1. Find the factored form of f(x) given it has x-intercepts (-3,0) and (4,0) and f(1)= -6. 2. Find the equation for f(x) given that it has roots of 2 and -3 and f(0)=12. Please someone help

Answers

Answer 1

Answer:

1) f(x) = 0.5*(x + 3)*(x - 4)

2) f(x) = -2*x^2 - 2*x + 12

Step-by-step explanation:

Wen we have a quadratic function like:

f(x) = a*x^2 + b*x + c*x

And it has roots at x1 and x2, we can write the function in the factored form as:

f(x) = a*(x - x1)*(x - x2)

then:

1) we have x-intercepts at: (-3, 0) and (4, 0) (then the roots of this function are x = -3 and x =4) and we know that f(1) = -6

we have:

x1 = -3

x2 = 4

then we can write f(x) as:

f(x) = a*(x - (-3))*(x - 4)

f(x) = a*(x + 3)*(x - 4)

Where a is a real number.

and now we can use the fact that f(1) = -6

then:

f(1) = a*(1 + 3)*(1 - 4) = -6

       a*4*(-3) = -6

       a*-12 =  -6

       a = -6/-12 = 1/2 = 0.5

Then the function is:

f(x) = 0.5*(x + 3)*(x - 4)

2) Now we have roots x = 2 and x = .3

Then:

x1 = 2

x2 = -3

Then this function is something like:

f(x) = a*(x - 2)*(x - (-3))

f(x) = a*(x - 2)*(x + 3)

Now we know that f(0) = 12.

then:

f(0) = a*(0 - 2)*(0 + 3) = 12

         a*(-2)*3 = 12

          a*(-6) = 12

          a = 12/-6 = -2

f(x) = -2*(x - 2)*(x + 3)

And we do not want this one written in factored form, so we can just distribute the multiplications to et:

f(x) =  -2*(x - 2)*(x + 3) = (-2*x + 4)*(x + 3) = -2*x^2 + 4*x - 6*x + 12

f(x) = -2*x^2 - 2*x + 12


Related Questions

What is 9867 rounded to the nearest 1000

Answers

Answer:

10,000

Hope it helps

Have a good day

10,000



Hole this helps

Please teach me how to do this thank youuu.

Answers

Answer:

-10.2

Step-by-step explanation:

To find the equation you have to pick to random points, find the slope, and the y-intercept.

(1,-2) (2,2)

Slope = 2 - - 2 / 2 - 1

Slope = 4 / 1

Slope = 4

an estimate of the y-intercept is -2.2 meaning the function is f(x) = 4x - 2.2

when x is replaced by -2 like the question is requesting f(-2) = 4(-2) - 2.2

f(-2) = -10.2

* i really hope this made sense

A right triangle has side lengths 5, 12, and 13 as shown below.
Use these lengths to find cos B, tan B, and sin B.
COS
B
13
5
5
tan
A
12
с
Sin

Answers

Answer:

c

Step-by-step explanation:

a. 3in, 4in, 5 in

5^2 ?  3^2 + 4^

25   ?  9 + 16

25   =  25

Because the two sides are equal, this is a right triangle.

b. 5in, 6in, 7in

7^2  ?  5^2 + 6^2

49   ?  25 + 36

49   <  61

Because 49 < 61, this is an acute triangle.

c. 8in, 9in, 12in

12^2  ?  8^2 + 9^2

144    ? 64 + 81

144    < 145

Because 144< 145, this is an acute triangle.

