7 + 3x is not a factor of expression 3x^3 + 7x
Consider given expression 3x^3 + 7x
Let f(x) = 3x^3 + 7x
Assume that 7 + 3x is a factor of 3x^3 + 7x
This means, 7 + 3x = 0 would be the root.
x = -7/3
If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0
We find the value of given polynomial for x = -7/3
f(x) = 3x^3 + 7x
f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)
f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)
f(-7/3) = [(-343) - 147] / 9
f(-7/3) = -490 / 9
f(-7/3) ≠ 0
Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial f(x) = 3x^3 + 7x
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A total of 4 pennies are put into 4 piles so that each pile has a different number of pennies. What is the smallest possible number of pennies that could be in the largest pile
Answer:
Step-by-step explanation:
iF THERE MUST BE 4 PILES, and you have only 4 pennies, then there must be 1 penny in each pile.
The lateral urface area of cone A i equal to the lateral urface area of cylinder b
A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.
We know that the formula for the lateral surface area of cone:
Area = π × radius × slant height
and the formula for the lateral surface area of cylinder:
Area = 2π × (radius) × (height)
Here we have been given a cone A with radius r and slant height 2h.
Using the above formula, the lateral surface area of cone A would be:
A1 = π × r × 2h
A1 = 2π × r × h ..................(1)
Also, we have been given a cylinder B with radius r and height h.
Using the above formula, the lateral surface area of cylinder A would be:
A2 = 2π × r × h ..............(2)
From (1) and (2) we can observe that,
A1 = A2
Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.
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What is the additive inverse of 6 /- 5 of Class 8?
The additive inverse of 6 /- 5 is 6/5
We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0
i.e., b = -a
An additive inverse of 'a' is -a.
The means, an additive inverse is nothing but changing sign + to - OR - to +
Here we have been given a rational number 6/(-5)
Let m be the additive inverse of number 6/(-5)
From the definition of additive inverse,
6/(-5) + m = 0
[6/(-5) + m] - 6/(-5) = -6/(-5)
[6/(-5) - 6/(-5)] + m= -6/(-5) ...........(associative property of addition)
0 + m = 6/5
m = 6/5
Hence, the additive inverse is 6/5
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Find the slope between (3,-2) (-4,1)
Answer:
- [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
Change in y over the change in x.
(3,2)(-4,1)
The y values are 1 and 2.
The x values are -4 and 3.
You find the change by subtracting.
[tex]\frac{1--2}{-4-3}[/tex] = [tex]\frac{1+2}{-7}[/tex] = [tex]\frac{3}{-7}[/tex]
Can be written - [tex]\frac{3}{7}[/tex]
The cost of a certain cell phone plan can be modeled by C(m) = 2m + 15, where C(m) is the total cost for m minutes of cell phone usage. State the meaning of the slope with respect to the cost associated with the cell phone plan.
The interpretation of the slope is that the cost per minute is $2
How to determine the interpretation of the slope?From the question, we have the following parameters that can be used in our computation:
C(m) = 2m + 15
Where
m = number of minutes
C(m) = cost function
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 2
This means that the slope is 2
And it means that the cost per minute is $2
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Solve |x| + 7 < 4.
{x | x < -11 or x > -3}
Ø
{x | -3 < x < 3}
The solution of equation is ∅.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.
Given equation |x| + 7 < 4
subtract 7 from both sides
|x| + 7 - 7 < 4 - 7
|x| < -3
but |x| ≥ 0, for all real values,
so solution is ∅.
Hence the solution of equation is ∅.
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The function w (t) = 29 + 0.0674t gives the estimated weight, in pounds, of a beaver t days
after June 1, where t < 90. Which of the following is the best interpretation of 29 in this context?
1)The estimated weight, in pounds, of the beaver 90 days after June 1
2)The estimated weight, in pounds, of the beaver on June 1
3)The estimated number of pounds by which the beaver's weight increased each day after June 1
4)The estimated number of pounds by which the beaver's weight increased in the 90 days after
June 1
Answer:
2) The estimated weight, in pounds, of the beaver on June 1.
Step-by-step explanation:
Given function:
[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]
where:
w = weight of a beaver (in pounds)t = time after June 1 (in days)When t = 0:
[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]
Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.
As t = 0 is June 1:
29 is the estimated weight, in pounds, of the beaver on June 1.Find the area of the following color regions?
Answer:
Step-by-step explanation:
I need help, I don’t know what comes next I’m confused???
Answer:
x^2-9
Step-by-step explanation:
-3 + 3 = 0 so the x terms cancel out. This leaves you with only x^2-9
The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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GIVING BRAINLIEST AND 50 POINTS
Answer:
2x + 2
Step-by-step explanation:
Combine all the like terms:
-5x + 7x -12 + 14 = 2x + 2
Answer:
2x + 2
Step-by-step explanation:
(- 5x - 12) + (14 + 7x) ← remove parenthesis
= - 5x - 12 + 14 + 7x ← collect like terms
= (- 5x + 7x) + (- 12 + 14)
= 2x + 2
An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A
The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .
What does the term magnitude of the force mean?The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.
