[tex]\large\underline{\sf{Solution-}}[/tex]
Given that:
[tex]\sf p(y) = 2y^3+my^2+11y+m+3 [/tex]
We are also given that, p(y) is divisible by 2y - 1.
So, 2y - 1 is a factor of p(y).
[tex]\sf\longmapsto 2y-1=0[/tex]
[tex]\sf\longmapsto y=\dfrac{1}{2}[/tex]
So, 1/2 is a zero of p(y).
[tex]\sf\longmapsto p(1/2) =0 [/tex]
[tex]\sf\longmapsto p(y) = 2y^3+my^2+11y+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{2}\right)^3+m\left(\dfrac{1}{2}\right)^2+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
So,
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = 2\left(\dfrac{1}{8}\right)+m\left(\dfrac{1}{4}\right)+11\left(\dfrac{1}{2}\right)+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) = \dfrac{1}{4}+\dfrac{m}{4}+\dfrac{11}{2}+m+3 [/tex]
[tex]\sf\longmapsto p\left(\dfrac{1}{2}\right) =\dfrac{1}{4}+\dfrac{m}{4}+\dfrac{22}{4}+\dfrac{4m}{4}+\dfrac{12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{1+m+22+4m+12}{4} [/tex]
[tex]\sf\longmapsto 0 =\dfrac{5m+35}{4}[/tex]
[tex]\sf\longmapsto 5(m+7)=4\times0[/tex]
[tex]\sf\longmapsto 5(m+7)=0[/tex]
[tex]\sf\longmapsto m+7=0[/tex]
[tex]\longmapsto\bf m=-7[/tex]
Therefore, the value of m is -7.
Assume that adults have IQ scores that are normally distributed with a mean of ?=100 and a standard deviation ?=20. Find the probability that a randomly selected adult has an IQ less than 140.
Answer:
The probability that a randomly selected adult has an IQ less than 140 is 0.9772
Step-by-step explanation:
Given:
Standard deviation: σ=20
Mean: μ=100
P(X<140)=?
Calculate:
normalcdf(lower,higher,μ,σ) = normalcdf(0,140,100,20) = 0.9772496509 ≈ 0.9772 ≈ 97.72%
The midpoint of AB is M (4,2). If the coordinates of A are ( 6,-4) what are the coordinates of B?
Answer:
(2,8)
Step-by-step explanation:
m (4,2)
(6,-4)
(2,8)
What is the solution to the equation 3 − 5 + 10 = 36
Answer:
False (no solution)
Step-by-step explanation:
What is the solution to the equation 3 − 5 + 10 = 36?
3 − 5 + 10 = 36
8 = 36
it's false
Some banks now use continuous compounding of an amount invested. In this case, the equation that models the value of an initial investment of P dollars in t years at an annual
interest rate of r is given by A = Pelt. Using this equation, find the value in 5 years of an investment of $2000 that earns 7% annual interest. (Round your answer to the nearest cent.)
Answer:
In this case, the equation that models the value of an initial investment of P dollars in t years at an annual interest rate of r is given by A = Pert.
Step-by-step explanation:
What is the domain of y=log 4(x+3)?
Answer:
Y= log 4(x+3)
then you should do (x+3)= 3x= log 4.
Step-by-step explanation: Sorry I'm not 100 % sure so yeah
But let's see 3x = log 4
oh so then you need to divide 3 at both sides so then what's 4/3= 1.3333333333.
So now I think it's C). All real numbers are les than 3.
81 x
3y + 72x
2y
2 + 16xy
3
Answer:
Step 1 :Equation at the end of step 1
((81•(x4))-((72•(x2))•(y2)))+24y4
Step 2 :
Equation at the end of step 2 :
((81 • (x4)) - ((23•32x2) • y2)) + 24y4
Step 3 :
Equation at the end of step 3 :
(34x4 - (23•32x2y2)) + 24y4
Step 4 :Trying to factor a multi variable polynomial
4.1 Factoring 81x4 - 72x2y2 + 16y4
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (9x2 - 4y2)•(9x2 - 4y2)
Detecting a perfect square :
4.2 81x4 -72x2y2 +16y4 is a perfect square
It factors into (9x2-4y2)•(9x2-4y2)
which is another way of writing (9x2-4y2)2
How to recognize a perfect square trinomial:
• It has three terms
• Two of its terms are perfect squares themselves
• The remaining term is twice the product of the square roots of the other two terms
Trying to factor as a Difference of Squares:
4.3 Factoring: 9x2-4y2
Put the exponent aside, try to factor 9x2-4y2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : 4 is the square of 2
Check : x2 is the square of x1
Check : y2 is the square of y1
Factorization is : (3x + 2y) • (3x - 2y)
Raise to the exponent which was put aside
Factorization becomes : (3x + 2y)2 • (3x - 2y)2
Final result :
(3x + 2y)2 • (3x - 2y)2
Step-by-step explanation:
Answer:
81x+16y
should be the correct one
I am using remainders
Answer:
Step-by-step explanation:
Is there an image or question?
Combine the like terms to create an equivalent expression:
−
2
k
−
(
−
5
)
+
1
Answer:
-2k + 6
Step-by-step explanation:
We start out with the expression -2k - (-5) + 1. We should first distribute the negative outside of (-5), which gets us to 5: -2k + 5 + 1. Now, we can combine like terms with 5 and 1 to get 6, giving us a final answer of -2k + 6. We can't simplify any further since there aren't any like terms.
If you have any questions or need clarification on anything, let me know!
Estimate and solve 3,836 ÷ 63
Answer:
estimating it's 548/9
Step-by-step explanation:
What is the inverse of the function?
f(x) = 3^x + 1
f^-1(x)= log3 (x) +1
f^-1(x)= log3(x)-1
f^-1(x)=log3(x+1)
f^-1(x)=log3(x-1)
Answer:
f^-1(x)=logs3(x+1)
Step-by-step explanation:
Let y=f(x)
[tex]\\ \rm\Rrightarrow y=3^x+1[/tex]
Interchange[tex]\\ \rm\Rrightarrow x=3^y+1[/tex]
[tex]\\ \rm\Rrightarrow lnx=ln(3^y+1)[/tex]
[tex]\\ \rm\Rrightarrow x=\dfrac{ln(y-1)}{ln3}[/tex]
Again interchange
[tex]\\ \rm\Rrightarrow f^{-1}(x)=\dfrac{ln(x-1)}{ln3}[/tex]
Find the length of the side of a square whose area is equal to the area of a rectangle with side measures 4.9 m and 1.6 m
Given :
Area of square equals to the area of rectangle of sides 4.9m and 1.6m .To find :-
The side of the square .Solution :-
As we know ,
Area = side² 4.9 * 1.6 = a²a = √ 49/10 * 16/10 a = 7/10 * 4/10 a = 28/100 a = 0.28 mHelp as soon as possible please if the answer is correct I’ll give brainliest
Answer:
The slope is 4, while the y intercept is 2
...starting with 2 cards and adding 4 cards each week
Step-by-step explanation:
The slope is always the coefficient (the number in front) of x.
The y intercept is the number on its own.
Hope this helps!
HELP HELP
Referring to the Fig. in Question #19, given FGHI≅WXYZ,
find m∠Y
Answer:
m∠Y= 120
Step-by-step explanation:
Given,
FGHI≅WXYZ
m∠H=m∠Y [ Corresponding parts of congruent figures]
m∠Y= 120
Construct five examples of simple sentences.
Answer:
Open the jar carefully.
Read the directions.
Don't cry.
Use common sense.
Make the best of things.
Catch up!
She doesn't study German on Monday.
Does she live in Paris?
He doesn't teach math.
Cats hate water.
Every child likes an ice cream.
Step-by-step explanation:
The scale drawing at right shows the first slope of a house, the actual dimensions of the garage are 20 feet by 25 feet. All angels are right angels.
A. how many feet does each inch represent? That is, what is the scale?
B. What are the length and width of the living room on the scale and drawing( in inches)?
C. What are the actual length and width of the living room( in feet)?
D. if the family wants to lay carpet in the living room and carpeting cost $1.25 per square foot, how much will carpet cost
Answer:
See belowStep-by-step explanation:
A)
According to dimensions of the garage, the scale is:
1 in : 20 ft, as the width of the garage is 20 ft and on paper is 1 inB)
Living room
Dimensions on paper:
2 in x 1 1/4 inC)
Actual dimensions:
2*20 ft = 40 ft and1 1/4 * 20 ft = 25 ftD)
The area of the living room:
A = lw = 25*40 = 1000 ft²Cost of carpet:
1000*$1.25 = $1250Length
20(2)=40ftWidth
1.25(20)25ftArea
25(40)1000ft²Total cost
1000(1.25)$1250How much is does 8×10 equal to?
Answer:
80
Step-by-step explanation:
8x10= 80
Find the missing side
Answer:
A. 8
The missing side is 8
Anyone know this? ..........
Answer:
Yes, Each value in the domain goes to only one value in the range.
Step-by-step explanation:
Since each x goes to a different y value, the relation is a function
Each value in the domain goes to only one value in the range.
An aquarium has 5 gallons of water in it and is being filled up at a rate of g gallons every m minute. The amount of water w in the tank can be represented by the equation
w = 5 + g - m. Write an equation that can be used to find the number of minutes m the tank has been filled if we know w and g.
Write an equation that can be used to find the number of minutes g the tank has been filled if we know w and a.
Answer:
m=5+g-w
Step-by-step explanation:
This should be the answer based on the equation given.
Answer:
See belowStep-by-step explanation:
The equation for the amount of water is:
w = 5 + gmSolve for m:
gm = w - 5m = (w - 5)/gNow solve for g:
gm = w - 5g = (w - 5)/m5m > 45 I need help
Answer:
m = 10
5 x 10 = 50
50 > 45
Step-by-step explanation:
I know how to do it just then one’s a bit confusing
Answer:
208 ft^3
Step-by-step explanation:
Let the plane through the 4 ft X 4ft square at the top of the figure break the figure into 2 boxes, one has dimensions (8-7) by 3 by 4 = 1ft X 3ft X 4ft, and the other has dimensions 7 by 7 by 4 = 7ft X 7ft X 4ft.
They have volumes of (1)(3)(4) = 12 ft^3, and (7)(7)(4) = 196 ft^3, respectively, so the total volume = 12 + 196 = 208 ft^3, the answer.
Human population numbers are in constant flux. Suppose a country has a population of 20 million people at the start of one year and during the year there are 600,000 births, 350,000 deaths, 100,000 immigrants, and 5,000 emigrants. You and your classmates will determine the total population at the end of the year and then model expected change over a longer period.
nothing yw listen to your teacher
x / 2.5 = 10
plz helppp
Answer:
x=25
Step-by-step explanation:
Can someone please help me with this question
Answer:
40 degrees
Step-by-step explanation:
i'm use......
what decimal is equivalent to 8 9/100
Answer:
8.09
Step-by-step explanation:
8.09 I think. I’m not positive but I think so.
PLEASE HELP ITS MATH THANK YOUUUU
9 inches = 14 yard
Formula: divide the value in inches by 36 because 1 yard equals 36 inches. So, 9 inches = 936 = 14 or 0.25 yard.
Answer:
4 yards
Step-by-step explanation:
Use a ratio and then cross multiply
120 yd x yd
--------- = ---------
270 in 9 in
270x = 1080
x= 1080 / 270
x = 4 yd
6 (31 + 163 72)6 +2=
NO LINKS!!!
Find the coordinates of point on the directed segment from (1,6) to (-2,-3) that divides it into a ratio of 5:1.
a. (-1.5,-1.5)
b. (1.5, 1.5)
c. (-1,-1)
d. (-2.5, -3.5)
Answer:
A. (-1.5, -1.5)Step-by-step explanation:
Find the coordinates:
x = 1 + 5/6(- 2 - 1) = 1 - 5/2 = -1.5y = 6 + 5/6(-3 - 6) = 6 - 15/2 = -1.5Correct choice is A
IF Tyler s currently 5 inches
tal, how many inches more
does he need to grow to be
feet tal?
Hey there! Your answer is:
7 inches
Explanation:
If Tyler is 5 inches tall, he needs to grow 7 inches to be a foot tall. This is because 12 inches are in 1 foot. We can do a simple subtraction problem to figure this out.
12 inches - 5 inches = 7 inches
Since Tyler is 5 inches tall, we know that if we subtract 12 inches from 5 inches we will get the number of inches he needs to grow.
I hope this answer helps you out! Let me know if you have any questions and have a wonderful day/night!
x-10<-26
help lololololol
Hope this will help you!! <3
Answer:
Step-by-step explanation:
1) -90 ≥ 18x
Divide both sides by 18
-90/18 ≥ 18x/18
-5 ≥ x
2)x/3 > -8
Multiply by 3,
3*(x/3) > -8*3
x> -24
3)x - 10 < -26
Add 10 to both sides
x < -26 +10
x < -16
4) 19 -x ≥ 21
Subtract 19 from both sides,
-x ≥ 21 - 19
-x ≥ 2
Divide both sides by (-1)
x < -2