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3 years ago

2) Find the remainder when x3 + x2 - 20 is divided by

Mathematics

1 answer:

Dahasolnce [82]3 years ago

4 0

Answer:

Remainder = –24

Step-by-step explanation:

x³ + x² – 20 divide by x + 2

We can obtain the remainder when

x³ + x² – 20 is divided by x + 2 using the remainder theorem as follow:

We'll begin by calculating the value of x from x + 2. This is illustrated below:

x + 2 = 0

Collect like terms

x = 0 – 2

x = –2

Finally, we shall determine the remainder by substituting –2 for x in

x³ + x² – 20. This is illustrated below:

x³ + x² – 20

x = –2

Remainder = (–2)³ + (–2)² – 20

Remainder = –8 + 4 – 20

Remainder = –24

Therefore, the ramainder when

x³ + x² – 20 is divided by x + 2 is –24

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Answer:

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Step-by-step explanation:

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3 years ago

. Write 2:3 in the form of 1:n

artcher [175]

Answer:

1 : 1.5

Step-by-step explanation:

Given the ratio

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3 years ago

Read 2 more answers

Solve for x given that <br><img src="https://tex.z-dn.net/?f=%20%7B64%7D%5E%7B2x%20-%201%7D%20%3D%20%20%7B32%7D%5E%7Bx%20%2B%201

marissa [1.9K]

Answer:

x = $\frac{11}{7}$

Step-by-step explanation:

note that 64 = $2^{6}$ and 32 = $2^{5}$ , thus

$(2^{6}) ^{2x-1}$ = $(2^{5}) ^{x+1}$ , that is

$2^{6(2x-1)}$ = $2^{5(x+1)}$

$2^{12x-6}$ = $2^{5x+5}$

Since the bases on both sides are equal, then equate the exponents

12x - 6 = 5x + 5 ( subtract 5x from both sides )

7x - 6 = 5 ( add 6 to both sides )

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4 years ago

The perimeter of a basketball court is 9696 meters and the length is 6 meters longer than twice the width. what are the length a

irina1246 [14]

P=2(l+w) = 9696
-> l+w= 9696/2= 4848
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4 years ago

Lesson 4.10 - Analytic Geometry

Nadusha1986 [10]

Geometric shapes are mathematical shapes that include squares and triangles

<h3>How to prove the shape is a square</h3>

The side lengths of a square are congruent, and the adjacent sides are perpendicular.

So, we start by calculating the side lengths using the following distance formula

$d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}$

Using the above formula, we have:

$AB = \sqrt{(3-2)^2 + (4+2)^2} = \sqrt{37$

$BC = \sqrt{(2+4)^2 + (-2+1)^2} = \sqrt{37$

$CD = \sqrt{(-4+3)^2 + (-1-5)^2} = \sqrt{37}$

$DA = \sqrt{(-3-3)^2 + (5-4)^2} = \sqrt{37}$

The above shows that the side lengths of the square are congruent.

Next, calculate the slope of the sides using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{AB} = \frac{4 +2}{3 -2} = 6$

$m_{BC} = \frac{-2 + 1}{2+4} = -\frac 16$

$m_{CD} = \frac{-1 -5}{-4+3} = 6$

$m_{DA} = \frac{5 -4}{-3-3} = -\frac 16$

Notice that the opposite slopes are congruent, and the adjacent slopes are opposite reciprocal.

The above highlight, and the equal side lengths show that the figure (1) is a square

<h3>How to prove the shape is a right isosceles triangle</h3>

The legs of a right isosceles triangle are congruent, and the legs are perpendicular.

So, we start by calculating the lengths of the legs using the following distance formula

$d = \sqrt{(x_1 -x_2)^2 + (y_1 -y_2)^2}$

Using the above formula, we have:

$XY = \sqrt{(5-4)^2 + (-1-4)^2} = \sqrt{26$

$XZ = \sqrt{(5-0)^2 + (-1+2)^2} = \sqrt{26$

The above shows that the legs of the right isosceles triangle are congruent.

Next, calculate the slope of the legs using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m_{XY} = \frac{5-4}{-1 -4} = -\frac{1}{5}$

$m_{XZ} = \frac{5-0}{-1+2} = 5$

Notice that the slopes are opposite reciprocal.

The above highlight, and the equal legs show that the figure (2) is a right isosceles triangle

Read more about geometric shapes at:

brainly.com/question/14285697

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3 years ago