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3 years ago

14

A plane flies 720 miles with the wind in 3 hours. The return trip against the wind takes 4 hours. What is the speed of the wind

and the speed of the plane in still air?

1 answer:

Mandarinka [93]3 years ago

4 0

Let p and w represent the speed of the plane and the speed of the wind, respectively.
.. speed = distance/time
.. p +w = 720/3 = 240
.. p -w = 720/4 = 180

Add the two equations to eliminate w.
.. 2p = 420
.. p = 210
.. w = p -180 = 30

The speed of the wind is 30 mph.
The speed of the plane in still air is 210 mph.

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Zach's parents put $1,500 in her bank account for college tuition. At an interest rate of

jolli1 [7]

Answer:

After 18 years, Zach's account balance will be $ 6,614.66.

Step-by-step explanation:

Given that Zach's parents put $ 1,500 in her bank account for college tuition at an interest rate of 8.25% compounded weekly, to determine what will be the balance after 18 years the following calculation must be performed:

1,500 x (1 + 0.0825 / 52) ^ 18x52 = X

1,500 x 1.00158653 ^ 936 = X

6,614.66 = X

Therefore, after 18 years, Zach's account balance will be $ 6,614.66.

8 0

3 years ago

Can someone help me with algebra 2 with an explanation?

sammy [17]

Answer: This took me a long time to type, hope you read it and find it helpful and easy to understand...

1. $x=1$

2. $x=\frac{3}{2}$

3. $x=1$

4. $x=\frac{6}{5}$

Step-by-step explanation:

1.

$\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}$

To make it easier to add / subtract fractions, we are looking for common denominators. I can see that if I move the fraction on the left with a denominator 3x to the right, I'll be able to add two equations with like denominator.

Let's add $\frac{x-2}{3x}$

$\frac{1}{x}=\frac{4}{3x}+\frac{x-2}{3x}$

Add the numerators and keep the same denominator.

$\frac{1}{x}=\frac{4+x-2}{3x}$

$\frac{1}{x}=\frac{2+x}{3x}$

To get rid of the denominator x on the left side, we can multiply by x.

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

$1=\frac{2+x}{3}$

Now multiply by 3.

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

$3=2+x$

Subtract 2.

$3-2=x\\1=x$

The value of x is 1.

Proof.

$\frac{1}{x}-\frac{x-2}{3x}=\frac{4}{3x}$

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

$1-\frac{-1}{3}=\frac{4}{3}$

$1+\frac{1}{3}=\frac{4}{3}$

$\frac{1*3+1}{3} =\frac{4}{3}\\\frac{4}{3}=\frac{4}{3}$

I can't show the proof to the following problems because I have a 5000 character limit.

-----------------------------------------------------------------------------------------

2.

$\frac{5x-5}{x^2-4x} -\frac{5}{x^2-4x}=\frac{1}{x}$

Again, we have like denominators, therefore, we can simply subtract the numerators and keep the same denominator.

$\frac{5x-5-5}{x^2-4x}=\frac{1}{x}$

$\frac{5x-10}{x^2-4x}=\frac{1}{x}$

Again, we can multiply by x to get rid of the x in the denominator.

$(x)\frac{5x-10}{x^2-4x}=\frac{1}{x}(x)$

Do not distribute the x in the numerator yet because we're gonna eliminate it later.

$\frac{(x)(5x-10)}{x^2-4x}=1$

Factor the denominator.

$\frac{(x)(5x-10)}{(x)(x-4)}=1$

Simplify x's.

$\frac{5x-10}{x-4} =1$

Multiply by x-4 to get rid of the denominator.

$(x-4)\frac{5x-10}{x-4} =1(x-4)$

$5x-10=x-4$

Add 10

$5x=x-4+10$

Subtract x

$5x-x=-4+10$

Combine like terms;

$4x=6$

Divide by 4.

$\frac{4x}{4}=\frac{6}{4}$

$x=\frac{6}{4}$

Simplify by 2.

6/2 = 3

4/2 = 2

$x=\frac{3}{2}$

-----------------------------------------------------------------------

3.

$\frac{x^2-7x+10}{x}+\frac{1}{x}=x+4$

Same denominator, add numerators.

$\frac{x^2-7x+10+1}{x}=x+4$

$\frac{x^2-7x+11}{x}=x+4$

Multiply by x to get rid of the x.

$(x)\frac{x^2-7x+11}{x}=(x+4)(x)$

$x^2-7x+11=x^2+4x$

Subtract $-x^2-4x$

$x^2-7x+11-x^2-4x=0$

Combine like terms;

$-11x+11=0$

Subtract 11.

$-11x=-11$

Divide by -11

$x=\frac{-11}{-11} \\x=1$

-------------------------------------------------------------------------

4.

$\frac{x^2+7x+10}{5x-30}+\frac{x}{x-6}=\frac{x^2-13x+40}{5x-30}$

It's easier if you move the operation with denominator x+6 to the right side with negative sign and bring the operation on the right side to the left side with negative sign as well.

$\frac{x^2+7x+10}{5x-30}-\frac{x^2-13x+40}{5x-30}=-\frac{x}{x-6}$

Now, since we have the same denominators, we can simply subtract numerators.

$\frac{x^2+7x+10-(x^2-13x+40)}{5x-30} =-\frac{x}{x-6}$

Distribute the negative sign.

$\frac{x^2+7x+10-x^2+13x-40}{5x-30} =-\frac{x}{x-6}$

Combine like terms;

$\frac{20x-30}{5x-30}=-\frac{x}{x-6}$

Factor.

I can see that I can factor a 5 on both numerator and numerator. This will allow me to simplify them.

$\frac{(5)(4x-6)}{(5)(x-6)} =-\frac{x}{x-6}$

Simplify.

$\frac{4x-6}{x-6}=-\frac{x}{x-6}$

Multiply by x-6

$(x-6)\frac{4x-6}{x-6}=-\frac{x}{x-6}(x-6)$

This will simplify the denominators.

$4x-6=-x$

Add x and 6.

$4x+x=6\\$

Combine like terms;

$5x=6$

Divide by 5.

$x=\frac{6}{5}$

4 0

3 years ago

Solve 13+x/2=3x for x

skad [1K]

13=3x-x/2 13=5x/2 26=5x X=5.2

7 0

2 years ago

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Help please! Will give brainly! A rock is dropped from the top floor of a 500-foot tall building. A camera captures the distance

Anna [14]

Answer:

Step-by-step explanation:

1. No it does not as the rock will accelerate downwards (because of gravity) but we can also see that at the first second the rock fell 16 feet compared to the 2 to 3 seconds gap where it fell 80 feet (144-64).

2. All the way down to the ground. Each time gap is getting bigger and bigger (it's accelerating) and the gap between 5 and 6 s should be bigger than 4 to 5 and it is not as the rock cannot fall through the ground but only hit the ground

you may have to change the english a bit and english is not my first language

hope this will help

3 0

3 years ago

I’m so bad at this pls-

dolphi86 [110]

Answer:

$5 \sqrt{2}$

Step-by-step explanation:

$\sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt[]{5} \times \sqrt{2} \\ = 5\sqrt{2}$

<h3>Hope it is helpful....</h3>

3 0

3 years ago

Read 2 more answers