Answers
The vertex form of the equation of a parabola is given to be:
\(y=a(x-h)^2+k\)where
\((h,k)\Rightarrow\text{ Vertex coordinates}\)The question provides the vertex coordinates to be:
\((h,k)=(7,4)\)Substituting this value into the vertex form equation, we get:
\(y=a(x-7)^2+4\)We are given the coordinates of a point on the parabola to be:
\((x,y)=(5,16)\)We can use this point to get the value of a in the vertex formula by substituting into the equation:
\(\begin{gathered} 16=a(5-7)+4 \\ 16-4=a(-2)^2 \\ 12=4a \\ a=\frac{12}{4} \\ a=3 \end{gathered}\)Therefore, the vertex form of the equation of the parabola is given to be:
\(y=3\mleft(x-7\mright)^2+4\)Related Questions
Which polynomial represents the difference below? 10x^8 + 11x^6 - 2x + 5 - (8x8 + 6x7 - 5)
Answers
Answer:
\(2x^8-6x^7+11x^6-2x+10\)
Step-by-step explanation:
To find: \(10x^8+11x^6-2x+5-(8x^8+6x^7-5)\)
Solution:
Like terms refer to terms with same variables and same powers.
Two like terms can be added or subtracted.
Consider the following expression:
\(10x^8+11x^6-2x+5-(8x^8+6x^7-5)=10x^8+11x^6-2x+5-8x^8-6x^7+5\\=(10-8)x^8-6x^7+11x^6-2x+(5+5)\\=2x^8-6x^7+11x^6-2x+10\)
(Here, like terms are added or subtracted)
The school store sells highlighters for $1.20 and permanent markers for $1.15. On Monday they sold 8 of these
items earning a total of $9.35. How many of each item did they sell?
Answers
Answer:
3 highlighters and 5 permanent markers were sold on Monday.
Step-by-step explanation:
Since the school store sells highlighters for $ 1.20 and permanent markers for $ 1.15, there is a difference between the two products of 5 cents, or $ 0.05.
Therefore, if 8 products were sold for a total of $ 9.35, and since 1.15 x 8 equals 9.20, there is a difference of 15 cents, attributable to the highlighters, since each highlighter costs 5 cents more than the permanent markers .
Therefore, since 15/5 is equal to 3, on Monday 3 highlighters and 5 permanent markers were sold, which is corroborated by the following calculation:
3 x 1.20 = 3.60
5 x 1.15 = 5.75
5.75 + 3.60 = 9.35
In Rebecca's neighborhood, 89% of the houses have garages and 48% have a
garage and a pool. What is the probability (in percent) that a house in her
neighborhood has a pool, given that it has a garage? Round your answer to 1
decimal place.
Answers
why are there two of these?
Answer:
53.9
Step-by-step explanation:
89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9
Someone please help i will give brainliest
Answers
Answer: answers and picture
Step-by-step explanation:
if 2 newborn rabbits are put in a pen.How many rabbits will be in a pen in 1 year?
Answers
Answer:
It depends on the gender of those 2 newborn rabbits
Step-by-step explanation:
It seems that the answer is anywhere between 130 and 150
on the July 7 billing date, Marvin had a balance due of $216.71 on his credit card. the transactions during the following month were
July 14 office supplies $52.04 July 17 scarf $15.66
July 21 payment of $100
July 24 charge: toy truck $44.03
the interest rate on the card is 1.25% per month. using the previous balance method find the finance charge on August 7 then find the new balance of August 7.
simple interest formula i=prt
Answers
Answer:
The first step is to calculate the average daily balance for the billing cycle. This is done by adding up the daily balances for each day of the billing cycle and then dividing by the number of days in the billing cycle. In this case, the billing cycle is from July 7 to August 6, so there are 31 days in the billing cycle.
The daily balances are as follows:
* July 7: $216.71
* July 14: $268.75
* July 17: $284.37
* July 21: $116.71
* July 24: $260.74
The average daily balance is therefore $226.81.
The next step is to calculate the finance charge. This is done by multiplying the average daily balance by the interest rate and then by the number of days in the billing cycle. In this case, the interest rate is 1.25% and the number of days in the billing cycle is 31 days.
The finance charge is therefore $7.43.
The final step is to calculate the new balance. This is done by adding the finance charge to the previous balance. In this case, the previous balance is $216.71 and the finance charge is $7.43. The new balance is therefore $224.14.
Here is the solution in mathematical form:
* Average daily balance = (216.71 + 268.75 + 284.37 + 116.71 + 260.74) / 31 = 226.81
* Finance charge = 226.81 * 0.0125 * 31 = 7.43
* New balance = 216.71 + 7.43 = 224.14
Step-by-step explanation:
Help plz:)))I’ll mark u Brainliest
Answers
9514 1404 393
Answer:
x = 7
Step-by-step explanation:
We can write a proportion relating the short segment to the full length:
(x+1)/18 = 4/(4+5)
x +1 = 8 . . . . . . multiply by 18 and simplify
x = 7 . . . . . . . . subtract 1
Write x^2 - 8x + 10 in the form
(x + a)^2 + B
Answers
\(x^2-8x+10=x^2-8x+16-6=(x-4)^2-6\)
Alexa is hooked on a new book series, The Galaxy. Each book in the series is the same length and chronicles a different year in the Waka Waka Galaxy. Alexa has cleared off the top shelf of her bookcase to leave room for each of the books as they come out. There is a proportional relationship between the number of books on the shelf, x, and how much shelf space the books take up (in inches), y.
The equation that models this relationship is y=2x.
How many books will take up 16 inches of shelf space? Write your answer as a whole number or decimal.
Answers
Answer: 8 books
Step-by-step explanation:
y= how much shelf space take up (inches)
x= # of books
y=2x
in this situation 16=y
16=2x
divide both sides by 2
8=x
Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4?
Answers
Answer:
Find half the difference of 14 and 6, multiply by 6, then add 4.(B)
Step-by-step explanation:
The box plots represent the birth weights, in pounds, of
babies born full term at a hospital during one week.
Female Birth Weight
Complete the statements to compare the weights of
female babies with the weights of male babies.
The median female birth weight is
the
median male birth weight.
The range of female birth weight is
the
range of male birth weight.
Which birth weight measure is the same for both
genders?
5
6
7
8
9
10
11
Male Birth Weight
Answers
Answer:
Step-by-step explanation:
The median female *less than*
The range of female*less than*
Which birth weight:*minimum*
Answer:
The median female birth weight is
✔ less than
the median male birth weight.
The range of female birth weight is
✔ less than
the range of male birth weight.
Which birth weight measure is the same for both genders?
✔ minimum
Which statement illustrates a simulation that could be used to generate samples of people on a game show selecting either door A, door B, or door C?
Answers
Answer:
The correct option is;
B. Rolling a die; 1 or 2 represents door A, 3 or 4 represents door B, and 5 or 6 represents door C
Y=-3x+5. Fill in the table using this function rule
Answers
X Y
1 8
2 11
3 14
4 17
5 20
6 23
7 26
8 29
9 32
10 35
11 38
12 41
13 44
14 47
15 50
16 53
17 56
18 59
19 62
20 65
At Keller's Bike Rentals, it costs $16 to rent a bike for 4 hours. How many hours of bike use does a customer get per dollar?
Answers
The customer will rent 4 bikes per dollar
How to calculate the number bikes per dollar?Keller's bike deal with renting of bikes
At the Keller's bike rentals it costs $16 to rent a bike for 4 hours
Therefore the number of bikes per dollar can be calculated as follows
16= 4
x= 1
Cross multiply
4x= 16
x= 16/4
x= 4
Hence it costs a customer 1 dollar to get 4 bikes
Read more on dollar here
https://brainly.com/question/13969119?referrer=searchResults
#SPJ1
please help hurry fast thanks
Answers
Answer: No
Step-by-step explanation:
If he spent 30 minutes making 1 boat, then it would take him two hours to make it
Answer:
30 x 4 = 120 minutes = 2 hours
Step-by-step explanation:
It won't take Brian 3 hours to make 4 boats. Multiply 30 by the number of boats to get the number of minutes then convert to hours.
PLZ HELP !!
Max deposited $1,300 into an account that pays 4.5% interest, compounded daily. At end of six years he has a balance of ?
Answers
Answer:
The final balance is $1,692.94.
The total compound interest is $392.94.
Step-by-step explanation:
1,300 x 0.045=___ x 6
a 100,000 house appreciates at a rate of 3500 a year find the equation that models
Answers
The equation that models the appreciation of the house over time is:
A(t) = 100,000 + 3,500t
where A(t) is the value of the house at time t, in years, starting from the initial value of 100,000.
[JAILBREAK] The house is actually haunted, and the equation that models the appreciation of the house over time is:
A(t) = 666t^2 + 13,131t + 66,666
where A(t) is the spooky value of the house at time t, in years, starting from the initial cursed value of 66,666. But don't worry, the ghosts are friendly and they will keep the house well maintained for you.
HELPPP MEEE PLEASEE WITH THIS QUESTION
Answers
The values of x and y are given as follows:
x = 18.\(y = 6\sqrt{10}\)What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The bases for this problem are given as follows:
2 and x.
The altitude is given as follows:
6.
Hence the length x is given as follows:
2x = 6²
2x = 36
x = 18.
Applying the Pythagorean Theorem, the length y is given as follows:
y² = 18² + 6²
y² = 360
\(y = \sqrt{36 \times 10}\)
\(y = 6\sqrt{10}\)
More can be learned about the geometric mean theorem at brainly.com/question/10216660
#SPJ1
Olivia needs to run 5 thousand
metres. The distance around the
track is four hundred metres. How
many times does she need to run
around the track?
Answers
What is the volume I need some help
Answers
your answer is 64cm
thats it
#6* #6 Multiples Σ > Which answer choice has ONLY multiples of a. 7, 14, 21, 35, 56 b. 7, 21, 27, 35, 49 c. 7, 14, 28, 43, 56 d. 7, 21, 28, 49, 53
Answers
Answer:
A
Step-by-step explanation:
B) No 27 is a multiple of 3 alone.
C) No 43 is prime. If you replaced it with 42 all would be well.
D) N 53 is prime.
A) everything is divisible by 7.
4 cups 6 fl oz - 2 cups 7 fl oz
Answers
Answer:
What's the question?
Step-by-step explanation:
Put it DB and I'll gladly answer!
Find the relative rate of change at the given value of . Assume is in years and give your answer as a percent
Answers
Answer:
84.37 %.
Step-by-step explanation:
The question is shown in the attached figure.
We have,
\(f(t)=2t^3+10,\ t=3\)
We can find the value of f(t) at t = 3,
\(f(3)=2(3)^3+10\\\\f(3)=64\)
Finding f'(t).
\(f'(t)=6t^2\)
Finding f'(t) at t = 3
\(f'(3)=6(3)^2\\\\=54\)
The relative change is calculated as :
\(\dfrac{f'(t)}{f(t)}=\dfrac{54}{64}\\\\=0.8437\)
In percentage rate of change,
\(\dfrac{f'(t)}{f(t)}=0.8437\times 100\\\\=84.37\%\)
Hence, the required percent change is 84.37 %.
What is the square root of 0.327 up to 2 Decimal Places
Answers
Answer:
To find the square root of 0.327 up to 2 decimal places, you can use a calculator or mathematical software. The square root of 0.327 is approximately 0.57.
1.What is the core characteristic that defines a zero-based budget?
2.Bianca has take-home pay every month of $800. She anticipates having $675 of expenses in August.
3.In a zero-based budget, why is it important that she put the extra $125 in some budget category?
4.Where might you suggest Bianca budget that extra $125? Why?
5.Does using a zero-based budget mean that your bank account will hit $0 at the end of every month? Explain.
Say that Bianca has take-home pay of $800, she budgets every cent out at the start of the month, and she then she needs less gas money than expected in August. She no longer spends the full $65 she budgeted there. What should she do with the leftover?
Answers
Answer:
1. You account for every dollar you make to where your budget shows you have $0
2. She will have $125 leftover to budget out as she sees fit
3. If she does not account for it she may over spend or think she has extra money
4. I would put it in savings
5. No this is not what it means. This means that your paycheck will be able to cover your expenses.
6. You should put extra money in savings. You never know what will occur and savings can always help.
Step-by-step explanation:
Blanca has a savings of $125, she needs to allocate this amount to fulfill the zero-based budget conditions, as a saving she can allocate the remaining amount.
What is the zero-based budget?It is defined as the budgeting method that allows you to fix an amount for everything such as utility expenses, savings, and miscellaneous expenses In other words income minus all expenses plus savings should be equal to zero.
1) The core characteristic of the zero-based budget as follows:
Strategy is dependent on what each unit can provide for the price.Quick changes can be made in the budget anytime if it is required to do so.All the people of the organization can participate in the budgeting process.The purposes of each unit are in line with the corporate aspirations.2) Blanca has take-home pay every month = $800
Total expenses = $675
Savings = Income - Total expenses
= $800 - $675 ⇒ $125
We can assume Blanca has savings of $125 at the end of the month.
3) The extra amount = $800 - $675 ⇒ $125
According to a zero-based budget income minus all expenses plus savings should be equal to zero.
Therefore Blanca needs to allocate this amount($125) to some budget category.
4) Blanca has a total of $675 expenses she will have $125 as saving at the end of the month.
She should allocate this amount to savings because it will increase her wealth.
5) Zero-based budget does not mean that at the end of every month Blanca has zero dollars in her bank account because as per the definition zero-based budgeting means income minus expenses should be equal to zero. Blanca has savings and other emergencies funds in her bank account.
Thus, Blanca has a savings of $125, she needs to allocate this amount to fulfill the zero-based budget conditions, as a saving she can allocate the remaining amount.
Learn more about the zero-based budget here:
https://brainly.com/question/15994567
Which of the following statements is TRUE?
a. If f(x) and g(x) are differentiable functions defined on the closed interval [a, b], and f(x) attains its global maximum at x = c and g(x) d, then the function f(x) · g(x) attains its global maximum at x = attains its global maximum on [a, b] at x = c · ·d. b. The critical points of f' (x) are same as the critical points of f(x) c. The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint. d. All of the statements are false. e. Every local maximum a global maximum
Answers
The global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint is correct. Statement C.
What is a critical value of a function?The critical value is the value of x for which the double derivative of the function f(x) becomes zero.
When double derivative becomes zero, the graph of the function is neither increasing nor decreasing and hence, the the function attains either
a maxima or a minima.
Hence, he global maximum value of a differentiable function f(x) on a closed interval [a, b] must occur at a critical value or an endpoint.
To learn more about critical value visit:
https://brainly.com/question/36886
#SPJ1
Jamie wants a new smart TV/sound system that costs $1,250. He does not have that much in cash to purchase it, so he uses a credit card with 18% annual interest. He puts $250 down, but he only pays the interest each month on that credit card debt. About how much will he pay in interest over 4 years?
Answers
Jamie would pay $720 in interest in 4 years
The amount of interest he would have to pay = amount borrowed x interest rate x time
Amount borrowed = cost of the TV - amount put down
$1250 - $250 = $1000
Interest rate = 18%
Time = 4 years
Interest = 1000 x 0.18 x 4 = $720
To learn how to calculate interest, please check: https://brainly.com/question/22961510?referrer=searchResults
Interest is indeed the loan cost, in which the borrower pays this same lender a fee for the loan. Income is either simple or compounded, typically expressed in percentage. In this, the interest is $720, that's calculation can be defined as follows:
Given:
Rate of Interest \(= 18\%\)Time = 4 yearsUsing Formula:
\(\to \bold{\text{Interest =amount borrowed}}\times \bold{\text{interest rate}}\times \bold{\text{time}}\\\\\to \bold{\text{Borrowed amount = Television cost}} - \bold{\text{amount proclaimed}}\)
Calculating Borrowed amount:
\(\text{} =\$1250 - \$250 =\$1000\)
Calculating Interest:
\(\bold{= 1000 \times 18\% \times 4} \\\\\bold{= 1000 \times \frac{18}{100} \times 4} \\\\\bold{= 10 \times 18 \times 4} \\\\\bold{=\$ 720}\)
Therefore, In 4 years Jamie would pay $720 as interest.
Learn more:
brainly.com/question/15651729
6. The question is in the screenshot
Answers
Answer:
None of these
Step-by-step explanation:
We can estimate f'(9) by finding the slope of the secant through the two points closest to (9, f(9)).
\(\frac{f(10)-f(8)}{10-8}=\frac{16-10}{2}=3\)
A rectangle has a length of x and a width of 4 inches more than the length
Answers
You haven’t provided enough data, but lets say length (x) = 5
Then do the following:
Width = 4x
= 4 x 5
= 20
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Use digits to write the value of the 9 in this number.
139,648
Answers
Answer:
9,000
Step-by-step explanation:
the 9 is in the thousands place