-step explanation:
The six basic types of quadrilaterals are:
Square: All interior angles are 90°. Side lengths are equal.Rectangle: All interior angles are 90°. Opposite sides lengths are equal.Rhombus: Side lengths are equal.Trapezoid: One pair of parallel sides.Parallelogram: Opposite sides are parallel.Kite: Two pairs of equal length sides (these sides are adjacent to each other).a) "My quadrilateral has four equal sides"A quadrilateral by definition is a four-sided shape. Therefore, it is possible for all types of quadrilateral to have four equal sides. However, for it to be a square and a rhombus, it must have four equal sides.
The interior angles of a square are all right angles, and its opposite sides are parallel. So as we haven't been told anything about the interior angles of the quadrilateral, or if any of its sides are parallel, we can conclude that:
The quadrilateral must be a rhombus.The quadrilateral could be a square, a rectangle, a parallelogram, a trapezoid, or a kite.b) "My quadrilateral has two sets of parallel sides"The types of quadrilateral that can have two sets of parallel sides are square, rectangle, rhombus, parallelogram and kite (all squares are kites).
The interior angles of a square and a rectangle are 90°.
The side lengths of a rhombus are congruent.
As we haven't been told anything about the interior angles or the side lengths of the quadrilateral, we can conclude that:
The quadrilateral must be a parallelogram.The quadrilateral could be a square, a rectangle, a kite, or a rhombus.c) "My quadrilateral has four right angles"All quadrilaterals, apart from a trapezium, can have interior angles that are all right angles. However, for a quadrilateral to be a square or a rectangle, it must have interior angles that are right angles.
As we don't know if the side lengths of the quadrilateral are equal, we cannot know if it's a square. Therefore, we can conclude that:
The quadrilateral must be a rectangle.The quadrilateral could be a square, a kite, a rhombus or a parallelogram.cómo representar el 2010 en número maya
According to the information we can infer that in the Mayan numeral system, the year 2010 is represented as follows: snail, point, snail, point, point, point, point, point
How to represent 2010 in Mayan numbers?The number 2010 is broken down into Mayan units, using the symbols corresponding to the different positional values. In the Maya system, three main symbols are used:
The point The bar The snail (or shell)To represent the number 2010 in Maya, the combination of these symbols is used as follows:
Two shells represent the value of 2000. One point represents the value of 10. So, the representation of the year 2010 in Mayan numbers would be:
snail, point
Remember that the Mayan number system is positional, similar to the decimal system, so the value and position of each symbol are important to determine the complete number.
Note: The question in English is: How to represent 2010 in Mayan numbers?
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Look for Relationships Does increasing the
3 to 6 change the mode? If so, how?
Increasing the value from 3 to 6 can potentially change the mode of a dataset. The mode represents the most frequently occurring value(s) in a dataset. If there are no repeated values or if the repeated values remain the same, then increasing the value from 3 to 6 will not change the mode. If there are new values introduced or if the frequency of certain values changes as a result of increasing the value, then the mode may indeed change.
1. Identify the initial dataset: Take note of the dataset where the mode is currently determined based on a value of 3.
2. Determine the mode: Calculate the mode of the dataset when the value is 3. The mode represents the most frequently occurring value(s) in the dataset.
3. Increase the value to 6: Modify the dataset by increasing the value from 3 to 6.
4. Analyze the dataset: Examine the modified dataset to observe any changes in the frequency distribution of values.
5. Compare the modes: Calculate the mode of the modified dataset with the value of 6 and compare it to the initial mode.
6. Assess changes: If the mode remains the same, it implies that the most frequently occurring value(s) in the dataset did not change. However, if the mode differs from the initial mode, it indicates that the increase from 3 to 6 has affected the frequency distribution and altered the most frequently occurring value(s).
7. Determine the impact: Analyze the specific changes in the dataset that led to the mode alteration. Identify any newly introduced values or shifts in the frequency of existing values.
