Factor the following polynomial 9x2 + 21x – 18

Answers

Answer 1

Answer:

factors are

21 and x

Step-by-step explanation:

equation 9 × 2 + 21x - 18

terms 9 , 2, 21x, -18

factors 21x = 21 and x

Answer 2

Answer:

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

Step-by-step explanation:

Given

9x² + 21x - 18 ← factor out 3 from each term

= 3(3x² + 7x - 6) ← factor the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term

product = 3 × - 6 = - 18 and sum = + 7

The factors are + 9 and - 2

Use these factors to split the x- term

3x² + 9x - 2x - 6 ( factor first/second and third/fourth terms )

3x(x + 3) - 2(x + 3) ← factor out (x + 3) from each term

(x + 3)(3x - 2)

Then

9x² + 21x - 18 = 3(x + 3)(3x - 2) ← in factored form


Related Questions

A store bought a tent for $230 and marked it up 65% The store sells the tent with the 8% tax what is the total cost of the tent

Answers

Answer:

$409.86

Step-by-step explanation:

To find the price after marking it up, 230 x 0.65 = 149.5

230 + 149.5 = 379.5

Usually we add tax after the discount/markup.

379.5 x 0.08 = 30.36

379.5 + 30.36 = $409.86

Hope this helps!

I need to know the transformation of the shape

Answers

Answer:

is there anything underneath it? it says which of the following

Step-by-step explanation:

solve for x,ty!
No links

Answers

Answer:

Step-by-step explanation:

[tex]\frac{-3x}{2}[/tex] = 5

multiply both sides by 2

2 ( [tex]\frac{-3x}{2}[/tex] = 5 )

-3x = 10

divide both sides by  [tex]\frac{-1}{3}[/tex]

[tex]\frac{-1}{3}[/tex] ( -3x = 10 )

x = [tex]\frac{-10}{3}[/tex]

got it?

Answer:

x = -10/3

Step-by-step explanation:

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

-3x = 10

-----    ---

-3     -3

x = -10/3

For summer school do u only go for the class you failed or all the classes you took that year?

Answers

Answer:

I am not sure.

Step-by-step explanation:

I've never been to summer school so- :/

You only go for the class that you failed and you get that credit and you only have to take one semester of the class you failed. I took summer school

Help on number 1 pls

Answers

Answer:

A

Step-by-step explanation:

5 is 50/1000, and 1/2% is equal to 5/1000

Answer:

A) 55/ 1,000

5 1/2% = 11 / 200 = 55/ 1,000

factor x^2-3x-28 using the x method

Answers

Answer:

[tex] {x}^{2} - 7x + 4x - 28 \\ = x(x - 7) + 4(x - 7) \\ = (x - 7)(x + 4)[/tex]

The graph of a function is shown.

​What is the maximum value of the function?

Answers

Answer:

3

Step-by-step explanation:

The maximum value of the function is 3.

What is a function?

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

The maximum value of a function is the highest output value that the function can attain over its entire domain.

Now,

From the graph,

The y-values are called the output.

The y-value is from -∞ to 3 and 3 to -∞.

This means,

The range of the function is -∞ to 3 and 3 to -∞.

Now,

The highest output is 3.

Thus,

The maximum value of the function is 3.

Learn more about functions here:

https://brainly.com/question/28533782

#SPJ2

Is each line parallel, perpendicular, or neither parallel nor perpendicular to a line whose slope is −34?

Parallel Perpendicular Neither

Line M, with slope3/4 Line N, with slope 4/3 Line P, with slope -4/3 Line Q, with slope -3/4

Answers

Given:

The slope of a line is [tex]-\dfrac{3}{4}[/tex].

To find:

The lines in the options are parallel, perpendicular or neither parallel nor perpendicular to the given line.

Solution:

We know that the slopes of parallel lines are equal.

The slope of line Q and the slope of given line are same, i.e., [tex]-\dfrac{3}{4}[/tex]. So, the line Q is parallel to the given line.

The slope of a perpendicular line is the opposite reciprocal of the slope of the line because the product of slopes of two perpendicular lines is -1.

The slope of a line is [tex]-\dfrac{3}{4}[/tex]. It means the slope of the perpendicular line must be [tex]\dfrac{4}{3}[/tex]. So, the line N is perpendicular to the given line.

The slopes of line M and P are neither equal to the slope of the given line nor opposite reciprocal of the slope of the line.

Therefore, the lines M and P are neither parallel nor perpendicular.

stuck on a maths question please help with an explanation thank you stay safe :)​

Answers

Answer is  7:13

======================================================

Explanation:

He answered 5/7 of the 35 short-answer questions correctly. So he got (5/7)*35 = 25 of those questions correct. At 2 marks each for these questions, he earned 25*2 = 50 points from this group alone.

There are 35 short-answer questions and 15 long-answer questions. That's 35+15 = 50 questions total.

We're told that he answered 60% of all the questions correctly. So he answered 0.60*50 = 30 questions correctly.

Earlier we found that he answered 25 short-answer questions, which must mean he got 30-25 = 5 long-answer questions done correctly. At 4 marks a piece, Keith earns 5*4 = 20 points in this group.

So overall, he earned 50+20 = 70 points from both types of questions.

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

If he got all answers correct, then he would earn 35*2 = 70 points from the short-answer questions and 15*4 = 60 points from the long-answer questions. That's a total of 70+60 = 130 points to get a perfect score.

The ratio of his score to the perfect score is 70:130 which reduces to 7:13 when dividing both parts by the GCF 10.

9514 1404 393

Answer:

  70/130 . . . . reduces to 7/13

Step-by-step explanation:

Strategy

The problem statement describes 2 kinds of quiz questions, and different relations regarding the numbers of questions answered correctly. The problem asks for the number of marks Keith had relative to the total number of marks.

This means you need to find Keith's marks and the available marks for each question type (4 numbers).

Because of the way the problem tells you the number of long-answer questions answered, additional computations are required to find the total number of questions Keith answered and the number of short-answer questions Keith answered. (The difference of these is the number of long-answer questions answered.) That's 3 more computations.

You have to keep in mind the purpose of each computation and how it fits in to the final result. This is why we label the intermediate results.

Solution

Short Answer Marks

There were 35 short-answer questions for 2 marks each. That's a total of ...

  (35)(2) = 70 . . . . marks for all short-answer questions

Keith got 5/7 of those, so got ...

  (5/7)×70 = 50 . . . . Keith's marks for short-answer questions.

__

Long Answer Marks

There were 15 long-answer questions for 4 marks each. That's a total of ...

  (15)(4) = 60 . . . . marks for all long-answer questions

The total number of questions on the quiz was 35 +15 = 50. Keith answered 60% of them, so answered ...

  0.60×50 = 30 . . . . total number of questions Keith answered

We know Keith answered (5/7)(35) = 25 short-answer questions, so must have answered 30-25 = 5 long-answer questions. His marks for those were ...

  (5)(4) = 20 . . . . Keith's marks for long-answer questions

__

Total Marks

Then the total number of marks for all answers on the quiz is ...

  short marks + long marks = 70 +60 = 130 . . . available marks

And Keith's overall score was ...

  (Keith's short marks + Keith's long marks)/(available marks)

  = (50 +20)/130 = 70/130 . . . . Keith's score ratio for the quiz

in 1990 sausage cost an average of $2.42 per pound. In 1994 it cost 51.35 per pound. What was the percent of depreciation (percent of decrease)?
*(show your work)*​

Answers

Answer:

Cumulative price change 105.96%

Average inflation rate 2.36%

Converted amount ($100 base) $205.96

Price difference ($100 base) $105.96

CPI in 1990 130.700

Step-by-step explanation:

Please i need the correct answer, no funny business.

Answers

Answer:

Age of the spear head = 6349 years.

Step-by-step explanation:

Expression to be used to calculate the age of the spear head,

[tex]N_t=N_0e^{-kt}[/tex]

Here, [tex]N_t[/tex] = Final amount of C-14

[tex]N_0[/tex] = Initial amount

[tex]k[/tex] = 0.0001

[tex]t[/tex] = Time in years

If [tex]N_t[/tex] = 53% of [tex]N_0[/tex] = [tex]N_0\times (0.53)[/tex]

[tex]0.53N_0=N_0e^{-0.0001\times t}[/tex]

[tex]0.53=e^{-0.0001t}[/tex]

[tex]\text{ln}(0.53)=\text{ln}(e^{-0.0001t})[/tex]

[tex]-0.634878=(-0.0001)t[/tex]

[tex]t=6348.78[/tex] years

[tex]t[/tex] ≈ [tex]6349[/tex] years

Therefore, age of the spear head = 6349 years.

Determine whether the mapping is a relation or a function or neither.

















the 4th awnser was cannot be determined

Answers

Answer:

The answer is not a function

Step-by-step explanation:

I think at least

Daniel expanded the expression as shown.



What errors did he make? Select three options.

Answers

Answer:

Below.

Step-by-step explanation:

The second term should be positive.

The last term should be -1 1/2 not -1 1/4.

He did not correctly multiply -8 and -2.

Answer:

b,c,d

Step-by-step explanation:

(.*_*)hope this helps(- _-.)

Mary's Mum said she would pay 2/5 of the cost of
her new dress. If the dress cost £165, how much
money did Mary have to pay?
HELPPP

Answers

Answer:

66 dollars im pretty sure

Step-by-step explanation:

help please! also an explanation would be helpful

Answers

There are two shapes a rectangle and a triangle.

Area of a rectangle = Length x width = 10 x 8 = 80 square ft.

Area of triangle = 1/2 x base x height = 1/2 x 6 x 8 = 24 square ft.

Total area = rectangle + triangle = 80 + 24 = 104 square ft.

Answer 104 square ft.

Answer:

104 ft^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w = 10*8 = 80

Then find the are of the triangle

A = 1/2 bh = 1/2 (6) * 8 = 24

Add the areas together

80+24 = 104

2. Dentre as formas de representar um número decimal, a mais comum é a que utiliza vírgula. Valor como 0,25 está presente nos comércios, nos hospitais, nas lanchonetes e em muitos outros lugares. Esse valor também pode ser representado por A. ( ) 25/10 B. ( ) 1/4 C. ( )1/25 D. ( ) 1/25

Answers

Answer:

B: 0.25 = 1/4

Step-by-step explanation:

Queremos encontrar otra representación del número 0.25

Notar que hay dos decimales luego de la coma, por lo que podemos multiplicar este número y dividir por 100.

0.25 = 0.25*1 = 0.25*(100/100) = (0.25*100)/(100) = 25/100

Ahora tenemos el número escrito como una fracción, la cual debemos simplificar.

25/100

Podemos ver que tanto el numerador como el denominador son multiplos de 5, por lo que podemos dividir ambos por 5:

25/100 = (25/5)/(100/5) = 5/20

Nuevamente, ambos son multiplos de 5, por lo que podemos dividir ambos por 5.

5/20 = (5/5)/(20/5) = 1/4

así tenemos:

0.25 = 25/100 = 5/20 = 1/4

0.25 = 1/4

La opción correcta es B.

When a coin and die are tossed together find the probability of getting:
a)coin with head and die with prime number
b)coin with head and die with composite number
c)coin with tail and die with even prime number

Answers

Answer:

a) 1/4

b) 1/6

c) 1/12

Step-by-step explanation:

Let S be the sample space.

S={H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

n(s) =12

Events

A: coin with head and die with prime number .

B:coin with head and die with composite number.

C:coin with tail and die with even prime number.

a) A={H2,H3,H5}

n(A) = 3

P(A) =n(A)/n(S)

=3/12

= 1/4

b) B={H4,H6}

n(B)= 2

P(B) = n(B)/n(S)

= 2/12

= 1/6

c) C ={T2}

n(C) = 1

P(C) = n(C)/n(S)

= 1/12

how to do?? helppppp

Answers

Answer:

x = - 3, x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

(2x - 1)(x + 3) = 0

Equate each factor to zero and solve for x

x + 3 = 0 → x = - 3

2x - 1 = 0 ⇒ 2x =  1 ⇒ x = [tex]\frac{1}{2}[/tex]

Answer:

x = 0.5 and -3

Step-by-step explanation:

(2x - 1)(x + 3) = 0

We are solving for the two x values (since this is a polynomial)

(2x-1) = 0/(x + 3)

2x - 1 = 0

2x = 1

x = 1/2 = 0.5

And the second x value

(x + 3) = 0 / (2x - 1)

x + 3 = 0

x = -3

Consecutive numbers are whole numbers that follow in order such as 7, 8, 9, 10, and so forth. Suppose the average of 15 consecutive numbers is 15. What is the average of the first five numbers of the set?

Answers

Answer:

10

Step-by-step explanation:

First, we need to find the sum of the 15 consecutive numbers. The formula to finding the average of a set of numbers is the sum of the terms divided by the number of terms. So to find the sum, you do 15x15 because the average is 15 and there are 15 numbers. 15x15=225, so you know the sum of the consecutive numbers is 225. Let X be equal to the first consecutive number of the 15 consecutive numbers.

X+(X+1)+(X+2)+(X+3)....+(X+14)=225

=15X+(105)=225

=15X=225-105

=15X=120

=X=8

So the first consecutive number of the 15 is 8. Therefore, the second consecutive number is 9, the third is 10, and so on. The question asks for the average of the first five numbers, which is 8, 9, 10, 11, and 12.

The summation formula is [tex]S=(\alpha_{1}+\alpha_{n})\frac{n}{2\\}[/tex].

[tex]S=(\alpha_{1}+\alpha_{n})\frac{n}{2\\}\\ S=(8+12)\frac{5}{2}\\ S=(20)2.5\\ S=50[/tex]

So the sum of the first five consecutive numbers is 50. Since there are 5 numbers, you do 50÷5=10. Therefore, the answer is 10.

use the information in the diagram, set up a proportion to solve for the height of the tree

Answers

Answer:

Step-by-step explanation:

There are a couple of ways you could solve this problem. B is one of them.

