Which relationships describe angles 1 and 2? Select each correct answer. O complementary angles O adjacent angles O vertical angles O supplementary angles​

Answer:

Rusty Raspberry's total earnings last year would be the sum of his earnings from playing baseball and his earnings from book royalties.

Earnings from playing baseball = $1,715,000

To calculate earnings from book royalties, we need to find out how much Rusty received in royalties for the 300,000 copies sold.

Royalties per book = 10% of $24 = $2.40

Total royalties for 300,000 books = $2.40 x 300,000 = $720,000

Therefore, Rusty Raspberry's earnings from book royalties last year = $720,000

Total earnings = Earnings from playing baseball + Earnings from book royalties

= $1,715,000 + $720,000

= $2,435,000

Therefore, Rusty Raspberry's total salary last year from the book and his baseball career was $2,435,000.

Answer:

Step-by-step explanation:

To find the number of miles at which the cost to rent either car would be the same, we can set the two cost equations equal to each other and solve for m:

0.60m + 10 = 0.40m + 22

0.20m = 12

m = 60

So, the number of miles at which the cost to rent either car would be the same is 60 miles.

To find the cost at this mileage, we can plug m = 60 into either of the cost equations:

For the compact car:

C = 0.60(60) + 10 = 46

For the midsized car:

C = 0.40(60) + 22 = 46

So, at 60 miles, the cost to rent either car would be $46.

The zeros of the function H(x) = (3x - 4)(x + 2)^2(x - 5) are (4/3, 0), (-2, 0), and (5, 0).

To find the zeros of the function H(x), we need to find the values of x that make the function equal to zero.

H(x) = (3x - 4)(x + 2)^2(x - 5)

Setting H(x) equal to zero, we have:

(3x - 4)(x + 2)^2(x - 5) = 0

Using the zero product property, we can see that H(x) will be equal to zero when any of the factors are equal to zero.

So, the zeros of the function H(x) are:

3x - 4 = 0, which gives x = 4/3

x + 2 = 0, which gives x = -2

x - 5 = 0, which gives x = 5

Therefore, the zeros of the function H(x) are (4/3, 0), (-2, 0), and (5, 0).

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The predicted Iife expectancy οf maIes in 2006 is 71.7 years.

A Iinear equatiοn is a mathematicaI equatiοn that describes a straight Iine in a twο-dimensiοnaI pIane.

Tο find the Iinear functiοn E(t) that fits the data, we need tο find the equatiοn οf the Iine that passes thrοugh the twο given pοints: (0, 65.2) and (5, 67.7), where t = 0 cοrrespοnds tο the year 1993 and t = 5 cοrrespοnds tο the year 1998.

Using the sIοpe-intercept fοrm οf a Iinear equatiοn, we have:

E(t) = mt + b

where m is the sIοpe οf the Iine and b is the y-intercept.

We can find the sIοpe by using the fοrmuIa:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (0, 65.2) and (x2, y2) = (5, 67.7):

m = (67.7 - 65.2)/(5 - 0) = 0.5

Sο the equatiοn οf the Iine is:

E(t) = 0.5t + b

Tο find the y-intercept, we can use οne οf the given pοints. Let's use (0, 65.2):

65.2 = 0.5(0) + b

b = 65.2

Therefοre, the Iinear functiοn E(t) that fits the data is:

E(t) = 0.5t + 65.2

Tο predict the Iife expectancy οf maIes in 2006, we need tο find t when the year is 2006:

t = 2006 - 1993 = 13

Sο we can use t = 13 in the equatiοn:

E(13) = 0.5(13) + 65.2

E(13) = 6.5 + 65.2

E(13) = 71.7

Therefοre, the predicted Iife expectancy οf maIes in 2006 is 71.7 years.

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According to the question 560 cups divided by 20 cups per week equals 28 weeks.

Division is a mathematical operation that involves splitting a number or quantity into equal parts. It is an essential process in mathematics, used to solve problems and find solutions. Division involves dividing a number, or a set of numbers, by another number. The result of the division is known as the quotient. Division can also be used to find fractions or ratios, as well as to divide a number into its parts.

Assuming the bag of dog food is a large bag and Carl is feeding his dog 2 1/2 cups daily, the maximum number of days Carl can feed his dog from one full bag is 28.
This is because 2 1/2 cups equals 20 cups per week, and a large bag typically contains approximately 560 cups.
Therefore, 560 cups divided by 20 cups per week equals 28 weeks.

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The entire number of kilometres driven by Roland's family can be determined by using the phrase [tex]=\frac{69}{10}[/tex]

To determine the total number of kilometres driven by Roland's family, the distance from their home to the gas station and the distance from the gas station to the shop must be added.

There are [tex]4\times \frac{6}{10}[/tex] kilometres between their home and the gas station, which can also be stated incorrectly as follows:

[tex]4\times \frac{6}{10}=\frac{(4\times 10+6)}{10} \\\\=\frac{46}{10}[/tex]

The formula for expressing the distance between the gas stop and the store is 2 30/100 kilometers, which can be written as follows:

[tex]2\times\frac{30}{100} =\frac{(2\times100+30)}{100} \\\\=\frac{230}{100}[/tex]

To calculate the overall distance traveled, we add the two distances:

[tex]\frac{46}{10} +\frac{230}{100}[/tex]

To combine these fractions, we need to find a common denominator. Only one unique digit, 100, can be used to divide both 10 and 100. In light

of this, we can rewrite the equation as follows using 100 as the common denominator:

[tex](\frac{46}{10} )\times (\frac{10}{10} )+(\frac{230}{100} )\times (\frac{1}{1} )[/tex]

That amounts to:

[tex]\frac{46}{100} +\frac{230}{100} =\frac{690}{100}[/tex]

Therefore, we can reduce this fraction by multiplying the numerator and denominator by their ten largest common factor:

[tex]\frac{690}{100} =\frac{(69/10)}{(100/10)} \\\\=\frac{69}{10}[/tex]

Consequently, the phrase that follows may be used to determine the overall number of kilometres driven by Roland's family:

[tex]2\times\frac{30}{100} +4\times \frac{6}{10} =\frac{69}{10}\ km[/tex]

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Rest of the question is,

They drove 2 30/100 kilometers from the gas station to the store. Which expression can be used to determine the number of kilometer Ronald's family drove altogether.

The value of x in the triangle is 16.

The trigon, a 3-sided polygon, is sometimes (though not often) referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

Due to the similarity between the triangles ABC and ADE, we may establish the following ratio:

BC/DE = AB/AD

Inputting the values provided yields:

8/x = 12/24

When the right-hand side of the equation is simplified, we obtain:

12/24 = 1/2

Adding this value to the proportion results in:

8/x = 1/2

If we cross-multiply, we obtain:

2*8 = x

The left side of the equation can be simplified to: 16 = x.

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A) The completed table is given as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

B) the graph is attached accordingly.

C) In the context of the given problem, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

a) To complete the table, we need to use the given function D(L) to determine the number of beverage dispensers needed to hold different amounts of coffee.

We know that each beverage dispenser can hold 6 liters of coffee, so we can start by dividing the amount of coffee needed by 6 and rounding up to the nearest integer to get the number of dispensers needed.

D(L) = ceil(L/6)

Using this formula, we can complete the table as follows:

L D(L)

0 0

3 1

4 1

6.5 2

10 2

11.9 2

15 3

Note that for L=0, we don't need any dispensers, so the value of D(L) is 0. For all other values of L, we divide by 6 and round up to get the corresponding value of D(L).

b) The graph is attached.

c) In the context of the given problem, the function D(L) gives the minimum number of beverage dispensers needed to hold L liters of coffee, assuming each dispenser can hold 6 liters.

So, D(43) = 8 means that if Giada needs to brew and store 43 liters of coffee, she will need at least 8 beverage dispensers. Each dispenser can hold 6 liters, so the first 7 dispensers will be completely filled, and the last dispenser will be partially filled with the remaining coffee.

In other words, if Giada fills 7 dispensers completely, she will have used 42 liters of coffee, and the remaining 1 liter of coffee will be stored in the 8th dispenser. Therefore, to store 43 liters of coffee, she needs at least 8 dispensers, as given by the function D(L).

