The sum of two numbers is 21. The first number is 2/5 of the second number. What are the numbers?

Answers

Answer 1

Answer: Let's call the bigger number n
So the smaller number is 2/5n
So n + 2/5n = 21
Which is equivalent of n + 2n/5 = 21
Then you need to get rid of the fraction by multiplying everything by 5
5n + 2n = 105
Or simply
7n = 105
Divide both sides by 7 to isolate n
n = 15
So the larger number is 15
Now we need to work out 2/5 of 15 to work out the smaller number
(15/5 [the denominator])*2 [the numerator] = 6
So the two numbers are 15 and 6

Answer 2

Answer:

Final answer:

The two numbers are 6 and 15; since 6 is 2/5 of 15 and their sum is 21.

Explanation:

In this problem, we want to find two numbers, which we'll call x and y, such that their sum is 21. That is, x + y = 21. Additionally, we know that the first number is 2/5 of the second number, or x = 2/5 * y.

First, solve for x in the equation x = 2/5 * y, we get x = 2y/5.

Next, substitute x in the equation x + y = 21 by 2y/5 to get 2y/5 + y = 21. When you solve that, you'll find y = 15. Then substitute y = 15 in the equation x = 2/5 * y, you'll get x = 6.

So, the two numbers are 6 and 15.

Learn more about Solving Equations here:

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What is the slope of the line y = 2x + 1 ?

Answers

y = 2x + 1

The slope of the line y is 2.

In the formula: y = mx + b

m is the slope while b is the y-intercept. Since 2 is the number that is in the place of m, it is the slope of the line while 1 is the y-intercept.

y=mx+b

M is the slope, and B is the Y-intercept.

y=2x+b

In this case, 2 is m.

The slope is 2/1, or 2.

I hope I helped! :)

A right triangle has a hypotenuse of length 59 and one leg of length 23. Part A: Determjne the angle measure of the other two acute angles in the triangle. Round to the nearest hundredth.

Part B: Determine the side length of the other leg.

Answers

Answer:

Part A) The measure of the other two acutes angles are $=67.06\°$ and $22.94\°$

Part B) The side length of the other leg is equal to $54.33\ units$

Step-by-step explanation:

Part A)

see the attached figure to better understand the problem

we know that

In the right triangle ABC

$cos(A)=(AB)/(AC)$

substitute the values

$cos(A)=(23)/(59)$

$A=arccos((23)/(59))=67.06\°$

Remember that

$A+C=90\°$ -------> by complementary angles

$C=90\°-67.06\°=22.94\°$

Part B)

Applying the Pythagoras Theorem

$CB^(2)=AC^(2)-AB^(2)$

substitute

$CB^(2)=59^(2)-23^(2)$

$CB^(2)=2,952$

$CB=54.33\ units$

Item originally costs $80, 25% discount

Answers

$20 would be the answer
The percent is a decimal in disguise.
You turn the percent mark into a decimal so .25
It would be multiplication
80 times .25 would be $20

On a scientific calculator you can press the symbol with a rectangle over a line with another rectangle underneath then add the number 80 to the top of the fraction and 100 on the bottom. You then x the fraction by 25 which will give you 25 % of 80. Next you can take away the 25% you found from your original price (80) and there is your answer= 80/100 x 25 =20
80 - 20= 60
Therefore the discounted price is $60

How do I solve this?

Answers

i would first make it 5+-2x and so then you would have I5+-2xI * IxI and then you have I5+ (-2*-4)I*I-4I then you have I5+8I*4 then you would have 13*4 and then your answer is 52 :)

|5 - 2x| · |x|
|5 - 2(-4)| · |-4|
|5 + 8| · 4
|13| · 4
13 · 4
52

Bill cleans house windows for $20/houseplus $1/window. If your house has 22
windows; how much will it cost?

Answers

Answer:

$20 (house) + $22 (windows) = $42

It will cost $42 to have Bill clean a house with 22 windows.

$42

explanation:

$1 per window x 22 windows =$22

$20 per house x $22 = $42

grant plans to evaporate enough water from 22 gallons of a 16% ammonia solution to make a 24% ammonia solution. Which equation can he use to find n, the number of gallons of water he should remove?

Answers

The equation to get the number of gallons of water he should evaporate
= 22 - (22 x 0.16)/0.24

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