Identify the missing justifications.

(a) =

(b) =

A 2-column table has 7 rows. The first column is labeled Step with entries 2 x minus 7 = 15, 2 x minus 7 + 7 = 15 + 7, 2 x + 0 = 22, 2 x = 22, (one-half) 2 x = (one half) 22, 1 x = 11, and x = 11. The second column is labeled Justification with entries Given, Addition property of equality, (a), Additive identity, (b), Multiplicative inverse, and Multiplicative identity

The function g(x) is [tex]g(x) = (x + 7)^3[/tex]

The function f(x) is given as:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.

So, we have:

[tex]f(x) = \sqrt[3]{x} - 7[/tex]

Rewrite as:

[tex]y = \sqrt[3]{x} - 7[/tex]

Swap x and y

[tex]x = \sqrt[3]{y} - 7[/tex]

Add 7 to both sides

[tex]x + 7 = \sqrt[3]{y}[/tex]

Take the cube of both sides

[tex]y = (x + 7)^3[/tex]

This implies that

[tex]g(x) = (x + 7)^3[/tex]

Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]

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Answer:

z = -60

Step-by-step explanation:

1/6z= -10

To find the value for z, multiply each side by 6

6*1/6z= -10*6

z = -60

Answer:

Center of the Sphere is a fixed point in its interior which is equidistant from each point on sphere. Option A is not right because it says center is line segment. Option B is right as it says it is fixed and equidistant from point of surface.

Step-by-step explanation:

Hello !

[tex]F(x) = \frac{1}{3} \times {4}^{x} [/tex]

[tex]F(3) = \frac{1}{3} \times {4}^{3} \\ = \frac{1}{3} \times 64 \\ = \frac{64}{3} [/tex]

==> B

Have a nice day ;)

Hello,

Answer: 64/3

B

Step-by-step explanation:

F(x) = 1/3 × 4ˣ

F(3) = 1/3 × 4³ = 1/3 × 64 = 64/3

Answer:

20x^2 + 47x + 24

Step-by-step explanation:

The area of a rectangle is LENGTH * WIDTH. From the diagram, we see that  LENGTH = 4x + 3 and WIDTH = 8 + 5x. Therefore the area is:

A = LENGTH*WIDTH

  = (4x+3)(5x+8)

  = 20x^2 + 32x + 15x + 24

  = 20x^2 + 47x + 24

Answer: C. 20x²+47x+24

Step-by-step explanation: Use the FOIL Method (First, Outer, Inner, Last). Equation: (5x+8) (4x+3). Hope this helps!

Hello,

[tex]\boxed{P(X = k) =( {}^{n} _{k}) \times p {}^{k} \times (1 - p) {}^{n - k} }[/tex]

[tex]P(X= k) = ( {}^{12} _{6}) \times 0.51 {}^{6} \times (1 - 0.51) {}^{12 - 6} [/tex]

We have :

[tex]( {}^{n} _{k}) = \frac{n!}{k!(n - k)!} [/tex]

[tex]( {}^{12} _{6}) = \frac{12!}{6!(12 - 6)!} = \frac{12!}{6!6!} = \frac{12 \times 11 \times 10 \times ... \times 1}{2(6 \times 5 \times 4 \times... \times 1) } = \frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 }{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 924[/tex]

[tex]P(X = k) = 924 \times 0.51 {}^{6} \times 0.49 {}^{6} = 0.2250[/tex]

Answer:

Olive's age = 32

Lisbeth's age = 8

Step-by-step explanation:

Declaration

Let Eisbeths present age = x

Let Olive's age = y

Equations

(x - 2) = 1/5 (y - 2)

x + 4 = 1/3(Y + 4)

Solution

1st equation

(x - 2) = 1/5 (y - 2)                 Multiply both sides by 5

5(x - 2) = y - 2                       Remove the brackets

5x - 10 = y - 2                       Add 10 to both sides

5x -10+10 = y - 2+10            Combine

5x = y + 8                            Subtract 8 from both sides

5x - 8 = y + 8 - 8                 Combine

5x - 8 = y

2nd Equation

x + 4 = 1/3(y + 4)                 Multiply both sides by 3

3(x + 4) = y + 4                   Remove the brackets

3x + 12 = y + 4                     Subtract 3 from both sides

3x + 12 - 4 = y + 4 - 4          Combine

3x + 8 = y

Note Since y is the same in both equations, the left side of each can be thought of as equal to each other.

3x + 8  = 5x - 8                    Add 8  to both sides

3x + 8 + 8 = 5x - 8 + 8        Combine

3x + 16 = 5x                         Subtract 3x from both sides

3x - 3x + 16 = 5x - 3x           Combine

16 = 2x                                  Divide by 2

16/2 = 2x/2

8  = x

y = 3x + 8

y = 32

The equation of the segments perpendicular bisector is; y = -¹/₂x + 2

i) Since it is a perpendicular bisector, hence point M is the midpoint. Thus;

Midpoint (AB) = [(x₁ + x₂)/2], [(y₁ + y₂)/2] = (x_m, y_m)

Slope AB will be;

m₁ = ((x₁ - x₂)/(y₁ - y₂))

Slope of perpendicular bisector is;

m₂ = -1/m₁

Equation of perpendicular bisector is;

(y - y_m) = m₂(x - x_m)

ii) Midpoint (AB) = [(-2 + 6)/2], [(3 - 1)/2] = (2, 1)

Slope AB will be;

m₁ = ((6 + 2)/(-1 - 3)) = -2

m₂ = -1/-2 = 1/2

Equation of perpendicular bisector is;

(y - 1) = -¹/₂(x - 2)

y - 1 = -¹/₂x + 1

y = -¹/₂x + 2

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Answer:

y = 95

Step-by-step explanation:

x + 120 = 180

25 + x + y = 180

flipping the first equation 180 - 120 = 60 so x is 60.

so plug in 60 into the second equation

25 + 60 + y =180 --> 85 + y =180 flip equation 180 - 85 = 95

so y is 95

The quantity of baking powder needed to bake 100 muffins is 6 tablespoons of baking powder

Number of muffins : quantity of baking powder

= 50 : 3

How much baking powder is needed for 100 muffins

let

Equate the ratio of muffins to baking powder

50 : 3 = 100 : b

50/3 = 100/b

50 × b = 3 × 100

50b = 300

b = 300/50

b = 6 tablespoons

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Answer: 1st graph (3,2)

Step-by-step explanation:

For systems A and B we have:

1) Change the first equation in A by a multiple of itself. (the multiple is 1/3).

2) Yes, the systems are equivalent.

Here we have the systems of equations:

A:

-3x + 12y = 15

7x - 10y = -2

B:

-x + 4y = 5

7x - 10y = -2

Notice that the second equation is the same in both systems, so we only need to work with the first ones.

If we take the first equation in system A:

-3x + 12y = 15

If we divide both sides by 3, we get:

-x + 4y = 5

Which is the first equation of B.

So we just need to replace the first equation in system A by a multiple of itself to get system B.

Because of that, we conclude that both systems are equivalent (because are made of the same equations) which means that both systems have the same solutions.

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Answer: C), Yes

Step-by-step explanation:

The most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

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

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations:

0.02x - 0.05y =  -0.38

0.03x + 0.04y = 1.04

We can write above equations as follows:

2x - 5y = -38

3x + 4y = 104

After solving with the substitution method:

x = 16

y = 14

-20 ≤ x ≤ 20

-15 ≤ x ≤ 15

Thus, the most suitable viewing window to solve the system is -20 ≤ x ≤ 20 and -15 ≤ x ≤ 15 option fourth is correct.

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a. The unit rate is 9 d per t

b. Find the graph in the attachment

To graph the line, we need to find its gradient or unit rate

Since t has an increase of 0.20 units in t corresponds to an increase of 1.8 units in d.

The gradient or unit rate of change is m = change in d/change in t

= Δd/Δt

Since

So, substituting the values of the variables into the equation, we have

m = Δd/Δt

= + 1.8 units/+ 0.2 units

= 9 d per t

So, the unit rate is 9 d per t

To graph the function, we need to know the equation of the graph.

So, the equation of a graph in gradient form is

m = (y - y')/(x - x') where (x', y') = (0, 0) since the graphs both start at the origin

Since m = 9, we have

m = (y - y')/(x - x')

9 = (y - 0)/(x - 0)

9 = y/x

y = 9x

So, the equation of the line is y = 9x

Find the graph in the attachment.

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Answer:

Therefore the slope is 13

Step-by-step explanation:

Using Slope intercept formula y = mx + b.

Note : m is the slope ( the number near x).

y+6=13(x−4)

y+6 = 13x - 52

Add -6 to both sides

y+ 6- 6 = 13x- 52- 6

y= 13x -58

Therefore the slope is 13

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line y+6=13(x-4)

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

The slope of this particular graph is: the constant multiplied by the parentheses.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

            [tex]\bf{=Slope \:13}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]

The measure of <2 is 60.

The tangent is defined as a line touching circles or an ellipse at only one point.

given:

VU = 80° and ST = 40°

By using theorem,

The measure of the internal angle is the semi- sum of the arcs comprising it and its opposite.

<2= 1/2 (80+ 40)

<2= 60

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Answer:

It should look like a v with the origin at +0.5

Step-by-step explanation:

Answer:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

Step-by-step explanation:

The temperature at any time t can be represented as:

D(t)=A+B*sin(2*pi*t/T)+C*cos(2*pi*t/T)

where A is the average temperature, B is the amplitude of the sine wave, C is the amplitude of the cosine wave, and T is the period.

In this case, we are given that the average temperature is 60, the high temperature is 73, and the low temperature is 47. We can therefore calculate that the amplitude of the sine wave is 23 and the amplitude of the cosine wave is 26. The period is 24 hours. Therefore, the equation for the temperature in terms of time is:

D(t)=60+23*sin(2*pi*t/24)+26*cos(2*pi*t/24)

The company should focus attention on 17515 people.

The term percentage means a denominator of 100. We can proceed to find the people to which the company must reach as follows;

The percentage that is over the age of 65, and immunocompromised =  27%

so;

27/100 × 50,000 = 13500 people

50,000 - 13500 = 36,500

Now;

11% of this number are under 65 and immunocompromised so;

11/100 ×  36,500 = 4015 people

Total number that the company should reach = 13500 + 4015  = 17515 people

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Answer:

71°

Step-by-step explanation:

So, angle A measures 66+5=71°

The regression equation is  mathematically given as

[tex]\=Y = 5 + 0.3 X[/tex]

This is further explained below.

The line is passing through (0, 5) and (15, 10).

Generally, the equation for Slope  is  mathematically given as

[tex]S=\frac{ (10 - 5)}{(15 - 0) }[/tex]

Therefore

S= 5/15

S= 1/3

S= 0.3

Intercept = 5

In conclusion,Regression equation:

[tex]\=Y = 5 + 0.3 X[/tex]

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Answer:

Step-by-step explanation:

9w^{321+15+6}

9w^{342}

The effective tax rate based on the assumed information is 2.5%.

Let's assume that the figures are:

Income tax expense = $50

Income before tax = $2000

It should be noted that tax rate is calculated as:

= Income tax expense / Income before tax

= 50/2000

= 0.025

= 2.5%

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hellooo

Step-by-step explanation:

so sine is 0 and (-1/3 isnt gonna positive out on the other side no is positive so ur last answer E is it

Using the permutation formula, it is found that the probability that the CDs end up in alphabetical order is:

[tex]p = \frac{1}{8,204,716,800}[/tex]

For this problem, the order in which the CDs are chosen is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

8 CDs are chosen from a set of 21, hence the number of ways they can be chosen is:

[tex]P_{(21,8)} = \frac{21!}{13!} = 8204716800[/tex]

Only one arrangement is in alphabetical order, hence the probability is:

[tex]p = \frac{1}{8,204,716,800}[/tex]

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Step-by-step explanation:

gfyiaycoeayclpb tydivh.

Answer:

-2 3/8

Step-by-step explanation:

since point A is left of 0, it means it is a negative value.

so, the positive answer options are automatically out.

then we see that point A is 2 full units and a little bit left of 0.

that means it has to be lower than -2 but higher than -3.

-22/7 = -3 1/7

so, that is too low.

-3 7/8 is too low.

so, that leaves -2 3/8 (confirmed also by the fact that A is a little bit higher than half between -2 and -3, which is the case for -2 3/8).

Answer:

1) a
2) b

Step-by-step explanation:

1) Lets check all the options

a) Cannot be simplified

b) [tex](6^2)^5=6^{10}[/tex] because [tex](a^m)^n=a^{mn}[/tex]

c) [tex](2\times3)^{10}=6^{10}[/tex] fairly self-explanatory because [tex]2\times3=6[/tex]

d) [tex]2^{10}\times3^{10}=6^{10}[/tex] because [tex]a^m\times b^m=ab^m[/tex]

Hence a is the answer.

2) [tex]25\frac12\div\frac12=\frac{51}2\times\frac21=51[/tex]

Hence b is the answer

The solution of the given Inequality is; D: x ≤ 6

We want to find the solution to the Inequality;

5x - 9 ≤ 21

Using Addition property of equality, add 9 to both sides to get;

5x ≤ 30

Using division property of equality, divide both sides by 5 to get;

x ≤ 6

All real numbers less than or equal to 6

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Answer:

30,000

Step-by-step explanation:

place value of 3 is tens of thousands (10,000)

therefore its total value is : 3×10,000=30,000