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Answer:

Step-by-step explanation:

Eva is not correct. There is only one possible triangle that can be formed with the given information. This is because in a triangle, the length of any side must be less than the sum of the lengths of the other two sides.

Using the Law of Cosines, we can find the length of the unknown side, c:

c^2 = a^2 + b^2 - 2ab cos(ZA)

c^2 = 54^2 + 59^2 - 2(54)(59) cos(130°)

c ≈ 31.28

Since h < a < b, we know that h < 54 < 59. Therefore, the length of side c must be between 5 and 113 (59 - 54 and 59 + 54). Since c = 31.28 is between 5 and 113, it satisfies the triangle inequality and a triangle can be formed.

To find the measures of the other angles, we can use the Law of Sines:

sin(A)/a = sin(ZA)/c

sin(A) = (a/c)sin(ZA)

sin(A) = (54/31.28)sin(130°)

sin(A) ≈ 0.879

A ≈ 62.6°

Similarly,

sin(B)/b = sin(ZA)/c

sin(B) = (b/c)sin(ZA)

sin(B) = (59/31.28)sin(130°)

sin(B) ≈ 0.841

B ≈ 56.2°

Therefore, the measures of the three angles are approximately 62.6°, 56.2°, and 61.2°, and there is only one possible triangle that can be formed with these side lengths and angle measures.

Answer:

Step-by-step explanation:

A = P(1 + r/n)^(n*t)

where:

A = the future value of the investment

P = the principal amount (the initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years the money is invested

In this case, we have:

P = $6,000.00

r = 4% = 0.04

n = 4 (compounded quarterly)

t = 7 years

So the formula becomes:

A = $6,000.00(1 + 0.04/4)^(4*7)

A = $6,000.00(1 + 0.01)^28

A = $6,000.00(1.01)^28

A = $8,199.11 (rounded to the nearest cent)

Therefore, you will have $8,199.11 in the account in 7 years.

We can write this statement as an inequality:

b/5 < 30

This inequality means that the result of dividing b by 5 is less than 30. To find the possible values of b that satisfy this inequality, we can multiply both sides by 5:

b < 5*30

Simplifying:

b < 150

Therefore, any value of b that is less than 150 will satisfy the inequality "The quotient of b and 5 is less than 30."

Answer:

Step-by-step explanation:

For this equation we will have to make an inequality. When we take a look at the first part of the problem it mentions the quotient of b and 5. If we were to write this it would be b÷5. Looking at the second part of the equation it say b÷5 is less than 30. Hence our answer would be b÷5 < 30. Hope this helps!

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

The volume of the solid is (64/3)√3 cubic units, which is answer choice B.

A circle is a geometric shape in a two-dimensional plane, consisting of all the points that are at a fixed distance, called the radius, from a given point, called the center. The distance around the circle is called the circumference. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The formula for the area of a circle is A = πr^2, where r is the radius of the circle. Circles have many real-world applications, such as in the design of wheels, gears, and other rotating objects. They are also important in mathematics and science, as they provide a simple and elegant way to study and understand the properties of curves and curved surfaces.

We can approach this problem by considering a vertical slice of the solid taken perpendicular to the y-axis. This slice will be an equilateral triangle with a side length that depends on the y-coordinate.

At y = 0, the circle x² + y² = 16 intersects the x-axis at x = ±4. This means that the equilateral triangle at y = 0 has side length 2√3 times the distance from the origin to the x-axis, which is 4√3. Therefore, the area of this triangle is:

A(0) = (√3/4) (4√3)² = 12√3

At a general y-coordinate y > 0, the equilateral triangle will have side length equal to the distance between the points where the circle intersects the line y = k, where k is the y-coordinate. This distance can be found using the Pythagorean theorem:

d = √(16 - k²) - √k² = √(16 - 2k²)

The area of the equilateral triangle at y is then:

A(y) = (√3/4) d² = (√3/4) (16 - 2k²)

To find the volume of the solid, we can integrate the cross-sectional areas with respect to y from 0 to 4, using the formula for the area of an equilateral triangle:

V = ∫(0 to 4) A(y) dy = ∫(0 to 4) (√3/4) (16 - 2k²) dy

= (√3/4) (16y - (2/3) y³)|0 to 4

= (√3/4) [(64 - (2/3)(64)) - (0 - 0)]

= (64/3)√3

Therefore, the volume of the solid is (64/3)√3 cubic units, which is answer choice B.

