Mathematics: Which is the graph of the inequality in which y must be at least 5 greater than 3 times x?

Which is the graph of the inequality in which, №13181621, 25.09.2022 20:21

Mathematics

Subtract (enter answer is standard form) (-2x^4-2x^3+8x^2+-5x^3+2x+7) which graph represents the inequality? (has picture) 2x-3y≤6 multiply 8y^4(2y^4-3y^3+5y) solve for x 0=7x^2+x+5 harold and helen both spend 3 hours reading a novel. helen reads 30 more pages than harold. helen reads at least 40 pages in 1 hour, but no more than 70 pages in 1 hour. which statement correctly describes the range of pages harold reads? harold reads more than 90 pages, but less than 180 pages. harold reads at least 90 pages, but no more than 180 pages. harold reads

Step-by-step answer

P Answered by PhD

15

Part 1) -3x^4+3x^3+8x^2-2x-5

Part 2) The graph in the attached figure

Part 3) 16y^8-24y^7+40y^5

Part 4) $x1=\frac{-1+\sqrt{139}i} {14}$ and $x2=\frac{-1-\sqrt{139}i} {14}$

Part 5) Harold reads more than pages, but less than 180 page

Part 6) (30,68) , (40,60)

Part 7) $\$576$

Part 8) 23 + 2i

Step-by-step explanation:

The complete answers in the attached figure because is too long

Part 1) Subtract (enter answer is standard form)

we have

(-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)

Eliminate parenthesis

-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7

Combine like terms

(-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)

-3x^4+3x^3+8x^2-2x-5 ------> standard form

Part 2) Which graph represents the inequality?

we have

$2x-3y\leq 6$

Rewrite the inequality ------> $3y\geq2x-6$

the solution is the shaded area above the solid line

the equation of the line is equal to 3y=2x-6

the slope of the line is positive

the y-intercept of the line is the point (0,-2) ---> value of y when the value of x is equal to zero

the x-intercept of the line is the point (3,0) ---> value of x when the value of y is equal to zero

The solution in the attached figure

Part 3) Multiply

we have

$8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5$

Part 4) Solve for x

we have

0=7x^2+x+5

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

7x^2+x+5=0

so

$a=7\\b=1\\c=5$

substitute in the formula

$x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}$

$x=\frac{-1(+/-)\sqrt{-139}} {14}$

remember that

$i=\sqrt{-1}$

so

$x=\frac{-1(+/-)\sqrt{139}i} {14}$

$x1=\frac{-1+\sqrt{139}i} {14}$

$x2=\frac{-1-\sqrt{139}i} {14}$

Part 5) Harold and Helen both spend hours reading a novel. Helen reads more pages than Harold. Helen reads at least pages in hour, but no more than pages in hour.

Which statement correctly describes the range of pages Harold reads?

Let

x------> the number of pages that Harold read

y------> the number of pages that Helen read

we know that

y=30+x -----> equation A

$y\geq 40\ pages$ ------> in one hour

so

in three hours -------> $y\geq 120\ pages$ ------> inequality B

$y\leq 70\ pages$ ------> in one hour

so

in three hours -------> $y\leq 210\ pages$ ------> inequality C

Substitute equation A in the inequality B

$x+30\geq 120\ pages$ ------> $x\geq 90\ pages$

Substitute equation A in the inequality C

$x+30\leq 210\ pages$ ------> $x\leq 180\ pages$

therefore

Harold reads more than pages, but less than 180 page

Part 6) Let

x------> the number of Standard Specials sold last Monday

y------> the number of Deluxe specials sold last Monday

we know that

$2x+4y\geq 200$ -----> inequality A

$0.50x+1.25y\leq100$ -----> inequality B

$x\geq30$ -----> inequality C

Remember that

If a ordered pair representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

then

the ordered pair must satisfy all restrictions

Verify

A) (30,68)

Substitute the value of x and y in each inequality

Inequality A

$2(30)+4(68)\geq 200$

$332\geq 200$ ------> is true

Inequality B

$0.50(30)+1.25(68)\leq100$

$100\leq100$ -----> is true

Inequality C

$30\geq30$ -----> is true

The ordered pair (30,68) represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

B) (80,40.5)

The value of y=40.5 not make sense in the context of the situation, because is not a whole number

C) (60,70)

Substitute the value of x and y in each inequality

Inequality A

$2(60)+4(70)\geq 200$

$400 \geq 200$ ------> is true

Inequality B

$0.50(60)+1.25(70)\leq100$

$117.5\leq100$ -----> is not true

therefore

the ordered pair (60,70) is not a solution

D) (40,60)

Substitute the value of x and y in each inequality

Inequality A

$2(40)+4(60)\geq 200$

$320\geq 200$ ------> is true

Inequality B

$0.50(40)+1.25(60)\leq100$

$95\leq100$ -----> is true

Inequality C

$40\geq30$ -----> is true

The ordered pair (40,60) represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

