Geometry In the figure below, and . Find the values of y and z.

The number on same team with same number of students and staff is 8.

A factor of a number simply means a number that divides another number without having a reminder.

In this case, there are 40 students and 24 staff members. Therefore, to have same team, we have to find the highest common factor for the numbers.

The highest common factor for 24 and 40 will be:

24 = 2, 3, 4, 6, 8, 12 and 24

40 = 2, 4, 5, 8, 10, 20 and 40

The highest factor is 8 which is the correct answer regarding the question.

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Answer:

x = 20°

I hope it helps!

Step-by-step explanation:

80+a=180

a=100

a=2x+3x

100=5x

x=20

Answer: 14a + 1

Step-by-step explanation:

( 7a x 3 - 2a - 2 ) + ( -5a + 3 )

( 21a - 2a - 2 ) + ( -5a + 3 )

21a - 2a - 2 - 5a + 3

14a + 1

Answer:

-x+6

Step-by-step explanation:

the slope is negative because the line is moving down. the y intercept is positive 6 because the line goes through the line (0,6)

Based on the calculations, each missing height of this cylinder is; 6 and 5 inches.

Mathematically, the volume of a cylinder can be calculated by using this formula:

V = πr²h

Where:

V is the volume of a cylinder. h is the height of a cylinder. r is the radius of a cylinder.

Now h the subject of formula, we have:

h = V/πr²

When V = 96π and r = 4, the volume of this cylinder is;

h = V/πr²

h = 96π/π(4)²

h = 96/16

Height, h = 6.

When V = 31.25π and r = 2.5, then the volume of this cylinder is;

h = V/πr²

h = 31.25π/π(2.5)²

h = 31.25/6.25

Height, h = 5.

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Answer: Mary 10 Sue 6

Step-by-step explanation:

Answer:

Sue is 6 and Mary is 10

Step-by-step explanation:

let Sue's age be x then Mary is x + 4 and the sum of their ages is

x + x + 4 = 16

2x + 4 = 16 ( subtract 4 from both sides )

2x = 12 ( divide both sides by 2 )

x = 6

x + 4 = 6 + 4 = 10

then Mary is 10 and Sue is 6

Answer:

Yes, this equation represents a direct variation equation

constant of variation = 2

=========================================================

Explanation:

Let's solve for y

y - 6 = 2(x-3)

y - 6 = 2x - 6

y - 6+6 = 2x - 6+6

y + 0 = 2x + 0

y = 2x

The equation is in the form y = kx which fits a direct variation equation. The constant of variation is k = 2.

Question 9.

In the construction of a frequency distribution, it is NOT a good idea to have overlaping class limits such as 10-20, 20-30, 30-40.

Let's determine if the above statement is true or false.

A frequency distribution shows a representation of the num ber of observations within a given interval either in tabular or grahical format.

In the construction of a frequency distribution, the class limits should be made very clear in order for each observation to fall into only one class.

It is not a good idea to have ovelaping class limits like 20-30, 30-40. This is because overlaping limits such as this would make it dificult to determine the class where 30 is located.

Therefore, this statement ''it is NOT a good idea to have overlaping class limits such as 10-20, 20-30, 30-40'' is TRUE.

ANSWER:

True.

Answer:

The most obvious way the government is involved in the U.S. economy is providing public goods and services like education, military protection, national parks and federal highways.

Step-by-step explanation:

The monomial in standard form will be written as 5y³x².

A Monomial may be defined as a type of polynomial which contains only one term. For example, 3x², 5x and 6x are called monomials. When written in standard form it is the product of one or more factors which can be a constant coefficient and one factor for each variable in the expression. While writing in standard form the terms having the highest power is written first and then the succeeding powers are written. Here, the expression given is 5x²y³ which is not in standard form. The terms having highest power is y³ so it should be written before the term x² as 5y³x² which will be the required standard form.

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The 12th term of the sequence is:

[tex]T_{12} = T_{11}*r = -18*3 = -54[/tex]

For a geometric sequence with a common ratio r and a first term T₁, the equation for the n-th term is:

[tex]T_n = T_1*(r)^{n-1} = T_{n-1}*r[/tex]

Such that the second formula (the right one) is called the recursive formula or recursive relation for the sequence.

We know that r = 3, and T₁₀ = -6, then we can use the recursive relation:

T_{11} = T_{10}*r = -6*3 = -18

T_{12} = T_{11}*r = -18*3 = -54

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A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.

A symbol (typically a letter) used in algebra to represent an unknowable numerical value in an equation. X and Y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are examples of frequently used variables (arc length).

The price to produce x yearbooks will be 15x.

Additionally, software has a fixed cost of $800.

So the total price would be:

y = 800 + 15x

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The x and y coordinates of Q are negative according to the transformation rule of a 90 degree counterclockwise rotation about the origin, which is (x, y)→  (-y, x).

C) Both x and y are negative.

When a function is transferred without undergoing any form or rotation changes, it has been "translated." A function may be translated both horizontally and vertically. Dilation, reflection, as well as rotation are additional "transformations" of a function that are feasible.

The following is the transformation formula for a 90° counterclockwise rotation about the origin:

(x, y) →  (-y, x)

the triangle is then reflected across the x-axis,

the following transformation rule:

(x, y) → (x, -y)

So, we have:

(x, y) → (-y, -x)

From the graph, we have:

Q = (1,2)

So,

the coordinates of Q" are

Q" = (-2, -1)

Both the x and y coordinates of Q " are negative.

Therefore,

the correct answer is option:

C) Both x and y are negative.

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I understand that the question you are looking for is:

Triangle PQR is rotated 90 degrees counterclockwise about the origin to form the image triangle P'Q'R' (not shown). Then triangle P'Q'R' is reflected across the x-axis to form triangle P"Q"R" (not shown). What are the signs of the coordinates (x, y) of Point Q"?

A) Both x and y are positive

B) x is negative and y is positive

C) Both x and y are negative

D) x is positive and y is negative

Answer:

7.08661

Step-by-step explanation:

step 1

Find out the area of the complete quadrant of the circle (1/4 of the complete circle)

where

r=2 units

substitute

step 2

Find out the area of the semicircle removed

where the radius of the semicircle removed is half of the radius of the circle

so

r=2/2=1 unit

therefore

to find out the area of the falcata, subtract the area of the removed semicircle from the area of the quadrant of the circle

The area of the falcata is

A=pi-pi/2=pi/2 unit2

Answer:

12·(2 + 7)

Step-by-step explanation:

24 + 84

= 12·2 + 12·7

= 12·(2 + 7)

The formula predicts that the triangle's perimeter will be 12f+9g+3.

What is a triangle?

The sides of a triangle are (10f +6) centimetres, (2f-4) centimetres, and (9g+1) centimetres long, respectively.

The expression for the triangle's perimeter will be

P = (10f+6) + (2f- 4) + (9g+1)

P = 12f+9g+3

The formula predicts that the triangle's perimeter will be 12f+9g+3.

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Answer:

588 cm

Step-by-step explanation:

The constant of proportionality in the given representation is 3 .

The proportionality constant is the ratio that connects two given numbers in a connection that is thought to be proportional. The proportionate constant is also known as constant ratio,  unit rate, variable of variation, and even rate of change.

The proportionality constant is calculated by a proportionality constant illustration.

Finding the proportionality constant begins with identifying the x and y elements. To figure out the weight to stick ratio, x will stand for size and Y for the number of butter sticks. We use the equations k = y/ x to calculate the proportionality constant.

Given the value of x is 4 and the value of y is 12

therefore using the equation we get

k= 12 / 4 = 3 .

Therefore the complete table will be

length (x)       (y)

4                     12

50                  150

88.49             265.47

Hence the proportionality constant is 3 .

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The value of CX as asked will be √29 when two points are given as (6,-4) and (1,-2) by using the distance formula √((x2-x1)²+(y2-y1)²).

In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that extends in both directions indefinitely. It has a single length dimension.

Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.

Here,

distance formula =√((x2-x1)²+(y2-y1)²)

CX=√((x2-x1)²+(y2-y1)²)

=√((1-6)²+(-2+4)²)

=√(25+4)

=√29

When two points are given as (6,-4) and (1,-2) by the distance formula √((x2-x1)²+(y2-y1)²), the value of CX as asked will be 29.

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The interpretations are

The slope

From the question, the slope is given as

Slope = 2 1/4

From the question, we have

y = Amount of money

x =Number of hot dogs

This means that the amount of money per 1 hot dog is $ 2 1/4

The y​-intercept

From the question, the y​-intercept is given as

y​-intercept = 10

From the question, we have

y = Amount of money

x =Number of hot dogs

This means that the initial amount of money is $10

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The quadratic function has an equation of f(x) = -2x² - 4x - 3

From the question, the ordered pairs are given as

(−1,−1), (2,−19), and (3,−33).

A quadratic function is represented as

f(x) = ax²+ bx + c

Using the point (-1, -1), we have

a(-1)²+ b(-1) + c = -1

So, we have

a - b + c = -1

Using the point (2, -19), we have

a(2)²+ b(2) + c = -19

So, we have

4a + 2b + c = -19

Using the point (3, -33), we have

a(3)²+ b(3) + c = -33

So, we have

9a + 3b + c = -33

So, we have

a - b + c = -1

4a + 2b + c = -19

9a + 3b + c = -33

Using a graphing tool, we have

a = -2, b = -4 and c = -3

Substitute a = -2, b = -4 and c = -3 in f(x) = ax²+ bx + c

So, we have

f(x) = -2x² - 4x - 3

Hence, the equation is f(x) = -2x² - 4x - 3

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The side of the square with area 169 mm² is 13 mm.

The side of the square and it's area are related to each other by the following relation -

Area = side². According to the known fact, all the sides of the square are same..

Keep the value of area in formula to find the value of the length of the side of the square

169 = side²

Side = ✓169

Taking square root of the value of area to find the value of the length of the side of the square

Side = 13 mm

Therefore, the length of the side of the square is 13 mm.

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Answer:the same as sid length

Step-by-step explanation:all sides are the same

Answer: n + 3

Step-by-step explanation:

Solution

n+3

Evaluate

(n 2 +n−6)

(n−2)

​Remove the parentheses

n−2n 2 +n−6

​Factor the expression

n−2

(n+3)(n−2)

Step-by-step explanation:

Absolute value equation:

[tex] |x - 120| = 920[/tex]

least no of runners = 800 - ( 920 - 800) = 680

Answer:

11/8 or 1.375

Step-by-step explanation:

2 3/4 => 11/4

1/2 x 11/4 = 11/8

Answer:

[tex]x -4 \leq -1\\x -4 + 4 \leq -1 + 4\\x\leq -1 +4\\x\leq +3[/tex]

Answer:

x ≤ 3

Step-by-step explanation:

This is the answer because I say it is

Given the equation of a line as shown below :

To determine the slope and the y - intercept of the line, compare the equation with straight line equation

After comparing the equation of a line

Therefore slope = -3 and y - intercept = -2