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3 years ago

What is the slope of a line that is perpendicular to the line y = x + 5?

Mathematics

2 answers:

Tanzania [10]3 years ago

7 0

Answer:

-1

Step-by-step explanation:

the line is exactly opposite like a mirror image when it is perpendicular,

so the gradient of the first line is 1 (because there is no number beside x, the gradient would be 1), that means the opposite of 1 would be -1.

The answer is -1

Lelu [443]3 years ago

5 0

Answer:

-1.

Step-by-step explanation:

The standard form of a line can be written y = mx + b where m is the slope.

y = x + 5 can be written as y = 1x + 5 which shows that the slope is 1.

If the slope of a line is m then the slope of a line perpendicular to it is -1/m.

So the required slope is -1/1 = -1.

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Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.

GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = $x$

m∠D = $2x-20$ °.

Now, let m∠A = m∠B = $y$

So, m∠C = m∠A + 30° = $y+30$

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B + m∠C = 180

$y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50$

Therefore, m∠A = 50°, m∠B = 50° and m∠C = m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

$2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50$

Therefore, m∠F = 50°

m∠E = 50° and

m∠D = $2x-20=2(50)-20=100-20=80\°$

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

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rodikova [14]

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Archy [21]

Answer:

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Step-by-step explanation:

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klio [65]

Answer:

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rodikova [14]

Answer:

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Step-by-step explanation:

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