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3 years ago

What is the remainder when when f(x)=x3+3x2−10x−14 is divided by (x-4) ?

Mathematics

1 answer:

Lera25 [3.4K]3 years ago

7 0

Answer:

Step-by-step explanation:

With Horner's Method.

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Chris earns a fixed amount of money every month. At the end of 2 years, chris had earned $86,688. He earned $ each year. He earn

dmitriy555 [2]

Answer:

Chris earned $ 43,344 each year

Monthly Chris earns $ 3,612

Step-by-step explanation:

If you earn a fixed amount of money each month, for 2 years and one year you have 12 months, then 2 years equals 24 months.

To know how much you earn each month we divide the total amount earned in the two years between 24 months

I = $ 86,688 / 24

I = $ 3,612

Monthly Chris earns $ 3,612

To calculate what he earned each year we divided $ 86,688 / 2

I = $ 86,688 / 2

I = $ 43,344

Chris earned $ 43,344 each year

6 0

3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

Slope:

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

Slope:

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

4 years ago

If a student did not travel to a Spanish-speaking country, how many times more likely is it that the student did not take Spanis

olasank [31]

Answer:

It is 2.2 times as likely.

3 0

3 years ago

It is given 5 and h + 1 are the roots of the quadratic equation x² + (k - 1)x - 5 = 0,where h and k are constant.Find the value

Liono4ka [1.6K]

Answer:

Hello,

k=-3 and h=-2

Step-by-step explanation:

$5\ is\ a \ root \of \ x^2+(k-1)*x-5=0\\\\5^2+(k-1)*5-5=0\\\\5*(k-1)+20=0\\\\k-1=\dfrac{-20}{5} \\\\k=-4+1\\\\\boxed{k=-3}\\$

h+1 is thus a root of x²+(-3-1)*x-5=0

x²-4x-5=0

x²+x-5x-5=0

x(x+1)-5(x+1)=0

(x+1)(x-5)=0

h+1=-1

h=-2

6 0

3 years ago

Please help!! is it 16?

sweet-ann [11.9K]

Answer:

area of trapezium: -

formula...

½(sum of parallel sides)×height=area

=>240=½(12+x)×12

=>240=(12+x)×6

=>240=60+6x

=>6x=240-60

=>6x=180

=>x=180/6

=>x=30cm

therefore, the value of x is 30 cm.

Step-by-step explanation:

hope it helps u

6 0

2 years ago