1. Refer to the equation 3x - 2y = -18 Complete the table of values for at least 2 points. Show your work.
Use the table of values to graph the line.

2. Use the equation y = 4x to answer the questions. Graph y = 4x.
What is the slope of y = 4x and what does this mean?

Final answer:

To solve the system of equations using elimination, we need to eliminate one variable at a time by adding or subtracting the equations. The solution to the system of equations is x = 1, y = 2, z = 3.

Explanation:

To solve the system of equations using elimination, we need to eliminate one variable at a time by adding or subtracting the equations. Here are the steps:

Therefore, the solution to the system of equations is x = 1, y = 2, z = 3.

To solve the given system of equations by elimination, eliminate one variable at a time. Solve the new set of equations simultaneously to find the values of the remaining variables.

To solve the given system of equations by elimination, we'll eliminate one variable at a time. First, let's eliminate the variable 'z' by adding the second equation to the third equation. This gives us a new third equation:

2x - 3y + z = 4

+ 3x + 4y - z = -2

------------------

5x + y = 2

Now, let's eliminate the variable 'y' by multiplying the second equation by -6 and adding it to the first equation. This gives us a new first equation:

X - 6y + 2z = 5

- 6(2x - 3y + z) = -6(4)

------------------------

-11x - 11z = -19

Finally, we can solve these two new equations simultaneously to find the values of 'x' and 'z'. Once we have 'x' and 'z', we can substitute these values back into any of the original equations to find the value of 'y'.

Answer:

c

Step-by-step explanation:

495/220 can be simplified to 9/4 by dividing the numerator and denominator by 55

the answer to what is 495/220 in simplest form is 9/4

The boy is 9

9x2=18

18+9=27

In this explanation, we'll determine the age of the boy using algebraic equations based on the given information. Let's represent the boy's age as X and his sister's age as 2X.

Let's set up the equations based on the information provided:

1. The boy's age: X years

2. His sister's age: 2X years (twice as old as the boy)

3. The sum of their ages: 27 years

Using these three pieces of information, we can create an equation to find the value of X (the boy's age).

1. The first equation represents the sum of their ages:

X + 2X = 27

2. Simplify the equation by combining like terms:

3X = 27

3. Now, isolate X by dividing both sides of the equation by 3:

X = 27 / 3

4. Calculate X:

X = 9

So, the boy is 9 years old.

Let's represent the boy's age as X and his sister's age as 2X. The sum of their ages is given as 27 years.

1. We can express the sum of their ages in an equation:

X + 2X = 27

2. Combine the like terms on the left side of the equation:

3X = 27

3. To find the value of X, isolate X on one side of the equation. We do this by dividing both sides of the equation by 3:

X = 27 / 3

4. Simplify the expression:

X = 9

Thus, the boy is 9 years old, and his sister is twice as old, which makes her 18 years old (2 * 9 = 18).

The sum of their ages, 9 + 18, indeed equals 27.

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A manufacturing company has the following fixed monthly costs and unit variable costs:

Rent = $2,200

Utilities = $375

Variable costs for materials and assembly = $13.25/unit

Monthly labor = $750

Given is the product is sold at $24.99 per unit

Let the number of units sold be x

Adding total cost = [tex]2200+375+750=3325[/tex]

Equation becomes:

[tex]3325+13.25x=24.99x[/tex]

[tex]11.74x=3325[/tex]

x= 283.21

So, rounding it to nearest whole number we get, 283 units.

D) -(-a) = a because -(-a) is the same thing as positive a

120

bc its grater than four in this case forty

Answer:

3n - 8 > 22

Step-by-step explanation:

Let the number be n.  Then "eight less than three times the number" is represented by 3n - 8 > 22.

Answer:

i need help too yall

Step-by-step explanation:

Simplifying

x + -3(2x + -7) = 76

Reorder the terms:

x + -3(-7 + 2x) = 76

x + (-7 * -3 + 2x * -3) = 76

x + (21 + -6x) = 76

Reorder the terms:

21 + x + -6x = 76

Combine like terms: x + -6x = -5x

21 + -5x = 76

Solving

21 + -5x = 76

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-21' to each side of the equation.

