Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a) Simplify the expression and explain each step. (2 points)
4(3x+2)−2
b) Factor the expression completely. (1 point)
20b−16

Answer:

18x + 1

Step-by-step explanation:

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

6x + 21 + 12x - 20

6x + 12x + 21 - 20

18x + 1

Answer:

18x+1

Step-by-step explanation:

3(2x+7)-4(-3x+5)= 6x+21+12x-20

Combine Like Terms:

6x+12x= 18x

21-20=1

=18x+1

Answer:

Answer below

Step-by-step explanation:

It would be 36×2=72

since we're doubl8ng it so there would be 72 hooded sweatshirts

Answer:

24 Hooded Sweatshirts

Step-by-step explanation:

36/3=12

2x12=24 or hooded sweatshirts

1x12=12 or crewneck sweatshirts

12+24=36 total sweatshirts :)

Answer:

10¢

Step-by-step explanation:

First, to be able to differentiate between the B&W and Color copies, use x in place of the B&W copies and y in place of the Color copies.

Then, write a system of equations to solve (the system of equations input was not working, so there is no brace):

 8x + 2y = $1.20

 10x + 10y = $3.00

Then, solve the system of equations:

   8x +  2y = $1.20

 10x + 10y = $3.00

Isolate x to be able to substitute:

8x + 2y = $1.20

8x = -2y + 1.2

x = -2/8y + 1.2/8

x = -0.25y + 0.15

Substitute:

10x + 10y = $3.00

10 (-0.25y + 0.15) + 10y = 3

-2.5y + 1.5 + 10y = 3

7.5y + 1.5 = 3

7.5y = 1.5

y = $0.20

Now that you have the cost of the Colored copies, you can plug it in to find the B&W copies:

8x + 2y = $1.20

8x + 2(0.2) = 1.2

8x + 0.4 = 1.2

8x = 0.8

x = $0.10

Answer:

y = -7

Step-by-step explanation:

The equation of a line is:

y = mx + b    where m = slope

To find b, plug in a point and solve.

(-6,-7)

y = mx + b

-7 = 0(-6) + b

- 7 = 0 + b

-7 = b

So the equation is:

y = 0x + b or

y = -7

No matter what you plug into x, y = -7, because your slope is 0.

The equation of the line that passes through the point (-6,-7) and with slope 0  is [tex]y=-7[/tex].

Point through which the given line passes ≡ (-6,-7)

The slope of the line =0

The equation of a straight line passing through the point (x₁, y₁) is given by: [tex]y-y_1 =m(x-x_1)[/tex]

where m is the slope of the line.

So, the equation of the line that passes through the point (-6,-7) and with slope 0 will be:

[tex]y-(-7) = 0(x-(-7))[/tex]

[tex]y+7 =0[/tex]

[tex]y =-7[/tex]

So, the required equation of the line is y=-7.

Therefore,  the equation of the line that passes through the point (-6,-7) and with slope 0  is [tex]y=-7[/tex].

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Answer:

A

Step-by-step explanation:

Step-by-step explanation:

this is a linear programming problem, and we are expected to draw up the linear program for the solution of the problem.

The objective function is

Maximize

35A+42B+20C=P    

subject to constraints(board and wicker)

The constraints are

  board

7A+5B+4C=3000

 wicker

4A+5B+3C=1400

A>0, B>0, C>0

Step-by-step explanation:

Hey there!

The given points are; (2,2) and (5,y).

Slope (m) =2

Using formula for slope, we get;

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Put all values.

[tex]2 = \frac{y - 2}{5 - 2} [/tex]

Simplify it to get value of"y".

[tex]2 = \frac{y - 2}{3} [/tex]

[tex]6 = y - 2[/tex]

[tex]y = 6 + 2[/tex]

Therefore, y= 8.

Hope it helps...

Answer:

17.2

Step-by-step explanation:

Answer:

13/18

Step-by-step explanation:

See attachment

Answer:

3 meters or 9.9 feet rounded up is 10 feet because they only sell wood by the foot.

Step-by-step explanation:

6 meters - 3 meters = 3 meters

1meter = 3.3 feet

3 meters x 3.3ft = 9.9 feet

Answer:

The first and third ones are correct

Step-by-step explanation:

Hope this helps (:

Answer:

The 4th and 5th one seem to be correct.

