Given:
The vertex of a quadratic function is (4,-7).
To find:
The equation of the quadratic function.
Solution:
The vertex form of a quadratic function is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where a is a constant and (h,k) is vertex.
The vertex is at point (4,-7).
Putting h=4 and k=-7 in (i), we get
[tex]y=a(x-4)^2+(-7)[/tex]
[tex]y=a(x-4)^2-7[/tex]
The required equation of the quadratic function is [tex]y=a(x-4)^2-7[/tex] where, a is a constant.
Putting a=1, we get
[tex]y=(1)(x-4)^2-7[/tex]
[tex]y=(x^2-8x+16)-7[/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]y=x^2-8x+9[/tex]
Therefore, the required quadratic function is [tex]y=x^2-8x+9[/tex].
Find the arc length along a circle of radius 10 subtended by an angle of 215 degrees
Answer:
arc = 25.29
Step-by-step explanation:
first find the circumference:
C = 2r(Pi) = 2(10)(3.14) = 62.8
since subtended, then we're looking for these opposite angle of 215 degrees:
360 - 215 = 145 degrees
62.8/360 = 0.1744 per degree
0.1744 x 145 = 25.29
What is the surface area of the square pyramid?
6 square meters
16 square meters
28 square meters
49 square meters
Answer:
It's 16, there's so many question on this one.
Step-by-step explanation:
3 people can build a shed in 8 hours how long would it take 5 people give your answer in minutes
Answer:
798 minutes
Step-by-step explanation:
The original cost of a piano is $19,100, and it is on a sale for 19% off its original price. If the total cost includes a 5% sales tax, the total cost of the piano is ____________.
Answer: $16,244.55
Step-by-step explanation: Multiply $19,100 by .19 to find the discount. Then subtract that number from the original to find the discounted price. Then multiply the discounted price by .5 to find the tax. Add the tax to the discounted price to find the discounted taxed price. This is the final price and is $16,244.55
Which is greater 27 or 72
Answer:
72??? For greater wise? Then yeah, 72.
Step-by-step explanation:
Answer:
there both equal if you add 2 and 7 equals 9
if you had 7 and 2 equals 9
Step-by-step explanation:
Find the Principal when the Interest is $200, the Rate is 3%, and the time is 18 months.
Answer:
Step-by-step explanation:
Which expressions are equivalent to the one below? Check all that apply. 9^x
a. 3^x•3^x
b. 3•3^2x
c.3^2•3^x
d.(3•3)^x
e.3^2x
f. 3•3^x
Answer:
using law of indices, A,D and E.
can someone please help me. my grade is very low in this class although i have no idea how to do this PLEASE HELP!!
Answer:
download symbolab or download photo math it gets I covered on most of that your grade should go up
Answer: How to solve equations
Step-by-step explanation:
You have to use Pemdas the order of operations to solve these types of equations.
Parenthesis,Exponents,multiplication,Division,Addition,subtraction.
Multiplication and division fit in a group left to right.
Addition and subtraction come last but depends on which comes first left to right.
Here you first have to use the distributive property.
3(y+5)=39 multiply 3 times y that gives you 3y. Then multiply 3 times 5 that gives you 15 . So, now you have simplified the left side of the equal sign so you have 3y+15=39 now subtract 15 from both sides and you get 3y=24 then you divide both sides by 3 to get y=8. What I just went over you do again and again to solve all these types of equations. Your trying to solve for the variable so you try to get y or m or n or any variable by itself.
Find ƒ–1 for the function ƒ(x) = –2x + 1.
Answer:
Step-by-step explanation:
y = -2x+1
rearrange to solve for x
2x = -y+1
x = -½y + ½
f⁻¹(x) = -½x + ½ = -(x-1)/2
The school newspaper surveyed 100 commuter students and asked two questions. First, students were asked how many courses they were currently enrolled in. Second, the commuter students were asked to estimate how long it took them to drive to campus. Considering these two variables, number of courses would best be considered a _________ variable and drive time would be considered a _________ variable.
Answer:
Number of courses would best be considered a discrete variable and drive time would be considered a continuous variable.
Step-by-step explanation:
Discrete variable:
Countable amounts(0, 1, 2, 3,...)
Continuous variables:
Can be decimal values.
In this question:
The number of courses is a countable amount(0,1,2,3,...), you cant take half a course, for example, so it is discrete. Otherwise, drive time accepts half minutes, for example, 10.5 minutes, so is continuous.
Number of courses would best be considered a discrete variable and drive time would be considered a continuous variable.
ABCD is a square. What is the measure of
Answer:
Step-by-step explanation:
Since it is a square, a line from one corner to the other cuts the right angles in half. this is only because it is a square, if you don't see why I can explain.
Since each right angle is cut in half each smaller angle on the corners is 45 degrees.
ABD is one of those cut in half angles, specifically from the right angle ABC. So it is 45 degrees
Camila baked 150 cookies 60% of the cookies are chocolate chip cookies how many cookies are chocolate chip cookies
Answer:
90
Step-by-step explanation:
150 x 0.6 = 90
or
150/10 = 15
15 x 6 = 90
Answer:90 is correct
Step-by-step explanation:
Look at the picture.
Thank u!
Answer:
option 2
Step-by-step explanation:
Step-by-step explanation:
option 2 is the right answer... I m sure , the formula is 1/2 × base× height...
What is 3 divided by 1/3?
Answer:
It will be 9
hope this helps
Answer:
9
Step-by-step explanation:
3/1 ÷ 1/3 = 3/1 · 3/1 = 9
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.) Advertising Expenditure ($ millions) Number of Companies 25 up to 35 5 35 up to 45 10 45 up to 55 21 55 up to 65 16 65 up to 75 8 Total 60
Mean
Standard deviation
The estimated mean of advertising expenses is $52 million, and the estimated standard deviation is $11.23 million.
To estimate the mean and standard deviation of advertising expenses, we need to calculate the midpoint of each class interval, the product of the midpoint and the frequency, and the squared deviation from the mean.
Here's a table to organize the calculations:
Class Interval (x) Frequency (f) Midpoint (x) fx
25 up to 35 5 30 150
35 up to 45 10 40 400
45 up to 55 21 50 1,050
55 up to 65 16 60 960
65 up to 75 8 70 560
To calculate the mean, we need to find the sum of the products of the midpoint and the frequency, divided by the total frequency.
Mean = (fx) / Total Frequency
Mean = (150 + 400 + 1,050 + 960 + 560) / 60
Mean = 3,120 / 60
Mean = 52
Calculate the squared deviation from the mean for each class interval.
(x - mean)² × f
(30 - 52)² × 5 = 484 × 5 = 2,420
(40 - 52)² × 10 = 144 × 10 = 1,440
(50 - 52)² × 21 = 4 × 21 = 84
(60 - 52)² × 16 = 64 × 16 = 1,024
(70 - 52)² × 8 = 324 × 8 = 2,592
Calculate the sum of the squared deviations.
Sum of (x - mean)× f = 2,420 + 1,440 + 84 + 1,024 + 2,592
= 7,560
Standard Deviation =√(Sum of (x - mean)² × f / Total Frequency)
Standard Deviation = √(7,560 / 60)
Standard Deviation = √(126)
Standard Deviation = 11.23
Hence, the estimated mean of advertising expenses is approximately $52 million, and the estimated standard deviation is approximately $11.23 million.
To learn more on Statistics click:
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Complete question
Advertising expenses are a significant component of the cost of goods sold. Listed below is a frequency distribution showing the advertising expenditures for 60 manufacturing companies located in the Southwest. Estimate the mean and the standard deviation of advertising expenses. (Round squared deviations to nearest whole number and final answers to 2 decimal places.)
Advertising Expenditure ($ millions) Number of Companies
25 up to 35 5
35 up to 45 10
45 up to 55 21
55 up to 65 16
65 up to 75 8
Total 60
Need it now. I'll give you another 100 when done if all i right.
This it the test please do as fast as posible and show work. thank you and sorry
Somebody help me with this
40 points ☺️
1. The temperature on a winter night in Kansas is - 6 Celsius. The
temperature decreases by 8 Celsius. What is the new temperature, in
degrees Celsius? *
A + A =2,A + B =3,A + B × 2 =??..only for geniuses
Answer: 5
Step-by-step explanation:
Find the measure of 46.
{
62°
46
46 = [?]
Answer:
118
Step-by-step explanation:
Same side interior angles are supplementary, or add up to 180.
?=118°
Answer:
<6+62=180 co interior angle
<6=180-62=118°
PLS HELP!
0.99 is what percent of 9.90?
Answer:
10%
Step-by-step explanation:
first let's write out the problem
0.99 is what percent of 9.90 = 0.99=9.90*x
We need to what c is so we would do the opposite operation of multiplication, division so we get,
0.99/9.90= .1
now we turn .1 into percent and get out answer
0.1= 10%
Answer:
Step-by-step explanation:
ahh that's like a math tongue twister :P
so just remember that when you are given the final amount, as the 0.99 is, then you want to divide by the total, like this
0.99 / 9.90 =
we don't really need a calculator for this, b/c you can see that the answer will come out to a one, but, where is the decimal, huh
my calculator put the decimal here 0.1
so that's 10% right? which totally makes sense.. right? 0.99 is 10% of 9.90... just move the decimal one place in the 9.9 to get .99 see? so that kinda helps us know where the decimal goes in the answer, if that make sense? The decimal gets moved one place to the LEFT of the one, in our answer when we just did the math in our head.
anyway.. leave a comment if you have more questions :)
ill mark brainlistnplss help
Nate ordered a pizza to be delivered. The bill with 5% tax and 20% tip was $24.00. What was the original cost of the pizza?
a
12.60
b
16.65
c
15.40
d
19.20
Answer:
d. $19.20
Step-by-step explanation:
Let C = original cost of pizza
24 = .05C + .20C + C
= 1.25C
C = 19.20
Find the mean: 17.4 mm, 20.3 mm, 84.1 mm, 31.2 mm, 53.7 mm, 11.7 mm
You toss a coin 100 times and get only 12 heads. Do you have reason to suspect the coin is unfair
Answer:
No
Step-by-step explanation:
The coin has 2 sides. Heads and tales. If you flipped a million heads in a row, on your next flip, there is still a 50 percent chance of flipping tales. Just become the outcome has been favorable to tales doesn't mean the probability changes
Help please thank you
Answer:
The answer is two dollars.
Step-by-step explanation:
She had 10.00 to begin with and she spent $4.25 and $3.75. If you add the money she spent, and then subtracted the 10 dollars she had to begin with she would have $2.00.
In ABCD, the measure of D=90°, CD = 5.4 feet, and DB = 2.2 feet. Find the measure
of C to the nearest degree.
Answer:
the answer is 22
gggggggggggggggfffffgg
A car is driven 600 miles and uses 20 gallons of gas. If gas is $1.05 per gallon, what is the gasoline cost per mile?
Answer:
hi
Step-by-step explanation:
Can the sides of a triangle have lengths 2, 6, and 9
Answer:
no.
Step-by-step explanation:
the sum of the two smallest sides of the triangle must be greater than the largest side in order to form a triangle. 2+6<9
please help me !! find the missing sides
Answer:
B
Step-by-step explanation:
Hello There!
That is a 45-45-90 special right triangle
so we use the same rules provided in the image
y is = to 10
x is = to [tex]10\sqrt{2}[/tex]
so we can conclude that the answer is B