Answer:
6840
Step-by-step explanation:
multiply combinations
n!/(r!(n − r)!)
n choose r
n (objects) = |n
r (sample) = r
(4 teachers, CHOOSE 2)*(20 students, CHOOSE 3)
C(4,2) times C(20,3) =
C(n,r)=?
C(n,r) = C(4,2)
4! / (2!(4-2)!)
4! /2! x 2!
= 6
C(n,r)=?
C(n,r) = C(20,3)
20! / (3!(20-3)!)
20! / 3! x 17!
= 1140
6 * 1140 = 6840
alegbracom Edwin McCravy
D₁ vide using x² - 2x² 2× +3× -5 by ×-3 using synthetic division.
Answer:
Step-by-step explanation:
I think you are trying to use synthetic division for
[tex]x^{4} -2x^{3} -2x^{2} +3x-5[/tex] divided by x-3
First
x -3 = 0 , make it equal to 0 and add 3 to both sides
x = 3
Then we write all the coefficients and continue with
a pattern of multiply by 3 and add to the next coefficient.
See attachment.
Starting from the geometric series, use power series operations to
determine the Maclaurin series. See picture
a. By replacing [tex]x[/tex] with [tex]-x^2[/tex] in the power series, we get
[tex]\displaystyle \frac1{1+x^2} = \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n}[/tex]
Integrate both sides to recover [tex]\arctan(x)[/tex] on the left.
[tex]\displaystyle \int \frac{dx}{1+x^2} = \int \sum_{n=0}^\infty (-x^2)^n = \sum_{n=0}^\infty (-1)^n x^{2n} \, dx[/tex]
[tex]\displaystyle \arctan(x) = C + \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]
By letting [tex]x=0[/tex] on both sides, we find [tex]C=0[/tex], so that
[tex]\displaystyle \arctan(x) = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n+1} \, dx[/tex]
Then dividing both sides by [tex]x[/tex] gives
[tex]\displaystyle \boxed{\frac{\arctan(x)}x = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} x^{2n} \, dx}[/tex]
b. Let [tex]x=\frac1{\sqrt3}[/tex]. Then
[tex]\displaystyle \frac{\arctan\left(\frac1{\sqrt3}\right)}{\frac1{\sqrt3}} = \sum_{n=0}^\infty \frac{(-1)^n}{2n+1} \left(\dfrac1\sqrt3\right)^{2n}[/tex]
[tex]\displaystyle \sqrt3 \arctan\left(\frac1{\sqrt3}\right) = \sum_{n=0}^\infty \frac1{2n+1} \left(-\frac13\right)^n[/tex]
Taking the first few terms from the infinite series, we can approximate
[tex]n=0 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1[/tex]
[tex]0\le n\le1 \implies \sqrt3\arctan\left(\dfrac1{\sqrt3}\right) \approx 1+\dfrac13\left(-\dfrac13\right) = \dfrac89[/tex]
which together suggest the value we want is bounded between 8/9 and 9/9 = 1, hence [tex]\boxed{p=8}[/tex].
Since the series is alternating and converges on [tex]-1<x<0\cup0<x<1[/tex],
[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^0 a_n \right| < |a_1| = \left|\frac13 \left(-\frac13\right)^1\right| = \frac19[/tex]
and
[tex]\displaystyle \left| \sum_{n=0}^\infty a_n - \sum_{n=0}^1 a_n \right| < |a_2| = \left|\frac15 \left(-\frac13\right)^2\right| = \frac1{45}[/tex]
which tells us the first approximation is off by at most 1/9 from the actual value of [tex]\frac\pi{2\sqrt3}[/tex], whereas the second approximation is off by at most 1/45 from the actual value. In other words, the second approximation is closer, so [tex]\frac\pi{2\sqrt3}[/tex] is closer to [tex]\frac p9[/tex] :
[tex]\dfrac89 \approx 0.8889[/tex]
[tex]\dfrac{\pi}{2\sqrt3}\approx0.9069[/tex]
[tex]\dfrac99 = 1[/tex]
Find the coordinates of the point on the curve y = 2x² - x - 1 at which the gradient is 7
Answer:
See below
Step-by-step explanation:
The derivative of the function is the slope
2x^2 - x -1 take derivative ( f ' )
4x -1 equate to 7
7 = 4x -1
x = 2 sub into the original equation to find y = 5
9-Volume of Solids
Find the volume of each solid. Round to the nearest tenth,
31)
33)
11 yd
8t
5 yd
5 yd
6 yd
11 yd
10 R
10 %
8 t
32)
34)
8m
6m
5m
4m
10 m
10 m
The volume of the solids are 240 cubic yards and 125.6 cubic cm
How to determine the value of the solids?The complete question is added as an attachment
Solid 1
The shape is a rectangular prism.