Cos b) 5/13
Tan b) 12/5 or 2 1/6 or 2 2/12
Sin b) 12/13

what is the value of x
10= 3x - 6
X=

Answers

Answer:

[tex]x= \frac{16}{3}[/tex]

Step-by-step explanation: Can i get brain plz!

add 6 to both sides of the equation
simply/ 16=3x
divide both sides by 3
x = 16/3

Six added to the quotient of 84 and seven

Answers

Answer:

84 divided by 7 is 12 + 6 = 18

-2/9 +1/5 help me please

Answers

Answer:

-1/45

Step-by-step explanation:

I did the equation okay hope this help!! <3

Answer:

1/40

Step-by-step explanation:

-2/9+ 1/5=0.2r

0.2r convert to fraction=1/40

hope that helps

plz mark as brainliest

A 34-foot pole is casting a shadow that is 17 feet long. How far is the top of the flag pole from the end of the shadow?

Answers

Answer:

108

Step-by-step explanation:

GEOMETRY STUFF PLEASE ANDWER DUE IN 20 MINUTES

Answers

Answer:

Statement 2: m∠ ELD = (2x)°

Reason 4: Sum of angles on a straight line is equal to 180°

Statement 6: 2x = 56

Step-by-step explanation:

Since the first step talks about we being given m∠ ELG = 124°, the next thing we are given in the question is that; m∠ ELD = (2x)°

In statement 4,it is written that;

m∠ ELD + m∠ ELG = 180°

The reason behind this is that;

Sum of angles on a straight line is equal to 180°.

For reason 6, we are told it is a subtraction property.

Now the preceding statement gave us;

2x + 124 = 180

Which means that for subtraction property here, we will have;

2x = 180 - 124

2x = 56

The system of equations has .
the options are
1. one solution
2. no solution
3. infinitely many solutions

Answers

Answer: 3. Infinitely many solutions

Step-by-step explanation:

If you simplify the first equation you get the same equation of y=-2 which is infinitely many solutions

The answer is 3, I don’t know how I just need the option to ask someone

please, I need your help!! I will mark correct answer as brainliest.

Answers

Answer:

3, -3, 0

Step-by-step explanation:

The exlcusions of x are where the denominator =0

So we can write the following equations

x²-9=0

and

5x=0

Let's solve the first one

x²-9=0

x²=9

x= ±3

and

5x=0

x=0

Therefore x cannot equal 3, -3, 0

Answer: 3, -3, 0

So, yea. The answer ontop is also correct

hhhhheeeeeellllllppppp pppppllllllzzzzz!!!!!!!!

Answers

Answer:

c

Step-by-step explanation:

Answer:

HMMMMMM

Step-by-step explanation:

i think its b or c

Simplify a^5/a^3 and c^4/c^3

Answers

Answer:

Step-by-step explanation:

a^5/a^3 = a^(5-3) = a²

c^4/c^3 = c^(4-3) = c¹

-4(y-2)=12
what does y equal

Answers

Answer:

y = -1

Step-by-step explanation:

-4 (y - 2) = 12

1. Multiply: -4y + 8 = 12

2. Subtract: -4y = 4

3. Divide: y = -1

What is the slope (-5,5) and (5,1)

Answers

Answer:

m= - 2/5

Step-by-step explanation:

Sports team is building a new stadium on a rectangular lot of land. It's a lot measures 10 X by five eggs and the sports field will be 6X by 2X, how much of the lot will be left over to build bleachers on

Answers

Answer:

4 X 2

8 unit²

Step-by-step explanation:

Given that:

Lot size = 10 X 5

Sport field = 6 X 2

Dimension of lot left :

(10 - 6) X (5 - 2)

4 X 2

Area left :

Length x width

4 * 2

= 8 units²

Write a linear equation in slope Intercept form of a line with a slope of -3 and y Intercept of 0​

Answers

Answer:

y=-3x

Step-by-step explanation:

THe equation formula is y=mx+b, with m being the slope and b being the y-intercept. Because the y intercept is 0, you don't need to include it.

if a circle has an area of 100 cm squared, what would be the area of a section of 45 degrees?

Answers

Answer:

45 degrees/360 degrees=1/8

So the area would be 1/8 *100=100/8=25/2

Step-by-step explanation:

If a Canada savings Bond is worth $6225 after 7 years, and was originally bought for $5000, what was the annual simple interest rate? Answer as a percentage.

