A student solved the equation 7 = 3(t - 1) - 2(t - 3) as shown below. Assume there is a value for t that satisfies the equation. Provide a justification for each step of the solution process. LaTeX: 7\:=\:3\left(t-1\right)-2\left(t-3\right)7 = 3 ( t − 1 ) − 2 ( t − 3 ) LaTeX: 7\:=\:3t\:-3-2t\:+67 = 3 t − 3 − 2 t + 6 LaTeX: 7\:=\:t\:+37 = t + 3 Justification: ? like terms

PLEASE ANSWER!!

Answer:

(x - 6)(x + 4)(x - 2)

Step-by-step explanation:

since x = 6 is a root then (x - 6) is a factor

x³ - 4x² - 20x + 48 ÷ (x - 6)

= (x - 6)(x² + 2x - 8)

= (x - 6)(x + 4)(x - 2) ← factors of f(x)

By using the Remainder Theorem, all the factors of the function are,

⇒ (x - 6) (x + 2) (x - 4)

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

One root of function f (x) = x³ -4x² -20x + 48 is,  x = 6.

Hence, (x - 6) is divide the function  f (x) = x³ -4x² -20x + 48 as;

(x - 6) ) x³ -4x² -20x + 48 ( x² + 2x - 8

           x³ - 6x²

         --------------

                 2x² - 20x

                 2x² - 12x

                 -----------------

                         - 8x + 48

                         - 8x + 48

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

                                      0

Hence, We get;

f (x) = x³ -4x² -20x + 48

f (x) = (x - 6) (x² + 2x - 8)

⇒ f (x) = (x - 6) (x² - 4x + 2x - 8)

⇒ f (x) = (x - 6) (x(x - 4) + 2(x - 4))

⇒ f (x) = (x - 6) (x + 2) (x - 4)

Thus., By using the Remainder Theorem, all the factors of the function are,

⇒ (x - 6) (x + 2) (x - 4)

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Answer:

2c + 15 = 25

Step-by-step explanation:

The total he wants to earn is $25, so we know the equation must be an expression that equals 25.

____ = 25

He earns a fixed $15. He also earns $2 per customer.

The total he earns is the sum of the fixed amount ($15) and the amount he earns per customer. Let the number of customers be c. The amount he earns from the number of customers is 2c.

fixed amount + amount per customer = 25

15 + 2c = 25

2c + 15 = 25

Answer: 2c + 15 = 25

Answer:

3(2a+4b+7)+6a = 12a+12b+21

Step-by-step explanation:

The square of a number minus TWICE the number is 48

let the number be" X "

X^2-2X-48 = 0

(X - 8)(X + 6) = 0

x = 8 ᴏʀ X = -6

mark brainliest

The values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively

From the question,

The given function is g(x) = 4 - 3x

We are to evaluate the function for the given values of x

put the value x = -3 into the function

That is,

g(x) = 4 - 3x becomes

g(-3) = 4 - 3(-3)

g(-3) = 4 + 9

g(-3) = 13

Put the value x = 0 into the function

That is,

g(x) = 4 - 3x becomes

g(0) = 4 - 3(0)

g(0) = 4 - 0

g(0) = 4

Put the value x = 5 into the function

That is,

g(x) = 4 - 3x becomes

g(5) = 4 - 3(5)

g(5) = 4 - 15

g(5) = -11

Hence, the values of the given function when x = -3, 0, and 5 are 13, 4, and -11 respectively

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Answer:

6 days

Step-by-step explanation:

Let the time taken by Carpenter working alone = [tex]C[/tex] days

Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2[tex]C[/tex] days

Time taken working together = 2 days

Work done in one day working together = [tex]\frac{1}{2}[/tex]

Work done in one day by Carpenter working alone = [tex]\frac{1}{C}[/tex]

Work done in one day by apprentice working alone = [tex]\frac{1}{2C}[/tex]

Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone =  [tex]\frac{1}{C}[/tex]+[tex]\frac{1}{2C}[/tex] = Work done in one day working together = [tex]\frac{1}{2}[/tex]

[tex]\dfrac{1}{C}+\dfrac{1}{2C}=\dfrac{1}{2}\\\Rightarrow \dfrac{2+1}{2C}=\dfrac{1}{2}\\\Rightarrow C = 3\ days[/tex]

Time taken by Carpenter alone to complete the work = 3 days

Time taken by Apprentice alone to complete the work = 3 [tex]\times[/tex] 2= 6 days

We are required to calculate the number of days it would take the apprentice working alone