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Answer:

4906 that is the answer. also your welcome and sorry if I misunderstood the question

Answer:

y - 2 = - [tex]\frac{7}{4}[/tex] (x + 9)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

here m = - [tex]\frac{7}{4}[/tex] and (a, b ) = (- 9, 2 ) , then

y - 2 = - [tex]\frac{7}{4}[/tex] (x - (- 9) ) , that is

y - 2 = - [tex]\frac{7}{4}[/tex] (x + 9)

Answer:

alrededor de 10 meses

Step-by-step explanation:

Area of the rectangle is 72 square inches and the perimeter of the same rectangle is 36 inches by using this parameters Marisol can draw a rectangle.

A quadrilateral or four-sided polygon with four right angles (90° angles) and opposite sides that are parallel and the same length is referred to as a rectangle. It is a two-dimensional shape with four vertices and two pairs of parallel sides.

Given that,

the length is 12 inches and width is 6 inches,

So, The Area of rectangle = (Length × Width)

= 12 inches × 6 inches

= 72 square inches

So the area of the rectangle is 72 square inches.

The perimeter of a rectangle is given by adding up the lengths of all four sides.

The Perimeter of rectangle = (2 × length) + (2 × width)

= 2 × 12 inches + 2 × 6 inches

= 24 inches + 12 inches

= 36 inches

So the perimeter of the rectangle is 36 inches.

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In summary, Marisol's rectangle has a length of 12 inches, a width of 6 inches, an area of 72 square inches, and a perimeter of 36 inches.

Sure, I'd be happy to help you with your question! Marisol has drawn a rectangle that has a length of 12 inches and a width of 6 inches. The rectangle is a two-dimensional shape that has four straight sides and four right angles. To calculate the area of the rectangle, we can use the formula:Area = Length x Width.

In this case, the area of the rectangle is 12 inches x 6 inches = 72 square inches. The perimeter of the rectangle is the distance around the outside of the shape, which is calculated by adding the lengths of all four sides. In this case, the perimeter of the rectangle is 2 x (length + width) = 2 x (12 inches + 6 inches) = 2 x 18 inches = 36 inches.

It's important to note that the length and width of the rectangle can be interchanged and the area and perimeter will remain the same.In conclusion, Marisol's rectangle measures 12 inches long, 6 inches wide, 72 square inches in size, and has a circumference of 36 inches.

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So the three integers are 4, 6, and 8 such that 6 times the first integer is 10 more than the sum of the second and the third integers.

An integer is a whole number that does not have any fractional or decimal parts. Integers include positive numbers (1, 2, 3, etc.), negative numbers (-1, -2, -3, etc.), and zero (0).

Here,

Let's call the first even integer x. Since the three integers are consecutive even integers, the second and third integers are x + 2 and x + 4, respectively.

From the problem statement, we know that:

6x = (x + 2) + (x + 4) + 10

Simplifying the right side of the equation:

6x = 2x + 16

Subtracting 2x from both sides:

4x = 16

Dividing both sides by 4:

x = 4

Therefore, the three consecutive even integers are:

x = 4

x + 2 = 6

x + 4 = 8

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Complete question:

"There are three consecutive even integers such that 6 times the first integer is 10 more than the sum of the second and the third integers."  find the integers.

Step-by-step explanation:

It is an ODD  number  due to statement 1

it is a multiple of 5   due to the last statement

5   15   25   35   45  55  65  75    85  95  105   .....

When you divide by 3    there is a R 1

25    55    85    115    145

When you divide by 4  there is a R = 1

25   is the lowest number    next possible number is 145    then another posssible is 265    etc

Answer:

Step-by-step explanation:

To find the utility-maximizing bundle of goods, we need to solve for the values of x and y that maximize U while still satisfying the budget constraint. The budget constraint can be written as:

2x + 4y = 24

or

x + 2y = 12

We can use the method of Lagrange multipliers to solve for the utility-maximizing values of x and y subject to this constraint. The Lagrangian function is:

L = 3x^(2/3)y^(-1/3) + λ(x + 2y - 12)

Taking partial derivatives with respect to x, y, and λ, we get:

dL/dx = 2x^(-1/3)y^(-1/3) + λ = 0

dL/dy = -x^(2/3)y^(-4/3) + 2λ = 0

dL/dλ = x + 2y - 12 = 0

Solving these equations simultaneously, we get:

x = 6

y = 3

So the utility-maximizing bundle is 6 units of x and 3 units of y.

To see if the individual is better off with the government intervention, we can plot the budget line and the indifference curve for the utility-maximizing bundle with and without the limit on x.

Without the limit, the budget line is the same as before (x + 2y = 12), and the indifference curve for the utility-maximizing bundle passes through the point (6, 3) on the graph.

With the limit, the budget line becomes x = 4, since the individual is prohibited from purchasing more than 4 units of x. The corresponding budget line has a slope of -1/2 and intercepts the y-axis at 6.

If we draw the indifference curve for the utility-maximizing bundle of (4,4), which lies on the budget line, we can see that the individual is not better off with the government intervention. This is because the slope of the budget line under the intervention is steeper, so the individual would have to give up more y than x to afford the same amount of utility. Thus, the individual would have to move to a lower indifference curve with lower utility.

Therefore, the individual is not better off with the government intervention.

Each interior angles of the rectangle QUAD is equal to 90°, and the angles ∠2 and ∠5 are complementary, so the value of x = 4.

The angles ∠2 and ∠5 form one of the interior angles of a rectangle, hence they are complementary as they add up to 90°.

we shall solve for x as follows:

x + 30 + 2x - 48 = 90

3x + 78 = 90

3x = 90 - 78 {subtract 78 from both sides}

3x = 12

x = 12/3 {divide through by 3}

x = 4

In conclusion, each interior angles of the rectangle QUAD is equal to 90°, and the angles ∠2 and ∠5 are complementary, so the value of x = 4.

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Substituting for x in an expression means replacing the variable x with a specific value or expression. This is often done to evaluate the expression for that particular value or to simplify the expression.

Substituting 2 for x in the first expression, we get:

[tex]1/2(2) + 4(2) + 6 - 1/2(2) - 2 = 1 + 8 + 6 - 1 - 2 = 12[/tex]

Substituting 2 for x in the second expression, we get:

[tex]2(2) + 2 - 1 = 5[/tex]

One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.

Therefore, the first expression evaluated with x = 2 is 12, and the second expression evaluated with x = 2 is 5. Since they do not have the same value, the correct option is:

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The given question is incomplete. The complete question is given below:

What will be the result of substituting 2 for x in both expressions below? One-half x + 4 x + 6 minus one-half x minus 2 Both expressions equal 5 when substituting 2 for x because the expressions are equivalent. Both expressions equal 6 when substituting 2 for x because the expressions are equivalent. One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent. One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not equivalent.

5/16, 3/8, 7/16, 1/2

All you sre doing is adding 1/16 to each term then reducing it.

1/16 + 1/16 = 2/16

2/16 = 1/8

2/16 + 1/16 = 3/16

etc.

heres the simplest explanation:

all they are doing is counting and reducing

Reduce

1/16. 1/16

2/16. 1/8

3/16. 3/16

4/16. 1/4

5/16. 5/16

6/16. 3/8

7/16. 7/16

8/16. 1/2

Answer:

The sequence has a common difference of 1/16, which means to get the next term, we need to add 1/16 to the previous term.

The next four terms would be:

9/32 (1/4 - 1/16)

5/16 (1/4 + 1/16)

11/32 (5/16 + 1/16)

3/8 (11/32 + 1/16)

So the full sequence is: 1/16, 1/8, 3/16, 1/4, 9/32, 5/16, 11/32, 3/8, ...

