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3 years ago

Triangle MNO ~ triangle PRQ. If 89o 69o 79o 99o

Mathematics

1 answer:

lana66690 [7]3 years ago

7 0

Answer:

The measure of angle R is 99° ⇒ Last answer

Step-by-step explanation:

In similar triangles

Corresponding angles are equal in measures
Corresponding sides are proportion

∵ Δ MNO is similar to Δ PRQ

∴ m∠M = m∠P

∴ m∠N = m∠R

∴ m∠O = m∠Q

In Δ MNO

∵ m∠M = 23°

∵ m∠O = 58°

- The sum of the measures of the interior angles of a Δ is 180°

∵ m∠M + m∠N + m∠O = 180°

∴ 23 + m∠N + 58 = 180

- Add the like terms in the left hand side

∴ 81 + m∠N = 180

- Subtract 81 from both sides

∴ m∠N = 99°

∵ m∠R = m∠N ⇒ proved up

∴ m∠R = 99°

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In ΔRST, t = 16 inches, s = 19 inches and ∠S=113°. Find all possible values of ∠T, to the nearest degree

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3 years ago

Part 1: What mistake did AJ make in the graph?

grigory [225]

Answer:

Part 1) AJ drawn the parabola opening upwards, instead of drawing it opening downwards

Part 2) see the explanation

Step-by-step explanation:

Part 1) What mistake did AJ make in the graph?

we have

$f(x)=-(x+2)^2-1$

This is the equation of a vertical parabola written in vertex form

The parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

The vertex is the point (-2,-1)

therefore

AJ drawn the parabola opening upwards, instead of drawing it opening downwards

Part 2) Evaluate any two x-values (between -5 and 5) into AJ's function. Show your work. How does your work prove that AJ made a mistake in the graph?

take the values x=-4 and x=4

For x=-4

substitute the value of x in the quadratic equation

$f(x)=-(-4+2)^2-1\\f(x)=-5$

For x=4

substitute the value of x in the quadratic equation

$f(x)=-(4+2)^2-1\\f(x)=-37$

According to AJ's graph for the value of x=-4 the function should be positive, however it is negative and for the value of x=4 the function should be positive and the function is negative

therefore

AJ made a mistake in the graph

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