8. Conclude: Based on the comparison of the initial mode and the mode with the increased value, determine whether increasing from 3 to 6 has changed the mode and describe the nature of the change.
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NO LINKS!! URGENT HELP PLEASE!!
Answer:
7. a. 16 units b. 96 square units.
8. 30 units
Step-by-step explanation:
7.
a. The perimeter of a rhombus is 40, and PR is 12.
This means that all four sides are equal, and each side is 10.
Since diagonal bisect each other creating right angle.
so
In ΔPMS
PS=10
PM=1/2 of PR= 1/2*12=6
Now by using Pythagoras theorem:
PS²=MS²+PM²
10²=MS²+6²
MS²=100-36
MS²=64
MS=[tex]\sqrt{64}=8[/tex]
Therefore, diagonal QS=2*MS=2*8=16 units
b.
Since the area of a rhombus is half the product of its diagonals. The diagonals of this rhombus are QS=16 and PR=12,
So, Area=1/2*PR*QS
=1/2*12*16
=96 square units.
8.
The perimeter of a rhombus is the total length of all four sides.
Since the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean Theorem to find the length of one side of the rhombus.
let d1=9 and d2=12
[tex]s = \sqrt{(d1/2)^2 + (d2/2)^2}[/tex]
[tex]s = \sqrt{(9/2)^2 + (12/2)^2}[/tex]
s=7.5
we have
P = 4s where p is perimeter
P=4*7.5
Therefore, the perimeter of the rhombus is 30 units.
Answer:
7a) QS = 16 units
7b) 96 square units
8) 30 units
Step-by-step explanation:
Question 7aThe sides lengths of a rhombus are equal.
Therefore, if the rhombus has a perimeter of 40, each side length is 10, since 40 ÷ 4 = 10.
PQ = QR = RS = SP = 10
The diagonals of a rhombus are perpendicular bisectors of each other.
Therefore, if PR is 12, then PM = 6.
Also, if QM + MS = QS, and QM = MS, then QS = 2·QM.
As the diagonals bisect each other at right angles, triangle PMQ is a right triangle, where:
PM = 6PQ = 10m∠PMQ = 90°Using Pythagoras Theorem to find the length of QM:
[tex]PM^2+QM^2=PQ^2[/tex]
[tex]6^2+QM^2=10^2[/tex]
[tex]36+QM^2=100[/tex]
[tex]QM^2=64[/tex]
[tex]QM=8[/tex]
As QS = 2·QM, then:
[tex]QS = 2 \cdot 8[/tex]
[tex]QS = 16[/tex]
[tex]\hrulefill[/tex]
Question 7bThe formula for the area of a rhombus is half the product of its diagonals.
[tex]\boxed{\begin{minipage}{5 cm}\underline{Area of a rhombus} \\\\$A=\dfrac{1}{2}pq$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the diagonals.\\\end{minipage}}[/tex]
Therefore, given the diagonals of the rhombus are PR = 12 and QS = 16, the area of the rhombus is:
[tex]\begin{aligned}\textsf{Area}&=\dfrac{1}{2} \cdot 12 \cdot 16\\\\&=6 \cdot 16\\\\&=96\; \sf square\;units\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Question 8The formula for the perimeter of a rhombus given its diagonals is:
[tex]\boxed{\begin{minipage}{5 cm}\underline{Perimeter of a rhombus} \\\\$P=2\sqrt{p^2+q^2}$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the diagonals.\\\end{minipage}}[/tex]
If the diagonals are 9 and 12, the perimeter is:
[tex]\begin{aligned}\textsf{Perimeter}&=2\sqrt{9^2+12^2}\\&=2\sqrt{81+144}\\&=2\sqrt{225}\\&=2 \cdot 15\\&=30\end{aligned}[/tex]
Therefore, the perimeter of the rhombus is 30 units.
Find the length of AB.
The measure of the length of segment AB in the triangle is 20 units.
