If the following two triangles are similar, find X.

Show work please

Answer:

The given equation of the curve is

 y= x² - 36

To find it's inverse we have to convert y in terms of x.

So, adding 36 to both sides of equation

→ y + 36=x² -36 + 36

→ y + 36 = x²

→ x² = y+ 36

→ x =[tex]\pm[/tex][tex]\sqrt{y+36}[/tex]

Now, to find inverse you can replace x by y, so by replacing x by y, the above equation becomes

y =[tex]\pm\sqrt{x+36}[/tex]

Second option is correct.

The function representing the relationship between the number of employees and the number of days it takes to complete the task is[tex]\[ e \times d = 16 \][/tex].

To represent the relationship between the number of employees (e) and the number of days (d) it takes to complete a task, we can use the formula:

[tex]\[ e \times d = k \][/tex]

where  k is a constant representing the amount of work to be done.

Given the information that 4 employees complete the task in 4 days, and 2 employees complete it in 8 days, we can set up two equations using the formula:

[tex]\[ 4 \times 4 = k \][/tex]

[tex]\[ 2 \times 8 = k \][/tex]

Now, solve each equation for ( k):

[tex]\[ 4 \times 4 = 16 \][/tex]

[tex]\[ 2 \times 8 = 16 \][/tex]

Since both equations give us the same constant ( k ), we can conclude that:

[tex]\[ e \times d = 16 \][/tex]

Therefore, the function representing the relationship between the number of employees and the number of days it takes to complete the task is:

[tex]\[ e \times d = 16 \][/tex]

The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

The number lines shows the weights of the car seats which is designed for in comparison the weight of the 32lb child.

Three car seats are designed as follows:

As the seat designed for a child upto and including 30 lb would not be suitable for 32 lb child. Because 32lb is more than the 30 lb.

Now, the seat designed for a child between 30 lb and 85 lb, 30lbs and 85lbs would be suitable as the child is within these weight ranges that is 32lb.

The interval notation is:

0 < x ≤ 30; 15 < x < 40; 30 ≤ x ≤ 85;

The  second and third car seats are suitable.

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Answer:

(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares

Step-by-step explanation:

The formula for difference of squares

[tex]a^2 - b^2 =(a+b)(a-b)[/tex]

(–7x + 4)(–7x + 4) both parenthesis having same terms so this will not result in difference of squares

(–7x + 4)(4 – 7x) both parenthesis having same terms so this will not result in difference of squares

(–7x + 4)(–7x – 4) Sign changes in the middle of both parenthesis , so this will result in difference of squares

(–7x + 4)(7x – 4) sign changes for both terms in both parenthesis so this will not result in difference of squares

Answer:

Decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:

3.2,3.4 and 3.6

Step-by-step explanation:

We have to find decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals

3.0

3.0+0.2= 3.2

3.2+0.2= 3.4

3.4+0.2= 3.6

3.6+0.2= 3.8

Hence, decimals between 3.0 and 3.8 with an interval of 0.2 between each pair of decimals are:

3.2,3.4 and 3.6

Answer:

(−6, 0) , (−1, −2)  and (−5, −1)

Step-by-step explanation:

The given inequality is  x+3y ≥ −8

Substitute all the given points in this inequality and check which points satisfy.

For (−6, 0)

-6+3(0) ≥ −8

- 6 + 0  ≥ −8

- 6 ≥ −8   => True.

Hence, (−6, 0) is a solution.

For (−1, −2)

-1 + 3(-2) ≥ −8

-1 - 6 ≥ −8

- 7 ≥ −8 => True.

Hence, (−1, −2) is a solution.

For (−5, −1)

-5 + 3 (-1) ≥ −8

- 5 -3  ≥ −8

-8 ≥ −8=> True.

Hence, (−5, −1) is a solution.

For (−16, 2)

-16 +3 (2) ≥ −8

-16 + 6 ≥ −8

-10≥ −8 => False.

Hence,(−16, 2) is not a solution.

For (0, -3)

0 + 3(-3) ≥ −8

-9  ≥ −8=> False.

Hence, (0, -3) is not a solution.

Therefore, below ordered pairs are solutions of the given inequality

(−6, 0) , (−1, −2)  and (−5, −1)

Answer:

Closed circle on -108 and shaded to the left, I took the same lesson and got 100%

Step-by-step explanation:

But your missing part of the question, it's how would you graph the solution set of x/-6 ≤ -18?

Final answer:

The slope-intercept equation of the line that passes through (1, 2) and (3, 4) is y = x + 1, with a slope of 1 and a y-intercept of 1.

Explanation:

To find the slope-intercept equation of a line that passes through the points (1, 2) and (3, 4), we first need to determine the slope of the line. We use the formula for the slope (m) given by the change in y over the change in x, or Δy/Δx. Calculating the slope, we get:

m = (4 - 2) / (3 - 1) = 2 / 2 = 1.

Now we have the slope, we can use the slope-intercept form of the line, which is y = mx + b, where m is the slope and b is the y-intercept. Plugging in one of the points, say (1, 2), into this equation gives us:

2 = (1)(1) + b

Which simplifies to:

b = 2 - 1 = 1

So the y-intercept (b) is 1. Therefore, the slope-intercept equation of the line is:

y = x + 1

Relative maxima and relative minima are called relative extrema.

Given:

The given statement is:

Relative maxima and relative minima are called relative_____.

To find:

The correct word to fill the given blank.

Explanation:

Relative maxima: If the function changes from increasing to decreasing, then the turning point is known as relative maxima.

Relative minima: If the function changes from decreasing to increasing, then the turning point is known as relative minima.

Relative extrema: The turning points relative maxima and relative minima are known as relative extrema.

Therefore, the relative maxima and relative minima are called relative extrema.

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