A line drawn on the coordinate plane passes through the points (5.3) and (9,- 13). What is the equation of the line?

Ali, Carrie and Bryan received a sum of money. Bryan's money was 3/5 as much as Ali's money. The ratio of Ali's money to Carrie'

monitta

Answer:

The sum of money received by Ali, Carrie and Bryan is $ 740.

Step-by-step explanation:

At first we translate mathematically each sentence:

(i) Ali, Carrie and Bryan received a sum of money.

$a$ - Ali's money.

$b$ - Bryan's money.

$c$ - Carrie's money.

(ii) Bryan's money was $\frac{3}{5}$ of Ali's money.

$b = \frac{3}{5}\cdot a$ (1)

(iii) The ratio of Ali's money to Carrie's money was 4 : 1.

$\frac{a}{c} = 4$ (2)

(iv) Ali had $ 160 more than Bryan.

$a = b + 160$ (3)

After some algebraic handling, we have the following system of linear equations:

$3\cdot a - 5 \cdot b = 0$ (1b)

$a - 4\cdot c = 0$ (2b)

$a - b = 160$ (3b)

The solution of the system is: $a = 400$ , $b = 240$ , $c = 100$

The sum of money is:

$s = a + b + c$

$s = 740$

The sum of money received by Ali, Carrie and Bryan is $ 740.

4 0

3 years ago

Write a division problem that has a quotient of 1/20

alexdok [17]

Answer:

5 divided by 100

Step-by-step explanation

5 divided by 100 is 0.05 but as a fraction, it's 1/20

6 0

3 years ago

Rock-music sales represented 24.8% of the total music sales in 2000. By 2007, rock-music sales represented 32.4% of the total mu

baherus [9]

Answer:

Unit Rate of Change = 1.27%

Step-by-step explanation:

In 2000, t=1 and Total Music sales = 24.8%

In 2007, t=7 and Total Music sales = 32.4%

The Slope $m=\dfrac{32.4-24.8}{7-1} =\dfrac{7.6}{6}=1.27\%$

The Unit Rate of Change is 1.27% and it means that the Total Music Sales Increased by approximately 1.27% every year.

8 0

3 years ago

Read 2 more answers

A manufacturer produces bolts of a fabric with a fixed width. A quantity q of this fabric (measured in yards) that is sold is a

BigorU [14]

Answer:

$R'(20) = 2000$

Step-by-step explanation:

We are given the following in the question:

Quantity, q

Selling price in dollars per yard, p

$q=f(p)$

Total revenue earned =

$R(p)=pf(p)$

f(20)=13000

This means that 13000 yards of fabric is sold when the selling price is 20 dollars per yard.

f′(20)=−550

This means that increasing the selling price by 1 dollar per yards there is a decrease in fabric sales by 550.

We have to find R'(20)

Differentiating the above expression, we have,

$R'(p) = \displaystyle\frac{d(R(p))}{dp} = \frac{d(pf(p))}{dp} = f(p) + pf'(p)$

Putting the values, we get,

$R'(p) = f(p) + pf'(p)\\\\R'(20) = f(20) + 20(f'(20))\\\\R'(20) = 13000 + 20(-550) = 2000$

7 0

3 years ago

On the function machine shown below, the function rule is given as a variable expression. When the output is 99, what is the inp

beks73 [17]

Answer: option d.

Step-by-step explanation:

We have the function:

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

The output is 99 when y = 99, and the input is x.

Then we need to solve:

y = 99 = x^2 - 1

for x.

99 = x^2 - 1

99 + 1 =x^2

100 = x^2

√100 = x

10 = x

The correct option is d, input equals 10.

7 0

2 years ago