The volume of a rectangular prism is
Volume = Length * Width * Height
So, we have
Volume = 8 yd * 5 yd * 6 yd
Evaluate
Volume = 240 cubic yards
Hence, the volume of the solid is 240 cubic yards
Solid 2
The shape is a cylinder.
The volume of a rectangular prism is
Volume = πr²h
So, we have
Volume = 3.14 * 2^2 * 10
Evaluate
Volume = 125.6 cubic cm
Hence, the volume of the solid is 125.6 cubic cm
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A botanist secures a 30-year mortgage for $513,000 at an annual interest rate of 4.175% with 1.4 points. The loan origination fee is 0.65 points of the loan amount. Calculate the APR (in percent) for the loan. (Round your answer to the nearest thousandth of a percent.)
Answer:
4.346%
Step-by-step explanation:
The points and origination fee are assumed to be capitalized, so the loan payment amount is based on the total of the original loan amount and those fees. The APR is calculated as the rate that would be charged on the original loan value to produce that payment.
Loaned amountThe loaned amount is the sum of the original loan value and the added points.
P = $513,000×(1 +1.4% +0.65%) = $523,516.50
PaymentThe monthly payment on this amount is given by the amortization formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where r=0.04175, the annual interest rate, t=30, the period in years
A = $523,516.50(0.04175/12)/(1 -(1 +0.04175/12)^-360)) ≈ $2552.45
APRThere is no formula for calculating the APR. It must be developed iteratively or graphically. The attached calculator images show a couple of different ways the value can be found.
The payment of $2552.45 on a loan value of $513,000 represents an APR of 4.346%.
Which of the following shows one way to simplify 43Σn=1(3+9n)?
Based on the given summation notation, the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n
How to determine the summation expression?The expression is given as:
43Σn=1(3+9n)
As a general rule, if a summation notation is represented using the following expression
Σ(a + bn)
The equivalent expression of the above summation notation is
Σa + bn
Where the variable a is a constant in the expression
This means that:
Σ(a + bn) = Σa + bn
Using the above equation as a guide, we have the following equivalent equation
43 Σ n=1 (3+9n) = 43 Σ n=1 3 + 43 Σ n=1 9n
Hence, based on the given summation notation; the expression that shows one way to simplify 43 Σ n=1 (3+9n) is (a) 43 Σ n=1 3 + 43 Σ n=1 9n
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Answer:
D on 3dg I took the best
Step-by-step explanation:
MY NOTES
lim
n18
ASK YOUR TEACHER
Use the Limit Comparison Test to determine the convergence or divergence of the series.
00
n=1
n3
converges
O diverges
n+ 3
n+ 3
n3-5n+8
- 5n+ 8
Need Help?
-
=L>0
Read It
9,433
PRACTICE ANOTHER
Watch It
AUG
3
tv♫♬
(a
A
Part 1) [tex]\displaystyle \frac{1}{n^2}[/tex] or 1/(n^2) goes in the box.
Part 2) The series converges
======================================================
Work Shown:
[tex]\displaystyle L = \lim_{n\to \infty} \frac{a_n}{b_n}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{\frac{n+3}{n^3-5n+8}}{\frac{1}{n^2}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n+3}{n^3-5n+8}\times\frac{n^2}{1}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{n^3+3n^2}{n^3-5n+8}\\\\\\[/tex]
[tex]\displaystyle L = \lim_{n\to \infty} \frac{\frac{n^3}{n^3}+\frac{3n^2}{n^3}}{\frac{n^3}{n^3}-\frac{5n}{n^3}+\frac{8}{n^3}}\\\\\\\displaystyle L = \lim_{n\to \infty} \frac{1+\frac{3}{n}}{1-\frac{5}{n^2}+\frac{8}{n^3}}\\\\\\\displaystyle L = \frac{1+0}{1-0+0}\\\\\\\displaystyle L = 1\\\\\\[/tex]
Because L is finite and positive, i.e. [tex]0 < L < \infty[/tex], this means that the original series given and the series
[tex]\displaystyle \sum_{n=1}^{\infty} \frac{1}{n^2}[/tex]
either converge together or diverge together due to the Limit Comparison Test.
But the simpler series is known to converge (p-series test).
Therefore, the original series converges as well.
The two series likely don't converge to the same value, but they both converge nonetheless.
A DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr. Find the speed of the plane and the speed of the wind.
The speed of the plane will be 875km/h and the speed of the wind will be 125km/h.
How to calculate the speed?It should be noted that the speed is calculated as:
= Distance/Time
Based on the information, the DC10 airplane travels 3000 km with a tailwind in 3 hr. It travels 3000 km with a headwind in 4 hr.
Therefore, (v + w) = 3000/3
v + w = 1000 .... I
(v - w) = 3000/4
v - w = 750 .... ii
We'll then add both equations together. Therefore, the speed of the plane will be 875km/h and the speed of the wind will be 125km/h.
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Find the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3.
The remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
How to determine the remainder?The function is given as:
f(x)=−2x3+x2−4x+1 is divided by x+3.
Set the divisor to 0
x + 3 = 0
Solve for x
x = -3
Calculate f(-3)
f(-3)=−2(-3)^3+(-3)^2 − 4(-3) + 1
Evaluate the expression
f(-3)= 76
Hence, the remainder when f(x)=−2x3+x2−4x+1 is divided by x+3. is 76
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Scenario 2 You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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A two digit number has 6 more ones than tens. Twice the sum of the number and its reverse is 6 more than ten times the number. Find the number.
The number with the given characteristics is 17
How to determine the numbers?Let the tens be x and the units be y.
So, the number is 10x + y
The relationship between the digits is
y = x + 6
The relationship between the number and the reverse is
2(10x + y + 10y + x) = 6 + 10 * (10x + y)
Simplify the second equation
2(11x + 11y) = 6 + 100x + 10y
Open the brackets
22x + 22y = 6 + 100x + 10y
Substitute y = x + 6
22x + 22(x + 6) = 6 + 100x + 10(x + 6)
Expand
22x + 22x + 132 = 6 + 100x + 10x + 60
Collect like terms
22x + 22x - 100x - 10x = 6 + 60 - 132
Evaluate the like terms
-66x = -66
Divide by -66
x = 1
Substitute x = 1 in y = x + 6
y = 1 + 6
y = 7
Recall that the number is 10x + y
So, we have
Number = 10 * 1 + 7
Evaluate
Number = 17
Hence, the number is 17
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4x-9y=36 find the missing y-coordinate
The y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4
How to find the y-intercept of a function?The y-intercept of a function is the point where the value of x is zero. Given the function below;
4x-9y=36
when the value of x is zero, hence;
4(0) - 9y = 36
Simplify to have:
0 - 9y = 36
-9y = 36
Divide both sides by -9 to have:
-9y/-9 = 36/-9
y = -4
Hence the y-intercept of the function is given as (0, -4). This also shows that the value of y missing from the coordinate is -4
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USH financial is a small bank that is examining its customers use of its website.the number of online transactions made per day during the past 9 days are as follows
The mean, median, and mode are;
median=77
Mean=73.33
Mode= 78, 67
This is further explained below.
