Answer:
A
Step-by-step explanation:
[tex]f(x) = (x + 2)^2(x-4)(x + 1)^3[/tex]
x+2=0
x+2-2=0-2
x=-2.....(x+2) was squared...exponent of 2...multiplicity of 2
x-4=0
x-4+4=0+4
x=4....(x-4) has no visible exponent which means it is essentially to the power of 1...multiplicity of 1
x+1=0
x+1-1=0-1
x=-1....(x+1) was cubed...exponent was 3...multiplicity of 3
The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct.
What are the roots of an equation?The roots of an equation are the solution of that equation, since an equation consists of hidden values of the variable so to determine them by different processes and then the resultant is called roots.
For example root of x -4 = 0 is x = 4 so 4 will be the only root of this linear equation.
As per the given function,
f(x) = (x + 2)²(x - 4)(x + 1)³
The roots are the points at which the value of the function is zero.
f(x) = 0
(x + 2)²(x - 4)(x + 1)³ = 0
(x + 2)² = 0
x = -2 (with a multiplicity of 2)
(x - 4) = 0
x = 4 (with a multiplicity of 1)
(x + 1)³ = 0
x = -1 (with a multiplicity of 3)
Hence "The roots and their respective multiplicity are –2 with multiplicity 2, 4 with multiplicity 1, and –1 with multiplicity 3 thus option (A) is correct".
To learn more about the roots of equations,
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Jimmy earns money for babysitting his little
brother. He earns the same amount every
week. He is saving all the money he earns for a
summer trip. The table shows how Jimmy's
savings have been growing.
please help and I will mark big brain
If ƒ (x ) = 3x2 - x, find ƒ (-2).
Answer:
f(-2) is 14.
Step-by-step explanation:
We have been given the function:
We have to find f(-2)
That means put x= -2 in the given function we get:
After simplification we will get:
After further simplification we will get the required result:
Hence, ƒ (-2) is 14
Given that R= 4x +6y find x when y= 4 and R=11
Answer:
The value of x:
[tex]x=-\frac{13}{4}[/tex]Step-by-step explanation:
Given the equation
[tex]R=4x+6y[/tex]
substituting the values y=4 and R=11
[tex]R=4x+6y[/tex]
[tex]11=4x+6\left(4\right)[/tex]
[tex]11=4x+24[/tex]
[tex]11-24=4x[/tex]
switching the sides
[tex]4x=11-24[/tex]
Subtract the numbers: 11-24=-13
[tex]4x=-13[/tex]
Divide both sides by 4
[tex]\frac{4x}{4}=\frac{-13}{4}[/tex]
[tex]x=-\frac{13}{4}[/tex]
Therefore, the value of x:
[tex]x=-\frac{13}{4}[/tex]A box on kitty litter is 8 3/4 inches tall. How many boxes can be stacked on a shelf in the warehouse that is 40 inches tall?
Answer:
Probably about 4 boxes
According to Bill Nye, How many people need to be in a room for there to be 50% chance of atleast 2 people having the same birthday?a. 128 b. 56 c. 29 d. 12
Answer:
the answer is actually 23 people
Step-by-step explanation:
Bill Nye's birthday paradox can be explained in the following manner:
first we must find the probability that in a room with 23 people, no two people have the same birthday
probability of no two people having the same birthday = 365/365 x 364/365 x 363/365 x 362/365 ... you keep multiplying until 343/365 = 0.492703
so the probability that in a room with 23 people, no two people have the same birthday = 49.2703%
the probability of two people having the same birthday = 1 - probability of no two people having the same birthday = 1 - 49.2703% = 50.7297%
Please hurry please
Answer:
No
Step-by-step explanation:
it doesn't add up so. No.
Ffind an equation for the tangent to the curve at the given point. Then sketch the curve and the tangent together.
y=8 âx,(1,8)
Answer:
y = 4x + 4
Step-by-step explanation:
given :
y = 8 [tex]\sqrt{x}[/tex] , (1,8)
The equation for the tangent to the curve at the given point
y' = 8. ( [tex]( \frac{1}{2\sqrt{x} } ) = \frac{4}{\sqrt{x} }[/tex]
next calculate the slope of the tangent (m) = y' at x = 1 = 4
hence the equation of the tangent is
y - y' = m( x - x1 )
y - 8 = 4 ( x - 1 )
y = 4x + 4
attached below is the sketch of the curve and the tangent together
The number 0.003 is 1/10 of which decimal?
Answer:
I'd say it's 0.03
Step-by-step explanation:
0.03 divided by 10 is 0.003 so it's 1/10
0.003 is 1/10th of 0.03.
What is a decimal ?A decimal is represented by a point or a dot it separates the decimal part and the fractional part for example 24.75 here the whole part is is 24 and the fractional part is 75.
if we divide 0.03 by 10 = [tex]\frac{0.03}{10}[/tex] = 0.003. (dividing a number by 10
moves the decimal point
to the left by 1 because
10 has 1 no. of zeroes)
Learn more about decimals here :
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Sarah graphed the function. y =-1/2x+4 if the domain is restricted to this on the photo what’s the answer I pick
Answer:
Option (4)
Step-by-step explanation:
Domain of a function is defined by the x-values or input values of the function.
Similarly, Range of a function is defined by the y-values of output values for the corresponding input values.
From the graph attached,
Domain is restricted to 0 ≤ x ≤ 8.
Therefore, Range will be 0 ≤ y ≤ 4.
Option (4) will be the answer.
Which term describes the figure? Please help
Answer:
C . None of these
Is the answer.
Step-by-step explanation:
Because parallel lines do not intersect.
And perpendicular lines form angle of 90°.
Answer:
None of the above.
Step-by-step explanation:
Those lines are intersecting lines. Parallel lines face each other and never meet. Perpendicular lines do meet, but they form a 90 degree angle, which this doesn't. Intersecting lines meet, but don't form a 90 degree angle.
Hope this helps!
Given h (x) = -x -3, find h (-6)
Answer:
h(-6) = 3
Step-by-step explanation:
h(x) = -x - 3 when h(-6).
~Substitute
h(-6) = -(-6) - 3
~Simplify
h(-6) = 6 - 3
~Subtract
h(-6) = 3
Best of Luck!
Gretta wants to buy a jar of fossils that is 10% off. The original price is
$47.82.
What is amount of discount (nearest penny)?
Answer:
4.78
Step-by-step explanation:
=47.82 x 10/100
=47.82 x 1/10
=4.782
=~ (approx) 4.78
Please help please help
Answer:
Do Y divided by X.
Step-by-step explanation:
This is normally what I do so hope I helped.
Can someone help with this problem? ASAP
HELP PLEASE HELP ILL GIVE U 15 points and BRAINLIEST to the correct answer (DONT guess please)
Consider the function.
f (x)= -80 +4
What is the value of f (-1/4)?
A. 0
B.2
C. 3
D. 6
Answer: the answer is b
Step-by-step explanation:
Just trust me
¿ Qué porcentaje de 70 es 35?
Answer:
Step-by-step explanation:
50% mi amigo
Can someone please tell me if I got this right or wrong? I’ll give brainliest
Please be honest
Answer:
yes your answer is correct
Step-by-step explanation:
James says that 12 is a common factor of 3 and 4. June says that 12 is a common multiple of 3 and 4. Who is correct?
Answer:
June is correct.
Step-by-step explanation:
June is correct because Common Multiples are what we get after multiplying the number while common factors are what we can multiply to get the number.
0.2 4/15 0.21 1/4 in least to greatest
Answer:
0.2, 0.21, 0.25 (1/4), 0.2666666 (4/15)
Step-by-step explanation:
A 3-pound bag of carrots costs $11.52. What is the price per ounce?
Answer:
3.75
Step-by-step explanation:
Just divide it in the future!! :)
Answer:
$0.24
Step-by-step explanation:
There are 48 ounces in 3 pounds. Divide 48 by 11.52 to get the unit rate, and the unit rate is $0.24 per ounce
A cold water pipe can fill a swimming pool in 4 hours, and a hot water pipe in 6 hours. If cold water pipe is turned on and hot water pipe is turned on 3 hours later then how long will it take them to fill the pool together?
answer = 5
Step-by-step explanation:
A cold water pipe can fill a swimming pool in 4 hours
And a hot water pipe in 6 hours.
If cold water pipe is turned on and hot water pipe is turned on 3 hours later
6-4 = 2
2+3 = 5
5 answer
Answer:
0.6 of an hour
Step-by-step explanation:
A cold pipe takes 4h hours so we can assume ¼ of our job is done in one hour.
After 3 hours go by with the cold pipe on, we have ¼ of the job left.
Now we have our hot pipe, which takes 6 hours for the entire pool, so we can assume that it has a rate of ⅙ per hour. Now since these two pipes are working together we can add them.
⅙ + ¼ = ⁵/₁₂
Now we divide.
Since at the start 3 hours had gone by with the cold pipe that would have been ¾ of our time so, 1 - ¾ = ¼
¼ ÷ ⁵/₁₂ = ⅗ or 0.6 of an hour
HELP EMERGENCY!!!! (2.5 x 10-10) (7 x 10-5)
Express your answer in scientific notation.
Answer:
[tex]1.75[/tex] × [tex]10^{-15}[/tex]
I hope this helps!
What fraction is equivalent to the decimal and percent below? Enter your
answer in simplest form, using the slash (/) as the fraction bar.
Fraction Decimal Percent
? 0.50 50%
Answer here
SUBMIT
Answer: 1/2
Step-by-step explanation:
PLS HELP DONT ANSWER IF YOU DONT KNOW ALSO I WILL MARK BRAINLIEST
PLEASE HELP FAST & CORrect 50 POINTS
Answer:
105
Step-by-step explanation:
mumbai is 845 km away from bangalore whats that distance in cm
Compute 41, 42, 43, 44, 45, 46, 47, and 48. Make a conjecture about the units digit of 4n where n is a positive integer. Use strong mathematical induction to prove your conjecture.
Answer:
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
Step-by-step explanation:
[tex]4^1 = 4\\4^2 = 16\\4^3 = 64\\4^4 = 256 \\4^5 = 1024\\4^6 = 4096\\4^7 = 16384\\4^8 = 65536[/tex]
The conjecture is that the unit digit of 4^n = 4 when n = odd also 4^n = 6 when n = even
To prove this conjecture
[tex]4^1 = 4\\4^2 = 16[/tex] unit digit = 6
hence the property is true for ; n = 1 and n = 2 and also for every odd and even number ( i.e. from 1 to 8 )
Evaluate this expression when p = 4 and q = -2:
4(√p+q²)
A. 4
B. -8
C. 12
D. 24
Answer:
24
Step-by-step explanation:
x2 + 5x +4=0
How do we do this
Answer: x=−1 or x=−4
Step-by-step explanation: Solve by factoring
Answer:
(x+1)(x+4)
Step-by-step explanation: