Answer:
(3) 3
Step-by-step explanation:
Arithmetic Sequence:An arithmetic sequence is a sequence of numbers in which each of them can be defined by adding a common difference to a term to find the next term.
So for example, let the first term, or number be expressed as: [tex]a_1[/tex] and the common difference be expressed as: [tex]d[/tex] That means the second term, or number can be defined as: [tex]a_2=a_1+d[/tex]. If we now add the common difference to the second term, we would get the third term, and so on.
An arithmetic sequence can be compared to that of a linear equation, except it's a sequence of numbers... and also it's restricted to integers greater than zero (starts at first term, second term.... and so on)
So the common difference can be compared to the slope, and we can actually just use the slope formula! The "x" value being the term number, and the "y" value being the term. So the first term in the sequence is 5 can be expressed as: (1, 5) and the fifth term is 17 can be expressed as (5, 17). Now using the slope formula we would get: [tex]d=\frac{17-5}{5-1}=\frac{12}{4}=3[/tex]
Another way to think of it is the first term is 5, and if we add "d" or the common difference to it, we get the second term, if we add another "d" we get the third term, if we another "d" we get the fourth term and if add yet another "d" we get the fifth term. We add a total of four "d's" which can be expressed as: [tex]5+4d[/tex] and this equals the fifth term, but we also know this to be equal to 17, so we can set them equal to each other: [tex]5+4d=17[/tex] now just subtract 5 and divide by 4 to get: [tex]d=3[/tex]
A textbook store sold a combined total of 426 math and sociology textbooks in a week. The number of math textbooks sold was 46 more than the number of sociology textbooks sold. How many textbooks of each type were sold?
Answer:
The number of books sold were:
Math textbooks: 426
Sociology textbooks = 46
Step-by-step explanation:
Let us use the variable [tex]m[/tex] to represent the number of math books sold
Let us use the variable [tex]s[/tex] to represent the number of math books sold
Combined total of 426 math and sociology books were sold is represented by the equation:
[tex]m + s = 426\quad\quad\quad(1)[/tex]
Number of math books sold was 46 more than the number of sociology textbooks sold is given by
[tex]m - s = 46\quad\quad\quad(2)[/tex]
Adding the equations (1) + (2):
[tex](m + s) + (m - s) = 426 + 46\\\\2m = 472\\\\m = \dfrac{472}{2}\\\\m = 236\\\\[/tex]
Using Equation (1): [tex]m + s = 426[/tex] we get
[tex]236 + s = 426\\\\s = 426 - 236\\\\s = 190[/tex]
Question
What is the relative minimum of the function?
Enter your answer in the box.
A coordinate plane with x axis increments of one increasing from negative 5 to 5 and y axis increments of one increasing from negative 5 to 5. The coordinate plane contains a parabola opening up with a vertex at begin ordered pair one comma negative five end ordered pair. The parabola crosses the y axis at begin ordered pair 0 comma negative 3 end ordered pair.
The relative minimum's coordinates are (1, -5).
How can you determine a function's relative minimum?The first derivative test can be used to determine if a continuous function's critical point is a relative minimum or maximum. Simply put, the first derivative is a relative minimum if it is negative to the left of the critical point and positive to the right of it.
The parabola's equation takes the following form because its vertex is at (1, -5).
y = a(x - 1)² - 5
where "a" is a constant that determines the shape of the parabola. Since the parabola crosses the y-axis at (0, -3), we can substitute these coordinates into the equation and solve for "a" as follows:
-3 = a(0 - 1)² - 5
-3 = a - 5
a = 2
Thus, the equation of the parabola is:
y = 2(x - 1)² - 5
The x-coordinate of the vertex is given by x = 1
find the corresponding y-coordinate by substituting x = 1 into the equation:
y = 2(1 - 1)²- 5 = -5
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What is an equation of the line that passes through the points (0, -3) and (0, -8)?
Answer:
Step-by-step explanation:
here is a step-by-step explanation for finding the equation of the line that passes through the points (0, -3) and (0, -8):
Identify the two points that the line passes through: (0, -3) and (0, -8)
Determine the slope of the line: The slope of a line is given by the formula "rise over run," or (y2 - y1) / (x2 - x1). However, in this case, the line is vertical and has an undefined slope.
Write the equation of the line in slope-intercept form: y = mx + b, where "m" is the slope and "b" is the y-intercept. Since the slope of the line is undefined, the equation of the line cannot be written in slope-intercept form.
Write the equation of the line in point-slope form: y - y1 = m(x - x1), where "m" is the slope and (x1, y1) is a point on the line. Since the slope of the line is undefined, the equation of the line cannot be written in point-slope form.
Write the equation of the line as an x-intercept form: The x-intercept form of a line is given by the equation x = a, where "a" is the x-coordinate of the point that the line passes through. In this case, the line passes through the point (0, -3) and (0, -8), so the equation of the line is x = 0.
So, the equation of the line that passes through the points (0, -3) and (0, -8) is x = 0.
Which quadratic inequality in vertex form represents
the relationship in the graph?
y²²(x-4)² +28
y>(x-4)²+28
y2-2(x+4)² +28
y>(x+4)² +28
Answer:
Y> (x - 4)² + 28
Step-by-step explanation:
Which of the following graphs matches the equation y=-4x+3
The equation of line is y = -4x + 3 , where the slope is m = -4
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
y = -4x + 3 be equation (1)
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = -4
And , the y intercept is 3
The equation of line is plotted on the graph
Hence , the equation of line is y = -4x + 3
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The complete question is :
Which of the following graphs matches the equation y=-4x+3?
On a coordinate plane, a line goes through (0, 3)
On a coordinate plane, a line goes through (-2, 5) and (0, -3).
On a coordinate plane, a line goes through (0, 3) and (3, -1).
Marvin was 1.55m tall a year ago. now,he is 1.62m tall. find the percentage increase in Marvin's height correct to 2 decimal places
The percentage increase in Marvin's height is 4.51%
How to calculate the percentage increase in Marvin's height?
Marvin was 1.55m tall a year ago
Now her present height is 1.62m
The first step is to calculate the increase
= 1.62-1.55
= 0.07
The percentage increase can be calculated as follows
0.07/1.55 × 100
= 0.0451 × 100
= 4.51
Hence the percentage increase is 4.51%
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The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040. Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
The average hourly wage for police officers is $30.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.
In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.
Assume that police officers generally work 40 hours a week.
There are 52 weeks in the year.
The average hourly wage for police officers is,
= 62040 ÷ (52 x 40)
= 62040 / 2080
= 29.8
≈ $30
Therefore, $30 is the hourly wage.
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A verbal description of a linear function g is given. Express the function g in the form
g(x) = ax + b.
The linear function g has rate of change −12 and initial value 100.
g(x) =
G is a linear function with a rate of change of -12 and an initial value of 100. Its equation is: g = -12x + 100.
What is a linear function?Straight lines make up the graph of linear functions. The following is the format of a linear function. y = f(x) = a + bx A linear function has a independent variable so one dependent variable.
What does the described linear function look like?As a result of the task's objectives, it is necessary to identify the linear expression that corresponds to the verbal description that has been provided.
Since f(x) = axe + b is the typical slope-intercept form of a linear function,
an is the slope (rate of change), and b is the y-intercept (initial value).
g = -12x + 100 is the necessary linear function, which is what has been presented.
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Which of the following WAS NOT an impact of the crusades?
A. Change in culture in Europe
B. End of the Roman Empire
C. Monarchs grew more powerful
D. Many Christians were killed or badly injured
One thing that was not an impact of the Crusades was B. End of the Roman Empire.
What did the Crusades lead to ?The Crusades were a series of religious wars fought between Christians and Muslims in the 11th, 12th, and 13th centuries. The main objective of the Crusades was to recapture the Holy Land, which was considered the birthplace of Christianity, from Muslim rule.
The Crusades had a significant impact on the medieval world, but the end of the Roman Empire was not one of them. The Roman Empire ended several centuries before the start of the Crusades in the 11th century.
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As manager for a construction firm, you are in charge of bidding on two large contracts. You believe the probability you get contract #1 is 0.4. If you get contract #1, the probability you also get contract #2 will be 0.3, and if you do not get #1, the probability you get #2 will be 0.5. Complete parts (a) through (c).
Question content area bottom
Answer: a) Calculate the probability of getting both contracts:
The probability of getting both contracts is given by P(Contract 1 and Contract 2) = P(Contract 1) * P(Contract 2|Contract 1) = 0.4 * 0.3 = 0.12
b) Calculate the probability of getting either contract:
The probability of getting either contract is given by P(Contract 1 or Contract 2) = P(Contract 1) + P(Contract 2) - P(Contract 1 and Contract 2) = 0.4 + 0.5 - 0.12 = 0.78
c) Calculate the probability of not getting either contract:
The probability of not getting either contract is given by P(Neither Contract) = 1 - P(Contract 1 or Contract 2) = 1 - 0.78 = 0.22.
So, there is a 22% chance that the construction firm will not get either contract.
