ANALYZE The table below shows the values of a cubic function. Could there be a zero between
x= 2 and x = 3? Justify your argument.
ONLY QUESTION 30
Answers
Answer:
No; no sign change of g(x) in that interval
Step-by-step explanation:
The intermediate value theorem tells you there will be at least one zero between any two points where the function changes sign. The table shows sign changes in the intervals [-2, -1], [0, 1], and [1, 2]. So, the three zeros of the cubic lie in those intervals.
There are no additional zeros to be found, and there are no sign changes of g(x) between x=2 and x=3, so there is no zero in the interval [2, 3].
_____
Additional comments
We can only answer this with certainty because we have already found the locations of the three real zeros this cubic has. If there were two that were unaccounted for, then the possibility might exist for the graph to make an excursion across the x-axis and back in the interval [2, 3].
__
First differences of the table values are ...
-5, +1, +2, -3, 0
Second differences are ...
6, 1, -5, 3
Third differences are ...
-5, -6, +8
This table cannot represent a real cubic function. For evenly-spaced x-values, a cubic polynomial must have constant 3rd differences. If the last two values in the table were -1 and -12, the function would be ...
g(x) = -5/6x^3 +1/2x^2 +7/3x -1
You may want to discuss this question with your teacher.
Related Questions
what is mixed number
help me pleas
Answers
Answer:
A mixed number is a number with both a whole number and a fraction. For example 6 3/4, 2 1/2, 7 8/15. Hope this helped:)
Answer:
A mixed number is a number consisting of a whole number and a proper fraction.
Below are examples of mixed numbers:
[tex]4 \frac{1}{2}[/tex]
[tex]1 \frac{3}{5} [/tex]
7/8 * 1/2 =7/16 yes but wouldn't you have to divide it though like divide 16 / 7 = 3 3/7???
Answers
1/2 is a simplified version of 4/8.
So then putting it back into the original equation:
7/8 * 4/8 = 7/16 or 0.4375
The final answer would be 7/16 because there isn’t another way to simplify that.
I hope that makes sense, let me know if you have any questions.
Answer:
No.
Step-by-step explanation:
I think you're talking about simplifying/reducing the fraction.
You would not do that in this case because the numbers 7 and 16 have no common factors besides 1.
The answer is already in its lowest/reduced form. You do not divide.
Please let me know if this was not what you were talking about!
help me answer this 100 POINTS!!!!!
Answers
Answer:
1 C
2 A
Step-by-step explanation:
1 C No it cannot be defined because A and B are not congruent
2 A Yes, the lines will remain parallel
PS. It's only 50 points because two answers are allowed. Each answerer gets half.
For questions 3 - 6, find F'(x), the inverse of F(x).
3. F(x) = x-10
4. F (x) = x/6 + 3
5. F(x) = 3x + 7
6. F(x) = 8x
Answers
Answer:
3) f'(x) = x + 10
4) f'(x) = 6x - 18
5) [tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex]
6) f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex]
Step-by-step explanation:
3. f(x) = x - 10Step 1: In order to find the inverse function of f(x) = x - 10, start by replacing f(x) with y.
y = x - 10
Step 2: Switch x and y:
x = y - 10
Step 3: Add 10 to both sides to isolate y:
x + 10 = y - 10 + 10
x + 10 = y
Step 4: Replace y with f'(x):
f'(x) = x + 10 ⇒ This is the inverse function of f(x).
4. [tex]\displaystyle\mathsf{f(x)=\:\frac{x}{6}\:+\:3}[/tex]Replace f(x) with y:
[tex]\displaystyle\mathsf{y=\:\frac{x}{6}\:+\:3}[/tex]Switch x and y:
[tex]\displaystyle\mathsf{x=\:\frac{y}{6}\:+\:3}[/tex]Subtract 3 from both sides:
[tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}\:+\:3-3}[/tex][tex]\displaystyle\mathsf{x-3=\:\frac{y}{6}}[/tex]Multiply both sides by 6 to isolate y:
[tex]\displaystyle\mathsf{6(x-3)=\:\frac{y}{6}(6)}[/tex]6x - 18 = y
Replace y with f'(x):
f'(x) = 6x - 18 ⇒ This is the inverse function of f(x).
5. f(x) = 3x + 7Replace f(x) with y:
y = 3x + 7
Switch x and y:
x = 3y + 7
Subtract 7 from both sides:
x - 7 = 3y + 7 - 7
x - 7 = 3y
Multiply both sides by ⅓:
⅓(x - 7) = 3y (⅓)
[tex]\displaystyle\mathsf{\frac{1}{3}x-\frac{7}{3}=y}[/tex]
Replace y with f'(x):
[tex]\displaystyle\mathsf{f'(x)=\frac{1}{3}x-\frac{7}{3}}[/tex] or [tex]\displaystyle\mathsf{f'(x)=\frac{x - 7}{3}}[/tex] ⇒ This is the inverse function of f(x).
6. f(x) = 8x
Replace f(x) with y:
y = 8x
Switch x and y:
x = 8y
Multiply both sides by ⅛:
⅛(x) = ⅛(8y)
⅛x = y or [tex]\displaystyle\mathsf{\frac{x}{8}=y}[/tex]
Replace y with f'(x):
f'(x) = ⅛x or [tex]\displaystyle\mathsf{f'(x)=\frac{x}{8}}[/tex] ⇒ This is the inverse function of f(x).
rewrite in slope intercept
a(bx + y) = c
Answers
(27×3^-2)(8×2^-3)
(27×3^-2)(8×2^-3)
(27×3^-2)(8×2^-3)
(27×3^-2)(8×2^-3)
Answers
Answer:
(27×3^-2)(8×2^-3) = 3
Step-by-step explanation:
(27×3^-2)(8×2^-3) = 3 or 3/1
First, we do PEMDAS (Please Excuse My Dear Aunt Sally)
↳ (27×3^-2)
↳ 27×1/9=3
Second, do the other one in parentheses because of PEMDAS
↳ (8×2^-3)
↳ 8×1/8=1
—————
Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle
—————
Simplify.
81‾‾‾√
18
9
−3
−18
Answers
9514 1404 393
Answer:
(b) 9
Step-by-step explanation:
Maybe you want to simplify ...
[tex]\sqrt{81}=\sqrt{9^2} =\boxed{9}[/tex]
Senna was having a party for 15 friends. She bought 3 jars of
pickles for $4.50. What is the cost per jar?
Answers
Answer:
it is 1.5
Step-by-step explanation:
if u do 4.50÷3 you will get 1.5 so the cost per jar is 1.5
167.67 divided by 8.1
Answers
Answer:
167.67 divided by 8.1 = 20.7
Which distance formula or formulas show(s) a joint variation?
Answers
Answer:
II and III only
Step-by-step explanation:
One variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product.
what would the numerical answer be??
Answers
Answer:
Step-by-step explanation:
all graphs range from -10 through 10 ;)
Answers
Answer:B
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
First, we want to find out what is X.3x = -6 ---> x = -2
X is -2 so we want the graph point to start at -2 and from there go down to -10.Heeeeelllllllppppppp
Answers
1.
[tex]y=\frac{5}{3} x-2[/tex]
2.
[tex]y=-2x+2[/tex]
3.
[tex]y=x+5[/tex]
4.
[tex]y=\frac{1}{4}x[/tex]
Kyle has two snakes fluffy is 2 meters long muffy is 900 millimeters long compare their lengths to fill in the blanks
_____ is the longest snake.
_____ is ______
millimeters longer than ____
PLSS HELP!!
Answers
Fluffy is longer than Muffy
Step-by-step explanation:
There are 1000 millimeters in a meter
Fluffy = 2000 millimeters
Muffy = 900 millimeters
Fluffy is longer than Muffy
2000 > 900
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me
as brainliest!
Find the equation of the line passing through the point (-5,2) with slope 1/3. Show work.
Answers
Hello!
First, let's write our equation in point-slope form.
Point-Slope Form:
y-y1=m(x-x1)
y1= the y-coordinate of the point
m=the slope
x=the x-coordinate of the point
y-2=1/3(x-(-5)
y-2=1/3(x+5)
y-2=1/3x+5/3
y=1/3x+5/3+2
y=1/3x+3.7
Hope it helps.
~A smiley teen
#CarryOnLearning
[tex]MagicalNature[/tex] here to help
HURRY!! (No links please and please include an explanation)
If A is the set of all whole numbers, choose the set B that will make the following
statement false.
B ⊆ A
B = {0, 2, 4, 6)
B = {0}
B = {-1, 0, 1)
B = {1, 2, 3, 4)
Answers
Answer:
B= (-1,0,1)
Step-by-step explanation:
because -1 is not a whole number.
Answer:
B = {-1, 0, 1)
Step-by-step explanation:
The answer is B = {-1, 0, 1) because -1 is not a whole number.
Hope this helps :)
what do I do next???
Answers
Answer: You have to get rid of the variables (the x's) so subtract 2x from 2x and 11x then go from there.
Step-by-step explanation:
Answer:
3 and 6
Step-by-step explanation:
11x - 53 = x^2 + 2x - 35
Subtract 11x - 53 on both sides,
0 = x^2 + 2x - 35 - ( 11x - 53 )
= x^2 + 2x - 35 - 11x + 53
= x^2 + 2x - 11x + 53 - 35
0 = x^2 - 9x + 18
x^2 - 9x + 18 = 0
Now this equation need to factorized.
x^2 - 9x + 18 = 0
x^2 - 3x - 6x + 18 = 0
x ( x - 3 ) - 6 ( x - 3 ) = 0
( x - 3 ) ( x - 6 ) = 0
x - 3 = 0
x = 3
x - 6 = 0
x = 6
The solutions to this system are 3 and 6.
Give TWO different ways to write EACH expression in WORDS.
a. -8n
b. a - 1
c. x/2-4
d. 5y + 9
Answers
Answer:
a. negative eight times a number, the product of a number and negative eight
b. one less than a number, a number minus one
c. four less than the quotient of a number and two, half of a number minus four
d. nine more than the product of five and a number, five times a number plus nine
lemme know if this was a help :P
Step-by-step explanation:
What is the gradient of the graph shown ? Give your answer in its simplest form
Answers
Answer:
-2
Step-by-step explanation:
choose any point on the graph
Answer:
Step-by-step explanation:
Yo you man its 3
(x+5)(x-5) factoring
Answers
Answer: x² - 25
Step-by-step explanation:
The answer will be x^2-25+5x-5x
So that factorised is x squared -25
What is the value of point P?
Answers
Answer:
-8
Step-by-step explanation:
Because it moved 2 to the right.
Answer:
-8
Hope this helps :)
Does each function describe exponential growth or decay?
Drag and drop the equations into the boxes to correctly complete the table.
Growth
Decay
y = 250(1 + 0.004)^t
y = 426(0.98)^t
y = 12,000(1/2) ^t
Answers
9514 1404 393
Answer:
growthdecaydecayStep-by-step explanation:
An exponential function will describe growth if the base of the (positive) exponent is greater than 1. It will describe decay of the base is less than 1.
y = 250(1 + 0.004)^t . . . . . 1.004 > 1 ⇒ growth
y = 426(0.98)^t . . . . . . . . . 0.98 < 1 ⇒ decay
y = 12,000(1/2) ^t . . . . . . . 1/2 < 1 ⇒ decay
Number 13
I’ll reward you brainiest!!
Answers
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x2, x = y2; about y = 1
Answers
D? y
= VE
Now we find the points of intersection first: 27?
-
VE
2 = 0, 1 so when x is O y is also 0
and when x is 1, y is also 1
Hence the points of intersection are (0,0) and (1,1)
Given it is rotated about y
=1
So using disk method, the volume is given by:
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units.
Procedure - Determination of the volume of a solid of revolutionLet [tex]f(x) = 1[/tex], [tex]g(x) = x^{1/2}[/tex] and [tex]h(x) = x^{2}[/tex], both [tex]g(x) [/tex] and [tex]h(x)[/tex] have the following intersection points: [tex](x_{1}, y_{1}) = (0, 0)[/tex] and [tex](x_{2}, y_{2}) = (1,1)[/tex]. This means that the interval of x-coordinates for the solid of revolution is [tex]x \in [0, 1][/tex].
The integral formula for the volume of the solid of revolution ([tex]V[/tex]), in cubic units, is:
[tex]V = \pi \int\limits^{1}_{0} {[h(x)-f(x)]^{2}} \, dx - \pi \int\limits^{1}_{0} {[g(x)-f(x)]^{2}} \, dx [/tex] (1)
After substituting on each function and simplifying terms we get the following integral:
[tex]V = \pi \int\limits^{1}_{0} {(x^{2}-1)^{2}} \, dx - \pi \int\limits^{1}_{0} {(x^{1/2}-1)^{2}} \, dx [/tex]
[tex]V = \pi\left[\int\limits^{1}_{0} {x^{4}} \, dx - 2\int\limits^{1}_{0} {x^{2}} \, dx -\int\limits^{1}_{0} {x} \, dx + 2\int\limits^{1}_{0} {x^{1/2}} \, dx \right][/tex]
And the volume of the solid of revolution is:
[tex]V = \pi \cdot \left(\frac{1}{5}-\frac{2}{3} -\frac{1}{2}+\frac{4}{3} \right)[/tex]
[tex]V = \frac{11\pi}{30} [/tex]
The volume of the solid obtained by rotating the region bounded by the given curves about [tex]y = 1[/tex] is [tex]\frac{11\pi}{30} [/tex] cubic units. [tex]\blacksquare[/tex]
To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504
At the store the ratio of books sold to movies sold was 4:5.For every_books sold there were _ movies sold.
Answers
Answer:
At the store the ratio of books sold to movies sold was 4:5.For every 4 books sold there were 5 movies sold.
Step-by-step explanation:
Drag the descriptions of each investment in order from which will earn the least simple interest to which will earn the most simple interest.
Answers
Answer:
Hello! I know I am a bit late but for those who come here in the future,
This is the order (Least to Greatest)
1) 1,500 at 8% simple interest for 6 years
2) 1,500 at 6% simple interest for 10 years
3) 1,500 at 8% simple interest for 10 years
Hope this helps!
In situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given for the three cases as,
P =$1500, R=8% , T = 10 years
P =$1500, R=8% , T = 6 years
P =$1500, R=6% , T = 10 years
The formula for the simple interest is,
Case 1,
SI = (P×R×T) / 100
SI = (1500×8×10)/100
SI = $ 1200
Case 2,
SI = (P×R×T) / 100
SI = (1500×6×10)/100
SI = $ 900
Case 3,
SI = (P×R×T) / 100
SI = (1500×8×6)/100
SI = $ 720
The simple interest for cases 1, 2, and 3 will be $ 1200, $ 900, and $ 720.
Thus, in situation 3, a person will earn the least simple interest in situation 1, a person will earn the most simple interest.
Learn more about the simple interest here:
brainly.com/question/22621039
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The new Apple Watch series 7 cost $799. There is an additional 7% sales tax rate . If Oscar has a total of 850.00 to spend, will he be able to purchase the new Apple Watch Series 7? Explain.
Answers
The total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.
The given parameters;
cost of new Apple Watch Series 7, = $799sales tax, = 7%Oscars available cash = $850The total cost of the new Apple Watch Series 7 is calculated as follows;
Total cost = 0.07(799) + 799
Total cost = $854.93
Thus, we can conclude that the total available cash with Oscar will not be able to purchase the new Apple Watch Series 7 because the total cost of the watch is greater than available cash.
Learn more here:https://brainly.com/question/20990309
Which of the following is not one of Garner’s Theory of Multiple Intelligences?
Question 4 options:
Linguistic intelligence
Interpersonal intelligence
Muscular intelligence
Answers
Answer:
I would say muscular
Step-by-step explanation:
none of these are really wrong, but muscular intelligence should be bodily intelligence
what is 5/8 divided 6
Answers
[tex]\sf \longmapsto \frac{5}{8} \div6[/tex]
[tex]\sf \longmapsto \frac{5}{8} \times \frac{1}{6} [/tex]
[tex]\sf \longmapsto \frac{5 \times 1}{8 \times 6} [/tex]
[tex]\sf \longmapsto \frac{5}{48} [/tex]
Answer In DECIMAL:
[tex]\sf \longmapsto0.1041[/tex]
If the equation of the line is f(x) = 1/3x - 5 , what would be the new equation if there was a reflection over the y- axis, a dilation of -6, and a translation of 4 units up?
pls help I already solved but I'm not sure if I did a step out of order
Answers
Answer: Thus, after the transformation, the graph consists of points (x,y) satisfying y=2(x−3)2. This is the equation of the transformed graph.
Step-by-step explanation:
Consider the graph y=x2. Suppose the graph is dilated from the x-axis by a factor of 2, and then translated 3 units to the right. What is the equation of the resulting graph?
Solution
The transformation given is Trans(3,0)∘Dilx-axis,2. Denote by (x′,y′) the image of a point (x,y) under this transformation. A point (x,y) is sent to (x,2y) by the dilation, and then to (x+3,2y) by the translation, so (x′,y′)=(x+3,2y).
The original graph consists of points (x,y) such that y=x2. Then it is transformed so that (x,y)↦(x′,y′)=(x+3,2y). We must find what equation is satisfied by x′ and y′.
Since x′=x+3 and y′=2y, we have x=x′−3 and y=y′/2. Thus y=x2 implies
y′2=(x′−3)2or equivalentlyy′=2(x′−3)2.