Answer:
Step-by-step explanation:
Polynomial f(x) has the following conditions: zeros of -4 (multiplicity 3), 1 (multiplicity 1), and with f(0) = 320.
The first part zeros of -4 means (x+4) and multiplicity 3 means (x+4)^3.
The second part zeros of 1 means (x-1) and multiplicity 1 means (x-1).
The third part f(0) = 320 means substituting x=0 into (x+4)^3*(x-1)*k =320
(0+4)^3*(0-1)*k = 320
-64k = 320
k = -5
Combining all three conditions, f(x)
= -5(x+4)^3*(x-1)
= -5(x^3 + 3*4*x^2 + 3*4*4*x + 4^3)(x-1)
= -5(x^4 + 12x^3 + 48x^2 + 64x - x^3 - 12x^2 - 48x - 64)
= -5(x^4 + 11x^3 + 36x^2 + 16x -64)
= -5x^3 -55x^3 - 180x^2 - 80x + 320
Answer:
Step-by-step explanation:
-4 is a root for 3 times and 1 is root for once
so (x+4)^3 * (x-1) is part of f(x)
the constant term there is 4^3*(-1)=-64
so there is a multiplier of 320/-64=-5
f(x) = -5 * (x+4)^3 * (x-1)
The graph below has the same shape as the graph of G(x) = x, but it is
shifted three units to the left. Complete its equation. Enter exponents using
the caret (-); for example, enter x as x^4. Do not include "G(x) =" in your
answer.
G(x) =
Answer:
G(x) = x+3
Step-by-step explanation:
The equation of the graph is G (x) = (x - 3)⁴
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A relation between a set of inputs having one output each is called a function.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The graph of function G (x) is shown in image.
Here, the graph is 3 units left to function F (x) = x⁴.
The equation of the graph is G (x) = (x - 3)⁴
Hence, the equation of the graph is G (x) = (x - 3)⁴
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Find the missing term in the pattern.
Answer:
20
Step-by-step explanation:
If the probability that an event happens is 0.76, what will be the probability that the event will not happen?
Answer:
24% or 0.24
Step-by-step explanation:
100% or 1 minus 76% or 0.76. That makes 24% or 0.24.
To answer the question you should prob just put in 0.24.
express ratio as a fraction in it's lowest terms.48s to 5minutes
Answer:
4/25.
Step-by-step explanation:
We need to have the 2 values in the same unit so:
converting minutes to seconds:
5 mins = 5*60 = 300 seconds.
The require fraction =
48/300
The GCF of 48 and 300 is 12 so we have:
48/12 / 300/12
= 4/25
The required fraction of 48 seconds to 5 minutes is 4 / 5 minutes.
Given that,
To express the ratio as a fraction in its lowest terms.48s to 5 minutes.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
60 second = 1 minute
1 second = 1 / 60 minute
multiply both sides by 48
48 second = 48 / 60 minute
48 second = 4 / 5 minute
Thus, the required fraction of 48 seconds to 5 minutes is 4 / 5 minutes.
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: Use the image to complete the equation below.
Vertically opposite angles are equal.
So,
(11y - 36)° = 63°
=> 11y - 36 = 63
Answer:
11y-36=63
Step-by-step explanation:
use the concept of vertically opposite angle
What is the range of the function shown in the graph?
у
A
8
6
2
2
X
8
- 6
2
4
6
8
2
4
6
ce
I
OA. -5 < y < 0
OB -00
O c. - < y < -5
-
5
Answer:
-∞ <y<5
Step-by-step explanation:
The range of the graph is the values that y can take. The graph can go from negative infinity to 5
-∞ <y<5
Can someone give me the letter to all answers 1-4 or at least one 3
Answer:
hello there here are your answers:
1) a- 12, 18, 24, 30, 36
2) b- 31
3) a-communitive property of addition
4) a- 6a
Step-by-step explanation:
1: go through all the numbers and add 6 like 12+6=16 etc.
2: the common difference is 4 so 27+4 =31
3: communitive property because you can change the number in any order and still get the same sum
4: 6a because only 24ab has a b in it
1. Find the exact value of sin( a−B), given that sin a=−4/5 and cos B=12/13, with a in quadrant III and B in quadrant IV.
