Answers
Answer:
k = -10
Explanation:
f(x) = 4x³ - 3kx² + 44x - 30
The divisor is:
(x - 2)Set divisor to zero:
(x - 2) = 0x = 2Insert this into equation.
⇒ 4(2)³ - 3k(2)² + 44(2) - 30 = 210
⇒ 32 - 12k + 88 - 30 = 210
⇒ -12k + 90 = 210
⇒ -12k = 210 - 90
⇒ -12k = 120
⇒ k = 120/-12
⇒ k = -10
Answer:
k = -10
Step-by-step explanation:
From the remainder theorem, we know that the remainder, 210, is equal to f(2).
∵ [tex]f(2) = 210[/tex] ,
⇒ [tex]4(2)^3 - 3 k(2)^2+44(2) - 30 = 210[/tex]
⇒ [tex]32 -12k + 88 - 30 = 210[/tex]
⇒ [tex]90 - 12k = 210[/tex]
⇒ [tex]-12k = 120[/tex]
⇒ [tex]k = -10[/tex]
Related Questions
Here is a right-angled triangular tile.
A hollow shape is made using four of these
triangular tiles and four square tiles.
Work out the perimeter of the hollow shape.
Answers
The perimeter of the hollow shape is 16d + 4(a + b + c)
How to determine the perimeter?The question is incomplete, and the missing parameters cannot be found.
So, I will give a general explanation on how to determine perimeter.
The given information are:
4 right triangles4 squaresThe perimeter of a right triangle that has sides a, b and c is:
P = a + b + c
Since there are 4 triangles, the perimeter of the 4 triangles is:
P = 4(a + b + c)
The perimeter of a square that has side length d is:
P = 4d
Since there are 4 squares, the perimeter of the 4 triangles is:
P = 4 * 4d
P = 16d
Add the perimeters of the squares and the triangles
P = 16d + 4(a + b + c)
Hence, the perimeter of the hollow shape is 16d + 4(a + b + c), where a, b, c and d are the unknown variables
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what term does the dormula sinA/a =sinB/b represent
Answers
Answer:
Law of sines
Step-by-step explanation:
The law of sines is a formula used to find either an angle or side in a non-right triangle.
You have to have at least three parts to use it.
For example, if you have angle A and its side (a) along with angle B, you can use it to find side b.
The quotient of a number and 4, minus 2, equals 5/4.
Find the number.
Answers
Answer:
n=16
Step-by-step explanation:
To measure the height of a tree, Alma walked 125 ft from the tree and
measured a 32° angle from the ground to the top of the tree. Estimate the
height of the tree to the nearest foot.
Answers
Answer:
78.11 ft
Step-by-step explanation:
[tex]=125 tan 32\\=78.11 ft[/tex]
FIFO and LIFO Costs Under Perpetual Inventory System The following units of an item were available for sale during the year: Beginning inventory 30 units at $40 Sale 21 units at $62 First purchase 30 units at $42 Sale 19 units at $64 Second purchase 26 units at $44 Sale 23 units at $64 The firm uses the perpetual inventory system, and there are 23 units of the item on hand at the end of the year. a. What is the total cost of the ending inventory according to FIFO? $fill in the blank 1 b. What is the total cost of the ending inventory according to LIFO?
Answers
The ending inventory using LIFO is $920.
The ending inventory using FIFO is $1,472.
What is the ending inventory?
LIFO means last in first out. It means that it is the last purchased inventory that is the first to be sold. Ending inventory would consist of first purchased inventory.
23 x $40 = $920
FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold. Ending inventory would consist of last purchased items in inventory.
23 x $64 = $1,472
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f (x) = 7 |x-5| + 9 does the absolute graph shrink or stretch
Answers
Answer:
it shrink
if the number outside the absolute value is greater than 1 it shrinks
if the numerous is smaller than 1 it stretches
remember the saying about the parent function if you run less than 1 mile you are wider than the parent
if you run more than a mile here the number is 7 so it's skinner yhan the
Step-by-step explanation:
Consider the following couple, who are engaged to be married. Assume that each person takes one exemption and the standard deduction. Answer the questions below using the tax rates in the table to the right.
Answers
The income tax of Rebecca and Steve will be $27020 and $20625.
How to illustrate the tax?Rebecca has an income of $96500. The income tax will be:
= 28% × $96500
= 27020
Steve has an income of $82500. The income tax will be:
= 25% × $82500
= 20625
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At a harvest 16 ears are being picked foot every 18 peppers. If 19 peppers have been picked, how many eats of corn have been picked?
Answers
The number of eats of corn which have been picked is; 16.9 corns.
How many eats of corn have been picked?According to the question; 16 eats of corn are being picked foot every 18 peppers. In essence, the ratio of corns to peppers is; 16/18.
Hence, it follows that the number of corns which corresponds to 19 peppers been picked can be evaluated as follows;
16/18 = x/19
x = (19×16)/18
x = 16.9 eats of corn.
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A standard pair of six-sided dice is rolled. What is the probability of rolling a sum greater than 8? Express your answer as a fraction or a decimal
number rounded to four decimal places.
Answers
Answer:
Step-by-step explanation:
Nines: (3,6), (4,5), (5,4), (6,3)
Tens: (4,6), (5,5), (6,4)
Elevens: (5,6), (6,5)
Twelves: (6,6)
4 + 3 + 2 + 1 = 10 outcomes possible
36 outcomes total for rolling two dice.
P(sum > 8) = 10/36 or 5/18 simplified.
If using the method of completing the square to solve the quadratic equation x^2-9x+2=0 which number would have to be added to "complete the square"?
Answers
The number that would have to be added to complete the square is 81/4.
What is a Quadratic Equation ?Quadratic equations are polynomials of degree 2 , It is represwented by ax² + bx +c = 0.
The quadratic equation given is
x² -9x +2 = 0
x² -9x + (81/ 4) - (81/4) + 2 = 0
x² -9x + (9/2)² - (81/4) +2 = 0
(x - 9/2)² - (73/4) = 0
Therefore , 81/4 will be added to complete the square to solve the quadratic equation.
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Find the values of x and y.
Answers
Answer: is C
Step-by-step explanation:
5 5/6 + 2 2/3 mixed number
Answers
Step by step
5-5/6 + 2-2/3
We need to find common denominator
Change 2/3 to 4/6
5-5/6 + 2-4/6 = 7-9/6
Simplify
9/6 is the same as 1-3/6
So now we have 8-3/6
You can reduce the fraction to its simplest form, 3/6 is the same as 1/2
So your final answer is 8 1/2
Marlon's TV plan costs $40.66 per month plus $6.71 per first-run movie. How many first-run movies can he watch if he wants to keep his monthly bill to be a maximum of $100?
Answers
Answer:
He can watch 8 movies
Step-by-step explanation:
100-40.66=59.34
6.71 x 8 = 53.68
therefore the most amount of movies he can watch is 8
PLEASE HELP
For j(x) = 4x − 2, find j of the quantity x plus h end quantity minus j of x all over h period
4 to the power of the quantity x minus 2 end quantity times the quantity 4 to the power of h end quantity all over h
4 to the power of the quantity x minus 2 end quantity times the quantity 4 to the power of h plus 1 end quantity all over h
4 to the power of the quantity x minus 2 end quantity times the quantity 4 to the power of h minus 1 end quantity all over h
the quantity x minus 2 end quantity times the quantity 4 to the power of h plus 1 end quantity all over h
Answers
Step-by-step explanation:
The figure below shows a portion of the graph of the function [tex]j\left(x\right) \ = \ 4^{x-2}[/tex], hence the average rate of change (slope of the blue line) between the [tex]x[/tex] and [tex]x+h[/tex] is
[tex]\text{Average rate of change} \ = \ \displaystyle\frac{\Delta y}{\Delta x} \\ \\ \rule{3.7cm}{0cm} = \dsiplaystyle\frac{f\left(x+h\right) \ - \ f\left(x\right)}{\left(x \ + \ h \right) \ - \ x} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{f\left(x + h\right) \ - \ f\left(x\right)}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x+h-2} \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{4^{x-2+h} \ - \ 4^{x-2}}{h}[/tex]
[tex]\\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h}\right) \ - \ 4^{x-2}}{h} \\ \\ \\ \rule{3.7cm}{0cm} = \displaystyle\frac{\left(4^{x-2}\right)\left(4^{h} \ - \ 1 \right)}{h}[/tex]
3 gallons of milk having a hole in it and leaking at the rate of 1.5 ounces a second for 2 minutes. How much milk is left at the end?
Answers
Answer: 1.59375. Round to 1.6 if need be.
Step-by-step explanation:
Their are 384oz in 3 gallons (multiply gallons by 128)
Their are 120 seconds in 2 minutes (multiply minutes by 60)
Multiply 1.5 * 120 = 180 to get how many oz have drained after 2 minutes.
Subtract 384 - 180 = 204 to get how many oz left in the milk container.
Convert 204oz to gallons by dividing by 128. 204 / 128 = 1.59375gallons.
Pls Help! Geometry
What is the area of the blue section?
Answers
Considering the area of the circles, the area of the blue section is of [tex]50\pi[/tex] cm².
What is the area of a circle?
The area of a circle of radius r is given as follows:
[tex]A = \pi r^2[/tex].
The area of the blue section is given by the area of the larger circle, of radius 10 cm, subtracted by the area of the two smaller circles, each with radius of 5 cm, hence:
[tex]A_G = \pi 10^2 = 100\pi[/tex]
[tex]A_S = 2 \times \pi \times 5^2 = 50\pi[/tex]
[tex]A_B = A_G - A_S = 100\pi - 50\pi = 50\pi[/tex]
The area of the blue section is of [tex]50\pi[/tex] cm².
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Adrian exercised three days during the past week. He exercised 58 minutes and 45 seconds during the
first day, 40 minutes and 40 seconds on the second day, and 20 minutes and 35 seconds on the third
day. How many hours did he spend exercising during the week?
Answers
Answer:
2h 1' 1"
Step-by-step explanation:
1h = 1 hora
1' = 1 minute
1" = 1 secind
The sum of the three days is:
58' 45"
+ 40' 40"
20' 36"
= 118' 121"
118' 121" = 118' + 121"
1' = 60"
121" = 120" + 1" = (120/60) + 1 = 2' + 1"
Then:
118' + 121" = 118' + 2' ´+ 1" = 120' + 1"
1 h = 60'
(120/60) + 1 = 2h + 1'
then:
118' + 121" = 2h + 1' + 1"
= 2h 1' 1"
A restaurant sells burritos for $8.00 each. The cost of the meat is $1.50 and the cost of the other ingredients is $1.00 for each burrito.
Money made from selling burritos is positive. The cost of making burritos is negative. Profit is the money left after paying the costs.
How much profit would the restaurant make by selling 100 burritos?
Answer these questions to find out.
1. How much money would the restaurant take in by selling 100 burritos
Answers
Answer:
1. How much profit would the restaurant make by selling 100 burritos?
Answer: The restaurant would make $550
2. How much money would the restaurant take in by selling 100 burritos
Answer: The restaurant would take in $800
Step-by-step explanation:
First we have to add all the negatives.
-1.50 + -1.00
= -2.50
Now that we have that, we just need to multiply both the 8 dollars and the -2.50 by 100.
8 * 100 = 800
-2.50 * 100 = -250
Now we have the answer for the second question.
The restaurant would take in $800 before the cost of the ingredients.
But now we need to find the profit. (Which is the amount of money they made minus the cost of the ingredients and meat)
800 - 250 = 550
So the restaurant will make $550 in profit.
Hope this helped! :D
Answer:
$550
Step-by-step explanation:
what is the dependent variable of "i did 60 brush strokes in 1 minute"
Answers
The dependent variable is time
How to determine the dependent variable?The statement is given as:
"I did 60 brush strokes in 1 minute"
The dependent variable is the variable that is dependent on the action that is done.
From the statement.
The action is the strokes of brush
And time is dependent on the number of strokes
Hence, the dependent variable is time
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I need help solving this problem
Answers
Kathy Beckhardt weighs four of her sheep at the fair. She can weigh two of them at a time on the big scale. Sheep A and sheep B have an average weight of 150 pounds, sheep B and sheep C have an average weight of 127 pounds, and sheep C and sheep D have an average weight of 168 pounds. What is the average weight of sheep A and sheep D?
Answers
Using a system of equations, it is found that the average of sheep A and sheep D is of 191 pounds.
What is a system of equations?
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are the weights of the sheep, given by A, B, C and D.
Sheep A and sheep B have an average weight of 150 pounds, hence:
[tex]\frac{A + B}{2} = 150[/tex]
A + B = 300 -> B = 300 - A
Sheep B and sheep C have an average weight of 127 pounds, hence:
B + C = 254
300 - A + C = 254
C - A = -46.
A - C = 46.
C = A - 46.
Sheep C and sheep D have an average weight of 168 pounds, hence:
C + D = 336
A - 46 + D = 336.
A + D = 382.
The average weight of sheep A and sheep D in pounds is:
[tex]\frac{A + D}{2} = \frac{382}{2} = 191[/tex]
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In a plane, line b is parallel to line f, line f is parallel to line g, and line h is perpendicular to line b.
Answers
The statement that cannot be true is that g cannot be parallel to h (g ║h)
How to know parallel lines in a plane?On the plane ,
line b is parallel to line f.
Therefore,
b ║ f
line f is parallel to line g,
Therefore,
f ║ g
line h is perpendicular to line b.
h ⊥ b
Therefore,
Since line h is perpendicular b, line b is perpendicular to h.
b can be parallel to g on the plane.
g cannot be parallel to h because h is perpendicular to b.
h can be perpendicular to f because b is parallel to f.
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Explain a detailed solution to the advanced function 4096^x = 8
Answers
The value of x in 4096^x = 8 is 0.25
How to solve the equation?The equation is given as:
4096^x = 8
Express 4096 as 8^4
8^(4x) = 8
Cancel the common base
4x = 1
Divide by 4
x = 0.25
Hence, the value of x in 4096^x = 8 is 0.25
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Using the figure, which is an example of a diameter?
Answers
Answer: Segment AD
Reason:
Any diameter goes through the center of a circle, with both endpoints on the circle edge.
Another diameter is segment FC.
Answer:
CF and AD
Step-by-step explanation:
Hello!
Parts of a CircleA Radius is the line segment that stretches from the center of the circle to the outer curve.A Diameter is the line segment that stretches from side to side of a circle that goes through the center of the circle.The Circumference is the length of the outer border of the circle.Given the definitions, we are simply looking for any line that goes through the center of the circle, and touches twice on the circumference of the circle.
There are only two lines that seem to go through the circle, and have endpoints on the circle:
CFAD
the area of a right triangle is 6 square units. if the length of one leg is 4, what is the length of the altitude to the hypotenuse?
a) 6/5 d)12/5
b)4/3 e)15/4
c)3/2
Answers
The length of the altitude to the hypotenuse of the right triangle is 3 / 5
How to find the altitude of a right triangle?A right triangle has one of it's angle as 90 degrees. Therefore,
area of right triangle = 1 / 2 bh
where
b = baseh = heightHence,
6 = 1 / 2 × 4 × h
6 = 4h / 2
cross multiply
12 = 4h
divide both sides by 4
h = 12 / 4
h = 3 units
Hypotenuse² = 4² + 3²
c² = 16 + 9
c = √25
c = 5
Therefore, the length of the altitude to the hypotenuse of the right triangle is 3 / 5
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easy points for geometry
Answers
Step by step:
X is translated 2 units to the right
Y is translated 8 units downs
Substitute 4 for the x value to
Substitute -5 for the y value
( (4) + 2, (-5) - 8 )
4+2=6
-5-8= -13
Answer: (6, -13)
Hope this helps!
Jack pays 1.74$ for 6 packs of gum. How much does he pay for one
Answers
Answer:
$0.29 and if you want to round it up then it is going to be $0.30
Step-by-step explanation:
You are asking what 1 pack of gum costs. We already know that 6 packs of gum costs $1.74 and we need to find the unit rate which is basically what one pack of gum costs so in order to do that we need to [tex]\frac{1.74}{6}[/tex] which is 0.29 and that is the cost of 1 pack of gum. Hope that helps and also can you please mark me as brainlist. Thank you
Suppose N1 can be exchanged for £0.12, what is the value of N12 in pounds?
Answers
Answer:
£1.44
Step-by-step explanation:
N1 = £0.12
N12 = 12 × N1 = 12 × £0.12 = £1.44
how many 4 digit numbers can I make only using the numbers 5533?
Answers
Need help with this
Answers
Answer:
23 degrees
Step-by-step explanation:
We can use basic trigonometric equations to solve for the angle x because we are given a right triangle.
I will use the sin x = opposite / hypotenuse
sin x = 5 / 13
x = sin^-1 (5 / 13)
x = 22.61986 degrees
The question requires us to round to the nearest degree which is 23.
Other alternative methods you can use include the tangent and cosine functions or the law of cosines.
Answer:
x = 23°
Step-by-step explanation:
I will use
[tex]tanx=opposite/adjacent[/tex]
[tex]tanx=\frac{5}{12}[/tex]
[tex]x=tan^{-1} (\frac{5}{12} )=tan^{-1} (0.417)=22.62^{o}[/tex]
rounded to the nearest degree : 23°
Hope this helps