Solve the system by substitution. y = 2x 3x + 2y = 21

An airplane left Miami, FL. At the same time another plane left Santiago, Chile. The two planes flew toward each other at rates

Nina [5.8K]

Since we know that LCM of both 625&575 is 14375, we must find the hours it took for both planes to arrive at this same destination.

Plane 1(625): Took 23 hours to arrive.

Plane 2(575): Took 25 hours to arrive.

Therefore, the answer should be from 23-25 hours to arrive or if looking for middle number, 24 hours exactly.

Hope this helps.

7 0

3 years ago

Find the right quotient. 36m 5 n 5 ÷ (12m 3)

polet [3.4K]

ANSWER

The right quotient is

$3 {m}^{2} {n}^{5}$

EXPLANATION

The given expression is :

$\frac{36 {m}^{5} {n}^{5} }{12 {m}^{3} }$

$\frac{36 {m}^{5} {n}^{5} }{12 {m}^{3} } = \frac{36}{12} \times \frac{ {m}^{5} }{ {m}^{3}} \times {n}^{5}$

$\frac{36 {m}^{5} {n}^{5} }{12 {m}^{3} } = 3\times \frac{ {m}^{5} }{ {m}^{3}} \times {n}^{5}$

Recall that,

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$
We apply this property to obtain;

$\frac{36 {m}^{5} {n}^{5} }{12 {m}^{3} } = 3 \times {m}^{5 - 3} \times {n}^{5}$

$\frac{36 {m}^{5} {n}^{5} }{12 {m}^{3} } = 3 {m}^{2} {n}^{5}$

5 0

3 years ago

Read 2 more answers

9. Water is added to two containers for 16 minutes. The equations below model the ounces of

Vladimir [108]

The two containers hold 328 ounces at the they hold same amount of water.

Step-by-step explanation:

The equations below model the ounces of water, y, in each container after x minutes.

$y = 16x + 104$

$y = -2x^{2} +40x+160$

At the time after the start when the containers hold the same amount of water, the two equations must be equal.

⇒ $16 x + 104 = -2x^{2} + 40 x + 160$

The first step is to divide everything by 2 to make it simplified.

⇒ $8 x + 52 = - x^2 +20 x + 80$

Now put everything on the left .

$x^2 + 8 x - 20 x + 52 - 80 = 0$

Add the like terms together to further reduce the equation

$x^2 - 12 x - 28 = 0$

Factorizing the equation to find the roots of the equation.

Here, b = -12 and c = -28

where,

b is the sum of the roots ⇒ -14 + 2 = -12
c is the product of the roots ⇒ -14 × 2 = -28

Therefore, (x-14) (x+2) = 0
The solution is x = -2 or x = 14

Take x = 14 and substitute in any of the given two equations,

⇒ $y = 16(14) + 104$

⇒ $y =224+104$

⇒ 328 ounces

∴ The two containers hold 328 ounces at the they hold same amount of water.

5 0

3 years ago

What are the first four terms of the sequence represented by the expression n(n - 2) -3 ?

Sonbull [250]

Answer:

the first four terms is 3, 0, -3, -6

7 0

3 years ago

A complete graph is defined as what ???

galina1969 [7]

Answer:

A complete graph is a graph in which each pair of graph vertices is connected by an edge. The complete graph with graph vertices is denoted and has (the triangular numbers) undirected edges, where is a binomial coefficient. In older literature, complete graphs are sometimes called universal graphs.

Step-by-step explanation:

3 0

3 years ago