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3 years ago

8

Mr. Frankel bought 7 tickets to a puppet show and spent $43. He bought a combination of child tickets for $4 each and adult tick

ets for $9 each. Which system of equations below will determine the number of adult tickets, a, and the number of child tickets, c, he bought?

2 answers:

pav-90 [236]3 years ago

8 0

A + C = 7
$9(A) + $4(C) = $43

Stels [109]3 years ago

8 0

3 adult tickets and 4 kids tickets

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A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the

Alexandra [31]

Answer:

length=53 in

width= 23 in

Step-by-step explanation:

First, we know that each corner has now a square of 6 in long, so the heigth of the box will be of this size (as you can see in the picture attached). Then, the length and the width of the box would be the same as the piece, but with 12 in less. Therefore the equations to solve the problem are:

$h=6 in\\w=x-12\\l=x+30-12\\l=x+18\\\\V: volume of the box\\V=6*(x-12)*(x+18)\\2706=6x^{2}+36x-1296\\0=6x^{2}+36x-4002\\\\$

We factorize the 6 and we get:

$0=x^{2}+6x-667\\$

Finally we solve for x, and we get the initial dimensions of the piece of metal:

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3 years ago

Solve y=.80x+100 based on bread machine costs 100. Ingredients for one loaf is .80 and what is the cost to make 50 loaves of bre

Ugo [173]

Substitute 50 loaves into the given equation

y= cost to make 50 loaves

y= 0.80x + 100
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multiply first, then add
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Hope this helps!

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3 years ago

you burn 200 calories by walking for 60 minutes how many calories will you burn if you walk 12 minutes?

shusha [124]

Answer:

16.666

Step-by-step explanation:

divid 200 by 12

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3 years ago

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telo118 [61]

Answer:

2/3

Step-by-step explanation:

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3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago