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2 years ago

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Evelyn borrowed $30 from her mother to buy a sweater. After 3 weeks of babysitting, she pays her mother back $24. What percent

of the debt has Evelyn paid her mother back?

1 answer:

Goryan [66]2 years ago

6 0

Answer:

80%

Step-by-step explanation:

We know that Evelyn paid off $24 of the $30. To find the percentage, we divide the part by the whole and then multiply by 100. The multiplying by 100 is optional, but it just makes the calculation easier. In this case, the part is 24 and the whole is 30, so our expression would be $\frac{24}{30} * 100$ , or 80%. Hope this helps!

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the graph of f(x) shown below has the same shape as the graph of g(x)=x^2 but is shifted down 5 units and to the left 4 units (t

schepotkina [342]

Answer:

Option C

Step-by-step explanation:

A function g(x) = x² has been given as the parent function.

This function then shifted 5 units down.

Translated function formed will be f(x) = x² - 5

Further this graph has been shifted 4 units to the left then the function will become

f(x) = [x - (-4)]² - 5

f(x) = (x + 4)² - 5

Therefore, option C is the answer.

6 0

1 year ago

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An animal park has lions, tigers and zebras. 20% of the animals are lions and half of the animals are zebras. If there are 120 a

RoseWind [281]

Answer:

$36\ tigers$

Step-by-step explanation:

Let

x ----> the number of lions

y ----> the number f tigers

z ----> the number of zebras

we know that

$x+y+z=120$ ----> equation A

Remember that

$20\%=20/100=0.20$

$50\%=50/100=0.50$

To find out the number of lions, multiply the total animals by the percentage of lions

$x=0.20(120)=24\ lions$

To find out the number of zebras, multiply the total animals by the percentage of zebras

$z=0.50(120)=60\ zebras$

Substitute the value of x and the value of z in equation A and solve for y

$24+y+60=120$

$y+84=120$

$y=36\ tigers$

6 0

1 year ago

When 27x^2z/-3x^2z^6 is completely simplified, the exponent on the variable z is _____.

Savatey [412]

<span>The expression given (27x^2)z/(-3x^2)(z^6), can be simplify as below:

By properties of powers, if you have the same base, you can substract the exponents. Then:

=(</span>27x^2)z/(-3x^2)(z^6)
=-9z/z^6 (As you can see: x^2-2= x^0=1)
=-9/z^5 (Then, z^6-1=z^5)
<span>
Therefore, the answer is: The exponent on the variable z is 5.</span>

7 0

2 years ago

Learning Task 3. Find the equation of the line. Do it in your notebook.

Wewaii [24]

Answer:

1) The equation of the line in slope-intercept form is $y = 5\cdot x +9$ . The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ . The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) The equation of the line in slope-intercept form is $y = 3\cdot x +4$ . The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ . The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ . The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: ( $m = 5$ , $x = -1$ , $y = 4$ )

$4 = (5)\cdot (-1)+b$

$4 = -5 +b$

$b = 9$

The equation of the line in slope-intercept form is $y = 5\cdot x +9$ .

Then, we obtain the standard form by algebraic handling:

$-5\cdot x + y = 9$

The equation of the line in standard form is $-5\cdot x + y = 9$ .

2) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = 3$ , $y_{1} = 4$ , $x_{2} = -2$ , $y_{2} = 2$ )

$3\cdot m + b = 4$ (Eq. 1)

$-2\cdot m + b = 2$ (Eq. 2)

From (Eq. 1), we find that:

$b = 4-3\cdot m$

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

$-2\cdot m +4-3\cdot m = 2$

$-5\cdot m = -2$

$m = \frac{2}{5}$

And from (Eq. 1) we find that the y-Intercept is:

$b=4-3\cdot \left(\frac{2}{5} \right)$

$b = 4-\frac{6}{5}$

$b = \frac{14}{5}$

The equation of the line in slope-intercept form is $y = \frac{2}{5}\cdot x +\frac{14}{5}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{2}{5}\cdot x +y = \frac{14}{5}$

$-2\cdot x +5\cdot y = 14$

The equation of the line in standard form is $-2\cdot x +5\cdot y = 14$ .

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: ( $m = 3$ , $b = 4$ )

$y = 3\cdot x +4$

The equation of the line in slope-intercept form is $y = 3\cdot x +4$ .

Then, we obtain the standard form by algebraic handling:

$-3\cdot x +y = 4$

The equation of the line in standard form is $-3\cdot x +y = 4$ .

4) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -3$ , $y_{1} = 0$ , $x_{2} = 0$ , $y_{2} = 6$ )

$-3\cdot m + b = 0$ (Eq. 3)

$b = 6$ (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

$-3\cdot m+6 = 0$

$3\cdot m = 6$

$m = 2$

The equation of the line in slope-intercept form is $y = 2\cdot x + 6$ .

Then, we obtain the standard form by algebraic handling:

$-2\cdot x +y = 6$

The equation of the line in standard form is $-2\cdot x +y = 6$ .

5) We begin with a system of linear equations based on the slope-intercept form: ( $x_{1} = -1$ , $y_{1} = -2$ , $x_{2} = 5$ , $y_{2} = 3$ )

$-m+b = -2$ (Eq. 5)

$5\cdot m +b = 3$ (Eq. 6)

From (Eq. 5), we find that:

$b = -2+m$

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

$5\cdot m -2+m = 3$

$6\cdot m = 5$

$m = \frac{5}{6}$

And from (Eq. 5) we find that the y-Intercept is:

$b = -2+\frac{5}{6}$

$b = -\frac{7}{6}$

The equation of the line in slope-intercept form is $y = \frac{5}{6}\cdot x -\frac{7}{6}$ .

Then, we obtain the standard form by algebraic handling:

$-\frac{5}{6}\cdot x +y =-\frac{7}{6}$

$-5\cdot x + 6\cdot y = -7$

The equation of the line in standard from is $-5\cdot x + 6\cdot y = -7$ .

6 0

1 year ago

If 24= 2f+3f+f, find f

VashaNatasha [74]

Answer:

6f = 24

f = 4

Step-by-step explanation:

3 0

1 year ago

Read 2 more answers