21 + -21 + -5x = 76 + -21

Combine like terms: 21 + -21 = 0

0 + -5x = 76 + -21

-5x = 76 + -21

Combine like terms: 76 + -21 = 55

-5x = 55

Divide each side by '-5'.

x = -11

Simplifying

x = -11

The solution of expression is, x = - 11

We have to give that,

An expression to simplify,

x - 3 (2x - 7) = 76

Now, Simplify the expression as,

x - 3 (2x - 7) = 76

x - 6x + 21 = 76

- 5x = 76 - 21

- 5x = 55

x = - 55/5

x = - 11

Therefore, Solution is, x = - 11

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The equivalent ratios are calculated as;

1) 16/20

2) 8/12

3) 8/9

4) 9/21

5) 4/5

6) 6/9

Equivalent ratio is a ratio that is equal to another ratio when broken down or when numerator and denominator are multiplied by same number.

1) The ratio is given as 4/5.

If the denominator is 20, then it means the equivalent numerator will be;

(20/5) * 4 = 16.

Equivalent ratio = 16/20

2) The ratio is given as 2/3.

If the denominator is 12, then it means the equivalent numerator will be;

(12/3) * 2 = 8.

Equivalent ratio = 8/12

3) The ratio is given as 24/27

If the denominator is 9, then it means the equivalent numerator will be;

(9/27) * 24 = 8

Equivalent ratio = 8/9

4) The ratio is given as 3/7.

If the numerator is 9, then it means the equivalent denominator will be;

(9/3) * 7 = 21.

Equivalent ratio = 9/21

5) The ratio is given as 8/10.

If the denominator is 5, then it means the equivalent numerator will be;

(5/10) * 8 = 4.

Equivalent ratio = 4/5

6) The ratio is given as 30/45.

If the numerator is 6, then it means the equivalent denominator will be;

(6/30) * 45 = 9.

Equivalent ratio = 6/9

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Answer:

A. [tex]\frac{1}{4}n=5[/tex]

The solution is: n=20

Step-by-step explanation:

1. You have the following information given in the problem above:

- The hitter batted [tex]\frac{1}{4}[/tex] of the runs the team scored.

- The hitter batted in 5 runs.

2. If [tex]n[/tex] is the number of run the team scored, then [tex]\frac{1}{4}[/tex] of [tex]n[/tex] must be equal to five runs batted by the hitter. Therefore, the equation is:

[tex]\frac{1}{4}n=5[/tex]

3. Solve for [tex]n[/tex], as following:

[tex]\frac{1}{4}n=5\\n=(5)(4)\\n=20[/tex]

Answer:

2/3

Step-by-step explanation:

8/10 is 0.800, and 1/3 is 0.333333333337, so without going over 1 but saying below 0.800 would be 2/3 or 0.66666666667

1/3= 0.333

8/10=0.8

so 2 1/3 can go into 8/10

point slope form  (y-y1) = m(x-x1)

y-5=(2/3)(x-(-3))

y-5=(2/3)(x+3)                    add 5 to each side and distribute

y= 2/3x +2/3 *3 +5

y = (2/3)x +2 +5  

y = (2/3) + 7                        

well, 112 divided by 7 is 16 :)

you dont need to split it because 112 can already be divided by 7, youre answer sould be 16. I hope this helps!!!

The equation of the line parallel to y=3x-2 and containing the point (2,11) is y=3x+5.

The equation of a line that is parallel to y=3x-2 will have the same slope as this line. Since the slope of the given line is 3, the parallel line will also have a slope of 3. The equation of a line can be represented in the form y=mx+b, where m is the slope and b is the y-intercept. We can find the equation of the parallel line by substituting the given point (2,11) into the equation.

Start with the equation y=3x+b and substitute x=2 and y=11.

11=3(2)+b

Now solve for b.

11=6+b
b=11-6
b=5

The equation of the parallel line is therefore y=3x+5.

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Answer:

40

Step-by-step explanation:

Got it on edge

Answer:

Step-by-step explanation:

Simplifying

16 = -12 + -7x

Solving

16 = -12 + -7x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '7x' to each side of the equation.

