Given that f(x) is a cubic function with zeros at -3, 0, and 7, find an equation for f(x) given that f(-8) = -5.
Answer:
[tex]\huge\boxed{f(x)=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x}[/tex]
Step-by-step explanation:
[tex]f(x)=a(x+3)(x-0)(x-7)=ax(x+3)(x-7)\\\\=ax\bigg((x)(x)+(x)(-7)+(3)(x)+(3)(-7)\bigg)\\\\=ax(x^2-7x+3x-21)=ax(x^2-4x-21)\\\\=(ax)(x^2)+(ax)(-4x)+(ax)(-21)\\\\=ax^3-4ax^2-21ax\qquad(*)\\\\f(-8)=-5[/tex]
[tex]\text{substitute}\ x=-8\\\\f(-8)=(a)(-8)^3-(4a)(-8)^2-(21)(-8)a=-512a-(4a)(64)+168a\\\\=-512a-256a+168a=-600a\\\\f(-8)=-5\\\\\text{therefore}\\\\-600a=-5\qquad|\text{divide both sides by (-600)}\\\\a=\dfrac{-5}{-600}\\\\a=\dfrac{1}{120}[/tex]
[tex]\text{Substitute to}\ (*):\\\\f(x)=\dfrac{1}{120}x^3-4\cdot\dfrac{1}{120}x^2-21\cdot\dfrac{1}{120}x=\dfrac{1}{120}x^3-\dfrac{1}{30}x^2-\dfrac{7}{40}x[/tex]
Derrick earns $14 per hour working at Pizza Palace. What will Derrick's new hourly rate be after a 4.5% raise.
14x4,5÷100=0,63
14+0,63=14,63
Find the slope of the line
A -3
B 3
C -2
D 2
The table shows the results of a survey of 100 people selected at random at an airport. Find the experimental probability that a person selected at random is going to City D
Answer: 12% of people responded as City D
Review the incomplete equation below. Select the number that makes the equation true.
35 × 64 = 1800 +_____ + 120 +20
Answer:
300
Step-by-step explanation:
find what's 35 x 64 its 2240
then you add up 1800 and 120 and 20 n you get 1940
Then you subtract to see what's missing and you get
300
if you don't understand pls tell me
8 times the sum of 2 and a number that is 32
Answer:
Step-by-step explanation:
d) 8(n+2) = 32
Im so confused- please help
Step-by-step explanation:
a/q
x + x - 3 + 2x - 9 = 36
4x - 12 = 36
4x = 36 + 12 = 48
x = 48/4 = 12
x = 12
so,
x = 12
x - 3 = 12 - 3 = 9
2x - 9 = 2(12) - 9 = 15
we know,
area = 1/2 × base × height
so,
→ 1/2 × 12 × 9
→ 1 × 6 × 9
→ 54 inches.
HOPE THIS ANSWER HELPS YOU DEAR! TAKE CARE
What is the midline of the function y=19cos(9x+3)+34 ?
plss help mee
The midline of the function is y = 34.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The midline of a periodic function is the horizontal line that divides the graph of the function into two equal parts.
For a cosine function of the form y = A cos(Bx - C) + D, the midline is given by the equation y = D.
In this case, the function is y = 19cos(9x+3)+34, so the midline is given by the constant term, which is D = 34.
Therefore,
The midline of the function is y = 34.
Learn more about functions here:
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Kenrick mows lawns on Sundays. Last
week it took him 5 hours to finish.
This week it took only 5 hours. How
many times longer did it take last
week than this week?
Answer:
0 hours.
Step-by-step explanation:
He finished at the same time than Kenrick finished last week. So, he/she did not delay in mowing the lawn. Hoped this helped.
henry is designing a tablecloth for his dining room table. He wants to buy fabric in his favorite color to make the tablecloth. use the dimensions below to determine how much fabric he need to buy. 12 feet 7 feet
Sierra is getting a loan to purchase a car, but she has a few options for loan
comparing the cost of each loan to determine which loan will cost the least in terms of interest
paid. (Interest is the fee paid for the use of borrowed money, and it is expressed as a
percentage of the amount borrowed multiplied by the amount of time the borrower takes to
repay the loan.) All of the loan offers are for $10,000, and include an upfront fee of $200. They
are all simple interest loans (as opposed to compound interest loans). Loan A is to be paid back
over five years with an annual interest rate of 6 percent Loan B is to be paid back over four
years with an annual interest rate of 4 percent. Loan C is to be paid back over three years with
an interest rate of 5 percent. How Sierra figure out which loan will require the lowest interest
payments?
Answer:What would be the interest cost(simple interest) for a $3000 loans with a 8% rate for nine months of a years? [Simple interest= Principal Rate Time. In this case, time is 9/12(for 0.75 of a year).
Step-by-step explanation: The cost to borrow the money, expressed as a percentage of the loan. After you enter the details, the auto loan payment calculator automatically ...A finance charge is the dollar amount that the loan will cost you. Lenders generally charge what is known as simple interest. The formula to calculate ...
A jacket is on sale for 20% off. The
original price is $60. What is the new
price? Show your work.
Answer:
New price = $48
Step-by-step explanation:
New price = Original price - (original price × 20%)
New price = $60 - ($60 × .20)
New price = $60 - $12
New price = $48
Or If the jacket is 20%, you will pay 80% of the cost.
So Original price × the percentage that you paid = New price
$60 × 80% = New price
$60 × .80 = $48
A child is chosen at random from the group.
a)
What is the probability that the chosen child is a girl?
Give your answer as a fraction.
b)
What is the probability that the chosen child is a left-handed girl?
Give your answer as a fraction.
Answer:
A. 2/5
B. 1/10
Step-by-step explanation:
First off we need to calculate the probability that the chosen child is a girl So to calculate this probability, we have to know the num. of girls which is seen in the table. There are a total of 8 girls.
Therefore the probability of a girl being chosen is equivalent to the number of girls/exact number of children = 8/20 = 2/5 simplified.
Now to find the probability that the chosen girl is left-handed.
The amount of left-handed girls there is only 2. therefore the probability of selecting a left-handed girl will be 2/20 = 1/10 simplified.
What is the meaning of algebra and expressions
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expressio
Answer:
Algebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. Algebra can include real and complex numbers, matrices, and vectors. An algebraic equation represents a scale where what is done on one side of the scale is also done to the other and numbers act as constants.
Expressions is a Numbers, symbols and operators (such as + and ×) grouped together that show the value of something.
Examples:
• 2 + 3 is an expression
• 3 − x/2 is also an expression
What is the solution of the system of inequalities y>x^2+6x+10 y<-x^2-8x-14
Answer: hopefully this helps!
Which of the following does NOT reveal the variation (spread) of the data? Check all that apply. Mean Mode Standard Deviation Range Median
Mean, mode and median does NOT reveal the variation (spread) of the data.
When analyzing data, the most sort for characteristics is the variation (spread) in the data.
The values of the data in a sample might be more closely near the mean in some data sets whereas in other data sets the values of the data might be spread out from the mean.
Common measure of variation or spread are the standard deviation, range, variance.
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Solve algebraically :)
Answer:
x > 4
Step-by-step explanation:
Answer:
should be x > 4
Step-by-step explanation:
Analyze the table below and complete the instructions that follow.
Blue
Brown
Green
Total
Male
10
B
1
28
Female
D
15
C
26
Total
18
A
4
E
Solve for the variables in the table.
Answer:
C
Step-by-step explanation:
HELP PLEASE!!!!!!!!!
Answer:
2
Step-by-step explanation:
the formula is y^2-y^1 over x^2-x^1
so the y coordinates here are 5 and -5
5--5=10
the x coordinates are -2 and 3
3--2=5
so we are left with 10/5
the answer is 2
hope this helped
please help i seriously don’t know this at all lol
Answer:
156m^2
Step-by-step explanation:
label the shapes A and B) triangle=shape b and rectangle=shape a
shape a)10x12=120m^2
shape b)(12x6)/2=36m^2
add the values of shape a and b together to get the area of the shape)120+36=156m^2
It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate, how many pounds of mashed potatoes can be made with 15 pounds of potatoes?
Answer:
22.5 pounds of mashed potatoes will be made
CAN SOMEONE PLS HELP ME ILL GIVE YOU BRAINLIST IF YOU GET IT RIGHT
3rd option: A middle school student it more likely to own a phone than an elementary school student
Will give Brainliest. Amoli and Ella are converting measurements between inches and feet. Amoli says that the constant of proportionality is 12. Ella says it is 1/12. Who do you agree with? Explain your thinking.
find the sum of 6/12+1/2
Answer:
1
Step-by-step explanation:
[tex] \frac{6}{12} + \frac{1}{2} \\ = \frac{1}{2} + \frac{1}{2} \\ = \frac{2}{2} \\ = \frac{1}{1} \\ = 1[/tex]
Divide £945 in the ratio 2:5
A 480 page book is 2.4 cm thick(not counting the thickness of the covers.). Find the thickness of 380 pages of the book
Set up a proportion:
2.4/480 = x/380
Cross Multiply:
480x = 912
Divide both sides by 480:
x = 1.9
Answer: 1.9 cm thick
What is 3/1,000 as a decimal
Answer: 3/1000 as a decimal is 0.003.
Explanation;
3/10 = 0.3
0.3/10 = 0.03
0.03/10 = 0.003
Triangles FEG and FDH are similar. If segment DH is 28 units, what is the
measure of segment EG?
4. Find the sum of all the numbers from 100 to 199 that are not divisible by 13.
What is the formula for
this?
There are 100 numbers in the range 100-199. Find the smallest and largest multiple of 13 in this range. We have
104 = 8•13
195 = 15•13
so there are 15 - 8 + 1 = 8 multiples of 13 between 100 and 199.
Then the sum we want is
[tex]\displaystyle \sum_{k=100}^{199} k - \sum_{\ell=8}^{15}13\ell[/tex]
or equivalently,
(100 + 101 + 102 + … + 199) - 13 (8 + 9 + … + 15)
To compute these sums, recall the following formula:
[tex]\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2[/tex]
Then
[tex]\displaystyle \sum_{k=100}^{199} k = \sum_{k=1}^{199} k - \sum_{k=1}^{99} k = \frac{199\cdot200}2 - \frac{99\cdot100}2 = 14,950[/tex]
and
[tex]\displaystyle \sum_{\ell=8}^{15} 13\ell = 13 \left(\sum_{\ell=1}^{15} \ell - \sum_{\ell=1}^7 \ell\right) = 13 \left(\frac{15\cdot16}2 - \frac{7\cdot8}2\right) = 1,196[/tex]
which means the sum we want is 14,950 - 1,196 = 13,754.
Write an equation perpendicular to x-4y=20 that passes through the point (2,-5)
Answer:
x – 4y = 20
Step-by-step explanation:
Put the line above in Slope Intercept Form
You can do that by solving for y
y = (1/4)x - 5
The slope, m above is 1/4
The perpendicular will a negative inverse slope m = -4
In Slope Intercept Form your perpendicular line starts below
y = -4x + b
Use the coordinates of the given point on the line (2, -5) to insert and solve for b
-5 = -4(2) + b
-5 = - 8 + b
Add 8 to both sides of the equation
-5 + 8 = b
3 = b
Finally your perpendicular line
y = -4x + 3
I hope this helps
Check my arithmetic
Answer:
×4y=20
Step-by-step explanation:
mark me as brainlist please