Directions: In this last section, you will answer one problem. Be sure to read the
problem carefully and to answer the question completely. Show your work and circle
your answer. Use any method to solve this problem.
74. A restaurant has a total of 60 tables. Some of the tables can seat 4 people and some
seat 2 people. All of the seats are occupied when there are 160 people seated. How man
tables for 4 are there?

Answer:

a. D. f⁻¹(x) = x - 21, for all x

b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x

Step-by-step explanation:

See attached picture.

The required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:

x = y + 21

Now, let's solve for y:

y = x - 21

Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.

b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.

First, let's calculate f(f(x)):

f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42

Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.

Now, let's calculate f¯¹(f(x)):

f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x

Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.

Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

Therefore, the required answers are:

a. The inverse of the function is f1(x) = x - 21

b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.

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Answer:

C. interquartile range

Step-by-step explanation:

using this to show im right

"The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest."

Hope This Helped

Answer:

What is 2 raised to the power of 3?

2 x 2 x 2

= 8

Step-by-step explanation:

Hope this helps.

Answer:

12.6

Step-by-step explanation:

4.2×3=12.6

I hope this answer can help you

Answer:

1.4 kg

Step-by-step explanation:

Given :

⇒ Watermelon (Peter) = 3 × Papaya (Paul)

⇒ Watermelon (Peter) = 4.2 kg

=============================================================

Solving :

⇒ 4.2 = 3 × Papaya (Paul)

⇒ Papaya (Paul) = 1.4 kg

Therefore the mass of the papaya is 1.4 kg.

Answer:

m=200

Step-by-step explanation:

percent means 100,so we duvude 300:by 100 then m=200

#1

Volume

#2

Radius=10/2=5cm

Volume

#3

Volume

#4

#5

radius=8/2=4

Volume

Answer:

1)  314 cm³

2)  523.33 cm³

3)  87.92 in³

4)  11 cm

5)  502.4 cm³

Step-by-step explanation:

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 5^2 \cdot 4\\& = 3.14 \cdot 25 \cdot 4\\& = 3.14 \cdot 100\\& = 314 \: \sf cm^3\end{aligned}[/tex]

[tex]\textsf{Volume of a sphere}=\sf \dfrac43 \pi r^3\quad\textsf{(where r is the radius)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =\dfrac{4}{3} \cdot 3.14 \cdot 5^3 \\& =\dfrac{4}{3} \cdot 3.14 \cdot 125 \\& =\dfrac{500}{3} \cdot 3.14 \\& = 523.33\: \sf cm^3\:(2\:dp)\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 2^2 \cdot 7\\& = 3.14 \cdot 4 \cdot 7\\& = 3.14 \cdot 28\\& = 87.92\: \sf in^3\end{aligned}[/tex]

[tex]\textsf{Volume of a square pyramid}=\sf \dfrac{1}{3} a^2h \quad\textsf{(where a is the base edge and h is the height)}[/tex][tex]\textsf{Area of base of square pyramid}=\sf a^2 \quad\textsf{(where a is the base edge)}[/tex]

Given:

[tex]\implies 81=a^2[/tex]

[tex]\implies a=\sqrt{81}[/tex]

[tex]\implies a=9\: \sf cm[/tex]

Substitute the given values into the formula and solve for h:

[tex]\begin{aligned}\implies \textsf{297} & =\dfrac{1}{3} \cdot 9^2 \cdot h\\\\297 & =\dfrac{81}{3} h\\\\891 & =81 h\\\\h & = 11 \: \sf cm\end{aligned}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Volume} & =3.14 \cdot 4^2 \cdot 10\\& = 3.14 \cdot 16 \cdot 10\\& = 3.14 \cdot 160\\& = 502.4\: \sf cm^3\end{aligned}[/tex]

To factorize something:

 ⇒ need to simplify the equation to its most basic form

Let's solve:

  [tex]2x^2+6x=2(x^2+3x)=2x(x+3)[/tex]

Thus the factorized form is ⇒ [tex]2x(x+3)[/tex]

Answer: 2x(x+3)

Hope that helps!

Answer:

Solution:

→ 2x(x + 3)

Step-by-step explanation:

Method:

→ Common factor

→ Rewrite in factored form

Answer:

Step-by-step explanation:

           [tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]

[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]

           When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²

                            [tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]

Answer: some perfect cubes are

8 (2^3)

27 (3^3)

64 (4^3)

there are many perfect cubes

maybe there is more to this question?

Step-by-step explanation:

A perfect cube of a number is a number that is equal to the number, multiplied by itself, three times. If x is a perfect cube of y, then x = y3. Therefore, if we take the cube root of a perfect cube, we get a natural number and not a fraction. Hence, 3√x = y. For example, 8 is a perfect cube because 3√8 = 2.