16 + 7x = -12 + -7x + 7x

Combine like terms: -7x + 7x = 0

16 + 7x = -12 + 0

16 + 7x = -12

Add '-16' to each side of the equation.

16 + -16 + 7x = -12 + -16

Combine like terms: 16 + -16 = 0

0 + 7x = -12 + -16

7x = -12 + -16

Combine like terms: -12 + -16 = -28

7x = -28

Divide each side by '7'.

x = -4

Simplifying

x = -4

5.6 * 10^ 15 / 6.4 * 10^2

5.6 /6.4   10^ (15-2)

.875 * 10^13  this is not proper scientific notation  there must be 1 number before the decimal

8.75 * 10^12

C

Answer:

Step-by-step explanation:

THE ANSWER IS C. I DID IT

Step 1. Split the second term in 2x^2 - x - 21 into two terms

2x^2 + 6x - 7x - 21

Step 2. Factor out the common terms in the first two terms, then in the last two terms.

2x(x + 3) -7(x + 3)

Step 3. Factor out the common term x + 3

(x + 3)(2x - 7)

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10-9.

So, if we are dealing with 965000000000000, then the answer would be:

9.65 x 10^14

Answer:

a)Domain is all positive integers.

b)C(2000)=$7600

c) For C(x)<10000,  less than 3846 items should be manufactured.

Step-by-step explanation:

Given that cost function is C(x)=5000+1.3x, where x is the number of manufactured items.

a) The domain of C(x) means the range of values x can take. Since x is the number of manufactured items, it cannot be negative and fraction.

Hence domain is all positive integers.

b)To find the cost of 2000 items, we should plugin x=2000 in C(x).

That is cost of 2000 items, C(2000)=5000+1.3(2000)=5000+2600=$7600

c) We are asked to find the number of items such that cost is kept below 10,000 that is C(x)<10000

            5000+1.3x<10000

Subtract 5000 from both sides

                     1.3x<5000

Divide with 1.3 on both sides

                    [tex]x<\frac{5000}{1.3}[/tex]

                     x<3846.2

Hence number of items must be less than 3846 for C(x)<10000

Final answer:

The reasonable domain of the cost function is x >= 0. The cost of 2,000 items that must be kept below $10,000 is $7,600. The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).

Explanation:

The reasonable domain of the cost function is x >= 0 since the number of items manufactured cannot be negative. In other words, the function is valid for all non-negative values of x.

To find the cost of 2,000 items that must be kept below $10,000, we substitute x = 2,000 into the cost function:
C(2,000) = 5,000 + 1.3 × 2,000

Simplifying this equation, we get:
C(2,000) = 5,000 + 2,600 = $7,600

To determine the greatest number of items that can be manufactured with a cost below $10,000, we need to solve the inequality:
5,000 + 1.3x < 10,000

Simplifying this inequality, we have:
1.3x < 5,000

Dividing both sides of the inequality by 1.3, we obtain:
x < 3,846.15

The greatest number of items that can be manufactured with a cost below $10,000 is 3,846 (rounded down).

since you know Lainey has 20 markers and the total cost is $6, all you have to do is solve 20/6 to find the cost of each marker. So, the answer would be about $2.33 dollars, since 20/6 would equal $2.333333333... and I just rounded it up. Hope I helped you! Good luck (:

Final answer:

Each student will receive 2 slices of pizza, as there are a total of 32 slices from 4 pizzas divided among 16 students.

Explanation:

To determine the number of pizza slices each student receives, we need to calculate the total number of slices available and then divide this by the number of students. Given that there are 4 pizzas and each pizza is cut into 8 slices, we have:

Multiply the number of pizzas by the number of slices per pizza: 4 pizzas × 8 slices/pizza = 32 slices.

Divide the total number of slices by the number of students: 32 slices ÷ 16 students = 2 slices/student.

Therefore, the function that represents the number of pizza slices each student receives is 2 slices per student.

[tex]-3x^2+2y^2+5xy-2y+5x^2-3y^2[/tex]

Combine like terms:

[tex]2x^2-y^2+5xy-2y\\2x^2-y^2-2y+5xy[/tex]

There are 4 terms, 2 terms are negative.