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2 years ago

∠1 ≅ ∠2

Mathematics

1 answer:

maksim [4K]2 years ago

6 0

Answer:

∠1 ≅ ∠2 congruence

m∠1 = m∠2 property of equality

m∠2 + m∠3 = 180 definition of supplementary angles

m∠1 + m∠3 = 180 Vertical Angles Theorem

∠1 and ∠3 are supplementary angles.

Find the words that fit each one

Definition of Congruence

Substitution Subtraction

Property of Equality

Definition of Supplementary

Step-by-step explanation:

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natulia [17]

Answer: 4.5

Step-by-step explanation:

First, find the points of intersection by solving the system.

y = x² + 2x + 4

y = x + 6

Solve by substitution:

x² + 2x + 4 = x + 6 ⇒ x² + x - 2 = 0 ⇒ (x + 2)(x - 1) = 0 ⇒ x = -2, x = 1

Now, integrate from x = -2 to x = 1

$\int\limits^1_2 {(x+6)-(x^{2}+2x+4) } \,$ the bottom of the integral is -2

= $\int\limits^1_2 {x+6-x^{2}-2x-4 } \,$

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= $\frac{-x^{3}}{3} - \frac{x^{2}}{2}+2x\int\limits^1_2 {} \,$

= $(\frac{-1^{3}}{3} - \frac{1^{2}}{2}+2(1)) - (\frac{-(-2)^{3}}{3} - \frac{(-2)^{2}}{2}+2(-2))$

= $(\frac{-1}{3} - \frac{1}{2} +2) - (\frac{8}{3} -\frac{4}{2} -4)$

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2 years ago

What are the slope between (-5,-2) and (8,13)

Cerrena [4.2K]

Answer:

The slope:

$m = \frac{15}{13}$

Step-by-step explanation:

-To determine the slope of the following points shown, you need this formula:

$m = \frac{y_{2} - y{1}}{x_{2} - x_{1}}$

( $m$ represents the slope, $(x_{1}, y_{1})$ represents the first coordinate and $(x_{2},y_{2})$ represents the second coordinate)

-Apply the following points to the formula:

$m = \frac{13 + 2}{8 + 5}$

Then, solve:

$m = \frac{13 + 2}{8 + 5}$

$m = \frac{15}{13}$

So, the slope is $\frac{15}{13}$ .

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2 years ago