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
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
A tourist ignores the warning signs and leaves food in his car while he goes for a hike. A mama bear and her cub open the car door in six seconds. How long would it take each bear to open the car door alone if the cub needs 9 more seconds than the mama bear?
Answer:
The mama bear can do it in 9
seconds. The cub can do it in 18
seconds.
Step-by-step explanation:
1/x+9+1/x=1/6
Using the together rate, it is found that it would take each bear 9 hours to open the car door alone.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, the rates are as follows:
Given
A tourist ignores the warning signs and leaves food in his car while he goes for a hike.
A mama bear and her cub open the car door in six seconds.
Together with rate: 1/6.
Mama's rate: 1/x.
Cub's rate: 1/(x + 9).
Therefore,
[tex]\rm \dfrac{1}{x}+\dfrac{1}{x+9}=\dfrac{1}{6}\\\\\dfrac{x+9+x}{x(x+9)}=\dfrac{1}{6}\\\\\dfrac{2x+9}{x(x+9)}=\dfrac{1}{6}\\\\ 6(2x+9)=x(x+9)\\\\12x+54=x^2+9x\\\\x^2+9x-12x-54=0\\\\x^2-3x-54=0\\\\ x^2+6x-9x-54=0\\\\ x(x+6)-9(x+6)\\\\(x-9)(x+6)=0\\\\x-9=0 \ x=9\\\\x+6=0 \ x=-6[/tex]
The value of time can not be negative.
Hence, It would take each bear 9 hours to open the car door alone.
To learn more about the together rate, you can take a look at brainly.com/question/25159431
what's the area of this parallelogram?
Answer:
Letter B. sir
Step-by-step explanation:
pls give me a brainly
Answer:
A.16.5 if that’s incorrect try b.33
Step-by-step explanation:
The formula is: A = B * H where B is the base, H is the height, and * means multiply.
it may be wrong I’m not sure but 30 * 11 is 330 divded by 2 is 16.5
A bus that is traveling north at 48 km/h slows to a stop to pick up passengers. It then begins moving again. At the next corner, it turns to the east.
a. Identify the speed of the bus.
b. Identify one example of the velocity of the bus.
c. Identify each group of words or phrases that describe acceleration of the bus.
Answer:
A
Step-by-step explanation:
In 120 seconds, the speed of a bus travelling on a smooth road increases from 8 m/s to 32 m/s. This technique uses the bus's potential energy.
Explain about the velocity?
Velocity is the rate of travel in a specific direction and adds direction to speed. Divide the distance travelled by the time it took to travel that distance, then add direction to determine the velocity. Velocity is zero if one's position doesn't change.
By dividing the amount of time it took the object to go a certain distance by the overall distance, one can calculate the object's initial velocity. V is the velocity, d is the distance, and t is the time in the equation V = d/t.
Velocity can be defined as the rate at which something moves in a specific direction as the speed of a car driving north on a highway or the pace at which a rocket takes off.
To learn more about velocity refer to:
https://brainly.com/question/25749514
#SPJ2
Taikan has 3 riffle tickets. One hundred were sold. If his name was not drawn for the first place prize, what is the probability that his name will be drawn for the second place prize?
A. 1/1,100
B. 1/1650
C. 2/99
D 1/33
Answer:
Step-by-step explanation:
3/(100-1)
3/99
1/33
What are two different ways of factoring -3x – 9? Select all that apply. (2 answers)
A. -3(x + 3 )
B. 3(x+3)
C. 3(-x-3)
D. -3(x-3)
What percent of 210 is 168?
Answer:
160 is 80% of 210.
Step-by-step explanation:
cause im smart
please with explanation
Answer:
is this premite, volume or area
Step-by-step explanation:
7 (p – q)
for p
=
10 and q = 2
Answer:
56
Step-by-step explanation:
7(10-2)
7*8
=56
Answer:
56
Step-by-step explanation:
7(p(10-q(2))
70-14=56
Answer= 56
help..................
Answer:
2(x^7+x^5y^2+x^3y^4+y^3x^4+y^5x^2+y^7) under (x^2+xy+y^2)(x^2-xy+y^2)(x^4+x^2y^2+y^4)
Step-by-step explanation:
basically i need the answer to a) and b) thank you.
Answer:
a=8, b=8.14
Step-by-step explanation:
2^3 is the same as 2•2•2 which is 8.
If you cube root of 540 it is 8.14325 but I left it off with the second decimal which you could add or take off whichever you need.
C) Which of the items had the greatest increase in sales over the 3 years ? Give a reason for your answer
Answer: Tablets because they increase in sales by 467%
Step-by-step explanation:
The item with the greatest increase is the one that has the highest percentage increase in the 3 years.
Each box represents 20 units sold.
Desktop Computers:
= (2017 sales - 2015 sales) / 2015 sales * 100%
= (160 - 100) / 100 * 100%
= 60%
Laptops:
= (280 - 160) / 160 * 100%
= 75%
Tablets:
= (340 - 60) / 60 * 100%
= 467%
Please helpppppppppppppppppppppppppppppppppppppppp
Convert the following fractions into percent and decimals.
1/4, 1/25 , 1/6 , 1/3
Answer:
1/4 is 25% .25 1/25 is 4% 0.04 1/6 is .167 16.67% 1/3 is 0.33 or 33%
Step-by-step explanation:
can someone helppppppppp
Answer:
I hope so option c is answer
Answer:
Step-by-step explanation:
(X-6)(x-6)
Follow the steps in FOIL (first, outside, inside, last)
First= X x X= X^2
Outside= X x -6 = -6X
Inside= -6 x X = -6X
Last= -6 x -6 = 36
Ans = X^2 -6X - 6X + 36
Simplify: X^2-12X+ 36
Answer is C
One of the legs of a right triangle measures 4 cm and its hypotenuse measures 18 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
√308 or 17.5
Step-by-step explanation:
c^2=a^2+b^2
c^2-a^2=b^2
Substitute
18^2-4^2=b^2
324-16=b^2
b^2=308
b=√308 or b=17.5
How many ounces of a 19% alcohol solution and a 37% alcohol solution must be combined to obtain 90 ounces of a 24% solution
Answer:
19% alcohol solution = 65 ounces
37% alcohol solution = 25 ounces
Step-by-step explanation:
Let
19% alcohol solution = x
37% alcohol solution = y
x + y = 90 (1)
0.19x + 0.37y = 90*0.24
0.19x + 0.37y = 21.60 (2)
from (1)
x = 90 - y
Substitute into (2)
0.19x + 0.37y = 21.60
0.19(90-y) + 0.37y = 21.60
17.1 - 0.19y + 0.37y = 21.60
- 0.19y + 0.37y = 21.60 - 17.1
0.18y = 4.5
y = 4.5/0.18
y = 25 ounces
x + y = 90 (1)
x + 25 = 90
x = 90 - 25
x = 65 ounces
Evaluate:
26
(2n +5) = [?]
Answer:
52n + 130
Step-by-step explanation:
Distribute
26 (2n + 5)
52n + 130
Solution
52n + 130
In which set of ordered pairs Is y NOT a function of X? A
{(1, 3), (2, 3), (3, 3), (4,3)}
B) {(1,3), (-2,5),(-2,7),(3,5)}
C){(7,2), (2,5), (0,4), (1,5)
D) {(-1,5), (2,6), (4,8), (9,4)}
Answer:
b
Step-by-step explanation:
for every x, there must be exactly one y for it to be a function. so, if there is more than one x per y, it's not a function.
in b, -2 (x) has two different y's which are 5 and 7, making it not a function.
Pleaseee helppp answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!
Answer:
let the opposite angle of 44 be x
and let opposite angle of z be y
44+52 + x=180( by sum of all angle is 180°)
96+x=180
x= 180-96
x=84
y+x=180 ( linear pair angle)
y+84=180
y=180-84
y=96
now the y, z,40 are triangle.
y+z+40=180( by sum of all angle)
96+z+40=180
z+136=180
z=180-136
z=44
Factorize the following to answer the code below. Letters may be used more than once.
Q3. Find remainder if x 3 – 3x 2 + 4x – 14 is divisible by x + 2.
Q4. Factorize x 3 – x 2 – 22x + 40
Answer:
3.-42
Step-by-step explanation:
3.
x+2=0,x=-2
f(-2)=(-2)³-3(-2)²+4(-2)-14=-8-12-8-14=-42
4.
x³-x²-22x+40
put x=2
2³-2²-22(2)+40
=8-4-44+40
=48-48
=0
x=2
so x-2 is one factor.
by synthetic division.
2 | 1 -1 -22 40
| 2 2 -40
_____________
1 1 -20 | 0
x²+x-20=0
x²+5x-4x-20
=x(x+5)-4(x+5)
=(x+5)(x-4)
x³-x²-22x+40=(x+5)(x-2)(x-4)
3. John makes $7.25 per hour at work. If he works 17 hours a week, how much will he earn?
Answer:
He will earn $123.25
Step-by-step explanation:
You multiply $7.26 by 17.
Find sin B as a decimal and round to the nearest hundredth.
Answer:
sin B= 33.06
Step-by-step explanation:
Hope this Helped!
any smart people wanna help me
Answer:
B. 3x + 60
Step-by-step explanation:
You return a video that is 3 days overdue. In addition, you rent another video for $4.95. If the total bill is $13.92, what is the fine for having an overdue video for one day?
Write an equation in slope-intercept form that represents the situation:
Bill started with 15 pairs of shoes. On average, Bill buys 7 new pairs of shoes every 2 months.
Answer:
y = 3.5x + 15Step-by-step explanation:
Number of months is x, and number of pairs of shoes after each month is y.
7 new pairs of shoes every 2 months means that after each month:
y = 7/2 x
We need to add the 15 pairs from start.
y = 3.5x + 15
find the factors of (2y+1/3)^2- (3y+1/2)^2 pls reply fast!!!
And electrician needs 2 rolls of electrical wire to wire each room in a house how many rooms can he wire with 3/4 of a roll of wire
Answer:
3/8 room
Step-by-step explanation:
Given data
We are told that 2 rolls of wire are needed to wire 1 room
Hence if 1 room needs 2 rolls
x rooms will need 3/4 rolls
cross multiply we have
2x= 3/4
Multiply both sides by 1/2
x= 3/4*1/2
x= 3/8 room
Elizabeth swims 50 feet in ten seconds. Jesse swims 110 feet in 20 seconds.
Reagan swims 160 feet in half a minute. Who swims fastest?
Answer: Jesse
Step-by-step explanation:
Elizabeth - 50f/10s
Jesse - 55f/10s
Reagan - 53.3333333/10s
Jesse is the fastest
Answer:
I think that Jessie swam the fastest
Step-by-step explanation:
Jessie swam the fastest bc Reagan only swims 160 feet in half a minute and 110 is less than 160 and 20 + 20 =40 so if Jessies swimming speed and time was multiplied by 2, she would still swim faster!
(sorry Im not the best at math but I hope you can understand my logic lol)
The cost of downloading a video game app on the App Store is $1.75. Which equation can be used to find the c, the cost in dollar of downloading n video games?
A) c = n + 1.75
B) c = 1.75n
C) n = c + 1.75
D) n = 1.75 c
Answer:
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Have a blessed day;))
Step-by-step explanation:
P= x/3 - 2 when p equals -5
Answer:
x = -9
Step-by-step explanation:
Plug in -5 to P then simplify the expression.
-5 = x/3 - 2
-3 = x/3
-9 = x
Answer:
I think X= -9
Step-by-step explanation:
Sub in -5 for p
-5=x/3 - 2
then add the -2
-3 =x/3
then multiple the 3
and you get -9
Please give me brainliest!