The correct answer is going to be Small hypotenuse / Large hypotenuse = tree / building height

Let the tree equal x

100/220 = x / 176           Multiply both sides by 176

100 * 176 / 220 = x

x = 80

Notice that 80 is almost 1/2 of 176 so the answer should be right since 100 is nearly 1/2 of 220

help me with this math question

Answers

Answer:3

Step-by-step explanation:

Just count from -1 to positive 2 the dot doesn’t move

Will Mark brainlest !please help. (The probabilty of germenating a new flower seed is found to be 0.92,if you sow a packet of 500 seeds in the field ,how many seeds will you expect to be germinated) ​

Answers

Answer: 0. 92 = 92%

100% = 500

92% = 500 × 92/100 = 460

Step-by-step explanation:

Please help me solve this problem

Answers

The answer for this is X+2g= 0

Please help!!!!!!!!!!!!!!

Answers

Answer:

choice A is the answer

Step-by-step explanation:

[tex]5 + 2.75s \leqslant 21 \\ 2.75s \leqslant 21 - 5 \\ s \leqslant 16 \div 2.75 \\ s \leqslant 5.82[/tex]

but since we only can have a whole number in the number of stops, she can only travel 5 stops with the money she has.

How far apart are -14 1/2 and 2 on the number line

Answers

Its 16 and a 1/2 have a great day!

Which system of inequalities is shown in the graph?
&
A. y 2 X+1
yzx-3x
B. ys X+1
ys 2-3x
O C. ys x+1
yz x2-3x
O D. ys-x+1
ysx2-3x

Answers

Answer:

A

Step-by-step explanation:

because when i dentify graph theres y an x

The feasible region of the result is defined by the system of inequalities.

Correct response:

The system of inequalities shown in the graph is given by the option B.

B. y ≤ x + 1

y ≤ x² - 3·x

Methods used to find the system of inequalities

Please find attached the possible graph of the inequality

The possible graph obtained from a similar question has a straight line portion and a quadratic portion.

Points on the straight line are; (0, 1), (3, 4), and (5, 6)

Therefore;

[tex]Slope \ of \ the \ line = \dfrac{6 - 1}{5 - 0} = 1[/tex]

Equation of the line is; y - 1 = 1 × x

Therefore;

y = x + 1

The shaded region is below the line which gives;

y ≤ x + 1

Points on the quadratic graph are; (0, 0), (4, 4), and (2, -2).

The general form of a quadratic equation is; y = a·x² + b·x + c

Therefore, we have;

0 = a × 0 + b × 0 + c

Which gives;

c = 0

4 = a × 4² + b × 4 = 16·a + 4·b

-2 = a × 2² + b × 2 = 4·a + 2·b

4 = 16·a + 4·b...(1)

-2 = 4·a + 2·b...(2)

Multiplying equation (2) by 2 and subtracting from equation (1) gives;

2 × -2 = 2 × (4·a + 2·b) = 8·a + 4·b

-4 = 8·a + 4·b

4 - (-4) = 16·a + 4·b - (8·a + 4·b) = 8·a

8 = 8·a

[tex]a = \dfrac{8 }{8} = 1[/tex]

a = 1

-2 = 4 × 1 + 2·b

2·b = -2 - 4 = -6

[tex]b = \dfrac{-6}{2} = \mathbf{ -3}[/tex]

Which gives;

y = 1·x² - 3·x = x² - 3·x

The line is a solid line and shaded region is the region under the graph which gives;

y ≤ x² - 3·x

Therefore;

The inequalities in the graph are given by option B.

B. y ≤ x + 1

y ≤ x² - 3·x

Learn more about graph of inequalities here:

https://brainly.com/question/6749279

The front of the stage, side C , is 50 feet long. A 40-foot rope runs along the side of square B. A 30-foot rope runs along the side of a square A. Is the ropped off area, triangle ABC, a right triangle? Explain.

Answers

Answer: yes, because any triangle with the ratio of whole number 3:4:5 is a right triangle

Step-by-step explanation:

find the area of each triangle. Round intermediate values to the nearest tenth. use the rounded values to calculate the next value. Round your final answer to the nearest tenth, someone help me pelaseeeee!!!!

Answers

Answer:

54? or 5.4 I not really sure but I tried my best

Raegan needs 2 boards to make a shelf one board is 1 1/2 m long and the other is 3 1/2 m long what is the total length of the shelf

Answers

Answer:

5 m

Step-by-step explanation:

Find the total length of the shelf by adding together the lengths of the two boards:

1 1/2 + 3 1/2

= 5

So, the total length of the shelf is 5 m

What is the device that converts the signals to and from the wires so that the data can be sent and received by the computer?
A
domain name system

B
network

C
router

D
IP address

Answers

Answer:

C  router

Step-by-step explanation:

A router is a networking device whcich takes and forwards the packages and performs traffic functions. Data that is sent through the internet such as web page and email. All are forwarded through this device to the internet. A router may be connected to the IP Address network and reads the packet before sending it to its destination.
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