[Formulas are,
[I = P, R, T]
[A = P + I]
[A = P(1 + R times T)

Answers

Answer:

3.5%

Step-by-step explanation:

Given data

A=$6225

P=$5000

T= 7years

R=???

Simple interest

A=P(1+rt)

substitute

6225=5000(1+7r)

6225=5000+35000r

collect like terms

6225-5000=35000r

1225=35000r

r= 1225/35000

r=0.035

Hence the rate is 0.035*100= 3.5%

help with rounding off please !:(

Answers

I’m a thief who stole your points lol
The answers are given are below:

Answer:

(a) 3800

(b) 7000

(c) Does unit mean ones place? 31

(d) 82.8

(e) 1000

(f) 0.48

Step-by-step explanation:

Find the length of the
missing side of the triangle
to the nearest tenth.

Answers

Hey! So you’re gonna need to use the Pythagorean Theorem (a^2 + b^2 = c^2).
You’re looking for one of the legs here, so after inputting the values your equations should look like this: 6^2 + b^2 = 10^2.
Next, find what the numbers squared are: 36 + b^2 = 100.
Then, isolate the variable: b^2 = 64.
Lastly, square root both sides: √b^2 = √64.
You should find the answer is 8.

Trey is currently in debt and the balance of his account is -$24. If his
sister Catherine is in three times as much debt as he is, what is the balance
of Catherine's account?

Answers

-24 multiply by three equal to -72 this is what I believe

PLZ HELP 2/3*2
THXXX

Answers

Answer:

4/3 or 1 1/3

Step-by-step explanation:

2/3 x 2/1 gets you 4/3

That's an improper fraction, so you can simplify it to 1 1/3 if necessary.

What is a solution to the inequality m<25

Answers

Answer:

I think the answer is m= -91

TS is the height of a building. PQR is a pole in front of the building. QT is a horizontal cable that supports the pole to the building. Find the height of the pole?​

Answers

Answer:

The answer is 65.75

Step-by-step explanation:

Since tq is perpendicular to PR then qtsr becomes square

Then

[tex]qr = 30 \: \: \: \: \: and \: qt = 30 \\ [/tex]

Since the triangle pqt is right angled

Then

[tex]pq = qt \tan(50) = 30 \times \tan(50 ) = 35.75[/tex]

Then the height of the pole is equal to

[tex]pq + qr = 35.75 + 30 = 65.75[/tex]

HELP PLEASE IM GOING TO FAIL WILL GIVE BRAINLESS

Answers

Answer:

x= 20

AD= 23

DC= 23

AC= 46

Step-by-step explanation:

because it's a median that means that x+3=2x-17 solve for x and get x=20 which (I think) means that AD, DC= 23 and that AC= 46

F(x) = 24/x^2. When x=8

Answers

Answer:

3/8

Step-by-step explanation:

F(8)=24/8^2=24/(8*8)=24/64=3/8

4x³ + 9 + 16x² +4 + 12x³ + 17
combine like terms and order

Answers

Answer:

16x^3+16x^2+30

Step-by-step explanation:

what is $78 discounted 12%

Answers

Answer:

$78 discount off 12% you would get $68.64. That is $9.36 off

Find the side indicated by the variable. Round to the nearest tenth.​

Answers

Answer:

b ≈ 25.6

Step-by-step explanation:

From the figure attached,

By applying tangent rule in the given triangle,

tan(32°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan(32°) = [tex]\frac{16}{b}[/tex]

b = [tex]\frac{16}{\text{tan}(32)}[/tex]

b = [tex]\frac{16}{0.62487}[/tex]

b = 25.605

b ≈ 25.6

simplify the expression
3x +4 +yxy +7y -10x + 6

Answers

Answer:

- 7x + 10 + y² + 7 y

Step-by-step explanation:

Hope this will help

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