The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factors is f(c)=(x-1)(x+7)(4x-5)
To express the polynomial as a product of linear factors we have to find the zeros of the polynomial.
Here,
We have Given that f(c)=4x^3+19x^2-58x+35 and -7 is a zero of f(k) and we need to find the polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor
Now,
-7 is a zero of f(k)
i.e. (x+7) is a linear factor of f(k)
now,
we will find out the linear factor of f(c)
so,
f(c)=4x^3+19x^2-58x+35
f(c)=4x^3-4x^2+23x^2-23x-35x+35
f(c)=(x-1)(4x^2+23x-35)
f(c)=(x-1)(4x^2+28x-5x-35)
f(c)=(x-1)(4x(x+7)-5(x+7))
f(c)=(x-1)(x+7)(4x-5)
Hence,
The polynomial f(c)=4x^3+19x^2-58x+35 as a product of linear factor is f(c)=(x-1)(x+7)(4x-5)
Thus,
the linear factor of given polynomial is (x-1)(x+7)(4x-5)
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Consider the following system of two linear equations:
4y + 3x = 0
4y - x = 16
What is the point of intersection?
Answer: The two lines intersect at (-4,3)
Step-by-step explanation:
So our first step would be to turn both of these into standard slope-intercept form.
1.)
4y + 3x = 0
4y = -3x
y = -3/4x
2.)
4y - x = 16
4y = x + 16
y = 1/4x + 4
Now that we have our 2 equations, y = -3/4x and y = 1/4x + 4 we can graph them to get an intersection at (-4,3)
someone help please ty
The percentage reduction of the jacket is 20 percent.
How to find the percentage reduction of the jacket?Percentage decrease or reduction means subtracting a given percentage of a value from the original value.
Therefore, the jacket cost 80 dollars and it is reduced to 64 dollars.
The percentage reduction of the jacket can be calculated as follows:
% reduction = (Decreased Value / Original Value) × 100
Decreased value = 80 - 64 = 16
Original Value = 80
% reduction = 16 / 80 × 100
% reduction = 1600 / 80
% reduction = 20%
Therefore, the percentage reduction is 20%.
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PLS HELP IF U ARE GOOD AT MATH
Game Station 2: Amazing Race- Each team has to match 9 of the 20 banners with the word “Hello” in different languages with the 9 countries that speak that language
A. Determine the number of ways of selecting and matching nine banners with a country.
B. Determine the number of ways of selecting nine banners without having to match them with a country.
combinations problem btw
The number of ways to select the banners is given as follows:
a. Matching with the country: 362,880.
b. Not matching with the country: 60,949,324,800
How to select the banners matching the country?To select the banners matching the country, only the nine countries are chosen, and then the specific banner regarding the country is chosen, thus the arrangements formula is used.
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
Hence for item a the total number of outcomes is the factorial of nine, which is the number of countries, is given as follows:
Total = 9! = 362,880.
If the country does not have to be matchedThen just nine banners are taken at random from a set of 20. The order is important, hence the permutation formula is used.
The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 9 banners are selected from a set of 20, hence the number of ways is:
N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.
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Consider the ways the function , the cost of the shoes using the coupon, and the function , the cost of the shoes using the discount, can be combined to answer the following question. Which function could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost ?
The function that could be used to represent the total cost of the shoes by applying the $15 coupon first and the 20% member discount second for original cost, using proportions, is of:
C(x) = 0.8(x - 15).
What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially division and multiplication, to find the desired amounts in whichever context of the problem.
The value of shoe is given as follows:
x.
The discounts are given as follows:
$15 off coupon: x - 15.20% member discount: 0.8(x - 15) -> as the discount of 20% means that 80% of the original price will be paid.Hence the function that gives the total cost paid is presented as follows:
C(x) = 0.8(x - 15).
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Question 6 (1 point)
Consider the sequence defined by the recursive formula
AN=2AN-1 -3AN-2
with A₁ = -1, A2 = 1.
Find A8
A.12
B.-14
C.16
D.-17
For the given recursive formula of the sequence , the value of A₈ = -17.
As given in the question,
Recursive formula of the sequence is given by,
Aₙ = 2Aₙ₋₁ - 3Aₙ₋₂
And the value of
A₁ = -1 , A₂ = 1
Substitute the n = 3 , 4, 5, 6, 7, 8 in the recursive formula to get the value of A₈ we have,
A₃ = 2A₂ - 3A₁
= 2(1) -3(-1)
= 5
A₄= 2A₃ - 3A₂
= 2(5) - 3(1)
= 7
A₅ = 2A₄ - 3A₃
= 2(7) - 3(5)
= -1
A₆ = 2A₅ - 3A₄
= 2(-1) - 3(7)
= -23
A₇ = 2A₆ - 3A₅
= 2(-23) - 3(-1)
= -43
A₈ = 2A₇ - 3A₆
= 2(-43) - 3(-23)
= -17
Therefore, for the given recursive formula of the sequence , the value of A₈ = -17.
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DETERMINE THE TANGENT TO CIRCLE X²+y²=9 WHICH ARE PARALLEL To Y = √3x
[tex]2x+y+3\sqrt 5=0[/tex]
Step-by-step explanation:
hope this helped
Suppose that the function fis defined, for all real numbers, as follows.
-2 if x #2
4 if x = 2
Find f(-1), f(2), and f(5).
f(-1) =
f(2) =
ƒ (5) =
For the given defined function f(x) for all real numbers , value of required function are as follow:
f(-1) = -2 , f(2) = 4 and f(5) = -1.
As given in the question,
Function is defined as follow for all the real numbers,
f( x ) = -2 , if x ≠ 2
f(x) = 4 , if x =2
Values of the required function is given by :
f ( -1 ) for the required function x = -1 which is not equal to 2.
Hence , f( -1 ) = -2
f ( 2 ) for the required function x = 2 which is equal to 2.
Hence , f( 2 ) = 4
f ( 5 ) for the required function x = 5 which is not equal to 2.
Hence , f(5 ) = 4.
Therefore, for the given defined function f(x) for all real numbers , value of required function are as follow:
f(-1) = -2 , f(2) = 4 and f(5) = -1.
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I need the correct answer to this question
During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.
At the progressive era the citizens was given by a more direct voice in government because of the three principles they are initiative ,referendum and recall.
Initiative:
Proposed law with backing can be put on the ballot at election,in that case the petitions must be approved with valid signatures.
Referendum:
plebiscite is a kind of referendum in which meaning decree of the people it depends on nature of advisory called as referendum.
Recall:
Recall defines that voters may remove a public official from office that must be before the expiration.
Therefore During the progressive era many state and local governments adopted initiative referendum and recall together these procedures gave citizens a more direct voice in government.
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(Multiplying and Dividing with Scientific Notation MC)
How many times larger is 7 x 105 than 2 x 10³?
Answer:
1,265
Step-by-step explanation:
10^3=1000*2=2000
105*7=735
2000-735
The Problem
The school band is making a large banner for its annual fall concert. After the
band members worked for one hour, the band director entered the room and
asked how many feet long the completed banner would be. The trombone
section leader replied, "We're not sure. The trombone section and the
clarinet section work at different rates, but we are sure that the length of the
banner will be 40 feet and 1/2 the total banner's length."
How long will the banner be?
Answer:20
Step-by-step explanation:
Find the area of the shaded region in the figure below, if the radius of the outer circle is 12 and the radius of the inner circle is 2. Keep your answer in terms of π.
What is 5×5 Please give me the answer show your work
Answer:
It is the method by multiplication
Step-by-step explanation:
5×5=25
Learn at brainlyPlease help. The question is in the attached image
∠G+∠H+∠J=180 and ∠K+∠L+∠M=180 from the angle sum property of triangle, ∠H=∠L (3rd Angle Theorem) and ∆GHJ≅∆KLM from ASA congruency theorem.
In the given question we have to prove ∆GHJ congrurnce ∆KLM.
Given that: ∠G≅∠K, ∠J≅∠M, [tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex].
As given that;
∠G≅∠K
∠J≅∠M
[tex]\over{HJ}[/tex] ≅ [tex]\over{LM}[/tex]
So from the angle sum property of triangle
∠G+∠H+∠J=180................(1)
∠K+∠L+∠M=180.................(2)
Now equation equation 1 and 2
∠G+∠H+∠J=∠K+∠L+∠M
As we know that ∠G=∠K, ∠J=∠M
So now the expression is
∠G+∠H+∠J=∠G+∠L+∠J
After solving ∠H=∠L (3rd Angle Theorem)
Since, ∠H=∠L, HJ=LM and ∠G=∠K, so from the theorem Angle Side Angle(ASA) congruency,
∆GHJ≅∆KLM
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help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
f(x) = 3(x +1)² +2
Step-by-step explanation:
You want the equation in vertex form of the parabola 3x² after its vertex is translated to (-1, 2).