Answer:

The formation of the equation is odd, but I assume it's supposed to be:
4k - 10k = -8k

-6k = -8k
-6k + 8k = -8k + 8k
2k = 0
[tex]\frac{2k}{2}[/tex] = [tex]\frac{0}{2}[/tex]
k = 0

Answer:

2

Step-by-step explanation:

Answer:

His bank account now has 352 dollars in it.

Step-by-step explanation:

55+364-67=352

Answer:

$352

Step-by-step explanation:

1st balance: $55

amount deposited: $364

total: $55+$364=$419

amount withdrawed: $67

amount left in account: $419-$67=$352

ans=$352

Answer: aₙ = -11 + 7(n - 1)

Step-by-step explanation: The equation of an arithmetic sequence is

aₙ = a₁ + d(n - 1).

a₁ is the first term.

d is the common difference.

Answer:

B

Step-by-step explanation:

look at the graph. y is negative from x>2, so interval is 2<x<infinity.

in other case y=0 for x=2, y<0 for infinity<x<2

Answer:

The intervel that describes where the graph is negative is C :)

I hope this helps you!

Step-by-step explanation:

Answer:

280°

Step-by-step explanation:

using the relationship

π radians = 180° , then substituting gives

[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°

Answer:

5.6

Step-by-step explanation:

If you add all the numbers together then divide it by 15 you would get 5.6

Using it's formula, considering a loan of $10,000, the regular monthly payments required to pay off the loan will be of $221.3.

It is given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

In which:

In this problem, we have that the parameters are given as follows:

P = 10,000, r = 0.0299, n = 4 x 12 = 48.

Then:

r/12 = 0.0299/12 = 0.00249167.

Hence, the monthly payment will be given by:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 10000\frac{0.00249167(1+0.00249167)^{48}}{(1+0.00249167)^{48} - 1}[/tex]

A = 221.3.

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The equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Given that:-

The equation of the new line will be:-

y - y₁ = m ( x - x₁ )

Since the line is parallel to the line y = -2x - 5 so slope will be same m = -2 now the coordinates are ( -1, 3).

y - ( 3) = -2 [( x - (-1) ]

y - 3 = -2x - 2

y = -2x + 3 -2

Y = -2x + 1

Therefore the equation of the line parallel to y=-2x-5 and passing through the point (-1,3) is y = -2x + 1.

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Answer:

By proportional method

[tex] \frac{4}{6} = \frac{5}{x} [/tex]

4x= 30

x= 7.5

Answer:

(4, 3)

Step-by-step explanation:

The volume of the given cone.

[tex]\large\boxed{Formula:V= \frac{1}{3}\pi{r}^{2}h}[/tex]

[tex]\large\boxed{\red \pi \red = \red 3 \red . \red 1 \red 4}[/tex]

Let's solve!

Substitute the values according to the formula.

[tex]V= \frac{1}{3}×3.14×{3}^{2}×8[/tex]

[tex]\large\boxed{V= 75.36 \: {yd}^{3}}[/tex]

Therefore, the volume of the given cone is 75.36 cubic yards.

Step-by-step explanation:

Movement from one place to another

Answer:

A. [tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

First, let's find the slope of the line, so we can eliminate some answers.

From point (0,2) we can go up 1 and over to the right 2 to the point of (2,3). Slope is rise over run so 1 over 2.

This eliminates C and D.

The last part is to recognize that y being less than the equation will result in the shaded region being below the line. If y was greater than the equation then the shaded region would be above the line.

Therefore, the correct answer would be A. [tex]y\leq \frac{1}{2}x+2[/tex].

Hope this helps! If you have questions about my work please let me know down in the comments!

Answer:

[tex]y\leq \frac{1}{2}x+2[/tex]

Step-by-step explanation:

The first part of finding our answer is finding the slope of the line. The image attached shows this.

[tex]\frac{rise}{run} = \boxed{\frac{1}{2}}[/tex]

This means the slope is [tex]\frac{1}{2}[/tex], removing the bottom 2 answer choices.

Now we have to choose between the [tex]\leq[/tex] and [tex]\geq[/tex] sign. Since the shaded area is below the line, it will be the [tex]\leq[/tex]. (If it was the [tex]\geq[/tex] sign, the shaded area would be above the line.) This marks the first answer as the correct answer.

Answer:

Step-by-step explanation:

Formula:

Lateral surface area = perimeter of the base × height

………………………………………………………………

perimeter of the base = 2×(1.5+3) = 9

height = 4.

then

Lateral surface area = 9 × 4 = 36

Area of two bigger rectangles

Area of two smaller rectangles

LSA

Answer:

6 + 7/10x + 2/y

Step-by-step explanation:

Hope this helps :)