The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).
How to divide the polynomialUsing the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder
We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;
x⁴ divided by x equals x³
x + 1 multiplied by x³ equals x⁴ + x³
subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2
2x³ divided by x equals 2x²
x + 1 multiplied by 2x² equals 2x³ + 2x²
subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2
2x² divided by x equals 2x
x + 1 multiplied by 2x equals 2x² + 2x
subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2
-3x divided by x equals -3
x + 1 multiplied by -3 equals -3x - 3
subtract -3x - 3 from -3x - 2 will result to a remainder of 1.
Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).
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A wedding cake was cut into 30 slices. If 12 of the slices were eaten, what fraction represents the eaten portion of the cake? Reduce your answer to lowest terms.
Answer:
12/30, if you reduce then it would be 2/5 because you divided by 6 hope this helps! :D
Step-by-step explanation:
The fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]
Let the wedding cake be W.Let the eaten portion be E.Given the following data:
Total wedding cake slices = 30 slicesNumber of cake slices eaten = 12 slices.To find the fraction that represents the eaten portion of the cake;
In this exercise, you're required to find what fraction represents the eaten portion of the wedding cake.
[tex]Fraction = \frac{E}{W}[/tex]
Substituting the values into the equation, we have;
[tex]Fraction = \frac{12}{30}[/tex]
Dividing both sides by 6, we have;
[tex]Fraction = \frac{2}{5}[/tex]
Therefore, the fraction that represents the eaten portion of the cake is [tex]\frac{2}{5}[/tex]
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The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x. (A) Find the average cost per unit if 200 frames are produced. (B) Find the marginal average cost at a production level of 500 units. (C) Use the results from parts (A) and (B) to estimate the average cost per frame if 501 frames are produced.
The marginal average cost is -1 and The marginal average cost for 200 is $699.
What is marginal cost?The price to manufacture a second unit of output is known as the marginal cost. Since marginal cost aids in determining the level of production that is the most effective for a manufacturing process, it is a crucial topic in cost accounting. It is estimated by estimating the costs incurred even if just one more unit is produced.
Given The total cost (in dollars) of manufacturing x auto body frames is C(x)=40,000+500x.
Average cost = Cx / x
Average cost = (40,000 + 500x)/ x
For x = 200
Average cost = (40,000 + 500 * 200)/200
Average cost = 700$ per frame
Marginal average cost = d(Cx/x)/dx
d(Cx/x)/dx = -40,000/ x^2
at x = 200
Marginal average cost = -40,000/ 200^2 = -1
Marginal average cost = -1 tells us the average cost
decrease at the rate of -1 for every x
Average cost for 200 = 700$ per frame
Average cost for 200 = 700 + 1 (-1)
The average cost for 200 = 700 -1 = 699$
therefore, the Marginal average cost for 200 is $699.
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Pleaseee helppppp it’s timedddddd!!!!!!!
Answer:
Option (4)
Step-by-step explanation:
Point to remember for the dilation,
Area scale factor = (Dimension scale factor)²
It's given in the question,
Dimension scale factor = [tex]\frac{2x}{5y}[/tex]
Therefore, area scale factor = [tex](\frac{2x}{5y})^2[/tex]
= [tex]\frac{4x^2}{25y^2}[/tex]
Option (4) will be the correct option.
Darien uses 3 3/4 cups of flour for each loaf of bread he bakes enter an equation that represents the total number of cups of flower Darien uses, c, to bake n loaves of bread
Answer:
n=15/4c
Step-by-step explanation:
y=mx+b
b=0 as it does not state any initial value
y=n
x=c
m=3 3/4 or 15/4
combining these together you get:
n=15/4c+0
The equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Darien uses [tex]3\frac{3}{4}[/tex] cups of flour to make one loaf of bread, we need to establish an equation, that will represent the number of cups of flower Darien uses, c, to bake n loaves of bread,
So,
Since, she uses [tex]3\frac{3}{4}[/tex] cups for one loaf of bread so for n loaf =
(We will multiply the amount used in one loaf to the number of loafs needed)
Therefore,
To make n number of loafs = [tex]3\frac{3}{4} c[/tex]
Hence, the equation representing the number of number of cups of flower Darien uses, c, to bake n loaves of bread is [tex]n = 3\frac{3}{4} c[/tex]
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The graph shows Sam's earnings. What is the constant
of proportionality between Sam's earnings and the
number of hours he worked?
Answer:
8
Step-by-step explanation:
Constant of proportionality, k = y/x
y = earnings ($)
x = time (h)
Any point on the line can be used to determine the constant of proportionality. Let's use, (1, 8)
Constant of proportionality, k = y/x = 8/1
k = 8
Prove that limx→2 2^x=4 using the formal definition of limit.
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove that, [tex]\lim_{x \to \22} 2^{x}=4[/tex]
Plug in the value of 2 into the limit.
[tex](2)^{2}=4[/tex]
Thus we proved the limit.
Based on the family the graph below belongs to, which equation could represent the graph?
