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3 years ago

Jake and Abigail worked a job together. Jake earned 3/4 of what Abigail did. Together they earned $140. How much did each earn?

Mathematics

2 answers:

marissa [1.9K]3 years ago

7 0

Abigail: x

Jake: 3/4x

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Make their expressions add up to 140 in an equation.

(x) + (3/4x) = 140

Combine like terms.

1 3/4x = 140

Divide both sides by 1 3/4.

x = 80

Plug 80 for x into Jake and Abigail's expressions.

Jake: 3/4(80) = 60

Abigail: (80) = 80

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Jake earned $60 and Abigail earned $80.

lord [1]3 years ago

5 0

Let's represent Jake with the variable 'j' and Abigail with the variable 'a':

j = 3a/4

j + a = 140

j = -a + 140

3a/4 = -a + 140

3a = -4a + 560

7a = 560

a = 80

Abigail earned $80 and Jake earned $60

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Alice placed $1,900 in a savings account which earns 2.2% interest, compounded every year. How much will she have in the account

ella [17]

She will have $2118 in her account after five years

<h3>How to determine the amount in five years?</h3>

The given parameters about the compound interest are

Principal Amount, P = $1,900

Interest Rate, R = 2.2%

Time, t = 5

Compound interests are different from simple interest, and they are calculated using the following compound interest formula

CI = P(1 + R)^t - P

To calculate the amount, we have:

A = P + CI

So, the equation becomes

A = P + P(1 + R)^t - P

Evaluate the like terms

A = P(1 + R)^t

Substitute the known values in the above equation

A = 1900 * (1 + 2.2%)^5

Express 2.2% as decimal

A = 1900 * (1 + 0.022)^5

Evaluate the sum

A = 1900 * (1.022)^5

Evaluate the exponent

A = 1900 * 1.11495

Evaluate the product

A = 2118

Hence, she will have $2118 in her account after five years

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1 year ago

Equation of a line with an slope of 1/2 that contains (-4, 7)

nasty-shy [4]

Equation of a line with an slope of 1/2 that contains (-4, 7) is $y=\frac{1}{2} x+9$

Solution:

We have been given a point and slope of an equation and have been asked to write it in an equation. The two forms of writing a point and slope in equation are point slope form and standard form.

The standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers. The standard form of a line is just another way of writing the equation of a line.

To write in standard form we will first write it in point slope form and then rearrange it into a standard from.

The formula for point slope form:

$y-y_{1}=m\left(x-x_{1}\right)$