Determine the domain and range of the following and show/explain your work.
5 y = - x^4 + 4 Provide a graph to verify your answer.

6 y = 2x^3 - 1 Provide a graph to verify your answer.

7 y = 3√(2x+8) Provide a graph to verify your answer.

Answer:

14

Step-by-step explanation:

[tex] {x}^{2} = {4}^{2} \\ = 16\\ 4y = 4 \times - 3 \\ 4 \times - 3 = - 12 \\ 16 - - 12 =16 + 12 \\ - \times - = + \\ 16 + 12 = 28 \\ 28 \div 2 = 14[/tex]

The probability of selecting two prime numbers is 1/6.

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers  = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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The number of years it will take for the world’s population to increase to 8,252,000,000 people is 16

This implies that we calculate the value of x

The equation is given as:

8252=(6080)(1.02)^x

Divide both sides by 6080

1.36 = (1.02)^x

Take the logarithm of both sides

log(1.36) = x * log(1.02)

Divide both sides log(1.02)

x = log(1.36)/log(1.02)

Evaluate the quotient

x = 16

Hence, the number of years is 16

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Answer:

116

Step-by-step explanation:

zinc : copper

4      :     11

11 = 319

zinc = 4 / 11 * 319

Zinc = 116

1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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The number of ways when the choice is not relevant is 10

The number of objects are:

Object, n = 5

The object to choose are:

r = 3

Relevant choice

When the choice is relevant, we have:

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^{5}P_3[/tex]

Evaluate

Ways = 60

Hence, the number of ways when the choice is relevant is 60

Not relevant choice

When the choice is not relevant, we have:

[tex]Ways = ^nC_r[/tex]

This gives

[tex]Ways = ^{5}C_3[/tex]

Evaluate

Ways = 10

Hence, the number of ways when the choice is not relevant is 10

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Answer:

11  units

Step-by-step explanation:

We first need to solve for x

3x -28 +3x -30 + x = 33  Combine the x's

7x - 28 -30 = 33  Combine -28 and -30

7x - 58 = 33  Add 58 to both sides

7x = 91  Divide both sides by 7

x = 13  Now plug 13 into the expression for DE

3x - 28

3(13) - 28

39 -28

11

See below for the complete table and graph of y = x + 4

The function is given as:

y = x +4

Where x = -2, 0, 2, 6 and 8

So, we have

y = -2 +4 = 2

y = 0 +4 = 4

y = 2 +4 = 6

y = 6 +4 = 10

y = 8 +4 = 12

The above computation implies that the complete table is

Input x        x + 4        Output, y        (x, y)

-2               -2  + 4          2                  (-2,2)

0                 0  + 4          4                  (0,4)

2                 2  + 4          6                  (2,6)

6                 6  + 4          10                 (6,10)

8                 8  + 4          12                  (8,12)

See attachment for the graph of y = -x + 4

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Answer:

203681

203,681

Two hundred and three thousand, six hundred eighty-one

Step-by-step explanation:

The number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

In the question, we are asked to write the number 203681 in words.

In the given number, we have:

Keeping the thousands as different section, we have 203 in thousands section, and 681 in the remaining.

203 can be named as two hundred and three.

681 can be named as six hundred and eighty-one.

Since, 203 is in the thousands section, we add thousand in its name.

Thus, the name we get is two hundred and three thousands, six hundred and eighty-one.

Thus, the number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

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The length of AC is 12 units . Option D

The formula for area of a kite is given thus;

Area = [tex]\frac{p * q}{2}[/tex]

Where p and q are the lengths

Area of kite = 48 square units

BD, q = 8 units

AC , p = unknown

Substitute the values

[tex]48 = \frac{AC * 8}{2}[/tex]

Cross multiply

[tex]AC * 8 = 48 * 2[/tex]

[tex]8AC = 96[/tex]

[tex]AC = \frac{96}{8}[/tex]

[tex]AC = 12[/tex] units

Thus, the length of AC is 12 units . Option D

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Answer:option 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since diameter x pi=3.14,this should be easy.

4x3=12

4x14/100=.56

12+.56=12.56

12.56 is the answer

Answer:

C. (2;9)

Step-by-step explanation:

for more details see the attachment.

The total amount of Chandra's investments after 8 years exists at $110.03 Compound interest.

The formula for calculating the compound interest exists described as;

[tex]A = P(1+r/n)^{nt[/tex]

where, P is the amount invested = $75

r be the rate. = 0.048

t be the time = 8 years

n = 12 (monthly)

Substitute, the values in the above equation, then we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03 Compound interest.

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Answer: 97350

Step-by-step explanation:

The numbers (3251)(30) are separated by using parentheses by multiplying the numbers we get 97350.

When we notice two or more numbers together that exist divided by parentheses, then the parentheses exist pointing us to multiply.  In math, multiplying indicates adding equivalent groups. When we multiply, the number of things in the group rises. The two elements and the product exist as regions of a multiplication problem.

Given: (3251)(30)

Here, the numbers are separated by using parentheses, then the parentheses exist pointing us to multiply.

Therefore, by multiplying the numbers we get

(3,251)(30) = 97350

Therefore, the correct answer is 97350.

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Answer:

2

Step-by-step explanation:

You have the correct answer selected: 2.

The reason for this is that when there are exponents inside and outside of the parenthesis like this, they are multiplied.

2 times 2 is 4. That's why (8^2)^2 = 8^4

Answer:

p = 2

Step-by-step explanation:

[tex](8^{2}) ^{p}[/tex] = [tex]8^{4}[/tex]

  [tex]8^{2p}[/tex] =    [tex]8^{4}[/tex]

   [tex]8^{p}[/tex] = [tex]8^{\frac{4}{2}[/tex]

    p = 2

Step-by-step explanation:

++++5

+++++++_2

1=false

true

false

false

An appropriate numerical summary is descriptive statistics.

It should be noted that a numerical summary means a number used to describe specific characteristics of a data set.

In this case, descriptive statistics can be used. This is used to describe the data set.

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Answer:

CIRCLE

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

it should be that should be the answer it should be 9 bcuz he bout gum for 1 he got 5 peaces so dets 5$ then someone else got sumthing for 1$ and they got 4 peicea so thats 4$ 5+4 is 9

Answer:

it's answer came 20000o

The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

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Based on the multiplication property of equality, the statement that completes the proof is: C. CD = b(sin A) and CD = a(sin B).

The multiplication property of equality is given as, if a/b = y, then a = yb. Both sides of the equation is multiplied by the same value.

In step 5 where the multiplication property of equality is applied, we would have:

sin(A) = CD/b

Multiply both sides by b

sin(A) × b = CD/b × b

b(sin A) = CD

CD = b(sin A)

This same property is applied to sin B = CD/a to get CD = a(sin B).

Therefore, the missing statement is: C. CD = b(sin A) and CD = a(sin B).

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The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

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Answer: [tex](x,y)=\{(-1,1), (0,4) \}[/tex]

Step-by-step explanation:

[tex]3x^2 +6x+4=-3x^2 +4\\\\6x^2 +6x=0\\\\x^2 +x=0\\\\x(x+1)=0\\\\x=-1, 0\\\\x=-1 \longrightarrow y=1\\\\x=0 \longrightarrow y=4\\\\\therefore (x,y)=\{(-1,1), (0,4) \}[/tex]

The solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given quadratic equations are given as below:-

y = 3x² + 6x + 4

y = -3x² + 4

Equate the equations and solve for the value of x.

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

x² + x = 0

x ( x + 1 ) = 0

x = 0 and x = -1

At x=0 and x=-1 the values of y are calculated as below:-

y = -3x² + 4

y = 0+ 4 = 4

y = -3 + 4 = 1

Therefore, the solution of the quadratic equations will be ( 0, 4 ) and ( -1, 1).

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$13,000 was invested at 6% whereas $7,000 was invested at 10% using simple interest approach

What is simple interest?

Simple interest is determined as the amount invested multiplied by the interest rate and the number of years that investment lasts.

I=PRT

I=interest

P=principal

R=rate of return

T=time

Let X be the amount invested at 6%

I at 6%=6%*X*1

I=0.06X

The amount invested at 10% is 20,000-X

total interest=0.06X+0.10*(20000-X)

total interest=1,480

1480=0.06X+0.10*(20000-X)

1480=0.06X+2000-0.10X

1480-2000=0.06X-0.10X

-520=-0.04X

X=-520/-0.04

X=13,000

13,000 was invested at 6%

amount invested at 10%=20,000-X

amount invested at 10%=20,000-13,000

amount invested at 10%=7,000

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