Write an equation for each representation of a quadratic function given below.
Answers
Let, us assume that quadratic equation is :
[tex]y = ax^2 + bx + c[/tex]
Now, putting x = 0 and y = -4 :
[tex]c = -4[/tex]
Also, putting x = 1 and y = -3 :
[tex]ax^2 + bx + c =y\\\\a + b - 4 = -3 \\\\a + b = 1[/tex] ....2)
Also, putting x = 2 and y = 0 :
[tex]ax^2 + bx + c =y\\\\4a + 2b + c = 0\\\\4a + 2b = 4\\\\2a - b = 2[/tex]....3)
Solving equation 2 and 3, we get :
a = 1 and b = 0
Therefore, the quadratic equation is given by [tex]y = x^2- 4[/tex] .
Related Questions
A person invests 3000 dollars in a bank. The bank pays 4.25% interest compounded semi-annually. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 5600 dollars?
Answers
Answer:
The person must leave the money for approximately 14.8 years.
Step-by-step explanation:
This can be calculated using the formula for calculating the future value as follows:
FV = PV * (1 + r)^n …………………………………. (1)
Where;
FV = Future value of the investment = 5600
PV = Present value of the investment = 3000
r = semiannual interest rate = 4.25% / 2 = 0.0425 / 2 = 0.02125
n = number of semiannuals = ?
Substitute the values into equation (1) and solve for n, we have:
5600 = 3000 * (1 + 0.02125)^n
5600 / 3000 = 1.02125^n
1.02125^n = 1.86666666666667
Loglinearizing both sides, we have:
nlog1.02125 = log1.86666666666667
n = log1.86666666666667 / log1.02125
n = 0.271066772286539 / 0.0091320695404719
n = 29.6829509548973
Since n is number of semiannuals, we divide the answer by 2 obtain the number of years as follows:
Number of years = 29.6829509548973 / 2 = 14.8414754774487
Rounding to the nearest tenth of year, we have:
Number of years = 14.8
Therefore, the person must leave the money for approximately 14.8 years.
this is all i ask, just please give me the answer
Answers
Answer:
92
Step-by-step explanation:
161 divided by 7 is 23. so you just multiply 4 by 23. And that gets you the answer. Hope this helps:)
Answer:
x=92
Solve for x by simplifying both sides of the equation, then isolating the variable. hopes this helps have a great day <3 :)
Consider function h. h(x)= 3x-4 x<0 2x^2-3x+10 0<=x<4 2^x x>=5 What are the values of the function when x=0 and when x=4?
Answers
Answer:
[tex]h(0) = 10[/tex]
[tex]h(4) = NaN[/tex] (Not a number)
Step-by-step explanation:
According to the statement, we get the following piecewise function:
[tex]h(x) = \left\{ \begin{array}{ccc}3\cdot x -4,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x < 0\\2\cdot x^{2}-3\cdot x + 10,\,\,\,\,\, 0\le x < 4\\2^{x}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, x\ge 5\end{array}[/tex]
The value of the function when [tex]x = 0[/tex] is:
[tex]h(0) = 2\cdot (0)^{3}-3\cdot (0) +10[/tex]
[tex]h(0) = 10[/tex]
The value of the function when [tex]x = 4[/tex] is undefined, since 4 is out of any of the intervals covered by [tex]h(x)[/tex].
[tex]h(4) = NaN[/tex] (Not a number)
Answer: h(0)=10
h(4)=30
Step-by-step explanation:
Write the number seven hundred and ninety four in figures
Answers
Answer: 56 785 is written as fifty six thousand, seven hundred and eight five. The number 406 090 is written as four hundred and six thousand and ninety. Numbers with seven, eight or nine digits, are millions. 46 758 442 is forty six million, seven hundred and fifty eight thousand, four hundred and forty two.
Step-by-step explanation:
The number would be 794 in figure form which represents seven hundred and ninety-four.
What is the number system?A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.
Calculating the number of quantities for an object or the Number of things left in the container are only two examples of the types of mathematical operations that utilize the Number System.
We have to write the number seven hundred and ninety-four in figures
As per the given statement, the expression would be:
⇒ 700 + 94
⇒ 794
Therefore, the number seven hundred and ninety-four in figure form would be 794.
Learn more about the number system here:
https://brainly.com/question/21751836
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Christine's middle school total of 900 students and 45 teachers. The local high school has 110 teachers and a student-teacher ratio propotional to the middle school's. How many students find when she gets to high school
Answers
Answer:
2,200
Step-by-step explanation:
From the above, we were given that;
Total students in Christine's middle school = 900
Teachers in Christine's middle school = 45 teachers
Local high school = 110 teachers
Then, we can write an equation ratio and solve it.
900 students / X = 45 teachers / 110 teachers
If we cross multiply, we'll get
900 × 110 = 45 × X
45X = 99,000
Divide both sides by 45
45X/45 = 99,000/45
X = 2,200
Therefore, Christine would find 2,200 students when she gets to high school.
hii please please help i’ll give brainliest if you give a correct answer tyyyyy
Answers
there are 12 boys and 8 girls in the french club.
1) what is the ratio of boys to girls?
A. 2:5
B. 3:5
C: 2:3
D: 3:2
2) what percent of the members of the french group are girls?
A) 8%
B) 40%
C) 60%
D) 75%
Answers
Answer:
1)
D. 3:2
2)
B. 40%
as, no. of girls=8
total no. of students =12+8=20
now,
percentage of girls=no.of girls/total no. of students ×100%
=8/20×100%
=40%
I will give you the brainlist and 5 stars if you answer this. This is for simple probability.
A refrigerator has a variety of drinks. The contents are shown below. if one drink is picked randomly, then which of the following is NOT true. This is the content:
Drinks: Quantity:
Water - 14
Cola - 28
Lemonade - 7
A. You are twice as likely to select a cola than a water.
B. You are half as likely to select a lemonade than water.
C. You are more likely to select a cola than a water or a lemonade.
D. You are twice as likely to select a water than a cola.
Answers
Answer:
d is false
Step-by-step explanation:
water = 14 and cola is 28
you are half as likely to select a water than cola
Hello Pleasa help ASAP !!!!
Answers
Most of us have to invest in study time for recall at test time.
4(4x -4) + x +4= -46
Answers
Answer:
X=-2
Step-by-step explanation:
Let's solve your equation step-by-step.
4(4x−4)+x+4=−46
Step 1: Simplify both sides of the equation.
4(4x−4)+x+4=−46
(4)(4x)+(4)(−4)+x+4=−46(Distribute)
16x+−16+x+4=−46
(16x+x)+(−16+4)=−46(Combine Like Terms)
17x+−12=−46
17x−12=−46
Step 2: Add 12 to both sides.
17x−12+12=−46+12
17x=−34
Step 3: Divide both sides by 17.
17x
17
=
−34
17
x=−2
Answer:
x=−2
Answer:
x=2
Step-by-step explanation:
Hope this helps!! If you need step by step I'll comment it in the comments.
Simplify 30 - 5(15- 10).
A. -55
B. 125
c. 20
D. 5
Answers
Answer:
Your answer is D i guess
Step-by-step explanation:
Here you go mate
step 1
30 - 5(15- 10) equation/question
step 2
30 - 5(15- 10) simplify
30-(5)^2
30-25
answer
5
Please help me with question 4 thank you !!
Answers
Answer:
b) similar by SSS theorem
Step-by-step explanation:
Which is an example of a statistical question?
|
|How old am 1?
How old is the teacher?
How old will I be after my next birthday?
How old are the students ín math class?
Answers
Answer: how old are the students in the math class
Why: because their ages vary and can be used as data
Answer:
Question 4 is a statistical question aka answer D
Step-by-step explanation:
Correct on edge
Elwood invested $5,000 in a money market account and has been tracking its progress. He found that after 3 years, the account held $7,100 and after 8 years, the account held $10,350.
