The factor of the function will be x and (x³ – 6). Then the zeroes of the function will be 0 and √6.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The polynomial function is given below.
f(x) = x⁴ − 6x
Then the factor of the function will be
f(x) = x(x³ – 6)
Then the zeroes of the function will be
x = 0, √6
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look at the picture
thank you
The correct answer to this question is the first option
Greg has a piece of string that is 3 1/3 yards long. If he cuts off 3/4 yard, how many yards of the string
will be left?
Prove that C(50,3) + C(50,4) = C(51,4)
By definition of the binomial coefficient,
[tex]C(n,k) = \dfrac{n!}{k!(n-k)!}[/tex]
so we have
[tex]C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)[/tex]
as required.
Simplify the polynomial
x+2y+1−(2x+y+5)
Help its assignment
Answer:
- x + y - 4
Step-by-step explanation:
Given polynomial:
[tex] \rm \: x+2y+1-(2x+y+5)[/tex]
Solution:
Removing parentheses,we obtain
[tex]x + 2y + 1 - 2x - y - 5[/tex]Collecting and combining like terms,we obtain
[tex]x - 2x + 2y - y + 1 - 5[/tex][tex] \boxed{ - x + y - 4}[/tex]Done!
An asset has a cost of $50,000, with a residual value of $10,000. It has a life of 5 years and was purchased on January 1. Under double-declining-balance, what’s the asset’s fourth full year of depreciation expense?
The asset’s fourth full year of depreciation expense will be $6,666.67.
What is double-declining-balance?An enhanced technique for recording loss over the lifetime of a product by adjusting the item's starting sales price by a discount factor.
An asset has a cost of $50,000, with a residual value of $10,000.
It has a life of 5 years and was purchased on January 1.
Then the asset’s fourth full year of depreciation expense will be
Annual depreciation = (cost – salvage value)/ useful life
Annual depreciation = (50000 – 10000) / 5 = $8,000
Year 1 Depreciation (for 10 months, from March to December) = $8,000 × 10/12 = $6,666.67.
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Below what price level would the firm go out of business in the long run?
A firm should go out of business in the long run when its price level is less than the average total cost.
When should a firm go out of business in the long run?The long run is a period where all factors of production are varied. It is known as the planning time of a firm. In the long run, if the if the average total cost is greater than the price, the firm should exit the market.
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Which expression is equivalent to...
Answer:
first option
Step-by-step explanation:
[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]
What is the solution to the equation below? Round your answer to two decimal places. 3e2x + 12 = 42
Answer:
X= 5.52
Step-by-step explanation:
1. Solve the equation:
e×2x + 12= 42
x=15/e
2. Round x=15/e to the required place
x=5.52
Answer:
X=1.15
Step-by-step explanation:
The equation for the line of best fit for this situation is shown below.
Based on the line of best fit, complete the given statements.
The expected number of hot dogs sold when the temperature is 50° would be
hot dogs.
If the vendor sold 35 hot dogs, the temperature is expected to be
degrees.
Based on the line of best fit, for every 10-degree increase in temperature, she should sell
more hot dogs.
The expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.
Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]
[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
The question is incomplete.
The complete question is:
A hot dog vendor at the zoo recorded the average temperature in degrees, x, and the average number of hot dogs she sold, y.
The equation for the line of best fit for this situation is shown below.
[tex]\rm y=\dfrac{3}{10}x+8[/tex]
Based on the line of best fit, complete the given statements.
The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.If the vendor sold 35 hot dogs, the temperature is expected to be ___degrees.Based on the line of best fit, for every 10-degree increase in temperature, she should sell____more hot dogs.We have a line of best fits:
[tex]\rm y=\dfrac{3}{10}x+8[/tex]
Plug x = 50 in the line of best fit.
y = (3/10)50 + 8
y = 15+8
y = 23
Plug y = 35
35 = (3/10)x + 8
27 = (3/10)x
x = 90 degree
Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
Thus, the expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees, and based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.
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On a coordinate plane, an absolute value graph has a vertex at (10, 6).
The graph of h (x) = StartAbsoluteValue x minus 10 EndAbsoluteValue + 6 is shown. On which interval is this graph increasing?
(–∞, 6)
(–∞, 10)
(6, ∞)
(10, ∞)
Answer: (10, ∞)
Step-by-step explanation:
See the graph in the attached image.
Pls answer quickly, make sure to answer all parts
Find the area of the region bounded by the line y =3x -6 and line y=-2x+8 and
a) the x-axis. b) the y-axis. c) the line y=6. d) the line x=5.
The area of the region bounded by the line y =3x -6 and line y=-2x+8 is 12/5 units
How to find the area?y = 3x - 6
y = -2x + 8
Set these two equations equal to each other.
3x - 6 = -2x + 8
Add 2x to both sides of the equation.
5x - 6 = 8
Add 6 to both sides of the equation.
5x = 14
Divide both sides of the equation by 5.
x = 14/5
Find the y-value where these points intersect by plugging this x-value back into either equation.
y = 3(14/5) - 6
Multiply and simplify.
y = 42/5 - 6
Multiply 6 by (5/5) to get common denominators.
y = 42/5 - 30/5
Subtract and simplify.
y = 12/5
These two lines intersect at the point 12/5. This is the height of the triangle formed by these two lines and the x-axis.
Now let's find the roots of these equations (where they touch the x-axis) so we can determine the base of the triangle.
Set both equations equal to 0.
(I) 0 = 3x - 6
Add 6 both sides of the equation.
6 = 3x
Divide both sides of the equation by 3.
x = 2
Set the second equation equal to 0.
(II) 0 = -2x + 8
2x = 8
x = 4
The base of the triangle is from (2,0) to (4,0), making it a length of 2 units.
The height of the triangle is 12/5 units.
A = 1/2bh
Substitute 2 for b and 14/5 for h.
A = (1/2) · (2) · (12/5)
A = 12/5
The area of the region bounded by the lines y = 3x - 6 and y = -2x + 8 between the x-axis is 12/5 units.
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Which one is it I need to finish this page fast
Answer:
E; 10% off %20 sweater with $6 shipping
Step-by-step explanation:
Similar to what I said last time,
this time is with percentages,
How to calculate percent off?
Divide the number by 100 (move the decimal place two places to the left).
Multiply this new number by the percentage you want to take off.
Subtract the number from step 2 from the original number. This is your percent off number.
________________________________________________________
A. 35% off a $35 sweater with 4 dollar shipping is basically
0.35 x 35 = 12.25 and 35-12.25 = $22.75 + the $4 shipping fee (if no tax)
which the total would be $26.75
B. 20% off $35 is
0.2x35=7 and 35-7 = 28 so your total is $28
C. 30% off $30 with $6 for shipping is
0.3x30=9 and 30-9 is $21 plus the shipping fee
$27
D. $20 sweater with $5 shipping is $25 no discount involved :D
E. 10% off %20 sweater with $6 shipping is
0.1x20 is 2 which 20 - 2 = 18 and plus shipping fee 18+6 is $24
________________________________________________________
Hope this helped again.
On May 6, Jim Ryan borrowed $14,000 from Lane Bank at 712% interest. Jim plans to repay the loan on March 11. Assume the loan is on ordinary interest. How much will Jim repay on March 11?
The amount to be repaid by Jim Ryan is $14,891.78.
Given that, Principal (P) =$14,000, the rate of interest (R) =7[tex]\frac{1}{2}[/tex]% and T=310 days.
What is ordinary interest?Ordinary interest is calculated on the basis of a 360-day year or a 30-day month; exact interest is calculated on a 365-day year.
Now, the interest=14,000×7.5 %×[tex]\frac{310}{365}[/tex].
=$891.78
The amount to be repaid=14,000+891.78=$14,891.78
Therefore, the amount to be repaid by Jim Ryan is $14,891.78.
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Simplify the following expression.
(4x + 7)2
Answer:
=8x+14 or
=16x²+56x+49
[tex]\bf{(4x+7)2 }[/tex]
[tex]\bf{=2(4x+7)}[/tex]
[tex]\boldsymbol{Put \ the \ parentheses \ used \ \ :a(ab+c)=ab+ac. }[/tex]
[tex]\boldsymbol{2(4x+7)=2\cdot4x+2\cdot7 }[/tex]
[tex]\bf{=2\cdot 4x+2\cdot7}[/tex]
[tex]\boldsymbol{Simplify \ 2\cdot 4x+2\cdot7}[/tex]
Multiply 2 x 4 = 8Multiply 2 x 7 = 14[tex]\boldsymbol{8x+14 \ \ \to \ \ \ Answer }[/tex]
Pisces04Another day, another math problem 3
Answer:
[tex]2\sqrt{x+1}-3\\domain:[-1, \infty)[/tex]
Step-by-step explanation:
[tex]g(h(x)) = 2(\sqrt{x+1})-3\\g(h(x)) = 2\sqrt{x+1} - 3\\[/tex]
the function is only defined when (x+1) >= 0 (since square root) so the domain is when x >= -1
I have a quick geometry question! Thank you!
