The area of a square is 75 inches squared. A student correctly wrote the length of each side of the square as a√3. What is the value of a?

Hello!

Here we are given a composite shape, meaning that we can divide this shape up into ways that we are given formulas to solve for legs and such.

I can see here that this can be divided into a triangle and a rectangle using a horizontal line.

The leg lengths of this triangle would be 9, because it is congruent to the bottom side of the rectangle, and 7, because it is the left side minus the right side.

This would also make a right triangle, meaning we could solve for the hypotenuse utilizing the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

[tex]6^2+7^2=c^2[/tex]

[tex]36+49=c^2[/tex]

[tex]c^2=85[/tex]

[tex]c=\sqrt{85}[/tex]

Which is in simplest radical form.

Hope this helps!

Answer:

10x=180-80

x=100/10=10

:.x=10

9.

8x+2=7x+14 corresponding angle of parallelogram are equal

8x-7x=14-2

x=12

10.

4x+4=5x+1 corresponding sides of parallelogram are equal

4-1=5x-4x

x=3

11.

4+3x=19corresponding sides of parallelogram are equal

3x=19-4

x=15/3

x=5

Answer:

pretty simple, you should get 1824

Step-by-step explanation:

first find area of square, you should get 1536 in^2. Then triangle, the formula is base times height divided by 2. lmk if you need more help

Step-by-step explanation:

i don't have a step by step explanation so here you go the answer

Answer:

48 in³

Step-by-step explanation:

volume=length*breadth*height

=12*2*2

Answer:

slope = 2/3

Step-by-step explanation:

Step-by-step explanation:

6x + 3x = 180

9x = 180

x = 20

m<SVW= 3(20) = 60 degrees

Answer: try C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

It's c because you multiply 3 1/8 by 3 and 3 1/4 by 4 and 3 1/2 by 1.

Answer:

4080cm²

Step-by-step explanation:

Answer:

308 feet ^3

Step-by-step explanation:

Volume of a cylinder: V=πr^2h

Substituting radius = 7 and height = 2:

V = π (7)^2 (2) = 307.88 ~= 308 feet ^3

Answer:

angle Q is 68°

angle R is 112°

The perimeter of a triangle is (x+10)/(x+3) units.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

The sides of given triangle are 2/(x-3), (x²-21)/(x²-9) and 5/(x+3).

Perimeter = 2/(x-3) + (x²-21)/(x²-9) + 5/(x+3)

= 2(x+3)/(x²-9) + (x²-21)/(x²-9) + 5(x-3)/(x²-9)

= (2x+6+x²-21+5x-15)/(x²-9)

= (x²+7x-30)/(x²-9)

= (x²+10x-3x-30)/(x²-9)

= (x(x+10)-3(x+10)/((x-3)(x+3))

= ((x+10)(x-3))/((x-3)(x+3))

= (x+10)/(x+3)

Therefore, the perimeter of a triangle is (x+10)/(x+3) units.

To learn more about the perimeter visit:

https://brainly.com/question/6465134.

#SPJ2

Answer:

1.) Right triangle

2.) Not right triangle

3.) Not right triangle

4.) Not right triangle

5.) Right triangle

6.) Right triangle

Step-by-step explanation:

The ones that are a right triangle have at least one angle that has an L shape

Answer:

-1/2

Step-by-step explanation:

[tex]y^{2} = -4 \\y^{1} =-1\\x^{2} = 0\\x^{1} = -10[/tex]

Using the formula  [tex]\frac{y^{2}-y^{1} }{x^{2}-x^{1} }[/tex]

[tex]\frac{-4-1}{0-(-10)}[/tex]  

Simplifly

[tex]\frac{-5}{10} = \frac{-1}{2}[/tex]

Answer:

63.76

Step-by-step explanation:

85.95-30% 60.16

60.16+6% 63.76

Answer:

its 5/6

Step-by-step explanation:

we just group things around and we have this

36 m^2 - 60 m = -25

Alternate forms:

12 m (3 m - 5) = -25

36 m^2 - 60 m + 25 = 0

Solution:

m = 5/6

Answer:

4 = [tex]\sqrt{15[/tex]

Step-by-step explanation:

Answer:

short side = 4

Step-by-step explanation:

area = 1/2BH

18 = 1/2(x - 1)(x + 4)

18 = 1/2(x² + 4x - x - 4)

multiply both sides of the equation by 2:

36 = x² + 3x - 4

x² + 3x - 40 = 0

(x + 8)(x - 5) = 0

x = 5

short side = 5 - 1 = 4

The shortest length of the right angled triangle is 4 cm.

where

b = base

h = height

Therefore,

area = 18 cm²

18 = [tex]\frac{1}{2}[/tex] × (x - 1)(x + 4)

36 = (x - 1)(x + 4)

x² + 4x - x - 4 = 36

x² + 3x - 4 = 36

x² + 3x - 4 - 36 = 0

x² + 3x - 40 = 0

x² - 5x + 8x - 40 = 0

x(x - 5) + 8(x - 5) = 0

(x + 8)(x - 5) = 0

x = -8 or 5

we can only use positive numbers.

Therefore,

x = 5

The shortest sides is definitely one of the 2 legs . The hypotenuse of a triangle is the longest side.

Therefore,

h = x - 1 = 5 - 1 = 4 cm

b = x + 4 = 5 + 4 = 9 cm

learn more on right angled triangle here: https://brainly.com/question/2292567?referrer=searchResults

Answer:

120 pounds I think

Step-by-step explanation:

Answer:

120 pounds

Step-by-step explanation:

[tex]\frac{15}{45}[/tex] = [tex]\frac{40}{x}[/tex] so then you would cross multiply : 15x=40 times 45

                                          and then solve: 15x= 1800

                                                                         x= 120

Answer:

[tex]g(x) = \frac{6}{5}x + 8[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 6x + 8[/tex]

[tex]k = 5[/tex] --- horizontal stretch factor

Required

Find g(x)

When a function is stretched horizontally by k, the resulting function will be:

Rule: [tex]g(x) = f(\frac{1}{k}x)[/tex]

So, we have:

[tex]g(x) = f(\frac{1}{5}x)[/tex]

Solve for: [tex]f(\frac{1}{5}x)[/tex]

[tex]f(\frac{1}{5}x) = 6 * \frac{1}{5}x + 8[/tex]

[tex]f(\frac{1}{5}x) = \frac{6}{5}x + 8[/tex]

Recall that:

[tex]g(x) = f(\frac{1}{5}x)[/tex]

[tex]g(x) = \frac{6}{5}x + 8[/tex]

Answer:

f(1/5x) = 6 ^1/5x  +8

Step-by-step explanation:

A horizontal stretch by a factor of 5 means that the input, or x, is multiplied by : 1/5

Answer:

8

Step-by-step explanation:

sqrt8*sqrt8 = sqrt8^2 = 8

Answer:

The answer is B $23.

Step-by-step explanation:

You take 391 and divide it by 17

391/17=23

Hope this helps!

Answer:

The length of the other two sides are: 43.09 and 32.60

Step-by-step explanation:

Let the given side of the triangle be b(= 40), and the angles be;

A = [tex]72^{o}[/tex], B = [tex]62^{o}[/tex]and C = [tex]46^{o}[/tex].

Applying the Sine rule,

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]

So that,

[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]

[tex]\frac{a}{Sin 72}[/tex] = [tex]\frac{40}{Sin62}[/tex]

a = [tex]\frac{0.9511*40}{0.8829}[/tex]

  = 43.0898

a = 43.09

Also,

[tex]\frac{b}{SinB}[/tex] = [tex]\frac{c}{Sin C}[/tex]

[tex]\frac{40}{Sin62}[/tex] = [tex]\frac{c}{Sin46}[/tex]

c = [tex]\frac{0.7193*40}{0.8829}[/tex]

  = 32.5881

c = 32.60

The length of the other two sides are: 43.09 and 32.60

Answer:

the answer to the questions are c,b,a

Answer:

Yes this is a statistical question because of how  they want to measure the tress to find out how tall are all of them and then to find out which is the tallest.