Select the correct answer.

Which expression in factored form is equivalent to this expression?

4(x2 – 2x) – 2(x2 – 3)

A. (2x − 3)(x + 1)

B. 2(x + 1)(x + 3)

C. (2x + 3)(x + 1)

D. 2(x - 1)(x – 3)



Took the test. This is the answer.

Answers

Answer 1

Answer:

D. 2(x - 1)(x – 3)

Step-by-step explanation:

4(x2 – 2x) – 2(x2 – 3)

We would first of all expand the expression given

This becomes

= 4x2 - 8x - 2x2 + 6

Rearrange to enable us simplify

4x2 - 2x2 - 8x + 6

= 2x2 - 8x + 6

Factorize

2 (x2 - 4x + 3)

factorizing further using the factors of 3 that add up to -4

2(x2 - x - 3x + 3)

pick out the common factors

2(x(x-1) -3(x-1)

2(x-1)(x-3)

Option D. 2(x - 1)(x – 3) is right

Answer 2

Using the Factor Theorem, the factored form equivalent to this expression is:

[tex]2(x - 1)(x - 3)[/tex], given by option D.

The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient.

In this problem, the expression is:

[tex]4(x^2 - 2x) - 2(x^2 - 3) = 0[/tex]

[tex]4x^2 - 8x - 2x^2 + 6 = 0[/tex]

[tex]2x^2 - 8x + 6 = 0[/tex]

Which is a quadratic equation with coefficients [tex]a = 2, b = -8, c = 6[/tex].

Hence:

[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(6) = 16[/tex]

[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + 4}{4} = 3[/tex]

[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - 4}{4} = 1[/tex]

Hence, the expression is:

[tex]2(x - 1)(x - 3)[/tex], given by option D.

You can learn more about the Factor Theorem at https://brainly.com/question/24380382


Related Questions

is this correct? help please

Answers

yes! That graph matches the equation

Answer:

yes

Step-by-step explanation:

y = -4/3x + 8 so you would multiply - 4/3 * x. Then you would add 8 to your answer and if the y value equals the value on the graph then it's correct.

Ales read 1/3 of a book Monday. 28 pages Tuesday . still has 1/3 left to read. how many pages in book

Answers

Answer:

there are 84 pages in the book.

Step-by-step explanation:

let's call the pages in the book b.

1/3b + 1/3b + 28 = b

2/3b + 28 = b

subtract 2/3b from both sides of the equation

2/3b - 2/3b + 28 = b - 2/3b

28 = b - 2/3b

28 = b/3

multiply both sides of the equation by 3

28 * 3 = b/3 * 3

28 * 3 = b

84 = b

Answer:

The book has 84 pages

Step-by-step explanation:

Equations

Let's make:

x = number of pages of the book

Alex read 1/3x of the book on Monday, 28 pages on Tuesday, and still has 1/3x left to read. The sum of all these portions add up to the number of pages of the book, thus:

[tex]\displaystyle \frac{x}{3}+28+\frac{x}{3}=x[/tex]

Multiplying by 3:

[tex]x+84+x=3x[/tex]

Simplifying:

x = 84

The book has 84 pages

5
Explain
why 36% is
less than 3/8

Answers

Because 3/8 as a percentage would be 0.375%

Find the value of the power.

8^3 =

Answer

Answers

Answer:512

Step-by-step explanation:

Answer:

512

Step-by-step explanation:

8*8*8=512

Which graph represents a function?

Answers

the bottom right

it goes like \
~\

ish.


just going by the picture it’s the only one on the second row

What is the total cost with sales tax price $17.95 tax 6%

Answers

the answer would be 16.87

Answer:

$19.03

Step-by-step explanation:

Okay, this is a standard percentage problem, so learning how to do this is necessary. First, we have to find what 6% of $17.95 is, since of is our keyword and that means to multiply, and percentages turn into decimals:

17.95 x 0.06 = 1.08

So we have our tax, then we have to add that to our original price to get the whole thing:

17.95 + 1.08 = 19.03

So the total sale price is $19.03

what is the equation in slope-intercept form, of the line prependicular to y= -3/5x +6 that passes through the point with coordinants (12,25)

Answers

Answer:

y=5/3x+5

Step-by-step explanation:

change slope in equation given to the negative reciprocal since the line is perpendicular:

-3/5 to 5/3

put values into point slope form y-y1=m(x-x1)

     y1 = y in the point given, which is 25

     m = slope, which is 5/3

     x1 = x in point given, which is 12

y-25=5/3(x-12)

then solve for slope intercept form y=mx+b to get

y=5/3x+5

1). Solve for n n + 46 = 67


Help helps please help

Answers

Answer:

n=21

Step-by-step explanation:

Subtract 46 from both sides.

n+46−46=67−46

n=21

Answer:

n=21

Step-by-step explanation:

46-67=21

21=n

So the answer is 21.

What’s the percentage as a decimal

Answers

Answer:

0.0006

Step-by-step explanation:

Write the equation for line in slope intercept form, given the point (3,-7) and slope = 9.

Answers

Answer:

y = 9x - 34

Step-by-step explanation:

(3 , -7) ; slope (m) = 9

Slope intercept form:

y - y1 = m(x -x1)

y - [-7] = 9 (x - 3)

y + 7  = 9*x - 9*3

y + 7 = 9x - 27

    y = 9x - 27 - 7

    y = 9x - 34

a scientist recorded the temperature of the first day of spring for 24 hours starting from Midnight their hours the scientist recorded a low of 44°f and a high of 67°f.

Answers

Answer:

so what is the question?

A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the length of the rectangle.

Answers

Answer:

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Step-by-step explanation:

Step(i):-

Let 'x' be the length of the rectangle

Given that the width is 3 feet shorter than the length

The width of the rectangle = x -3

Area of the rectangle = length × width

Step(ii):-

Area of the rectangle = length × width

                                  = x ( x-3)

Given that the area of the rectangle = 70 square feet

                       x ( x-3) = 70

              ⇒   x² - 3x - 70 =0

              ⇒  x² - 10 x + 7 x - 70 =0

             ⇒  x (x -10) +7( x-10) =0

            ⇒ ( x+7) ( x-10) = 0

           ⇒  x =-7 and x=10

Final answer:-

we choose x=10

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

(4x-20)° what is the value of x

Answers

Answer: 4(x−5)

Step-by-step explanation:

I think this is right. If it’s not Im sorry. But if it is hope this helps!

Gordon types 3,572 words in 47 minutes. Find the unit rate.

Answers

Answer:

Gordon types at 76 wpm

Step-by-step explanation:

You can find this by dividing the number of words typed by the number of minutes:

[tex]\frac{3572w}{47m}\\\\= \frac{3572}{47}\frac{w}{m}\\\\= 76\frac{w}{m}\\\\[/tex]

Answer:

78 Words per minute

Step-by-step explanation:

Unit Rate = 3666 Words in 47 minutes

Unit Rate = 78 Words per minute


From a distance of 43 feet from the base of a building the angle of elevation to the top of the
building is 64º. Estimate the height of the building to the nearest foot.
A) 21 feet
B) 39 feet
C) 88 feet
D) 19 feet

Answers

Answer: B 39 ft I think

Step-by-step explanation:

What is the right answer for the ordered pairs?

Answers

Answer:

D. (2, -3) and E. (4,-1)

Step-by-step explanation:

In quadrant IV, the possible x-coordinate that can be gotten can only be positive, while the possible y-coordinate can only be a negative value. Thus, the coordinate pair we can get is a positive x-coory and a negative y-coordinate (x, -y).

Therefore, from the list of options given, the two ordered pairs that belong in Quadrant IV are D. (2, -3) and E. (4,-1)

What is the square root of nine

Answers

Answer: the square root of 9 is 3.

Find the two solutions to the equation below.
(x – 3)(x − 2) = 0
Anyone know how to do it

Answers

Answer:

You have two brackets..divide them as

x-3=0 and x-2=0

so x=3, x=2

The solutions to the equation ( x – 3 )( x − 2 ) = 0 using factors equal to zero are x = 3 and x = 2.

To find the solutions to the equation ( x – 3 )( x − 2 ) = 0, we set each factor equal to zero and solve for x. This is because the product of two factors is equal to zero only if at least one of the factors is zero.

Setting ( x – 3 ) = 0:

x – 3 = 0

x = 3

Setting ( x − 2 ) = 0:

x − 2 = 0

x = 2

Therefore, the solutions to the equation ( x – 3 )( x − 2 ) = 0 are x = 3 and x = 2.

To know more about equation click here :

https://brainly.com/question/28741857

#SPJ2

Susan subscribed to a video game rental service. She pays the same
amount for each video game she rents plus a monthly fee to subscribe to
the service. The cost for different numbers of video game rentals are
shown in the graph.

Answers

Answer:

C

Step-by-step explanation:

Answer: C. $6.00 monthly fee and $1.25 per video game

Step-by-step explanation:

I did the test

Evaluate y=3x for x=2.
y=

Answers

Answer:

y=6

Step-by-step explanation:

y=3x     x=2

y=3(2)

y=6

For the given expression, the value of y is 6.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ y = 3x

Now, For value of x = 2;

The value of y is,

⇒ y = 3x

Substitute x = 2;

⇒ y = 3 × 2

⇒ y = 6

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

pls help me i neeed it first to answer gets a brainliest

Answers

Answer:

A

Step-by-step explanation:

Its counting up by 10 and going up by 2

Answer:

its c

Step-by-step explanation:

Find the point slope equation of the line through (10, -4) with a slope of -6.

