Please help
Part A
Which is the vertex form of the function f(x) = 3x2 – 30x + 71?
O
A. 3(x - 5)2 - 4
B. 2(x – 6)2 - 1
C. 3(x – 4)2 + 23
D. 5(x – 4)2 – 9
Part B.
What is the vertex of the function?
vertex = (
Answers
Answer:
Option A:
y = 3*(x - 5)^2 - 4
Step-by-step explanation:
For a quadratic equation:
y = a*x^2 + b*x + c
with the vertex (h, k), we can rewrite the function as:
such that:
h = -b/2*a
y = a*(x - h)^2 + k
Here we have the function:
y = 3*x^2 - 30*x + 71
the x-value of the vertex will be:
h = -(-30)/(2*3) = 30/6 = 5
And k is given by:
k = y(5) = 3*(5)^2 - 30*5 + 71 = -4
Then the vertex is:
(5, - 4)
And we can rewrite the equation in the vertex form as:
y = 3*(x - 5)^2 + (-4)
y = 3*(x - 5)^2 - 4
Then the correct option is A.
Related Questions
Please help - How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?
Answers
Therefore the answer is 27 or more months to depreciate to less than £1200 at a rate of 5% per month.
What is depreciation?Depreciation is a phrase that covers two different elements of the same idea: first, the real decline in an asset's fair value, such as the annual decline in the worth of industrial equipment.
What is asset and liabilities?Your balance sheet may be broken down into two categories, assets and liabilities, in its most basic form. A company's assets are any possessions that have the potential to provide future financial gain. Your debts to other people are called liabilities. In other words, assets increase your wealth while obligations decrease it.
The value of the motorbike will decrease by 5/100 = 0.05 (or 5%) each month. So, to find out how many months it will take for the value of the motorbike to decrease from £2550 to less than £1200, you need to solve the following equation:
£2550 - (0.05 * x) < £1200
where x is the number of months.
You can re-arrange the equation to solve for x:
x > (2550 - 1200) / 0.05
x > (1350) / 0.05
x > 27
So it will take the motorbike 27 or more months to depreciate to less than £1200 at a rate of 5% per month.
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Help me plzzzzzzzzzzzzzzzzzzz
Answers
Answer:
5.5; 11.00; 16.50
[tex]E = 5.5h[/tex]
Step-by-step explanation:
Given
The attached table
Solving (a): Complete the table
First, calculate the slope (m)
[tex]m = \frac{E_2 - E_1}{h_2 - h_1}[/tex]
So:
[tex]m = \frac{27.5- 22.00}{5-4}[/tex]
[tex]m = \frac{5.50}{1}[/tex]
[tex]m = 5.50[/tex]
So, the equation of the table is:
[tex]E = m(h - h_1) + E_1[/tex]
[tex]E = 5.5(h - 4) + 22[/tex]
[tex]E = 5.5h - 22 + 22[/tex]
[tex]E = 5.5h[/tex]
When h =1,2,3
[tex]E = 5.5 * 1 = 5.5[/tex]
[tex]E = 5.5 * 2 = 11.00[/tex]
[tex]E = 5.5 * 3 = 16,50[/tex]
Nevaeh has $0.80 worth of nickels and dimes. She has a total of 11 nickels and dimes altogether. Graphically solve a system of equations in order to determine the number of nickels, x,x, and the number of dimes, y,y, that Nevaeh has.
Answers
Answer: We can set up a system of equations to represent this problem. The first equation represents the total value of the nickels and dimes in terms of the number of nickels and dimes that Nevaeh has:
0.05x + 0.1y = 0.80
The second equation represents the total number of nickels and dimes that Nevaeh has in terms of the number of nickels and dimes that she has:
x + y = 11
To graphically solve this system of equations, we can use the slope-intercept form of the linear equations.
y = -2x + 22
y = -1/2 x + 8
The solution would be the point where the lines intersect , which x = 4, and y = 7 .
So she has 4 nickels, and 7 dimes.
Step-by-step explanation:
-15 POINTS-
A.
B.
C.
Answers
Answer:
Trapezoid
Step-by-step explanation:
The math
The dot plot shows 20 students’ scores on a quiz in English class.
If one student from the class is chosen at random, what is the probability that he or she scored more than 15 points on the quiz?
A. 25
B. 35
C. 18
D. 112
Answers
Please help!!!
NO LINKS
Answers
Answer:
76 people
Step-by-step explanation:
3.809% will by more than one.
this times 2000 is 76.1904
you cant have fractions of people
Your parents allow you to borrow a car to get to your part-time job, but you have to pay for a tank of gas each month. Gasoline costs $2.76/gallon and the tank takes 15 gallons. You have 2 coworkers who are each willing to pay for a quarter of a tank each month to carpool with you to work. How much do you save each month?