Vertex form equationThe given form is the "vertex form" of the equation for a parabola. That is, in the form ...
f(x) = a(x -h)² +k
the value of 'a' is the leading coefficient, the scale factor, and the values of h and k are the x- and y-coordinates of the vertex.
ApplicationGiven that the scale factor of the desired parabola is a=3, and the desired vertex is (h, k) = (-1, 2). we can fill in these values in the equation to get ...
f(x) = 3(x -(-1))² +2
f(x) = 3(x +1)² +2
Help please tough question
I need assistance with this math assignment
The value at which acceleration is zero is t = 5/3
How to determine the value of t at which acceleration is zero?Acceleration is defined as the rate at which velocity changes with time, in terms of both speed and direction
Given: the equation of motion, velocity, s = t⁶ - 2t⁵
Since acceleration is the rate at which velocity changes with time. You need to differentiate the velocity with respect to time. Thus:
ds/dt = 6t⁵ - 10t⁴ (Note: ds/dt is the acceleration)
Also, acceleration is equal to zero. That is:
6t⁵ - 10t⁴ = 0
6t⁵ = 10t⁴
6t = 10
t = 10/6 = 5/3
Therefore, the value of t at which acceleration is zero is t = 5/3
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what is the value of 36x - 8y² when x = 3 and y = -6
can you add the explanation?
Answer:
-180
Step-by-step explanation:
You would plug in x=3 and y=-6 into the equation
So, the first part would be 36x when x=3, 36(3)=108
The second part would ne -8y^2 when y=-6 (-6 squared is 36), -8(36)=-288
Putting these together, you get 108-288 which is -180
Answer: -180
hops this helps
have a good day
Step-by-step explanation:
pls help ill give brainliest if right
Answer:
Step-by-step explanation:
{x,y}={0,-3}
Select all that apply. If 2x²-6x=0, then 2x = 0 x + 1 = 0 x - 3 = 0 x - 6 = 0
Answer:
x-3
Step-by-step explanation:
2x²-6x=0
divide both sides by x
2x²/x -6x/x=0
2x-6=0
2x=6
x=6/2
x=3
or (x-3)
Seven more than the product of a number and 4 equals 2.
Answer:
-5/4
Step-by-step explanation:
Step 1: Convert to algebraic equation.
4x +7 = 2
Step 1: Subtract 7 from both sides.
4x +7 −7 = 2 −7
Step 2: Divide both sides by 4.
(4x /4) = (-5 /4)
Step 3: Get your answer!
x = -5/4
Answer:
x = -1.25
Step-by-step explanation:
A number = x
7 + 4x = 2
Subtract 7 on both sides
4x = -5
Divide both sides by 4
x = -1.25 OR -5/4
A bike wheel has a diameter of 42 inches. If a rider is traveling 110 feet per minute,how many revolutions does the bike wheel make in 1 minute
The bicycle wheel performs 10 revolutions every minute
What is a revolution?A revolution in math is a full rotation, or a complete, 360-degree turn. In a 360-degree rotation, the object starts and ends in the same position. A mathematical revolution can be visualized when a top spins.
The bicycle wheel makes 1 complete revolution which is equal to the circumference of the wheel = πD
but D = diameter = 42 inches, converting inches to feet
12inches is 1 foot, then 42 inches = 42/12 = 7/2 inches
Also circumference = 22/7 x 7/2 = 11 feet/rev
Also if the rider travelled 110 feet per minute.
Then the wheel's revolution per minute = 110/11
= 10 rev/minute
In conclusion the bicycle wheel revolves 10 times every minute
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8. K is the midpoint of JL. If JL = 13x – 9 and JK = 28, find the value of x.
The value of x is 5 when the line is JL and the midpoint of the JL is K.
Given that,
The line is JL and the midpoint of the JL is K.
JL= 13x-9 and JK= 28.
We have to find the value of x.
The midpoint is the point on a line that connects two points that is exactly in the middle of the line.
We know that,
JL= JK+ JK
JL=2JK
13x-9 = 2×28
13x-9= 56
13x= 56+9
13x= 65
x=65/13
x=5
Therefore, The value of x is 5 when the line is JL and the midpoint of the JL is K.
