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kramer
3 years ago
7

The sum of a whole number and twice its square is 21. Find the whole number

Mathematics
1 answer:
I am Lyosha [343]3 years ago
6 0
SOLUTION:

Let whole number = x

x + 2x^2 = 21

2x^2 + x - 21 = 0

2x^2 + 7x - 6x - 21 = 0

x ( 2x + 7 ) - 3 ( 2x + 7 ) = 0

( 2x + 7 ) ( x - 3 ) = 0


2x + 7 = 0

2x = - 7

x = - 7 / 2

OR

x - 3 = 0

x = 3


ANSWER:

Therefore, as 3 is a whole number while - 7 / 2 isn't a whole number, the whole number must be 3.

Hope this helps! :)
Have a lovely day! <3
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Similar triangles may or may not have equal side lengths

Triangles ABC and DEF are similar by SSS theorem

<h3>How to determine the similarity statement</h3>

The coordinates of the two triangles are:

A (0,0), B (4,0), C (0,2), D (0,0), E (2,0), and F (0,1)

Calculate the lengths of both triangles using the following distance formula

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

For triangle ABC, we have:

AB = \sqrt{(0 -4)^2 + (0 -0)^2} = 4

BC = \sqrt{(4 -0)^2 + (0 -2)^2} = 2\sqrt 5

CA = \sqrt{(0 -0)^2 + (0 -2)^2} = 2

For triangle DEF, we have:

DE = \sqrt{(0 -2)^2 + (0 -0)^2} = 2

EF = \sqrt{(2 -0)^2 + (0 -1)^2} = \sqrt 5

FD = \sqrt{(0 -0)^2 + (1 -0)^2} = 1

Divide corresponding sides of the triangles to calculate the scale factor k

k = \frac{AB}{DE} = \frac{BC}{EF} = \frac{CA}{FD}

This gives

k = \frac{4}{2} = \frac{2\sqrt 5}{\sqrt 5} = \frac{2}{1}

Evaluate the quotients

k = 2 = 2 = 2

Since the quotients are equal, then the triangles are similar

Hence, triangles ABC and DEF are similar by SSS theorem

Read more about similar triangles at:

brainly.com/question/14285697

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