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4 years ago

Solve for x and y: 3x + 7y= 22 123 + 28y = 88

Mathematics

1 answer:

ale4655 [162]4 years ago

5 0

Answer:

Step-by-step explanation:

1. Since this is a equation we know we have to get the variables to one side and the constants/rational numbers to the other. So you take 7y and you add -7y. You do that to the other side which will give you -4y=22. Since we cant have a negative variable, you flip the y to positive and flip the constant to negative leaving you 4y=-22. Then you distribute y leaving you y=-5.5

2.since we know the constants must be on 1 side of the equal sign, we subtract 123 on both sides, leaving us with 28y=-35. Distribute y and you get y=-0.8

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An actor invests some money at 7%, and $24000 more than four times the amount at 8%. The total annual interest earned from the i

natita [175]

Answer:

$70,000 at 7%
$304,000 at 8%

Step-by-step explanation:

Given:

Total interest earned on two investments is $29,220.

An amount is invested at 7%.

$24,000 more than 4 times that amount is invested at 8%.

Find:

The amount invested at each rate.

Solution:

Our strategy will be to define a variable representing the amount invested at 7%, use that variable to write an expression for the amount invested at 8%, then write an equation for the total return on the investments.

Let x represent the amount invested at 7%. Then (24,000+4x) will be the amount invested at 8%. The total interest earned will be ...

interest on 7% account + interest on 8% account = total interest

0.07x + 0.08(24000+4x) = 29220

0.39x + 1920 = 29220 . . . . . . . . . . . simplify

0.39x = 27300 . . . . . . . . . . . . . . . . . .subtract 1920

x = 27300/0.39 = 70000 . . . . . . . . . divide by the coefficient of x

24,000 +4x = 24,000 +280,000 = 304,000 . . . . amount invested at 8%

He invested $70,000 at 7% and $304,000 at 8%.

Check

The answer must satisfy ...

7% interest + 8% interest = 29,220

0.07×70,000 +0.08×304,000 = 4,900 +24,320 = 29,220 . . . . as required

_____

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6 0

3 years ago

Write the equation of the line through the points (2,4)(-3,-1). write answer in a point slope form

luda_lava [24]

Answer:

The point-slope form would be y - 4 = x - 2

Step-by-step explanation:

In order to find the equation of the line, we first need to find the slope. For that, we use the slope formula.

m (slope) = (y1 - y2)/(x1 - x2)

Now we plug the numbers into the equation.

m (slope) = (y1 - y2)/(x1 - x2)

m (slope) = (4 - -1)/(2 - -3)

m (slope) = 5/5

m (slope) = 1

Now we can use point-slope form along with the slope and either point to write the equation.

y - y1 = m(x - x1)

y - 4 = (x - 2)

3 0

3 years ago

An ant population starts at 1200 for a certain colony. As each month goes by in the winter, 6.5% of the population dies off. How

Nitella [24]

Answer:

There will be 916 ants alive after 4 months.

Step-by-step explanation:

Step 1

Let's change the percentage to a decimal by dividing by a 100.

6.5% / 100 = .065

Step 2

So, for the first month we will multiply the initial amount of ants by .065 and this will give us the number of ants that die.

1200 * .065 = 78

This means that after the first month, 1200 - 78 = 1122 ants will be alive.

Step 3

Now for the second month: 1122 * .065 = 72.93 (rounded to 73)

1122 - 73 = 1049 ants will be alive

Step 4

For the third month 1049 * .065 = 68.185 (rounded to 68)

1049 - 68 = 981 ants will be alive

Step 5

For the fourth month 981 * .065 = 63.765 (rounded to 64)

981 - 64 = 916 ants will be alive

Hope this helps!

5 0

3 years ago

Read 2 more answers

Write the recurring decimal 0.4 as a fraction in its simplest form.

Ugo [173]

Answer:

2/5

Step-by-step explanation:

0.4 = 4/10 which in simplest form is 2/5

8 0

3 years ago

Read 2 more answers

Chang is estimating the volume of his bathtub the actual volume of his bathtub is 37 gal chang’s estimate is 31 gal find the abs

stepladder [879]

<h3>The absolute error is 6</h3><h3>The percent error is 16.22 %</h3>

Solution:

Given that,

Actual volume of his bathtub is 37 gal

Estimate is 31 gal

Find the absolute error

Absolute Error = | Measured Value - Actual Value |

Absolute Error = | 31 - 37 |

Absolute Error = 6

Find the percent error

$Percent\ error = \frac{\text{estimate - actual}}{actual} \times 100$

Substituting we get,

$percent\ error = \frac{31-37}{37} \times 100\\\\percent\ error = \frac{-6}{37} \times 100\\\\percent\ error = -16.22$

Negative sign means percent decrease

Thus percent error is 16.22 %

5 0

3 years ago