The measure of the exterior angle of the triangle is 144 degrees.
How to solve angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .
Let's solve for the exterior angle.
x - 10 + 4x + 4 = 3x + 54
5x - 6 = 3x + 54
5x - 3x = 54 + 6
2x = 60
x = 60 / 2
x = 30
Therefore,
exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees
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3. One batch of pancakes needs 1½ cups of pancake mix. One box has 9 cups of pancake mix.
How many batches of pancakes can be made with one box of pancake mix?
In linear equation, 27/2 pancakes are in the box .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a " of two variables," where x and y are the variables.Number of b pancake mix to be need = 1½ cups
Number of box has pancake mix = 9 cups
Therefore, in order to get the total number of batches of pancakes needed for the batches will be calculated thus
= 1½ * 9
= 3/2 * 9
= 27/2
therefore 27/2 pancakes are in the box .
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for sample size n, the margin of error is 3. how many more samples do we need to make the margin of error 0.3?
We will need 100 more samples to make the margin error of 0.3 .
What are sample errors?When the statistical characteristics of a population are estimated from a subset, or sample, of that population, sampling errors are made in statistics. Statistics of the sample (commonly referred to as estimators), such as means and quartiles, usually diverge from those of the total population because the sample does not include all individuals of the population (known as parameters). The sampling error is defined as the discrepancy between the sample statistic and the population parameter. For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million persons in the country.acc to our question-
Margin error is 3Margin error tobe 0.3 SAMPLE size ?0.3 =3/10Ratio =3/3/10=10n^2=10×10=100Samples in size of 100Hence, We will need 100 more samples to make the margin error of 0.3 .
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Consider the circle represented by this equation.
x² + 4x + y2² - 2y - 4 = 0
Which features are features of the circle?
000
radius of 1
center at (-2, 1)
center at (-4, 2)
radius of 3
radius of 9
center at (2,-1)
Reset
Next
The given circle equation [tex]x^2+4x+y^2-2y-4[/tex]=0 has center(-2,1) and radius r=3.
What is circle equation?
For all values of g, f, and c, the general equation of any type of circle is written as x2 + y2 + 2gx + 2fy + c = 0. The collection of all points in a plane that maintain a fixed, finite distance r from a fixed point is known as a circle. O = (a,b). The definition of a circle on the coordinate plane can be expressed using the equation of a circle. The equation is where r is the radius and if the centre of the circle is at the origin of the coordinate plane.
Here the given circle equation is,
=> [tex]x^2+4x+y^2-2y-4[/tex]=0
=>[tex]x^2+4x+y^2-2y =4[/tex]
[tex]= > x^2+4x+4+y^2-2y+1=4+4+1\\= > (x+2)^2+(y-1)^2=9[/tex]
we know that equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]
Here (a,b)= center and r is radius.
=> [tex](x+2)^2+(y-1)^2=3^2[/tex]
Then the Center (a,b)=(-2,1) and radius r=3.
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when 1515 is appended to a list of integers, the mean is increased by 22. when 11 is appended to the enlarged list, the mean of the enlarged list is decreased by 11. how many integers were in the original list?
In the initial list, there were 4 integers.
We have the following system if the mean is m, x is the list's initial sum, and n is the number of integers in the list:
m = x/n , m + 2 = (x + 15) / (n + 1) and m + 1 = (x + 16) / (n + 2).
The initial equation is x = mn.
Therefore, changing x in the other two equations:
m + 2 = (mn + 15) / (n + 1) ..............(1)
m + 1 = (mn + 16) / (n + 2)...............(2)
Based on equation (1):
(m + 2)(n + 1) = mn + 15
mn + m + 2n + 2 = mn + 15
m + 2n + 2 = 15
m + 2n = 13
m = 13 - 2n.
