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2 years ago

Is (x+1) a factor of the function f(x) = 7x^4 – 5x^3 – 10x² + 2x, and why?

Mathematics

1 answer:

Schach [20]2 years ago

7 0

Answer:

first option

Step-by-step explanation:

If ( x + h) is a factor of f(x) then f(- h) = 0 , then

If (x + 1) is a factor of f(x) then f(- 1) = 0

f(- 1) = 7 $(-1)^{4}$ - 5(- 1)³ - 10(- 1)² + 2(- 1)

= 7(1) - 5(- 1) - 10(1) - 2

= 7 + 5 - 10 - 2

= 12 - 12

= 0

Since f(- 1) = 0 then (x + 1) is a factor of f(x)

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Pie

$\bold{\huge{\underline{ Solution }}}$

We have, 

Line segment AB
The coordinates of the midpoint of line segment AB is ( -8 , 8 )
Coordinates of one of the end point of the line segment is (-2,20)

Let the coordinates of the end point of the line segment AB be ( x1 , y1 ) and (x2 , y2)

Also, 

Let the coordinates of midpoint of the line segment AB be ( x, y)

We know that,

For finding the midpoints of line segment we use formula :-

$\bold{\purple{ M( x, y) = }}{\bold{\purple{\dfrac{(x1 +x2)}{2}}}}{\bold{\purple{,}}}{\bold{\purple{\dfrac{(y1 + y2)}{2}}}}$

According to the question,

The coordinates of midpoint and one of the end point of line segment AB are ( -8,8) and (-2,-20) .

For x coordinates :-

$\sf{ -8 = }{\sf{\dfrac{(- 2 +x2)}{2}}}$

$\sf{2}{\sf{\times{ -8 = - 2 + x2 }}}$

$\sf{ - 16 = - 2 + x2 }$

$\sf{ x2 = -16 + 2 }$

$\bold{ x2 = -14 }$

For y coordinates :-

$\sf{ 8 = }{\sf{\dfrac{(- 20 +x2)}{2}}}$

$\sf{2}{\sf{\times{ 8 = - 20 + x2 }}}$

$\sf{ 16 = - 20 + x2 }$

$\sf{ y2 = 16 + 20 }$

$\bold{ y2 = 36 }$

Thus, The coordinates of another end points of line segment AB is ( -14 , 36)

Hence, Option A is correct answer

7 0

2 years ago

325 students and 36 students are going to college. What’s that percentage?

aleksklad [387]

Answer: 11% of students go to college

Step-by-step explanation: So simply take 36/325 since only 36 are going to college, divide and you get roughly 11%

5 0

2 years ago

A quantity with an initial value of 7600 decays exponentially at a rate of 55% every 7 days. What is the value of the quantity a

attashe74 [19]

Answer:

1539

Step-by-step explanation:

We solve the above question using the Exponential decay formula

= A(t) = Ao(1 - r) ^t

Ao = Initial Amount invested = 7600

r = Decay rate = 55% = 0.54

t = time in weeks = 2

Hence:

A(t) = 7600(1 - 0.55)²

A(t) = 7600 × (0.45)²

A(t) = 1539

Therefore, the value of the quantity after 2 weeks is 1539

6 0

3 years ago

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lisov135 [29]

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2 years ago

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Dafna1 [17]

Answer:

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Step-by-step explanation:

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2 years ago