The circles at the right are congruent. Which conclusion can you draw?

Triangle DEF has an angle D measuring 25 degrees and an angle E

andrew-mc [135]

Answer:

The angle F of the triangle DEF measures 105 degrees.

Step-by-step explanation:

Given that triangle DEF has an angle D measuring 25 degrees and an angle E measuring 50 degrees, to determine what is the measure of angle F in degrees, knowing that the sum of the internal angles of every triangle gives a total of 180 degrees, we must perform the following calculation:

180 - 50 - 25 = F

130 - 25 = F

105 = F

Therefore, the angle F of the triangle DEF measures 105 degrees.

5 0

3 years ago

Rewrite the equation of the parabola in vertex form. y= x2 + 8x - 21

sergey [27]

Answer:

$y=(x+4)^{2}-37$

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$y=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

if a> 0 then the parabola open upward (vertex is a minimum)

if a< 0 then the parabola open downward (vertex is a maximum)

In this problem we have

$y=x^{2}+8x-21$

Convert to vertex form

Complete the square

$y+21=x^{2}+8x$

$y+21+16=(x^{2}+8x+16)$

$y+37=(x^{2}+8x+16)$

$y+37=(x+4)^{2}$

$y=(x+4)^{2}-37$ --------> equation in vertex form

The vertex is the point $(-4,-37)$

the parabola open upward (vertex is a minimum)

4 0

3 years ago

Read 2 more answers

Assume that all grade-point averages are to be standardized on a scale between 0 and 6. How many grade-point averages must be

yanalaym [24]

Answer:

The sample size 'n' = 72,030

Step-by-step explanation:

Step(i):-

Given that the Estimate Error = 0.013

Given that the standard deviation of the Population = 1.5

The estimated error is determined by

$E = \frac{Z_{0.98} S.D }{\sqrt{n} }$

Step(ii):-

Given that the Level of significance = 0.98 or 0.02

Z₀.₀₂ = 2.326

The estimated error is determined by

$E = \frac{Z_{0.98} S.D }{\sqrt{n} }$

$0.013 = \frac{2.326 X 1.5 }{\sqrt{n} }$

$\sqrt{n} = \frac{3.489}{0.013} = 268.38$

Squaring on both sides, we get

n = 72,030

Final answer:-

The sample size 'n' = 72,030

7 0

3 years ago

The bike shop rents bikes for $5 and 5 per hour. John spends 15 dollars. How many hours did John rent the bike?

cestrela7 [59]

I think it is 15 hours If you wrote better I could've explained better but if that cost $5 per 5 Hour that means you spend $1 per 1 hour so if you spend $15 that mean you used bike for 15 hours

7 0

3 years ago

Read 2 more answers

How do I round 47,283 to the nearest 100,000

rosijanka [135]

The answer is zero.

Explanation:

The 4 is in the ten-thousands place.

Write the number 47,283 with an additional zero in the 100,000 place.

047,283

To round to the nearest 100,000, all digits to the right of the 100,000 place become zero. That means that the digits 47283 all become zero. Since 4 is less than 5, the digit to its left is not raised by 1, so the 100,000 place digit remains zero, and you end up with 000,000, which is simply 0.

Answer: 0

7 0

3 years ago