IMPORTANT, PLEASE HELP QUICKLY! 15 POINTS
Explain how to factor the expression q(x)=9x2−24x+16 to the expression q(x)=(3x−4)2 . You may show your work. Be sure to include a detailed explanation of your steps.

Answers

Answer 1

Answer:

Given function:

[tex]q(x)=9x^2-24x+16[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex],  find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:

[tex]ac=9 \cdot 16=144[/tex]

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies q(x)=9x^2-12x-12x+16[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies q(x)=3x(3x-4)-4(3x-4)[/tex]

Factor out the common term [tex](3x-4)[/tex]:

[tex]\implies q(x)=(3x-4)(3x-4)[/tex]

Therefore:

[tex]\implies q(x)=(3x-4)^2[/tex]


Related Questions

can someone help with this

Answers

Step-by-step explanation:

-10-2x = 3x+15

5x = -25

x= -5

9x-7=-52
Show all work and justify each step

Answers

Answer:

x = -5

Step-by-step explanation:

9x - 7 = -52

we want to single out x,

add 7 to both sides to be one step closer to getting x alone

9x - 7 + 7 = -52 + 7

9x = -45

divided both sides by 9 to get x alone

9x / 9 = -45 / 9

x = -5

Let me know if you need any clarification!

[tex] 9x - 7 = - 52[/tex]

Firstly rearrange the variable on the left side of the equation...

[tex]9x = - 52 + 7[/tex]

Calculate the sum or differences

[tex]9x = - 45[/tex]

[tex]x = - \frac{45}{9} \\ [/tex]

[tex]x = - 5[/tex]

:)

..

LK
2(x+2y-x-1⁄2y+3);
When 2(5
4
01x + 2 y +6
Ox+2y+6
07x+8y+6
0176x+4y+3
is simplified, what is the resulting expression?

Answers

2(x+2y-x-1/2y+3)2x+2(2y)-2x-2(1/2y)+2(3)2x-2x+4y-y+63y+6

What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread

Answers

The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

What is mean and standard deviation?

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

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sara scores -4 marks if she got 3 correct answers how many were incorrect

Answers

The number of answers that were incorrect will be 7.

How to depict the information?

From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:

3 - x = -4

where x = incorrect answer

3 - x = -4

-x - 4 - 3

-x = -7

x = 7

In conclusion, the number of answers that were incorrect will be 7.

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Analyze the graph of the cube root function shown
on the right to determine the transformations of
the parent function. Then, determine the values of
a, h, and k in the general equation.
y = a√√x-h+k
h =
k =
DONE✔

Answers

The values of a, h, and k in the general equation is h=1, k=4 and a=2

What is parent function?

The function which can be transformed into different ways is the parent function.

On a coordinate plane, a cubic function approaches the x-axis in quadrant 2, crosses the y-axis at (0, 2), has an inflection point at (1, 4), and the goes through (2, 6).

The given function is

y =a³ √(x -h) + k

Put the coordinate (0,2) in the equation, we get

2 = a³ √(0 -h) + k..................(1)

Plug (1, 4), we have

4 =  a³ √(1 -h) + k..................(2)

Plug (2, 6), we have

6 =  a³ √(2 -h) + k..................(3)

On solving these three equations, we have

h=1

k=4

a=2

Thus, value of h is 1, k is 4 and a is 2.

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Answer:

the rest of the answers are:

C

B

C

A

D F

A C D

A

D

H= 1

K=4

A=2

Step-by-step explanation:

4. Write the function of a linear equation that includes the
points (1,3) and (2,9).

Answers

Answer:

y = 6x - 3

Step-by-step explanation:

the equation of a line in slope- intercept form ( linear function ) is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )

m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then

y = 6x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (1, 3 ) , then

3 = 6 + c ⇒ c = 3 - 6 = - 3

y = 6x - 3 ← equation of linear function

What is the y-intercept of the function f(x) = 2.3*?
A. (0,6)
B. (2,0)
C. (0,2)
OD. (0,3)

Answers

The answer is C. (0,2)

Which value of x would make triangle s u v is-congruent-to triangle t u m by hl? 2 3 4 5

Answers

The question is incomplete. Below you will find the missing content and figure

Which value of x would make triangle ΔSUV is congruent to triangle ΔTUM by HL? Options are 2 3 4 5

The figure is shown below.

The correct option is Option D: the value of x is 5.

Triangles are congruent if the triangles are of the same size and shape. If triangles are congruent the corresponding length of the sides is the same.

Here given that triangle ΔSUV is congruent to triangle ΔTUM.

By the property of the congruent triangle, as triangle ΔSUV and ΔTUM are congruent the corresponding sides are also same.

ΔSUV ≅ΔTUM

⇒ VS≅WT

Given in the question

VS= 2x+9

WT= 4x-1

from above it is clear that

VS=WT

⇒ 2x+9=4x-1

⇒4x-2x=9+1

⇒2x=10

⇒x=10/2

⇒x=5

Therefore the correct option is Option D: the value of x is 5.

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Answer:

It will be 5 on EDG 2022 Your welcome :)

Step-by-step explanation:

17. What is the value of x in the rhombus
below?
A
C
(x+ 40)
B
3x⁰
D
18

Answers

Answer:

Answer is 12.5 degrees

Answer:

x = 12.5

Step-by-step explanation:

4(x + 40) + 4(3x) = 360

4x + 160 + 12x = 360

16x + 160 = 360

16x = 200

x = 12.5

The diagonals of a rhombus are: A. are the same length and intersect at different angles B. bisect each other at right angles C. bisect each other and intersect at different angles D. are the same length and intersect at a right angle

Answers

Answer:

Step-by-step explanation:

Comment

Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.

A rhombus and its diagonals have many interesting properties.  This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.

Answer: B

The table of values represents a linear function g(x) where c is the number of days that have passed and g(x) is the balance in the bank account

Answers

After 7 days, the balance will be Rs. 628.

(A) The slope of the given function is 40.

(B) In point - slope form it is y - 600 = 40x

   In Slope - intercept form it is y = 40x + 600

   In Standard form it is 40x - y + 600 = 0

(C) g(x) = 4x + 600

(D) After 7 days, the balance will be Rs. 628

Let g(x) = y

(A) We know slope = change in y/change in x

                               = 720-600/3-0

                               = 120/3

                               = 40

Therefore, the slope of the given function is 40.

(B) We know that the equation of a line

in point - slope form is y - y₁ = m(x - x₁)

where ( x₁, y₁ ) is a point on the line

where m is the slope

Therefore, substituting the values, we get,

y - 600 = 40(x - 0)

=> y - 600 = 40x                                    --(i)

What is the  Slope - intercept form?

Slope - intercept form is y  = mx + b

where m is the slope

and b is the y-intercept

To find y intercept, we substitute x = 0 in equation (i)

=> 40*0 - y + 600 = 0

=> -y + 600 = 0

=> y = 600

Therefore, substituting the values, we get,

     y = 40x + 600

in Standard form is ax + by = c

where a, b, and c is constant

Converting the equation found above into the standard form

=> y = 40x + 600

=> 40x - y + 600 = 0

(C) As we had assumed g(x) to be y

=> From equation (i),

 y - 600 = 40x    

can be written as g(x) - 600 = 4x

=> g(x) = 4x + 600                                    --(ii)

(D) We need to find the balance in the bank account after 7 days

=> Balance [g(x)] when x = 7

Therefore, substituting the value of x in equation (ii)

=> g(x) = 4*7 + 600

          = 28 + 600

          = 628

Therefore, after 7 days, the balance will be Rs. 628.

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Hi I need help
1) -15+4r=-9
2)5-y/3=-1
3)42=5x-8
That's all, you don't have to show work, but I'd appreciate it:) asap pls

Answers

Equation #1:

-15+4r=-9

We move all terms to the left:

-15+4r-(-9)=0

We add all the numbers together, and all the variables

4r-6=0

We move all terms containing r to the left, all other terms to the right

4r=6

r=6/4

r=1+1/2

Equation #2:

5-y/3=-1

We move all terms to the left:

5-y/3-(-1)=0

We add all the numbers together, and all the variables

-y/3+6=0

We multiply all the terms by the denominator

-y+6*3=0

We add all the numbers together, and all the variables

-1y+18=0

We move all terms containing y to the left, all other terms to the right

-y=-18

y=-18/-1

y=+18

Equation #3:

Simplifying

42 = 5x + -8

Reorder the terms:

42 = -8 + 5x

Solving

42 = -8 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.

42 + -5x = -8 + 5x + -5x

Combine like terms: 5x + -5x = 0

42 + -5x = -8 + 0

42 + -5x = -8

Add '-42' to each side of the equation.

42 + -42 + -5x = -8 + -42

Combine like terms: 42 + -42 = 0

0 + -5x = -8 + -42

-5x = -8 + -42

Combine like terms: -8 + -42 = -50

-5x = -50

Divide each side by '-5'.

x = 10

Simplifying

x = 10

Step-by-step explanation:

hope it's beneficial.

Draw my attention for further explanations.✨✨

What is 2*4*6.5*24.5

Answers

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

I need help answering these questions for geometry :)

1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.

Answers

The answers to the question have been written below

The changes to a polygon

1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.

2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0

Hence the value of the exterior would move towards 0 as its sides increases.

4. As the total sum of the of the polygon changes, it would tend towards infinity.

5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.

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The sides of a triangle are 5, 12 and 13 inches long. what is the angle between the 2 shortest sides?
a. 30
b. 45
c. 60
d. 90
e. 120

Answers

Answer: 90 degrees

Step-by-step explanation:

The hypotenuse is opposite the right angle, which is created by the two shortest sides.

A bag contains 4 red, 7 blue and 5 yellow marbles. Event A is defined as drawing a yellow marble on the first draw and event B is defined as drawing a blue marble on the second draw.
If two marbles are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?

A. 7/16
B. 7/15
C. 14/16
D. 14/15

Answers

Your answer should be C. 14/16 hope this helps!!!

Answer:

The answer is B. 7/15!!!

i just guessed and got it right, but i knew c. wasnt the answer.

What remainder is represented by the synthetic division below?

A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.

Answers

The remainder represented by synthetic division is -5.

What is synthetic division?

Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.

Given

A vertical line and a horizontal line combine to make an L shape.

There are two rows of entries within the shape.

Row 1 has entries 2, 10, 1, 5.

Row 2 has entries blank, -10, 0, -5.

Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;

x + 5 = 0

x = -5

Hence, the divisor of the synthetic division is -5.

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Answer:

its a) -5

Step-by-step explanation:

Which expression can be used to convert 22 Australian dollars to US dollars?

Assume 1.2 Australian dollars equals 1 US dollar.

Answers

Answer:

1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USD

Step-by-step explanation:

1 USD - 1.2 AUD

x USD - 22 AUD

cross multiply

1.2 · x = 1 · 22

1.2x = 22

multiply both sides by 10

12x = 220

divide both sides by 12

x=55/3 ≈ 18.33

USD - United States dollar

AUD - Australian dollar

David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?

Answers

Answer:

12.5 meters

Step-by-step explanation:

1 hour manually = 25/6 meters

1 hour using machine = 25/6 × 3 meters

1 hour using machine = 12.5 meters

Hope this helped and have a good day

A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?

Answers

Answer:

Step-by-step explanation:

số nữ là 65- 35= 30

vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13

if f(x)=-x+8 and f(-4), then the result is 12

True or False?

Answers

Answer:

[tex] \sf \blue{True✅}[/tex]

Step-by-step explanation:

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

Hope it help you

A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.

Answers

Answer:

im not too sure about that sorry!

Step-by-step explanation:

uiwgorihvncjkdnskv

It takes 15 seconds for the first cyclist to overtake the second cyclist.

How can you find how long it took before the first cyclist overtakes the second?

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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When given
Slope= -6/5
Y-intercept= 2
What is this in Point-Slope form?

Answers

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

Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

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

Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

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Which equation can be used to solve for xxx in the following diagram?




Choose 1 answer:
Choose 1 answer:

(Choice A)
A
2x = 4x2x=4x2, x, equals, 4, x

(Choice B)
B
2x + 4x = 1802x+4x=1802, x, plus, 4, x, equals, 180

(Choice C)
C
2x + 4x = 902x+4x=902, x, plus, 4, x, equals, 90

(Choice D)
D
2x + 4x = 1502x+4x=1502, x, plus, 4, x, equals, 150

Answers

The equation that can be used to determine the value of x is Option B.

What is an Equation ?

An equation is a mathematical statement formed when two algebraic expression are equated by an equal sign.

From the diagram ,

A straight line has an angle of 180 degree.

Therefore from the figure

To determine the value of x

2x + 4x = 180

6x = 180

x =30 degree

Thus the equation that can be used to determine the value of x is Option B.

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The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?

Answers

Answer: $55.25

Step-by-Step Explanation:

Price of the Coat = $65

Step 1 :- Find 15% of $65.

= 15/100 * 65
= 975/100
=> 9.75

15% of $65 = $9.75

Step. 2 :- Subtract $9.75 from $65.

= 65 - 9.75
=> 55.25

Price of the Coat in Sale = $55.25
55.25, 65*15%=55.25…….

Answer the following questions
A. 10 -4 ×5=?
B. 3+8×4=?
C. (3+8)×4=?

