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
Use the figure below to answer the questions. Unit 1 Test, Part 2: Basic Tools and Transformations
Answers
Answer: 35
Step-by-step explanation:
Leah took her friends for a ride in her hot air balloon. The function fff models the height of the hot air balloon above the ground (in meters) as a function of time (in minutes) after takeoff.
Plot the point on the graph of fff that corresponds to when the hot air balloon landed.
Answers
Answer: point (60,0)
Step-by-step explanation: the x-intercept (60,0) shows that at 60 minuetes the balloon is 0 meter above the ground
The coordinates of the function of height and time are (210, 0) and (60, 10). The graph is attached below.
What is function?The function is a relationship between a set of potential outputs and a set of possible inputs, where each input has a single relationship with each output. This means that if an object x is present in the set of inputs (also known as the domain), then a function f will map that object to exactly one object f(x) in the set of potential outputs (called the co-domain).
Given:
r(t) = 210 - 15t
Calculate the height after 10 minutes as shown below,
The height = 210 - 15 × 10
The height = 210 - 150
The height = 60
At time 0 the height will be,
The height = 210 - 15 × 0
The height = 210 - 0
The height = 210 meters,
Thus, the coordinates will be (210, 0) and (60, 10)
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The Lamborghini Sports Car reaches a maximum speed of 200km/h in 15.50s
The McLaren Sports Car displays the same time as the Ferrari Sports Car.
The Renault Sports Car is small in size.
The Ferrari Sports Car is a tenth second slower than the Lamborghini Sports Car.
The Renault Sports Car is three tenths of a second faster than the McLaren Sports Car.
What time does the Renault Sports Car displays to reache a maximum speed of 200km/h?
Answers
The Renault Sports Car displays 15.70 seconds to reache at maximum speed of 200km / h.
Since the Lamborghini Sports Car reaches a maximum speed of 200km / h in 15.50s, the McLaren Sports Car displays the same time as the Ferrari Sports Car, the Ferrari Sports Car is a tenth second slower than the Lamborghini Sports Car, and the Renault Sports Car is three tenths of a second faster than the McLaren Sports Car, to determine what time does the Renault Sports Car displays to reache a maximum speed of 200km / h the following calculation must be performed:
15.5 - 0.1 + 0.3 = X 15.4 + 0.3 = X 15.7 = X
Therefore, the Renault Sports Car displays 15.70 seconds to reache at maximum speed of 200km / h.
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Two customers went to a post office to buy postcards and large envelopes. Each postcard costs the same amount, and each large envelope costs the same amount. The first customer paid $12 for 14 postcards and 5 large envelopes. The second customer paid $24.80 for 10 postcards and 15 envelopes. What was the cost in dollars of each large envelope?
A-$1.42
B- $1.15
C- $0.35
D- $0.63
Answers
The cost in dollars of each large envelope is $1.42.
Two equations can be derived from this question:
14p + 5l = 12 equation 1
10p + 15l = 24.80 equation 2
Where:
p = postcards
l = large envelopes
To determine the cost of large envelopes, multiply equation 1 by 10 and equation 2 by 14.
140p + 50l = 120 equation 3
140p + 210 = 347.20 equation 4
Subtract equation 3 from 4
227.20 = 160l
Divide both sides of the equation by 160
l = 227.20 / 160
l = $1.42
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Kamile sells sandwiches.
In May, she sold 400 sandwiches.
In June, Kamile sold 20% more sandwiches than in May.
In July, Kamile sold 15% fewer sandwiches than in June.
Calculate the percentage change in her sales from May to July.
Answers
Answer:
b
Step-by-step explanation:
b is the correct answer
Question 10 of 10 According to this diagram, what is tan 62°? 62 i 7 28° tra OA. A. 15 B. 0 O C. OD D8 O E 17 F
Answers
9514 1404 393
Answer:
B. 15/8
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you that the tangent relation is ...
Tan = Opposite/Adjacent
The side opposite the 62° angle is marked 15.
The side adjacent the 62° angle is marked 8.
Then the tangent ratio for 62° is ...
tan(62°) = 15/8
What's the constant in 12n + 7 +13k⁴ + 4+ 39z
Answers
Answer:
7, 4 or 11
Step-by-step explanation:
No matter what n, k, or z is, 7 + 4 will always be constant. If you need to go farther, 7 + 4 is 11.
Have a nice day!
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Please help!!
Determine whether the inverse of F(x) is a function.
Answers
Answer:
Two crates, A and B, are connected with a rope of negligible mass over a frictionless pulley as represented in the diagram shown on the left. The crates are at rest.
Crate A has an unknown mass and hangs vertically to the right of the slope and crate B, with mass 14 kg, hangs on the slope to the left. The slope makes and angle of 68° with the horizontal.
The coefficient of static friction between crate B and the surface of the slope is 0.3. The direction of the frictional force is up the slope. Calculate the mass of crate A.
If AD = 12 and BD = 14, what is CD?
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
a. 7
b. 10.29
C. 12.54
d. 16.33
Answers
Answer: D. 16.33
Step-by-step explanation:
Due Tomorrow: answer question 1 with steps
Answers
Answer:
the 1 st qn that is no2 c is just down right corner am I right
Step-by-step explanation:
plzzz make me ans as the brainliest ans
What is an equation of the line that passes through the points (-2,1) and (6,-7)
Answers
Four candy stores are competing with each other. Which
store offers the best buy for candy?
A.) Sweet Store: 12 pack for $3.00
B.) Delicious Treats: 22 pack for $4.62
C.) Sugar Factory: 18 pack for $5.40
D.) Chocolate Shop: 36 pack for $7.20
Answers
Answer: The Chocolate shop
Step-by-step explanation:
We should get the cost per one pack for each store.
For the Sweet Store we divide 3.00 by twelve for the cost of one which is:
3 divided by 12 = 0.25
One pack at a sweet store is $0.25
Now do the same for the other stores:
4.67 divided by 22 = 0.21 (Rounded to 2 decimal points)
5.40 divided by 18 = 0.3
7.20 divided by 36 = 0.2
Sweet Store: one pack is $0.25
Delicious Treats: one pack is $0.21
Sugar Factory: one pack is $0.30
Chocolate Shop: one pack is $0.20
Therefore the Chocolate shop is giving you the best deal since each pack is cheaper.
Grace collected 7 2/3 bins of glass bottles to recycle. Kenneth collected 7 5/6 times as many
bins as Grace. How many bins of bottles did Kenneth collect?
Answers
Kenneth collected 60 bins of bottles.
Solution:
(7 2/5) * (7 5/6) = 60.05
When asked a certain question in a poll, 72% of the people polled answered yes. If 56 people did not answer yes to that question, what is the total number of people who were polled?
Answers
Answer:
i think its 200
Answer:
200people
Step-by-step explanation:
28 percent=56people100=?100 multiplied by 56=5600 5600 divide by 28=200The number 1000 has been rounded to the nearest 100. Find its lower and upper bounds.
Answers
950 ≤ 1000 < 1050
Explanation
Mark Brainliest please
The lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
What are the lower and upper bound?
The lower bound is the smallest value that would round up to the estimated value.
The upper bound is the smallest value that would round up to the next estimated value.
Here the number 1000 is rounded to the nearest 100 will be:
The Lower bound will be 950.
The Upper bound will be 1050
Hence the lower bound is 950 and the upper bound is 1050 when the number 1000 has been rounded to the nearest 100.
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-3(p+2) when p=6
Anybody
Answers
Answer:
-24
Step-by-step explanation:
-3(p+2)
-3 ( 6+2 )
-3(8)
-24
Would anyone help me with this please, worth 20 pts.
Answers
Answer:
Below in bold.
Step-by-step explanation:
The perimeter = length of 3 sides of the square + 1/2 the circumference of the circle. The radius of the circle = 2.5 in and its circumference = 2π r and 1/2 of this is π r.
So the perimeter = 3*5 + π r
= 15 + 2.5π
= 22.85 in to the nearest hundredth.
What is 6 3/4 percent of 800
Answers
Answer:
54
Step-by-step explanation:
6 3/4 = 6*4 + 3 / 4
= 27/4
=> 27/4 /100 * 800
=> 27/400 * 800
=> 27 * 2
=> 54
What the answer plz
Some anybody
Answers
Mariam only saves quarters and dimes. She has already saved 13 quarters and 5 dimes. She wants to purchase a book that costs 7.75. Not including the money she already has, what combinations of quarters and dimes could Mariam save so she has exactly enough money to buy the book?
Answers
Answer: 8 Quarters, 20 Dimes
Quarters:
Current/ 13
13x25= 3.25
Dimes:
Current/ 5
5x10= 50 …. 50 cents
Current price: $3.75
Need $4.00
What you need:
Quarters: +8
4 = 100 x2 is 200 …. $2.00
Dimes: + 20
10 = 100 x2 is 200 … $2.00
Solve for the value of p.
(6p-2)
न
(3p-7)|
Answers
Answer:
The sum of angles on a straight line is 180 degrees.
Therefore,
[tex](6p-2)+(3p-7)=180[/tex]
[tex]6p-2+3p-7=180[/tex]
[tex]9p-9=180[/tex]
[tex]9p=189[/tex]
[tex]p=21[/tex]
Ahh can someone helpppp
Answers
The first term of an arithmetic sequence is 4. The rule a↓n=a↓n+1 + 5 can be used to find the next term of the sequence.
a 4
b 5
c 9
d -1
Answers
Answer:
c. 9
Step-by-step explanation:
Using the rule, substituting 4 for a↓1, we find the next term to be ...
[tex]a_2 = a_1 +5\\\\a_2=4 +5\\\\\boxed{a_2=9}[/tex]
150-5r is greater than or equal to 87.5
Find the value of r?
Answers
Answer:
R=12.5
Step-by-step explanation:
Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truck (not the least of which is that it runs). The new truck would cost $55,440. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,400. At the end of 8 years, the company will sell the truck for an estimated $27,700. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset’s estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company’s cost of capital is 8%.
Answers
The payback period of the investment is 6.6 years.
The net present value is $7,797.22.
The payback period calculates the amount of time it takes to recover the amount invested from the cumulative cashflows.
Payback period = Amount invested / cost saving
$55,440 / $8,400 = 6.6 years
Net present value is the present value of after-tax cash flows from an investment less the amount invested.
NPV can be determined using a financial calculator
Cash flow in year 0 = $-55440
Cash flow in year 1 to 7 = $8,400
Cash flow in year 8 = $8400 + $27,700
I = 8%
NPV = $7,797.22
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Use the functions f(x)=-x^2+8x-11 and h(x)=-x-7
h(8)-2*f(3)
This is called question #18 on the worksheet images.
Answers
Answer:
Step-by-step explanation:
h(8) = -8 - 7
h(8) = -15
f(3) = -(3)² + 8(3) - 11
f(3) = -9 + 24 - 11
f(3) = 4
h(8) - 2 f(3) = -15 - 2(4) = -23
The value of the h(8) is -15, the value of f(3) 4 after plugging the values of x in the function and the value of h(8) - 2 f(3) is -23.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
Functions f(x) = -x²+8x-11 and
h(x)=-x-7
h(-8) = -8 - 7
h(-8) = -15
f(3) = -(3)² + 8(3) - 11
f(3) = -9 + 24 - 11
f(3) = 4
= h(8) - 2 f(3)
= -15 - 2(4)
= -23
Thus, the value of the h(8) is -15, the value of f(3) 4 after plugging the values of x in the function and the value of h(8) - 2 f(3) is -23.
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PLZ HElp 24nanjoshua PLZZZZ
Answers
Answer: 11/14
Step-by-step explanation:
1/7 = 2/14 (when you time 2 at the top and at the bottom)
2/14 + 9/14 = 11/14
Just do 2/14+9/14=11/14
What is the equation of the line that has a slope of 3 and goes through the point (-3,5)?
A. Y=3x +4
B. Y= 3x - 14
C. Y= 3x - 4
D. Y= 3x + 12
Answers
Answer:
C. y=3x-4
Step-by-step explanation:
I just know trust me
Help me please!!!!!!!!!!!
Answers
6-4x=-2x-6
6=2x-6
12=2x
6=x
SLOVE I GIVE BRAINLEST
18+ -27
A. -45
B. -9
C. 9
D. 48
Answers
Answer:
B: -9
Step-by-step explanation:
When you add a negative number, you subtract that number.
[tex]18+-27=18-27=-9[/tex]
= 18-27
= - 9
Answer will be B