The number of days it takes the apprentice working alone is 6 days

let

Number of days taken for the carpenter to work alone = x

Number of days taken by the apprentice to work alone = 2x

Number of days taken to work together = 2 days

Work done per day Carpenter = 1/x

work done per day apprentice = 1/2x

work done per day together = 1/2

So,

work done per day together = Work done per day Carpenter + work done per day apprentice

1/2 = 1/x + 1/2x

1/2 = (2 + 1) / 2x

1/2 = 3/2x

cross product

1(2x) = 2(3)

2x = 6

x = 6/2

x = 3 days

Therefore,

Number of days taken by the apprentice to work alone = 2x

= 2(3)

= 6 days

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Answer:

(-1, 6)

Step-by-step explanation:

Midpoint formula:

For G(-7, 3) and H(5, 9) the midpoint:

Answer:

(-1,6)

Step-by-step explanation

use the midpoint formula:

(x 1 + x2 /2 , y1 + y2/2)

(-7+ 5 /2, 3+ 9 /2)

after simplfying

(-1,6)

Answer:

second option

Step-by-step explanation:

Given

A = 4xy ( to isolate x divide both sides by 4y )

[tex]\frac{A}{4y}[/tex] = x , that is x = [tex]\frac{A}{4y}[/tex]

Answer:

Statements B, D, E are TRUE

Step-by-step explanation:

A. The expression 50ℎ represents the total charge for Rock the House Digital Designs.

NOT TRUE

The expression 500 + 50h represent total charge for Rock the house digital design

B. The expression 75ℎ represents the total charge for Elegance Home Architects.

TRUE

Elegance Home Architects

75h

C. The cost for using Rock the House Digital Designs for an initial consultation only is $550.

NOT TRUE

The cost for using Rock the House Digital Designs for an initial consultation only is $500

D. If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

TRUE

Rock the house digital designs

$500 + $50h

= 500 + 50(15)

= 500 + 750

=$1,250

Elegant home architect

$75h

= 75(15)

= $1,125

Elegant home architect is cheaper

E. If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

TRUE

Rock the house digital designs

$500 + $50h

= 500 + 50(40)

= 500 + 2,000

= $2,500

Elegant home architect

$75h

= 75(40)

= $3,000

Rock the House Digital Designs will be cheaper.

Answer:

The number of hours Moran wold have driven before Andre catches up with him is 14 hours

Step-by-step explanation:

The given information are;

The speed with which Andre will drive = 70 miles per hour

The speed with which Morgan will drive = 55 miles per hour

The time of departure of Morgan = 3 hours before Andre departs

Let the time at which Andre catches up with Morgan be, t

We have, from the definition of distance traveled;

Distance traveled =Speed × Time

The distance Morgan would have driven in t hours = 55 × t

Given that to catch up with Morgan, Andre has to travel the same distance, and that Andre starts 3 hours late, we have;

The distance Andre would  drive when Morgan has driven for t hours = 70 × (t - 3)

Therefore, since the distance at the point they meet is the same distance for them both, we have;

55 × t = 70 × (t - 3)

55 × t = 70 × t - 210

210 = 70 × t - 55 × t  = 15 × t

t = 210/15 = 14 hours

Therefore, Morgan would have driven for 14 hours before Andre catches uo with him.

Answer:

Morgan walks 2 miles per hour.

Step-by-step explanation:

took the test. ;)

Answer:

I'm pretty sure it's c and d

Step-by-step explanation:

5/(x + 2) + 3/(x - 4) = 2

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

5x - 20 + 3x + 6 = 2x^2 - 4x - 16

8x - 14 = 2x^2 - 4x - 16

4x - 7 = x^2 - 2x - 8

x^2 - 6x - 1 = 0

By using the quadratic formula, x = (-6 +/-√40)/2.

Answer:

4^-2

Step-by-step explanation:

Answer:

[tex] 2^{-2} [/tex]

Step-by-step explanation:

1/4 is between 0 and 1/2.

[tex] \dfrac{1}{4} = \dfrac{1}{2^2} = 2^{-2} [/tex]

Answer:

Basically  , anything  negative number.

