Rectangle ABCD is shown with diagonal AC drawn. Point F is on AC and point E on DC such that FE is perpendicular to DC. Prove triangle ABC is similar to triangle CEF

Answer:

[tex]d = 670,616,629h \ mi[/tex]

Step-by-step explanation:

Given:

Speed of the light = 670,616,629 mi\hr

We need to find the direct variation equation represents given situation.

Solution:

Speed is defined as the ratio of distance and time. So, the equation of the speed is as follows:

[tex]Speed = \frac{Distance}{Time}[/tex]

And also written as.

[tex]S = \frac{d}{h}[/tex]

Now, we write the above equation for distance.

[tex]d = S\times h[/tex] ------------(1)

Where:

d = distance travel by object.

S = speed of the object.

h = Total time taken

Substitute S = 670,616,629 mi\hr in equation 1.

[tex]d = 670,616,629h \ mi[/tex]

Therefore, direct variation equation to represents the given situation

[tex]d = 670,616,629h \ mi[/tex]

Answer:

8,160 lei

Step-by-step explanation:

The question in English is

136 children came to the ice rink in the morning, and three times in the afternoon. How much money was collected on the tickets sold, if an entrance ticket costs 15 lei?

step 1

Find the total number of children that came to the ice rink

we know that

The number of children that came to the ice rink in the morning was 136

The number of children that came to the ice rink in the afternoon was (136*3)=408

To find out the total number of children that came to the ice rink , adds the number of children that came in the morning plus the number of children that came in the afternoon

so

[tex]136+408=544\ children[/tex]

step 2

To find out the total money collected, multiply the total number of children by the cost of one ticket entrance

so

[tex]544(15)=8,160\ lei[/tex]

Yo sup??

This question can be solved by applying the properties of similar triangles

the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 35

The similarity property used here is called AAA ie angle angle angle property as all the three angles of the 2 triangles are equal.

therefore we can say

5x/45=20/36

x=5 units

Hope this helps

Answer:

Like terms are numbers with or without variables that have the same variables.

Step-by-step explanation:

5x and 3x are like terms because they have the same variable.

5x and 3y are not like terms because the variables are different.

To combine them, just add or subtract them. You cannot combine non-like terms!

Answer:

Definition: Like terms - Term in math that have the same variables or powers.

Ex. 2x, -5x, and 7x.

Combine Them: 2x + 7x = 9x - 5x = 4x

Step-by-step explanation:

Answer: 5 gallons of gas were used for city driving.

Step-by-step explanation:

Let x represent the number of gallons of gas that the car used on the highway.

Let y represent the number of gallons of gas that the car used in the city.

The car's gas tank can hold 21 gallons. This means that

x + y = 21

A car can travel 25 miles per gallon on the high way and 20 miles in the city. If the car traveled 500 miles on a full tank of gas, it means that

25x + 20y = 500 - - - - - - - - - -1

Substituting x = 21 - y into equation 1, it becomes

25(21 - y) + 20y = 500

525 - 25y + 20y = 500

- 25y + 20y = 500 - 525

- 5y = - 25

y = - 25/ - 5

y = 5

x = 21 - y = 21 - 5

x = 16

The number of miles used for city driving is: [tex]\[{100}\][/tex].

To determine how many miles were used for city driving, we start by defining the variables and equations based on the problem's information:

1. Let \( x \) be the number of miles driven on the highway.
2. Let \( y \) be the number of miles driven in the city.

Given the problem, we have the following information:
- The car traveled a total of 500 miles: [tex]\( x + y = 500 \)[/tex]
- The car's gas consumption rates are 25 miles per gallon on the highway and 20 miles per gallon in the city.
- The gas tank holds 21 gallons.

Next, we set up the equation for total gas consumption:
[tex]\[\frac{x}{25} + \frac{y}{20} = 21\][/tex]

We now have a system of two equations:
[tex]1. \( x + y = 500 \)\\2. \( \frac{x}{25} + \frac{y}{20} = 21 \)[/tex]

To solve this system, we start with the first equation:
[tex]\[x = 500 - y\][/tex]

Substitute [tex]\( x = 500 - y \)[/tex] into the second equation:
[tex]\[\frac{500 - y}{25} + \frac{y}{20} = 21\][/tex]

Next, we find a common denominator to simplify the left-hand side of the equation. The common denominator for 25 and 20 is 100:
[tex]\[\frac{500 - y}{25} = \frac{500 - y}{25} \cdot \frac{4}{4} = \frac{4(500 - y)}{100} = \frac{2000 - 4y}{100}\]\[\frac{y}{20} = \frac{y}{20} \cdot \frac{5}{5} = \frac{5y}{100}\]\\[/tex]
So the equation becomes:
[tex]\[\frac{2000 - 4y + 5y}{100} = 21\][/tex]

Combine the terms in the numerator:
[tex]\[\frac{2000 + y}{100} = 21\][/tex]

Multiply both sides by 100 to eliminate the fraction:
[tex]\[2000 + y = 2100\][/tex]

Subtract 2000 from both sides to solve for \( y \):
[tex]\[y = 100\][/tex]

Thus, the number of miles used for city driving is:
[tex]\[{100}\][/tex].

Answer:

There are 18 Sedans in the dealership shop.

Step-by-step explanation:

Let x represent the number of Sedans in the dealership shop.

Let y represent the number of SUV's in the dealership shop.

If there are a combined 24 sedans and SUVs, it means that

x + y = 24 - - - - - - - - - - - -1

At a car dealership, there are three times as many sedans as SUVs. This means that

x = 3y

Substituting x = 3y into equation 1, it becomes

3y + y = 24

4y = 24

y = 24/4 = 6

x = 3y = 6 × 3

x = 18

Answer:

a.) 1.23 seconds

b.) 14 m/s

Step-by-step explanation:

a.) Before commencing the calculation, we need to specify the information.

Data:

acceleration dues to gravity, g = 9.81 m/s²

initial velocity u = 2.0 m/s

height, s = 40 m

t = ?

The formula for finding the distance is s = ut + 1/2at²

Therefore, 40 = 2t + 1/2×(9.81) ×t²

                  80 = 4t + 9.81 t²

Solving for t by the quadratic equation gives t = 1.23 s [Note the other negative value for t is rejected because there is no negative time]

b) The final velocity is given by the following equation:

v = u + at

where v = final velocity just before the camera lands on the ground

            u = initial velocity

            t = time taken

            a = g = acceleration dues to gravity = 9.81 m/s²

Calculating gives

v = 2 + 9.81×1.23

  = 14 m/s Ans

Answer:

B) -3.464

Step-by-step explanation:

∫₀³ g'(x) cos²(2g(x) + 1) dx

Using u substitution:

u = 2g(x) + 1

du = 2g'(x) dx

½ du = g'(x) dx

When x = 0, u = 11.

When x = 3, u = -3.

½ ∫₁₁⁻³ cos²(u) du

You can use a calculator to solve this, or you can evaluate algebraically.

Use power reduction formula:

½ ∫ (½ + ½ cos(2u)) du

¼ ∫ du + ¼ ∫ cos(2u) du

¼ ∫ du + ⅛ ∫ 2 cos(2u) du

¼ u + ⅛ sin(2u) + C

Evaluating from u = 11 to u = -3:

[¼ (-3) + ⅛ sin(-6) + C] − [¼ (11) + ⅛ sin(22) + C]

-⁷/₂ + ⅛ sin(-6) − ⅛ sin(22)

−3.464

Answer:

Step-by-step explanation:

Why shouldn't classes overlap when one summarizes continuous data? If classes overlap, then some observations will be counted in more than one class. This means that certain observations will end up in more than one bar of a histogram, which will misrepresent the data!

Option C

The equation that represents this situation is -3x = 21

The second number is -7

Solution:

The first number is -3

The product of two numbers is 21

Let the second number be "x"

The equation that represents this situation is:

Product of first and second number = 21

[tex]-3 \times x = 21\\\\-3x = 21[/tex]

Thus the equation is found

Solve the equation

-3x = 21

Divide both sides by -3

[tex]x = \frac{21}{-3}\\\\x = -7[/tex]

Thus the second number is -7

Answer:

C.

The equation that represents this situation is -3x = 21. The second number is -7.

