Find the quotient and remainder using synthetic division for
x³ + 7x² + 12x + 5
x+2
The quotient is

The compound interest is obtained as $91.81, rounded off to the nearest hundredth.

In order to compute compound interest, multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. You will then be left with the principal amount of the loan plus compound interest. The entire compound interest is then obtained by deducting the initial principal.

The equation that results will look like this:

Compound Interest = [tex]P(\left(1+r\right)^{ t}-1)[/tex]

Amount, rate of interest and time is given as $1500, 2% and 3 years respectively.

First, change r as a percent to r as a decimal.

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for compound interest.

[tex]\text{Compound Interest}=1500(\left(1+0.02\right)^{3}-1)\\=1500(1.061208-1)\\=15000\cdot 0.061208\\\\=91.81[/tex]

So, the compound interest is obtained as $91.81, rounded off to the nearest hundredth.

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Answer: its 1591.81

Step-by-step explanation:

I took the test and tried with the answer on top and got it wrong.

The expression that equals semantics -1 D is - 2x² + x + 15.

One or more terms in an algebraic expression each include variables and constants. These expressions utilize separators like +, -, and that are symbols or operations. An algebraic statement with variables and constants is a quadratic trinomial. It is written as ax² + bx + c, where a, b, and c are real non-zero values and x is the variable. The leading coefficient "a," linear coefficient "b," and additive constant "c" all refer to the same constant.

The given trinomial is D = 2x² - x - 15

Multiply both sides by -1 to find -1D

-1D = -( 2x² - x - 15) = 0

-1 D = - 2x² + x + 15

So, this is the trinomial equal to the semantics -1D.

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Answer:

- 90

Step-by-step explanation:

substitute x = - 2 into f(x)

f(- 2) = 3[tex](-2)^{5}[/tex] - [tex](-2)^{4}[/tex] - 6(- 2) + 10

        = 3(- 32) - (16) + 12 + 10

        = - 96 - 16 + 22

        = - 112 + 22

        = - 90

[tex]{ \boxed{ \sf{f( - 2) = - 90}}}[/tex]

Step-by-step explanation:

[tex]{ \red{ \tt{f(x) = {3x}^{5} - {x}^{4} - 6x + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( { - 2})^{5} - ( { - 2})^{4} - 6( - 2) + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = 3( - 32) - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 96 - 16 + 12 + 10}}}[/tex]

[tex]{ \red{ \tt{f( - 2) = - 112 + 22}}}[/tex]

[tex]{ \green{ \boxed{ \bold{f( - 2) = - 90}}}}[/tex]

Answer:

The answer for number 7 is A

Step-by-step explanation:

I hope this helps

The Laplace transform of the given integral function is 1/s +4 / (s²+16) .

The integral transform, commonly known as the Laplace transform in mathematics, converts a function of either a real variable t in the time domain into a function of something like a complex variable s.

The Laplace transform is equal to the integral for the suitable functions

[tex]{\displaystyle {\mathcal {L}}\{f(t)\}(s)=\int _{0}^{\infty }f(t)e^{-st}\,dt.}[/tex]

Now we will use this to find the suitable Laplace transform of the trigonometric function:

(sin 2t-cos 2t)²

= sin² 2t + cos² 2t - 2sin 2tcos 2t

= 1 - sin 4t

Now we will use the Laplace transform of  the function.

L [1 - sin 4t] = L[1] - L[sin 4t]

Now L[1] = 1/s

L[sin 4t] = 4/ (s²+4²) = 4 / (s²+16)

Hence the Laplace transform will be

L [1 - sin 4t]  = 1/s +4 / (s²+16)

Pierre-Simon Laplace invented the complex frequency domain, often known as the s-domain or the s-plane. There are numerous uses for the transform, a method for solving differential equations, in both science and engineering.

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The slope of the line is - 2 with the equation as 2 x + y - 2 = 0

We are given that:

y intercept of the line = 2

Point is (0, 2)

It is parallel to the line 2 x + y = - 5

Slope of line 2 x + y = - 5:

y' = - 2

m = - 2

Slope of parallel lines are equal

m = m'

m' = - 2

Equation of the line:

y - y₁ = m( x - x₁)

y - 2 = - 2( x - 0)

y - 2 = - 2 x

2 x + y - 2 = 0

a) standard form of the equation = 2 x + y - 2 = 0

b) slope of the line = m' = - 2

c) point-slope form = (y - 2) / (x - 0) = - 2

d) Properties of algebra used = cross multiplication and simplification.

Therefore, we get that, the slope of the line is - 2 with the equation as 2 x + y - 2 = 0

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The number of cupcakes sold will be 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that, in the first hour, Brady sold 1/3 cupcakes and Jaquan sold 3/8 cupcakes. During the second hour, they sold 2 cupcakes. During the third hour, they sold 75% of the remaining cupcakes. During the fourth hour, they sold the remaining 3 cupcakes.

The number of cupcakes sold will be,

N = (1/3) + (3/8) +[(2-1/3-3/8)]+3

N = (1/3)+(3/8) + (7/24)

N = 96 / 24

N = 4

Therefore, the number of cupcakes sold will be 4.

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The number of rotations is 172.

Rotation is a circular movement about the specific axis or point of rotation. The two most prevalent directions for rotation are clockwise and counterclockwise, or anti-clockwise.

Rotation simply means going around a central point. Any point on the shape has a constant distance from the center.

Given, the clockwise rotation is by 62,000°.

To find the number of rotation (n),

[tex]n = \frac{62000}{360}[/tex]

n = 172.2

Therefore, the number of rotations is 172.

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The first number is 3 and the second number is -5.

According to the question,

We have the following information:

There are two mystery numbers. The sum of 6 times the first number and 4 times the second number is -2. The sum of 6 times the first number and 2 times the second number is 8.

Now, let's take the first number to be x and the second number to be y.

So, we have the following expressions:

6x+4y = - 2

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

6x+2y = 8

Putting the value of 6x from equation 1:

-2-4y+2y = 8

-2-2y = 8

-2y = 8+2

-2y = 10

y = -10/2

y = -5

Putting this value of y in equation 1:

6x = -2-4y

6x = -2-4*(-5)

6x = -2+20

6x = 18

x = 18/6

x = 3

Hence, the first number is 3 and the second number is -5.

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The total cost of the hooded sweatshirts will be 29 × 31 = $899.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers by each other to find a new multiplied number.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Number of hooded sweatshirts = 29

Cost of one hooded sweatshirt = $31

Total cost = 29 × 31 = $899.

Hence "The total cost of the hooded sweatshirts will be 29 × 31 = $899".

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By taking some simple quotients, we will see that the cost per student is:

$26.36

First, we know that the school spends $643.34 on passes for 38 people, then the cost of each pass is given by the quotient:

p = $643.34/38 = $16.93

Then there is also lunch for the 36 students, which costed $339.48, then the cost in lunch per student is.

l = $339.48/36 = $9.43

The total cost per student is:

$16.93 + $9.43 = $26.36

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In the equation given 2[(4m * 3.5) / 400] = 171.5, m has a value of 2450.

Equations are mathematical statements containing two algebraic expressions on both sides of an equal to sign. This can be expressed as the relationship of equality between the expression written on the left side with the expression written on the right side. Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

In the equation given;

2[(4m * 3.5) / 400] = 171.5

We can find the value of m by applying changing the subject of formula

2[(4m * 3.5) / 400] = 171.5

28m / 400 = 171.5

28m = 400 * 171.5

28m = 68600

m = 68600 / 28

m = 2450

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Answer:

answer should be d

Step-by-step explanation:

it's d because if u fraction 6 u will get d

Answer:

[tex]x\leq -7 or x > -2[/tex]

Step-by-step explanation:

-8x+14 ≥ 60 or - 4x + 50 < 58
     -8x ≥ 56 or         - 4x < 8
        [tex]x \leq -7[/tex] or            [tex]x > -2[/tex]

Answer:

$318.90

Step-by-step explanation:

Turn the percent into a decimal and multipy it by 344.76

0.075 × 344.76 = 25.857

after you get your answer you subtract 344.76 and 25.857

$344.76 - 25.857 = $318.903

round you answer to the nearest cent

= $318.90

The coordinate of point C will be (5, 5). Then the correct option is A.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

On a direction plane, the place of two companions can be characterized by the focuses A(1,3) and B(7,6). Their instructor is remaining at point C, and the educator's separation from point An is two times the separation from Point B.

