Hi, I need help please!! Given that x=3 and x=-4 are the solution of the equation x2+ax+b=0, find the value of a and of b. Answer: a=1, b=-12. I don’t know how to get the answer. Please show your workings and explain. If you help me, I will give Brainliest Answer Award to you. The topic is simultaneous equations, algebra. This question is from a Grade 8 workbook.

Answers

Answer 1

Answer:

a = 1, b = - 12

Step-by-step explanation:

we know that x = 3 and x = - 4, so (x - 3) and (x + 4) must be the factors of the equation:

(x - 3)(x + 4)

x^2 + - 3x + 4x - 12

x^2 + x - 12

therefore a = 1 and b = - 12

Answer 2

Step-by-step explanation:

firstly substitute x=3 into [tex]x^{2} +ax+b=0[/tex]

[tex]3^{2} +3a+b=0[/tex]

9+3a+b = 0

          b = -3a-9

secondly substitute x=-4 into [tex]x^{2} +ax+b=0[/tex]

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

16-4a+b = 0

          b = 4a-16

combine the equations above,

-3a-9 = b = 4a-16

so -3a-9 = 4a-16

     7a = 7

       a = 1

then substitute a = 1 into b = 4a-16 or b = -3a-9 (both are ok)

b = 4(1)-16 = -12     or        b = -3(1)-9 = -12


Related Questions

PLS HELP ITS DUE TODAY!!
If you have 75 Dollars, then number of nickels, y
- y = 75 ÷ 20
- y = 20 x 75
- y = 20 ÷ 75

Answers

Answer:

y=20x75 is the answer

Step-by-step explanation:

You can basically eliminate other two choices since they are division

The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right angle. Yes. No.

Answers

Answer:

Yes

Step-by-step explanation:

3 , 4 & 5 are Pythagorean Triplet numbers. When lengths of a triangle's 3 sides are Pythagorean Triplet , the triangle is a right angled triangle.

The triangle will be a right angled triangle only when the hypotenuse will have length of 5 and other 2 sides will have length of either 3 or 4.

Answer:

[tex]\boxed {\boxed {\sf Yes, \ the \ side \ lengths \ 3, \ 4, \ and \ 5\ can \ make \ a \ right \ triangle}}[/tex]

Step-by-step explanation:

If the triangle is a right triangle, then the sides will check out in the Pythagorean Theorem.

[tex]a^2+b^2=c^2[/tex]

Where a and b are the legs and c is the hypotenuse.

1. Define Sides

The legs are the 2 shorter sides and the hypotenuse is the longest.

The sides given are 3, 4 (shorter), and 5 (longest). Therefore:

[tex]a=3 \\b=4 \\c=5[/tex]

2. Check the Sides in the Theorem

Substitute the values into the theorem.

[tex](3)^2+(4)^2=(5)^2[/tex]

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction.

Solve all of the exponents first.

(3)² = 3*3= 9 (4)²= 4*4= 16

[tex]9+16=(5)^2[/tex]

(5)²= 5*5= 25

[tex]9+16=25[/tex]

Add the numbers on the left side of the equation.

[tex]25=25[/tex]

This is true. 25 is equal to 25, so this triangle can be a right triangle.

The graph of an exponential function is given. Which of the following is the correct equation of the function?

y = [tex]2.4^x[/tex]
y = [tex]0.31^x[/tex]
y = [tex]0.45^x[/tex]
y = [tex]1.8^x[/tex]

Answers

Answer:

[tex]y = 2.4^x \\ from \: intercepts \: using \: natural \: log( ln)[/tex]

Answer:

2.4

Step-by-step explanation:

Sofia spent $157.25 to make facemasks. After selling 500 facemasks, her revenue was
estimated to be $364.43. Did Sofia make a profit or loss? How do you know? Explain.

Points will be given!!

Answers

Profit because 364.43>157.25 since revenue (income) is greater than money spent she made a profit
She made a profit even tho it wasn’t as high as a profit, because she made more in revenue than she did spending to make the product itself !

What is the solution to the system below?
3x + y = 11
y = x + 3

Answers

Answer:

x = 2

y = 5

Step-by-step explanation:

3x + y = 11 equation (1)

-x + y = 3 multiply this equation by -1

x - y = -3 equation (2)

by adding 2 equations

4x = 8

x = 2

by sub. in Equation (2)

2 - y = -3

y = 2+3

y = 5

formula of pythagorean identity ​

Answers

I have this same question can you let me know when someone answers it?

Answer:

\sin ^{2} \theta+\cos ^{2} \theta=1

Step-by-step explanation:

Guys plz help me I need the answer fast.

Answers

Answer:

can you put the problem and the answer choices in the ch.at or something so i can answer, or just the problem

Step-by-step explanation:

There’s nothing to answer

Ava solved the compound inequality+7<-1 or 2x-129 for all possible values of x. Which graph represents
the solution set?
30 -24 -18
06 12
30 -24 -18 -2 -6 0 6 12
36 -30 -24 -18 -12 -6 06 12
-36 -30 -24 -18 -12 -6 0 6 12

Answers

Answer:

D

Step-by-step explanation:

To get the graph, we will need to solve each inequality differently

For the first one, we have that

x/4 < -1-7

x/4 < -8

x < -8 * 4

x < -32

For the second side;

2x-1 ≥ 9

2x ≥ 10

x ≥ 5

So we have two arrows facing different directions

On the left should be unshaded while the right hand side should be shaded

So, the correct answer here is the 4th option

What is the answer to r-5r-6s+8s-15

Answers

Answer:

-4r+2s-15

Step-by-step explanation:

collect like terms

r-5r= -4r

-6s+8s= 2s

therefore -4r+2s-15

Evan is making fruit punch. He adds 3 scoops of fruit punch mix to a pitcher containing 5 cups of water. Evan wants to use a larger pitcher, and he does not want to change the flavor of his fruit punch.

How many scoops of fruit punch mix should Evan add to 15 cups of water?

Answers

9 scoops shhshshsjsjs

I need help thank you

Answers

Answer:

C. none of the above

Step-by-step explanation:

-6 + 4q -6q

-2q - 6

Answer

C.

Step-by-step explanation:

sorry im late again

Evaluate 18y when y
= 2/3

Answers

Answer:

12

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Step-by-step explanation:

Step 1: Define

18y

y = 2/3

Step 2: Evaluate

Substitute in y:                    18(2/3)Multiply:                               12

Answer:

The answer (rounded) is 12.

Step-by-step explanation:

2/3=0.66666666666

18x0.666666666=11.999998 or 12

I know its a little confusing with the decimals but I can't solve problems with fractions, I have to convert them to decimals. XD

What is the value of a+b+c explain your reasoning

Answers

Answer:

im not sure but maybe d

Step-by-step explanation:

= fbecause a+b= e and then you add c to that so c+e=f

PLEASE HELP WILL GIVE BRAINLIEST IF CORRECT!!
find: x, y

Answers

Answer:

y=2

x=3

Step-by-step explanation:

I'm not sure, but considering that 3/2 = 1.5 I'm assuming that the rest is proportional as well. Therefore, making x=3 and y=2 (4/2=2 and 6/2=3)

Answer:

x = 3, y = 2

Step-by-step explanation:

the diagram shows two triangles that are similar (angle measures are equal and sides are proportional)

1.5 corresponds to 3; therefore, the ratio of sides is  1:2

'x' corresponds to 6  (x must be half of 6)

'y' corresponds to 4 (y must be half of4)

Find the coordinates of the points of intersection of the parabola y=x^2+3x-4 and the line y=2x+2

Answers

You can set the y values equal to each other and solve the system:

x^2+3x-4=2x+2
x^2+x-6=0
(x+3)(x-2)=0
x=-3,2

So, these are the x values of the intersection. To get the y values, you can just plug them back into either formula:

y=2(-3)+2
y=-4

y2(2)+2
y=6

So the coordinates are (-3,-4) and 2,6).

Geoffrey used 7 out of his 20 tokens on one game at the arcade. What is this fraction written as a decimal?

Answers

Answer:

0.35

Step-by-step explanation:

[tex]\frac{7}{20}[/tex]

  20 ) 7   ( 0.35

          0

           70

          60

            100

            100

                0

Answer:

7\20 as a decimal is

0.35

how many solutions can be found by the equation 3y+5-2y=11?

Answers

We can solve the equation to find it's number of solutions, but we already know it only has 1 solution because it is a linear equation (y is raised to the first power).

3y + 5 − 2y = 11
y + 5 = 11
y = 6

This confirms that there is only 1 solution.

please answer this....................................

Answers

Answer:

Step-by-step explanation:

YET it was a rahi that had a chart of a rahi in her own words that 66inches the heights in cm and the same were all her friends hy 6AM 66inches ir and a great amount

Find the volume of the potato chip container. Use 3.14 for 7. Round to the nearest tenth place,
LZ
Potato
Chips
20 cm
Ranch
7 cm

Answers

Step-by-step explanation:

[tex]v \: cylinder = \pi \times r {}^{2} \times h \\ 3.14 \times 3.5 {}^{2} \times 20 \\ 3.14 \times 12.25 \times 20 \\ = 769.3[/tex]

you should round to nearest tenth place...I dont know...hope it helps

HELP
If you don’t know it then please don’t answer.

Answers

the answer is 4.8. Your welcome

Plz answer quickly will mark brainless

Answers

Answer:

She must read more than 5 hours

Step-by-step explanation:

equation 12h+10>70

12h>60

h>5

So she must read more than 5 hours

(can I get brainliest now)

Answer:

She must read more than 5 more hoursD.

12h+10=5

12x5=60+10=70 pages.

She reads 12 pages per hour, so if she read for 5 hours, she would have read 60 pages. She has already read 10 pages, so that would equal 70 Pages.