Answer:
its A
Step-by-step explanation:
just took the test
Answer:
The first graph on edge 2021
Simisola wants to compare the time take
to make yoghurt at different temperature
List the variables she should control.
Yogurt production is affected by the production technological conditions.
What is yoghurt different temperature?Yogurt production is affected by the production technological conditions. Increase in the incubation temperature (42-45ᵒC) resulted to increase in the coagulation of the milk protein present (induced by thermophilic bacteria) and viscosity. This also resulted in increased acidity of the yoghurt.The temperature must be 108°F to 112°F for yogurt bacteria to grow properly. Too high a temperature inactivates bacteria; too low a temperature prohibits growth. Inhibitor substances such as detergent from dishes. Wash and rinse dishes well before making yogurt.Making yogurt at home is a fairly straight-forward process. Heat milk to 180F (82C), cool that milk to at least 110F (43C), add live cultures, usually in the form of yogurt with said cultures, incubate, then chill.There are several variables in the process, some of which are: The fat content of the milk (I typically use whole), how long to hold the milk during the initial heat step, how long it takes to cool the milk, the temperature of the incubation step, and the length of time for incubation, to name a few.To learn more about yoghurt different temperature refers to;
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What is the measure of Angle B A C?
Triangle A B C. Angle B is 50 degrees, angle C is 50 degrees, and angle A is blank.
50 degrees
80 degrees
100 degrees
130 degrees
find in how many ways can two admirals, three generals and 4 lieutenants can be seated in a row of nine seats if the admirals must sit at each end?
Answer:
They can be seated in 10,080 ways.
Step-by-step explanation:
Arrangements of n elements:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
In this question:
In each end, the two admirals, so 2 possible outcomes.
In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). So
[tex]2A_{7} = 2*7! = 10080[/tex]
They can be seated in 10,080 ways.
The number of ways they can be seated is 10,080 ways.
Permutations and combinationThe number of possible ways fof arranging n elements is given as:
P = n!
According to the question, there are 2 admirals! 3 generals and 4 lieutenant.
In each end, the two admirals, so 2 possible outcomes.
In the middle seats, arrangements of 7 elements(3 generals, 4 lieutenants). Hence the required number of combination will be given as:
Number of ways = 2*7!
Number of ways = = 100802
Hence the number of ways they can be seated is 10,080 ways.
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Find the sketch the domain of the function f(x,y,z) = ln(144 - 9x² - 16y² - z²)
The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12) which forms an ellipsoid.
What is the domain?Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.
Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, the function 144 − 9x² − 16y² − z² should be greater than 0. So,
144 − 9x² − 16y² − z² > 0
9x² + 16y² + z² < 144
x²/ 4² + y²/ 3² + z²/ 12² < 1
Therefore, the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
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i need help, this is pythagorean theorem !! i do not understand
In mathematics, the Pythagorean theorem is a fundamental relationship in Euclidean geometry between the three sides of a right triangle. State that the area of the square whose side is the hypotenuse
Fórmu
Given f(x)+3f(-x) = 2x+6, find f(x)
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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Simplify the expression. 7x + 6 + 3x -2 -5x
Answer:
5x+4
Step-by-step explanation:
5x + 6 - 2
5x + 4
Two regular polygons are inscribed in the same circle where the first has 1,174 sides and the second has 2,935. If the two polygons have at least one vertex in common, how many vertices in total will coincide?
Answer:
vertices in total will coincide = 1174/2 = 587
Step-by-step explanation:
1st polygon: 1174 sides, 1174 vertex, arc for between 2 vertex= 360°/1174 (arc1)
2nd polygon: 2935 sides, 2935 vertex, arc for between 2 vertex= 360°/2935 (arc2)
360°/1174 = (360°/2935) x (5/2) (every 2.5 arc2 = 1 arc1)
It means every 5 arc2 = 2 arc1, this is the 2nd vertex coincide
vertices in total will coincide = 1174/2 = 587
check: 2935/5 = 587
Equations of Exponential Functions
Given the following table, determine the missing value.
a. 1.15 c. 15
b. 115 d. .15
Please select the best answer from the choices provided
Answer:
A. 1.15
Step-by-step explanation:
I calculated it logically
5+1r-2=9
Please explain step by step
Answer: 6
Step-by-step explanation:
Which measure of center is the most appropriate for the data in Table 1 (Height) in Task 1? Give a reason for your answer.
Answer:
it is 62 or 58 because they are show the most times
Answer:
The answer is 61.
Step-by-step explanation:
20 ounces at $7
17 ounces at x dollars
225 bushels for 3 acres
x bushels for 9.6 acres
9514 1404 393
Answer:
$5.95720 buStep-by-step explanation:
We assume the given ratios are proportional. I find it easiest to write the proportion with the unknown in the numerator.
a) dollars/ounces = x/17 = 7/20
Multiply by the inverse of the coefficient of x to solve.
x = 17(7/20) = 5.95 . . . dollars
__
b) bushels/acres = x/9.6 = 225/3
x = 9.6(225/3) = 720 . . . bushels
PLEASE Help. The answers I got so far are A. 72. B. 301. C 90 and D 252. I am having the most trouble with B and D.
