Answers
Answer:
a = - 2, b = - 1
Step-by-step explanation:
If a polynomial f(x) is divisible by (x + h) then f(- h) = 0
P(x) is divisible by (x + 1), thus P(- 1) = 0 , that is
P(- 1) = (- 1)³ + a(- 1)² - b + 2 = 0 , that is
- 1 + a - b + 2 = 0
a - b + 1 = 0 ( subtract 1 from both sides )
a - b = - 1 → (1)
P(x) is divisible by (x - 2) thus P(2) = 0 , that is
P(2) = 2³ + a(2)² + 2b + 2 = 0 , that is
8 + 4a + 2b + 2 = 0
4a + 2b + 10 = 0 ( subtract 10 from both sides )
4a + 2b = - 10 → (2)
Solve (1) and (2) simultaneously
Multiply (1) by 2
2a - 2b = - 2 → (3)
Add (2) and (3) term by term eliminating the term in b
6a = - 12 ( divide both sides by 6 )
a = - 2
Substitute a = - 2 into (1) and solve for b
- 2 - b = - 1 ( add 2 to both sides )
- b = 1 ( multiply both sides by - 1 )
b = - 1
Related Questions
A circle has a radius of 5 inches. What is the circumference of the circle? Use 3.14 for pi.
185 m
English
Support | Schlogging | PROFPOLICE | Tesale
Answers
Answer:
C =31.4 inches
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
C = 2 * 3.14 * 5
C =31.4 inches
________________________________
Solution,
Radius(r)=5 inches
Circumference of the circle=?
Now,
Circumference of circle= 2 pi r
=2*3.14.5
=31.4 inches.
Hope it helps...
Good luck on your assignment
_______________________________
What is the angle of rotation from figure D to figure D’ ? Assume that the center of rotation is the origin.
A. 270° clockwise
B. 90° clockwise
C. 90° counterclockwise
D. 180° counterclockwise
Answers
Answer:
Option B.
Step-by-step explanation:
We take a point D from the figure attached,
Coordinates for the point D → (-1.5, 3.5)
And coordinates of D' → (3.5, 1.5)
Coordinates of D when rotated about the origin,
Option A. Rotated by 270° clockwise.
Rule to be followed,
D(x, y) → D'(-y, x)
D(-1.5, 3.5) → D'(-3.5, -1.5)
Therefore, Option A. is incorrect
Option B. rotation by 90° clockwise
Rule to be followed
D(x, y) → D'(y, -x)
D(-1.5, 3.5) → D'(3.5, 1.5)
Therefore, Option B. is correct.
Option C. 90° counterclockwise
Rule to be followed,
D(x, y) → D'(-y, x)
D(-1.5, 3.5) → D'(-3.5, -1.5)
This option C is incorrect.
Option D. 180° counterclockwise
Rule to be followed,
D(x, y) → D'(-x, -y)
D(-1.5, 3.5) → D'(1.5, -3.5)
Therefore, option D is incorrect.
Answer:
B. 90 clockwise
Step-by-step explanation:
A new club sent out 195 coupons to boost sales for next years memberships they provided four times as many then to existing members how many coupons that they sent to existing members
Answers
Answer:idk
Step-by-step explanation:
sorry
What is 181.5% of 18?
Answers
Answer:
32.67
Step-by-step explanation:
18% of 181.5 is 32.67, which is much easier to solve than 181.5% of 18. It works flipped over.
The solution of expression is,
⇒ 32.67
We have to given that;
To find the value of 181.5% of 18.
Since, To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Hence, We can simplify as;
⇒ 181.5% of 18
⇒ 181.5/100 × 18
⇒ 1.815 × 18
⇒ 32.67
Thus, The solution of expression is,
⇒ 32.67
Learn more about the percent visit:
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Alice was flying a kite when a gust of wind caught the kite in a tree. Alice is standing 10 feet from the base of the
tree, looking up at her kite at an angle of 25°. If Alice is 5 feet tall, approximately how high is the kite off of the
ground?
