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kompoz [17]
3 years ago
5

Can someone PLEASE help me with 4 and 5??? I’m legitimately struggling.

Mathematics
2 answers:
puteri [66]3 years ago
4 0
4) The key here is recognizing that the diagonals of a rectangle are congruent, and that they bisect each other. Therefore, AE = BE, and AE + BE = BD. Substituting, you get (2x+3)+(12-x)=BD \\ x+15=BD.
BD=x+7

5) The sides of a rectangle are parallel to each other. When you draw lines extending the sides, the implications of this become obvious. Suddenly, you have two parallel lines intersected by a transversal, and you probably know those angle relationships. BAC = ACD, so 3x+5=40-2x. x=7.

To find AED (I believe there's an easier way, but I'm not sure), see that AED is the supplement of AEB, and AEB is 180° - 2(BAC) = 180-6x-10 = 170-6(7)=128. Therefore, AED is 180-128=52. 
AED=52°

zzz [600]3 years ago
3 0
Problem 4.

In a rectangle, the diagonals are congruent and bisect each other.
You have AC = BD, and AE = CE = BE = DE.
Also each segment of a diagonal is half the length of the diagonal.

AE = BE

2x + 3 = 12 - x

3x = 9

x = 3

AE = 2x + 3 = 2(3) + 3 = 6 + 3 = 9

BD = 2(AE) = 2(9) = 18

Problem 5.

Sides AB and CD are parallel.
Angles BAC and ACD are alternate interior angles of parallel lines, so they are congruent.

m<BAC = m<ACD

3x + 5 = 40 - 2x

5x = 35

x = 7

m<ACD = 40 - 2x = 40 - 2(7) = 40 - 14 = 26

m<BDC = m<ACD = 26

<AED is a remote exterior angle to angles BDC and ACD.

m<AED = m<BCD + m<ACD = 26 + 26 = 52
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Answer:

Part 1) 30\ coupons

Part 2) 12\ sandwiches

Part 3) 60\ push-ups

Part 4) 96\ minutes

Part 5) \$95

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Step-by-step explanation:

Part 1) we know that

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so

Using proportion

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\frac{1}{3}=\frac{10}{x} \\\\x=3(10)\\\\x=30\ coupons

Part 2) we know that

Kim orders catering for $35

She spend $5 on a large order of potato salad and the rest on turkey sandwiches

Each sandwich is $2.50

How many sandwiches does Kim buy?

step 1

Find out how many Kim spent on turkey sandwiches

Subtract $5 from $35

35-5=$30

step 2

Using proportion, find out the number of sandwiches

so

\frac{1}{2.50}=\frac{x}{30}\\\\x=30/2.50\\\\x= 12\ sandwiches

Part 3) we know that

Molly does 10 push-ups at the same time as Liza does  15 push-ups

so

Using proportion

Find out how many push-ups Liza does when Molly does 40 push-ups

\frac{10}{15}=\frac{40}{x}\\\\x=15(40)/10\\\\x=60\ push-ups

Part 4) we know that

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Using proportion

Find out how long in minutes the shark swim 40 miles

Remember that

1\ h=60\ min

\frac{25}{60}\ \frac{miles}{minutes}=\frac{40}{x}\ \frac{miles}{minutes}\\\\x=60(40)/25\\\\x=96\ minutes

Part 5) we know that

For every bar of soap that Aly sells, she earns $5

For every mug that Janet sells, she earns twice as much as Aly

Aly sells 5 bars of soap and Janet sells 7 mugs

How much money did they make altogether?

step 1

Find out the amount earned by Aly

using proportion

\frac{1}{5}=\frac{5}{x}\\\\x=5(5)\\\\x=\$25

step 2

Find out the amount earned by Janet

Remember that

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so

For every mug that Janet sells, she earns 2($5)=$10

using proportion

\frac{1}{10}=\frac{7}{x}\\\\x=10(7)\\\\x=\$70

step 3

Adds the amount earned by Aly plus the amount earned by Janet

25+70=\$95

Part 6) we know that

Ted is making trail mix for a party

He mixes 1 1/2 cups of nuts, 1/4 cup of rising and 1/4 cup of pretzel

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Adds the quantities

1\frac{1}{2}+\frac{1}{4} +\frac{1}{4}=2\ cups\ of \ trail\ mix

That means

For every 2 cups of trail mix we need 1/4 cup of pretzel

using proportion

Find out how many cups of pretzel does Ted need to make 15 cups of trail mix

\frac{2}{(1/4)}=\frac{15}{x}\\\\x=15(1/4)/2\\\\x=\frac{15}{8}\ cups\ of\ pretzel

Convert to mixed number

\frac{15}{8}=\frac{8}{8}+\frac{7}{8}=1\frac{7}{8}\ cups\ of\ pretzel

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Step-by-step explanation:

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