Step-by-step explanation:

I just did it and got it right on edmentum/plato

hope this helps good luck

Answer:

X = 93

Step-by-step explanation:

Angles of a polygon = (n - 1)180

The above polygon is heptagon (with 6 sides)

(6-1) × 180

5×180 = 900

Add the given Angles and equate it to 900 (as gotten above)

4x + 3x + 47 + 93 + 46 + 62 = 900

7x + 248 = 900

Collect like term of the number

7x = 900-248

7x = 652

Divide both side by the coefficient of x

7x/7 =652/7

X = 93.1429

Answer:

12 (5x - 2)

Step-by-step explanation:

First to know if we can get a common factor we have to find a number by which it is divisible on 24 and 60

first we will try with 2

60/2 = 30            both are divisible by 2

24 /2 = 12

then we will take common factor 2

60x - 24

we multiply and divide by 2

2 (60x - 24)/2

we distribute the 2

2(60x/2 - 24/2)

and solve

2(30x - 12)

Now we continue with the same procedure until there is no more number in common to divide

we will try with 2

30/2 = 15            both are divisible by 2

12 /2 = 6

then we will take common factor 2

2(30x - 12)

we multiply and divide by 2

2*2 (30x - 12)/2

we distribute the 2

4(30x/2 - 12/2)

and solve

4(15x - 6)

continue with the same procedure

we will try with 2

15/2 = X            only one is divisible by 2

6 /2 = 3

we will try with 3

15/3 = 5          both are divisible by 3

6 /3 = 2

then we will take common factor 3

4(15x - 6)

we multiply and divide by 3

4*3 (15x - 6)/3

we distribute the 3

12(30x/3 - 6/3)

and solve

12(5x - 2)

there is no number other than 1 by which we can divide 5 and 2

12(5x - 2)

The question is incomplete. The complete question is here;

Half of u is less than or equal 43, find the greatest possible value of u

The greatest possible value of u is 86

Step-by-step explanation:

To solve an inequality:

∵ [tex]\frac{1}{2}[/tex] u ≤ 43

- Divide both sides by [tex]\frac{1}{2}[/tex]

∴ u ≤ 86

- That means u could be any numbers less than or equal 86

∵ You need the greatest possible value of u

∴ u = 86

The greatest possible value of u is 86

Learn more:

You can learn more about inequalities in brainly.com/question/1465430

#LearnwithBrainly

Answer:

D. 286 deg

Step-by-step explanation:

Think of both triangles as just one single large triangle.

The exterior angles at the bottom have measure 127 deg.

That means the two interior angles at the bottom have measure

180 deg - 127 deg = 53 deg

The measures of the interior angles of triangle add to 180 deg.

The upper interior angle has measure:

180 deg - 53 deg - 53 deg = 74 deg

A full circle has 360 degrees.

Angle r is a full circle minus the upper interior angle of the combined triangle.

r = 360 deg - 74 deg

r = 286 deg

Answer:

y² / 81  -  x² / 19   = 1

Step-by-step explanation: See Annex ( vertices and foci in coordinates axis)

The equation in standard form for the hyperbola is:

x² / a² - y²/b² = 1       or    y²/a²  -  x² / b²  = 1

In cases of transverse axis parallel to x axis  or y axis respectively.

As per given information in this case hyperbola has a transverse axis parallel to  y  axis the equation is

y²/a²  -  x² / b²  = 1

a is a distance between  center and vertex therefore a = 9

c is a distance between center and a focus c = 10

and  b will be:

c² = a²  +  b²    ⇒   b²  = c²  - a²     ⇒ b²  =  (10)² - (9)²    ⇒  b² = 100 - 81

b = √19

And the equation in standard form is:

y² / a²  -  x² / b²  = 1

y² / ( 9 )²   -  x² / √(19)²     ⇒   y² / 81  -  x² / 19   = 1

Answer:

B

Step-by-step explanation:

Answer:

[tex] 12C5 *(12C3) = 792*220 =174240 ways[/tex]

Step-by-step explanation:

For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52

First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:

[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]

So then 12 C5 would be equal to:

[tex] 12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792[/tex]

So we have 792 was in order to select 5 diamonds from the total of 12

Now in order to select 3 clubs from the total of 12 we have the following number of ways:

[tex] 12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220[/tex]

So then the numbers of ways in order to select 5 diamonds and 3 clubs are:

[tex] (12C5)*(12C3) = 792*220 =174240 ways[/tex]

Answer:

In order the sequences defined by the expressions on the left are ...

Step-by-step explanation:

One of the first steps in working multiple choice questions (in any subject) is to look at the answers to see what you need to know to be able to tell a correct answer from an incorrect one.