What is the measure of length AB?The figure in the image is of two similar triangles:
From the image,
For the smaller triangle:
Leg 1 AP = 12
Leg 2 AQ = 8
For the larger triangle:
Leg 1 AC = 12 + 18 = 30
Leg 2 AB = 8 + QB
First, we determine length QB, we take the ratio of the sides of the two triangle since they similar:
Hence:
Leg 1 AP : Leg 2 AQ = Leg 1 AC : Leg 2 AB
12 : 8 = 30 : ( 8 + QB )
12/8 = 30/( 8 + QB )
Solve for QB:
12( 8 + QB ) = 8 × 30
96 + 12QB = 240
12QB = 240 - 96
12QB = 144
QB = 144/12
QB = 12
Now,
Leg 2 AB = 8 + QB
Plug in QB = 12:
Leg 2 AB = 8 + 12
Leg 2 AB = 20
Therefore, AB measure 20 units.
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8th graders are asked to take a survey.
73 said yes and 5 said no which in total are 78 students that answer the question.
How can you write the percentages for 73 and 5 out of 100%
73 students represent approximately 93.59% and 5 students represent approximately 6.41% out of the total of 78 students.
How to write the percentagesTo calculate the percentages for 73 and 5 out of 100%, you can use the following formulas:
Percentage = (Number of students / Total number of students) * 100%
For 73 students:
Percentage = (73 / 78) * 100% = 93.59%
For 5 students:
Percentage = (5 / 78) * 100% = 6.41%
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One day Evelyn and her friends had lunch while sitting at the tables of 19. Another day, they had lunch of tables of 18. What is the smallest number of people that could be in the group
Using the least common multiple of 19 and 18, the smallest number that could be in the group is 342
What is the smallest number of people that could be in the group?To find the smallest number of people that could be in the group, we need to find the least common multiple (LCM) of 19 and 18. The LCM is the smallest positive integer that is divisible by both 19 and 18.
The prime factorization of 19 is 19 (since 19 is a prime number), and the prime factorization of 18 is 2 * 3^2.
To find the LCM, we take the highest power of each prime factor that appears in either number:
LCM = 2 * 3² * 19
LCM = 2 * 9 * 19
LCM = 342
Therefore, the smallest number of people that could be in the group is 342.
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NO LINKS! URGENT HELP PLEASE!
Solve for the missing variables
Answer:
x ≈ 21.8
Step-by-step explanation:
You want the side length opposite the 98° angle in a triangle with side length 10 between that angle and one marked 55°.
Law of SinesThe law of sines can be used when angles are known and at least one side is known. The unknown angle is found by using the fact that the sum of angles is 180°.
angle opposite 10 = 180° -98° -55° = 27°
The law of sines tells you ...
a/sin(A) = b/sin(B)
x/sin(98°) = 10/sin(27°)
x = 10(sin(98°)/sin(27°)) ≈ 21.8
The value of x is about 21.8 units.
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Jenny invests $2,000 at an interest rate of 5%. The amount of money, ma, in Jenny's account after t years can be
represented using the equation m,- 2000(1.05). If Jenny would have invested the same amount of money at the same
interest rate four years ago, the equation representing the amount of money, mb, in her account would be represented
using the equation m-2000(1.05)+4. Which of the following is equivalent to mo?
O mb-
Omb-
2000(1.05)
1.05
2000(1.05)'
1.054
Om-2000(105)*(1.05)4
Om=2000(105)*+(1.05)*
The equivalent exponential function for this problem is given as follows:
[tex]m_b = 2000(1.05)^t(1.05)^4[/tex]
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is given as follows:
[tex]m_b = 2000(1.05)^{t + 4}[/tex]
Applying the addition of exponents rule, the equivalent expression is given as follows:
[tex]m_b = 2000(1.05)^t(1.05)^4[/tex]
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you sailed 0.032 units to the left and found treasure at 0.248 units find where the ship started