Answers

Answer:

A=30

B=35

C=44

Step-by-step explanation:

12. For which of the following quadratic equations are the roots 2 and 57
O A. x²-3x - 10=0
B. x² - 11x 10 = 0
c. x² - 7x + 10 = 0
D. x² + 7x-10=0
O
O
O

Answers

Answer: x²-59x+114=0

explanation:

If the roots are 2 and 57, then:-

sum of roots = 2+57 = 59

and, product of roots = 2×57 = 114

the quadratic equation is given by,

x²-(sum of roots)x+(product of roots)=0

so, x²-59x+114=0 will be the desired quadratic equation.

so, none of the options are correct.

the correct answer is x²-59x+114=0.

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$9,500 is invested in an account earning 9.1% interest (APR), compounded
quarterly. Write a function showing the value of the account after t years, where t
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
growth per year (APY), to the nearest hundredth of a percent.

Answers

Answer:

$100.5000

Step-by-step explanation:

becuse $9,500 is fived and it got it

When 3 times a number is subtracted from 45 the result is 5 plus the number. what is the number?

Answers

Answer:

n = 10

Step-by-step explanation:

let the number be n , then

45 - 3n = n + 5 ( subtract n from both sides )

45 - 4n = 5 ( subtract 45 from both sides )

- 4n = - 40 ( divide both sides by - 4 )

n = 10

Other Questions
can someone please help and explain its due in a littleee A bottom-up process is involved in fixating on an area of a scene that: Read the passage from chapter 8 of The Prince.Agathocles, the Sicilian, became King of Syracuse not only from a private but from a low and abject position. This man, the son of a potter, through all the changes in his fortunes always led an infamous life. Nevertheless, he accompanied his infamies with so much ability of mind and body that, having devoted himself to the military profession, he rose through its ranks to be Praetor of Syracuse. Being established in that position, and having deliberately resolved to make himself prince and to seize by violence, without obligation to others, that which had been conceded to him by assent, he came to an understanding for this purpose with Amilcar, the Carthaginian, who, with his army, was fighting in Sicily. One morning he assembled the people and the senate of Syracuse, as if he had to discuss with them things relating to the Republic, and at a given signal the soldiers killed all the senators and the richest of the people; these dead, he seized and held the princedom of that city without any civil commotion. . . .How does Machiavelli support his claim that rulers can be cruel if it benefits their subjects and is necessary for security?Machiavelli uses anecdotal evidence through historical examples to support his claim.Machiavelli uses empirical evidence about politics and society to support his claim.Machiavelli uses logical evidence through historical examples to support his claim.Machiavelli uses empirical and logical evidence to support his claim. An organization with a(n) _____ structure, sometimes called a "franchiser," uses highly centralized information systems The event in the life of a star that begins its expansion into a giant is Group of answer choices almost all the hydrogen in its core that was hot enough for fusion has been turned into helium as much as 90% of the star explodes violently the core reaches a temperature of ten million degrees the star's internal structure reaches equilibrium for the first time in its life Graph the inequality.-6 y + 2x < 15 Please Help ASAPPP..Match the phrase to the term (to make a complete thought).1.a play is divided into episodes calledRoget2.connect sentence elements of lesser valuepossessive nouns3.conversation between characters is calledclimax4.wrote the best known thesaurusscenes5.connect sentence elements of equal valueencyclopedia6.show ownershippassive listening7.drama is meant to be performed before a(n)critical listening8.is a good source for report materialaudience9.is the turning point in a playcoordinating conjunctions10.listening to a political speech is an example ofsubordinating conjunctions11.a car going by on the street is an example ofdialogue this money is to be shared between _____A we and themB us and theyC us and themD we and theyQ2 you should not blame me; it's no fault of __________A meB IC mineD my x= and y=1/x * y = 1How is the answer 1? Please tell me why it is 1 and how to do the operation correctly. What law requires you to slow down and change lanes when approaching a roadside incident where emergency personnel might be working?. If an area has shallow, intermediate, and deep earthquakes, what can you infer about the area?. Solve the following subtraction problem. Remember to borrow as necessary. 9cu yd113cu in 4cu ft129cu in How long does bath and body works semi annual sale last. Write a short story ending with a phrase but it was a dream What mass of sodium chloride (nacl) forms when 7.5 g of sodium carbonate (na2co3) reacts with a dilute solution of hydrochloric acid (hcl)? type in your answer using the correct number of significant figures. na2co3 2 hcl 2nacl h2o co2 7.5 g na2co3 = g nacl Which country in Africa is located north of the equator?O A. TanzaniaOB. NamibiaO C. EthiopiaOD. Angola options for 1 or two are not available but i got c= radical 125 What is the definition of Sweet Soul? Make a list of mushroom products High population densities in urban areas have advantages and disadvantages. List as many of each as you can and defend your conclusion. How could the disadvantages be eliminated or reduced? Use evidence to support your conclusion.