Answer: [tex]2+i5,\ 29[/tex]
Step-by-step explanation:
Given
Complex number is [tex]2-i5[/tex]
Its conjugate is obtained by changing the sign of the original number i.e. [tex]2+i5[/tex]
The product of the two numbers is
[tex]\Rightarrow (2-i5)(2+i5)=2^2-(5i)^2\quad \quad [(x+y)(x-y)=x^2-y^2]\\\\\Rightarrow (2-i5)(2+i5)=4-25i^2\\\\\Rightarrow (2-i5)(2+i5)=4+25=29[/tex]
Given the function f(x) = 4x3 + 13x, what is the gradient of the function when x = 2 ?
Answer:
y=45x+115
Step-by-step explanation:
We can find the slope of a line tangent to a curve at a point by evaluating the derivative of the function at that point.
We are given the function
f ( x ) = 4 x 3 + 12 x 2 + 9 x + 7
= f ( x ) = 4 x 3 + 12 x 2 + 9 x 1 + 7 x 0
Using the power rule, let's now compute the derivative of f( x )
f ' ( x ) = ( 3 ⋅ 4 x 2 ) + ( 2 ⋅ 12 x ) + ( 1 ⋅ 9 x 0 ) + 0 ⋅ 7 x − 1
f ' ( x ) = 12 x 2 + 24 x + 9
We can now find the slope of f ( x ) at x = − 3 by substituting this value into f ' ( x )
f ' ( − 3 ) = 12 ( − 3 ) 2 + 24 ( − 3 ) + 9
f'(-3)=12(9)+24(-3)+9
f'(-3)=108-72+9
f'(-3)=45(slope of the tangent line at x = − 3
Now that we have a slope for the tangent line, we need to identify a point on the line.
We know the tangent line touches the function f ( x ) at the point x = − 3 , so let's find the value of f ( x ) at this point:
f(-3)=4(-3)3+12(-3)2+9(-3)+7
f(-3)=4(-27)+12(9)+9(-3)+7
f(-3)=108+108-27+7
f'(-3)=-20
So we know the tangent line goes through the point
(-3,-20)
Finally, we can use the point-slope formula for a line to find the equation of the tangent line.
y=mx+b
To find the value of b , substitute the values we have calculated for the point and slope of the tangent line:
(-20)=(45)(-3)+b
-20=-135+b
b=115
So our final answer for the equation of the tangent line is:
y=45x+115
Determine the nature of the roots: 5x2 + 20x + 20 - 0
. no real solutions
C.
. a unique real solution
d.
cannot be determined
two distinct real solutions
Write an equation of the line that passes through a pair of points:
(negative 5, negative 2), (4, 5)
a.
y = StartFraction 7 Over 9 EndFractionx – StartFraction 17 Over 9 EndFraction
c.
y = StartFraction 7 Over 9 EndFractionx + StartFraction 17 Over 9 EndFraction
b.
y = StartFraction 7 Over 9 EndFractionx – StartFraction 9 Over 17 EndFraction
d.
y = Negative StartFraction 7 Over 9 EndFractionx + StartFraction 17 Over 9 EndFraction
Answer:
c.
y = StartFraction 7 Over 9 EndFractionx + StartFraction 17 Over 9 EndFraction
Step-by-step explanation:
a circle centered ar the the orgin has a radius of 1/2 what is the equation of the circle
Answer:
The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]
Step-by-step explanation:
Equation of a circle:
The equation of a circle with center [tex](x_0,y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
Centered at the the origin
Center (0,0), which means that [tex]x_0 = 0, y_0 = 0[/tex]
radius of 1/2
This means that [tex]r = \frac{1}{2}[/tex]
Equation:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
[tex](x - 0)^2 + (y - 0)^2 = (\frac{1}{2})^2[/tex]
[tex]x^2 + y^2 = \frac{1}{4}[/tex]
The equation of the circle is [tex]x^2 + y^2 = \frac{1}{4}[/tex]
Give another real object for the following solid figures. Write your answer in the blank
provided
1. Sphere -
2. Cube -
3. Cylinder -
4. Rectangular Prism -
5. Triangular Prism -
matinong sagot po rereport ko ung di matinong sagot
Answer:
1 bowling ball
2 box
3 can
4 book
5 pyramid
An elevator has a maximum capacity of 950 pounds, and there must be an attendant working in the elevator at all times. A customer asks for the range of the number of people that the elevator can hold, not including the attendant. Assume that the average person weighs 155 pounds. Answer the customer's question. Include in your answer the equation or inequality that you used to find the solution.