Answers

Answer:

y=-6x+56

Step-by-step explanation:

The point-slope equation of a line is given as

y=mx+c   where m is slope and c is y-intercept of a line.

We are given m=-6 and a point (10,-4) which can be put into y=mx+c to find the only unknown c. Thus,

c=-4+6x10=56.

Now we can easily form the point-slope equation of the line

y=-6x+56.

pls help solve question 3

Answers

Answer:

If m is the midpoint of ab it means am is equal to mb

am = 3x + 8 and mb = 6x-4

and ab  = am + mb

first find the value of x by using am = mb

3x + 8 = 6x - 4

8 + 4 = 6x - 3x

12 = 3x

x = 4

ab = 3 (4) + 8

= 12 + 8 = 20 = mb

ab = am + mb

= 20 + 20

40

so, the value of ab is 40

11. A man is buying a lot which measures 7,860 square meters. How many
hectares of land is he buying?
A. 78,600 hectares
B. 0.7860 hectare
C. 786,000 hectare
D. 0.07860 hectare​

Answers

Answer:

C. 786,000 hectare

Step-by-step explanation:

This question can be solved by proportions, using conversion of units.

Each hectare has 10 000 square meters.

So 7,860 square meters is equal to:

7,860*10000 =  786,000 hectares

The answer is given by option C.

Parker drank 36 fluid ounces of a sports drink at her basketball game. How many pints did she drink

Answers

Answer:

2 1/4 pints

Step-by-step explanation:

create a ratio with the fact there are 16 ounces in 1 cup

let 'p' = number of pints

16 = 36

 1         p

cross-multiply:  16p = 36

                            p = 36/ 16, which is 9/ 4, or 2 1/4

Ayo help a girly out

(1)Simplify each expression. (Make sure to find those "like" terms)

3x + 9 + 2x − 5
Options: 6x + 4

14x - 5

9x

5x + 4
______________________________________________________________
(2)Simplify each expression. (Make sure to find those "like" terms)

7m + 2(m − 5y)

Options: 14m - 5y

9m - 10y

9m - 5y

7m + 10y
_________________________________________________________________
If you're helping tysm my guy ily

Answers

Answer 1: 5x + 4

Answer 2: 9m + -10y

Step-by-step explanation:

To simplify 3x + 9 + 2x − 5, you have to find the like terms which are 3x and 2x, and 9 and -5. So you get 3x + 2x + 9 - 5 which gives you the result of 5x + 4. Now to simplify 7m + 2 (m − 5y), you have to distribute first, so 7m + (2) (m) + (2) (−5y) which gives you 7m + 2m + −10y. So now you just have to add. 7m + 2m = 9m and then you have -10y so basically the answer is 9m + -10y.

I hope this helps you bro

Three of the vertices of square ABCD are located at A(0,3), B(4,0), and C(7,4).
Determine the area of square ABCD.​

Answers

Answer:

The area of the square ABCD is 25 square units

Step-by-step explanation:

The square ABCD has three of its vertices at A(0,3), B(4,0), and C(7,4). The fourth vertex has been also plotted in the image attached below.

The area of the square is

[tex]A = a^2[/tex]

Where a is the length of any of the square's sides. We only have to find the distance from any two consecutive vertices, for example, A(0,3), B(4,0):

[tex]a=\sqrt{(4-0)^2+(0-3)^2}[/tex]

[tex]a=\sqrt{16+9}=\sqrt{25}=5[/tex]

a = 5

Calculating the distance between any other pair of consecutive vertices would yield the same result. The area is now calculated:

[tex]A = 5^2 = 25[/tex]

The area of the square ABCD is 25 square units

2) An $80 text book was on sale for $49.60 at the used book store. By what percent did the book decrease in price?​

Answers

The answer fam is......... 38%

Answer: 38%

Step-by-step explanation:

80x0.62=49.60

Write an algebraic expression for the phrase. 12 minus m
A. m/12 B. 12-m C. 12m D. m-12

Answers

Answer:

it's b

Step-by-step explanation:

literally twelve minus m

Answer:

B

Step-by-step explanation:

12 minus m is, 12 - m


Solve for the angle x.

Answers

Answer:

x=45

Step-by-step explanation:

An entire triangle is 180 degrees and you already know that one angle is 90 degrees. 180 - 90 is 90. Now you have the equation 2x=90.

You then divide each side by 2 to get the x by itself which leaves you with x=45.

Answer:

if I did my math right it's 45 if not please fix me

Step-by-step explanation:

First thing is the the sides are congruent meant the angles have to be the same.

Next is the box indicates 90°.

Last thing is that every triangle is 180°

so if I did this right the equation is 2x+90=180

and using algebra in this you eliminate the 90 by subtract because - is the opposite of + which cancels itself and leaving the total with 90.

Then divide the 90 by 2 as it cancels out 2x leaving the answer with x=45

I hope this helps you

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