$16.46
$20.70
$15.91
$18.55
Answers
Decide whether the relation is a function
Answers
Step-by-step explanation:
im not sure but,
i think its a Functionhope it helps.Answer:
function is the correct answer in my opinion hope it's helps you
I need help finding the median :)
Answers
Answer:
15
Step-by-step explanation:
Can somebody help me please
Answers
Exact answer: 34.25/6.5
Answer:
[tex] \frac{34.25}{6.5} [/tex]
What kind of shoes are these not sure? I know they’re Jordan but be specific
Answers
Abigail goes to a restaurant and the subtotal on the bill was x dollars. A tax of
6% is applied to the bill. Abigail decides to leave a tip of 22% on the entire bill
(including the tax). Write an expression in terms of x that represents the total
amount that Abigail paid.
Answers
Answer:
Step-by-step explanation:
Total after tax:
x(1+0.06)
x(1+0.06)
x(1.06)
x(1.06)
1.06x
1.06x
{Total after tip:}
Total after tip:
1.06x(1+0.22)
1.06x(1+0.22)
1.06x(1.22)
1.06x(1.22)
1.2932x
1.2932x
find quotient 5/4 divided by 13/12
Answers
Answer: 1.15384615385
Step-by-step explanation:
divide
We are asking everyone to focus on reducing their average transaction time by 10%. The average transaction time for this location is 6 minutes and 52 seconds."So we have to get the average transaction time down to __________."
Answers
Answer:
Step-by-step explanation:
The average transaction time of this location reduced to 371 seconds.
HEPL MEEEE
1. 1/2(x+1)-1/3(x-1)
2. x-2/3(x-1)
Answers
Answer:
1. 1/6x + 5/6
2. 1/3x + 2/3
Step-by-step explanation:
Answer:
- 1/6x + 5/6, 1/3x + 1
Step-by-step explanation:
1. 1/2 (x + 1) - 1/3 (x - 1) = 1/2x + 1/2 - 1/3x + 1/3 = - 1/6x + 5/6
2. x - 2/3 (x - 1) = x - 2/3x + 1 = 1/3x + 1
A sign is 4 1/2 feet wide and 5 1/4 feet long. Find the area of the surface of the sign.
Answers
Answer:
I think it is 23 5/8
Step-by-step explanation:
b*h
15 POINTS PLEASE HELP ME
Answers
Answer:
<QRS = 40 degrees
Step-by-step explanation:
Supplementary angles are 180 degrees therefore if angle ABC is 140 degrees that would mean that angle QRS has to be 40 degrees.
Hope this helped!
Have a good day!
HELPP!! PLSS ANSWER HOW YOU GOT THAT ANSWE.I will add points who answers fully!!
Kevin purchased 5 hamburgers for $1.40 each and 6 sodas for $1.25 each. The tax on his order was 8%. What was the total cost of Kevin's purchase?
A $22.50
B $I5.66
C $14.58
D $14.31
Answers
Answer:
B. $15.66
Step-by-step explanation:
Hamburgers: 5 x 1.40 = 7
Sodas: 6 x 1.25 = 7.5
Total food cost = 14.50
tax is 8%, 0.08 as a decimal
14.50 x 0.08 = 1.16 tax
add food total and tax:
14.50 + 1.16 = $15.66
speeeed brainlest
eeee
Answers
I need help asap , this is geometry. I need it solve in the simplest radical form.
Answers
let the third side be b then use the pythagoras theorem
Mieko said that the difference between the longest rose and the shortest rose is 1 inch. Is she correct?
Use the drop-down menus to show and explain your answer.
Mieko is Choose
The longest rose is
Choose:
inches, and the shortest rose is
Choose...
So, the difference is
Choose...
inch
Review progress
Question 7
of 7
Bac
HELP WHO EVER SNSWERS FIRST I WILL MARK BRAINLYEST
Answers
Answer:
Step-by-step explanation:
lol no
Solve for x and show your steps. Is the solution extraneous? Check your work to show how you extraneous or not.
1 1x + 5 = 7
Answers
For the given issue, x has a value of 4. The offered solution is the solution extraneous .
What does the mathematical concept of superfluous mean?When we solve equations, we often obtain values that aren't actually the answer to the equation.
What makes an equation unnecessary?A root of a transformed equation that isn't a root of the previous iteration because it was left out of the original equation's domain is known as a extraneous solution.
According to the given information:√(11x + 5) = 7
(11x + 5) = 7²
11x + 5 = 49
11x = 49 - 5
11x = 44
x = 4
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A company that makes fasteners has government specifications for a self-locking nut. The locking torque has both a maximum and minimum specified. The offsetting machine used to make these nuts has been producing nuts with an average locking torque of 8.62 in-lb and variance of 4.49 squared in-lb. Torque is normally distributed. If the upper specification is 13.0 in-lb and the lower specification is 2.25 in-lb, what percent of these nuts will meet the specification limits
Answers
Answer:
97.95% of these nuts will meet the specification limits.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The offsetting machine used to make these nuts has been producing nuts with an average locking torque of 8.62 in-lb and variance of 4.49 squared in-lb.
This means that [tex]\mu = 8.62, \sigma = \sqrt{4.49}[/tex]
Torque is normally distributed. If the upper specification is 13.0 in-lb and the lower specification is 2.25 in-lb, what percent of these nuts will meet the specification limits?
The proportion is the p-value of Z when X = 13 subtracted by the p-value of Z when X = 2.25. So
X = 13
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{13 - 8.62}{\sqrt{4.49}}[/tex]
[tex]Z = 2.07[/tex]
[tex]Z = 2.07[/tex] has a p-value of 0.9808.
X = 2.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.25 - 8.62}{\sqrt{4.49}}[/tex]
[tex]Z = -3.01[/tex]
[tex]Z = -3.01[/tex] has a p-value of 0.0013.
0.9808 - 0.0013 = 0.9795
0.9795*100% = 97.95%
97.95% of these nuts will meet the specification limits.
In which step was the addition property of equality applied?
Answers
Answer:
Step-by-step explanation:
Dans le calcul d'une somme, ou d'un produit, de deux nombres, on peut échanger la place de deux nombres. Dans le calcul d’une somme, ou d'un produit, de trois nombres (ou plus), on peut associer de différentes façons les nombres deux par deux. Pour calculer le produit d’une somme par un nombre, on peut calculer le produit de chacun des termes par ce nombre, puis calculer la somme des résultats obtenus.
The temperature is dropping at a rate of five degrees per hour.
Let d represent the number of degrees the temperature drops.
Lett represent the number of hours that pass.
Which is the independent variable?
the number of hours
the number of degrees the temperature drops
the rate at which the temperature drops
the day of the week
Help me plz I’ll give Brainlyest
Answers
Answer:
the rate at which the temperature drops
the day of the week
Step-by-step explanation:
Since we can choose the number of hour, it is dependent on us.
If we set time = 2, then it would 5 x 2 = 10 degree
Similarly, if we change time, the temperature changes. Thus, it is dependent.
Temperature is dropping at a rate of five degrees per hour.
If t = 1, T = 5*1 = 5°, rate = 5
if t = 2, T = 5*2 = 10°, rate = 5
if t = 3, T = 5*3 = 15°, rate = 5
Notice that rate doesnt change, even the temperature and time changes.
Thus, rate is independent.
Which of the following would not be an example of a compound event?
(1) having a coin land on heads three consecutive times
(2) pulling a king out of a deck of cards
(3) missing two free throws in a row
(4) answering four true/false questions correctly by guessing
Answers
The only option that is not a compound event is; (2) pulling a king out of a deck of cards
How to identify a compound event?Compound probability is defined as a mathematical term that relates to the likeliness of two independent events occurring.
Thus, a simple event has only one outcome while a compound event involves the probability of more than one outcome
1) For a coin to land on heads three consecutive times means that there can only be three possible independent outcome and so this is a compound event.
2) Pulling a king out of a deck of cards is a simple event and not compound because it has only one outcome.
3) This is a compound event because we are dealing with two independent probabilities.
4) This is a compound event because we are dealing with two independent events which are true or false answers.
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Write the number 4,207 in expanded form
Answers
Answer:
That's easy! four thousand two hundred and seven or 4,000+200+7
Step-by-step explanation:
6. Name the polygon. Write whether it is regular
or not regular
Answers
Answer:
this shape is a pentagon. this is a regular shape because all the sides are even and all the angles on the inside are also even.
Step-by-step explanation:
pls mark brainliest!
Solve for X
Pls help
Answers
Answer:
xxxtentacion=6&20
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
The sum of any two intieior angles in a triangle equal to the opposite angle.
So 30 + 5X + 15 = 9X - 3
Solving for X
48 = 4X
X = 12
15m+20g=300
m+g=17
solve by elimination and SHOW YOUR WORK
Answers
Answer:
change the order, so the terms line up
20g+15m=300
g+m=17
multiply the second equation by 20, so the 20g and -20g can cancel out
20g+15m=300
-20g-20m=-340
solve the equation, then divide -5 to both sides to isolate the m
-5m=-40
m=8
substitute the value of m into one equation to find the other value
g+8=17
g=9
write them in ordered paired form
(9, 8)
Step-by-step explanation:
hope this helps :)