A4.66
B 9.66
C 21.45
D 9.23
Answers
Answer:
B. 9.66
Step-by-step explanation:
To find how high the kite is off the ground, we will follow the steps below;
we will use trigonometric ratio to solve the problem. That is;
SOH CAH TOA
sinФ = opposite / hypotenuse
cosФ = opposite / hypotenuse
tanФ = opposite / adjacent
from the diagram below
Ф = 25°
opposite = x
adjacent = 10 feet
The best trig ratio to use is tan
we can now proceed to insert the values into the formula
tanФ = opposite / adjacent
tan 25° = [tex]\frac{x}{10}[/tex]
cross-multiply
x = 10 tan25°
x ≈4.66 feet
height of the kite off of the ground = x + height of Alice
=4.66 + 5
=9.66 feet
Therefore, the kite is 9.66 feet high off of the ground
Pizza is often circular shape and size of the pizza is the length of diameter with included crust. A 16 inch pizza is one with a 16 inch diameter. What is the area of a 16 inch pizza?
Answers
Answer:
≈201 in²
Step-by-step explanation:
Area= π×r²= π×d²/4Area of 16 in pizza= π×16²/4= 3.14× 256/4 ≈201 in²Answer:
201 in²
Step-by-step explanation:
Hope this helps! :)
Juanita rolls a number cube x times. For which value of x are the experimental probability and the theoretical probability most likely to be equivalent? 1, 6, 600, 1,000
Answers
Answer:
1,000
Step-by-step explanation:
The more rolls you make, the closer the experimental and theoretical probabilities get closer together
Answer:
1000
Step-by-step explanation:
The last time Andy went bowling he had a mean score of 158
per game.
After three games Andy has a total score of 473. He thinks he
needs to score over 160 in game four to get a mean score
greater than 158.
(a) Is Andy correct?
Show why you think this.
Show a check of your working.
Your answer:
Answers
Answer:
no
Step-by-step explanation:
suppose he will get exactly the score of 160 in the game four, the mean score this time will be (473+160)/4=158.25
which has already reached the mean score 158 and even higher than it
therefore, his statement is wrong
Find the equation of the line through point (-4,-4) and perpendicular to 2x+3y=3
Answers
2y=3x+4
37
35
Х
x =
What’s the answer?
Answers
Answer:
12
Step-by-step explanation:
use Pythagorean theorem
37^2 = 35^2 + x^2
x= ±[tex]\sqrt[2]{37^2-35^2}[/tex]
x1 = 12
x2= -12 but it is illogical as length cannot be negative
answer: x = 12
Answer: x = 12
Step-by-step explanation:
a^2 + b^2 = c^2
35^2 + b^2 = 37^2
b^2 = 1369 - 1225
b = √144 = 12
A rectangular prism has a width of 5 cm, a height of 8 cm and a depth of 2 cm. What is the volume of the
prism?
Answers
So the volume of the prism would be 80 cubic centimeters
the volume of the rectangular prism is 80 cubic centimeters.
The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the width is 5 cm, the height is 8 cm, and the depth is 2 cm.
Volume = length × width × height
Substituting the given values into the formula:
Volume = 5 cm × 8 cm × 2 cm
Calculating the multiplication:
Volume = 80 cm³
Therefore, the volume of the rectangular prism is 80 cubic centimeters. This means that the prism can hold 80 units of a cubic centimeter, such as water or any other substance.
Learn more about volume here
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Given what is the domain in set notation? {x|x ∈ R, x ≥ 4} {x|x ∈ R, x ≤ 4} {x|x ∈ R, x ≥ 2} {x|x ∈ R, x ≤ 2}
Answers
Answer:
A
Step-by-step explanation:
answer on edg 2020
Wich property is represented by the equation shown below? 6 x 3 = 3 x 6 A) Multiplicative inverse property B) Multiplicative identity property C) Associative property of multiplication D) Commutative property of multiplication
Answers
Answer:
D) Communicative Property of Multiplication
Please give brainliest -3-
Can someone help me with this, I will mark you as brainliest!