Answers
Answer:
The percent of interest is 12.3% per year
Step-by-step explanation:
According to the question Elwood invested 5000 $ in market account
The market account gives the compound interest annually
let p be the interest per year then
At the end of 1st year
amount =(1+0.p) x 5000 = 1.p x 5000
similarly at the end of 2nd year
amount =(1+0.p) x(1+0.p)x 5000 = [tex](1.p)^{2}[/tex] x 5000
similarly at the end of 3rd year
amount = 7100 $ = [tex](1.p)^3[/tex] x 5000
⇒ [tex]\frac{71}{50}[/tex] = [tex](1.p)^3[/tex]
1.392 = [tex](1.p)^3[/tex]
on further solving we get
1.p = [tex](1.42)^{1/3}[/tex] = 1.123
thus 1.p = 1 + 0.p = 1.123
thus p = 0.123
thus the percent of interest is 12.3% per year
Answer:
drop down 1 a slower rate per year
drop down 2 670
Step-by-step explanation:
as in three years you get $7100
you take that and subtract it by your starting amount (5000)
7100-5000= 2100
then divide 2100 by the number of years (3)
to get your annual rate of 700$
then you take the 8 year total and subtract it from your 3 year total
10350-7100= 3250
Then divide that by 5 because that how many years it has been
to get the annual rate of 650
making the 5 year rate slower.
The to find the average rate over all 8 year you take 10350 and subtract it from your starting number 5000
10350-5000= 5350
then take 5350 and divide it by the number of years (8)
you then get you average rate of 668.75
668.75=670
Hope this helps!
Does anyone know this??? I need help please
Answers
Answer:
32
Step-by-step explanation:
QC = 16 and CS = 16 so 16 + 16 = 32
Skyler has twice as many apples in her grocery bag as her
friends Macy and Janelle combined. Macy has 15 apples
in her bag. Skyler has 50 apples in her bag. How
many apples does Janelle have in her grocery bag?
The equation 2(x + 15) = 50 models this situation. Which choice shows the
sequence of operations needed to solve this problem, using both arithmetic
and algebra?
A. Subtract 15 divide by 2 X = 35/2
B. Subtract by 15 divide by 2 X = 10
C. Divide by 2 subtract by 15 X = 10
D. Divide by 2 subtract by 15 X = 35/2
Answers
Answer:
Step-by-step explanation:
It's C.
0.5a - 1.96
a=17, b=3
0.5a - 1.9b =
(Type an integer or a decimal.)
Answers
Answer:
2.8
Step-by-step explanation:
0.5a - 1.9b
~Substitute
0.5(17) - 1.9(3)
~Simplify
8.5 - 5.7
~Subtract
2.8
Best of Luck!
What’s the answer???
Answers
Answer:
i'm not sure what is it ?
Step-by-step explanation:
What is 2+2
A) 22
B) 4
C) 38
D) 55
Answers
Answer:
B
Step-by-step explanation:
Answer: 4
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= ===(_________D
can someone help me pls
Answers
WILL GIVE BRAINLIEST !! Ella needs at least $360 to pay for her spring break expenses and she is saving $25 from each of her weekly paychecks. How long will be before she can pay for her trip?
Answers
Answer:
At least 15 weeks
Step-by-step explanation:
If Ella needs at least $360, she will have to save her $25 constantly for about 15 weeks.
25*15=375, which is more than 360, so she will have leftover money.
Answer:
2 weeks + 1day
Step-by-step explanation:
7 days a week. 7 + 7 = 14
25 x 14 = $350, missing another 10 dollars.
25 x 15(adding a extra day) = 275.
in change, you have 15 dollars left.
Solve pls
for the function -2x²+x+1 find f(3)
Answers
Answer:
f(3) = -14
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = -2x² + x + 1
f(3) is x = 3
Step 2: Evaluate
Substitute: f(3) = -2(3)² + 3 + 1Exponents: f(3) = -2(9) + 3 + 1Multiply: f(3) = -18 + 3 + 1Add: f(3) = -15 + 1Add: f(3) = -14I need help please ten points for question number three !!!!!!!!.......!!!!!!.....
Answers
Answer:
where is the question though
Step-by-step explanation:
Answer:
what
Step-by-step explanation:
Martin has 13 liters of soda.
Each glass can hold of a liter
of soda. How many glasses can
Martin completely fill with soda?
Answers
Answer:
13
Step-by-step explanation: If each glass can hold 1 liter than 13 glasses can hold 13 liters.
A company provides commisssion to its agent at the following rate.
-0.5% in the sale upto Rs.15 lakh
-1% in the sale from 15 lakh to Rs.25 lakh
-1.5% in the sale from Rs.25 to Rs.40 lakh
-2% in the sale above Rs.40 lakh
calculate the amount of commission that can be obtained from the following sale amount by using the above rate of commission
a.Rs.12 lakh
b.Rs.24 lakh
c.Rs.38 lakh
d.60 lakh
Answers
Answer:
A company provides commisssion to its agent at the following rate.
-0.5% in the sale upto Rs.15 lakh
-1% in the sale from 15 lakh to Rs.25 lakh
-1.5% in the sale from Rs.25 to Rs.40 lakh
-2% in the sale above Rs.40 lakh
calculate the amount of commission that can be obtained from the following sale amount by using the above rate of commission is 38 lakh
for the function -2x²+x+1 find f(3)
Answers
Answer:
-14
Step-by-step explanation:
Plug 3 in for x
-2 (3)² + 3 + 1
-2 (9) + 3 + 1
-18 + 3 + 1
-14
Answer:
f(3) = -14
Step-by-step explanation:
[tex]f(x)=-2x^{2} +x+1\\f(3)=-2(3)^2+3+1\\f(3) = -2(9)+4\\f(3) = -18+4\\f(3) = -14[/tex]
A bag contains five red marbles and six blue marbles. Another bag contains five green marbles and five yellow marbles. You randomly pick one marble from each bag. One marble is blue and one marble is yellow.
Answers
Solve the equation for y.
4x = -2y
A. y= 1/2x + 2
B. y= -1/2x
C. Y= -2x
D. y = x + 2
Answers
Answer:
Answer is C...........................
Step-by-step explanation:
Answer:
C.) y = -2x
Step-by-step explanation:
To solve for y, u gotta divide both sides by -2 to get y by itself. When u do that, u get -2x.
Use the Product Rule to find the derivative of :
a.[tex]y=(3x-1)^3(2x+5)[/tex]
b. [tex]y=(3x-2)(2x^2+3)[/tex]
Answers
Answer:
see explanation
Step-by-step explanation:
Using the product rule
Given
y = f(x)g(x) , then
[tex]\frac{dy}{dx}[/tex] = f(x).g'(x) + g(x).f'(x) ← product rule
(a)
let
f(x) = (3x - 1)³ , then using the chain rule
f'(x) = 3(3x - 1)² × [tex]\frac{d}{dx}[/tex](3x - 1) = 3(3x - 1)² × 3 = 9(3x - 1)²
let
g(x) = 2x + 5 ⇒ g'(x) = 2
Then
[tex]\frac{dy}{dx}[/tex] = (3x - 1)³ . 2 + (2x + 5) × 9(3x - 1)²
= 2(3x - 1)³ +9(3x - 1)²(2x + 5) ← factor out (3x - 1)²
= (3x - 1)²[ 2(3x - 1) + 9(2x + 5) ]
= (3x - 1)² [ 6x - 2 + 18x + 45 ]
= (3x - 1)²(24x + 43)
--------------------------------------------------------------
(b)
let
f(x) = 3x - 2 ⇒ f'(x) = 3
let
g(x) = 2x² + 3 ⇒ g'(x) = 4x
Then
[tex]\frac{dy}{dx}[/tex] = (3x - 2).4x + (2x² + 3). 3 ← distribute parenthesis
= 12x² - 8x + 6x² + 9
= 12x² - 8x + 9
Note
It is usual to simplify after differentiating the expressions
help???????
dhdjdjmsjd
Answers
Answer:
1/2 over 7/8
Step-by-step explanation:
becauseim smartt
Answer:
the bridge is 90ft long.
Step-by-step explanation:
3/18=15/x
solve for x
use reciprocals to get x as numerator for easier calculation
18/3=x/15
270/3=x
x=90ft