A 330-lb gorilla climbs a tree to a height of 21 ft. Find the work done if the gorilla reaches that height in the following times.
(a)
10 seconds
W =
(b)
W =
5 seconds
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Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles. The value of x is 13.

Each of the pairs of opposite angles made by two intersecting lines are called a pair of vertical angles.

Given that ∠A and ∠B are vertical angles. Therefore, the measure of the two of the given angle will be equal to each other. Thus, we can write the measure of the two angles as,

∠A = ∠B

(5x + 5)° = (6x - 8)°

5x + 5 = 6x - 8

Bring the like terms on the same side of the equation,

5 + 8 = 6x - 5x

13 = x

x = 13

Hence, the value of x is 13.

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The vertex of the quadratic function f(x) = (x + 3)² - 4 is (-3,-4)

Given a quadratic function, the equation of the quadratic function in vertex form is given by f(x) = a(x - h)² + k where

Now, given the quadratic function f(x) = (x + 3)² - 4, we require the vertex of the quadratic function.

Comparing the function f(x) = (x + 3)² - 4 with f(x) a(x - h)² + k, we see that

Since the vertex of the quadratic function is (h, k), we see that the vertex of the quadratic function f(x) is (-3,-4)

So, the vertex of the quadratic function is (-3,-4)

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well, we know they sell a total of about 1100 books monthly, and that nonfiction is 24% of that, what's 24% of 1100?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{24\% of 1100}}{\left( \cfrac{24}{100} \right)1100}\implies 264[/tex]

Answer:

x = 71°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

The measure of two angles out of three is given, we will use the following equation to find the value of the missing angle:

82 + 27 + x = 180 add like terms

109 + x = 180 subtract 109 from both sides

x = 71

The system of nonlinear equations have two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

In this problem we find a system of two nonlinear equations involving radical expressions. We proceed to resolve the system of nonlinear equations by algebra properties:

(2 · x - 1)² + 8√(2 · x · y) = 4

8√(2 · x · y) = 4 - (2 · x - 1)²

8√(2 · x · y) = 4 - 4 · x² + 4 · x - 1

8√(2 · x · y) = 4 · x - 4 · x² + 3

64 · (2 · x · y) = [(4 · x + 3) - 4 · x²]²

128 · x · y = (4 · x + 3)² - 8 · (4 · x + 3) · x² + 64 · x⁴

128 · x · y = 16 · x² + 24 · x + 9 - 32 · x³ - 24 · x² + 64 · x⁴            (1)

4 · y - √(8 · x · y - 1) = 1

4 · y - 1 = √(8 · x · y - 1)

(4 · y - 1)² = 8 · x · y - 1

16 · y² - 8 · y + 2 = 8 · x · y                                                             (2)

Now we plot two equations on a graphing tool and find that the system has the following two solutions: (x, y) = (0.114, 0.354), (x, y) = (1.432, 1.103).

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Temperature is a physical quantity that expresses the hotness of matter or radiation. The heat increases an objects temperature.

Temperature is a physical quantity that expresses the hotness of matter or radiation.

The temperature of the object increases due to the absorbed part of the heat. An object decreases its temperature by releasing energy in the form of heat to its surroundings. And an object increases its temperature by gaining energy in the form of heat from its surroundings.

So the temperature changes according to the heat of the surrounding.

Therefore the heat increases an objects temperature.

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The function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

The given parameters are:

Perimeter = 210 meters

Let the length parallel to the wall be represented as z and the width be x

So, the perimeter of the fence is

P = 2x + z

This gives

210 = 2x + z

Make x the subject

x = 1/2(210 - z)

The area of the wall is calculated as

A = xz

So, we have

A = 1/2(210 - z) * z

This gives

A = z/2(210 - z)

Rewrite as

A(z) = z/2(210 - z)

Hence, the function of the length z in meters of the side parallel to the wall is A(z) = z/2(210 - z)

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Answer:

This formula has no values, it is a false inequality. X can not be greater than 5, and less than 3.

Step-by-step explanation:

x < 3 or x > 5

This means, x is less than 3, but greater than 5.

Technically, you would write this as 5 < x < 3, however, this is a false inequality, and does not work.

5x-15=5+4x

    +15 +5

   5x=20+4x

  -4x       -4x

     x= 20

Step-by-step explanation:

Answer:

tianna has saved $300 and genesis has saved $100

Step-by-step explanation:

3 plus 1 is 4

400 divided by four is 100

3 times 100 is 300

1 times 100 is 100

tianna saved 300

genesis saved 100

Answer:

c = 11

Step-by-step explanation:

96 - 8c = 20 - 12 , that is

96 - 8c = 8 ( subtract 96 from both sides )

- 8c = - 88 ( divide both sides by - 8 )

c = 11

Answer:

29

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

One of our exponent rules tells us that [tex](\frac{x}{y} )^{z}[/tex] =  [tex]\frac{x^{z} }{y^{z} }[/tex]. So, knowing that exponent rule, we know that it has to be the third option. But what if we didn't know that rule? Then how could we solve this?

We know that 3/2 = 1.5. Do some math and you can figure out that 1.5^3 is 3.375. If we were to evaluate expression number 3, we would get 27/8, which, if you were to further evaluate it, you would also get 3.375.

Let me know if you have any questions!

$32 is the cost of each necktie at full price.

