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3 years ago

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Noralie has a home-based business putting on children’s parties. She charges $45 to design the party and then $5.50 per child. W

rite a function rule that relates the total cost of the party to the number of children n.
f(n) = 5.5 – 55n

f(n) = 5.5n – 55

f(n) = 5.5 + 45n

f(n) = 45 + 5.5n

1 answer:

Olin [163]3 years ago

5 0

Answer:

The answer would be C because n is the number of children and it costs $5.50 per child plus an extra design fee of $45

Step-by-step explanation:

Design = $45

rate per child = $5.50

number of children, x

total cost, f(x) = $5.5x + $45

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Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

$m_1m_2=-1$

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

$(y-y_1)=m(x-x_1)$

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0

3 years ago

-17+ 1/4 x + 1/4 x + 31 = 24

wlad13 [49]

<h2><u>Answer:</u></h2><h2><u></u> $\boxed{x=20}$ <u></u></h2><h2><u></u></h2><h2><u>Solution Steps:</u></h2>

______________________________

<h3>1.) Combine like terms:</h3>

$\frac{1}{4}x+\frac{1}{4}x=\frac{1}{2}x$

<em> - We do this because we need 1 Number/Variable left over. </em>

<u>Equation at the end of Step 1:</u>

<u /> $-17+\frac{1}{2}x+31=24$ <u />

<em />

<h3>2.) Add −17 and 31:</h3>

$-17+31=14$

<em> - We do this because we can only have 1 number on each side of the equals. (This doesn't count towards the number connected to the variable.)</em>

<u>Equation at the end of Step 2:</u>

<u /> $14+\frac{1}{2}x=24$ <u />

<h3>3.) Subtract 14 from both sides:</h3>

$14-14=$ Cancels Out

$24-14=10$

<em> - We do this because now we just need the 1 variable and the 1 number on opposite sides of the equal.</em>

<u>Equation at the end of Step 3:</u>

<u /> $\frac{1}{2}x=10$ <u />

<h3>4.) Multiply both sides by 2:</h3>

<em /> $\frac{1}{2}x$ <em> </em>× $2=x$ <em />

<em /> $10$ <em> </em>× $2=20$

<em> - We multiply by 2 since we have a fraction. In this case the reciprocal is 2 meaning we multiply by 2. </em>

<em></em>

______________________________

4 0

3 years ago

Solve for x. x^2=1/4

inessss [21]

Answer:

c) x= +/- 1/2

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Nataliya [291]

Are you asking something?? Or did you just answer your own question? EITHER WAY. Pretty chill... should give me brainliest if you’re up for it ;)

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3 years ago

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the area of a rectangle is 28 ft squared, and the length of the rectangle is 5 ft less than 3 times the width. find the length a

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3 years ago