The triangles are similar. Find x.
Please help me!

Answer:

[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]

Step-by-step explanation:

Given

[tex]g(x) = 3\sqrt x - 72[/tex]

[tex]h(x) = -(x +72)^3[/tex]

Required

Show that they are inverse functions

For g(x) and h(x) to be inverse, then:

[tex]g(h(x)) = h(g(x))[/tex]

We have:

[tex]g(x) = 3\sqrt x - 72[/tex]

Replace x with h(x)

[tex]g(h(x)) = 3\sqrt{h(x)} - 72[/tex]

Substitute value for h(x)

[tex]g(h(x)) = 3\sqrt{-(x +72)^3} - 72[/tex]

Similarly;

[tex]h(x) = -(x +72)^3[/tex]

Replace x with g(x)

[tex]h(g(x)) = -(g(x) +72)^3[/tex]

Substitute value for g(x)

[tex]h(g(x)) = -(3\sqrt x - 72 +72)^3[/tex]

Recall that:

[tex]g(h(x)) = h(g(x))[/tex]

So:

[tex]\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3[/tex]

Its c

explanation:

on edge

Answer:

putting the value of X=8 in f(X)

f(8)= 8-5

f(8)= 3

Answer:

3

Step-by-step explanation:

We must plug in 8 into the equation of the function since f(x) = x - 5 for all values of x. Since 8 could be a value of x, we can plug it in:

[tex]f(8) = 8-5[/tex]

The value of 8 minus 5 is 3, so the value of f(8) is 3.

Answer:

Tedyxhcj eydyfhxrstetdhsawe

Answer:

number 7 the answer is 50,000

Answer:

1:3

Step-by-step explanation:

because you would get 1 of 3 flavours

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\text{When you hear/see the word of in mathematics, it usually means }\\\large\text{\bf multiplication. }[/tex]

[tex]\large\text{So, when you think of think of the word \underline{of} think of its asking you to}\\\large\text{\bf multiply }[/tex]

[tex]\large\text{Now that we got that run down out of the way lets answer your given}\\\large\text{question}[/tex]

[tex]\large\textsf{0.25\% of 2,000}[/tex]

[tex]\large\textsf{= 0.25\%} \times \large\textsf{2,000}[/tex]

[tex]\large\textsf{0.25\%} = \mathsf{\bf \dfrac{25}{100}}[/tex]

[tex]\mathsf{= \dfrac{25}{100} \times 2,000}[/tex]

[tex]\mathsf{\dfrac{25}{100}= \bf 0.0025}[/tex]

[tex]\large\textsf{= 0.0025} \times \large\textsf{2,000}[/tex]

[tex]\large\text{= \bf 5}[/tex]

[tex]\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf 5}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

45x=-44

x=-44/45

Step-by-step explanation:

is this a free question?

Answer:

8x-3

Step-by-step explanation:

Average of 2 numbers means add the two numbers and divide by 2

(y+z)/2 = 5x

Let z = 2x+3

(y+2x+3)/2 = 5x

Multiply each side by 2

y+2x+3 = 10x

Subtract 2x from each side

y+3 = 10x-2x

y+3 = 8x

Subtract 3

y = 8x-3

The other number is 8x-3

Answer:

x = 6; y = -6

Step-by-step explanation:

-4x - 2y = -12

4x + 8y = -24

Add the two equations, so x is eliminated:

6y = -36

6y/6 = -36/6

y = -6

Plug in y, to solve for x

-4x - 2y = -12

-4x - 2(-6) = -12

-4x +12 = -12

-4x = -12 -12

-4x = -24

-4x/-4 = -24/-4

x = 6

Answer from Gauthmath

Answer:

the answer is D. infinitely many

The number of solutions there are to the system of equations is Infinitely many, the correct option is D.

The equation of the straight line has its slope and given point.

If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation

y-y₁ = m(x-x₁)

Which is the required equation of a line in a point-slope form.

We are given that;

The two identical lines

Now,

We can find the equations of the two lines by using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.

For line 1, we have two points (0,2) and (1,0), so we can find the slope as:

m1 = (0 - 2) / (1 - 0) = -2

Using point-slope form, we can write the equation of line 1 as:

y - 2 = -2(x - 0)

y = -2x + 2

For line 2, we have two points (-1,4) and (2,-2), so we can find the slope as:

m2 = (-2 - 4) / (2 - (-1)) = -2

Using point-slope form, we can write the equation of line 2 as:

y - 4 = -2(x - (-1))

y = -2x + 2

We can see that the two lines have the same slope and the same y-intercept.

Therefore, by the given slope of the line the answer will be infinitely many.

Learn more about slope here:

https://brainly.com/question/2503591

#SPJ7

9514 1404 393

Answer:

  y = 4x/(x -2)

Step-by-step explanation:

Subtract 1/x

  2/y = 1/2 -1/x

Combine terms

  2/y = (x-2)/(2x)

Cross multiply

  4x = y(x -2)

Divide by the coefficient of y

  y = 4x/(x -2) . . . . simplest

  y = 2^2/(x -2) . . . . in terms of x and 2

Answer:

a=35

b=55

c=110

Step-by-step explanation:

a=35

Opposite angles which are non-adjacent angles formed by two intersecting lines are equal

b+35+90=180 sum of interior angle of a triangle equal to 180

b=180-125

  =55

c+70=180  Angles on a straight line add up to 180°

c=180-70

 =110

Answer:

l = 15 feet

Step-by-step explanation:

l = 2w + 3

First you solve for the width(w)

(2w+15) (w-6) = 0

This means

2w+15=0 OR. w-6=0

First let’s solve 2w+15=0

2w = -15

w = -7.5

Width can’t be negative so that can’t be the answer. So we look at the second equation w-6=0

w= 6

Since we found the width now we can find the length by using the formula l = 2w + 3

= 2(6) + 3

= 12 + 3

= 15 feet

You can check this by using the given area which is 90.

A = lw = 15*6 = 90

Answer:

x = 19.2

Step-by-step explanation:

tan(58)=x/12

x=12×tan(58)

x=19.2

Answered by GAUTHMATH

Answer:

The hottest month for the northern hemisphere is August.

The hottest month for the southern hemisphere is January and February (these top two might be the opposite)

It's globally warmer during the months of June July and August

During april and november, the southern hemisphere and northern hemisphere are the same, or very close.

During July and August the southern and northern hemispheres have the largest difference in temperature

Answer:

26 cm

Step-by-step explanation:

P = 2a + 2b

a = side

b = base

Answer:

The area=base×height

=10×4

=40cm^2

perimeter=2(length+breadth)

I think to find the height Dc you use the pythagoras theorem of

Dc^2=de^2+ce^2

=√16+9

=5

therefore the perimeter will be

p=2(5+10)

=20cm

I hope this helps and sorry if it's wrong

Answer:

here's the answer to your question

Answer:

2 24" X 24" square cakes are needed.

Step-by-step explanation:

This question is solved by proportions.

Area of a square:

The area of a square of side l is given by:

[tex]A = l^2[/tex]

8" X 8" square cake serves 8 people

Thus:

[tex]A = 8*8 = 64[/tex]

Area of 64 serves 8 people, so for 1 people, an area of 64/8 = 8 is needed.

144 people

The total area needed is:

[tex]A = 144*8 = 1152[/tex]

How many 24" X 24" square cakes?

24*24 = 576

1 cake - 576

x cakes - 1152

Applying cross multiplication:

1152/576 = 2

2 24" X 24" square cakes are needed.

Answer:

Hypotenuse = XY = 17 cm

Base = YZ = 15 cm

Perpendicular = XZ = 8 cm

Answer:

[tex]\frac{\sqrt{2} }{2}[/tex]

Step-by-step explanation:

[tex]\frac{2}{2\sqrt{2} }[/tex] * [tex]\frac{2\sqrt{2} }{2\sqrt{2} }[/tex]    =[tex]\frac{4\sqrt{2} }{8}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex]

Answer:

2.665 < σ < 3.379

Step-by-step explanation:

Given :

s = 2.97

Sample size, n = 60

α = 80%

χ² Critical value (two - tailed), df = (60-1) = 59

χ² = 45.577 ; χ² = 73.279

The 80% confidence interval for the standard deviation :

s * √(n - 1) / χ² critical

2.97 * √(60 - 1) / 73.279 < σ < 2.97 * √(60 - 1) / 45.577

2.665 < σ < 3.379

Explanation:

A = values on the die greater than 1

A = {2,3,4,5,6}

B = values on the die less than 5

B = {1,2,3,4}

Union those two sets together

C = A u B = {1,2,3,4,5,6}

Effectively, we get every possible value on the die. This is due to the "or" keyword. If it was "and", then it would be a difference story.

So the probability of getting anything in set C is 100% or just 1. We have guaranteed certainty we'll have this event happen.

9514 1404 393

Answer:

  10 and 24

Step-by-step explanation:

We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).

These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).

For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)

The side lengths are 10 and 24.

__

Check

For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.

__

In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...

  x² +y² = (x+2)²   ⇒   y² = (x² +4x +4) -x²   ⇒   y² = 4x +4 = 4(x +1)

_____

Additional comment

The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.

Using the third equation in the attachment to write an expression for y, we have ...

  y = 58 -2x

Substituting that into the second equation gives ...

  (x(58 -2x)/2 = 120

  29x -x² = 120

  x² -29x +120 = 0

  (x -5)(x -24) = 0 . . . . x = 5 or 24.

The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.

Answer:

N=18

Step-by-step explanation:

Hope it will help you

If it does pls give me Brainlest

Have a nice day

Answer:

18

Step-by-step explanation:

use the concept of similarity and enlargement.

[tex] \frac{15}{n} = \frac{5}{6 } [/tex]

[tex]n = \frac{15 \times 6}{5} [/tex]

[tex]n = 18[/tex]

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

dime: 5 cents

nickel: 10 cents

quarter: 25 cents

let's start with quarters, (2)

25 + 10 + 5

25 + 5 + 5 + 5

nickels, (4)

10 + 10 + 10 + 10

10 + 10 + 10 + 5 + 5

10 + 10 + 5 + 5 + 5 + 5

10 + 5 + 5 + 5 + 5 + 5 + 5

dimes, (1)

5 + 5 + 5 + 5 + 5 + 5 + 5 + 5

7 combinations.

hope it helps :)

Answer:

A. 4

Step-by-step explanation:

The diagonals are also congruent to each other. Diagonals of a square bisect each other. This implies that:

MO bisects LN, thereby dividing LN into two equal segments, LG and GN.

Thus, LG = GN.

Since the length of LG = 4, therefore:

GN = 4