What is median?Generally, The middle number in a list that is arranged from smallest to greatest is referred to as the median. On the list, the value that occurs most often is known as the mode. Therefore
median=77
Generally, In mathematics, particularly statistics, the term "mean" may refer to a number of different concepts. The purpose of each mean is to summarize a certain collection of data, often for the purpose of gaining a better understanding of the overall value of a specific data set.
A dataset's mean (also known as the arithmetic mean, which is distinct from the geometric mean) is calculated by dividing the sum of all of the values in the dataset by the total number of values in the dataset. It is the measure of central tendency that is used the most often, and it is sometimes referred to as the "average."
[tex]mean=\frac{\sum x}{n}\\\\Mean=\frac{78+67+98+50+67+78+67+77+78}{9}[/tex]
Mean=73.33
Mean=73.3 in one dp
What exactly is the mode in math?In conclusion, The mode is the number that appears the most often, or the number that stands out as having the most occurrences overall. The number 2 is the mode of the sequence 4, 2, 4, 3, 2, 2 because it appears three times, which is more than any other number in the sequence.
The mode of 78, 67, 98, 50, 67, 78, 67, 77, 78 is
Mode= 78, 67
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if sin 0=12/13 and 0 is in quadrant II, cos 20= and cos0=
a. The value of cos2θ = -119/169
b. The value of cosθ = -5/13
The question involves trigonometric identities
What are trigonometric identities?Trigonometric identities show the relationship between trigonometric ratios.
How to find the value of cos2θ?Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.
Using trigonometric identity
cos2θ = 1 - 2sin²θ
Substituting sinθ = 12/13 into the equation, we have
cos2θ = 1 - 2sin²θ
cos2θ = 1 - 2(12/13)²
cos2θ = 1 - 2(144/169)
cos2θ = 1 - 288/169
cos2θ = (169 - 288)/169
cos2θ = -119/169
So, the value of cos2θ = -119/169
How to find the value of cosθ?Since sinθ = 12/13 and θ is the quadrant II, it means that 90° ≤ θ ≤180° and sinθ is positive.
Using trigonometric identity
cosθ = √(1 - sin²θ)
Substituting sinθ = 12/13 into the equation, we have
cosθ = √(1 - sin²θ)
cosθ = √[1 - (12/13)²]
cosθ = √[1 - (144/169)]
cosθ = ±√(169 - 144)/169
cosθ = ±√25/169
cosθ = ±5/13
θ is the quadrant II, it means that 90° ≤ θ ≤180° it means that cosθ is negative.
So, cosθ = -5/13
So, the value of cosθ = -5/13
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Determine which quadrilaterals have the properties given in the table.
kite
square trapezoid rectangle
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
rhombus
parallelogram
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
The two quadrilateral with the listed properties are kite and rhombus respectively.
Properties of a kiteIt has two diagonals intersecting at right anglesA kite is symmetrical about its main diagonalAngles opposite to the main diagonal are equalThe kite can be viewed as a pair of congruent triangles with a common baseIts diagonals are perpendicularProperties of a rhombusAll sides of the rhombus are equalThe opposite sides are parallelOpposite angles are equalDiagonals bisect each other at right anglesDiagonals bisect the anglesThe sum of two adjacent angles is equal to 180 degrees, that is, are supplementaryThus, the two quadrilateral with the listed properties are kite and rhombus respectively.
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Answer:
your welcome
Step-by-step explanation:
help me solve this asap
Answer:
a) A = 3, B = 8.
b) C = 2, D = 25
Step-by-step explanation:
See the image below.
A newsletter publisher believes that over 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.05 level of significance, the advertiser failed to reject the null hypothesis.