The surface area of the otter's back is A = 0.55 m2.
The fluid pressure at the depth of the otter is P = 11500 Pa.
Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .
The complete question is
An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.
Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.
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What is the volume of this rectangular prism?
Answer:
40
Step-by-step explanation:
5 x 4 x 2 = 40
length x width x height = volume
Gary, Mary, and Rory have the same number of candies. If Gary gives Mary half of all his candies, then Mary gives Rory half of all the candies she has at the moment, and then Rory gives Gary half of all the candies he (Rory) has at the moment, Gary would have 12 more candies than he had originally. How many candies do Gary, Mary, and Rory have altogether
Gary, Mary, and Rory have 96 candies altogether.
Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".
After Gary gives Mary half of all his candies, he would have x/2 candies.
Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.
And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.
Now, we know that Gary would have 12 more candies than he had originally, which means:
x/2 + x/8 = x/2 + x/4 - 12
We can combine like terms and simplify the equation:
x/2 + x/8 = x/4 + x/4 - 12
x/8 = 12
x = 8 * 12
x = 96
Thus, Gary, Mary, and Rory have 96 candies altogether.
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Melissa made pancakes using a circle
mold. The circumference of the mold
is 8 centimeters. Which measurement
is closest to the area of the mold in
centimeters?
A 50.24 cm
B 200.96 cm
C 25.12 cm
D 100.48 cm
Answer:
c
Step-by-step explanation:
The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c
Approximately how tall is the streetlight? Round your answer to the nearest tenth.
Note: your teacher may not want you to enter "feet" and instead may just want the number only.
===================================================
Work Shown:
tan(angle) = opposite/adjacent
tan(40) = h/20
20*tan(40) = h
h = 20*tan(40)
h = 16.7819926 which is approximate
h = 16.8
The streetlamp is approximately 16.8 ft tall.
When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.
round 34.171875 to the nearest 100th
The rounding off of 34.171875 to the nearest 100th gives us= 34.17
The nearest hundredth should be the second digit after the decimal point. To round off any decimal figures, we need to see if the digit after the hundredth is greater than or equal to 5. If such is the case, then add 1 to the hundredth, or else remove the digits.
Here, the nearest hundredth digit is 7, and the digit after it (i.e, the third place after decimal) is smaller than 5. So, there is no need of adding an extra 1 to the hundredth. Now, after casting off the remaining digits, we get 34.17.
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Prove that:
Question 1 :
[tex]\sqrt{\frac{1-sin\theta }{1+sin\theta} } =sec\theta -tan\theta[/tex]
Question 2 :
[tex]\sqrt{\frac{1+cos \theta}{1-cos\theta} } +\sqrt{\frac{1-cos\theta}{1+cos \theta} } =2cos \:ec\theta[/tex]
Answer:
Identities used:
1/cosθ = secθ1/sinθ = cosecθsinθ/cosθ = tanθcosθ/sinθ = cotθsin²θ + cos²θ = 1Question 1 (1 - sinθ)/(1 + sinθ) = (1 - sinθ)(1 - sinθ) / (1 - sinθ)(1 + sinθ) = (1 - sinθ)² / (1 - sin²θ) = (1 - sinθ)² / cos²θSquare root of it is:
(1 - sinθ)/ cosθ = 1/cosθ - sinθ / cosθ = secθ - tanθQuestion 2The first part without root:
(1 + cosθ) / (1 - cosθ) = (1 + cosθ)(1 + cosθ) / (1 - cosθ)(1 + cosθ) (1 + cosθ)² / (1 - cos²θ) = (1 + cosθ)² / sin²θIts square root is:
(1 + cosθ) / sinθ =1/sinθ + cosθ/sinθ =cosecθ + cotθThe second part without root:
(1 - cosθ) / (1 + cosθ) = (1 - cosθ)²/ (1 + cosθ)(1 - cosθ) = (1 - cosθ)²/ (1 - cos²θ) =(1 - cosθ)²/sin²θIts square root is:
(1 - cosθ) / sinθ = 1/sinθ - cosθ / sinθ =cosecθ - cotθSum of the results:
cosecθ + cotθ + cosecθ - cotθ = 2cosecθStep-by-step explanation:
Question 1:
Consider the left-hand side
[tex] \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} } = \sqrt{ \frac{ 1 - \sin\theta }{1 + \sin\theta} \times \frac{1 - \sin\theta }{1 - \sin\theta } }[/tex]
[tex] = \sqrt{ \frac{ {(1 - \sin\theta )}^{2} }{(1 - { \sin}^{2}\theta) } } = \frac{1 - \sin\theta }{ \cos\theta} [/tex]
[tex] = \frac{1}{ \cos\theta} - \frac{ \sin\theta}{\cos\theta } [/tex]
[tex] = \sec\theta \: - \tan\theta[/tex]
Question 2:
The left-hand side can be rewritten as
[tex] \sqrt{\frac{1+ \cos \theta}{1- \cos\theta} \times \frac{1+ \cos \theta}{1+ \cos \theta} } \: +\sqrt{\frac{1- \cos\theta}{1+ \cos \theta} \times \frac{1 - \cos \theta}{1 - \cos \theta} }[/tex]
[tex] = \frac{1 + \cos\theta}{ \sin\theta} + \frac{1 - \cos\theta}{ \sin\theta}[/tex]
[tex] = \frac{2}{ \sin\theta } = 2 \csc\theta[/tex]
A triangle has the sides of 7 in, 14 in, and 25 in. Is it a right triangle?
Answer:
No it does not equal a right triangle.
Fine the measure of the arc or angle indicated
Answer:
Step-by-step explanation:
? = 1/2( big ∠ - small ∠)
? = 1/2(184 - 84)
? = 1/2(100)
? = 50 °
Solve for x. Solve for x.
Answer:
23
Step-by-step explanation:
7(x+1) = 8(x-2)
7x+7 = 8x-16
x = 23
What are the domain and range of the function fix) = x* - 2x2 - 4?
Answer: domain(-oo,oo). range= f(x) >-5
Step-by-step explanation:
Jessie has 8 more pencils than Dylan. Together they have a total of 18 pencils. How many pencils did Dylan have?
Options:
A. 5
B. 8
C. 13
(NOT 10)
Answer:
Dylan has 5
Step-by-step explanation:
jessie 8+x
‘Dylan x
so
8+x+x=18
2x=10
x=5
jessie has 13
dylan has 5
Answer:
C.) 13
Step-by-step explanation:
So, I'm going to break this down to the three sentences. If you look at the key words in each sentence, grammatically the last one stands out.
In the first sentence it is saying Jessie HAS 8 more pencils than Dylan
In the second sentence it is saying Together they HAVE a total of 18 pencils
In the third sentence it is asking How many pencils DID Dylan have
The word MORE implies in addition to. And this very well could mean at least. I believe the answer is 13.
Saying Dylan had 5 pencils (+ J's 8), would be 13
Saying Dylan had 8 pencils (+J's 8), would be 16
Both of which are not AT LEAST 18
Saying Dylan had 13 pencils (+J's 8), would be 21
If 10 is incorrect, your answer should be 13
A line is drawn so that is passed through the points (2, -1) and (0, 5). What is the slope of the line
If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then slope of line is -3 .
What is Slope ?
The slope of a line is defined as measure of steepness and direction of line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.
The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;
the points are given as [tex](2,-1)[/tex] and [tex](0,5)[/tex] ;
So , on substituting the values in the slope formula ,
we get ;
[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;
= [tex]\frac{6}{-2}[/tex]
= -3 .
Therefore , the required slope of the line is -3 .
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42minutes:5hours in ratio form
Answer:
31:150
Step-by-step explanation:
First of all we convert the hours into minutes:
5×60=300
which gets us 42:300, which we can simplify to:
31:150
and is 31 is prime and 150 can't be divided into it without a remainder, it is in it's simplest form and it is the answer.
Answer:
7:50
Step-by-step explanation:
The ratio:
42 min
-------------- can be rewritten in the equivalent
5 hours
42 min
--------------- = 42/300 = 7/50 or 7:50
300 min
Kayla had 20 candie. Kayla have 1/5 of the candie to her iter. Of the amount left , he gave 3/8 of her friend. How many candie doe Kayla have left for herelf ?
The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.
Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.
Remaining candies = total number of candies - 1/5×total candies
Keep the values in formula
Remaining candies = 20 - 1/5×20
Remaining candies = 20 - 4
Remaining candies = 16
Total candies for Kyla = remaining candies - 3/8×remaining candies
Candies for Kyla = 16 - 3/8×16
Candies for Kyla = 16 - 3×2
Candies for Kyla = 16 - 6
Candies for Kyla = 10
Thus, Kyla received 10 candies.
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In the Himalaya Mountains along the border of Tibet and Nepal, Mount Everest reaches a record height of 29,035 feet. How high is Mt. Everest in miles
The height of the mt. Everest in miles exists 5.499 miles.
What is meant by unit conversion?By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.
By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.
The height of the mt. Everest is : 29035 feet.
The unit conversion is given as :
5280 feet = 1 mile
1 feet = 1/5280 mile
So, 29035 feet =29035 × 1/5280 miles
29035 feet = 29035/5280 miles
29035 feet = 5.499 miles
So, the height of the mt. Everest in miles is 5.499 miles.
The complete question is:
In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.
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Answer: The height of the Mount Everest in miles is 5.499 miles
Step-by-step explanation:
1 miles = 5,280 feet
For feet to miles conversion, you should multiply your length value by 0.0001894: mi = ft × 0.0001894 .For miles to feet conversion, you should multiply your length value by 5,280: ft = mi × 5,280 .1 feet = 1/5280 mileso So, 29035 feet = 29035×1/528029035 feet = 29035/5280in the given question, 29035 feet = 5.499 milesSo, the height of the mt. Everest in miles is 5.499 mileTo learn more about it refer to:
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Someone please say the correct answer!
i need help with this pleasee
Answer:
25%
Step-by-step explanation:
1 out of 4 chance = 25% chance to get 2
6 is 20% of what number
I don’t really need the answer but I have to do a lot of these so I need like instructions on how to figure out the answer