E) (50.5,40)

The value of x=50.5 not make sense in the context of the situation, because is not a whole number

Subtract (enter answer is standard form) (-2x^4-2x^3+8x^2+-5x^3+2x+7) which graph represents the ine

Mathematics

Subtract (enter answer is standard form) (-2x^4-2x^3+8x^2+-5x^3+2x+7) which graph represents the inequality? (has picture) 2x-3y≤6 multiply 8y^4(2y^4-3y^3+5y) solve for x 0=7x^2+x+5 harold and helen both spend 3 hours reading a novel. helen reads 30 more pages than harold. helen reads at least 40 pages in 1 hour, but no more than 70 pages in 1 hour. which statement correctly describes the range of pages harold reads? harold reads more than 90 pages, but less than 180 pages. harold reads at least 90 pages, but no more than 180 pages. harold reads

Step-by-step answer

P Answered by PhD

15

Part 1) -3x^4+3x^3+8x^2-2x-5

Part 2) The graph in the attached figure

Part 3) 16y^8-24y^7+40y^5

Part 4) $x1=\frac{-1+\sqrt{139}i} {14}$ and $x2=\frac{-1-\sqrt{139}i} {14}$

Part 5) Harold reads more than pages, but less than 180 page

Part 6) (30,68) , (40,60)

Part 7) $\$576$

Part 8) 23 + 2i

Step-by-step explanation:

The complete answers in the attached figure because is too long

Part 1) Subtract (enter answer is standard form)

we have

(-2x^4-2x^3+8x^2+2)-(x^4-5x^3+2x+7)

Eliminate parenthesis

-2x^4-2x^3+8x^2+2-x^4+5x^3-2x-7

Combine like terms

(-2x^4-x^4)+(-2x^3+5x^3)+8x^2-2x+(2-7)

-3x^4+3x^3+8x^2-2x-5 ------> standard form

Part 2) Which graph represents the inequality?

we have

$2x-3y\leq 6$

Rewrite the inequality ------> $3y\geq2x-6$

the solution is the shaded area above the solid line

the equation of the line is equal to 3y=2x-6

the slope of the line is positive

the y-intercept of the line is the point (0,-2) ---> value of y when the value of x is equal to zero

the x-intercept of the line is the point (3,0) ---> value of x when the value of y is equal to zero

The solution in the attached figure

Part 3) Multiply

we have

$8y^4(2y^4-3y^3+5y)\\=( 8y^4*2y^4)-(8y^4*3y^3)+(8y^4*5y)\\=16y^8-24y^7+40y^5$

Part 4) Solve for x

we have

0=7x^2+x+5

we know that

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

7x^2+x+5=0

so

$a=7\\b=1\\c=5$

substitute in the formula

$x=\frac{-1(+/-)\sqrt{1^{2}-4(7)(5)}} {2(7)}$

$x=\frac{-1(+/-)\sqrt{-139}} {14}$

remember that

$i=\sqrt{-1}$

so

$x=\frac{-1(+/-)\sqrt{139}i} {14}$

$x1=\frac{-1+\sqrt{139}i} {14}$

$x2=\frac{-1-\sqrt{139}i} {14}$

Part 5) Harold and Helen both spend hours reading a novel. Helen reads more pages than Harold. Helen reads at least pages in hour, but no more than pages in hour.

Which statement correctly describes the range of pages Harold reads?

Let

x------> the number of pages that Harold read

y------> the number of pages that Helen read

we know that

y=30+x -----> equation A

$y\geq 40\ pages$ ------> in one hour

so

in three hours -------> $y\geq 120\ pages$ ------> inequality B

$y\leq 70\ pages$ ------> in one hour

so

in three hours -------> $y\leq 210\ pages$ ------> inequality C

Substitute equation A in the inequality B

$x+30\geq 120\ pages$ ------> $x\geq 90\ pages$

Substitute equation A in the inequality C

$x+30\leq 210\ pages$ ------> $x\leq 180\ pages$

therefore

Harold reads more than pages, but less than 180 page

Part 6) Let

x------> the number of Standard Specials sold last Monday

y------> the number of Deluxe specials sold last Monday

we know that

$2x+4y\geq 200$ -----> inequality A

$0.50x+1.25y\leq100$ -----> inequality B

$x\geq30$ -----> inequality C

Remember that

If a ordered pair representing a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

then

the ordered pair must satisfy all restrictions

Verify

A) (30,68)

Substitute the value of x and y in each inequality

Inequality A

$2(30)+4(68)\geq 200$

$332\geq 200$ ------> is true

Inequality B

$0.50(30)+1.25(68)\leq100$

$100\leq100$ -----> is true

Inequality C

$30\geq30$ -----> is true

The ordered pair (30,68) represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

B) (80,40.5)

The value of y=40.5 not make sense in the context of the situation, because is not a whole number

C) (60,70)

Substitute the value of x and y in each inequality

Inequality A

$2(60)+4(70)\geq 200$

$400 \geq 200$ ------> is true

Inequality B

$0.50(60)+1.25(70)\leq100$

$117.5\leq100$ -----> is not true

therefore

the ordered pair (60,70) is not a solution

D) (40,60)

Substitute the value of x and y in each inequality

Inequality A

$2(40)+4(60)\geq 200$

$320\geq 200$ ------> is true

Inequality B

$0.50(40)+1.25(60)\leq100$

$95\leq100$ -----> is true

Inequality C

$40\geq30$ -----> is true

The ordered pair (40,60) represent a combination of Standard specials and Deluxe specials could have been sold last Monday and make sense in the context of the situation

E) (50.5,40)

The value of x=50.5 not make sense in the context of the situation, because is not a whole number

Mathematics

Determine which expression is equivalent to 15a + 6. (5 points) a 3(5a + 6) b 3(5a + 2) c 5(3a + 6) d 5(3a + 2) Question 2 (5 points) (03.01 LC) Excellence Middle School charges $6.25 for students from all grade levels to attend the school dance. If s represents the number of seventh grade students who came to the dance and g represents the number of eighth grade students at the dance, which expression best represents the total money collected for attending the dance. (5 points) a 6.25s + g b 6.25(s + g) c 13.50(s + g) d 13.50s + g Question 3 (5

Step-by-step answer

P Answered by PhD

1

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)

Hence, the equivalent expression of the given expression is 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

Hence, 20 more people preferred Fortnite to Among Us

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

$Captain\ America = 60 - 15 -12 - 21$

$Captain\ America = 12$

By comparison, Thor cleaned the highest number of cities

7. This question is not clear

$Total = \$70$

$Glass = \$30$

$Each\ Cape = \$8$

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:

$10.01 * p + 9.96 \leq 50$

$10.01 p + 9.96 \leq 50$

$10.01 p \leq 50 - 9.96$

$10.01 p \leq 40.04$

$p \leq 4$

Mathematics

Determine which expression is equivalent to 15a + 6. (5 points) a 3(5a + 6) b 3(5a + 2) c 5(3a + 6) d 5(3a + 2) Question 2 (5 points) (03.01 LC) Excellence Middle School charges $6.25 for students from all grade levels to attend the school dance. If s represents the number of seventh grade students who came to the dance and g represents the number of eighth grade students at the dance, which expression best represents the total money collected for attending the dance. (5 points) a 6.25s + g b 6.25(s + g) c 13.50(s + g) d 13.50s + g Question 3 (5

Step-by-step answer

P Answered by PhD

1

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)

Hence, the equivalent expression of the given expression is 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

Hence, 20 more people preferred Fortnite to Among Us

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

$Captain\ America = 60 - 15 -12 - 21$

$Captain\ America = 12$

By comparison, Thor cleaned the highest number of cities

7. This question is not clear

$Total = \$70$

$Glass = \$30$

$Each\ Cape = \$8$

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:

$10.01 * p + 9.96 \leq 50$

$10.01 p + 9.96 \leq 50$

$10.01 p \leq 50 - 9.96$

$10.01 p \leq 40.04$

$p \leq 4$

Mathematics

Ava, grace, jayden, and zoe together stacked a total of 50 brownies on a tray. ava stacked 0.14 of the brownies, grace stacked 4 of the 50 brownies, jayden stacked 24% of the brownies, and zoe stacked the remaining brownies. who stacked the most brownies? ava grace jayden zoe question 6(multiple choice worth 5 points) (03.04 mc) solve for x: negative 4 over 3, multiplied by x minus 6 equals negative 26 −27 −15 15 27 question 7(multiple choice worth 5 points) (03.05 mc) natalie works in a toy shop and earns $43 per day. she earns an extra $3 for

Step-by-step answer

P Answered by PhD

6

1. Zoe stacked the most brownies. She stacked 27 brownies out of the 50 brownies.

2. 15

3. 43 + 3n ≥ 70, so n ≥ 9

4. D. 58x + 13 + 58y

5. The answer would be ≤4

6. 9.94 + 10.01p ≤ 70, so p ≤ 6

7. C4089

8. D. x+(x+5)=77

Hope I helped you! Please consider marking my answer the brainliest :)

Mathematics

Ava, grace, jayden, and zoe together stacked a total of 50 brownies on a tray. ava stacked 0.14 of the brownies, grace stacked 4 of the 50 brownies, jayden stacked 24% of the brownies, and zoe stacked the remaining brownies. who stacked the most brownies? ava grace jayden zoe question 6(multiple choice worth 5 points) (03.04 mc) solve for x: negative 4 over 3, multiplied by x minus 6 equals negative 26 −27 −15 15 27 question 7(multiple choice worth 5 points) (03.05 mc) natalie works in a toy shop and earns $43 per day. she earns an extra $3 for

Step-by-step answer

P Answered by PhD

6

1. Zoe stacked the most brownies. She stacked 27 brownies out of the 50 brownies.

2. 15

3. 43 + 3n ≥ 70, so n ≥ 9

4. D. 58x + 13 + 58y

5. The answer would be ≤4

6. 9.94 + 10.01p ≤ 70, so p ≤ 6

7. C4089

8. D. x+(x+5)=77

Hope I helped you! Please consider marking my answer the brainliest :)

Mathematics

In order to raise money for holiday gifts for your family, you are planning on starting a dog walking and car wash business. you earn $12 per hour while dog walking and $18 per hour washing cars. you need to earn at least $600 during the month of november. 1.assign a variable to represent the number of hours that you will spend dog walking in november. write an expression to represent the amount of money you need to earn while dog walking. 2.assign a variable to represent the number of hours that you will spend washing cars in november. write an

Step-by-step answer

P Answered by PhD

5

1.

x= number of dog walking hours; x≈300

2.

y= number of car washing hours; y≈300

3.

Ax+By≥600

4.

The download

5.

a- The graph can only exist in the first quadrant because you cannot work a negative amount of hours and/or get a negative amount of money.

b- You are able to earn a exact $600 if you work 23 hours of dog walking and 18 hours of car washing.

23x12=276 18x18=324 276+324=600

c- It is possible to earn greter than $600.

30x12=360 22x18=396 360+396>600

all combinations that occur on the graph are in quadrant one

d- If you work for 10 hours walking dogs and 10 hours washing cars, you will not have enough money.

10x12=120 10x18=180 120+180=300 300<600

(10,10) is not on the line therefore it is not a possible solution for the equation

6.

The model would be changed from Ax+By≥600 to Ax+By>600 becuase you need to earn MORE than 600 so there should not be a line under the symbol. The graph of the model would not be changed because you still are earning $12 and/or $18 an hour. A dotted line and the shaded area under the line represents more than.

7.

The difference between a dotted line and a solid line is that a dotted line is either more than or less than, while a solid line is more than or equal to and less than or equal to. When graphing, you would use a dotted line for equations that are not equal to or more or less.

8.

You determine whether or not that a shaded area is either he solution to a problem or not the solution.

Mathematics

In order to raise money for holiday gifts for your family, you are planning on starting a dog walking and car wash business. you earn $12 per hour while dog walking and $18 per hour washing cars. you need to earn at least $600 during the month of november. 1.assign a variable to represent the number of hours that you will spend dog walking in november. write an expression to represent the amount of money you need to earn while dog walking. 2.assign a variable to represent the number of hours that you will spend washing cars in november. write an

Step-by-step answer

P Answered by PhD

5

1.

x= number of dog walking hours; x≈300

2.

y= number of car washing hours; y≈300

3.

Ax+By≥600

4.

The download

5.

a- The graph can only exist in the first quadrant because you cannot work a negative amount of hours and/or get a negative amount of money.

b- You are able to earn a exact $600 if you work 23 hours of dog walking and 18 hours of car washing.

23x12=276 18x18=324 276+324=600

c- It is possible to earn greter than $600.

30x12=360 22x18=396 360+396>600

all combinations that occur on the graph are in quadrant one

d- If you work for 10 hours walking dogs and 10 hours washing cars, you will not have enough money.

10x12=120 10x18=180 120+180=300 300<600

(10,10) is not on the line therefore it is not a possible solution for the equation

6.

The model would be changed from Ax+By≥600 to Ax+By>600 becuase you need to earn MORE than 600 so there should not be a line under the symbol. The graph of the model would not be changed because you still are earning $12 and/or $18 an hour. A dotted line and the shaded area under the line represents more than.

7.

The difference between a dotted line and a solid line is that a dotted line is either more than or less than, while a solid line is more than or equal to and less than or equal to. When graphing, you would use a dotted line for equations that are not equal to or more or less.

8.

You determine whether or not that a shaded area is either he solution to a problem or not the solution.

Mathematics

Neil places £2000 in a bank account that pays 1.5% simple interest per year. How much interest will he earn in 6 years?

Step-by-step answer

P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics

You can buy jars of the same jam in 2 sizes large jar:440g for £1.54 small jar:340g for £1.26 By considering the price per gram, work out which jar is the best value for money. Working must be shown

Step-by-step answer

P Answered by PhD

Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

Which is the graph of the inequality in which y must be at least 5 greater than 3 times x?

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