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3 years ago

Find the remainder when f(x) = x3 − 14x2 + 7x − 10 is divided by x − 3.

Mathematics

1 answer:

serious [3.7K]3 years ago

4 0

Answer: -88

Step-by-step explanation:

To find the remainder, you can use long division, synthetic division, or input the x-value. I am going to input because it is the fastest method.

f(x) = x³ - 14x² + 7x - 10 divided by x - 3 = 0 ---> x = 3

f(3) = 3³ - 14(3)² + 7(3) - 10

= 27 - 126 + 21 - 10

= -88

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For which system of equations is (5, 3) the solution? A. 3x – 2y = 9 3x + 2y = 14 B. x – y = –2 4x – 3y = 11 C. –2x – y = –13 x

Alla [95]

The correct answer is:

D) $\left \{ {{2x-y=7} \atop {2x+7y=31}} \right.$ .

Explanation:

We solve each system to find the correct answer.

For A:
$\left \{ {{3x-2y=9} \atop {3x+2y=14}} \right.$

Since we have the coefficients of both variables the same, we will use elimination to solve this.

Since the coefficients of y are -2 and 2, we can add the equations to solve, since -2+2=0 and cancels the y variable:
$\left \{ {{3x-2y=9} \atop {+(3x+2y=14)}} \right. 
\\
\\6x=23$

Next we divide both sides by 6:
6x/6 = 23/6
x = 23/6

This is not the x-coordinate of the answer we are looking for, so A is not correct.

For B:
$\left \{ {{x-y=-2} \atop {4x-3y=11}} \right.$

For this equation, it will be easier to isolate a variable and use substitution, since the coefficient of both x and y in the first equation is 1:
x-y=-2

Add y to both sides:
x-y+y=-2+y
x=-2+y

We now substitute this in place of x in the second equation:
4x-3y=11
4(-2+y)-3y=11

Using the distributive property, we have:
4(-2)+4(y)-3y=11
-8+4y-3y=11

Combining like terms, we have:
-8+y=11

Add 8 to each side:
-8+y+8=11+8
y=19

This is not the y-coordinate of the answer we're looking for, so B is not correct.

For C:
Since the coefficient of x in the second equation is 1, we will use substitution again.

x+2y=-11

To isolate x, subtract 2y from each side:
x+2y-2y=-11-2y
x=-11-2y

Now substitute this in place of x in the first equation:
-2x-y=-13
-2(-11-2y)-y=-13

Using the distributive property, we have:
-2(-11)-2(-2y)-y=-13
22+4y-y=-13

Combining like terms:
22+3y=-13

Subtract 22 from each side:
22+3y-22=-13-22
3y=-35

Divide both sides by 3:
3y/3 = -35/3
y = -35/3

This is not the y-coordinate of the answer we're looking for, so C is not correct.

For D:
Since the coefficients of x are the same in each equation, we will use elimination. We have 2x in each equation; to eliminate this, we will subtract, since 2x-2x=0:

$\left \{ {{2x-y=7} \atop {-(2x+7y=31)}} \right. 
\\
\\-8y=-24$

Divide both sides by -8:
-8y/-8 = -24/-8
y=3

The y-coordinate is correct; next we check the x-coordinate Substitute the value for y into the first equation:
2x-y=7
2x-3=7

Add 3 to each side:
2x-3+3=7+3
2x=10

Divide each side by 2:
2x/2=10/2
x=5

This gives us the x- and y-coordinate we need, so D is the correct answer.

7 0

3 years ago

Find the value of f(-1) for the function below

mrs_skeptik [129]

Put the value of x = -1 to the equation of a function f(x):

$f(x)=\dfrac{2}{3}\times3^{3x+12}\\\\f(-1)=\dfrac{2}{3}\times3^{3(-1)+12}=\dfrac{2}{3}\times3^{-3+12}=\dfrac{2}{3}\times3^9=\dfrac{2}{1}\times3^8=13,122\to\boxed{B.}$

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4 years ago

A salesperson sold 30% of their books in stock on Monday. Then they sold 60% of their remaining books on Tuesday. What percent o

Valentin [98]

Answer:

10%

Step-by-step explanation:

60% + 30%=90%

so they have 10%of the original amount left.

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4 years ago

Helpppp me pleaseee

mixer [17]

Answer:

1 st questions answer is third option

while the answer of other question is 3

Step-by-step explanation:

2nd qestions explanation

put value of x=2 in equation as x-2=0 from equation

(2)^3-6(2)^2+a2+10=2

8-24+a2+10=0

2a=-18+24

2a=6

a=3

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3 years ago

A furniture store had a chair that cost $33. After a few months the owner owner took 9% off the price. How much is the chair now

yawa3891 [41]

Answer:

$30.03

Step-by-step explanation:

To find what 9% of 33 is we need to divide 9% by 1

9% ÷ 1 = 2.97

33 - 2.97 = 30.03

4 0

3 years ago

Read 2 more answers