The conclusion regarding the publisher's claim regarding the hypothesis is that have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.
What is a null hypothesis?The null hypothesis is a statistical theory that suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.
Since we reject the null hypothesis , we have sufficient evidence to support the claim. In this case, we have sufficient evidence to support the claim that the proportion is less than 30% of their readers own a Rolls Royce.
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Complete question:
A newsletter publisher believes that less than 30% of their readers own a Rolls Royce. For marketing purposes, a potential advertiser wants to confirm this claim. After performing a test at the 0.02 level of significance, the advertiser decides to reject the null hypothesis. What is the conclusion regarding the publisher's claim?
Some banks charge a fee on savings accounts that are left inactive for an extended period of time.
The equation `y=5000\left(0.98\right)^{x}` represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, is the balance in this account increasing or decreasing?
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
How to recognize Exponential Function.Exponential Function can be used for increase rate and also for decay rate. The difference between the two are the plus and minus signs. To put it in another perspective, If Y = P(M)³
If M is less than one, that means it is decaying or decreasing. And if M is greater than one, that means it is increasing.
Given that Some banks charge a fee on savings accounts that are left inactive for an extended period of time. And the equation
y = 5000(0.98)^x represents the value, y, of one account that was left inactive for a period of x years.
According to the equation, to know if the balance in this account is increasing or decreasing, we will analyze the value 0.98.
Since the value 0.98 is less than 1, we can therefore say that balance in this account is decreasing.
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on the graph, sketch f(x)=x+3 as well as g(x)=x
Answer:
below
Step-by-step explanation:
Number #2 please, I don’t know how to solve it.
Answer:
See below
Step-by-step explanation:
Here is HOW to solve this problem:
b = pounds of blue candy then r = 11-b = pounds of red candy
.79b = cost of blue candy 1.29 (11-b) = cost of red candy
these two costs sum to 11.19
.79b + 1.29 ( 11-b) = 11.19 Now you can solve for 'b' the 'r' = 11-b
Answer:
Red candy =5
Blue candy = 6
Step-by-step explanation:
Let the pounds of red candy be x and blue candy y. Then y=11-x
Also 1.29x + 0.79y=11.19
1.29x+0.79(11-x)=11.19
0.5x=11.19–8.69
0.5x=2.5
X=5
Red candy =5
Blue candy = 6
How do you get the statistical notation?
The new curriculum significantly affects the earning potential.
According to the question, Eight kids were chosen at random to take part in a brand-new educational program that emphasizes both academics and mental health education between middle school and high school. The average annual income is $29432. The standard deviation is unknown.
The probability level is given to be 5%.
When the p-value is less than or equal to your significance level, reject the null hypothesis. The alternative theory, which contends that the effect is widespread, is supported by your sample data.
A probability level of 0.05 means that the new curriculum significantly affects the earning potential.
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Can someone please help me with this question asap!?
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
HJ = 23.5 in[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Take HJ = a, GH = b and GJ = c
a = b + 2c = a + b - 17a + b + c = 73put the value of a from equation 1 in equation 2
c = (b + 2) + b − 17c = 2b − 15now, put the value of a and c in equation 3
b + 2 + b + 2b − 15 = 734b − 13 = 734b = 86b = 21.5 inNow, we need to find HJ (a)
a = b + 2a = 21.5 + 2a = 23.5 in[tex]{ \qquad \large \sf {Conclusion} :} [/tex]
HJ = 23.5 inplease help i would really appreciate it pallas athena
The fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively. option D
Long division9√4.000
= 4.000/9
= 0.444
Approximately,
= 0.4
Fraction
This is a ratio of two numbers, the numerator and the denominator, usually written one above the other and separated by a horizontal bar.
Decimal
This is a number expressed in the decimal system (base 10).
Therefore, the fraction and decimal forms which match the long division problem is 4/9 and 0.4 respectively.
