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3 years ago

8

How to answer because I struggle to answer

1 answer:

SpyIntel [72]3 years ago

5 0

5: AA 47=47 36=36 similar

6: SSS 32/16 =2, 24/12 =2, 9/4.5 = 2 similar

7: SAS 72/53= 1.3, 55=55, 48/12 = 4 not similar

8: SAS 45/15= 3, 54=54, 9/3=3 Similar

9.SAS 20/10 =2, 10/8 = 1.25 not similar

10.SAS 32/14= 2.29, 46=46, 12/7= 1.79 not similar

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What is the circumference of a circle<br> with radius 64 inches? Write your answer<br> using PI.

yarga [219]

Answer:

C≈402.12in

Step-by-step explanation:

The circumference of a circle is equal to pi times the diameter. The diameter is two times the radius, so the equation for the circumference of a circle using the radius is two times pi times the radius

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2 years ago

Complete the point-slope equation of the line through ( − 5 , 4 ) (−5,4)left parenthesis, minus, 5, comma, 4, right parenthesis

Tanzania [10]

The point slope form of equation through given points is:

$y-6=\frac{1}{3}(x-1)$

Step-by-step explanation:

Given points are:

(x1,y1) = (-5,4)

(x2,y2) = ((1,6)

First of all we have to find the slope of line

So,

$m=\frac{y_2-y_1}{x_2-x_1}\\=\frac{6-4}{1+5}\\=\frac{2}{6}\\=\frac{1}{3}$

Point-slope form is given by:

$y-y_1=m(x-x_1)$

Putting m=1/3

$y-y_1=\frac{1}{3}(x-x_1)$

Putting (1,6) in the equation

$y-6=\frac{1}{3}(x-1)$

The point slope form of equation through given points is:

$y-6=\frac{1}{3}(x-1)$

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3 years ago

A pizza restaurant has 21 topping choices and 3 dough choices. How many different 3-topping pizzas can be made if toppings can b

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189 because you have to multiply by 3 twice.

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3 years ago

Two men, 400 feet apart, observe a balloon between them it is the same vertical plane as they are. The respective angles of elev

slava [35]

The answer is 471 feet.

If A = man to left of balloon
<span>B = balloon </span>
<span>C = man to right of balloon </span>

<span>∠BAC = 75°20' </span>
<span>∠BCA = 49°30' </span>
<span>∠ABC = 180 - 75°20' - 49°30' = 55°10' </span>
<span>AB = 400 ft </span>

<span>Now we have to find the value of x, which is the side opposite to angle of 75°20' </span>

<span>Using Law of Sines: </span>
<span>x/sin(75°20') = 400/sin(55°10') </span>
<span>x = 400 * sin(75°20') / sin(55°10') </span>
<span>x = 471.44 </span>
<span>x = 471 ft </span>

4 0

3 years ago

If it exists, solve for the inverse function of each of the following:

nata0808 [166]

Answer:

<em>The solution is too long. So, I included them in the explanation</em>

Step-by-step explanation:

This question has missing details. However, I've corrected each question before solving them

Required: Determine the inverse

1:

$f(x) = 25x - 18$

Replace f(x) with y

$y = 25x - 18$

Swap y & x

$x = 25y - 18$

$x + 18 = 25y - 18 + 18$

$x + 18 = 25y$

Divide through by 25

$\frac{x + 18}{25} = y$

$y = \frac{x + 18}{25}$

Replace y with f'(x)

$f'(x) = \frac{x + 18}{25}$

2. $g(x) = \frac{12x - 1}{7}$

Replace g(x) with y

$y = \frac{12x - 1}{7}$

Swap y & x

$x = \frac{12y - 1}{7}$

$7x = 12y - 1$

Add 1 to both sides

$7x +1 = 12y - 1 + 1$

$7x +1 = 12y$

Make y the subject

$y = \frac{7x + 1}{12}$

$g'(x) = \frac{7x + 1}{12}$

3: $h(x) = -\frac{9x}{4} - \frac{1}{3}$

Replace h(x) with y

$y = -\frac{9x}{4} - \frac{1}{3}$

Swap y & x

$x = -\frac{9y}{4} - \frac{1}{3}$

Add $\frac{1}{3}$ to both sides

$x + \frac{1}{3}= -\frac{9y}{4} - \frac{1}{3} + \frac{1}{3}$

$x + \frac{1}{3}= -\frac{9y}{4}$

Multiply through by -4

$-4(x + \frac{1}{3})= -4(-\frac{9y}{4})$

$-4x - \frac{4}{3}= 9y$

Divide through by 9

$(-4x - \frac{4}{3})/9= y$

$-4x * \frac{1}{9} - \frac{4}{3} * \frac{1}{9} = y$

$\frac{-4x}{9} - \frac{4}{27}= y$

$y = \frac{-4x}{9} - \frac{4}{27}$

$h'(x) = \frac{-4x}{9} - \frac{4}{27}$

4:

$f(x) = x^9$

Replace f(x) with y

$y = x^9$

Swap y with x

$x = y^9$

Take 9th root

$x^{\frac{1}{9}} = y$

$y = x^{\frac{1}{9}}$

Replace y with f'(x)

$f'(x) = x^{\frac{1}{9}}$

5:

$f(a) = a^3 + 8$

Replace f(a) with y

$y = a^3 + 8$

Swap a with y

$a = y^3 + 8$

Subtract 8

$a - 8 = y^3 + 8 - 8$

$a - 8 = y^3$

Take cube root

$\sqrt[3]{a-8} = y$

$y = \sqrt[3]{a-8}$

Replace y with f'(a)

$f'(a) = \sqrt[3]{a-8}$

6:

$g(a) = a^2 + 8a- 7$

Replace g(a) with y

$y = a^2 + 8a - 7$

Swap positions of y and a

$a = y^2 + 8y - 7$

$y^2 + 8y - 7 - a = 0$

Solve using quadratic formula:

$y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$a = 1$ ; $b = 8$ ; $c = -7 - a$

$y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$ becomes

$y = \frac{-8 \±\sqrt{8^2 - 4 * 1 * (-7-a)}}{2 * 1}$

$y = \frac{-8 \±\sqrt{64 + 28 + 4a}}{2 * 1}$

$y = \frac{-8 \±\sqrt{92 + 4a}}{2 * 1}$

$y = \frac{-8 \±\sqrt{92 + 4a}}{2 }$

Factorize

$y = \frac{-8 \±\sqrt{4(23 + a)}}{2 }$

$y = \frac{-8 \±2\sqrt{(23 + a)}}{2 }$

$y = -4 \±\sqrt{(23 + a)}$

$g'(a) = -4 \±\sqrt{(23 + a)}$

7:

$f(b) = (b + 6)(b - 2)$

Replace f(b) with y

$y = (b + 6)(b - 2)$

Swap y and b

$b = (y + 6)(y - 2)$

Open Brackets

$b = y^2 + 6y - 2y - 12$

$b = y^2 + 4y - 12$

$y^2 + 4y - 12 - b = 0$

Solve using quadratic formula:

$y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$

$a = 1$ ; $b = 4$ ; $c = -12 - b$

$y = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}$ becomes

$y = \frac{-4\±\sqrt{4^2 - 4 * 1 * (-12-b)}}{2*1}$

$y = \frac{-4\±\sqrt{4^2 - 4 *(-12-b)}}{2}$

Factorize:

$y = \frac{-4\±\sqrt{4(4 - (-12-b))}}{2}$

$y = \frac{-4\±2\sqrt{(4 - (-12-b))}}{2}$

$y = \frac{-4\±2\sqrt{(4 +12+b)}}{2}$

$y = \frac{-4\±2\sqrt{16+b}}{2}$

$y = -2\±\sqrt{16+b}$

Replace y with f'(b)

$f'(b) = -2\±\sqrt{16+b}$

8:

$h(x) = \frac{2x+17}{3x+1}$

Replace h(x) with y

$y = \frac{2x+17}{3x+1}$

Swap x and y

$x = \frac{2y+17}{3y+1}$

Cross Multiply

$(3y + 1)x = 2y + 17$

$3yx + x = 2y + 17$

Subtract x from both sides:

$3yx + x -x= 2y + 17-x$

$3yx = 2y + 17-x$

Subtract 2y from both sides

$3yx-2y =17-x$

Factorize:

$y(3x-2) =17-x$

Make y the subject

$y = \frac{17 - x}{3x - 2}$

Replace y with h'(x)

$h'(x) = \frac{17 - x}{3x - 2}$

9:

$h(c) = \sqrt{2c + 2}$

Replace h(c) with y

$y = \sqrt{2c + 2}$

Swap positions of y and c

$c = \sqrt{2y + 2}$

Square both sides

$c^2 = 2y + 2$

Subtract 2 from both sides

$c^2 - 2= 2y$

Make y the subject

$y = \frac{c^2 - 2}{2}$

$h'(c) = \frac{c^2 - 2}{2}$

10:

$f(x) = \frac{x + 10}{9x - 1}$

Replace f(x) with y

$y = \frac{x + 10}{9x - 1}$

Swap positions of x and y

$x = \frac{y + 10}{9y - 1}$

Cross Multiply

$x(9y - 1) = y + 10$

$9xy - x = y + 10$

Subtract y from both sides

$9xy - y - x = y - y+ 10$

$9xy - y - x = 10$

Add x to both sides

$9xy - y - x + x= 10 + x$

$9xy - y = 10 + x$

Factorize

$y(9x - 1) = 10 + x$

Make y the subject

$y = \frac{10 + x}{9x - 1}$

Replace y with f'(x)

$f'(x) = \frac{10 + x}{9x -1}$

8 0

3 years ago