Answers
What is the area of the triangle?
8
10
6
units
Answers
Answer:
A = 24 units^2
Step-by-step explanation:
The area of a triangle is given by
A = 1/2 bh
The base is 6 and the height is 8
A = 1/2(6) *8
A = 24 units^2
Dominique is buying water. She needs 2 liters. A half-liter of water costs $2.46. A 250-milliliter container of water costs $1.48. What should Dominique buy so she gets 2 liters at the lowest price? Explain.
Answers
Answer:
[tex]\fbox{\begin{minipage}{15em}A half-liter of water costs 2.46$\end{minipage}}[/tex]
Step-by-step explanation:
Dominique wants to buy [tex]2[/tex] liters of water.
Case 1:
A half-liter of water costs [tex]2.46[/tex].
The [tex]2[/tex] half-liters is [tex]1[/tex] liter => The cost of a liter of water ([tex]A[/tex]) is calculated by multiply the cost of [tex]1[/tex] half-liter by [tex]2[/tex]:
[tex]A = 2.46[/tex] x [tex]2[/tex] = [tex]4.92[/tex]
=> The cost of two liters: [tex]A_{1}[/tex] = [tex]A[/tex] x [tex]2[/tex] = [tex]4.92[/tex] x [tex]2[/tex] = [tex]9.84[/tex] $
Case 2:
A quarter-liter of water costs [tex]1.48[/tex].
The 4 quarter-liters is [tex]1[/tex] liter => The cost of a liter of water ([tex]B[/tex]) is calculated by multiply the cost of [tex]1[/tex] quarter-liter by [tex]4[/tex]:
[tex]B = 1.48[/tex] x [tex]4[/tex] = [tex]5.92[/tex]
=> The cost of two liters: [tex]B_{1} = 5.92[/tex] x [tex]2[/tex] = [tex]11.84[/tex] $
Compare [tex]A_{1}[/tex] and [tex]B_{1}[/tex], the cost of second buying method is more expensive.
=> She should buy the water, in which a half-liter of water costs $[tex]2.46[/tex]
Hope this helps!
:)
What is a constant of proportionality in the equation 3y equals 2x?
Answers
Answer:
y=2/3x (y equals two-thirds x)
Step-by-step explanation:
3y=2x
(divide by 3 on both sides to get just the y value)
3/3y=2/3x
y=2/3x
Find the product:
-2x(-y - 3x + 3)
Answers
Answer:
[tex]=2xy+6x^2-6x[/tex]
Step-by-step explanation:
[tex]-2x\left(-y-3x+3\right)\\\mathrm{Distribute\:parentheses}\\=\left(-2x\right)\left(-y\right)+\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:3\\\mathrm{Apply\:minus-plus\:rules}\\\left(-a\right)\left(-b\right)=ab,\:\:+\left(-a\right)=-a\\=2xy+2\cdot \:3xx-2\cdot \:3x\\\mathrm{Simplify}\:2xy+2\cdot \:3xx-2\cdot \:3x:\quad 2xy+6x^2-6x\\2xy+2\cdot \:3xx-2\cdot \:3x\\2\cdot \:3xx=6x^2\\2\cdot \:3x=6x\\=2xy+6x^2-6x[/tex]
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
algebra applications: find the value of x and y
Answers
Answer:
x = 10°
y = 35°
Step-by-step explanation:
9x + 20 + 7x = 180 (supplementary angles)
16x = 180 - 20
16x = 160
x = 10°
2y = 7x ( opposite angles)
2y = 70
y = 35°
Mr. Hammar is painting his house. He uses a 16 foot extension ladder to reach the top peak of the house. The ladder is positioned 5 feet away from the house. How far up the house does the ladder reach? Round your answer to the nearest tenth.