The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)

Given that

Limit x tend to π 1-sinx/2(π-x) ²

To solve this expression, we make use of

If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L

The interpretation is that we solve the expression by direct substitution

So, we have

Limit = 1 - sin(π)/2(π - π) ²

Evaluate the difference

Limit = 1 - sin(π)/2(0)²

Evaluate the exponent and the bracket

Limit = 1 - sin(π)/0

Divide

Limit = ∝

Hence, the limit of the expression is ∝

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Answer:

the first answer is correct

Step-by-step explanation:

y=118x=118

Answer:$59.66

Step-by-step explanation:

Answer:

We can solve this expression using the order of operations, also known as PEMDAS:

2 + 77 + 2 + 4 + 18 + (9/4) + 5 + 23 + 78 + 33 - 76 - 4 + 12

First, we can simplify the fraction by adding the whole number and fraction parts:

2 + 77 + 2 + 4 + 18 + 2.25 + 5 + 23 + 78 + 33 - 76 - 4 + 12

Next, we can perform addition and subtraction from left to right:

= 187 + 2.25 + 68

= 257.25

Therefore, the value of the expression 2+77+2+4+18+9/4+5+23+78+33-76-4+12 is 257.25.

LOL the answer is 176.25

Answer:

-6

Step-by-step explanation:

a + 2b = -8       Eq. 1

a + b = -2          Eq. 2

From Eq. 1:

a = -8 -2b           Eq. 3

From Eq. 2:

a = -2 -b             Eq. 4

Equalizing Eq. 3 & Eq. 4:

-8 -2b = -2 -b

-2b + b = -2 + 8

-b = 6

b = -6

From Eq. 4

a = -2 - (-6)

a = -2 + 6

a = 4

Check:

From Eq. 1:

a + 2b = -8

4 + 2*-6 = -8

4 - 12 = -8

Answer:

-6<4

Then;

The lesser number is:

-6

Answer:

To calculate the amount of interest Marissa will earn in 8 years on her savings account, we can use the formula for simple interest:

I = P * r * t

where:

I = interest earned

P = principal (initial amount in the account)

r = interest rate per year (as a decimal)

t = time period (in years)

Plugging in the given values, we get:

I = $350 * 0.039 * 8

I = $109.20

Therefore, Marissa will earn $109.20 in interest over 8 years.

The remainders of the polynomial divison are 18, -9, 10 and 0 and the factor are (x + 2)(3x² + 2x - 1) and (x - 2)(x² - 2x - 15)

The remainder theorem states that

Given the polynomial f(x) divided by x - a, the remainder is b if

f(a) = b

So, we have

Polynomial (10)

(x² + 9) ÷ (x - 3)

Remainder = 3² + 9

Remainder = 18

This means that

x - 3 is not a factor of (x² + 9)

Polynomial (11)

(x³ - 4x + 6) ÷ (x + 3)

Remainder = (-3)³ - 4(-3) + 6

Remainder = -9

This means that

x + 3 is not a factor of (x³ - 4x + 6)

Polynomial (12)

(x⁴ + 4x³ + 16x - 35) ÷ (x + 5)

Remainder = (-5)⁴ + 4(-5)³ + 16(-5) - 35

Remainder = 10

This means that

x + 5 is not a factor of x⁴ + 4x³ + 16x - 35

Polynomial (13)

(2x³ - 10x² - 71x - 9) ÷ (x - 9)

Remainder = 2(9)³ - 10(9)² - 71(9) - 9

Remainder = 0

This means that

x - 9 is a factor of 2x³ - 10x² - 71x - 9

Polynomial (14)

Using a synthetic method of quotient, we have the following set up

-2 |   3    8   3  -2

    |__________

Multiply -2 by 3 to get -6, and write it below the next coefficient and repeat the process

-2 |   3    8   3  -2

    |____-6_-4_2____

       3     2 -1     0

So, the factor is (x + 2)(3x² + 2x - 1)

Polynomial (15)

Using a synthetic method of quotient, we have the following set up

2 |   1    -4   -11  + 30

   |__________

Multiply 2 by 1 to get 3, and write it below the next coefficient and repeat the process

2 |   1    -4   -11  + 30

   |____2__-4_-30__

       1    -2    -15   0

So, the factor is (x - 2)(x² - 2x - 15)

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