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lisabon 2012 [21]
2 years ago
10

Determine which expression is equivalent to 15a + 6. (5 points)

Mathematics
1 answer:
Lina20 [59]2 years ago
6 0

Answer:

1. Expression: 3(5a + 2)

2. Total\ charges = 6.25(s+g)

3. Total = 65x + 18 + 65y

4. Michelle

5. 20 friends

6. Thor

8. x\leq 5

9. x + x + 5 = 32

10. 7n + 9 \leq 44 so: n \leq 5

11. 40 + 5n \leq 70 So: n \leq 6

12. 10.01  p + 9.96 \leq 50 so p \leq 4

Step-by-step explanation:

1. Given

Expression: 15a + 6

Required

Determine the equivalent expression

Expression: 15a + 6

Expand:

Expression: 3 * 5a + 3 * 2

Factorize:

Expression: 3(5a + 2)

<em>Hence, the equivalent expression of the given expression is </em>3(5a + 2)

2.

Given

Charges = \$6.25

s = seventh grade students

g = eight grade students

Required

Determine the total charges

First, we need to calculate the total number of charges:

Total=s+g

Total\ charges = Charges * Total

Total\ charges = 6.25(s+g)

3. Given

Ken

Duration = x\ weeks

Extra\ Earnings = \$18

Weekly\ Earnings = \$65

Paul

Weekly\ Earnings = \$65

Duration = y\ weeks

Ken's total charges is:

Weekly\ Earnings * Duration + Extra\ Earnings

65 * x + 18

65x + 18

Paul's total charges is:

Weekly\ Earnings * Duration

65 * y

65 y

Total = Ken + Paul

Total = 65x + 18 + 65y

4.

To calculate the percentage, we simply divided the number of pop albums by the total number of albums.

For Michelle.

\%Pop = \frac{33}{60} * 100\%

\%Pop = \frac{3300\%}{60}

\%Pop = 55\%

For Sasha

\%Pop = \frac{36}{78} * 100\%

\%Pop = \frac{3600\%}{78}

\%Pop = 46.2\%

For Kat:

\%Pop = \frac{40}{89} * 100\%

\%Pop = \frac{4000\%}{89}

\%Pop = 44.9\%

For Monica:

\%Pop = \frac{24}{59} * 100\%

\%Pop = \frac{2400\%}{59}

\%Pop = 40.7\%

From the calculation above, Michelle has the highest percentage of Pop music

5.

People = 80

Fortnite = 0.55

Among\ Us = 30\%

Required

Determine number of friends that prefer fortnite more than among us

First, we need to calculate the number of people that prefer Fortnite.

Fortnite = 0.55 * 80

Fortnite = 44

Next, we need to calculate the number of people that prefer Among Us.

Among\ Us = 30\% * 80

Among\ Us = 24

The difference is:

Difference = 44 - 24

Difference = 20

<em>Hence, 20 more people preferred Fortnite to Among Us</em>

6.

Hulk = 0.25

Iron\ Man = 12

Thor = 35\%

Captain America cleaned the rest

Total = 60

Number of cities by each is:

Hulk = 0.25 * 60

Hulk = 15

Iron\ Man = 12

Thor = 35\%

Thor = 35\% * 60

Thor = 21

Captain\ America = 60 - 15 -12 - 21

Captain\ America = 12

<em>By comparison, Thor cleaned the highest number of cities</em>

<em>7. This question is not clear</em>

Total = \$70

Glass = \$30

Each\ Cape = \$8

Let the number of cape be x.

We have that:

8 * x + 30 \leq 70

8 x +\leq 70 - 30

8 x +\leq 40

x\leq 5

9.

Let the first number be x and the second be y

x + y = 32

y = x + 5

Substitute x + 5 for y in the first equation

x + x + 5 = 32

10.

Savings = \$9

Earnings = $7 per hous

Total = $44

The inequality is:

7 * n + 9 \leq 44

7n + 9 \leq 44

7n \leq 44 - 9

7n \leq 35

n \leq 5

11.

Earnings = $40

Extra = $5 per lasso

Total Earnings = At least $70 daily

The inequality is:

40 + 5n \leq 70

5n \leq 70 - 40

5n \leq 30

n \leq 6

12.

Each\ Cake = \$0.01

Shipping = \$9.96 per order

Available = \$50 --- maximum

The inequality is:

10.01 * p + 9.96 \leq 50

10.01  p + 9.96 \leq 50

10.01  p \leq 50 - 9.96

10.01  p \leq 40.04

p \leq 4

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See below:

Step-by-step explanation:

Problem 1:

Multiply Equation 1 by 4, keep Equation 2 the same.

x+y=8, multiply each term by 4:

4*x=4x, 4*y=4y, 8*4=32

so, the equivalent system is: 4x+4y=32 and x-y=2

Solve the system of equations:

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4(y+2)+4y=32---> 4y+8+4y=32--->8y=24---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 1 Answer:

Equivalent system: 4x+4y=32, x-y=2; solution: x=5, y=3

Problem 2:

Keep Equation 1 the same. Add 1 and 2.

To add an equation, add the left sides together, and then the rights.

so: x+y=8 + x-y=2 gives us: 2x=10

solve for x ---> 2x/2=10/2--->x=5

plug x into x+y=8--->5+y=8--->y=3

Problem 2 answer:

Equivalent system: x+y=8, 2x=10; solution:x=5, y=3

Problem 3:

Subtract Equation 2 from 1, and keep 2 the same.

To subtract an equation, subtract the left sides, then the rights. We are subtracting 1<em> from </em>2, so its 2-1.

x-y=2 - x+y=8 gives us: -2y=-6

Solve for y by dividing by -2-->-2y/-2=-6/-2---> y=3

Plug into x-y=2---> x-3=2---> x=5

Problem 3 answer:

Equivalent system: -2y=-6, x-y=2; solution: x=5, y=3

Problem 4:

Multiply the sum of Equation 1 and 2 by a factor of 3. Keep equation 2 the same.

First we add 1 and 2: (we did this earlier) ---> 2x=10 ---> now we multiply it all by 3---> 2x*(3)=10*(3)---> this gives us: 6x=30---> now divide by 6 to solve for x: 6x/6=30/6 gives us: x=5

Now, solve for y by plugging x into equation 2: x-y=2---> 5-y=2--->y=3

Problem 4 answer:

Equivalent system: 6x=30, x-y=2; solution: x=5, y=3

______

Quick Tip: One thing inherent of Equivalent systems is that they have the same set of solutions. Thus, we know the systems are equivalent when they have the same set of solutions for x and y. Moreover, you don't need to solve every time after you attempt to find an equivalent system, instead, just plug in the values found in problem 1 to each new set of equations to test if they are equivalent.

If we find x=5 and y=3 for x+y=8 and x-y=2, then all we have to do is plug them in to 6x=30 and -2y=-6 to see if they are equivalent.

6(5)=30 ---> true

-2(3)=-6 ---> true

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