Step-by-step explanation:
Consider the following ordered data. 10 13 13 14 15 15 16 17 18 Find the low, Q_1, median, Q_3, and high. low ________ Q_1 ___________ median _________ Q_3 ___________ high ___________ Find the interquartile range. _________
The low Q₁ is 13 and the median Q₃ is 16.5, the high is 18 and the interquartile range is 3.5
The interquartile range is a measure of dispersion that tells us how spread out the middle 50% of a dataset is. To calculate the IQR, we first need to find the quartiles of the dataset. Quartiles divide a dataset into four equal parts, with the first quartile (Q₁) representing the 25th percentile, the second quartile (Q₂) representing the 50th percentile (also known as the median), and the third quartile (Q₃) representing the 75th percentile.
To find the quartiles of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18}, we first need to order the data in ascending order:
10, 13, 13, 14, 15, 15, 16, 17, 18
The low is the smallest value in the dataset, which is 10.
To find Q₁, we need to find the value that is 25% of the way through the dataset. Since we have 9 values in our dataset, 25% of 9 is 2.25. This means that Q₁ lies between the 2nd and 3rd values in the dataset, which are both 13. To find the exact value of Q₁, we can take the average of these two values:
Q₁ = (13 + 13) / 2 = 13
The median is the middle value in the dataset, which is 15.
To find Q₃, we need to find the value that is 75% of the way through the dataset. 75% of 9 is 6.75, which means that Q₃ lies between the 6th and 7th values in the dataset, which are 16 and 17, respectively. To find the exact value of Q₃, we can take the average of these two values:
Q3 = (16 + 17) / 2 = 16.5
The high is the largest value in the dataset, which is 18.
Now that we have found the quartiles, we can calculate the IQR by subtracting Q1 from Q₃:
IQR = Q₃ - Q₁ = 16.5 - 13 = 3.5
Therefore, the interquartile range of the dataset {10, 13, 13, 14, 15, 15, 16, 17, 18} is 3.5. This tells us that the middle 50% of the dataset is relatively tightly clustered around the median, with values ranging from 13 to 16.5.
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Use this table to answer the question. Round to the nearest percent.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total is made up of Planes?
There are 33% of the total is made up of Planes.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The table is given in the question, as follows:
Car Plane Train Total
Green: 120 250 500 870
Blue: 150 350 750 1250
Yellow: 170 200 450 820
Red: 200 300 300 800
Brown: 220 450 320 990
Total: 860 1550 2320 4730
Total number of planes = 1550
The total number of all vehicles = 4730
The percent of planes = (number of planes/number of all vehicles) x 100
The percent of planes = (1550/4730) x 100
The percent of planes = 0.3276 x 100
The percent of planes = 32.76
Round to the nearest percent, and we get
The percent of planes = 33%
Thus, 33% of the total is made up of Planes.
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Solve for x !
[tex] \it \large {3x + 5 = 5( x + 3)}[/tex]
Thank You!:)
Answer:
[tex]\mathrm{x=-5}[/tex]Step-by-step explanation:
[tex]\mathrm{3x+5=5(x+3)}[/tex]
Expand:-
[tex]\mathrm{3x+5=5x+15}[/tex]
Subtract 5x from both sides:-
[tex]\mathrm{-2x+5=15}[/tex]
Subtract 5 from both sides:-
[tex]\mathrm{-2x=15-5}[/tex]
[tex]\mathrm{-2x=10}[/tex]
Divide both sides by -2:-
[tex]\mathrm{\cfrac{-2x}{-2}=\cfrac{10}{-2}}[/tex]
[tex]\mathrm{x=-5}[/tex]
___________________
Hope this helps!
Suppose that 22 inches of wire costs 66 cents. At the same rate, how much (in cents) will 49 inches of wire cost?
Answer: 147 cents
Step-by-step explanation:
Unit rate is what we need here: i.e., how much does 1 inch of wire cost?
22in --> 66cents
1 in --> 66/22 = 3
3 cents per inch!
so 49 inches will cost 49 x 3 = 147 cents
Leyan bought 2 3/4 pounds of apples for $1.32 per pound, 1 1/2 pounds of peaches for $1.20 per pound, and some tomatoes, all from a grocery store. The total cost of his purchase was $9.63.
How much money did Leyan spend on tomatoes?
Which precedents did the u. S. Constitution establish for other governments? select all that apply.
Erica built a fort out of big foam blocks that are 1 /4 of a foot tall. She is adding a 5-foot tower to one side of the fort. How many blocks tall will the tower be?
By the equation formed by the relation to build 5 feet tall tower, Erica will need 20 bricks.
What is an equation?
An equation is a mathematical statement consisting of two expressions joined by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation gives the value of the variable x as x = 7.
According to the information given in the question:
1 brick = 1/4 Feet
Which means, 4 bricks = 1 feet
As Erica wants to make 5 feet tall tower,
5 feet tower = 5 x 4
= 20 bricks
Hence, Erica will need 20 bricks to build 5 feet tower.
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ACTIVITY 2 1. Mr Nkomo lives in Three Rivers, in the Emfuleni municipality and uses prepaid electricity that is sold to customers at a VAT inclusive rate. The table below shows the cost of prepaid units of electricity. BLOCK UNITS (kWh) 2 3 4 0-50 51-350 351-600 >600 *Prepaid electricity: Paying for electricity before using it. *VAT = 15% *The municipality buys electricity from Eskom at an average VAT inclusive price of R1,33 per kWh. 1.1. State any two reasons why it is an advantage for the municipality to sell prepaid electricity. Verify, by showing ALL calculations, If his claim is VALID. You may use the formula: % Profit = (4) 1.2. Determine the number of units Mr Nkomo received when he bought prepaid electricity for R68,02. (3) 1.3. How much will Mr Nkomo pay if he wanted to buy 310 kWh of electricity? (3) 1.4. Mr Nkomo stated that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34%. RATE c/kWh (Including vat) sell price for the units-cost price for the units 144,72 186,06 261,87 308,37 ✓ 1000z IC) 2
Answer:
Step-by-step explanation:
1.1. Advantages of Selling Prepaid Electricity
Two advantages of selling prepaid electricity are:
a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.
b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.
1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02
The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:
Units = Amount / Rate
Units = R68,02 / R1,33
Units = 51.04 kWh
So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.
1.3. Cost of 310 kWh of Electricity
The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:
Cost = Units * Rate
Cost = 310 kWh * R1,33
Cost = R411,30
So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.
1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity
To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.
Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.
For 2-50 kWh:
Cost = 2-50 kWh * R1,33
Cost = 50 kWh * R1,33
Cost = R66,50
Selling price = R144,72
Profit = Selling price - Cost
Profit = R144,72 - R66,50
Profit = R78,22
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R78,22 / R66,50) * 100
Percentage profit = 17.7%
For 51-350 kWh:
Cost = 51-350 kWh * R1,33
Cost = 350 kWh * R1,33
Cost = R466,50
Selling price = R186,06
Profit = Selling price - Cost
Profit = R186,06 - R466,50
Profit = R29,56
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R29,56 / R466,50) * 100
Percentage profit = 6.3%
For 351-600 kWh:
Cost = 351-600 kWh * R1,33
Cost = 600 kWh * R1,33
Cost = R798,00
Selling price = R261,87
Profit = Selling price - Cost
Profit = R261,87 - R798,00
Profit = -536,13
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-536,13 / R798,00) * 100
Percentage profit = -67.3%
For over 600 kWh:
Cost = over 600 kWh * R1,33
Cost = R1,33 * 1000
Cost = R1330,00
Selling price = R308,37
Profit = Selling price - Cost
Profit = R308,37 - R1330,00
Profit = -1021,63
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-1021,63 / R1330,00) * 100
Percentage profit = -76.7%
The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.
For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.
For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.
For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.
For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.
The average percentage profit for the municipality for the four ranges of units is calculated as follows:
Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4
Average percentage profit = -34.05%
Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 30.4 mmHg (millimeters of mercury) for a sample of size 686 and a sample standard deviation 5.5 mmHg. How much of mmHg will lower for a typical patient's systolic blood pressure after taking the drug? Estimate with a 90% confidence.
What is the 90% confidence interval to estimate the population mean? Round your answer to one decimal place.
Answer:
{30.1,30.7}
Step-by-step explanation:
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}\\\\CI_{90\%}=30.4\pm1.645\biggr(\frac{5.5}{\sqrt{686}}\biggr)\\\\CI_{90\%}\approx30.4\pm 0.3\\\\CI_{90\%}=\{30.1,30.7\}[/tex]
Thus, we are 90% confident that the true amount of mmHg that is lowered will be between 30.1 and 30.7 mmHg.
Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
The distance of the point P to the plane is 42/√629 units. The solution has been obtained by using vectors.
What are vectors?
An item with both magnitude and direction is said to contain a vector. An object's motion from one point to another is described by a vector.
We are given three points Q, R and S. So, we will find equation of the plane defined by the three points.
Vector RQ = < 5, 1, -4 > and RS = < 7, 6, -7> and their cross product
RQ x RS = < 5, 1, -4 > x < 7, 6, -7> = < 17 , 7, 23> = n
This is a vector normal to the plane.
