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3 years ago

Start with x2 + 4x = 12 and complete the square, what is the equivalent equation?

Mathematics

1 answer:

IgorLugansk [536]3 years ago

3 0

Answer:

(x + 2)² = 16

Step-by-step explanation:

Given

x² + 4x = 12

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 12 + 4, that is

(x + 2)² = 16

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the frame of a picture is 28 cm by 32 cm outside and is of uniform width.What is the width of the frame if 192 cm2 of the pictur

natita [175]

Answer:

The width of the frame is equal to $8\ cm$

Step-by-step explanation:

Let

x-------> the width of the frame picture

we know that

$(28-2x)(32-2x)=192$

$896-56x-64x+4x^{2} =192$

$4x^{2}-120x+704=0$

Simplify

$x^{2}-30x+176=0$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$x^{2}-30x+176=0$

$a=1\\b=-30\\c=176$

substitute in the formula

$x=\frac{30(+/-)\sqrt{(-30)^{2}-4(1)(176)}} {2(1)}$

$x=\frac{30(+/-)\sqrt{196}} {2}$

$x=\frac{30(+/-)14} {2}$

$x=\frac{30+14} {2}=22\ cm$ ----> this solution is not logic

$x=\frac{30-14} {2}=8\ cm$

The width of the frame is equal to $8\ cm$

8 0

4 years ago

State of the triangles in each pair are similar. If so, state how you know they are similar and complete the similarity statemen

Blababa [14]

Answer:

SSS, UVD, the answer is D

Step-by-step explanation:

90/9 = 10

70/7 = 10

80/8 = 10

triangle LMN congruent triangle UVD

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3 years ago

What expression can be used to 80% of 120

12345 [234]

Answer:

59%

Step-by-step explanation:

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4 years ago

Read 2 more answers

frank has two same size rectangles divided into the same number of equal parts. one rectangle has 3/4 of the parts shaded, and t

lidiya [134]

This question basically asks for the LCM of 3 and 5, which is 3 x 5 =15
This is the answer: 15
Check : The first rectangle had 1/3 shaded; ( one in every three parts)
So for 15 parts altogether, 5 would be shaded ( 1/3 = 5/15)
The second rectangle had 2/5 shaded ( two for every five parts)
So for 15 parts altogether, 6 would be shaded (2/5 = 6/15)

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3 years ago

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Arisa [49]

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<h3>What is the parabola?</h3>

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.