Answer:
6 lol just do 155x 6 people
Answer:
the answer is 6 that's not including the attendant
Step-by-step explanation:
do 950/6 and that should help you sorry if this does not help you it is hard to explain. (I'm just not good at explaining)
What is p shaded sector
Answer:
elaborate or take a picture so I understand the question.
Step-by-step explanation:
Calculate the value of (1/2)^4
Answer:
D
Step-by-step explanation:
(1/2)^4 = 0.063
0.063 as a fraction is 1/16
Simplify:
(13x+4x) - (9x+3x)
Answer:
5x
Step-by-step explanation:
13x + 4x - 9x - 3x
5x
BODMAS QUESTIONS
10-4×0+3÷3
Answer: 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
Kendra spent 1/3 of her allowance on a book and snack. If she had 4 dollars remaining after purchasing a book and snack, what was the total amount of her allowance.
Kendra's allowance is $15.
Answer:
Step-by-step explanation:
What is the value of x???
Answer:
22.5
Step-by-step explanation:
22.5 x 3 = 67.5
67.5 + 22.5 = 90
4x-3=9 what does x equal show work
Answer:
x = 3
Step-by-step explanation:
4x - 3 = 9
4x = 9 + 3
4x = 12
x = 12/4
x = 3
The size your dog and the number of times you take it to the vet, The amount your drive to school and the amount you have to pay for gas, The number of people at your party and the number of sodas you have in the refrigerator. What correlation are all of these. None, Positive, or Negative thanks so much.
1. No correlation
Those things don't really relate to each other.
2. Positive correlation
The higher the amount you drive your car, the more you'll have to pay for gas.
3. Negative correlation
More people = less soda.
Graph the line with the equation y = 1/2 x + 5
Find two points and draw a line through them
y = 1/2(2) + 5
y = 1 + 5, 6
One point is (2,6)
y = 1/2(0) + 5
y = 5
Second point is (0,5)
I inserted a graph on desmos for example
Step-by-step explanation:
Rewrite in slope-intercept form.
[tex]y = \frac{1}{2} x + 5[/tex]
Use the slope-intercept form to find the slope and y-intercept.
Slope is : 1/2
y-intercept: (0,5)
Any line can be graphed using two points. Select two x values, and plug them into the equation in order to find the corresponding y values.
Find f(-1)
f(x) = (1/5)^x
The red string r is 20 centimeters less than 5 times as long as the orange string s ." This can be represented by the expression r = 5 s − 20. Find the length of the red string if the length of the orange string is 10 centimeters. The length of the red string is centimeters.
A news article estimated that only 5% of those age 65 and older who prefer to watch the news, rather than to read or listen, watch the news online. This estimate was based on a survey of a large sample of adult Americans. Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05. A random sample of n = 100 people will be selected from this population and p, the proportion of people who prefer to watch online, will be calculated.
(a) What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.)
(b) Is the sampling distribution of p approximately normal for random samples of size n 100? Explain.
i. The sampling distribution of p is approximately normal because np is less than 10.
ii. The sampling distribution of p is approximately normal because np is at least 10.
iii. The sampling distribution of p is not approximately normal because np is less than 10
iv. The sampling distribution of p is not approximately normal because np is at least 10
v. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10.
Answer:
a) The mean is 0.05 and the standard deviation is 0.0218.
b) v. The sampling distribution of p is not approximately normal because n(1 - p) is less than 10.
Step-by-step explanation:
Central Limit Theorem
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex].
If [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex], the sampling distribution of the sample proportion p will be approximately normal.
Consider the population consisting of all adult Americans age 65 and older who prefer to watch the news, and suppose that for this population the actual proportion who prefer to watch online is 0.05.
This means that [tex]p = 0.05[/tex]
A random sample of n = 100 people
So [tex]n = 100[/tex]
(a) What are the mean and standard deviation of the sampling distribution of p?
Mean [tex]\mu = p = 0.05[/tex]
Standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.05*0.95}{100}} = 0.0218[/tex]
The mean is 0.05 and the standard deviation is 0.0218.
(b) Is the sampling distribution of p approximately normal for random samples of size n 100? Explain.
[tex]np = 100*0.95 = 95 > 10[/tex]
[tex]n(1-p) = 100*0.05 = 5 < 10[/tex]
As n(1-p) < 10, it is not approximately normal, option v.
