The function [tex]f(x)=\left(x-5\right)\left(x+1\right)[/tex] has a vertex at (2, -9).
Quadratic functionThe quadratic function can be represented by a quadratic equation in the Standard form: [tex]ax^2+bx+c[/tex] where: a, b and c are your respective coefficients. In the quadratic function the coefficient "a" must be different than zero ([tex]a\neq 0[/tex]) and the degree of the function must be equal to 2.
For solving this question, you should find the vertex of quadratic equation (h,k). Where, [tex]h=-\frac{b}{2a}[/tex] . On the other hand, the value of the k-coordinate will be found when you replace the value of h in the equation of your question.
1. [tex]f(x)=-(x-3)^2[/tex]
Write this equation in Standard form:
[tex]f(x)=-(x^2-6x+9)\\ \\ f(x)=-x^2+6x-9[/tex]
Find h, using the formula [tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{b}{2a} =-\frac{6}{2*(-1)} =-\frac{6}{-2}=-(-3)=3[/tex]
Find k, replacing x for the value of h
[tex]-x^2+6x-9\\ \\ -(3)^2+6*3-9=-9+18-9=-18+18=0[/tex]
The vertex of quadratic equation is (3,0). Incorrect Option.
2. [tex]f(x)=(x+8)^2[/tex]
Write this equation in Standard form:
[tex]f(x)=x^2+16x+64[/tex]
Find h, using the formula [tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{b}{2a} =-\frac{16}{2*1} =-\frac{16}{2}=-8[/tex]
Find k, replacing x for the value of h
[tex]x^2+16x+64\\ \\ (-8)^2+16*(-8)+64=64-128+64=128-128=0[/tex]
The vertex of quadratic equation is (-8,0). Incorrect Option.
3. [tex]f(x)=\left(x-5\right)\left(x+1\right)[/tex]
Write this equation in Standard form:
[tex]f(x)=(x^2+x-5x-5)\\ \\ f(x)=(x^2-4x-5)[/tex]
Find h, using the formula [tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{b}{2a} =-\frac{-4}{2*1} =-\frac{-4}{2}=-(-2)=2[/tex]
Find k, replacing x for the value of h
[tex]x^2-4x-5\\ \\ 2^2-4*2-5=4-8-5=-4-5=-9[/tex]
The vertex of quadratic equation is (2,-9). Correct Option.
4. [tex]f(x)=-\left(x-1\right)\left(x-5\right)[/tex]
Write this equation in Standard form:
[tex]f(x)=-\left(x-1\right)\left(x-5\right)\\ \\ f(x)=-(x^2-5x-x+5)\\ \\ f(x)=-(x^2-6x+5)\\ \\ f(x)=-x^2+6x-5[/tex]
Find h, using the formula [tex]h=-\frac{b}{2a}[/tex]
[tex]h=-\frac{b}{2a} =-\frac{6}{2*(-1)} =-\frac{6}{-2}=-(-3)=3[/tex]
Find k, replacing x for the value of h
[tex]-x^2+6x-5\\ \\ -(3)^2+6*3-5=-9+18-5=18-14=4[/tex]
The vertex of quadratic equation is (3,4). Incorrect Option.
Learn more about the vertex of the quadratic function here:
https://brainly.com/question/26203210
What’s the answer??????
Answer:
-186,624
Step-by-step explanation:
Because you multiply each time by -6
-4 x -6 = 24
24 x -6 = -144
-144 x -6 = 864
864 x -6 = -5,184
-5,184 x -6 = 31,104
31,104 x -6 = -186,624
Ruth has a piece of wood that measures 2 2/9 feet. She cut off 1 1/3 feet of wood for a project. How much wood does she have remaining?
An electronics manufacturing process has a scheduled mean completion time of 70 minutes. It is claimed that, under new management, the mean completion time,u , is less than 70 minutes. To test this claim, a random sample of 18 completion times under new management was taken.
The sample had a mean completion time of 64 minutes and a standard deviation of 11 minutes. Assume that the population of completion times under new management is normally distributed. At the 0.05 level of significance, can it be concluded that the mean completion time ,u, under new management is less than the scheduled mean?
Perform a one-tailed test. Then complete the parts below.
Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
Answer:
one or three I'm not sure
If a number is raised to a power of 2, It Is
Answer: a square i think
Step-by-step explanation:
because you multiply the number by itself, you're squaring it.
Kennedy is working two summer jobs, making $11 per hour babysitting and making $8 per hour clearing tables. In a given week, she can work at most 17 total hours and must earn no less than $160. If x represents the number of hours babysitting and y represents the number of hours clearing tables, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
| x+y(less than or equal to)17
| 11x+8y(greater than or equal to)160
Step-by-step explanation:
Hope this helped! ·∪·
pls help I don't get it
[They got it, putting this here so it stops showing up as unanswered]
Given the equation in standard form, put it in slope-intercept form. Show all work.
25x + 5y = 50
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
Mr. Garza has a picture that measures 4 by 12 inches. It must be reduced so that the longest side measures 4 inches to fit in the school newspaper. Find the length of the shorter side of the picture once it has been reduced.
A. 2in
B. 1 1/2in
C. 1 1/3in
D. 1in
Answer:
The answer is C
Step-by-step explanation:
Divide 4 by 3
4 ÷ 3 = 1.33
1 1/3 as a fraction
Answer:
cCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
Step-by-step explanation:
A rancher uses a bucket that holds 15,000 milliliters of water to fill a water trough for her horse. The trough holds 2.7 x 10^5 milliliters of water. How many buckets of water will the rancher need to fill the trough?
Step-by-step explanation:
the volume of the bucket is
15,000 = 1.5 × 10⁴ ml
the trough holds
2.7 × 10⁵ ml
by calculating how often the volume of the bucket fits into the volume of the trough, we will know how many buckets of water are needed :
2.7 × 10⁵ / (1.5 × 10⁴) = 2.7/1.5 × 10⁵/10⁴ = 2.7/1.5 × 10¹ =
= 27/1.5 = 18
the rancher needs 18 buckets of water to fill the trough.
a pet supply company makes a small bag that holds 2 pounds of dog food.they want to make a bag for large dogs that holds 40 pounds of dog food. by approximately what scale factor will the surface area of the bag increase? round your answer to the nearest tenth
Please help…. Will mark brainliest plus 50 points!!!!
Answer:
k = 3
Step-by-step explanation:
Expanding the first term, we find 1/x at 10(kx)²(1/x)³ = 10k²/x
Expanding the first term, we find 1/x at 8*1⁷(-2/x)¹ = -16/x
Then
10k² - 16 = 74
k = 3
Kiran’s backpack weighs 3 pounds less than Clare’s backpack. Clare’s backpack weighs 14 pounds. Select all the equations that describe this situation. Group of answer choices 3x = 14 x + 3 =14 x = 14 -3 x = 14/3
Answer:
x + 3=14
x=14 - 3
Want some more help? With other questions?
Go to Quiz.izz
Write in search bar "OUR Unit 6 Lesson 4"
Click on the first option, (there should be a picture of a meme with a person who is black.
Thanks!
Answered by: FieryAnswererGT
#learnwithbrainly
C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours. If 20 children between the ages of 2 and 5 are randomly selected, find the probability that the mean of the number of hours they watch television will be greater than 26.3 hours.
Please explain!
The following information about the mean and standard deviation has been provided:
ц=25, б=3,n=20
We need to compute Pr(X⁻≥26.3).
The corresponding z-value needed to be computed is:
[tex]Z=\frac{X-u}{o/\sqrt{n} } =\frac{26.3-25}{3/\sqrt{20} }=1.9379[/tex]
Therefor, we get that
[tex]Pr(X\geq 26.3)=Pr(Z\geq \frac{26.3-25}{3/\sqrt{20} } )=Pr(Z\geq 1.9379)\\=1-0.9737=0.026[/tex]
How nice are your teachers 1-20
Answer:
69
Step-by-step explanation:
The two triangles
are similar.
What is the value of x?
Enter your answer in the box.
X =
Solution:
Note that:
(3x)/20 = (4x + 2)/28Using cross multiplication:
(3x)/20 = (4x + 2)/28=> (3x) × 28 = (4x + 2) × 20Simplifying both sides:
=> 84x = 80x + 40Subtracting 80x both sides:
84x = 80x + 40=> 84x - 80x = 80x + 40 - 80xSimplify the LHS:
=> 84x - 80x = 40=> 4x = 40=> x = 10Ratio remains same
[tex]\\ \rm\bull\rightarrowtail \dfrac{20}{3x}=\dfrac{28}{4x+2}[/tex]
[tex]\\ \rm\bull\rightarrowtail 84x=20(4x+2)[/tex]
[tex]\\ \rm\bull\rightarrowtail 84x=80x+40[/tex]
[tex]\\ \rm\bull\rightarrowtail 4x=40[/tex]
[tex]\\ \rm\bull\rightarrowtail x=10[/tex]
Select the corn Which function does this graph represent? y 3 N 1 -3 -21 -1 1 3 N E 1 2
Answer:
ml
Step-by-step explanation:
pag dawload Gani og ml nana nanam na answer
The length of time (T)in seconds it takes the pendulum of a clock to swing through one complete cycle is given by the formula
T=2π√L/32
Where L is the length, in feet, of the pendulum, and π is approximately 22/7. How long must the pendulum be if one complete cycle takes 6 seconds?
Answer:
T = 2 pi sqrt (L/g)
g = 32 ft/s2
here
2 = 2 (22/7) sqrt (L/32)
sqrt (L/32) = 7/22
L/32 = 49/484
L = 3.24 ft
check by hanging a weight from a 3' 3" string
Step-by-step explanation:
a) Work out the size of angle x.
b) Give reasons for your answer.
105°
Answer:
m∠x = 75°
Step-by-step explanation:
m∠x and m∠F are corresponding angles.
As lines AD and EH are parallel, m∠x = m∠F
m∠F and 105° form a linear pair
⇒ m∠F + 105° = 180°
⇒ m∠F = 180° - 105° = 75°
As m∠x = m∠F,
⇒ m∠x = 75°
Diffusion is the movement of a substance
a.only in liquids.
b. through only a lipid bilayer.
c. down its concentration gradient.
d. against its concentration gradient.
Answer:
A
Step-by-step explanation: not sure how i can explain it but im pretty sure that is correct, theres not really an explanation as much as thats just how it is if you understand.
Help me answer this question please Its not hard IM JUST REALLY TIRED I about 5 hours worth of khan lol
I will consider marking Brainliest
Answer:
A= -13 - b/4
Step-by-step explanation:
Hoped this helped!
From: Aug1e
[tex]4a+b=-52\\4a=-52-b\\a=-(52+b)/4=-52/4-b/4=-13-b/4[/tex]
OK done. Thank to me :>
Please please look at the picture and answer it. Thank you!
it took the Phillips family 6 hours
to drive to their vacation
destination. Due to traffic, it took
them 8 hours and 42 minutes to
drive home.
Percentage for Increase or Decrease!!
Answer:
Percentage increase.
Step-by-step explanation:
It took the Phillips family 6 hours to drive to their vacation destination. 2 hours and 42 minutes extra because of traffic.
8 hours 42 minutes
-
6 hours 0 minutes
=
2 hours and 42 minutes
Percentage increase.
PLEASE ANSWER I HAVE 5 MINS
WILL MARK BRAINLIEST IF CORRECT (PICTURE)
Answer:
Step-by-step explanation:
A = l × W
A = 4 × 2.5
A = 10 ft squared
Please answer quickly
Answer:
Step-by-step explanation:
1. the diameter of the circle is like in the diagram: d = 18 in ;
2. the radius of a circle measures the half of its diameter so: r = d/2 = 18 / 2 = 9 in ;
please show steps it help help alot
The Answer is in the attached file, I'm sorry if I can't write it on laptop, hope this helps man! :) and tell me if it's correct or wrong when your teacher see's it.
What is the answer and how did you get it
Answer:
You didn't include a picture!
Step-by-step explanation:
Fun fact ; More twins are born now then they ever were before!
Quadrilateral ABCD is similar to EFGH
Answer:
m∠A = 60°
m∠G = 100°
m∠D = 40°
m∠F = 360 - 60 - 100 - 40 = 160°
Step-by-step explanation:
m∠A = 60°
m∠G = 100°
m∠D = 40°
m∠F = 160°
Help me on this pls
I will give brainliest
Also 20 points
(all of it)
Answer:
12/32?
Step-by-step explanation:
Answer:6/16 & 9/24
Step-by-step explanation: Look at the grey highlighted parts. Match up the numbers to each row. 3 is on the same row as 8, 6 is on the same row as 16, and it continues up until 15/40.
Please help! The interest rate on a five year $8000 loan is 3%. Use the formula A=P*I^t, where P is the principle, I is the interest, and t is the term.