Now change m in equation (2) to:
13 - 2n + 1 = ( n(13 - 2n) + 16) / (n + 2)
14 - 2n = (13n - 2n^2 + 16) / (n + 2) Through-multiplication by n + 2:
(14 - 2n)(n + 2) = 13n - 2n^2 + 16
14n + 28 - 2n^2 - 4n = 13n - 2n^2 + 16
10n + 28 = 13n + 16
12 = 3n
n = 4.
Hence, there were 4 integers in the original list.
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In quadrilateral BADC, AB=AD and BC=DC. Which of the following contains only true statements?
Answer:
abad
Step-by-step explanation:
If 8^y =16^y+2what is the value of y?
O-8.
O-4.
O-2.
O-1.
Answer:
-8
Step-by-step explanation:
Graph each side of the equation. The solution is the x-value of the point of intersection.
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
If the teammates were to have a combined time of less than 250 seconds to qualify to the next round, did they qualify or not? How do you know?
help me please i really need help!
Find the slope on the line going through the points (36, -21) and (-14, -21)
Answer:
0
Step-by-step explanation:
[tex]m=\frac{-21-(-21)}{-14-36}[/tex]
Answer: slope = 0
Step-by-step explanation:
slope = Δy ÷ Δx = (-21 - (-21)) / (-14 -36) = 0 / -5 = 0
It's a horizontal line
Britney is buying a shirt and a hat at the mall. The shirt costs $30.70, and the hat costs $20.79. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
Answer:
$48.51
Step-by-step explanation:
30.70+20.79 = 51.49
100-51.94 = $48.51
your welcome :)
Answer: $48.51
Step-by-step explanation:
If you add both $30.70 and $20.79, you would get $51.49. Then you subtract it from the $100 & you get a total of $48.51. So Britney is going to receive $48.51.
find three consecutive integers such that 3 times the smallest is 18 more than the largest
The value of the three consecutive integers will be 10, 11, and 12.
What is Algebra?
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
Three consecutive integers are such that three times the smallest is 18 more than the largest.
Let the three consecutive number be x, x + 1, and x + 2. Then the equation will be:
3x = (x + 2) + 18
Simplify the equation, then the value of the variable x will be:
3x = x + 2 + 182x = 20x = 20 / 2x = 10
Then the value of the integers will be:
x + 1 = 10 + 1 = 11x + 2 = 10 + 2 = 12
The value of the three consecutive integers will be 10, 11, and 12
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angela is following this recipe to make biscuits. angela uses 3.3 litres of syrup. how much sugar is needed in kg
The quantity of sugar that is needed in kg would be = 1.8kg
What is recipe?Recipe is defined as the list of components of ingredients that makes up a food product.
From the recipe given by Angela, the quantity of syrup that is used to make up to 14 biscuits= 275 ml.
The quantity of sugar that is used to make up to 14 biscuits= 150g
Therefore the quantity of sugar that would be used for syrup of 3.3 liters would be= X
That is;
275ml = 150g
3.3L = X
Convert 3.3L to ml = 3,300ml , then make x the subject of formula;
X = 3300×150/275
X = 495000/275
X= 1,800g
Then convert 1,800g to kg by dividing through with 1000;
1800/1000 = 1.8 kg
Therefore, the quantity of sugar that would be used for 3.3L of syrup would be 1.8kg.
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Complete question:
Angela is following this recipe to make biscuits.Angela uses 3.3 litres of syrup.
How much margarine is needed in kg?
Recipe: Makes 14 biscuits
120 g margarine
150 g sugar
275 ml syrup
200 g oats
60 g sultanas
How much sugar is needed in kg?
The top of a 15-foot ladder is 3 feet farther up a wall than the foot of the ladder is from the bottom of the wall. How far up is the foot of the ladder from the bottom of the wall?
The answer is 9 but I don’t know how to get there.
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}\implies 15^2=x^2+(x+3)^2 \\\\\\ 225=x^2+(x^2+6x+9)\implies \implies 225=2x^2+6x+9 \\\\\\ 0=2x^2+6x-216\implies 0=2(x^2+3x-108) \\\\\\ 0= x^2+3x-108\implies 0=(x-9)(x+12)\implies x= \begin{cases} 9 ~~ \checkmark\\\\ -12 \end{cases}[/tex]
let's notice that "x" does have two valid values, however for this scenario 'x" cannot be negative, so we don't use that one.
Could someone help quick
The constant of proportionality is 1/7
What is constant of proportionality?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided quantities determine the proportionality constant's value.Direct Variation: The direct proportionality equation is y = kx, which demonstrates that as x rises, y rises at the same pace. Example: y x represents the cost per item(y), which is directly proportional to the number of items(x) purchased.Inverse Variation: The indirect proportionality equation, y = k/x, demonstrates that when y rises, x falls, and vice versa. As shown by the formula y 1/x, the speed of a moving object (y) inversely varies with the amount of time (x) needed to travel a distance.K is constant in both circumstances. The coefficient of proportionality is the name given to this constant's value. The unit rate is another name for the proportionality constant.To learn more about constant of proportionality, refer to https://brainly.com/question/26171814
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how many positive integers less than 1000 a) are divisible by 7? b) are divisible by 7 but not by 11? c) are divisible by both 7 and 11? d) are divisible by either 7 or 11? e) are divisible by exactly one of 7 and 11? f ) are divisible by neither 7 nor 11? g) have distinct digits? h) have distinct digits and are even?
The set of positive integers less than 1000 that are:
a)Divisible by 7 are 142
b)Divisible by 7 but not by 11 are 130
c)Divisible by both 7 and 11 are 12
d)Divisible by either 7 or 11 are 220
e)Divisible by exactly one of 7 and 11 are 220
f)Divisible by neither 7 nor 11 are 780
g)Having distinct digits are 576
f)Having distinct digits and even are 337
What is a positive integer?A whole number that is greater than zero is known as positive integer
a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.
Total terms: 994, divided by 7, plus (n-1)
There are 142 total terms below 1000 that are divisible by 7.
b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.
The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.
c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.
There are 12 total integers below 1000 that can be divided by 77.
d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.
The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.
Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.
e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.
f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.
Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),
=> Unique digits from 1 to 100 equal 90.
=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),
=> Unique digits from 101 to 200 are: 100 to 28, 72.
=> Unique numbers between 201 and 1000 = 72 x 8 = 576.
h)Different digits and even values equal to 337
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Calculate the length of the unknown side of this right-angled triangle.
9 cm
8 cm
Another thing you will need to know before you can perform a rotation is
direction of rotation
corresponding angles
corresponding sides
the angle measures
A plumber has a 36-inch pipe that he has to cut into two
pieces so that one piece is 8 in. longer than the other. Find
the length of each piece.
A plumber has a 36-inch pipe that he needs to cut into two pieces, one 8 inches longer than the other. Each piece's length is x = 14, while the other piece's length is 22.
What is meant by length?The measurement or extent of something from end to end is defined as length. In other words, it is the larger of the two or the highest of three geometrical shapes or objects' dimensions. A rectangle, for example, has length and breadth dimensions.Centimeters, meters, kilometers, inches, feet, yards, and other standard units of length measurement are some examples.A segment's length or the dimensions of a room are examples of length measurements. Distance is the distance between two objects, such as two cities or two points. There will never be a negative value for length or distance.Therefore,
let x = the first piece and x+14 is the second.
2x + 8 = 36
2x = 28
x = 14, the other piece is 22
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Which answer is correct?
(A)4x + y = 6
−2x + y = −5
(B)x + y = 8
2x − 9y = 4
(C)x − 4y = −6
−2x − y = 5
(D) −x + y = 9
9x + 2y = 4
The system of equations best represented by the graph are 4x + y = 6 and −2x + y = −5
How to determine the system of equations represented by the graph?The solution of the equations plotted in the graph can be found by checking the point of intersection of the lines
By examining the given graph we can guess the x and y values of the point of intersection. We need to guess because we do not have a means of getting the exact value from the graph. I guess x = 1.9 and y = -1.4
In order to find the system of equations represented by the graph, we need to solve the equations given in the option and check which one gives us x and y values close to what we guessed from the graph
By Solving 4x + y = 6 and −2x + y = −5:
4x + y = 6 (1)
−2x + y = −5 (2)
Using elimination, subtract (2) from (1), this gives:
6x = 11
x = 11/6 = 1.83
Put x = 11/6 into (1):
4(11/6) + y = 6
y = 6 - 4(11/6)
y = 6 -44/6 = -4/3 = -1.33
Since these calculated values are very close to the guessed values
Therefore, 4x + y = 6 and −2x + y = −5 are the system of equations best
represented by the graph. So option A is the answer
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Which equation represents a line which is perpendicular to the line y=7/6x-8
The equation of a line that is perpendicular to y = 7 / 6 x - 8 is y = -6 / 7 x + 8.
How to find the equation of a line?The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form.
The lines that are perpendicular to each other will have the products of their slopes as negative 1.
Therefore, let express the equation in slope intercept form.
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = 7 / 6 x - 8
The slope of the equation is 7 / 6.
Therefore, let's find the equation of the line that is perpendicular to y = 7 / 6 x - 8.
m₁m₂ = -1
7 / 6 m₂ = -1
cross multiply
7m₂ = -6
m₂ = - 6 / 7
Hence, the equation of the line perpendicular to y = 7/6x - 8 should have the slope as - 6 / 7.
Hence, the equation can be y = -6 / 7 x + 8.
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K(15) = ?
Please find what k(15) is of the following graph below
A hiking guide recommends that a person wear snowshoes when the accumulated snow has a depth of at least 6 inches. At 8:00 a.m., the depth of snow in a certain area is 4 inches. The predicted average rates of change of the depth of snow for different time intervals are shown in the table. For which of the following time periods between 8:00 a.m. and 8:00 p.m. would the guide recommend wearing snowshoes?
A. 8:00 a.m.-10:00 a.m. and 1:00 p.m.-3:00 p.m.
B. 8:00 a.m.-11:00 a.m. and 3:00 p.m.-4:00 p.m.
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
D. 9:00 a.m.-11:00 a.m. and 2:00 p.m.-4:00 p.m.
Considering the average rate of change, the time periods in which snowshoes are recommended are given as follows:
C. 10:00 a.m.-12:00 p.m. and 5:00 p.m.-8:00 p.m.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output of the function (change in the numeric value) divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given by the fraction presented as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The initial amount is of 4 inches, hence, considering the rates, the amounts of snow on the ground are given as follows:
11 am: 4 + 3 x 0.75 = 6.25 inches. (>6 at 10 am).3 pm: 6.25 - 4 x 0.25 = 5.25 inches.8 pm: 5.25 + 5 x 0.50 = 7.75 inches. (>6 at 5 pm).Hence the intervals are given by option c.
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I GIVE you 20 points if you answer ASP PLS
The function graphed shows the total cost of a gym membership for x months.
Select from the drop-down menus to correctly identify the gym membership information provided by the graph.
The Slope is
The Slope Represents
Answer: Y=mx+b
Step-by-step explanation:
If you use the formula you can figure it out.
Answer:
the slope is 10
The slope represents the cost of gym membership per month.
16. Points X, Y, and Z are collinear, and Y is
the midpoint of XZ. Find the value of b.
Answer:
b=11
Step-by-step explanation:
lets set up the equation. we know that both sides equal each other so the equation is
2b+7=3b-4 let's move the 2b to the other side so we get
7=b-4 now add the 4 to the other side
11=b
Answer:
B is 11
Step-by-step explanation:
Evaluate Each expression show your work
1. Evaluate 3 + 4x if x = 5
Answer:
23
Step-by-step explanation:
3+4x
3+4(5)
3+20
23
Hopes this helps please mark brainliest
Match the vocabulary word with the correct definition.
Base
Exponent
Scientific Notation
a.
The number that is going to be raised to a power.
b.
The number that tells you how many times you will multiply the base number.
c.
A way of writing VERY large or VERY small numbers so the numbers are easier to compare or calculate.
Answer:
Exponent: B
Base: A
Scientific Notation: C
Step-by-step explanation:
vocabulary
Answer:
Exponent and A
Base and B
Scientific Notation and C
Step-by-step explanation:
Because the Exponent is the number that is going to raise the Base and that Base is the number that you are going to multiply by.
Two parallel lines are cut by a transversal as shown below.
Suppose m2 = 46°. Find m5 and m 27.
Use three unit multipliers to convert 5280ft to meters
The three-unit multipliers are follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters.
What is unit conversion?To convert any unit into another is called a unit conversion.
In order to convert units, we need to care about their dimensions their dimension should not be changed.
For example conversion of a kilometer to a meter is to multiply by 1000 but meter and kilometer both unit is for distance only.
As per the given,5280ft
It is known that 1 ft = 12 inches.
5280ft = 5280 x 12 inches
It is known that 1 inch = 2.54 cm
5280 x 12 inches = 5280 x 12 x 2.54 cm
It is known that 1 cm = 0.01 meter
5280 x 12 x 2.54 cm = 5280 x 12 x 2.54 x 0.01 meter
⇒ 1609.344 meters
Hence "The three-unit multipliers are as follows, 5280ft × 12 inches × 2.54 cm × 0.01 meter and it will be 1609.344 meters".
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11. √1156
12. √1024
13. √1225
14. √1764
15. √1936
please ahh little help please
The evaluation of the square roots of the numbers using prime factorization gives;
11. √1156 = 32
12. √1024 = 32
13. √1225 = 35
14. √1764 = 42
15. √1936 = 44
What are prime factors?Prime factors are the factors of a number that are also prime numbers.
The square roots of the numbers found using prime factorization are as follows;
11. √1156
1156 ÷ 2 = 578
578 ÷ 2 = 289
289 ÷ 17 = 17
17 ÷ 17 = 1
√1156 = √(2 × 2 × 17 × 17) = √(2² × 17²)
√1156 = √(2² × 17²) = 2 × 17 = 34
√1156 = 34
12. √1024
1024 ÷ 2 = 512
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
Therefore; √(1024) = √(2×2×2×2 ×2×2×2×2×2×2) = √(2¹⁰) = 2⁵ = 32
√1024 = 32
13. √1225
1225 ÷ 5 = 245
245 ÷ 5 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
Therefore;
√(1225) = √(5 × 5 × 7 × 7) = √(5² + 7²) = 5 × 7 = 35
14. √1764
1764 ÷ 2 = 882
882 ÷ 2 = 441
441 ÷ 3 = 147
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
√1764 = √(2 × 2 × 3 × 3 × 7 × 7) = √(2² × 3² × 7² = 2 × 3 × 7 = 42
15. √1936
1936 ÷ 2 = 968
968 ÷ 2 = 484
484 ÷ 2 = 242
242 ÷ 2 = 121
121 ÷ 11 = 11
11 ÷ 11 = 1
Therefore; √(1936) = √(2 × 2 × 2 × 2 × 11 × 11) = √(2⁴ × 11²) = 2² × 11
√(1936) = 2² × 11 = 44
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Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
The short word problem that illustrates the given equation is seen below. The value of the variable is 9.
Expression of the algebraic equation into word problems:Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.
A.
In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?
B.
6x + 18 = 72
Subtract 18 from both sides;
6x + 18 - 18 = 72 - 18
6x = 54
Divide both sides by 6.
6x/6 = 54/6
x = 9
C.
The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.
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When $720 is divided in the ratio 3:5, the larger share is
Answer:
The larger share is $450.
Step-by-step explanation:
[tex]\frac{3}{5} =\frac{3x}{5x} \\\\3x-the smaller share\\5x-the larger share\\3x+5x=8x\\8x-money to split\\8x=720 /:8\\x=90\\5x=5*90=450[/tex]