2. Find all real numbers in the interval [0,2pi) that satisfy the equation.
3sec^2 x tan x =4tan x
3. Simplify the following trigonometric expressions, using identities as needed:
sin(x)/1−cos(x) + 1−cos(x)/sin(x)
(1) Recall that
sin(x - y) = sin(x) cos(y) - cos(x) sin(y)
sin²(x) + cos²(x) = 1
Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have
• sin(α) < 0 and cos(α) < 0
• sin(β) < 0 and cos(β) > 0
Solve for cos(α) and sin(β) :
cos(α) = -√(1 - sin²(α)) = -3/5
sin(β) = -√(1 - cos²(β)) = -5/13
Then
sin(α - β) = sin(α) cos(β) - cos(α) sin(β) = (-4/5) (12/13) - (-3/5) (-5/13)
==> sin(α - β) = -63/65
(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,
sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)
==> tan²(x) + 1 = sec²(x)
Rewrite the equation as
3 sec²(x) tan(x) = 4 tan(x)
3 (tan²(x) + 1) tan(x) = 4 tan(x)
3 tan³(x) + 3 tan(x) = 4 tan(x)
3 tan³(x) - tan(x) = 0
tan(x) (3 tan²(x) - 1) = 0
Solve for x :
tan(x) = 0 or 3 tan²(x) - 1 = 0
tan(x) = 0 or tan²(x) = 1/3
tan(x) = 0 or tan(x) = ±√(1/3)
x = arctan(0) + nπ or x = arctan(1/√3) + nπ or x = arctan(-1/√3) + nπ
x = nπ or x = π/6 + nπ or x = -π/6 + nπ
where n is any integer. In the interval [0, 2π), we get the solutions
x = 0, π/6, 5π/6, π, 7π/6, 11π/6
(3) You only need to rewrite the first term:
[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]
Then
[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]
Which statement is false?
A. Every irrational number is also real.
B. Every integer is also a rational number.
• C. Every rational number is also an integer.
D. No rational number is irrational.
Answer:
A. false B. true C. false D. true
Whope you all like this answer
Simplify your answer
Answer:
= F^2 x^2
Step-by-step explanation:
(F(x))^2
Apply the rule: (a) =a (x) = x
= (Fx)^2
Apply exonent rule: (a . b)^n = a^n b^n (Fx)^2 = F^2 x^2
= F^2 x^2
Given a parametric curve
{x = 2 cost
{y = 4 sint 0 <= t <= π
a. Set up but do NOT evaluate an integral to find the area of the region enclosed by the curve and the x-axis.
b. Set up but do NOT evaluate an integral to find the area of the surface obtained by rotating the curve about the x-axis.
(a) The area of the region would be given by the integral
[tex]\displaystyle\int_0^\pi y(t)\left|x'(t)\right|\,\mathrm dt = 8 \int_0^\pi \sin^2(t)\,\mathrm dt[/tex]
(b) The area of the surface of revolution would be given by
[tex]\displaystyle\int_0^\pi y(t)\sqrt{x'(t)^2+y'(t)^2}\,\mathrm dt = 4\int_0^\pi\sin(t)\sqrt{4\sin^2(t)+16\cos^2(t)}\,\mathrm dt[/tex]
Joan has raised $306 by selling 34 equally priced boxes of chocolate for the team fund-raiser. Which of the following equations can be used to find the price, n, of each box of chocolate?
n ÷ 34 = 306
34n = 306
n − 34 = 306
n + 34 = 306
Answer:
34n=306
Step-by-step explanation:
Use inverse operation to find it, 306÷34= 9, check again 34(9)=306, so it's correct!
In the diagram below, LATE is an isosceles trapezoid with LE ≅ AT , LA = 24, ET = 40, and AT = 10. Altitudes LF and AG are drawn.
What is the length of LF?
Answer:
6
Step-by-step explanation:
From the Trapezoid attached :
EF = GT
FG = LA
LE = AT = 10
LA = 24 ; FG = 24
FG + EF + GT = 40
Let : EF and GT = x
FG + 2x = 40
24 + 2x = 40
2x = 40 - 24
2x = 16
x = 16 ÷ 2 = 8
Hence, EF = GT = 8
Using Pythagoras :
Opposite² = hypotenus² - Adjacent²
LF² = LE² - FE²
LF² = 10² - 8²
LF² = 100 - 64
LF² = 36
LF = √36
LF = 6
g(x)=(cosθsinθ)^4 what's the differential
Answer:
sin²2θ. (cos θ sin θ). cos 2θ
Step-by-step explanation:
finding g'(x)
g'(x)
(x^n)' = nx^(n -1)= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }
(cosθ)' = - sinθ (sinθ)' = cosθ= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}
= 4 (cosθsinθ)³{ cos²θ - sin²θ}
cos²θ - sin²θ = cos 2θ2sinθ cosθ = sin 2θ= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}
= sin²2θ. (cos θ sin θ). cos 2θ
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
Answer:
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level.
The null and alternative hypothesis would be: H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : p M = p F H 1 : p M ≠ p F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F H 0 : μ M = μ F H 1 : μ M ≠ μ F
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 40 men, 25%Based on a sample of 40 men, 25% owned cats
Based on a sample of 40 women, 40% owned cats
The test statistic is:
The p-value is:
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis
Which is the graph of the function y = 2(4)^x
Answer:
the second graph is correct
Step-by-step explanation:
Find the size of angle XZY give your answer
Answer:
yeah u forgot to add the picture ig
If ∆ABC is an isosceles triangle and ∆DBE is an equilateral triangle, find each missing
measure.
Answer:
Step-by-step explanation:
The measure for each angle is shown below.
What is Equilateral Triangle?A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.
Given:
As, ∆ABC and ∆DBE is an equilateral triangle.
In Equilateral Triangle all the angles are Equal.
So, 4x+ 3= 9x- 7
5x = 50
x= 10
and, <1 = <9 = 4x+ 3= 43
and, <4 = <5 = <6 = 180/ 3= 60
ans, <3 = <8 = 180-60= 120
Also, <2 = < 7 = 180- <1- <3= 17
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A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: (5x+1)(7x−7) where x is measured in meters. Multiply the binomials to find the area of the plot in standard form
Answer:
35x^2 - 28x - 7
Step-by-step explanation:
Kala drove 819 miles in 13 hours.
At the same rate, how long would it take her to drive 441 miles?
Answer:
[tex]{ \tt{ \frac{819}{13} = \frac{441}{h} }} \\ { \tt{h = \frac{(441 \times 13)}{819} }} \\ h = 7 \: hours[/tex]
100 POINTS!!
Directions: Respond to this question to demonstrate your understanding of the topic/content. Be sure to provide adequate and relevant details learned in the module to support your response. Pay close attention to organizing your response so it makes sense and uses correct grammar. Your response should be at least 5-7 sentences at a minimum.
Question: Your friend claims that the only solution to the equation sin(x)=1 is x=90 degrees. Is your friend correct? If there are more solutions, explain how to determine additional solutions.
......hope it helps......
Answer:
yes,.to obtain sinx as 1 the angle must be 90degrees
so the answer is correct
but there are more solutions like when the cosine angle is 45 the answer is 1
and when x is 450 still sinx = 1..that is to say sin450= 1
1.055.
Determine whether the statement is true or false. If the statement is false, give a reason.
{5, 6, 7} = {5, 5, 6, 7, 7}
Given:
The statement is:
{5, 6, 7} = {5, 5, 6, 7, 7}
To find:
Whether the given statement is true or false.
Solution:
Two sets are equal if they have exactly the same elements.
The given set {5, 6, 7} has three elements and the set {5, 5, 6, 7, 7} has five elements but we known that all the elements of a set are distinct. It means, it has no repeated element.
Set {5, 5, 6, 7, 7} has three distinct elements 5, 6, 7. So,
{5, 5, 6, 7, 7} = {5, 6, 7}
Therefore, the given statement is true.
Please help meeee pleaseeee
Explanation:
Refer to the diagram below. There are n = 9 sides
S = 180(n-2)
S = 180(9-2)
S = 180(7)
S = 1260
This nonagon (9 sided polygon) has its interior angles add up to 1260 degrees.
For P = {5, 12, 13, 14), Q = {2, 7, 11), and R = {4, 7, 8, 11}, find PU (Q n R).
Answer:
(5 7 11 12 13 14)
Step-by-step explanation:
Q inter R = 7 and 11
So the union between p and 7 and 11 is the answer above
[tex]3x+7=12-2x;1[/tex]
Step-by-step explanation:
[tex]3x + 7 = 12- 2x \\ 3x + 2x = 12 - 7 \\ 5x = 5 \\ x = \frac{5}{5} \\ x =1[/tex]
the mean of 5 numbers is 198. the numbers are in ratio 1:2:3:4:5 find the smallest number
Answer: 13.2
In fraction form, this is 66/5
=============================================================
Explanation:
The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.
Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.
1x+2x+3x+4x+5x = 198
15x = 198
x = 198/15
x = 66/5
x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.
You are designing an experiment using human subjects. The study will include 30 participants. Of these, 16 will be placed in the experimental group and the remaining 14 will be placed in the control group. In how many ways can you assign participants to the two groups?
Answer:
The participants can be assigned in 224 different ways.
Step-by-step explanation:
Given that you are designing an experiment using human subjects, and the study will include 30 participants, of which 16 will be placed in the experimental group and the remaining 14 will be placed in the control group, to determine in how many ways can you assign participants to the two groups the following calculation must be performed:
16 x 14 = X
224 = X
Therefore, the participants can be assigned in 224 different ways.
Which graph has a domain of all real numbers?
Help ask anyone have any more answers for the eye level program
Answer:
1) -[tex]\sqrt{32}[/tex]
2) -[tex]\sqrt{108}[/tex]
3) -[tex]\sqrt{80}[/tex]
4) -[tex]\sqrt{112}[/tex]
5) -[tex]\sqrt{40}[/tex]
6) -[tex]\sqrt{99}[/tex]
7) -[tex]\sqrt{50}[/tex]
8) -[tex]\sqrt{150}[/tex]
Step-by-step explanation:
please mark this answer as brainlist
I need help answering this question.
Answer:
hello dude
x - 9 = - 12
x = 9 -12
x = -3
HAVE A NİCE NİGHT
Step-by-step explanation:
Greetings from Turkey
We have to,
find the required value of x.
Let's start,
→ x - 9 = -12
→ x = -12 + 9
→ x = -3
Thus, -3 is the value of x.
