Please help me Please this is due today
Show that p(x) is divisible by q(x) in each of the
following cases.
Answers
Answer:
See Below.
Step-by-step explanation:
By the Factor Theorem, if we divide q(x) into p(x) and the resulting remainder is 0, then p(x) is divisible by q(x) (i.e. there are no remainders).
Problem 1)
We are given:
[tex]p(x)=x^3+3x^2+3x+1\text{ and } q(x)=x+1[/tex]
We should find the remainder when dividing p(x) and q(x). We can use the Polynomial Remainder Theorem. When dividing a polynomial p(x) by a binomial in the form of (x - a), then the remainder will be p(a).
Here, our divisor is (x + 1) or (x - (-1)). So, a = -1.
Then by the Polynomial Remainder Theorem, the remainder when performing p(x)/q(x) is:
[tex]p(-1)=(-1)^3+3(-1)^2+3(-1)+1=0[/tex]
The remainder is 0, satisfying the Factor Theorem. p(x) is indeed divisible by q(x).
Problem 2)
We are given:
[tex]p(x)=x^3-2x^2+6x-27\text{ and } q(x)=x-3[/tex]
Again, use the PRT. In this case, a = 3. So:
[tex]p(3)=(3)^3-2(3)^2+6(3)-27=0[/tex]
It satisfies the Factor Theorem.
Problem 3)
We are given:
[tex]p(x)=x^n-10^n\text{ and } q(x)=x-10[/tex]
Use the PRT. In this case, a = 10. So:
[tex]p(10)=(10)^n-10^n=0[/tex]
It satisfies the Factor Theorem.
Since all three cases satisfy the Factor Theorem, p(x) is divisible by q(x) in all three instances.
Related Questions
Adam went to McDonald's and bought a Big Mac and 2 small fries. Adam spent
$10.93. The Big Mac cost 5.99. How much did the two small fries cóst each? Write
an equation to match the problem. Use f as the variable. *
Answers
Answer:
the answer is 4.94 because you subtract 10.93-5.99
Over the next two days, Benton Employment Agency is interviewing clients who wish to find jobs. On the first day, the agency plans to interview clients in groups of 6. On the second day, the agency will interview clients in groups of 8. If the employment agency will interview the same number of clients on each day, what is the smallest number of clients that could be interviewed each day?
I DONT NEED LINKS PLEASE I NEED A ANSWER
Answers
A company sells fruit smoothies in two sizes: 6 ounces and 20 ounces. You know that a 6-ounce bottle contains 96 milligrams of sodium. If the amount of sodium is directly proportional to the fluid ounces of smoothie, how many milligrams of sodium does a 20-ounce bottle contain?
And can yall put an explanation please
Answers
Answer:
320 milligrams of sodium
Step-by-step explanation:
Create a proportion where x is the milligrams of sodium a 20 ounce bottle has:
[tex]\frac{96}{6}[/tex] = [tex]\frac{x}{20}[/tex]
Cross multiply and solve for x
1920 = 6x
320 = x
So, a 20 ounce bottle will have 320 milligrams of sodium
PLZ HELP
-7x - 2y = 14
6x + 6y = 18
Answers
Answer:
x=-4, y=7
Step-by-step explanation:
Answers : x = (15/6), y =
(1/2).
Step-by-step explanation:
Explanation: To solve this equation through elimination, you need to isolate one of the variable. You can isolate the y variable since the x variables can be subtracted and go away. Add the two equations to get rid of one variable. (6x + 6y = 18) + (-6 + 2y = -14) = (8y = 4). Now you need to solve for y. y = 4/8, y = 1/2. Now, plug the y back into one equation and solve for x. 6x + 6(1/2) = 18. 6x + 3 = 18. 6x = 15. x = 15/6. Plug the two answers back in to the equation to check your answers. 6(15/6) + 6(1/2) = 18, 15 + 3 = 18. -6(15/6) + 2(1/2) = -14, -15 + 1 = -14.
Which expression is equivalent to 2(x2 – 1) + 3x(x – 4)?
(1) 5x2 – 5
(3) 5x2 – 12x – 1
(2) 5x2 - 6
(4) 5x2 – 12x – 2
Answers
The equivalent expression of 2(x² – 1) + 3x(x – 4) is 5x² - 12x - 2
How to find equivalent expression?
The equivalent expression of the expression can be found as follows;
2(x² – 1) + 3x(x – 4)
open the brackets
2x² - 2 + 3x² - 12x
Therefore, let's combine like terms
2x² + 3x² - 12x - 2
Let's do the arithmetic for like terms
2x² + 3x² - 12x - 2
5x² - 12x - 2
Therefore, the equivalent expression of 2(x² – 1) + 3x(x – 4) is 5x² - 12x - 2
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You are making a fruit salad for a family dinner and only have $32 to spend making it. Grapes(x) cost $4 per pound and watermelon(y) cost $2 per pound.
Model the problem situation with a linear inequality.
Answers
Answer:
this is easy. you just need to write and equation that shows how many pounds of each fruit you can buy in total (x for 1 pound of grapes and y for 1 pound of watermelon). this would make the equation 32 = 4x + 2x.
which expression represent a number that is one fourth as great as 10 - 2
Answers
Answer:
5
Step-by-step explanation:
Answer:
vyvjkyivfiytgigtf 7igggg8t79
Step-by-step explanation:
Show that each statement is false by providing a comterexample
Answers
Answer:
Step-by-step explanation:
One
Length = 16
Width = 1
Two
<P = 120
<Q = 30
<R = 30
Three
xy = 45
yz = 1
Four
<1 = 45
<2 = 45
The solid below is made from 1 meter cubes. Find its surface area. Please help & no links!!
Answers
Answer:
48 meters
Please Mark Brainliest, Hope It Helps
Step-by-step explanation:
A=2(wl+hl+hw)
A=2 ( (2)(5)+(2)(5)+(2)(2) )
A= 2(24)
A=48
The school is raising money by selling wrapping paper. Each roll of paper earns the school $4,00. If the
PTA would like to raise a minimum $600.00, then how many rolls of wrapping paper must be sold?
I will mark Brainiest and I will give you a hundred points.plzzz
Answers
Answer:
A: 600=1.05x
B: 600=1.06x
Step-by-step explanation:
:-)
Help me for Brainlyiest ong provide proff
Answers
Answer:
5-(-7)=5+7
Step-by-step explanation:
When there are two negative signs, that means it switches into a plus sign.
If this helps please mark as brainliest would really appreciate it
Plz give me the answeeerrrr
Answers
Answer:
cannot see properly,take it again and send
Answer:
first mark me as a brainleast forst
solving exponential equations 5^x-1 = 125
Answers
Answer:
x = 4
Step-by-step explanation:
5^(x-1) = 125
log₅(5^(x-1)) = log₅(125)
x-1 = 3
x = 4
The volume of a cylinder is 256 in height of the cylinder is 1 in. What is the radius of the cylinder?
Answers
Answer:
5.903 for radius
Annie's homemade chili recipe calls for 2 pounds of ground beef for every 5 cans of beans. How many pounds of ground beef does she need for 1 can of beans? *
Answers
If Laura were able to find a 0 iron, about how far could she hit it?
Answers
Answer:
I got 219 but I'm not sure that's the answer.
Step-by-step explanation:
√-1
factor completely without any 'i'
Answers
Answer:
the root of -1 is -1
Step-by-step explanation:
When multiplied by itself, the root is typically a specified number of times gives a specified number or quantity. So -1 × -1 = -1
So there you go
A ball falls vertically after being dropped.
The ball falls a distance dmetres in a time of t seconds.
dis directly proportional to the square of t.
The ball fals 20 metres in a time of 2 seconds.
(a) Find a formula for din terms of t.
Answers
Answer:
d = 5t^2
Step-by-step explanation:
"d is directly proportional to the square of t"
d = kt^2
To find k use
"The ball falls 20 metres in a time of 2 seconds."
20 = k(2^2)
20 = k(4)
Divide both sides by 4
5 = k
Using k = 5 the formula becomes
d = 5t^2
Check all statements that are true,
1) In Euclidean geometry, the sum of the angle measures of a triangle is equal to 180°
2) In both Eudidean and spherical geometry, a triangle can have two right angles.
3) In both Euclidean and spherical geometry, through any point not on a given line there is a line
parallel to the given line.
4) In spherical geometry, some quadrilaterals are parallelograms.
5) In spherical geometry, any two given lines must intersect.
6) None of these are true.
Answers
4) In spherical geometry, some quadrilaterals are parallelograms.
In spherical geometry, some quadrilaterals are parallelograms is a true statement. Thus option D is correct.
What is spherical geometry?Instead of the sort of geometries studied in trigonometry or solid geometry, the research of shapes on a structure's surface. White lines are large rounds in spherical, therefore any three layers intersect at two locations.
A spherical quadrilateral is a bounded surface that is homomorphic to a compact disk. It has four distinct local maxima called extremities, a Riemannian measurement that has constant curvature 1 everywhere else, aside from the corners, and or the demarcation arcs between it intersections. a dome shape. the collection of rectangular shapes with specified angles.
Therefore, option D is the correct option.
Learn more about spherical geometry, Here:
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57% of a number is 216.6.
What is the original number?
Answers
Answer:
340.062
Step-by-step explanation:
Answer:
163.4
Step-by-step explanation:
Patty made a banner that has an area of 112 square inches. The length and width of the banner are whole numbers. The length is 7 times greater than the width. What are the dimensions of the banner?
Answers
Answer:
The width of the banner is 4 inch and the length of the banner is 28 inch
Step-by-step explanation:
Given
Length is seven times its width
Let the width be "X", then length would be 7X
The banner is of rectangular shape.
Its area is 112 square inches
[tex]X* 7X = 112\\7X^2 = 112\\X^2 = 16\\X = 4[/tex]
Hence, the width of the banner is 4 inch and the length of the banner is 4*7 i.2 28 inch
please help! rate of change solving for Y, linear relationships
Answers
HELP ME
At a concession stand 6 hot dogs cost $6.72. At this rate, how much would 8 hot
dogs cost, in dollars and cents?
Can u pls explain how ty!
No links!!!!
Answers
1.12 is the cost of 1 hot dog
1.12 x 8=8.96
(5-2i)(1-3i) solve in steps
Answers
5*1-5*3i-1*2i+2i*3i
5-15i-2i+6i^2
Remember i^2=-1
5-15i-2i+6(-1)
5-15i-2i-6
Combine like terms
-1-17i
Comprei 15 rolos para uma instalação elétrica gastei 3/8 de 1 rolo quantos trabalhos eu posso realizar com o material comprado?
Answers
Responder:
40 instalações
Explicação passo a passo:
Rolos totais de instalações adquiridas = 15
Rolos usados por instalação = 3/8 de um rolo
O número de instalações que os 15 rolos podem durar pode ser calculado assim:
1 instalação = 3/8 rolo
x instalações = 15 rolos
Multiplicação cruzada
3/8 x = 15
x = 15 ÷ 3/8
x = 15 * 8/3
x = 5 * 8
x = 40
What is the distance between two points with coordinates (12,0) and (0,35)
Answers
Answer:
caca I I I ii I I I I I I I I I I I I I I I.
Answer:
37
Step-by-step explanation:
-use the distance formula
d²= (x2-x1)²+(y2-y1)² where d is the distance and x1 =12, x2=0, and y1=0, y2=35
d² = (0-12)² + (35-0) ²
d² = (-12)² + 35² = 144+ 1225 = 1369
d =√1369 = 37
Jorge compre una televisión a un costo de 3450 el cual incluía el 40% de descuento cual seri el precio original de la televisión?
Answers
Answer:
Precio original= $5.750
Step-by-step explanation:
Dada la siguietne información:
Precio de venta= $3.450
Descuento= 40%
Para calcular el precio original (previo descuento), debemos usar la siguiente formula:
Precio original= precio de venta / (1 - porcentaje de descuento)
Precio original= 3.450 / (1 - 0,4)
Precio original= $5.750
Mhanifa please help!!! This is due soon!
Answers
Answer:
Use the Pythagorean theorem
a² + b² = c² - right trianglea² + b² > c² - acute trianglea² + b² < c² - obtuse trianglec- longest side#9
5²+12² vs 13²169 = 169Right triangle#10
5² + 7² vs 8²73 > 64Acute triangle#11
2² + 10² vs 11²104 < 121Obtuse triangle#12
(√8)² + 4² vs 6²24 < 36Obtuse triangleWhat is the volume of the sphere in terms of ?
V =
.7 in 3
6 in.
Answers
Answer:
[tex]V = 288\pi[/tex]
Step-by-step explanation:
Given
[tex]r = 6[/tex]
Shape: Sphere
Required
The volume
The volume of a sphere is calculated using;
[tex]V = \frac{4}{3}\pi r^3[/tex]
Substitute 6 for r
[tex]V = \frac{4}{3}\pi * 6^3[/tex]
[tex]V = \frac{4}{3}\pi * 216[/tex]
Divide 216 by 3
[tex]V = 4\pi * 72[/tex]
[tex]V = 288\pi[/tex]
HELP APPRECIATED
WILL GIVE BRAINLIEST:)
Answers
Answer:13 1/8
(Decimal: 13.125)
Step-by-step explanation:
Answer:18 5/8
Step-by-step explanation:
Rewriting our equation with parts separated
=
10
+
1
2
+
8
+
1
8
Solving the whole number parts
10
+
8
=
18
Solving the fraction parts
1
2
+
1
8
=
?
Find the LCD of 1/2 and 1/8 and rewrite to solve with the equivalent fractions.
LCD = 8
4
8
+
1
8
=
5
8
Combining the whole and fraction parts
18
+
5
8
=
18
5
8