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victus00 [196]
3 years ago
7

one number is 7 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 307,

find the numbers. please help!
Mathematics
1 answer:
Svetach [21]3 years ago
6 0
The three numbers are 23, 161, and 123.
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If the present value of a growing perpetuity is 214, the required rate of return is 10%, and growth rate is 3%, what is the cash
Kryger [21]

The cash flow in year 1 is $15.

<h3>What is the cash flow in year 1?
</h3>

A growing perpetuity increases continuously and indefinitely.

Cash flow = present value x (rate of return - growth rate)

214 x (10% - 3%)

214 x 0.07 = $15

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3 0
2 years ago
Find the area of the figure below. Round your answer to one decimal place.
MAVERICK [17]

Answer: 57.1 (rounded)

Step-by-step explanation:

Area of triangle formula: 1/2 x base x height

Area of a semicircle: 1/2 x pi x r^2

(1/2 x 8 x 8) + (1/2 x pi x 4^2)

= 57.1 (rounded)

4 0
2 years ago
What is the simplified form of the quantity y-squared plus 7y plus 12 over the quantity y-squared plus 8y plus 15
Burka [1]
Firstly, let's factorise each equation individually - to do this, find 2 numbers that when summed add to the value of the second term, and when multiplied give the value of the third term.

7 and 12 give us 4 and 3 (4+3=7, 4*3=12) -- 8 and 15 give us 5 and 3 (5+3=8, 5*3=15)

Now we can rewrite these equations as (y+4)(y+3) and (y+5)(y+3) respectively.

Putting this in a fraction: (y+4)(y+3)/(y+5)(y+3) -- We can clearly see that there is a y+3 on both sides of the fraction, and given there are no terms outside of the brackets being multiplied, we can directly cancel.

This gives us our final answer:
(y+4)/(y+5)
8 0
3 years ago
How to solve this system of equal: x+y+z=1;x^2+y^2+z^2=1
swat32

There are infinitely many solutions.

Algebraically, we can eliminate z and try to solve for x,y:

x+y+z=1\implies z=1-x-y

Then

x^2+y^2+(1-x-y)^2=1

\implies x^2+y^2+1-2x+x^2-2y+y^2+2xy=1

\implies x^2-x+y^2-y+xy=0

which is the equation of an ellipse.

5 0
3 years ago
maeve likes to make her salads in advance she made 15 salads for 3 days how many salads does she eat per day unit rate
Tju [1.3M]

The number of salads Maeve eats per day if she made 15 salads for 3 days is 5 salads eaten per day.

<h3>Unit rate</h3>

Unit rate refers to the number of units of the first type of quantity corresponding to one unit of the second type of quantity.

  • Number of salads = 15 salads
  • Number of days = 3 days

Unit rate of salad eaten per day = Number of salads ÷ Number of days

= 15 ÷ 3

= 5 salads eaten per day

A salad is a food made primarily of a mixture of raw or cold ingredients, typically vegetables, usually served with a dressing such as vinegar or mayonnaise.

Therefore, the number of salads Maeve eats per day if she made 15 salads for 3 days is 5 salads eaten per day.

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7 0
1 year ago
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