The correct solutions for this question are as:
(A) Bearing of B from A = 72°
(B) Bearing of B from C = 342°
(C) Bearing of A from B = 252°
(D) Bearing of A from C = 293°
Step by step solution:
(A) Bearing of B from A:
= 72° (Given in question)
(B) Bearing of B from C: = 342°
Solution:
As sum of co-interior angles is 180° , i.e. ∠NBC +∠NCB =180°
so, 162° + ∠NCB = 180°
∠NCB = 180°-162°
∠NCB = 18°
reflexive angle NCB =360° - ∠NCB
reflexive angle NCB = 360° - 18°
reflexive angle NCB = 342°
So, bearing of B from C: = 342°
(C) Bearing of A from B: = 252°
Solution:
First extend the line AB to any point (let's say "X")
So, ∠NBX = 72° [BY USING CORRESPONDING ANGLES]
Bearing of A from B = ∠NBX + 180°
Bearing of A from B =72° + 180°
Bearing of A from B =252°
(D) Bearing of A from C: = 293°
Solution:
Bearing of A from C= 360° - (∠BCA + ∠BCN)
Bearing of A from C= 360° - (49° + 18°)
Bearing of A from C= 360° - (67°)
Bearing of A from C= 293°
Important Points for "Bearing of Angles":
A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.
The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.
Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.
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The data in the table represents the value of a savings account at the end of each year for 6 years. The relationship between the increasing years and the increasing value of the account is exponential.
Answer:
1. Constant multiplicative.
2. 1.05.
Step-by-step explanation:
Their savings increase by 1.05x every year.
Solve the equation 5(4x-1.5x) + 12 = 4x- 124 for X
[tex] \sf \: 5(4x -1.5x) + 12 = 4x - 124 \\ \sf \: 5 \times 2.5x + 12 = 4x - 124 \\ \sf \: 12.5x + 12 = 4x - 124 \\ \sf \: 12.5x - 4x = - 124 - 12 \\ \sf \: 8.5x = - 136 \\ \sf \: x = - 16[/tex]
How many tens do u need to make 280
Answer:
28
Step-by-step explanation:
280 divided by 10 = 28
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value for this test statistics is: a. 0.05 b. 0.0228 c. 0.0456 d. 0.025 brainly
Answer:
The appropriate answer is option b (0.0228).
Step-by-step explanation:
The given values are:
Random sample,
[tex]n=100[/tex]
Average length of time,
[tex]\bar{x}=3.1 \ minutes[/tex]
Waiting time,
[tex]\mu=3 \ minutes[/tex]
Standard deviation,
[tex]\sigma=0.5[/tex]
Now,
The test statistics will be:
⇒ [tex]z=\frac{(\bar{x}-\mu)}{\frac{\sigma}{\sqrt{n} } }[/tex]
On substituting the values, we get
⇒ [tex]=\frac{(3.1-3)}{\frac{0.5}{\sqrt{100} } }[/tex]
⇒ [tex]=\frac{0.1}{0.05}[/tex]
⇒ [tex]=2[/tex]
hence,
⇒ [tex]P(z >2 ) = 1 - P(z <2 )[/tex]
By using the table,
⇒ [tex]=1-0.9772[/tex]
⇒ [tex]=0.0228[/tex]
5. Is 1/4 and 4/16 equivalent? Explain your answer.
Answer:
Yes, 1/4 and 4/16 are equivalent
Step-by-step explanation:
1/4 = 0.25
4/16 = 0.25
Jordan is making a wreath that uses different colors of ribbon
Answer:
Step-by-step explanation:
he needs 10 inches of each color to make the wreath
10
+ 10
+ 10
+ 10
= 40
40 inches of ribbon
please be fast and pick an option
Answer:
5/14 * 5/14
Step-by-step explanation:
Yasmeen is setting up a business.
She borrows $5000 from a loan company.
The loan company charges 6% per year simple interest.
How much interest will Yasmeen pay after 3 years?
There are t counters in a box.
Write an expression for the total number of counters.
Answer: 4t
Step-by-step explanation:
You just do t times the amount of boxes you have, which is 4. So you have 4 times t, but in algebra, we don't write the multiplication sign. So the expression would be written as 4t. Yw!
Also please tell me if I was unhelpful/incorrect, thanks!
Which ordered pair is a solution to the inequality
y ≥ 4x-5
(3,0) (3,4) (1,1) (2,1)
Answer:
(1, 1)
Step-by-step explanation:
in the order pair you have (x, y) so if is ( 3, 0) it means is ( x=3, y=0)
substitute in the inequality those x, and y values and see if it checks
y ≥ 4x-5
for ( 3, 0) is 0 ≥ 4*3-5 false
for ( 3,4) is 4 ≥ 4*3-5 false
for (1,1) is 1 ≥ 4*1-5 true because 1 ≥ -1
for (2, 1) is 1 ≥ 4*2-5 false