You earn $49 for washing 7 cars. How much do you earn for washing 4 cars?

Mathematics

1 answer:

ICE Princess25 [194]3 years ago

4 0

Answer:

Step-by-step explanation:

We can use the rule of three!

We know we have the following relationship:

$\frac{49}{7} = \frac{x}{4}$

From here, we can solve this like any other equation:

$4(\frac{49}{7}) = x\\x = 28$

Therefore, you would earn $28 after washing 4 cars.

Good luck!

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In ¾ pound of a banana bread, there is ½ cup of cinnamon. How much cinnamon does the bread contain per pound?

Shkiper50 [21]

1 pound of bread contains $\frac{2}{3}$ cups of cinnamon.

<h3><u>Solution:</u></h3>

Given that , In $\frac{3}{4}$ pound of a banana bread, there is $\frac{1}{2}$ cup of cinnamon

Amount of cinnamon per pound in bread

Let "n" be the cinnamon per pound present in bread

$\frac{3}{4}$ pound of banana bread ⇒ $\frac{1}{2}$ cup of cinnamon

Then, 1 pound of bread ⇒ n cups of cinnamon

Now, let us use criss cross method (i.e. multiplying the diagonal ordered terms and equating them)

$\begin{array}{l}{\rightarrow n \times \frac{3}{4}=\frac{1}{2} \times 1} \\\\ {\rightarrow n \times \frac{3}{4}=\frac{1}{2}} \\\\ {\rightarrow n=\frac{1}{2} \times \frac{4}{3}} \\\\ {\rightarrow n=\frac{2}{3}}\end{array}$

Hence, 1 pound of bread contains $\frac{2}{3}$ cups of cinnamon.

3 0

4 years ago

The graph shows the functions f(x), p(x), and g(x): Graph of function g of x is y is equal to 1 plus the quantity 1.5 raised to

satela [25.4K]

Part A:

Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by

$\frac{y-2}{x} = \frac{-5-2}{1} =-7 \\ \\ \Rightarrow y-2=-7x \\ \\ \Rightarrow y=-7x+2$

Thus, p(x) = -7x + 2

</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by

$\frac{y-1}{x-4} = \frac{-3-1}{2-4} =\frac{-4}{-2}=2 \\ \\ \Rightarrow y-1=2(x-4)=2x-8 \\ \\ \Rightarrow y=2x-7$

Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by

p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1

Substituting for x into p(x), we have

p(1) = -7(1) + 2 = -7 + 2 = -5

Therefore, the solution to the pair of equations represented by p(x) and f(x) is (1, -5)

Part B:

From part A, we have that f(x) = 2x - 7

when x = -8

f(-8) = 2(-8) - 7 = -23

Thus, (-8, -23) is a solution to f(x).

When x = -10

f(-10) = 2(-10) - 7 = -27

Thus, (-10, -27) is a solution to f(x).

Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).

Part C:

From part A, we have that p(x) = -7x + 2, given that $g(x) = 1 + 1.5^x$

From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).

Therefore, the solution to the equation p(x) = g(x) is (0, 2).

3 0

4 years ago

The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Write an expo

xeze [42]

<h2>Hello!</h2>

The answer is:

In 2036 there will be a population of 32309 rabbits.

We can calculate the exponential decay using the following function:

$P(t)=StartAmount*(1-\frac{percent}{100})^{t}$