Answer:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

Step-by-step explanation:

The slope is 5000, this means that for each additional year Robert works at the company, he earns 5000 more dollars.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Here, given that,

Robert's salary after working for n years can be determined using the equation

S = 5000n + 60000.

Hence, The slope is 5000,

this means that for each additional year Robert works at the company, he earns 5000 more dollars.

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Answer:

Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes from boys? If 55 were girls then there were 123-55 = 68 boys. Thus the ratio would be 55 girls to 68 boys, or 55/68.

Answer:

60

Step-by-step explanation:

Answer:

STEP 3.) x = 9/8

Step-by-step explanation:

x + 5/8 = 7/4

x + 5/8 - 5/8 = 7/4 - 5/8

= x =9/8

Answer:

FV= $5,325.8

Step-by-step explanation:

Giving the following information:

Mr. Clopu buys an 18-month CD that pays 4.34% simple interest for $5,000.

To calculate the future value, we need to use the following formula:

FV= (P*r*t) + P

P= $5,000

r= 0.0434/12= 0.00362

t= 18

FV= [(5,000*0.00362)*18] + 5,000

FV= $5,325.8

The value of the CD at the end of its term is $39,060

Given:

Time = 18 month

Principal = $5000

Interest rate = 434%

Future value = ?

Future value = Principal × Rate × Time

= 5,000 × 434% × 18

= 5000 × 434/100 × 18

= 5000 × 4.34 × 18

= 39,060

Therefore, the value of the CD at the end of its term is $39,060

Read more:

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Answer:

y=408

Step-by-step explanation:

y is directly proportional to x

y=kx (where k is the constant)

102=6k

102÷6=k

17=k

y=17x

find y when x=24

y=17(24)

y=408

Step-by-step explanation:

solve by using the formula

The required equation of a circle with a center (5, -3) and radius of 9 is x² + y² -10x + 6y - 48 = 0.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

where h, k is the coordinate of the center of the circle on the coordinate plane and r is the radius of the circle.

As in the mentioned question,
center (5,-3) and radius is 9,
(x - h)² + (y - k)² = r²

(x - 5)² + (y +3)² = 9²
x² + y² -10x + 6y - 48 = 0

Thus, the required equation of a circle with a center (5, -3) and radius of 9 is x² + y² -10x + 6y - 48 = 0.

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Answer:

Zeros

Roots

Solution (Set)

Step-by-step explanation:

As you can tell there are a handful of different names!

Answer:

The answer is "[tex]\bold{11000(0.83)^t}[/tex]".

Step-by-step explanation:

[tex]\bold{ \text{selling price}} = \$ 11,000 \\\\\bold{ \text{loses}} = 17 \%[/tex]

[tex]\bold{\to f(t)= c (1-r)^t} \\\\[/tex]

           [tex]=11,000 (1- 0.17)^t\\\\=11,000(0.83 )^t[/tex]

Step-by-step explanation:

I hope it helps man this much .

Answer:

the answer is 4800

Answer:

What is mental math?

Mental math is definitely what it sounds like—doing math in your head. But it’s also more nuanced than that. Being good at mental math tricks doesn’t mean that you’re able to solve 8974387 x 396 in your head instantly; while cool, that wouldn’t be very practical for daily life. So what does mental math mean?

It really just means being able to calculate in your head. It doesn’t mean you can solve every type of problem every time, nor is it a skill that you either “have” or “don’t have”; it’s a skill that you can learn, practice, and improve so that you can solve a bigger range of problems. And mental math certainly doesn’t have to be entirely in your head, either. Jotting down the numbers you need to remember to give you a head start (no pun intended), or writing down your solutions at each “step,” does not negate the “mental”-ness of the math.

Is mental math useful?

Ask this question again next time you’re trying to figure out a tip or doing any kind of construction or home improvement project! And, in addition to handy practical uses, knowing how to do mental math can also just keep your brain sharp and curb your reliance on calculators. Because, come on, doesn’t it feel good to reach for a calculator only to realize, “Wait, I don’t need it!” and figure out the answer in your head? (Spoiler: It does!) Not to mention knowing how to mentally solve small, simple math problems can save you some steps and help you out if you do need to solve a more complicated, difficult problem. There are always going to be some math problems that it would be silly to not solve with a calculator, but, yes, mental math is useful. And if you’re wondering if math itself is useful, math lessons you’ll actually use in real life.

Step-by-step explanation:

it is 100 times greater because it is two places higher than 57,080

Answer:

y = 6

x = 0.2

Step-by-step explanation:

5x + y =7

20x + 2 = y

5x(4) + y(4) = 7(4)

20x + 4y = 28

(20x = 28 - 4y) = (20x = y - 2)

28 - 4y = y - 2

30 - 4y = y

30 = 5y

y = 6

5x + y =7

20x + 2 = y

y = 7 - 5x

7 - 5x = 20x + 2

5 - 5x = 20x

5 = 25x

x = 0.2

Answer:

m<WYZ = 23°

m<ACB = 87°

Step-by-step explanation:

Problem 1: Find WYZ

Given,

m<WVX = (3x - 7)°

m<VYZ = (16x - 3)°

∆WYZ ~ ∆WVX, therefore:

m<WYZ = m<WVX (corresponding angles of similar triangles are congruent)

m<WYZ = (3x - 7)° (substitution)

Create an equation to find the value of x.

m<WYZ + m<VYZ = 180° (linear pair)

(3x -7)° + (16x - 3)° = 180° (substitution)

Solve for x

3x - 7 + 16x - 3 = 180

Add like terms

19x - 10 = 180

Add 10 to both sides

19x - 10 + 10 = 180 + 10

19x = 190

Divide both sides by 19

19x/19 = 190/19

x = 10

m<WYZ = (3x - 7)

Substitute x = 10

m<WYZ = 3(10) - 7 = 30 - 7

m<WYZ = 23°

Problem 2: Find m<ACB

Given,

m<A = 62°

m<AED = (11x - 2)°

m<B = (6x + 13)°

∆ADE ~ ∆ACB, therefore:

m<AED = m<B (corresponding angles of similar ∆s are congruent)

(11x - 2)° = (6x + 13)°

Solve for x

11x - 2 = 6x + 13

Collect like terms

11x - 6x = 2 + 13

5x = 15

Divide both sides by 5

5x/5 = 15/5

x = 3

m<ACB + m<B + m<A = 180° (sum of ∆)

m<ACB + (6x + 13) + 62° = 180° (substitution)

Plug in the value of x and solve

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (6(3) + 13) + 62° = 180°

m<ACB + (18 + 13) + 62° = 180°

m<ACB + 31° + 62° = 180°

m<ACB + 93° = 180°

Subtract 93 from both sides

m<ACB = 180° - 93°

m<ACB = 87°

Answer:

D

Step-by-step explanation:

Cause the calculator says so...

Answer:

65.44

Step-by-step explanation:

I copied and pasted but this is the answer 65.44

Answer:

4,963.85

Step-by-step explanation:

Step-by-step explanation:

We have

87+86+x

T is the total scores

n is number of tests done = 3

T/n is greater than or equal to 90

To get minimum test

T/n = 90

T = 90*n

= 90n

We solve for x

Remember n = 3

90x3 = 270

270 = 87+86+x

270 = 173+x

X = 270-173

X = 97

1.

X = 97

2.

You didn't add a value in your part b question. I used 80 though.

T/n < 80

T<80n

80x3= 240

T<240

87+86+x<240

X<240-173

X<67

X has to be less than 67 so we conclude that if x <=67 b grade will be lost.

Answer:

A, melody completed factoring

Step-by-step explanation:

Melody has completely factored the expression which is correct option(A).

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given the expression,

⇒ x³ - 2x² + 4x - 8

⇒ x²(x - 2) + 4(x - 2)

⇒ (x² + 4)(x - 2)

So, factors of given expression are (x² + 4)  and (x - 2).

Hence, Melody has completely factored the expression.

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Answer:

y = 5.25x + 4

Step-by-step explanation:

(hours, money)

(6, 34.50)

(8, 46.00)

Slope: change in y/change in x

11.5/2

5.25

Y - intercept: b

46 = 5.25(8) + b

46 = 42 + b

4 = b

Put it all together