Justify the first step that David took in verifying that x = 5 is a solution for the equation
8x – 13 = 2x + 17.

8x – 13 = 2x + 17
8(5) – 13 = 2(5) + 17
A.
David multiplied 8 by 5.
B.
David subtracted 13 from both sides.
C.
David replaced x with 5.
D.
David added 17 to both sides.

Answer:

The Eastern Coachwhip is the longest of the listed snakes.

Step-by-step explanation:

Answer:

    \(\textsf{Choice A } \quad y = \dfrac{5}{3}x + 1\)

Step-by-step explanation:

Slope intercept form of a line equation is

y = mx + b

where

m = slope

b = y-intercept

A perpendicular line to y = mx + b will have a slope of -1/m

Let's first find the equation for line z in slope-intercept form
Slope m for a line  = (y2- y1)/(x2 - x1) where x1, y1 and x2, y2 are two points on the line

Slope of line z is
\(m = \dfrac { 2 - (-1) }{-2 - 3} = \dfrac{3}{-5} = - \dfrac{3}{5}\)

So line z will have an equation of the form
\(y = -\dfrac{3}{5}x + b\)

We know that a line perpendicular to this line will have a slope of
\(- \dfrac{1}{-\dfrac{3}{5}} = \dfrac{5}{3}\)

So the equation of the perpendicular line is
\(y = \dfrac{5}{3}x + b\)

Only one of the 4 choices, name choice A has this slope of 5/3

Therefore the correct answer choice is A

There is no need to compute b, the y intercept but if you wanted to, this is how you would do it:

The perpendicular line passes through (3, 6). This means when x = 3, y =6

Substitute these values of x, y into the equation for the perpendicular line and solve for b

\(y = \dfrac{5}{3}x + b\\\\\text{When x = 3, y = 6}:\\\\6 = \dfrac{5}{3} \cdot 3 + b\\\\6 = 5 + b\\\\b = 6 - 5 = 1\\\\\text{So, the equation of the perpendicular line is }\\y = \dfrac{5}{3}x + 1\)

This corresponds to Choice A

The equation of the line is y=1/3x.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given graph let us take two points through which the line passes.

(-6, -2) and (6, 2)

m=2-(-2)/6-(-6)

m=4/12=1/3

The slope of the line is 1/3.

Now we have to find the y intercept

2=1/3(6)+b

2=2+b

b=0

The equation of line is y=1/3x

Hence, the equation of the line is y=1/3x.

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Answer:

A sports coach bought 2 bats and 3 packs of tennis balls with 4 balls each. If one bat and one ball are of the same price, and he payed $990.50, write the equation for this

The population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

The mean is calculated by dividing the number of employees by the number of years of service. The total number of years of service is 417, hence the average will be

The average years worked = 417/30 = 13.9 ≈ 14 years

The % of workers who have worked there for at least ten years is calculated by calculating the number of employees who have ten or more years of service and dividing that number by the total number of employees.

The final result is presented as a percentage will be:

(10 years or more)/(total number) = 22/30 = 0.73 = 73%

Thus, the population means that the number of years worked is 14, and 73% of employees worked for the company for at least 10 years.

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Answer:.25

Step-by-step explanation:

there

Answer:

below

Step-by-step explanation:

Let’s assume the first digit can be 0. Then there are 10 choices for each of the 3 digits. 10 * 10 * 10 = 1000 3-digit combinations.

      OR

Now, if the first digit cannot be 0, then we have 9*10*10 = 900 possible 3-digit combinations.

Answer:

720

Step-by-step explanation:

you have 10 choices for the first digit,you have 9 choices for the second digit and 8 choices for the 3 digit .

It gives you 10×9×8=720 all in all

Answer:

Step-by-step explanation:

the dot would either (1,4) or (4,1)

a squared+ b squared= c squared

the length of the sides are 3

3 squared + 3 squared= c squared

9+9 =c squared

18= c squared

square root of 18 rounded to the nearest tenth is 4.2

Answer:

9 gallons per minute

Step-by-step explanation:

63 divided by 7 = 9. Dividing the overall amount by time finds the rates per minute.

to double check, if 9 gallons were coming out of a pipe for 7 minutes, how much would there be?

9 times 7 = 63 gallons

The intervals of each behavior of the function are given as follows:

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As you probably know, trinomials of the form y=ax²+bx+c,a≠1 can be solved by finding two numbers that multiply to a×c and that add to b.

∴ Two numbers that multiply to −2 and that add to −1 are −2 and +1.

(2cos²θ−2cosθ)+(cosθ−1)=0

(2cosθ+1)(cosθ−1)=0

cosθ=−1/2andcosθ=1

By special angles:

θ=120˚,240˚and0˚,or3π/2+2nπ,4π/ 3+2nπ and 2nπ, n being an integer.

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Answer:

y=39

Step-by-step explanation:

according to question;

13=1/3×y

or;13/y=1/3

or;13×3/y=1

or;39/y=1

or;39=y

Step-by-step explanation:

Find the factors of x that makes it zero.. Equate the equation to y and use it to find the value of y. Then get your values for x and y and plot the graph

If the total height between two floors is 9'0 1/2" and 14 risers are to be used in a set of stairs, the height of each riser would be approximately 7.75 inches.

To find the height of each riser in a set of stairs given the total height between two floors, we need to divide the total height by the number of risers.

First, let's convert the total height to a consistent unit. The distance between two floors is given as 9'0 1/2". We can convert this to inches by multiplying the feet by 12 and adding the remaining inches:

9 feet = 9 * 12 = 108 inches

0 1/2 inch = 0.5 inch

Total height = 108 + 0.5 = 108.5 inches

Next, we divide the total height by the number of risers (14) to find the height of each riser:

Height of each riser = Total height / Number of risers

Height of each riser = 108.5 inches / 14

Using a calculator, we can compute:

Height of each riser ≈ 7.75 inches

Therefore, the height of each riser in the set of stairs would be approximately 7.75 inches.

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Answer:

C

Step-by-step explanation:

 2

+2

-----

 4

The expressions  3x² - 7y, 2 - 8y, 4x² - 9  are polynomilas.

A polynomial is an algebraic expression of degree n where n belongs to whole numbers.

A polynomial of degree n can be written as a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + ... + aₙ.

Given, are 4 polynomials 3x² - 7y it is a polynomial because it has powers that are in whole numbers and it is of degree 2 in variables x and y.

2 - 8y is also a polynomial as the degree of y is 1 and it is a whole number.

3x⁻² + y is not a polynomial as the degree of x is - 2 and it is not a whole number.

4x² - 9 is also a polynomial as it has a degree of 2 a whole number.

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The value g(7) of the function g(x) = 7  / 8 x  - 1 / 2 is 45 / 8.

A function relates each element of a set with exactly one element of another set (possibly the same set).

In a simpler term, a function relates an input to an output.

Therefore, let's find the value of g(7) for the function below:

g(x) = 7  / 8 x  - 1 / 2

Hence,

g(7) = 7 / 8 (7)  - 1 / 2

g(7) = 49 / 8  - 1 / 2

g(7) =  49 - 4 / 8

Therefore,

g(7) = 45 / 8

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Navern's manufacturing cycle efficiency (MCE) for its elevators is: 41.4%

The formula for obtaining the manufacturing cycle efficiency is value-added time divided by the production cycle time * 100. In the data given, the process and inspection times qualify as a value-added time

Process time = 23 days

Inspection time = 13 days

Value added time = 23 + 13 = 36days

The production cycle time = Move time + process time + queue time + inspection time + wait time

= 22 + 12 + 23 + 13 + 17 days

= 87 days

So, the manufacturing efficiency time = 36/87 * 100

= 41.4%

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The vertical displacement is of 2 units down, the correct option is B.

Remember that for a function f(x), a vertical displacement of N units is written in general form as:

g(x) = f(x) + N

If N > 0, the translation is upwards.

if N < 0, the translation is downwards.

Here we assume that we start with the parent cosine function:

y = cos(x)

And the transformed function is:

y = -2 - cos(x - π)

So we have some transformations, but the vertical translation is of 2 units down. So the correct option is B.

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The total money spent on a pass and lunch for each student is $850.14.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division.

here,

As mentioned in the question, Passes for 28 pupils and 4 teachers cost the school $778.88 and the school also spends $241.64 on lunch for kids only.

Total number of person  = 28 + 4
                                     = 32
Cost per pass = 778.88 / 32
                     = $24.34
Total passes of students = 25 × 24.34 = 608.5
Total spend on lunch of student = 241.64
Total spend on lunch = 241.64 + 608.5 = $850.14

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Answer:

28 degrees

Step-by-step explanation:

We know that (4x + 7) + (2x + 5) add up to a straight angle = 180 degrees, so we have the equation 4x + 7 + 2x + 5 = 180.

By combining like terms, we get 6x + 12 = 180.

Subtract 12 from both sides of the equation to get 6x = 168. Divide both sides by 6 and you get x = 28.

Recall the rules for the cross product:

i x i = j x j = k x k = 0

i x j = k

j x k = i

k x i = j

For any two vectors a and b, we also have anticommutativity:

a x b = -(b x a)

(a) A = 2.0 i - 4.0 j + k, C = 3.0 i + 4.0 j + 10.0 k

A x C = 6.0 (i x i) - 12.0 (j x i) + 3.0 (k x i)

.......... + 8.0 (i x j) - 16.0 (j x j) - 4.0 (k x j)

.......... + 3.0 (k x i) + 4.0 (k x j) + 10.0 (k x k)

A x C = (4.0 + 4.0) i + (3.0 - 3.0) j + (12.0 + 8.0) k

A x C = 8.0 i + 20.0 k

With the same steps as in (a), we get

(b) A x C = 44.0 i + 17.0 j - 20.0 k

(c) A x C = -24.0 k

(d) A x C = -(C x A) = -18.0 i - 18.0 k

To solve the equation 7(x + 3) = 7(x + 5), we can start by simplifying both sides of the equation:

7x + 21 = 7x + 35

Subtracting 7x from both sides, we get:

21 = 35

This is a contradiction, as 21 is not equal to 35. Therefore, the equation has no solution.

However, the problem states that the equation has an infinite number of solutions. This can only happen if the missing number is a factor that appears on both sides of the equation, and therefore cancels out when we simplify the equation.

Looking at the equation, we can see that both sides have a factor of 7, which cancels out when we simplify the equation. Therefore, the missing number must be the factor that was torn off, which is 7 multiplied by the difference between the two numbers inside the parentheses:

7(5 - 3) = 14

Therefore, the missing number is 14, which corresponds to answer option B.

Answer:

3rd option

Step-by-step explanation:

One of our exponent rules tells us that \((\frac{x}{y} )^{z}\) =  \(\frac{x^{z} }{y^{z} }\). So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?

We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.

Let me know if you have any questions!

Answer:

statmen there for this should me solved and abcd are proof

reason bcz this is not equal square

Answer:

$48.15

Step-by-step explanation:

60.00 x 25% = $15.00

60.00 - 15.00 = $45.00

45.00 x 7% = $3.15

45.00 + 3.15 = $48.15

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

From the question, we have the following ordered pairs

x intercepts = (6,0) and (18, 0)

Vertex = (12, -36)

Points (21, 41.25)

The closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is the calculated using

m = [f(21) - f(18)]/[21 - 18]

This becomes

m = [f(21) - f(18)]/3

Substitute the known values in the above equation

m = [41.25 - 0]/3

Evaluate the difference

m = 41.25/3

Evaluate the quotient

m = 13.75

Approximate

m=14

Hence, the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month is 14

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Complete question

The graph below shows the value of Edna's profits f(t), in dollars, after t months:

What is the closest approximate average rate of change for Edna's profits from the 18th month to the 21st month?

See attachment for graph