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marissa [1.9K]
3 years ago
8

Two angles are supplementary. One angle is 40° more than three times the other. Find the measure of each angle.

Mathematics
2 answers:
Art [367]3 years ago
5 0
4x+40=180
4x=180-40
4x=140
x=35

angle A= 35°
angle B= 35(4)+40= 145°
siniylev [52]3 years ago
4 0
4x = 180 - 40

4x = 140 degrees

4x/4 = 140/4 degrees

x = 45 degrees

The smaller angle is 45<span>°</span>.

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Answer:  The correct line is

\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.

Step-by-step explanation:  We are given the following two sets of quadratic expressions in various forms:

\textup{Line 1: }x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25,\\\\\textup{Line 2 :}x^2+5x+6=(x+2)(x+3)=(x+2.5)^2+6.25.

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We can see that there are three different forms of a quadratic expression in each of the lines:

First one is the simplified form, second is the factorised form and third one is the vertex form.

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We have

\textup{Line 1: }\\\\x^2+3x+2\\\\=x^2+2x+x+2\\\\=x(x+2)+1(x+2)\\\\=(x+1)(x+2),

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x^2+3x+2\\\\=x^2+2\times x\times 1.5+(1.5)^2-(1.5)^2+2\\\\=(x+1.5)^2-2.25+2\\\\=(x+1.5)^2-0.25.

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\textup{Line 1 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2-0.25.

Thus, Line 1 contains three equivalent expressions.

Now,

\textup{Line 2: }\\\\x^2+5x+6\\\\=x^2+3x+2x+6\\\\=x(x+3)+2(x+3)\\\\=(x+2)(x+3),

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x^2+5x+6\\\\=x^2+2\times x\times 2.5+(2.5)^2-(2.5)^2+6\\\\=(x+2.5)^2-6.25+6\\\\=(x+2.5)^2-0.25\neq (x+2.5)^2+6.25.

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\textup{Line 2 :}x^2+3x+2=(x+1)(x+2)=(x+1.5)^2+6.25.

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