Write a polynomial in factored form that has the given zeros:
Zero at -4 with multiplicity of 2
Zero at 5 with multiplicity of 3
Answers to choose from.
1. f(x)=(x-4)^2(x+5)^3
2. f(x)=(x-2)^-4(x+3)^5
3. f(x)=(x+4)^2(x-5)^3
4. f(x)=(x+2)^-4(x+3)^5
Answer:
f(x) = (x + 4)^2*(x - 5)^3
Step-by-step explanation:
For a polynomial P(x) with zeros (or roots):
x₁, x₂, ..., xₙ
And a leading coefficient (the one that multiplies the term of highest degree) A, we can write the polynomial as:
P(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)
Now, some of these roots can be repeated.
For example if x₁ = x₂
Then we say that the root x₁ has a multiplicity of two.
And we write the polynomial as:
P(x) = A*(x - x₁)^2*(x - x₃)*....*(x - xₙ)
Now, if we have a polynomial with the roots (or zeros):
Zero at -4 with a multiplicity of 2 (we have the root x = -4 two times)
Zero at 5 with a multiplicity of 3 (we have the root x = 5 3 times)
(And a leading coefficient A = 1, I assume)
This polynomial will be written as:
f(x) = (x - (-4))*(x - (-4))*(x - 5)*(x - 5)*(x - 5)
f(x) = (x + 4)*(x + 4)*(x - 5)*(x - 5)*(x - 5)
f(x) = (x + 4)^2*(x - 5)^3
The correct option is the third one:
A cone has a radius of 5 cm and a height of 12 cm. What is the volume of the cone rounded to the tenth? Use pi = 3.14
Answer:
942m^3
Step-by-step explanation:
Given data
Radius of cone= 5m
Height= 12 m
We know that volume of a cone is given as
V= πr^2h
V= 3.14*5^2*12
V= 3.14*25*12
V= 942 m^3
Hence the volume is 942m^3
Find the sum of x^2+3x and
-2x^2+9x+5
Answer: The answer is -x^2 + 12x + 5
What is the probability that a randomly selected student who lives in Nebraska plans to stay in his or her home state after graduation? Round your answer to the nearest hundredth.
Answer:
[tex]P (Yes | Nebraska) = 0.10[/tex]
Step-by-step explanation:
Given
See attachment for contingency table
Required
[tex]P (Yes | Nebraska)[/tex]
From the contingency table, we have:
[tex]P (Yes\ n\ Nebraska) = 0.044[/tex]
[tex]P (No\ n\ Nebraska) = 0.400[/tex]
The required can be represented as:
[tex]P (Yes | Nebraska) = \frac{P(Yes\ n\ Nebraska)}{P(Nebraska)}[/tex]
Where
[tex]P (Nebraska) = P (No\ n\ Nebraska) +P (Yes\ n\ Nebraska)[/tex]
So, we have:
[tex]P (Nebraska) = 0.400 + 0.044[/tex]
[tex]P (Nebraska) = 0.444[/tex]
So, we have:
[tex]P (Yes | Nebraska) = \frac{P(Yes\ n\ Nebraska)}{P(Nebraska)}[/tex]
[tex]P (Yes | Nebraska) = \frac{0.044}{0.444}[/tex]
[tex]P (Yes | Nebraska) = 0.10[/tex] --- approximated
In a freefall skydive, a skydiver begins at an altitude of 10,000 feet. during a freefall, the skydiver drops toward earth towards earth at a rate of 175 ft per second. the height of the skydiver from the ground can be modeled using the function H(t)=10,000-175t.
What is the domain of the function for this situation?
Answer:
{[tex]t|0\leq t\leq 50[/tex]}
Step-by-step explanation:
We are given that
In a freefall skydive, a skydiver begins at an altitude during free fall =10,000 feet
The skydiver drops towards earth at a rate=175 ft/s
The height of the skydiver from the ground can be modeled using the function
[tex]H(t)=10000-175t[/tex]
We have to find the domain of the function for this situation.
When t=0
Then ,[tex]H(0)=10,000 feet[/tex]
From given graph we can see that the value of t lies from 0 to 50.
Therefore, the domain of the function for this situation is given by
{[tex]t|0\leq t\leq 50[/tex]}
What is the volume of the solld figure that has a helght of 11 feet and the following base?
volume___ft 3
Step-by-step explanation:
Area is 2D, and Volume is 3D
volume is L x W x H
area is L x W which has already been given to you so you just need to use the height given to you
38.28 x 11
Write each ratio in fraction form. Then write the percent equivalent.
9. 88 out of 132
Answer:
Step-by-step explanation:
=9.88/132 (this is in fraction form)
for calculating percentage just multiply the fraction by 100%
=9.88/132*100%
=9.88*100/132
=988/132
=7.48 %
I read an article saying that in the full population, there's a significant, positive correlation between the strength of your hand (grip strength) and the strength of your upper arm (arm strength). I want to see if that's true, and I have devices that can measure this accurately. I gathered a sample of average, healthy 21-year-olds and measured these two variables. My results were non-significant. Why didn't I find a significant correlation
Answer:
Restricted Range
Step-by-step explanation:
Required
Reason for insignificant correlation
From the question, we understand that the article discussed the full population while you restricted the correlation to only 21-year-olds age groups.
You left out other age groups included in the original dataset that was analyzed and reported by the article. The term that describes this act is restricted range, because other age groups are not represented in your analysis.
By rounding each number to 1 singnificant figure. estimate answers to:
a.) 8.2×6.7/0.46
b.) 23.4x13.9/0.18
(need answers for b.)
thank you!
Answer:
1000
Step-by-step explanation:
b.) 23.4x13.9/0.18= 1000
please answer for points
Answer:
4.9
Step-by-step explanation:
use this equation : [tex]a^2 + b^2 = c^2[/tex] (your hypotenuse is always going to be c)
[tex]7^2 - 5^2 = b^2[/tex]
[tex]49 - 25 = b^2\\[/tex]
[tex]24 = b^2[/tex]
[tex]\sqrt{24} = b[/tex]
[tex]4.9 = b[/tex]
Find the properties of the Quadratic Function: -x^2-8x=15
Step-by-step explanation:
-x²-8x=15
=> -x²-8x-15= 0
<=> x2+8x+15=0
(x+5)(x+3)=0
x= -5 or x = -3
The quotient of Alice’s income and 12 is 1,500
Answer:
125
Step-by-step explanation:
x = 1500 / 12
= 125
answer this question
Choose the correct equation of the circle. Center: (13,13) Radius: 4
(don't judge me i was 2 lazy 2 type all the answer options until i discovered the answers where pics so i copied and pasted options here)
Answer:
It's the second one
Step-by-step explanation:
what’s the correct answer
Answer:
D
Step-by-step explanation:
Point B is on line segment AC. Given AC = 20 and BC = 16, determine the length AB
Answer:
Answer is AB=AC-BC
20-16=4
The solution set of the inequality 2x – y > 2 consists of all the points ?_the line ?
O
above; y = 2x - 2
below; y = 2x - 2
above; y = -2x + 2
below; y = -2x + 2
0
Answer:
Step-by-step explanation:
4.
Which explanation provides the best real-world scenario of the graph?
A. If an object is dropped from a height of 120 feet, the function h(t) = –16t2 + 120 gives the height of the object after t seconds.
B. If an object is dropped from a height of –16 feet, the function h(t) = –16t2 + 120 gives the height of the object after t seconds.
C. If an object is dropped from a height of 120 feet, the function h(t) = –16t2 – 120 gives the height of the object after t seconds.
Answer:
C. If an object is dropped from a height of 120 feet, the function h(t) = –16t2 – 120 gives the height of the object after t seconds.
Step-by-step explanation:
.................................The last one is the only one that makes sense according to the standard position function. -16t^2 is the pull of gravity on an object in free fall, and the height is 120 feet above the ground. Hopefully that's what you need since there's no graph we can refer to
....................................................Answer:
The explanation that best provides the real-world scenario is:
If an object is dropped from a height of 120 feet, the function
gives the height of the object after t seconds.
Step-by-step explanation:
a)
If an object is dropped from a height of 120 feet, the function gives the height of the object after t seconds.
This option is incorrect.
Since when t=0 we have:
h(t)= -120
This is not possible as the object is above the ground and hence must have positive height initially.
b)
If an object is dropped from a height of -16 feet, the function gives the height of the object after t seconds.
This option is incorrect.
Since a object when is dropped from some height then it must be a positive height.
Also, when t=0 we have: h(t)= 120 feet.
This means that the object is dropped from a height of 120 feet.
c)
If an object is dropped from a height of 120 feet, the function gives the height of the object after t seconds.
In this when t=0 we have:
h(t)=120 that means the height of the object initially was 120 feet and then it decreases with the increase in time as the object will reach the ground with the time increase and hence height will decrease.
Hence, this option is correct.
........................................The equation that models the movement of the object is:
Where,
t: time
a: acceleration due to gravity
v0: initial speed
h0: initial height
Suppose that the object falls with zero initial velocity and from a height of 38 feet.
The equation that models the problem is:
Answer:
If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds
.................Answer: If an object is dropped from a height of 38 feet, the function h (t) = -16t2 + 38 gives the height of the object after seconds
Step-by-step explanation:
The explanation that best provides the real-world scenario is:
⇒ If an object is dropped from a height of 120 feet, the function
h(t) = - 16t² - 120 gives the height of the object after t seconds.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
a) If an object is dropped from a height of 120 feet, the function
h(t) = - 16t² + 120 gives the height of the object after t seconds.
Hence, This option is incorrect.
Since, when t=0 we have:
h (t) = -120
This is not possible as the object is above the ground and hence must have positive height initially.
b) If an object is dropped from a height of -16 feet, the function
h(t) = - 16t² + 120 gives the height of the object after t seconds.
This option is incorrect.
Since a object when is dropped from some height then it must be a positive height.
Also, when t = 0
we have: h (t) = 120 feet.
This means that the object is dropped from a height of 120 feet.
c) If an object is dropped from a height of 120 feet, the function
h(t) = - 16t² - 120 gives the height of the object after t seconds.
In this when t=0 we have:
h(t)=120
That means the height of the object initially was 120 feet and then it decreases with the increase in time as the object will reach the ground with the time increase and hence height will decrease.
Hence, this option is correct.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
PLZ HELP ME!!!
Find the volume of the triangular pyramid to the nearest whole number. Find the volume of the triangular pyramid to the nearest whole number.
A)72 units³
B)96 units³
C)144 units³
D)288 units³
Answer:
B
Step-by-step explanation:
6×8 /2 = 24
24 ×12 /3 = 96 units³
answer pls with a detailed explanation
Answer:
the surface area is 112 ft^2
Step-by-step explanation:
if you separate listen to two different rectangles you get what's a rectangle a being 3 + 10 + 3 equals 16 * 2 what gives you 32 okay and rectangle b being 3 + 2 + 3 what gives you 8 x 10 that gives you the area of 80 now you add the area both rectangles being 32 + 80 and to get a hundred and twelve feet squared
Anna's class has already collected 74 cans for the annual canned food drive. Her class
must collect more than 200 cans to reach their goal. The class plans to collect 15 cans
each day. Which inequality shows the number of additional days, d, Anna's class
needs to reach the goal?
CLEAR
15d + 74 > 200
15d - 74 > 200
15d + 74 > 200
150 – 74 > 200
Answer:
15d + 74 > 200
d > 8.4 days
Step-by-step explanation:
Total cans needed = over 200
Number of cans they have = 74
Number of cans needed per day = 15
Number of days = d
The inequality is
74 + 15d > 200
Also written as
15d + 74 > 200
15d > 200 - 74
15d > 126
d > 126/15
d > 8.4 days
Answer:
15d + 74 > 200
d > 8.4 days
Step-by-step explanation:
Total cans needed = over 200
Number of cans they have = 74
Number of cans needed per day = 15
Number of days = d
The inequality is
74 + 15d > 200
Also written as
15d + 74 > 200
15d > 200 - 74
15d > 126
d > 126/15
d > 8.4 days
How do I solve 6/10 = x/15
Answer:
the answer is 9
Step-by-step explanation:
6/10=x/15
10x=90
x=9
Please help I'll love you forever pleasdeeee
Answer:
[tex]30[/tex]; Obtuse, isosceles triangle OR "[tex]B[/tex]"
Step-by-step explanation:
If you replace the [tex]z^o[/tex] variable with [tex]30^o[/tex] on both angles.
The angles will be:
[tex]30^o[/tex]
[tex]120^o[/tex] ([tex]4(30)=120^o[/tex])
[tex]30^o[/tex]
This angle is isosceles (two sides are equal). It is obtuse (there is one angle that is greater than [tex]90^o[/tex]).
A rolled up sleeping bag and shaped like a cylinder with a radius of 5" and a volume of 1727.9 cubic inches. What is the height of the road up sleeping bag?
Answer:
I think the height is 22.
Find the product: (2 - 3i)(4 + 2i)
Answer:
(2 - 3i)(4+2i)
(2 x 4)(2 x 2i) (-3i x 4) (-3i x 2i)
8 x 4i x -12i -6i^2
6i^2 - 12i x 32
Step-by-step explanation:
Answer:
6i² - 8i + 8
Step-by-step explanation:
1. Expand Brackets: 8 + 4i - 12i - 6i²
2. Simplify equation: 8 - 8i - 6i²
3. Rearrange: 6i² - 8i + 8
Whats the volume of this prism? PLEASE HELP I AM SO CLOSE TO FAILING.
Answer:
36 cubic inches
Step-by-step explanation:
The prism is literally just the front section twice. Find the area of the front and then add it to itself
what's the value of x and y?
Answer:
x = 55
y = 70
Step-by-step explanation:
since it's all sides are equal its an equilateral triangle
each angle of an equilateral triangle is 60°
therefore,
y - 10 = 60 => y = 60 + 10
y = 70
x + 5 = 60 => x = 60 - 5
x = 55
Answer:
x+5=y-10
x-y = -15
y-10+X+5+X+5=180
2x+y =180
x-y+2x+y =180-15
3x.=165
x. =55
2x+y =180
y =180-(110)
y =70
The population of Country A is about 1,047,000 and the population of Country B is about 1,080,000,000. Approximately how many times greater is the population of Country B than the population of the Country A?
1.)10
2.)100
3.)1000
4.)10,000
are the choices
Answer:
1000
Step-by-step explanation:
1,080,000,000/1,047,000
i need help please hurry :)
Answer:
vertical, 47
Step-by-step explanation:
vertical, 47
Answer:
vertical; 47
Step-by-step explanation:
Vertical angles are opposites.
Write the factored form of each trinomial.
x^2 + 11x +28
Answer:=
=(x^2+4x)+(7x+28)
=x(x+4)+7(x+4)
=(x+4)(x+7)
Step-by-step explanation:
Answer:
[tex](x+4) (x+7)[/tex]
Step-by-step explanation:
Factor x^2 + 11x + 28 using the AC method.