Answers
Step-by-step explanation:
For every 4 feet that the ladder rises, the bottom of the ladder should be 1 foot away from the wall. If you are going to climb onto a roof, the ladder should extend 3 feet higher than the roof. Also, the upper and lower sections of an extension ladder should overlap to provide stability
If Tim Cook, CEO of Apple wants to make a list of the employees who are above 40, what process he will use? Option: 1.Data query 2.data sorting 3.data compiling
Answers
The space shuttle is accelerated off its launch pad to a velocity of 525 m/s in 18.0 seconds.
What is its average acceleration?
Answers
Answer:
29.17m/s²Step-by-step explanation:
Acceleration is defined as the change in velocity of a body with respect to time.
Acceleration = velocity/time
Given velocity of the space shuttle = 525m/s and time = 18.0seconds
Its average acceleration = 525/18
Its average acceleration (in m/s²) = 29.17m/s²
which answer justifies why 10 1/3= 3^10
Answers
Answer:
they are not equal
Step-by-step explanation:
10 1/3 = 10.33333
3^10 =59049
10.333 does NOT equal 59049
Answer:
Brainliest here!
Step-by-step explanation:
10 1/3 = 10.33333 3333333...
3^10 = 59049
10.333 < 59049
not equal to
Which algebraic expression is a polynomial with a degree of 5?
Answers
A laptop that costs $250 is on sale with a 20% discount. What is the amount of discount? What’s the explanation to do this
Answers
Answer: $50
Step-by-step explanation:
250 x 0.20 = 50
$50 discount
or you pay 80%, so
250 x 0.80 = 200
$200 final cost
$250 original cost - $200 final cost = $50 discount
Answer: 50
Step-by-step explanation:
Discount = 250 x .20 = 50
What is the equation of the line that contains (-5,1) and has a slope of 4
PLEASE HELP
Answers
Answer:
y=4x +21
Step-by-step explanation:
11. The chess club has 50 members. They want to raise $680 for a trip to a competition. The school will give $130. How much must each member pay?
Answers
Answer:
$11
Step-by-step explanation:
Total members = 50 , Raised amount = $680
If school gives $130 then all the 50 members will pay the remaining amount.
Remaining amount to be paid by the 50 members = $680 - $130 = $550
50 members = $550
1 member = $550/50
1 member = $ 11 ( Answer)
In the figure, PA and PB are tangent to circle O and PD bisects angle BPA. the figure is not drawn to scale
Answers
Answer:
C (46)
Step-by-step explanation:
Triangle PAO is congruent to Triangle PBO by Hypotenuse-Leg (I'm assuming you learned this already if you have this question let me know if you haven't). OA and OB are both radius of circle O, making them congruent because all radii are congruent. Also PO is congruent to PO by reflexive.
Angle AOC is the same thing is Angle AOP. Angle POB is congruent to Angle AOP by CPCTC (Congruent Parts of Congruent Triangles are Congruent). Therefore, Angle POB is 46 degrees.
Maria has a jewelry box and wants to increase its size. She decides she will double the length, width and height. How many times
bigger will the volume of the new box be?
2
3
5
8
Answers
Answer:
64 times bigger
Step-by-step explanation:
I will use random values for this explanation to make it more understandable.
Lets say the length of the box is 1 inch, width is 1 inch, and height is 1 inch.
The volume would be l*w*h = 1*1*1 = 1 cubic inch
If the dimensions were 4 times bigger, the length, width and height would all be 4 inches.
4*4*4 = 64 cubic inches, which is 64 times bigger than the smaller box with a volume of 1 cubic inch.
Hope this answer helped! :)
Step-by-step explanation:
Which equation represents the line that is parallel to 5x + y = 13 and
passes through the point (15, - 31)?
Answers
Answer:
y=-5x+44
Step-by-step explanation:
