Mathematics Middle School

The two expressions below are equivalent. Find the values of a and b that make them equivalent.

The two expressions are:
5x^2+bx-12
(5x+a)(x-4)

Answers

Answer 1

Answer:

[tex]a=3\text{ and } b=-17[/tex]

Step-by-step explanation:

We are given that:

[tex]5x^2+bx-12=(5x+a)(x-4)[/tex]

First, we can distribute the right-hand side:

[tex]5x(x-4)+a(x-4)[/tex]

Distribute:

[tex]=5x^2-20x+ax-4a[/tex]

Rewrite:

[tex]=5x^2+(-20+a)x-(4a)[/tex]

Since it is equivalent to the above expression, the coefficients of the variables must match. This means that:

[tex]-20+a=b\text{ and } 12=4a[/tex]

Solving for a in the second equation gives:

[tex]a=3[/tex]

Therefore:

[tex]b=-20+3=-17[/tex]

Related Questions

HELP HELP PLEASEEEE!!!!!!!!!!!!!!!!

Answers

Answer:

1,300 is the final answer

Step-by-step explanation:

Please help on this one question
Which of the following is equivalent to (2a + a)(3b + 1)?

Tip: Simplify the expression on the left first, and then use the distributive property.

Answers

Answer:

9ab+3a

Step-by-step explanation:

2a*3b=6ab

2a*1=2a

a*3b=3ab

a*1=a

adding everything together=6ab+2a+3ab+a=9ab+3a

Answer:

9ab+3a

Step-by-step explanation:

First Simplify:

(2a+a)*(3b+1)

2a*3b=6aba*3b=3ab1*2a=2a1*a=a

Combine like terms:

6ab+3ab=9ab

2a+a=3a

Add it all up:

9ab+3a

Done!!!

AS ALWAYS, DUE TODAY! Pls and thanks. NOTE- Legit answers only! Legit answers= Brainliest, 5.0 stars, and a Thanks.

Answers

Answer:

Natalie: 12

Fred: 24

Step-by-step explanation:

x= natalie

y= fred

x+y=36

y+4x=72

Let's start by isolating a variable

x+y=36

x-36= -y

-x+36=y

(we do this step because it's important that the y is a negative)

We can plug this into the second equation

-x+36+4x=72

solve for x

3x=36

x=12

Plug in this x value into any of the two beginning equations

12+y=36

y=24

I think it’s y=24 not positive

Rose has a rectangular patio that is 8 tiles long and 5 tiles wide. She is changing the dimensions to 10 tiles long by 9 tiles wide. Draw a picture to determine how many new tiles Rose will add to her patio.

A. 6
B. 8
C. 50
D. 90

Answers

jebdhevxhebdhebdhbrjfbidbwisbwidbjebshd
90 because 9 x 10 = 90 but first it was 8 x 5= 40

I REALLY NEED HELP ASAP!!!!!!!!!!!!!!

Answers

Answer:

cone V≈157.08

cylinder V≈502.65

sphere V≈113.1

the cubic units/ volume of each 3D shapes are:

cone .1                               =157.08

cilindar .2                          =502.65

sphere .3                          =113.1

What is the value of x? WILL MARK BRAINLIEST

Answers

Use the pythagorean theorem: a^2 + b^2 = c^2
24^2 + 7^2 = x^2
576 + 49 = x^2
x^2 = 625
√x^2 = √625
x = 25
Your answer would be X=25

HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

If two lines have the same y-intercept but different slopes, what can you conclude about the solution?

Answers

Answer:

You can conclude the statement that the x-intercept and the y-intercept is the same.

Step-by-step explanation:

hello please help me

Answers

Answer:

Question 1: square root of 109

Question 2: 2, 1, 1

Question 3: True

Step-by-step explanation:

The square root of 109 is about 10.4 which is greater than 5 and 9.

In the equation a^2 + b^2 = c^2, a and b represent the legs of a triangle and c represents the hypotenuse.

The Pythagorean Theorem states that For all right triangles the square of the hypotenuse is equal to the square of both sides. (a^2 + b^2 = c^2)

enjoy

Simplify the expressions.1 a. –2 t + 5 t – 2 – t
1 b. –5 z + 4 – 4 z2 a. 8 v + 3 – 10 v
2 b. –6 – 6 k – 3 – 7 k
3 a. –6 – 3 w + 4 + 10 w
3 b. 9 s + s
4 a. 6 + 8 b – 1 – 8 b
4 b. 1p + 6 + 5 – 4 p
5 a. 4 x – 3 x + 9 – 6 x5
b. 9 v + 6 v – 2 – 10 v6
a. n + 2 – (–4) n6
b. 6 n – 3 n7
a. –4 x – 4 x + 4 – 9 x7
b. –9 b + (–6) b

Answers

Answer:

1 a.) 2t – 2

1 b.) –9z + 4

2 a.) –2v + 3

2 b.) –13k – 9

3 a.) 7w  − 2

3 b.) 10s

4 a.) 5

4 b.) –3p + 11

5 a.) –29x + 9

b.) 15v – 60x – 2

a.) 25n + 2

b.) –15n

a.) –71x + 4

b.) –15b

Step-by-step explanation:

NOTE: I am kind of confused about the way this question is formatted, so I tried to answer everything I could decipher.

1 a.) –2t + 5t – 2 – t →  2t – 2

1 b.) –5z + 4 – 4z →  –9z + 4

2 a.) 8v + 3 – 10v →  –2v + 3

2 b.) –6 – 6k – 3 – 7k →  –13k – 9

3 a.) –6 – 3w + 4 + 10w →  7w  − 2

3 b.) 9s + s →  10s

4 a.) 6 + 8b – 1 – 8b →  5

4 b.) 1p + 6 + 5 – 4p →  –3p + 11

5 a.) 4x – 3x + 9 – 6x 5 →  –29x + 9

b.) 9v + 6v – 2 – 10x 6 →  15v – 60x – 2

a.) n + 2 – (–4)n 6 →  25n + 2

b.) 6n – 3n 7 →  –15n

a.) –4x – 4x + 4 – 9x 7 →  –71x + 4

b.) –9b + (–6)b →  –15b

what is the answer 1923 x 1476 =

Answers

Answer:

2,838,348

Step-by-step explanation:

hope this helps monkay

Answer:

2,838,348 love

Step-by-step explanation:

The temperature for the day starts at 37 degrees and rises to at least 60 degrees.

Which of the following inequalities could be used to find all the possible values of t, the amount the temperature could rise?

Answers

You could do 60-37 then that would give you 23. If that's what your looking for

Can someone help me?

Answers

Step-by-step explanation:

1. 1/13 2. 1/26

Simplify & Explain

4a(6) + 3a

Answers

You multiply 4a x 6 which give you 24a. Then add 3a to 24 a which gives you 27a.
The answer would be 27a,
4a(6)+3a
= 24a+3a
=27a

PLEASE HELP ME WITH MY MATH ;-; if you help I will give you 5 stars, a thanks, and a brainliest

Answers

Answer:

138 is an exterior angle

58 and x is interior

add

x is 80

Step-by-step explanation:

Use substitution to solve the system of equations. How many solutions are there?

1/2x − 1/3y = 5
x = 2/3y + 10

A. There are no solutions.
B. There is one solution.
C. There are infinitely many solutions.
D. It is not possible to determine the number of solutions.

Answers

Answer:

a

Step-by-step explanation:

The answer is “B” no solution

Can someone help me answer these 5 questions? the directions on what you do are in the questions. I will give brainliest as thanks for your help!

Answers

i hope this helps let me know if you have questions!

Step-by-step explanation:

question 1) equal angels

8+19)=(9x+9)

x=10°

8x+19=99°

question 2) equal angels

(3x-26)=2x

x=26°

3x-26= 52°

question 3) different angels

180-(x+10) = x+50

180-x-10=x+50

170-x=x+50

2x=120

x= 60°

x+10= 70°

x+50=120°

question 4) equal angels

3x-31=x+59

2x=90

x=45°

x+59=104°

question 5) equal angels

6x+3=7x-12

x=15°

6x+3=93°

Solve the equation.
−8(2 − x) = 4/5 (x + 43)
x =_____

PLZZ HELPP DUEE TODAYY

Answers

Answer:

-8(2 − x) = 4/5 (x + 43)

(-16+8x)5=4x+172

-80+40x=4x+172

-80-172=4x-40x

-252=-36x

x=-252/-36=7

Answer:

x= 35

hope it's helpful ❤❤❤

THANK YOU❤

David measures a line to be 4.87 in long. If the actual measurement is 5 in, find David's relative error to the nearest hundredth.


Ill give brainilest to whoever helps

Answers

Answer:

he was suppost to round up

Step-by-step explanation:

Answer:

measure value - actual value

Step-by-step explanation:

I need these to be simplified.
1) 6-10+1
2) -11+3+20
3) 8+(-15)+(-15)
4) 7-(-1)+18

Answers

1 would be -3

2 would be12

3 would be 22

4 would be 26

PLEASE HELP, WILL GIVE BRAINLIEST

The following steps are used to rewrite the polynomial expression (x + 4y + z) (x - 7y). Step 1: x(x - 7y) + 4y(x - 7y) + z(x - 7y) Step 2: x2 - 7xy + 4yx - 28y? + zx - 7zy Step 3: x2 - 7xy + 4xy - 28y? + xz - 7yz Step 4: x2 - 3xy - 28y? + xz - 7yz Identify the property used in each of the steps:

Answers

That’s a lot probably distributive property or commutative

The steps to simplify the expression is:

Step 1 :

x (x-7y) + 4y(x- 7y) + z (x- 4y)

Step 2:

x² - 7yx + 4yx - 28y² + zx - 4zy

Step 3:

x² -28y² - 3yx + zx - 4zy

What is Expression?

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

An absolute numerical number is referred to as a constant.Variable: A variable is a symbol that doesn't have a fixed value.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.

We have the Expression:

(x + 4y + z) (x - 7y).

Step 1 :

x (x-7y) + 4y(x- 7y) + z (x- 4y)

Step 2:

x² - 7yx + 4yx - 28y² + zx - 4zy

Step 3:

x² -28y² - 3yx + zx - 4zy

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ7

Need help with a math problem

Answers

Answer:

No

Step-by-step explanation:

Here's what's going on: some person buying their furniture sees this sofa and it's $1200. That person sees theres a 1/3 off sale! They're happy and buy their sofa with a 20% off discount they got.

Now we have to find out  if they should use the 20% off discount before or after adding the 1/3 off sale.

The answer is, they're both the same.

Say they add the 1/3 off sale discount and then use their 20% off discount. Find the 1/3 off sale: 1200 divided by 3 (because fractions are division problems) = 400. 20% of 400: 400 x 0.2 = 80. It's not just 80, because it's not an "only pay 20%" discount. 400 - 80 = 320. They'd pay $320 with this method.

This shows that using the 20% discount after the 1/3 off sale the customer spends $320.

Now let's calculate what happens if they use the discount after the 1/3 off sale. 20% of 1200: 1200 x 0.2 = 240. 1200 - 240 = 960. Now adding the 1/3 off sale: 960 divided by 3 = 320. They'd also pay $320 with this method.

If it's a short answer, you could just write something like, "No, both methods end up with the sales associate paying $320."

Hope this helps!

I would say no too for this word problem for the answer.

what is the area of the picture in square inches?
4 square inches
8 square inches
16 square inches
32 square inches

Answers

you forgot the photo but imma guess 16
We need the picture to figure that out

please help will mark brainliest. don't answer for points not unless flagged

Answers

Answer:

B.

Step-by-step explanation:

First, (3/2) is greater than 1, which therefore eliminates A and D.

Second, you must determine if the triangle gets larger or smaller. Lets suppose that X = 2 and Y = 3. If we were to multiply both of these values by (3/2), our points would change to X = 3 and Y = 4.5

Since there was an increase, this means that the triangle was larger.

This leaves B as the answer.

Remember: Any scale value greater than 1 is an enlargement, as proven by the hypothetical.

Answer:

The answer is b owo

Anita is making Fruit Baskets to sell in her store. She wants each basket to contain the same number of each type of fruit. What is the greatest number of baskets Anita can make?

A.) 4
B.) 8
C.) 16
D.) 72

Answers

I think 16. Is there an amount of fruit like how many apples or how many of each kind?
C is the correct answer

please help me with this and explain how you got your answer thank you!!

Answers

Answer:

jwjsbsbhwhwhhw

Step-by-step explanation:

cehehehehrghegeheheheh

Answer:

There is no question, but thanks for the free points.  :)

Step-by-step explanation:

Which relation is a function?

{0, –9, –2, –3}
{(0, –9), (–9, –2), (0, –3)}
{(0, –9), (–2, –3), (–2, 0), (–3, –2)}
{(0, –9), (–9, 0), (–3, –3)}

Answers

Last on - I think
{0,-9), (-9,0), (-3,-3)}
The last option is a function as no x-values repeat!

Can someone plz help me !!!

Answers

Answer:

53! good luck and stay safe<3

help plsssssssssshgruffgfieubf3rg;3

Answers

A, C, and D, are the correct ones I believe.

I’m pretty sure it’s a and c

Which relation is a function?

{(8, 1), (4, 1), (0, 1), (–15, 1)}
{(0, 1), (0, 2), (1, 2), (1, 3)}
{(–2, –12), (–2, 0), (–2, 4), (–2, 11)}
{(–4, –6), (–3, –2), (1, –2), (1, 0)}

Answers

Answer:

To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: If each input has only one line connected to it, then the outputs are a function of the inputs. Example: In the following mapping diagram, y is a function of x, but x is not a function of y: Line Test.

Step-by-step explanation:

Which describes the relationship between: ∠QVP and ∠PVU?

Answers

Answer:

Nothing to choose an answer from...

Step-by-step explanation:

you dont have answers!!
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