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3 years ago

When x3+ cx + 4 is divided by (x + 2), the remainder is 4. Find the value of c.

Mathematics

1 answer:

never [62]3 years ago

6 0

Answer:

-4

Step-by-step explanation:

x³ + cx + 4 divided by x + 2 has a remainder of 4, so:

(x³ + cx + 4) / (x + 2) = ax² + bx + d + 4 / (x + 2)

Multiply both sides by x + 2:

x³ + cx + 4 = (ax² + bx + d) (x + 2) + 4

Distribute:

x³ + cx + 4 = ax²(x + 2) + bx(x + 2) + d(x + 2) + 4

x³ + cx + 4 = ax³ + 2ax² + bx² + 2bx + dx + 2d + 4

x³ + cx + 4 = ax³ + (2a + b)x² + (2b + d)x + 2d + 4

Match the coefficients.

a = 1

2a + b = 0

2b + d = c

2d + 4 = 4

Solving, a = 1, b = -2, and d = 0. So c = -4.

We can also solve this using long division (see picture).

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Use the following table for questions 11-13.A baseball manager believes a linear relationship exists between the number of Home

slamgirl [31]

The regression equation of Y on X is given by the following formula:

$Y-\bar{Y}=b_{yx}(X-\bar{X})$

Where byx is given by the formula:

$b_{yx}=\frac{N\sum^{}_{}XY-\sum^{}_{}X\sum^{}_{}Y}{N\sum^{}_{}X^2-(\sum^{}_{}X)^2}$

Where N is the number of values (N=8). We need to find the sum of X values, the sum of Y values, the average of X, the average of Y, the sum of X*Y and the sum of X^2.

The table of values is:

The values we need to know are on the following table:

By replacing the known values in the formula we obtain:

$\begin{gathered} b_{yx}=\frac{8\cdot26125-167\cdot995}{8\cdot4649-(167)^2} \\ b_{yx}=\frac{209000-166165}{37192-27889} \\ b_{yx}=\frac{42835}{9303} \\ b_{yx}=4.6 \end{gathered}$

Now, the average of X and Y is the sum divided by N, then:

$\begin{gathered} \bar{X}=\frac{167}{8}=20.87 \\ \bar{Y}=\frac{995}{8}=124.37 \end{gathered}$

Replace these values in the formula and find the regression equation as follows:

$\begin{gathered} Y-124.37=4.6(X-20.87) \\ Y-124.37=4.6X-4.6\cdot20.87 \\ Y=4.6X-96.11+124.37 \\ Y=4.6X+28.26 \end{gathered}$

The answer is a) y=4.6x+28.26

7 0

2 years ago

Questions on the images

KiRa [710]

Answer: A

Step-by-step explanation:

12 x 12 = 144

39 x 39 = 1521

1521 - 144 = 1377

root 1377 = 37.1

6 0

3 years ago

Read 2 more answers

Solve the system of equations algebraically by using substitution method:

vredina [299]

Answer:

This system has infinite solutions and it would be much easier to solve it by elimination but substitution it is.

Step-by-step explanation:

-3x+3y=9

-x+y=3

Isolate either x or y in any of the equations. I'll go with the second.

y = 3+x

Now substitute this for y in the first equation.

-3x+3(3+x)=9

Distribute the 3

-3x+9+3x=9

Combine like terms:

9=9

0=0

It's infinite

3 0

3 years ago

Compare -1 3/4 -1 1/4

LUCKY_DIMON [66]

Answer:

-1 1/4 is greater than -1 3/4

Step-by-step explanation:

Positive and negative numbers are different. the bigger the positive number, the greater it is. The smaller the negative number, the greater it is.

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3 years ago

X=4y+7 2x-6y=12 System of equations using substitution

Sonja [21]

Answer:

x=3, y=-1

Step-by-step explanation:

We are already given an equation solved for x, making substitution much easier. We know x=4y+7, meaning we can put 4y+7 whenever we see x in the second equation

2x-6y=12

We substitute 4y+7 in place of x

2(4y+7)-6y=12

Now we only have one variable to work on, distribute the 2

8y+14-6y=12

Combine similar terms, 8y-6y=2y

2y+14=12

Subtract 14 from both sides

2y=-2

y=-1

Now we plug in -1 for y in the first equation to find x

x=4(-1)+7

x=-4+7

x=3

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3 years ago