A pentagon has 3 congruent sides and 2 other congruent sides. The perimeter of the pentagon is 36 centimeters. The three long congruent sides are 2 centimeters longer than the two shorter congruent sides.

Let x = length of a short side
Let y = length of a long side

The system of equations can be used to represent the situation.

y = x + 2
2x + 3y = 36

What is the length of one of the shorter congruent sides?

Answers

Answer:

Length of one of the shorter congruent side is: 6 cm

Step-by-step explanation:

In order to find the length of congruent sides we have to solve the system of equations

Given systems of equation is:

y = x + 2

2x + 3y = 36

Putting y = x+2 in second equation

[tex]2x + 3(x+2) = 36\\2x+3x+6 = 36\\5x+6 = 36\\5x = 36-6\\5x = 30\\\frac{5x}{5} = \frac{30}{5}\\x =6[/tex]

As we know that x represents the shorter side, the length of short side is: 6 cm

Hence,

Length of one of the shorter congruent side is: 6 cm

Choose all the factors of 12. (Check all that apply.)
1
5
8
7
6
3
12
11
4
2
10
9
plz help me

Answers

Answer:

1,2,3,4,6,12

Step-by-step explanation:

12•1= 12

2•6= 12

3•4= 12

the answer is 1, 2, 3, 4, 6, 12. 2 and 3 are prime factors so it has six factors and two prime factors

What is ½ + ⅙ rewritten with a common denominator?

Answers

Answer:

4/6

Step-by-step explanation:

look for the LCM of the denominators then divide with each denominator and multiply the answer you have got with the numerator after add it you want change it to it's simplest form

Find the value of f(-6).

Answers

Answer:

f(-6) = 5

Step-by-step explanation:

We want to find the value of the graph when x = -6

Go to where x = -6 and the y value is 5

f(-6) = 5

Answer: f(-6) = 5.

The number inside f(-6) is just x. So, use your finger to find -6 on the x-axis. Then, trace your finger in a vertical line to find where the function crosses where x = -6. This will be f(-6). We can see that this is 5.

In this multiplication problem every O stands for some odd digit and every E stands for some even digit. What is the product of the multiplication equal to?

Answers

Using multiplication rules, it is found that the product of the multiplication if an even digit.

What is the multiplication rule?

The rule is that a multiplication involving an even number will always result in an even number.

In this problem,two even numbers are multiplied, as they both finish with even digits, hence the result is also an even number, as evidenced by the fact that it finishes with an even digit.

You can learn more about multiplication rules of odd and even numbers at https://brainly.com/question/24657250

MATH PLEASE HELP!


A square field has an area of 479² ft What is the approximate length of a side of the field? Give your answer to the nearest foot. Explain your response.

Answers

Answer:

≈ 22 ft

Step-by-step explanation:

The area (A) of a square is calculated as

A = s² ( where s is the side length )

Given A = 479, then

s² = 479 ( take the square root of both sides )

s = [tex]\sqrt{479}[/tex] ≈ 22 ft ( to the nearest foot )

Answer:

A = 479 sq ft

479 = x²

square root of 479 = square root of x²

21.89 = x

rounded= 22 ft

Simplify to create an equivalent expression.
2 – 4(5p + 1)

Answers

Answer:

A. -20p - 2

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Algebra I

Combining Like Terms

Step-by-step explanation:

Step 1: Define

2 - 4(5p + 1)

Step 2: Simplify

Distribute -4:                    2 - 20p - 4Combine like terms:        -20p - 2

Answer:

Step-by-step explanation:

Apply the distributive property

2-20p-4

Simplify expression

-20p-2

Answer choice A is correct

tan2A - sin2A =sin2Atan2A​

Answers

Step-by-step explanation:

[tex]\tan^2\alpha-\sin^2\alpha=\sin^2\alpha\tan^2\alpha\\\\LS=\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2-\sin^2\alpha=\dfrac{\sin^2\alpha}{\cos^2\alpha}-\dfrac{\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}\\\\=\dfrac{\sin^2\alpha-\sin^2\alpha\cos^2\alpha}{\cos^2\alpha}=\dfrac{\sin^2\alpha(1-\cos^2\alpha)}{\cos^2\alpha}=\dfrac{\sin^2\alpha\sin^2\alpha}{\cos^2\alpha}\\\\=\sin^2\alpha\cdot\dfrac{\sin^2\alpha}{\cos^2\alpha}=\sin^2\alpha\left(\dfrac{\sin\alpha}{\cos\alpha}\right)^2=\sin^2\alpha\tan^2\alpha=RS[/tex]

Used:

[tex]\tan x=\dfrac{\sin x}{\cos x}\\\\\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\sin^2\alpha+\cos^2\alpha=1\to \sin^2\alpha=1-\cos^2\alpha\\\\\text{distributive property}\ a(b+c)=ab+ac[/tex]

What does 2x + 3x + 4x simlify to?

Answers

Answer:

9x does

Step-by-step explanation:

hope it helps

remind me if its wrong

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