So, the equation of the plane is 17x + 4y + 18z = 139
The distance is calculated using
⇒d = (|A·Mx + B·My + C·Mz + D| )/(√A² + B² + C²)
⇒d = (|-17·3 + (-4)·1 + (-18)·7 + 139|)/((-17)² + (-4)² + (-18)²)
⇒d = 42/√629
Hence, the distance is 42/√629 units.
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Solve the system by substitution.
y = 5x
y = 4x + 9
9) in Brayden's movie collection, 8 out of every 25 movies are comedy. What percentage of his movies are
not comedy?
Answer: 0.32 or 32%
Step-by-step explanation: 8/25
The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 2 and roots of multiplicity 1 at x = 0 and x = -2 . It goes through the point (5,189).
If "a" is a root of a polynomial, then (x-a) is a factor of the polynomial.
If the multiplicity of a root a is "p", then (x-a)^p is a factor of the polynomial.
Based on the roots and multiplicity, we have:
P(x) = k · (x-2)^2 · (x-0) · (x - (-2))
P(x) = k · (x-2)^2 · (x-0) · (x+2)
We need that "k" up front to account for any vertical stretch or compression to hit the exact point (5,189).
To find "k", we plug in that point and solve for "k":
189 = k · (5-2)^2 · (5-0) · (5+2)
189 = k · (3)^2 · (5) · (7)
189 = k · 315
0.6 = k
So the final answer is: P(x) = 0.6 · (x-2)^2 · (x-0) · (x+2)
Write the equation of a line that is perpendicular to y= 3/2x - 4 and goes through the points (2,-2)
Answer:
The equation of the line that is perpendicular to y= 3/2x - 4 and goes through the point (2,-2) is y = -2/3x + 4.
Step-by-step explanation:
Part D
What do the factors in the factored form represent?
BIUX² X₂ 15px
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Space used (includes formatting): 0/ 15000
AV
The factors in the factored form represents the value of the function when x = 0.
What are Quadratic Functions?Quadratic functions are defined as the polynomial functions consisting of variables and exponents with the degree of the variable being 2.
The general form of a quadratic function is f(x) = ax² + b x + c.
Given is a quadratic function,
y = x² + 2x - 15
This can be factorized as (x + p)(x + q) such that p × q = -15 and p + q = 2.
Two such numbers are -3 and 5.
-3 × 5 = -15 and -3 + 5 = 2
y = x² + 2x - 15
y = (x - 3) (x + 5)
Factors are x - 3 and x + 5
Here, the numbers 3 and -5 represents the input values of the function when the output value or the value of the function equals 0 or they are the x intercepts of the function.
Hence the factors in the factored form are the x intercepts of the function.
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The complete question is as follows :
What do the factors in the factored form represent?
y = x² + 2x - 15
A chest has a length of 0.8 m, a width of 0.5 m
and a height of 0.6 m. What is the volume of the
chest?
Write down all of the options which are true of
similar shapes.
They must be the same shape
They can be different shapes
They must be the same size
They can be different sizes
All of the options which are true of similar shapes include the following:
A. They must be the same shape.
D. They can be different sizes.
What are the properties of similar geometric shapes?In Mathematics, two (2) geometric shapes are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
What is scale factor?In Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
This ultimately implies that, two (2) similar geometric shapes can have different sizes depending on the scale factor that is applied.
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Swimming Pool On a certain hot summer's day, 507 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $761.75. How many children and how many adults swam at the public pool that day?
Answer:384 children and 123 adults swam at the public school.
Step-by-step explanation:
Need help quick pls and thanks
a) The average rate of change is -0.6333.
b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.
What is Rate of Change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given:
a) The average rate of change
= (15.9- 17.8)/ (1920 - 1917)
= -1.9 / 3
= -0.6333
So, the equation can be
y = -0.6333x + b
and, 17.8 = -0.63333(1917)+ b
b= 1231.79
So, y= -0.6333x + 1231.79
b) For $500 after the inflation rate from 1917 to 1920 the worth will be 242.20631771406.
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Para todo x en A:123,x+2 al cuadrado es igual a x al cuadrado+2, verdadero o falso?
The given conclusion "(x + 2)² = (x² + 2)" is false.
What are the various set representation methods?The two set representation methods are -
Roster formSet - builder formGiven is the set A{1, 2, 3}.
(x + 2)² should be equal to (x² + 2) for all x ∈ A.
We can write -
(1 + 2)² = 1² + 2
9 ≠ 3
Therefore, the given conclusion "(x + 2)² = (x² + 2)" is false.
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{Question in english -
For all x in A: {1, 2, 3}, (x + 2)² is equal to (x² + 2). True or false?}