Answer:
e4fodor8rsidididi2f2
Answer:
9
Step-by-step explanation:
3:4
AB:12
cross multiply giving
3×12:4AB
36: 4AB
divide both sides by 4,thus
AB=9
Express the radical using the imaginary unit, i sqrt{-27}
Answer:
27i
Step-by-step explanation:
Since we define i as [tex]\sqrt{-1}[/tex], [tex]\sqrt{-27} = 27i[/tex]
Answer:
Step-by-step explanation:
i [tex]i \sqrt{-27} =i\sqrt{-1 \times 27} =i\sqrt{27i^2} =i \times i\sqrt{27} =i^2\sqrt{9 \times 3} \\=-1\times 3\sqrt{3} \\=-3\sqrt{3}[/tex]
Solve for x:
5(1 – x) = 20
x = __
[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]
Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]
The value of x is -3! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] First multiply 5 times 1 and -x
[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]
[tex]\twoheadrightarrow\sf 5-5x=20[/tex]
[tex]\bullet[/tex] Now subtract 5 from both sides
[tex]\twoheadrightarrow\sf -5x=15[/tex]
[tex]\bullet[/tex] Now divide both sides by -5
[tex]\twoheadrightarrow\sf x=-3[/tex]
--
Hope that this helped! Best wishes.
--
A student draws two parabolas on graph paper. Both parabolas cross the x-axis at (-4, 0) and (6, 0). The y-intercept
of the first parabola is (0, -12). The y-intercept of the second parabola is (0, -24). What is the positive difference
between the a values for the two functions that describe the parabolas? Write your answer as a decimal rounded to
the nearest tenth.
Answer:
1/2
Step-by-step explanation:
First parabola f(x1) = a ( x+4)(x-6) use point 0,-12 to find a = 1/2
= 1/2 (x+4)(x-6)
Second parabola a ( x+4) (x-6) using point 0, -24 shows a = 1
f(x2) = (1)(x+4)(x-6)
Difference between the 'a' values = 1 - 1/2 = 1/2
if cp=rs 400, loss=10% find sp
Answer:
cp = rs 400
loss = 10%
Then SP = 400 - 10% of 400
= 400 - 40
= 360
Therefore SP = Rs. 360
Sam wants to measure the height of a tree. She walks 100 feet from the base of the tree and looks up. The angle of elevation from the ground to the top of the tree is 33°. How tall is the tree? Round your answer to the nearest hundredth.
The height of the tree from which Sam is standing 100 feet away from the base is 64.94 feet.
What is angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
To calculate the height of the tree , we use the formula below.
Formula:
tan∅ = H/B.............Equation 1Where:
∅ = Angle of elevation from the ground to the top of the treeH = Height of the treeB = Distance of the base of the tree to the point where Sam looks upFrom the question,
Given:
∅ = 33°B = 100 feetSubstitute these values into equation 1 and solve for H
tan33° = H/100H = tan33°×100H = 64.94 feetHence, the height of the tree is 64.94 feet.
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ξ = {x:x is an integer, 2 ≤ x ≤ 14}
� = {x:x is a prime number}
� = {x:x is a multiple of 3}
Given that C ⊂ A, n(C)=3 and B ∩ C = ∅, list the members of a possible set C
The members of a possible set C are {6, 9, 12}
Set theoryThe universal set is the set that contains all other sets. Given the following sets
ξ = {x:x is an integer, 2 ≤ x ≤ 14}
B = {x:x is a prime number}
A = {x:x is a multiple of 3}
The sets B and A are:
B = {2, 3, 5, 7, 11}
A = {3, 6, 9, 12}
If C is a subset of A with a cardinality of 3, hence the required set will be {6, 9, 12}. Note that 3 is excluded since B n C must be an empty set.
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rewrite the equation y-8=2 into slope form
Answer:
y=2x+16 is the slope intercept form
Step-by-step explanation:
sorry if its wrong tried!!!
Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene 97degree
Answer:
Obtuse and the rest of the question is incomplete.
Step-by-step explanation:
3 Three children share this chocolate equally.
What fraction does each child get?
Each child gets
CHALLENGE?
Answer: Each child gets 1/3
Step-by-step explanation: x/3
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. If you connect a 2 megohm resistor (2× 10^6 ohms) across a 2.4 kilovolt voltage source (2.4×10^3 volts),what would be the current in amps?
Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms. The current in the amp is 1.2 × 10⁻³.
What is Ohm's Law?Ohm's law states that the current (I) in amps equals the voltage (E) in volts divided by the resistance (R) in ohms.
The current in amps = (2.4×10³ volts)/(2× 10⁶ ohms)
= 1.2 × 10⁻³ amp
Hence, the current in the amp is 1.2 × 10⁻³.
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Factor the binomial expansion. 81x4 – 648x3 + 1,944x2 – 2,592x + 1,296
Answer:
[tex]648[/tex]([tex]x^{3} + 3x^{2} - 4x + 2[/tex])
Step-by-step explanation:
When factoring an expression like this, you need to divide all of the parts by a common number or variable. In this case, the only thing all of these numbers share is that they are divisible by 648. So, you would divide each number by 648 to simplify it, getting 1, 3, 4, and 2. Put these numbers in front of their respective variables, and put 648 outside of the parentheses to get the final answer.
Answer:
(3x – 6)4
Step-by-step explanation:
If Yang solves the inequality -4y> -40, then which of the following answers would be true for this claim?
Answer:
(a) 9, 8, 7, 6, 5, ...
Step-by-step explanation:
The solution to the inequality can be done a couple of ways. The solution is similar to that for a one-step linear equation.
__
reverse inequalityWe know that multiplying numbers by a negative value reverses their order. For example, 1 < 2, but -1 > -2. That is, multiplying by -1 requires a change in the comparison operator if it is to remain true.
For our inequality, we want to solve it by multiplying both sides by -1/4:
-4y > -40
(-1/4)(-4y) < (-1/4)(-40) . . . . . multiply both sides by -1/4 (reverses order)
y < 10 . . . . . . . . . . . simplify
The first few decreasing integer values that are part of this solution are ...
{9, 8, 7, 6, 5, ...}
__
make coefficients positiveWe can add 4y+40 to both sides of the inequality. The result will be an inequality with positive coefficients. This can be solved in one step.
-4y > -40 . . . . . given
(-4y) +(4y +40) > (-40) +(4y +40) . . . . . . add 4y+40 to both sides
40 > 4y . . . . . . . . . . . . . . . simplify
10 > y . . . . . . . . . . . . divide by 10 (order is unchanged)
y < 10 . . . . . . . . . rearrange to put y on the left
Integer solutions to this inequality are ...
{9, 8, 7, 6, 5, ...}
Find the volume of a cylinder that has a diameter of 7 and a height of 8.
28 Pi
392 Pi
448 Pi
98 Pi
Therefore,
Radius (r) = d / 2Radius (r) = 7/2We know that :
V = πr^2hSubstituting the values :
>> V = π × (7 / 2)^2 × 8
>> V = π × (49 / 4) × 8
>> V = π × 49 × 2
>> V = 98π
Henceforth,
98 pi is the answer.We know , the volume of a cylinder is given by the formula – πr²h, where r is the radius of the cylinder and h is the height.
Diameter - 7Height - 8radius = 7/2Therefore, putting the values, we get,
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: {r}^{2}h[/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \times \: \bigg(\frac{7}{2} \bigg)^{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{2} \: \times \: 8 \\ [/tex]
[tex] \Large \mathcal \purple {Volume } \large\red\implies \tt \large \:\pi \: \times \: \frac{7}{2} \: \times \: \frac{7}{ \cancel2} \: \times \: \cancel{8} \: ^{ \orange4} \\ [/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: \frac{7}{ \cancel2} \: \times \: {7} \: \times \: \cancel4 \: ^{ \orange2} \\ [/tex]
[tex] \\ \Large \mathcal \purple {Volume }\large\red\implies \tt \large \:\pi \: \times \: 7 \: \times \: 7 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\ \large\red\implies \tt \large \:\pi \: \times \: 49 \: \times \: 2[/tex]
[tex]\Large \mathcal \purple {Volume }\large\red\implies \tt \large \:98 \:\pi[/tex]
Hence , the volume of cylinder is 98 pi
Please answer! I will give you the brainliest :)
Answer:
K
Step-by-step explanation:
(1*500 * 5) + (10 * 3*500)