Given that

At Dapper Dave's annual end-of-season sale, every necktie in the shop gets marked down.

Dillon purchased 6 neckties during the sale. Each necktie cost $5 less than its full price.

He paid a total of $162.

To find

What is the cost of each necktie at full price ?

So, according to the question

we have,

On that end-of-season sale

Total purchased neckties = 6

Discount on each neckties = $5

Amount paid by him = $162

Let's assume the full price of one neckties is $x.

So,

    The price of one neckties after discount = x - 5.

     So the price of one neckties after discount = 6(x-5)

     He paid $162 for 6 neckties,

So we can say that

       the price of one neckties after discount =  $162

So,

         6(x-5) = 162

             x-5 = 162/6      

             x-5 = 27

                x = 27+5

                 x = 32

The cost of each necktie at full price is $32.

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Answer:

the slope is 9 and the y-intercept is -2

Answer:

[tex]\sqrt{4}[/tex], [tex]\sqrt{9}[/tex], [tex]\sqrt{16}[/tex]

Step-by-step explanation:

I think that you are asking for 3 examples of square roots that are rational.  All perfect squares are rational.  If the square root is not a perfect square then the number is irrational.

[tex]\sqrt{4[/tex] = 2 and -2.  The number multiplied by itself is an integer.  Integers are the whole numbers and their opposites: ...-3, -2, -1,  0, 1, 2, 3...  

1/2 is not an integers.  0.75 is not an integer.

[tex]\sqrt{9}[/tex]  is 3 and -3

[tex]\sqrt{16}[/tex] is 4 and -4

Numbers like:

[tex]\sqrt{3}[/tex] is irrational because this number in a decimal form never terminates or repeats.  

Answer:

No

Step-by-step explanation:

B/c trinomial has exactly 3 terms and binomial only have 2

Answer:

1. 11/12 2. 3/20 3. 18/4 or 4 1/2

Step-by-step explanation:

Answer:

A. (2x+4)/x

Step-by-step explanation:

The solution of the given expression (4 1/3) (-2) (5/13) is -130/13.

According to the given question.

We have an expression (4 1/3) (-2) (5/13).

Here, we have to solve the given expression.

So, the solution of the expression (4 1/3) (-2) (5/13) is given by

(4 1/3) (-2) (5/13)

= (13/3)(-2)(5/-13)   (by converting the mixed fraction into improper fraction)

= (-26/13)(5/13)

= -130/13

Hence, the solution of the given expression (4 1/3) (-2) (5/13) is -130/13.

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The value of the circle is 20 while the triangle is 35

From the figure, we have

Three circles and Two triangles

Such that:

Three circles = 60

One circle and Two triangles = 90

Represent the circle with x and the triangle with y

So, we have

3x = 60

x + 2y = 90

The above forms a system of linear equations

Divide 3x = 60 by 3

x = 20

Substitute x = 20 in x + 2y = 90

20 + 2y = 90

This gives

y = 35

So, we have

Circle = 20

Triangle = 35

Hence, the values of the shapes are 20 and 35, respectively

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Using it's concept, the probability that a randomly selected boy attended the dance is:

7/9.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

From the table, we have that:

Hence the probability that a randomly selected boy attended the dance is given as follows:

p = 49/63 = 7/9.

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Answer: 66.2=54.5+3gg

gg=3.9 gigabytes

Step-by-step explanation:

66.2=54.5+3gg

3gg=66.2-54.5

3gg=11.7

gg=3.9 gigabytes

3.9 number of gigabytes of data William can use while staying within his budget.

Two or more expressions with an Equal sign is called as Equation.

Given,

William pays a flat cost of $54.50 per month and $3 per gigabyte.

He wants to keep his bill at $66.20 per month.

We need to solve this and to find number of gigabytes of data William can use while staying within his budget.

This can be written as equation

66.2=54.5+3gg

Subtract 54.5 from both sides

66.2=54.5+3gg

3gg=66.2-54.5

3gg=11.7

Divide both sides by 3

gg=3.9 gigabytes

Hence, 3.9 number of gigabytes of data William can use while staying within his budget.

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Answer:

C) x = 3

Step-by-step explanation:

To find the solution value that satisfies the inequality 4 < 3x∕2 + 1 < 7, you must plug every x value into the x and see which one works.

Plug 0 into x

4 < 3(0)∕2 + 1 < 7

4 < 0∕2 + 1 < 7

4 < 0 + 1 < 7

Combine like terms

4 < 1 < 7

This is false, 1 is not greater than 4.

Plug 4 into x

4 < 3(4)∕2 + 1 < 7

4 < 12∕2 + 1 < 7

4 < 6 + 1 < 7

Combine like terms

4 < 7 < 7

This is false, 7 is not less than 7.

Plug 3 into x.

4 < 3(3)∕2 + 1 < 7

4 < 9∕2 + 1 < 7

4 < 4.5 + 1 < 7

Combine like terms

4 < 5.5 < 7

This is true, 5.5 is greater than 4 and less than 7.

Plug 6 into x.

4 < 3(6)∕2 + 1 < 7

4 < 18∕2 + 1 < 7

4 < 9 + 1 < 7

Combine like terms

4 < 10 < 7

This is false, 10 is not less than 7.

C) x = 3 is the only true solution that works, so that is your answer.

I hope that helped and have a lovely rest of your day! :)