(a) If the point (8, 5) is on the graph of an even function, what other point must also be on the graph?

(b) If the point (8, 5) is on the graph of an odd function, what other point must also be on the graph?
(x, y) =

The ordered pair that is a solution to the equation 3y = -2x - 4 is given as follows:

(1, -2).

The equation for this problem is defined as follows:

3y = -2x - 4

To verify whether an ordered pair is a solution to the equation, it must make the equation true.

When x = 1 and y = -2, we have that:

Hence the ordered pair (1,-2) is a solution to the equation for this problem.

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Answer:

9 pounds/135 cubic inches

= 1 pound/15 cubic inches

= .07 pounds/cubic inch

Answer:

92.5

Step-by-step explanation:

First, we need to put the data in order from smallest to largest:

$71, 81, 89, 92, 93, 94, 94, 99$

There are 8 numbers in the data set, which is an even number. To find the median, we need to average the two middle numbers.

The middle two numbers are 92 and 93, so the median is:

$(92+93)/2 = 92.5$

Therefore, the median of the data is 92.5.

Answer:

4(x-1)=2(6-2x)

4x-4=12-4x

4x+4xd=12+4

8x=16

x=2

Answer:

x=2

Step-by-step explanation:

Step 1: Distribute

To solve this problem, the first step is distributing the four and the 2.

[tex]4(x-1)=2(6-2x)\\\\4x-4=12-4x[/tex]

So this is our simplified problem.

Step 2: Solve for x

Step 2a: Add 4x to both sides:

(This is because we do not have two variables in the equation, making it easier to solve.

[tex]4x+4x-4=12-4x+4x\\\\8x-4=12+0\\\\8x-4=12[/tex]
Step 2b: Add 4 to both sides:

(We do this to leave the variable on one side and the constant on the other. )

[tex]8x-4+4=12+4\\\\8x+0=16\\\\8x=16[/tex]

Step 2c: Divide both sides by 8:

(The reason why we do this is to isolate the variable without any coefficient in front.)

[tex]\frac{8x}{8} =\frac{16}{8} \\\\x=2[/tex]

Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

We have,

From the given data, we can see that the number of mice is being multiplied by 2 every month.

That means the growth is exponential.

We can use the formula for exponential growth:

[tex]m(t) = a \timesr^t[/tex]

where m(t) is the total number of mice after t months, a is the initial number of mice (when t = 0), and r is the common ratio

From the given data, we can see that when t = 0, there are 3 mice.

So, a = 3.

Also, we can see that the common ratio is 2 (i.e., the number of mice is being multiplied by 2 every month).

Now,

The equation that models how many mice there will be in the lab after 10 months is:

m(10) = 3 × 2^10

Simplifying this equation gives:

m(10) = 3 × 1024

m(10) = 3072

Therefore,

The correct equation that models how many mice there will be in the lab after 10 months is m(10) = 3 × 2^10.

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The coordinates of point P are (-1, 1 8/11).

We have,

G(4, 4) and H(-7, 1)

m :n = 5:6

Using Section formula

x = (mx₂ + nx₁)/ (m+n) and y = (my₂ + ny₁)/ (m+n)

Here, x₁ = 4, y₁ = -7, x₂ = 4 and y₂ = -1

So, x = (5(-7) + 6(4))/ 11  and y = (5(-1) + 6(4))/ 11

x = -35+24/11 and y = -5 + 24/11

x = -11/11 and y = -19/11

x = -1 and y = 1 8/11

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Answer:

The angle of the intersection is 90 degrees

Step-by-step explanation:

How I know this is because EF is the diameter, which means that arc EF is equal to 180 degrees. Because we know this that means when it is spilt into two parts, the arc and angle measure has to be 90 degrees.

Another way to do this is to remember that a circle is 360 degrees and the circle is split into 4 parts. So all you have to do is divide 360/4 to get 90. Your answer.

Answer:

To determine the monthly deposit that Sophia must make in order to reach her retirement goal, we can use the formula for the future value of an annuity:

FV = P * ((1 + r/n)^(nt) - 1) / (r/n)

where:

FV = future value of the annuity (which is Sophia's retirement goal of $1,600,000)

P = monthly deposit

r = annual interest rate (which is 9%)

n = number of times interest is compounded per year (which is 12 for monthly compounding)

t = number of years until retirement (which is 65 - 28 = 37)

Substituting the given values, we get:

1600000 = P * ((1 + 0.09/12)^(12*37) - 1) / (0.09/12)

Simplifying and solving for P, we get:

P = 1600000 * (0.09/12) / ((1 + 0.09/12)^(12*37) - 1)

P ≈ $524.79

Therefore, Sophia must make a monthly deposit of approximately $524.79 in order to reach her retirement goal of $1,600,000.

Step-by-step explanation:

The distance between Garret and Dino to the nearest yard is: 21 yds

The Law of Cosines is defined as a numerical formula that expresses the relationship between  the side lengths and points of any triangle. It usually expresses that the square of any particular side of a triangle is equal to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them.

Numerically, the Law of Cosines can be expressed as:

c² = a² + b² - 2abcos(C),

where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.

Thus, the distance here is expressed as:

d² =  15² + 17² - 2(15 * 17)cos(81)

d = √434.218

d = 20.838 yds

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Answer:

Suppose X ~ N(12,2) represents a normal distribution with mean 12 and standard deviation 2. According to the empirical rule, about 68% of the x values lie within one standard deviation of the mean .