The ratio is given as 2:1.

x = (7 × 2 + 1 × 1) / (2 + 1)

x = 15 / 3

x = 5

y = (6 × 2 + 1 × 3) / (2 + 1)

y = 15 / 3

y = 5

The coordinate of point C will be (5, 5). Then the correct option is A.

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Answer:

4

Step-by-step explanation:

5-3m>-10

-5.     -5

-3m>-15

/-3.   /-3

m<5

so 4 is the highest integer since 4 is less than 5

Hopes this helps please mark brainliest

The probability that a single lottery has one correct number, using the hypergeometric distribution, is of:

0.4159 = 41.59%.

The probability mass function of the hypergeometric distribution is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

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

The parameters of the function are listed as follows:

In the context of this problem, the values of these parameters are given as follows:

N = 40, k = 7, n = 7.

The probability that a single lottery has one correct number is P(X = 1), hence x = 1 and the calculation is as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 1) = h(1,40,7,7) = \frac{C_{7,1}C_{33,6}}{C_{40,7}} = 0.4159[/tex]

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Applying the definition of exterior angle of a triangle, the value of m is: m = 32.

An exterior angle of a triangle can be defined as the angle formed outside the triangle when one of its side is extended.

The exterior angle to an interior angle, is supplementary to the interior angle. That is, they have a sum of 180 degrees when we add their angle measures together.

Given the following:

Measure of angle Z = 4m - 15

Measure of the exterior angle to angle Z = 2m + 3

Therefore:

4m - 15 + 2m + 3 = 180

Combine like terms

6m - 12 = 180

6m = 180 + 12

6m = 192

6m/6 = 192/6

m = 32

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The required pounds of peanut that can make one pound of peanut butter is given as 5 1/3

If  2/3 pounds of peanut = 1/8 pounds of peanut butter

? quantity of peanut = one pound of peanut butter

This would be better expressed in numbers as

2/3 = 1/8

? = 1

To solve for this , we would have to cross multiply

such that we would have

2/3 = 1/8?

to get the unknown, we have to divide through by 1/8

2/3 ÷ 1/8 = unknown

2/3 x 8/1

= 16/3

= 5 1/3

Hence the required pound that would be needed to make the peanut butter is given as 5 1/3

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Answer:

Step-by-step explanation:

50

Answer:

No, the point is on the x-axis, it is not a y-intercept.

Answer: ZYH

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!!

Step-by-step explanation:

1:

1/5 of 90 = 18 hours which are sold.Means are 72 houses left.

2.

1/3 of 72 =24 houses sold again. Sooo means there are 48 houses left to be sold

Answer: number 3

explanation: I took the

Answer:

A, C, D, E

Step-by-step explanation:

17 is a positive whole number

All whole numbers are integers and rational

Natural numbers are numbers that are positive whole numbers

It is real since you don't have any negative roots

Cash 2300

Accumulated Depreciation  4940

Gain one of fixtures 240

Store fixtures  7000

From the question, we have

Bonham’s Bakery sold shelving units (store fixtures) that were 13 years old for $2,300 cash.

Accumulated Depreciation = (7000-1300)/15*13

=4940

Gain one of fixtures = 240

Store fixtures = 7000

Multiplication:

Mathematicians multiply the numbers in order to calculate the sum of two or more. A fundamental mathematical operation, it is applied frequently in daily life. In order to combine groups of similar sizes, we use multiplication. An illustration of the fundamental concept of repeated addition of the same number is multiplication. The product of two or more numbers refers to the result of the multiplication, and the factors are the amounts that are being multiplied. It is easier to add the same number repeatedly after it has been multiplied.

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