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Which equations are equivalent to Negative one-fourth (x) + three-fourths = 12 Select all that apply. (StartFraction negative 4 x over 1 EndFraction + three-fourths = 12 Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12 StartFraction negative x + 3 over 4 EndFraction = 12 One-fourth (x + 3) = 12 (StartFraction negative x over 4 EndFraction + three-fourths = 12
Answer:
negative x over 4 + three-fourths = 12
Answer:
Step-by-step explanation:
(StartFraction negative x over 4 EndFraction + three-fourths = 12
Determine whether the relation represents y as a function of x.
y = x^2
The relation y = x² represents y as a function of x because every x-value returns a unique y-value.
Is the relation a function?Using the definition of a function, y=x² is a function because you will only get one unique y-value for each x-value in your domain.
The vertical line test is a quick check you can perform. The function y=x² is a parabola, and if you draw vertical lines anywhere on it, they will only cross the parabola once.
As a result, it is a function. A circle is not an example of a function because a vertical line drawn on a circle crosses at two different points.
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Will give brainliest!
Answer:
9: 71 , 10: 110, 11: 52
Step-by-step explanation:
the sum of angles in a triangel is 180°
so for 9:
180 = 78 + 31 + x
180 - 78 - 31 = x = 71
it's a sharp triangel because all angles are smaller than 90°
you can calculate the angles of 10 and 11 the same way
which gives 10: 110°
this is a stump triangel because there s an angle greater than 90°
The last one is a right triangel because it has a 90° angle (marked with the square)
What is the equation of a line that is perpendicular to the line y = 1/2x + 2 and passes through the point (–4, 1)?
The equation of line that is perpendicular to the line y = 1/2x + 2 is y = -2x - 7
Equation of Perpendicular LineA perpendicular line is a straight line through a point. It makes an angle of 90 degrees with a particular point through which the line passes. Coordinates and line equation is the prerequisite to finding out the perpendicular line.
The equation of perpendicular line is given as
(y - y₁) = m(x - x₁)
m = slope of the line.
But the slope of a perpendicular line is given as
m₁m₂ = -1
m₁ = 1/2, m₂ = ?
1/2m₂ = -1
m₂ = -2
The new slope is -2.
Substituting the values into the equation above,
(y - y₁) = m(x - x₁)
y - 1 = -2(x - (-4))
y - 1 = -2x - 8
y = -2x - 7
The new equation is y = -2x - 7
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Use prime factorization to rewrite 156 +36 as a product of the GCF and a sum of numbers. Enter the correct numbers in the boxes.
PLEASE HELP THIS IS DUE TOMORROW
Using prime factorization to rewrite 156 +36 as a product of the GCF and a sum of numbers will be 12(13 + 3).
What is prime factorization?Prime factorization simply means the process of writing all numbers based on the product of their prime.
In this case, it's important to note that:
156 = 13 × 12
36 = 3 × 12
Therefore, 156 + 36 will be:
= 12(13 + 3)
This illustrates the numbers.
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Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
(-8,-2) and (12,10)
HELP!!!!!
The distance between the points, (-8, -2) and (12, 10), is 23.3
Calculating the distance between two pointsFrom the question, we are to determine the distance between the two given points.
From the given information,
The points are (-8, -2) and (12, 10)
The distance between two points in given by the formula
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where d is the d is the distance between the points
Thus,
d = √[(12 - (-8))² + (10 - (-2))²]
d = √[(12 + 8)² + (10 + 2)²]
d = √[(20)² + (12)²]
d = √[400 + 144]
d = √[544]
d = 23.3
Hence, the distance is 23.3
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Angles W and X are complementary. Determine the degree measure of ∠W if m∠X = 53.4°.
36.6°
63.3°
90°
126.6°
Answer:
∠W = 36.6°
Step-by-step explanation:
Hello!
If angles are complementary, it means that they add up to 90°.
Since the measure of Angle X is 53.4, we can find measure of Angle W by subtracting 53.4 from 90.
Solve for WW = 90° - XW = 90° - 53.4°W = 36.6°The value of W is 36.6°.
There are 500 sheets of paper in one ream. The counter on a copier says that 23,500 copies have been made. How many reams of paper were used?
Answer:
All you simply do is divide 23,500 by 500....that is equal to 47. So 47 is the answer
Step-by-step explanation:To find out how many reams were used, all we have to do is divide 23,500 by 500.
This gives us: 47 reams