Given:
The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).
To find:
The equation of the quadratic function.
Solution:
A quadratic function is defined as:
[tex]y=ax^2+bx+c[/tex] ...(i)
It is passes through the point (0,11). So, substitute [tex]x=0,y=11[/tex] in (i).
[tex]11=a(0)^2+b(0)+c[/tex]
[tex]11=c[/tex]
Putting [tex]c=11[/tex] in (i), we get
[tex]y=ax^2+bx+11[/tex] ...(ii)
The quadratic function passes through the point (5,31). So, substitute [tex]x=5,y=31[/tex] in (ii).
[tex]31=a(5)^2+b(5)+11[/tex]
[tex]31-11=a(25)+5b[/tex]
[tex]20=25a+5b[/tex]
Divide both sides by 5.
[tex]4=5a+b[/tex] ...(iii)
The quadratic function passes through the point (3,11). So, substitute [tex]x=3,y=11[/tex] in (ii).
[tex]11=a(3)^2+b(3)+11[/tex]
[tex]11-11=a(9)+3b[/tex]
[tex]0=9a+3b[/tex]
Divide both sides by 3.
[tex]0=3a+b[/tex] ...(iv)
Subtracting (iv) from (iii), we get
[tex]4-0=5a+b-3a-b[/tex]
[tex]4=2a[/tex]
[tex]\dfrac{4}{2}=a[/tex]
[tex]2=a[/tex]
Putting [tex]a=2[/tex] in (iv), we get
[tex]0=3(2)+b[/tex]
[tex]0=6+b[/tex]
[tex]-6=b[/tex]
Putting [tex]a=2,b=-6[/tex] in (ii), we get
[tex]y=(2)x^2+(-6)x+11[/tex]
[tex]y=2x^2-6x+11[/tex]
Therefore, the required quadratic equation is [tex]y=2x^2-6x+11[/tex].
Match the items in a credit card statement to their descriptions.
the maximum credit available on a credit card
determines the finance charge
payable on credit purchases
the amounts debited to the credit card account
the period for which transactions are
recorded in a credit card statement
1.billing cycle
2.annual percentage rate
3.credit line
4.new purchases
Answer:
Billing cycle: The period for which transactions are
recorded in a credit card statement
Annual Percentage Rate: Determines the finance charge
payable on credit purchases
Credit Line: The maximum credit available on a credit card
New Purchases: The amounts debited to the credit card account
Step-by-step explanation:
Took the test on Edmentum and got 5/5
can someone help me solve for x
Answer: Possibly -4
Step-by-step explanation:
But wait for others to check I’m not fully sure
the amount of gas used by a household is shown in the table. what is the slope of the data from the table
Answer. i cant answer this without a pic of the slope
Step-by-step explanation:
Solve the system of equations.
{y=30x+10y=5x2−25
I need major help!!! Please!!!!
Correctly identify step 3 and 4 of the accounting process:
Answer:
Step 3: record transactions into the journal; Step 4: post entries into the ledger
I think you are happy with this answer
Which of the following is different from others?
(a) 100000 ones (b) 10 thousand (c) 1000 tens (d) 10 hundred
the answer is A I believe
Answer:
a = 100,000
b= 100,000
c = 10,000
d = 1,000
uhhh... a and b are the same... c and d are different.
Step-by-step explanation:
Nine people in a square
If there are nine people in a square, then there will be 3 rows and 3 columns.
Because 3² = 9 or √9 = 3
Ben rented a car. It cost $30.00 plus $0.25 per mile. If Ben paid $85.00 for the car rental, how many miles did he drive the car? Write an equation and then use your equation to find your answer.
Answer:
220 miles
Step-by-step explanation:
85-30=55
55/.25=220
220 = miles
Answer:
Equation:
30 + 0.25x = 85
Work:
30 + 0.25x = 85
85 - 30 = 55
55 / 0.25 = 220
Final answer:
200 miles
Step-by-step explanation:
Hope this helped and have a nice day!!!
URGENT NEED HELP CLICK TO SEE
Answer:
35
Step-by-step explanation:
- x - = +
Therefore :
-5 x - 7 = 35
Angle Relationships
Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.
The cosine of the complimentary angle to 38°
a. 0.68
b. -0.16
c. -0.22
d. 0.62
Please select the best answer from the choices provided
Answer:
D. 0.62
Step-by-step explanation:
I calculated it logically
plz answer these questions without putting links and files
what is 3/4 multiplied by 1/2 then add 3/4
what is 1 and 1/8 multiplied by 1/2 then add 3/4
Answer:
11/8 and 21/16
Step-by-step explanation:
3 x 1 = 3
4 x 2= 8
3/8+3/4(convert to eighth's)
3/8+6/8=11/8
1 1/8 = 9/8
9 x 1 = 9
8 x 2 = 16
9/16+3/4(convert to sixteenth's)
9/16+12/16
21/16
---
hope it helps
=3/4 × 1/2 + 3/4
=3/8 + 3/4
=9/8
2nd questions ans
=1×1/2 + 3/4
=1/2 + 3/4
=5/4
sum difference place value of 2 in 4242
Answer:
[tex]\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }[/tex]
4242
2 = 200 ( 2 is in hundred's place )
4242
2 = 2 ( one's place )
Difference = ?
[tex] = 200 - 2 \\ = 198[/tex]
Sum = ?
[tex] = 200 + 2 \\ = 2[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}[/tex]
Question is below in photo
what about using 20-30-40-5
Step-by-step explanation:
the sequence is that you are skipping ten to get the second nb which is 30 and keep on going on to get 50
select all the ordered pairs that satisfy the function y=8r+20
Answer:
r= 1/8 y + -5/2
Step-by-step explanation:
The value of a car is decreasing by 12% per year. If the car is worth $11,000 today, what will it be worth in two years?
Answer:
$8518.40
Step-by-step explanation:
FV = PV(1+r)^n
FV = future value
PV = present value
r = rate
n = # of years
Value in 2 yrs = 11,000 x (1 - 0.12)^2 = 8518.4
Find the dot product of u and v.
9514 1404 393
Answer:
-4
Step-by-step explanation:
The dot product is the sum of products of corresponding coefficients.
u·v = (4)(-1) +(0)(2) = -4
u·v = -4
Why is having a variety of plants important in a ecosystem
Answer:
It is better to have a variety of plants because if the species of plants die out, the whole ecosystem becomes extinct.
Step-by-step explanation:
Solve for x then find the measure of arc GF.
Answer:
Step-by-step explanation:
180 = x + 135 + x + 65
-20 = 2x
-10 = x
x = -10
GF = 55°
PLEASE help fast with attached question!! Thanks!
Answer: I thihnk it's 1x10^-2
Step-by-step explanation: This equals 0.1, and 6^-2 is equal to 0.1....the rest of the answers are either too big or too small
Soren's favorite cereal is on sale. A 20-ounce box costs $4.59. A smaller, 12-ounce box costs $2.52. Complete the statements to describe which box costs less per ounce.
Answer:
The smaller box, 12 oz, costs less per oz than the larger 20 oz box.
Step-by-step explanation:
$4.59 divided by 20 = $0.2295 per oz
$2.52 divided by 12 = $0.21 per oz
Which of the following would be in the solution set for x < 4
Group of answer choices
4
-4
4.2
4.002
Answer:
- 4
Step-by-step explanation:
The set of all possible value that would make the above statement true must be less than 4.
Therefore the only option we have is -4
q square =-1 what is q
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Answer:
±i
Step-by-step explanation:
q² = -1
q = ±√(-1) = ±i . . . . . . i is the name given to the square root of -1.
The surface area of a rectangular prism is increased by a factor of 16.
By what factor is the volume of the figure increased?
4
8
Оооо
32
64
Answer:
64
Step-by-step explanation:
Answer:
D 64
Step-by-step explanation:
The person above me is correct. Got it right on Edge 2021
What value of X makes the equation true -7x - (-5-x) = -9(2x-1) -
Answer:
x=17/9
Step-by-step explanation:
-7x-(-5-x)=-9(2x-1)
= -7x+5x+x= -18x+9
= -x= -18x+9
+18x +18x
=17x=9
x= 17/9
Hope this helps!
Answer:
-7x -(-5-x)=9(2x-1)
-7x+5x+x=18x+9
-x=-18x+18x
17x=9
x=17/9
Step-by-step explanation:
hopes this help
what is (20)+(475)? I need it now
Which expressions are not equivalent
? Thanks!
Answer:
D
Step-by-step explanation:
There is no 2x in D answer
What is the product of 2r2 - 5 and 3r
Answer: 6r^3 - 15r
Step-by-step explanation:
(3r) (2r^2 - 5)
Distribute.
6r^3 - 15r
Hope this helped.
Question 9 of 10
Which best describes how to find the length of an arc in a circle?
A. Divide the arc's degree measure by 360°, then multiply by the
circumference of the circle,
B. Divide the arc's degree measure by 360°, then multiply by the
radius of the circle.
C. Divide the arc's degree measure by 180°, then multiply by the
radius of the circle.
D. Divide the arc's degree measure by 180°, then multiply by the
circumference of the circle.
To find the length of an arc in a circle we use (a) Divide the arc's degree measure by 360°, then multiply by the circumference of the circle,
Which best describes how to find the length of an arc in a circle?From the question, we have the following parameters that can be used in our computation:
The length of an arc in a circle
The length of an arc in a circle is calculated as
Length = Angle/360 * Circumference
This is representd by the option (a)
Read more about arc length at
https://brainly.com/question/16552139
#SPJ1
The following is a geometric series.
6+8+11+15+20+26+...
O True
False
EXPLAIN ANSWER FOR BRAINLIEST
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Answer:
False
Step-by-step explanation:
The terms of a geometric series would have a common ratio. The terms of this series do not. (The differences increase by 1 each time, so it is a quadratic series.)
False, the series is not geometric.
Answer:
Solution :-We are given with the series
6 + 8 + 11 + 15 + 20 + 26
Since
the series is increasing by +1. So, it will be not a geometric series
[tex] \\ [/tex]
Multiplying polynomials
(4x+3y)(5x+y)
Answer:
20x^2 +19xy+3y^2
Step-by-step explanation:
See Image below :)
9514 1404 393
Answer:
20x² +19xy +3y²
Step-by-step explanation:
Use the distributive property.
(4x +3y)(5x +y)
= 4x(5x +y) +3y(5x +y)
= 20x² +4xy +15xy +3y²
Collect terms.
= 20x² +19xy +3y²