The absolute value can not be less than 0

Step-by-step explanation:

Example

[tex]\left|x+8\right|=-8\\\\\mathrm{Absolute\:value\:cannot\:be\:less\:than\:0}\\\mathrm{No\:Solution\:for}\:x\in \mathbb{R}\\[/tex]

Answer:

20

Step-by-step explanation:

Answer:

first option

Step-by-step explanation:

To find the product, that is

(4x + 1)(x² - 5)

Each term in the second factor is multiplied by each term in the first factor, that is

4x(x² - 5) + 1(x² - 5) ← distribute both parenthesis

= 4x³ - 20x + x² - 5

= 4x³ + x² - 20x - 5

Step-by-step explanation:

X2+ax+b=(x-9)(x+9)

X2+ax+b=x2-9x+9x-81

X2+ax+b=x2-81

therefore,a=0,b=(-81)

Then , ab = 0×-81 = 0

Answer:

Step-by-step explanation:

x² + ax + b = (x – 9)(x + 9)

x² + ax + b = x² – 9x + 9x – 81

x² + ax + b = x² + 0x – 81

x²=x²      +ax = +0x        +b = -81

                    a = 0            b = -81

ab = 0(-81) = 0    

Answer:

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

5^4 x 5^3/5^5

5^(3+4)/5^5

5^7/5^5

5^(7-5)

5^2

25

Answer:

5 to the power of 2.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the angles ∠ABF=8s-6, ∠ABE = 2(s + 11), we are to find the angle ∠EBF. The following expression is true for the three angles;

∠ABF = ∠ABE + ∠EBF

Substituting the given angles into the equation to get the unknown;

8s-6 = 2(s + 11)+ ∠EBF

open the parenthesis

8s-6 = 2s + 22+ ∠EBF

∠EBF = 8s-6-2s-22

collect the like terms

∠EBF = 8s-2s-22-6

∠EBF = 6s-28

factor out the common multiple

∠EBF = 2(3s-14)

Hence the measure of angle ∠EBF is 2(3s-14)

Answer:

m = -4

Step-by-step explanation:

m - 4 = 2m

Switch sides.

2m = m - 4

Subtract m from both sides.

m = -4

Answer:

-4

Step-by-step explanation:

cause mafs

Answer:

v^2 -4v-21

Step-by-step explanation:

Answer:

C.  Every integer is a rational number

Step-by-step explanation:

Integers are whole numbers which could be positive or negative and zero. Examples of integers are 330, 21, 10,052, 0, -425, -879, etc. Fractions are not integers.  Rational numbers are numbers that are expressed as the ratio of two integers. So numbers that have integers as their numerators and denominators can be rightly said to be rational numbers. Examples are, 5/7, 10,111/880, -365/15.

Since both the numerators and denominators are whole numbers, the entire figures can be said to be rational numbers. So, fractions are rational numbers.    

Answer:

95

Step-by-step explanation:

80+(200 divided by 2)+(420 divided by 4)=285

285 divided by 3=95

Answer:

y = (2-3d)/(7+c)

Step-by-step explanation:

-cy + 2 = 3d + 7y

To solve this equation in terms of y, we must first move all of the terms containing a y to one side of the equation and move all of the other terms to the other side.

Our first step is going to be to add cy to both sides of the equation.

- cy + cy + 2 = 3d + 7y + cy

2 = 3d + 7y + cy

Next, we can subtract 3d from both sides of the equation.

2 - 3d = 7y + cy

Next, we can factor out a y from the right side of the equation.

2 - 3d = y (7 + c)

Finally, we can divide both sides by the quantity (7+c) to get the y alone on the right side of the equation.

(2-3d)/(7+c) = y

Therefore, your answer is y = (2-3d)/(7+c).

Hope this helps!

Answer:

350 miles

Step-by-step explanation:

Let x represent the miles driven

The cost with the first plan will be represented by 0.40x + 70

The second plan will be represented by 0.60x

Set these 2 expressions equal to each other and solve for x:

0.40x + 70 = 0.60x

70 = 0.20x

350 = x

So, Susan will have to drive 350 miles for the cost to be the same

Answer:

9 cm

Step-by-step explanation:

Answer:

11 is the smallest whole number when divided by 4 gives a remainder of 3, when divided by 3 gives remainder of 2, when divided by 2 gives a remainder of 1

. Answer:1.when divide by 4 and gives a remainder of 3 = 12

2 .when divided by 3 gives a remainder of 2 = 6

3. when divided by 2 and gives a remainder of 1 = 2

Step-by-step explanation:

1. 12 ÷ 4 = 3

2. 6 ÷ 3 = 2

3.2 ÷ 2 = 1

Answer:

10

Step-by-step explanation:

478-2=476

476÷17= 10

therefore you put 10 fish in each tank.

Let me know if this helps:)

Answer:

10

Step-by-step explanation:

Answer:

hrheje

Step-by-step explanation:

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