ILL GIVE THE BRAINLIEST pls help me with this question EVERYTHING IS IN THE PICTURE PLS HELP DUE TODAY IF YOU PUT A WRONG ANSWER ILL REPORT YOU FASTER THAN ASSIGMENT IS DUE
Answer:
57 inches
Step-by-step explanation:
thanks, kid.
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Los números 4,3×-3,4× esta en progesion aritmética cuál es el cuarto termino
Answer: Le preguntaste a tu maestro?
Step-by-step explanation:
If $42.60 is in the tip jar and you share equally with 2 other people what is my share
Answer:
$14.20
Step-by-step explanation:
$42.60 ÷ 3
$14.20
In the relationship between hours driven and distance traveled is y = 45x, which of the following ordered pairs would be graphed on the line that represents the relationship?
Step-by-step explanation:
(0,0) (1,45) (2,90) (3, 135) (4, 180) etc, etc
Answer:
(4, 180)
Step-by-step explanation:
Choices: (3,5), (4,60), (4,180), (5,9)
y = 45x
The value of y is 45 times the value of x.
The only point in which that is true is (4, 180) since 45 * 4 = 180.
Answer: (4, 180)
Mr. Williams trains a group of student athletes. He wants to know how they are improving in the number of push-ups they can do.
These dot plots show the number of push-ups each student was able to do last month and this month.
How much did the mean number of push-ups increase from last month to this month?
Question 1 options:
2.75 more push-ups
4.375 more push-ups
7.5 more push-ups
There is not enough information given to answer the question.
Answer:
7.5 more push-ups
Step-by-step explanation:
From the dot plot attached :
Last month mean :
Σfx/Σf
Σfx = [(10*2)+(15*2)+(25*3)+(35*1)] = 160
Σf = (2 + 2 + 3 + 1) = 8
Mean = 160 / 8 = 20
This month mean :
Σfx/Σf
Σfx = [(10*1)+(15*1)+(25*1)+(30*3)+(40*2)] = 220
Σf = (1 + 1 + 1 + 3 + 2) = 8
Mean = 220/8
Mean = 27.5
Difference in mean :
This month mean - Last month mean
27.5 - 20
= 7.5
A farmer plants 987 apple trees in 9 rows. Can each row have the same number of trees? How do you know?
Each row cannot have the same number of trees.
What is Divisibility?In mathematics, the term "divisibility" describes a number's ability to be divided by another number in an equal amount without any residue. For instance, it's simple to understand how 40 by 4 can be divided. A huge piece of land that can be divided into smaller chunks and sold separately is said to be divisible, much as it is obvious when you cut into a pan of brownies and distribute equal amounts to each of your friends.
As per the given data:
Number of apple trees = 987
Number of rows = 9
To find whether each row has the same number of trees:
If 987 is divisible by 9 then, the same number of trees can be there else not.
= (987/9) = (329/3) = 109.667
Not divisible, so same number of trees cannot be there.
Hence, each row cannot have the same number of trees.
To learn more about divisibility, click:
brainly.com/question/21416852
#SPJ2
Please help 30 points and brainless
Answer:
Stats. for a basketball game and the graph could be a bar graph or could be a line graph. And yes the data would look good on a graph.
Step-by-step explanation:
I'm familiar with these types of problems.
What is the perimeter of a rectangle with a length of 20 inches and a width of 18 inches?
Answer:
76 in
Step-by-step explanation:
20+20+18+18=76
This morning, Manny took a history test. There were 50 multiple-choice problems on the test
and Manny answered 10% of them correctly. How many problems did Manny get right?
Answer:
He got 5 right
Step-by-step explanation:
10% = 0.1
50(0.1) = 5
Answer:
5 questions were answered correctly
Step-by-step explanation:
10% of 50 is 5. So that means 5 questions were answered correctly.
(a) An angle measures 86. What is the measure of its supplement?
(b) An angle measures 34. What is the measure of its complement?
Answer:
a) 94
b) 56
Step-by-step explanation:
a)
Supplement means it adds up to 180 so:
180 - 86 = 94
b)
Complement means it adds up to 90 so:
90 - 34 = 56
What is the width of a rectangular prism with a length of 13 feet, volume of 11,232 cubic feet, and height of 36 feet?
Answer:
24
Step-by-step explanation:
What is the least common multiple of 19 and 43?
Answer:
The Least Common Multiple (LCM) is: 19 x 43 = 817
Step-by-step explanation:
