Why do numbers raised to an exponent get greater but fractions raised to an exponent get smaller

I need you show me the answer what a or b or c

AlladinOne [14]

That would be A, its the only on where all the dots line with the numbers given

5 0

4 years ago

The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base and PA = 2sqrt5 in. The base edges AB = 10 in, AC

DIA [1.3K]

Answer:

PQ = √84 = 2√21 in ≈ 9.165 in

Step-by-step explanation:

The base edges AB = 10 in, AC = 17 in, and BC = 21 in

Q ∈ BC and AQ is the altitude of the base.

Let BQ = x in ⇒ CQ = (21 - x) in

ΔAQB a right triangle at Q

∴ AQ² = AB² - BQ² = 10² - x² ⇒(1)

ΔAQC a right triangle at Q

∴ AQ² = AC² - CQ² = 17² - (21-x)² ⇒(2)

Equating (1) and (2)

∴ 10² - x² = 17² - (21-x)²

∴ 10² - x² = 17² - (21² - 42x + x²)

∴ 10² - x² = 17² - 21² + 42x - x²

∴ 10² - 17² + 21² = 42x

∴ 42x = 252

∴ x = 252/42 = 6

Substitute at (1)

∴ AQ² = AB² - BQ² = 10² - x² = 100 - 36 = 64 = 8²

∴ AQ = 8 in

∵ The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base

∴ PA⊥AQ

∴ ΔPAQ is a right triangle at A,

PA = 2sqrt5 in and AQ = 8 in

∴ PQ (hypotenuse) = √(PA² + AQ²)

∴ PQ = √[(2√5)² + 8²] = √(20+64) = √84 = 2√21 in ≈ 9.165 in

6 0

3 years ago

The area of a rectangle is 12x^2-8x-15. The width is (2x-3). What is the length of the rectangle?

Aliun [14]

The length of the rectangle is (6x+5)

4 0

4 years ago

Kimiko works at the drive-thru window in a fast-food restaurant. At the end of a 2-hour shift, the display at her window shows t

Anastaziya [24]

Answer:

90 customers

Step-by-step explanation:

Total shift time = 2 hours

1 hours = 60 minutes

Total shift time minutes = 2*60 minutes = 120 minutes

Average Time taken to serve 1 customer = 1 minute 20 seconds

lets convert 1 minute 20 seconds in fraction

60 seconds = 1 minute

20 seconds = 20/60 minutes = 1/3 minutes

Thus,

Average Time taken to serve 1 customer = 1 minute + 1/3 minutes = 4/3 minutes

Lets assume she served x customer in her 2 hour shift

total time taken to serve x customer =x*Average Time taken to serve 1 customer = 4x/3 minutes

Given that she the customers for her shift time which is 120 minutes

4x/3 minutes = 120 minutes

x = 120*3/4 = 90

Thus,

Kimiko served 90 customers and this is the number of customer which came through the drive thru during those 2 hours.

3 0

3 years ago

Alice skates 2/5 mile in 1/5 hour. Elizabeth skates 2/3 mile in 2/9 hour. How far did elisabeth escape in in 1 hour?

sergeinik [125]

$Question$

Alice skates 2/5 mile in 1/5 hour. Elizabeth skates 2/3 mile in 2/9 hour. How far did elisabeth escape in in 1 hour?

Answer:

The Correct Answer is $\frac{8}{9}$

Complete the multiplication and the equation becomes

$\frac{2}{9}$ + $\frac{2}{3}$ = ?

The two fractions now have like denominators so you can add the numerators.

$\frac{2+6}{9}$ = $\frac{8}{9}$

Therefore, The Answer Is $\frac{8}{9}$

Hope this helps!

$xXxAnimexXx$

6 0

3 years ago