We can calculate the endpoints of the interval that represents one standard deviation from the mean as follows:

Lower endpoint: 12 - 2 = 10

Upper endpoint: 12 + 2 = 14

Therefore, about 68% of the x values lie between 10 and 14 1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the square base = 5 * 5 = 25

each of the triangular sides = 4*2.5=10

so… 25+(10*4)=25+40=65

The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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The polynomial equation of the smallest degree is f(u) = (u + 2)³(u - 1)²(u - 3)

Given that we have the graph of a polynomial

The degree of the graph is the number of times the graph intersect and/or crosses the x-axis

In this case, we have the following points at which the graph intersect and/or crosses the x-axis

When the multiplicities are added, we have

Degree = 3 + 1 + 2

Degree = 6

So, the degree is 6

In (a), we have

This means that

The zero at u = 1 has a multiplicity of 1

The equation is represented as

f(u) = (u - zero)^multiplicity

So, we have

f(u) = (u + 2)³(u - 1)²(u - 3)

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Answer:

1728 square ft²

Step-by-step explanation:

48x36=1728

Answer:

[tex]\large \boxed{\mathrm{Area}}[/tex] = [tex]\large \boxed{\mathrm{12 \ ft^2}}[/tex]

Steps:

12 inches = 1 foot

48 / 12 = 4 [tex]\meduim \boxed{\mathrm{feet}}[/tex]

36 / 12 = 3 [tex]\large \boxed{\mathrm{feet}}[/tex]

Answer:

3 x 4 = 12 ft²

Check the picture below.

bearing in mind that a vertical line always has that slope.

The number of days required to complete the job in exponent form is 10¹ = 10.

The exponent form of the number of days is calculated as follows;

number of pages that can be printed by all machines = n x P

where;

N = 100 x 104

N = 10400 pages/day

However, the Ted's company needs 10 days to print 106 pages, our equation is formed as follows;

x = log(y)

where;

10ˣ = y

10ˣ = 10

x = 1

so the exponential form = 10¹ = 10

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The amount she invested at each rate of interest for the simple interest are $39,100 and $78,200.

Given that,

Jolene invests her savings in two bank accounts.

Rate of interest for one account = 6% per year

Rate of interest for the other account = 10% per year

Let x be the principal amount invested in the account yielding 10% interest.

Interest amount = 0.1x

Principal amount in the account of 6% interest = 2x

Interest amount = 0.06 × 2x = 0.12x

Annual interest = $8602

0.1x + 0.12x = 8602

0.22x = 8602

x = $39,100

Amount invested for 10% interest account = $39,100

Amount invested for 6% interest account = 2 × $39,100 = $78,200

Hence the amount invested are $39,100 and $78,200.

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A statement which is correct include the following: A. Roses cost $2.75 more than daisies.

In order to write a system of linear equations to describe this situation, we would assign variables to the cost of roses and cost of daisies, and then translate the word problem into a linear equation as follows:

Based on the information provided about the flowers purchased by Marla and Kelly. we have the following system of linear equations;

7x + 10y = 40.5

3x + 15y = 30.75

By solving the system of linear equations simultaneously, we have:

x = 4 and y = 1.25

Difference = 4 - 1.25

Difference = $2.75

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The given equation in exponential form will be [tex]20 = x^e[/tex]

Given is an equation, x = ㏑ 20,

So, we know that,

㏑(x) = [tex]log_e(x)[/tex]

And,

logₐ (x) = b

x = bᵃ

Therefore,

x = ㏑ 20

will be converted into,

[tex]20 = x^e[/tex]

Hence, the given equation in exponential form will be [tex]20 = x^e[/tex]

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The expected values are 60 blues, 30 reds and 30 greens

From the question, we have the following parameters that can be used in our computation:

6 blue cubes, 3 red cubes, and 3 green cubes

This means that we have the following proportions

Blue = 6/(6 + 3 + 3) = 1/2

Red = 3/(6 + 3 + 3) = 1/4

Green = 3/(6 + 3 + 3) = 1/4

If you draw a cube and replace it in the bag 120 times, we have

Blue = 1/2 * 120 = 60

Red = 1/4 * 120 = 30

Green = 1/4 * 120 = 30

Hence, the expected values are 60 blues, 30 reds and 30 greens

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Answer:

Dividing both sides by 4, we get:

4m/4 = 28/4

Simplifying, we get:

m = 7

Therefore, the answer is D. 7.

The dimension of the rectangle is 50 meters by 10 meters

The perimeter of a figure is the sum of all the external sides of the figure

The formula for calculating the perimeter of rectangle [tex]= 2(\text{l}+\text{w})[/tex]

If the length is 40 meters longer than the width, then:

[tex]\text{l} = 40 + \text{w}[/tex]

Substitute

[tex]120 = 2(40+2\text{w})[/tex]

[tex]60 = 40 + 2\text{w}[/tex]

[tex]30 = 20+ \text{w}[/tex]

[tex]\bold{w = 10 \ meters}[/tex]

Since [tex]\text{l} =40 + \text{w}[/tex]

[tex]\text{l} =40 +10[/tex]

[tex]\bold{l=50 \ meters}[/tex]

Hence the dimension of the rectangle is 50 meters by 10 meters

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Answer:

The given pattern does not form an arithmetic sequence as there is no common difference between each term. An arithmetic sequence is a sequence in which there is a fixed difference between each consecutive term. For example, 1, 3, 5, 7 is an arithmetic sequence with a common difference of 2 (adding 2 to each term gives the next term). However, the given pattern of 1/2, 1, 2/3, 2 does not follow this pattern as the difference between each term varies. Therefore, this pattern does not fit the definition of an arithmetic sequence.

Step-by-step explanation:

Answer:

p

Step-by-step explanation:

ok so first u take away the underlined letter and give and carry sorry the first one