3. Mauro has 140 ft of rope. He will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. What will the length of the longer piece be?4. Maggie has only dimes and quarters in her purse. She has 27 coins with a total value of $4.05 in her purse. How many dimes does Maggie have in her purse?

Question 5.5. Choose the correct answer.

Kevin wants to make a mixture that is 50% lemon juice and 50% lime juice. How much 100% lemon juice should he add to a juice that is 40% lemon juice and 60% lime juice to make 6 gal of the 50% lemon/50% lime juice mixture?
(Points : 1)
0.5 gal
1 gal
2 gal
2.5 gal

Answers

Answer 1

Answer: 3. 140= 3x +x
140= 4x
140/4 = 4x/4
35=x
3x= 35 * 3
3x= 105
The length is 105 ft

4. Number of dimes= d and number of quarters=q
d+q= 27
10d + 25q= 405
d= 27-q
10(27 -q) +25 q= 405
270 -10q + 25q= 405
270 + 15q= 405
15q= 135
q=9
d + q= 27
d +9=27
d=18
She has 18 dimes

5. 6 gal with a 50-50 split means 3 gallons each. The 60-40 has 3 gallons of lime. If 3 gal is 60%, the volume is 5 gal. We need to add 1 gallon

Answer 2

Answer:

3- 105 ft

4- 21 dimes

5- 1.5 gallons

I just took the test.

Hope this helps someone in the future.

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A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week.Which statement describes when the plans are based on the same number of aerobic exercise sessions?

Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answers

Let y be the number of strength-training exercises per week.
Let x be the number of aerobic exercises per week.
For the beginner plan:
15y + 20x = 90 ..........(1)
For the advanced plan:
20y + 30x = 130 ........(2)
Multiply both sides of (1) by 3 to get:
45y + 60x = 270 ........(3)
Multiply both sides of (2) by2 to get:
40y + 60x = 260 .......(4)
Subtracting (4) from (3) we get:
5y = 10
y = 2
Plugging in the value of 2 for y in equation and solving, we find x = 3.
Therefore the correct statement is:
"Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."

Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

How to Solve Algebra Word Problems?

Let y be the number of strength-training exercises per week.

Let x be the number of aerobic exercises per week.

For the beginner plan, the equation would be gotten as;

15y + 20x = 90 ------(eq 1)

The equation to represent the advanced plan would be;

20y + 30x = 130 -------(eq 2)

Multiply both sides of eq 1 by 4 to get:

60y + 80x = 360 ------(eq 3)

Multiply both sides of eq 2 by 3 to get:

60y + 90x = 390 ------(eq 4)

Subtract eq(3) from eq(4) we get:

10x = 30

Thus; x = 3

Then; 15y + 20(3) = 90

15y = 30

y = 2

Thus, the correct statement is:

"Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."

Read more about Algebra Word Problems at; brainly.com/question/4344214

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What is the value of y so that the ordered pair (5, y) is a solution to the equation –5x + y = –40?A.
–65

B.
9

C.
–15

D.
7

Answers

$-5x + y = -40\n\nx=5\n\n-5(5)+y=-40\n-25+y=-40\ny-25 = -40\ny -25+ 25 = -40+25\ny = -40+25\n\n\boxed{\bf{y=-15}}$

Answer is C.

At the grocery store watermelon costs $1.27 per pound. If Heather buys a 5.5 lb watermelon, which proportion could she use to find out how much it will cost, c?

Answers

If you would like to know how much will the watermelon cost, you can calculate this using the following steps:

$1.27 ... 1 pound
$c = ? ... 5.5 pounds

1.27 * 5.5 = 1 * c
c = 1.27 * 5.5
c = $6.99

The correct result would be: c = $1.27 * 5.5 pounds = $6.99.

Answer:

It's D.) 1/1.27 = 5.5/c

Step-by-step explanation:

Set up the proportion to be

weight in pounds

cost

. Keeping the variables the same on both sides the correct proportion is

1 /1.27

5.5 /c .

Help help plz lol thanks

Answers

$(9)/(4):(3)/(16)=\ \ \ \ | multiply\ first\ fraction\ by\ inverse\ of\ the\ second\n\n(9)/(4)*(16)/(3)=(3*4)/(4)=3\n\nSolution\ is\ 3.$

$(9)/(4)/(3)/(16)=(9)/(4)\cdot(16)/(3)=3\cdot4=12$

Y=1/3x2+2x-3
Please sketch graph of the equation or inequality and show work

Answers

$y= (1)/(3)x^2+2x-3\n \nx=-9 \Rightarrow y=(1)/(3) \cdot (-9)^2+2 \cdot (-9)-3=(1)/(3) \cdot 81-18-3=27-21=6 \n \nx=-6 \Rightarrow y=(1)/(3) \cdot (-6)^2+2 \cdot (-6)-3=(1)/(3) \cdot 36-12-3=12-15=-3\n \nx=-3 \Rightarrow y=(1)/(3) \cdot (-3)^2+2 \cdot (-3)-3=(1)/(3) \cdot 9-6-3=9-9=0$

$x=0\Rightarrow y=(1)/(3) \cdot (0)^2+2 \cdot (0)-3=(1)/(3) \cdot 0-0-3=0-3=-3\n\nx=3\Rightarrow y=(1)/(3) \cdot 3 ^2+2 \cdot 3-3=(1)/(3) \cdot 9+6-3=3+3=6$

What is the slope of (2,3) , (6,7)

Answers

Answer:

If you're given two points (x1, y1) and (x2, y2), the slope is (y2 - y1)/(x2 - x1);

We have ( 7 - 3 )/(6 - 2) = 4 / 4 = 1;

Step-by-step explanation:

Answer:

4/4=1

Step-by-step explanation:

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I NEED HELP!!!! WITH NUMBER 9, & 10??

Marquis begins a career making $53,000 per year. Each year, he is to receive a $1,600 raise. After 25 years, how much total money will Marquis have earned from this career?

Find the slope of the line.The slope of the line is .(Type an integer or a simplified fraction.)