WILL GIVE BRAINLIEST! Consider the graph at right and answer the following questions.
Answers
Answer:
a.)A and B are the intersection between the two curves. The x coordinate is the equation
[tex]f(x) = g(x)[/tex]
Let's solve it
[tex]\frac12 (x-2)^3 +1 = 2x^2-6x-3\\x^3-6x^2+12x-8+2=4x^2-12x-6\\x^3-10x^2+24x=0\\x(x^2-10x+24)=0\\x(x-4)(x-6)=0[/tex]
We can see that if we substitute x= 0 or x= 4 the equation is verified.
b. The equation has a third solution, x = 6, that is too far to the right to be visible in the graph.
c. the x coordinate of C is the solution of [tex]f(x)=0[/tex] or [tex]\frac 12 (x-2)^3 +1=0\\(x-2)^3 = -2\\(x-2) = -\sqrt[3]2[/tex]
At this point let's guesstimate the cubic root of 2 -let's say the cubic root of 2 is equal to 1plus an error e, and since we know how to calculate the cube of a binomial, let's build it.
[tex](1+e)^3 = 2 \rightarrow 1+3e+3e^2+e^3 = 2[/tex] Now, assuming the error is small enough, it's square and its cube gets even smaller. (if the error is 0.1, it's square becomes 0.01 and the cube 0.01), let's ignore them. [tex]1+3e=2 \rightarrow 3e=1 e= \frac13[/tex] So, going back to our equation, we can tell that the right hand side is [[tex]\mathbb{R}[/tex]]-(1+\frac13)[/tex] Not perfect, but good enough. Let's solve it now.
[tex]x-2= -1-\frac13 \rightarrow x=1-\frac13 = \frac23[/tex]
Which seems close enough from the photo.
c. Domain of both function are the whole Real set, since they're polynomials. Range of f(x) is again the whole real set, since it's an odd degree polynomial. g(x) is a parabula and its range is for y above the vertex y-coord, which is [tex]y>g(\frac32) = 2(\frac94)-6(\frac32)-3 = \frac92 -3(\frac62) -\frac62 = \frac92-4\frac62= -\frac{24-9}2 = -\frac{15}2[/tex]
Related Questions
Determine if the point is a solution to the system of linear equations [tex] \huge \{{ \large \begin{array}{} 2x + 3y = 2 \\ 6y = 5 - 4x \end{array}} [/tex]
Answers
Answer:
The system has no solutions.
Step-by-step explanation:
If you stare at it for the bit you can tell the system is impossible. Let's see why:
First of all, rewrite the second equation by bringing all unknowns on the LHS:
[tex]4x+6y=5[/tex].
Then take twice the first equation, doubling every coefficient:
[tex]4x+6y=4[/tex] See how the LHS is the same? The system is asking you to find a quantity (4x+6y) which is at the same time equal to four AND five - emphasis on that "and" - which is obviously impossible, because it implies that 4=5. So the point - which you didn't provide - is not a solution. Nor is any other point.
Rewrite the following equation in slope-intercept form. 2x + 16y = 11 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answers
Answer:
y=-1/8x+11/16
Step-by-step explanation:
The slope-intercept form is y=mx+b. You have to move over 2x to the other side. After that you have to divide both sides by 16 to get to the y intercept form, so it would end up as y=-1/8x+11/16, where -1/8=m and 11/16=b
Answer Please will give brainliest.
Answers
Step-by-step explanation:
blue is natural: 1, 4, 0, 2 and root of 25.
green is whole: -9 and -15.
yellow is rational: 2/3
orange is irrational: pi and root of 15.
white is real numbers.
don't know about that purple one.
Rudolph will spend $150 on tickets to the Reindeer Games. Reserved seat tickets cost $25 and general admission
tickets cost $10. Write an equation that describes the number of tickets Rudolph can buy_How many tickets can
Rudolph buy if he buys only reserved seat tickets? Only general admission tickets?
Answers
The equation that describes the number of tickets Rudolph can buy will be 25r + 10g = 150.
Let the reserved tickets be represented by r.Let the general admission be represented by g.Therefore, the equation will be 25r + 10g = 150.
The number of tickets that Rudolph can buy if he buys only reserved seat tickets will be:
= $150 / $25 = 6
The number of tickets that Rudolph can buy if he buys only general admission tickets will be:
= $150 / $10 = 15
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3. Sally invested $5,000.00 in a savings account earning 3.49% simple interest. At the same time
Jon invested $3,000.00 in a money market account at a simple interest rate of 7.5%. How many
years will it take for the two to have the same amount of money in their accounts? How much
money do they have after that time period?
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Answer:
ic hch7y8gygdr6dr6d7twwt7tfx7yuc yc i
The Snyders went out to dinner and their bill was $54.15. How much would a 20% tip cost?
Answers
Answer:
$10.83
Step-by-step explanation:
bill/percent
Choose ALL of the transformations that have been applied to the linear function below.
()=−2−4
(It’s multiple choice)
1.Reflected over x-axis
2.Vertical stretched
3.Shifted down 4
4.None of the above
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Find the average rate of change between x=2 and x=4 for the function. F(x)=3x^3-1
Answers
Answer:
84Step-by-step explanation:
Average rate of change between x = 2 and x = 4 is:
[f(4) - f(2)]/(4 - 2) = (3*4³ - 1 - 3*2³ + 1)/2 = 168/2 = 84[tex]\boxed{\sf Average\: change=\dfrac{f(a)-f(b)}{a-b}}[/tex]
[tex]\\ \sf\longmapsto f(x)=3x^3-1[/tex]
[tex]\\ \sf\longmapsto f(4)=3(4)^3-1=3(64)-1=192-1=191[/tex]
[tex]\\ \sf\longmapsto f(2)=3(2)^3-1=3(8)-1=24-1=23[/tex]
Average change
[tex]\\ \sf\longmapsto \dfrac{192-23}{4-2}[/tex]
[tex]\\ \sf\longmapsto \dfrac{168}{2}[/tex]
[tex]\\ \sf\longmapsto 84[/tex]
Sam put $500 into a savings
account with a simple interest
rate of 6%. He earned $120 of
interest. How long was his
money in the bank?
.Write your response!
Answers
Answer: 6 years
Step-by-step explanation:
Marian is making accessories for the soccer team. She uses 666.12 inches of fabric on headbands for 36 players and 3 coaches. She also uses 310.68 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?
I need help with this
Answers
Answer:
answe is about 23. something
Step-by-step explanation:
Which table of values represents a linear function?
Answers
Answer:
I don't know it's very hart
Evaluate -1(-2)(-4)(-2)
Answers
Answer:
16
Step-by-step explanation:
Negative times negative = positive
-1(-2) = 2
2(-4) = -8
-8(-2) = 16
Please consider giving this answer brainliest if it helped you. Thanks!
Answer:
─16
Step-by-step explanation:
1(−2)(−4)(−2) when x=1, y=2, z=5 which equals, ─16
A factory puts 5/8 of a gallon of vinegar into each batch of salad dressing. How many gallons of vinegar will be used in 2 batches?
Answers
Answer:
1 1/4
Step-by-step explanation:
[tex]\frac{5}{8} +\frac{5}{8}=\frac{10}{8}= 1 \frac{2}{8}= 1\frac{1}{4}[/tex]
five eighths plus five eighths equals ten eighths simplified to one and two eighths and simplified again to one and one fourth.
You have a coupon for 25% off the price of a mystery book that sells for $7.00. You also have one for 20% off the price of a science fiction book that sells for $6.25. You have $5.00. Which book can you afford to buy? Explain.
Answers
Answer: you can afford to buy both
as $1.75+$1.25 adds up to $3 leaving you $2 to spare.
Step-by-step explanation-
Mystery book: 25% of 7.00= 1.75 ($1.75)
Science Fiction: 20% of 6.25=1.25 ($1.25)
Answer:
You can afford the science fiction book.
Step-by-step explanation:
How to get the amount for the 25% coupon:
$7.00 × 0.25 = $1.75
To get the price of the mystery book using the coupon:
$7.00 - $1.75 = $5.25
The mystery book will cost $5.25.
How to get the price of the 20% coupon:
$6.25 × 0.20 = $1.25
To get the price of the science fiction book using the coupon:
$6.25 - 1.25 = $5.00
The science fiction book will cost $5.00.
You can afford to buy the science fiction book because you have $5.00 and that is the price of the book. The mystery book costs $5.25 and you only have $5, which means that you don't have enough money to buy it.
You answer 21 out of 25 questions correctly on a test. Did you reach your goal of getting 80% or better?
Answers
Answer:
Yes
Step-by-step explanation:
20 needed to get 80 %. You got one more than that so you got slightly more. So yes you did. You can also make 25 to 100 and 21 x4 so that gives you 84 % . So you scored %84.
Good job
what is the length of a short leg of a 30-60-90 triangle shown below?
Answers
Answer:
5
Step-by-step explanation:
since 30-60-90 triangles are special right triangles, we know that if the short leg=x, the long leg= xsqrt(3). so the short leg= 5 sqrt(3) /(sqrt(3) = 5
20. The table shows the numberof days you keep a rented movie before returning it and the total cost of renting the
movie. Find the rate of change in cost with repect to time and interpret its meaning.
Time (days)
4
5
6
Cost (dollars)
6.00
8.25
10.50
Answers
Step-by-step explanation:
According to given table we have pairs of points:
(4, 6.00), (5, 8.25), (6, 10.50)The rate of change is:
(8.25 - 6.00)/(5 - 4) = 2.25or
(10.50 - 8.25)/(6 - 5) = 2.25It is 2.25 and the meaning is:
Rental per day is $2.25Which graph represents this equation?
y=-2 (24)
-2 -1
1 2314
O1 2 3 4
*232)
2 3 4
Answers
Answer:
its the second option under the first one... which is more than likely C.
Step-by-step explanation:
PLEASE HELP IM BEGGING. which is function and which is not function please answer all.
Answers
Answer:
B
Step-by-step explanation:
for every given input there is a unique output in B, there are two times in which 5 is the output. So it is not a function
Explain why 4xy and 5x²y are not like terms.
Answers
We could have the numbers
5x^2 and 5x and they wouldn’t be like terms because one has an exponent
order the values from least to greatest
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Answer:
[-1.8], [2.7], 3 2/5, [3.5]
thats the answer
Answer:
|-1.8| = 1
|2.7| = 2
|3.5| = 3
3 2/5 = 4
4.6 = 5
Step-by-step explanation:
Hope this helps!
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answers
Answer:
A. b ≤ -3
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
C
Step-by-step explanation:
Factorise: 3x²+17x+10
Answers
Answer:
(3x+2) (x+5)
Step-by-step explanation:
3x²+17x+10
SPLITTING OF MIDDLE TERM
3x²+15x+2x+10
COMMON FACTOR FROM PAIRS
3x(x+5) + 2(x+5)
= (3x+2)(x+5)
Annie bakes cookies and cupcakes in a ratio of 5 to 1 for her gift boxes. Her school needs 36 desserts to sell in a bake sale. How many cupcakes will she bake? How many cookies will she bake? Explain your answers.
Answers
Answer:
30 cookies and 6 cupcakes
Step-by-step explanation:
5+1=6
5:1=6
?:?=36
36/6=6
5x6=30
1x6=6
30 cookies
6 cupcakes
Julie spent $15 on 3 headbands. Mary spent $48 on 8 headbands. How much more
did Mary spend per headband?
$5.50
$1
$2.13
$4
Answers
Based on the information given, the amount of money that Mary will spend more for the headband will be $1.
Since Julie spent $15 on 3 headbands, the amount per headband will be:
= $15/3 = $5
Since Mary spent $48 on 8 headbands, the amount per headband will be:
= $48/8 = $6
Therefore, we can then calculate the difference between the values that are gotten. This will be:
= $6 - $5 = $1
Therefore, the difference is $1.
Learn more about division on:
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2) Find the area and perimeter of a semi -circular disc whose radius is 10cm. (take π = 3.14)
Answers
Answer:
Area =Pi r2=3.14×10x10
=3.14×100cm2
=3.14cm2
Perimeter = 2 pi r
=2 ×3.14×10
=6.28cm
Or =Pi d
= 3.14 ×20cm
=62.8cm
Note:R means radius
D means diameter
radius is half of a diameter e.g radius is10 and diameter is 20
I can recommend you watching yt videos it helped me alot
hoo this helps:)
i need help with how to reason it
Answers
Answer:
X=80
Step-by-step explanation:
As 100⁰ is Opposite to B and AD and EH Are PARALLEL so B=100⁰
180-100
=80⁰
MARK ME BRAINLIESTSolve (MAFS.912.A-REI.2.3)
4
15= 2
+8
A. =1
2 B. =−1
2
C. =2 D. =−2
Answers
Answer:
c,=2d=-2
Step-by-step explanation:
What is the slope intercept equation from the graph?
Please help me thank u!
Answers
Answer:
y = -3/2x+3
Step-by-step explanation:
Pick two points on the line
(0,3) and (2,0)
Using the slope formula
m = ( y2-y1)/(x2-x1)
= ( 0-3)/(2-0)
= -3/2
The y intercept is 3
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -3/2x+3
Mr. Ocampo has two kind of fruit in his basket. The ratio of apples to oranges is 3:2. If there are 18 apples then how many pieces of fruit are there.
Answers
Answer:
There are 27 pieces of fruits
Step-by-step explanation:
Given, apples=18
ratio of apples to oranges =3:2
Now, x/18 =3/2
or, 2x=18*3
or, x=54÷2
x =27„
please mark as branliest answer
hope it helps you