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7/3 4/2 as improper fraction
Answer:
If the question asked mixed fraction:
7/3 = 2 1/3
4/2 = 2
Step-by-step explanation:
I converted it to mixed fraction because it is already improper fraction.
The graph shows a point of equilibrium. A graph titled Daily Market for Graphic Tees at the Clothing Shop has Quantity supplied on the x-axis, from 0 to 30 in increments of 5, and price in dollars on the y-axis, from 0 to 30 in increments of 5. A line that represents supply has a positive slope and a line that represents demand has a negative slope. The lines intersect at (15, 20). How many goods must be supplied to achieve equilibrium? 15 20 25 30
The price at which equilibrium is achieved is $20.
How to illustrate the equilibrium?The equilibrium point is the point where the lines of the demand and supply functions meet.
From the question, we understand that price is plotted on the vertical axis (i.e. the y-axis).
Also from the question, the lines intersect at point (15, 20).
The y-coordinate of the intersection point is 20 in this scenario.
Hence, the price at which equilibrium is achieved is $20.
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Answer:
b
Step-by-step explanation:
A troupe of 12 dancers is going to line up on stage. Of these dancers, 6 are wearing green and 6 are wearing blue. A dancer wearing green must be in the first position and they must alternate between colors. In how many ways can the dancers line up?
The number of ways that the dancers can line up is; 518400 ways
What is the Fundamental Counting Theorem?The fundamental counting theorem is a theorem that states that if there are n things, each with ways to be done, each thing independent of the other, the number of ways they can be done is:
N = n1 * n2 * n3.....*nₙ
Total = 12
Dancers on Green = 6
Dancers on blue = 6
Number of ways for those wearing green = 6!
Dancers wearing green must be in the first position and so 6 places are left for the blue dancers.
Number of ways to arrange those wearing blue = 6!
Thus;
Number of ways that the dancers can line up = 6! * 6! = 518400 ways
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The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
1.72 1.8 1.86 1.88 1.74 1.86
What is the mean height of the ocean's first high tide for the 6 days?
1.81 meters
1.83 meters
1.86 meters
1.87 meters
The required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
Given that,
The list below shows the height, in meters, of an ocean's first high tide for each of 6 days.
Number of days = 1 2 3 4 5 6 Total = 6
1.72 1.8 1.86 1.88 1.74 1.86
The average of the values is the ratio of the total sum of values to the number of values.
Since the mean of the heights of the tides,
= sum of heights / number of heights observation
= (1.7 + 1.8 + 1.86 + 1.88 + 1.74 + 1.86)/6
= 10.86/6
= 1.81 meters
Thus, the required mean height of the ocean at first high tide is 1.81 meters. Option A is correct.
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Complete each statement describing the transformations you observed for the graph of y = 2x + k.
When the value of k increases, the graph of the function:
When the value of k decreases, the graph of the function:
.
Using translation concepts, it is found that:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The translation y -> y + k represents:
A shift up if k > 0.A shift down if k < 0.Hence:
When the value of k increases, the graph of the function shifts up.When the value of k decreases, the graph of the function shifts down.More can be learned about translation concepts at https://brainly.com/question/4521517
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3x^2 + 12x - 96 help please
Answer:
fully factored form = 3(x-4)(x+8)
Step-by-step explanation:
first you factor 3 out
3(x^2+4x-32)
then factor it
3(x-4)(x+8)
Answer:
3(x-4)(x+8) This is the answer :)
Step-by-step explanation:
3x^2+12x - 96
3(x^2+4x-32)
3(x^2+4x--32)
3(x^2+8x-4x-32)
3(x^2+8x-4x-32)
3(x(x+8)-4(x+8))
3(x(x+8)-4(x+8))
3(x-4)(x+8)
3(x=4)(x+8)
State and prove De Moivre's theorem
Answer:
assume the formula is true for n is equal to k prove that result is true for n is equal to k + 1 hence result proves since the thorum is true for n is equal to 1 and n k + 1 is unit through a and