Here, all of the first terms are different, except for the two sequences that both starts with 1. Those differ in the ratio between terms (1/2 vs 2).

This means you only have to evaluate the expression for the first domain value (x=1) and you can tell right away what the answer is. It is not complicated, and your calculator can help if you can't do it in your head.

___

Starting at the top of the list on the left, ...

  2^1 = 2 . . . . matches 2, 4, 8, ...

  2(2^1) = 4 . . . . matches 4, 8, 16, ...

  (1/2)^1 = 1/2 . . . . matches 1/2, 1/4, 1/8, ...

  2(1/2)^1 = 1 . . . .  double the previous sequence, so 1, 1/2, 1/4, ...

  1/2(2^1) = 1 . . . . half the first sequence, so 1, 2, 4, ...

  1/2(1/2)^1 = 1/4 . . . . matches 1/4, 1/8, 1/16, ...

See the explanation

I have corrected your diagram so ∅ is the angle at the top of the diagram. In order to solve this problem we have to use Pythagorean theorem and the law of sines. Moreover, I have named two sides as w and z so those variables will help us to solve this problem. So:

The triangle at the bottom is right, so by Pythagorean theorem is true that:

[tex]w^2=4^2+(2\sqrt{2})^2 \\ \\ w^2=24 \\ \\ w=\sqrt{24} \\ \\ w=2\sqrt{6}[/tex]

By law of sines:

[tex]\frac{z}{sin\theta}=\frac{w}{sin60^{\circ}} \\ \\ z=\frac{wsin\theta}{sin60^{\circ}} \\ \\ z=\frac{2\sqrt{6}sin\theta}{\sqrt{3}/2} \\ \\ z=4\sqrt{2}sin\theta[/tex]

By law of sines again:

[tex]\frac{y}{sin45^{\circ}}=\frac{z}{sin\phi} \\ \\ y=\frac{zsin45^{\circ}}{sin\phi} \\ \\ y=\frac{4\sqrt{2}sin\theta \sqrt{2}/2}{sin\phi} \\ \\ \\ Finally: \\ \\ \boxed{y=\frac{4sin\theta}{sin\phi}}[/tex]

Classification of triangles: https://brainly.com/question/10379190

#LearnWithBrainly

Question:

A square piece of paper has an area of x2 square units. A rectangular strip with a width of 2 units and a length of x units is cut off of the square piece of paper. The remaining piece of paper has an area of 120 square units.

Which equation can be used to solve for x, the side length of the original square?

x2 − 2x − 120 = 0

x2 + 2x − 120 = 0

x2 − 2x + 120 = 0

x2 + 2x + 120 = 0

Answer:

Option a: [tex]x^{2} -2x-120=0[/tex] is the equation

Explanation:

It is given that the area of the square paper is [tex]x^{2}[/tex] square units.

The area of the remaining piece of paper is 120 square units.

It is also given that the area of the remaining piece of paper is [tex]x^{2}-2 x[/tex]

Thus, equating the area of the remaining piece of paper, we have,

[tex]x^{2} -2x=120[/tex]

Subtracting 120 from both sides of the equation, we have,

[tex]x^{2} -2x-120=0[/tex]

Thus, the equation [tex]x^{2} -2x-120=0[/tex] can be used to solve for x.

Hence, Option a is the correct answer.

The coordinates of A'  after rotation  of 270 counterclockwise and then shifted down 3 units are (2, 4).

To find the coordinates of point A' after a 270-degree counterclockwise rotation around the origin and then shifting down 3 units, we first perform the rotation.

A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. So, when we rotate point A(-7, -2) 90 degrees clockwise, we swap the coordinates and change the sign of the former x-coordinate, which gives us the new point A''(2, 7). Next, we shift A'' down 3 units, which means we subtract 3 from the y-coordinate, resulting in A'(2, 4).

Answer:

$261

Step-by-step explanation:

The team hopes to earn three times more than it did last year

Last year the team earned $ 87

We are required to determine the team's goal this year.

Therefore;

Since they hope to raise three times than last year;

Then;

Goal this year = 3 × last year's earnings

                        = 3 × $ 87

                        = $261

Therefore, the team's goal this year is $261

Answer:

(1, -2)

(-8, -2)

Step-by-step explanation:

(1 , -6) and (-8 , -6)

1 - (-8) = 9

we know that the length of the side that we know the vertices is 9

from there we make an equation with the sum of the sides equal to the perimeter

we will have 2 times 9 and 2 times x beacause it is a rectangle

x + x + 9 +9 = 26

2x + 18 = 26

2x = 26 - 18

2x = 8

x = 8/2

x = 4

Now that we know the missing side we just have to add or subtract this value to the coordinate in and of the vertices we have and we will obtain the missing vertices

(1, -6 + 4)

(1, -2)

( -8, -6+4 )

(-8, -2)

The coordinates of the other two vertices of the rectangle are (1, -2) and (-8, -2), found by calculating the length of one side using the given vertices and then applying the rectangle's perimeter to find the length of the adjacent sides.

The subject of the question is to find the other two vertices of a rectangle given two of its vertices and the perimeter. We know that the opposite sides of a rectangle are equal in length. So, to solve this, we can use the distance formula to find the length of one side with the two given points (1, -6) and (-8, -6). The length of this side is the absolute value of the difference in the x-coordinates, which is 9 units. Since the perimeter is 26, and this length is 9, the sum of the lengths of the other two sides is 26 - 2*9 = 8 units. Therefore, each of these sides is 4 units long. Because the given points have the same y-coordinate, they lie on a horizontal side of the rectangle, so the other two vertices will have the same x-coordinates as the given ones and will be 4 units vertically away. If we add and subtract 4 units from the y-coordinate of the given points, we get the other two vertices: (1, -6 +4) and (-8, -6 +4). So the coordinates of the other two vertices are: (1, -2) and (-8, -2).

Answer:

x is a binomial random variable because a trial is independent and number of trials, n = 10.                                            

Step-by-step explanation:

We are given the following information:

We treat adult  reading at least one book in the past 12 months as a success.

P(Adult reading atleast one book) = 74% = 0.74

Then the number of adults follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

If x is a random variable representing the number of people who have read at least on book, then x follows a binomial distribution because:

Thus,

x is a binomial random variable because a trial is independent and number of trials, n = 10.

Answer:

Hurricanes

Step-by-step explanation:

We are given the following in the question:

Scientists are studying hurricanes to determine the number of hurricanes in the past 50 years that have caused greater than $1 million in damages.

Population:

Thus, for the given scenario

Population of interest:

Hurricanes

From this population a sample of hurricanes that have caused greater than $1 million in damages is taken.

Answer:

A)Hurricanes

Step-by-step explanation:

Function Z has a greater slope and a higher y-intercept compared to Function W, making Function Z steeper and intercepting the y-axis at a higher point. Here options A and B are correct.

The two lines in the graph represent linear functions, which means they can be expressed in the following form:

y = mx + b

where:

m is the slope of the line, which tells you how steep the line is and in which direction it is slanted.

b is the y-intercept, which is the point where the line crosses the y-axis.

x is the independent variable, and y is the dependent variable.

The steeper a line is, the greater the absolute value of its slope. A positive slope means the line slants upwards from left to right, while a negative slope means it slants downwards from left to right.

In the image, you can see the equations for the two lines are:

Function W: y = 2x - 5

Function Z: y = 3x - 2

By looking at the equations, we can see that:

The slope of function W is 2.

The slope of function Z is 3.

Since 3 is greater than 2, we can say that the slope of function Z is greater than the slope of function W. This means that function Z is steeper than function W.

The y-intercepts of the lines are also different:

The y-intercept of function W is -5.

The y-intercept of function Z is -2.

Since -2 is greater than -5, we can say that the y-intercept of function Z is greater than the y-intercept of function W.

Therefore, the following statements comparing the functions are true:

The slope of Function W is less than the slope of Function Z

The y-intercept of Function W is less than the y-intercept of Function Z. Here options A and B are correct.

Function W has a slope less than Function Z, and its y-intercept is also less than that of Function Z.(options a and d)

To compare the functions W and Z, let's analyze their slopes and y-intercepts:

Function W: [tex]\(y = 0.5x - 1\)[/tex]

Function Z: Given table of values

a. The slope of Function W is [tex]\(0.5\).[/tex]

b. The slope of Function Z can be calculated using the given points. We choose two points: [tex]\((-2, -2.5)\)[/tex] and [tex]\((4, -1)\)[/tex]. Using the slope formula:

[tex]\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\][/tex]

[tex]\[m = \frac{{-1 - (-2.5)}}{{4 - (-2)}}\][/tex]

[tex]\[m = \frac{{1.5}}{{6}}\][/tex]

[tex]\[m = 0.25\][/tex]

c. The y-intercept of Function W is -1, while the y-intercept of Function Z is the y-value when x=0, which is -2.

d. The y-intercept of Function W is greater than the y-intercept of Function Z.

e. To find the y-value when x=-4 for Function W, substitute x=-4 into the equation of Function W:

[tex]\[y = 0.5(-4) - 1 = -3\][/tex]

For Function Z, there is no direct way to determine the y-value when x=-4 as we only have specific points provided, not a continuous equation.

f. The y-value when x=-4 for Function W is not greater than the y-value when x=-4 for Function Z.

Therefore, the correct statements are:

a. The slope of Function W is less than the slope of Function Z.

d. The y-intercept of Function W is less than the y-intercept of Function Z.

The question probable maybe:

Given in the attachment

Answer:

There are 3120 chocolate eggs.                                

Step-by-step explanation:

We are given the following in the question:

Total number of eggs = 4680

Number f chocolate eggs =

[tex]\dfrac{2}{3}[/tex]  the number of real eggs

We have to find the number of chocolate eggs.

Number of chocolate eggs =

[tex]\dfrac{2}{3}\times \text{Total number of eggs}[/tex]

[tex]=\dfrac{2}{3}\times 4680\\\\=3120[/tex]

Thus, there are 3120 chocolate eggs.

Answer:

26/3 or 8.67

Step-by-step explanation:

Arc lengths are congruent and the radii are the same implies angle at the centre is also equal,

Hence length of the chords are equal too

4x+2 = x+7

3x = 5

x = 5/3 or 1.67

Length of QR = 4x+2

= 4(5/3) +2

= 20/3 + 2

= 26/3 = 8.67

Answer:

8.67

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The formula is the same whether the change in a compounding period is positive or negative. Here, it is negative.

  A = P(1 +r/n)^(nt)

for P = 100, r = -0.08, n = 6. So, you have ...

  A = 100(1 -0.08/6)^(6t)

Answer: option d is the correct answer

Step-by-step explanation:

Initial amount is $100. This means that the principal is

P = 100

It was compounded 6 times in a year. So

n = 6

The rate at which the principal was compounded is 8%. So

r = 8/100 = 0.08

The number of years is t

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years.

Since the amount is reducing,

A = P(1-r/n)^nt

Therefore

A = 100 (1 - 0.08/6)^6t

Answer:

The rock is 52.2 feet high

Step-by-step explanation:

Similar Triangles

The triangle formed by the rock, mirror and the ground is similar to the triangle formed by Carlos, the mirror and the ground (see image below). This means its sides are proportional, and

[tex]\displaystyle \frac{H}{h}=\frac{X}{x}[/tex]

We want to calculate the height of the rock, thus we solve for H

[tex]\displaystyle H=\frac{h.X}{x}[/tex]

[tex]\displaystyle H=\frac{5.8\times 36}{4}=52.2 feet[/tex]

[tex]\boxed{\text{The rock is 52.2 feet high}}[/tex]

Final answer:

Using the properties of similar triangles and the distances between Carlos, the mirror, and the wall, we determined the height of the rock wall to be 52.2 ft.

Explanation:

Before climbing, Carlos wants to know the height of the rock wall he will climb. To determine the height of the wall, we can use the properties of similar triangles formed by Carlos's height and the distances between him, the mirror, and the wall. The mirror effectively creates two sets of similar triangles, one involving the actual height of Carlos and the other involving the perceived height of the rock wall in the mirror.

Carlos's height is 5.8 ft. The distance from Carlos to the mirror is 4 ft, and the distance from the mirror to the wall is 36 ft. Since Carlos can see the top of the wall in the mirror placed 4 ft away from him, we can use the ratio of distances and heights to determine the wall's height. The setup is based on the principle that the ratio of the distance from Carlos to the mirror is to the distance from the mirror to the base of the wall as Carlos's height is to the unknown height of the wall.

Using the ratio 4:36, we can set up a proportion, keeping in mind that similar triangles have corresponding sides that are in proportion. Thus, the height of the wall is to Carlos's height of 5.8 ft as 36 ft is to 4 ft. This gives us the equation: Height of wall / 5.8 = 36 / 4. Calculating this, we find that the height of the wall is 52.2 ft.