so, -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and
3 - 4i are roots of f(x)
Therefore, option D is correct
Polynomial function:
A polynomial function, in general, is also stated as a polynomial or polynomial expression, defined by its degree. The degree of any polynomial is the highest power present in it.
given that
Patricia is studying a polynomial function f(x). three given roots of f(x) are
-11-[tex]\sqrt{2}[/tex]i , 3 + 4i and 10 . Patricia concludes that f(x) must be a polynomial with degree 4.
so -11-[tex]\sqrt{2}[/tex]i and 3 + 4i are roots of polynomial function f(x) so 11 + [tex]\sqrt{2}[/tex]i and
3 - 4i are roots of f(x)
Therefore, option D is correct
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dage measurs and finds that she can do a vertical jump 27.5% of her hight if age can jump 13.2 inches how tall is she
Her height is 48 inches
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The distance jump = 13.2 inches
The percentage of the distance jump = 27.5% of her height.
This means,
Height = x
x = 100%
Now,
13.2 inches = 27.5%
Multiply 100/27.5 on both sides.
100/27.5 x 13.2 inches = 100%
48 inches - 100%
Thus,
The height is 48 inches.
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in a standardized exam the mean score is 400 with a standard deviation of 50. if a random sample of 25 students is selected , what is the standard deviation of the sampling distribution of the sample mean ?
Standard deviation of the sampling distribution of the sample mean is 50.
We were asked to determine the mean of the sampling distribution of the sample mean. The mean score for a standardized exam is 400, the standard deviation is 50, and we have a random sample of 25 students. You take a sample of 25 students in total. You will obtain a sample average of X after averaging that sample. Take 70 student samples, then compute the mean.
The sampling distribution of the sample mean is the term used to describe how the mean varies from sample to sample. The question being posed here is, what is the mean of the sampling distribution of sample means?
Regardless of how the population distribution is shaped, the mean of sample averages is always the same as the mean of the population.
The sample mean is 400.
The spread of a data distribution is measured by standard deviation. The average distance between each data point and the mean is measured. Whether the data is being treated as a population unto itself or as a sample of a larger population will affect the standard deviation calculation formula.
So standard deviation of sample mean is also same as it is for random sample that is 50.
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139 + = 0
Question 3 options:
A: -139
B: 139
C: 39
D: 140
Answer:
A: -139
Step-by-step explanation:
139 + (-139) = 0
Answer: -139
Answer:
It would be A. -139
Step-by-step explanation:
139 + -139 is the same thing as 139 - 139
A positive plus a negative is saying a positive minus a positive. so it is A
How do you dilate a figure with a center of dilation?
Add the scale factor to the x- and y-coordinates of a point on a coordinate plane with the center of dilatation at the origin.
Given,
Dilation;
Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.
We have to dilate a figure with a center of dilation;
Dilations centered at the origin;
On the coordinate plane, figures can be enlarged. The centre of dilatation is frequently used to be the origin. The points in the picture can be found by multiplying the coordinates of the preimage's points by the scale factor when distorting a figure that is centered at the origin.
That is,
On a coordinate plane with the center of dilatation at the origin, multiply the point's x and y coordinates by the scale factor.
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Please! I need help.
Thank u. I appreciate it.
Answer:could you get a better picure
Thank you :)
A line passing through
the point (-8, 13)
with a slope of -3.
IN POINT-SLOPE FORM
Point-slope form: y - 13= -3(x + 8)
Slope-intercept form: y = -3x - 11
Identify the initial amount a and the rate of decay r (as a percent) of the exponential function y=575(1-0.6)^t. Evaluate the function when t=3 . Round your answer to the nearest tenth.
The required simplified value of the function when t= 3 is y = 36.8.
To Identify the initial amount a and the rate of decay r (as a percent) of the exponential functionⁿ.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
Given expression,
[tex]y=575(1-0.6)^t[/tex]
put t = 3
y=575(1-0.6)³
y = 36.8
Thus, the required simplified value of the function when t= 3 is y = 36.8.
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Elanor wants to estimate the number of frogs in a reservoir. She catches 90 frogs from the reservoir and marks them with a non-harmful dye. Elanor then returns the frogs to the reservoir. The next day she catches another 80 frogs and 10 of these are marked with the dye. Work out an estimate for the total number of frogs in the reservoir
The total number of frogs in the reservoir are 160.
What is Reservoir?
An enlarged lake behind a dam is a reservoir. Such a dam could be a man-made structure created to hold freshwater or it could be a natural formation.
Given:
Elanor wants to estimate the number of frogs in a reservoir.
She catches 90 frogs from the reservoir and marks them with a non-harmful dye.
Elanor then returns the frogs to the reservoir.
The next day she catches another 80 frogs and 10 of these are marked with the dye.
So on the first day the total frogs are 90.
On second day total frogs are 80 but 10 of them are dye, so the remaining are 70.
Therefore, the total frogs are 90 + 70 = 160.
Hence, the total number of frogs in the reservoir are 160.
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(a) a box contains 4 red balls, 3 white balls, and 3 black balls. two balls are drawn at random from the box (with replacement of the first before the second is drawn). what is the probability of getting a red ball on the first draw and a white ball on the second? (enter your probability as a fraction.)
The probability of getting a red ball on the first draw and a white ball on the second is 0.3.
Total number of balls = 10
Now we have to pick: 4 red balls or 3 black balls or 3 white balls.
Case-1:
In this case we pick 4 red balls.
Now, probability for picking one red ball is 3/10. Now, the 2nd ball is drawn which is also red, probability for picking 2nd red ball is 2/19. probability for picking two red balls is
P(r) = (3/10) (2/9)
Case-2:
In this case we pick 3 white balls
Probability for picking 3 white balls
P(w) = (3/10) × (4/9)
Case-3:
probability for picking 03 black balls:
P(b) = (03/10) (02/9)
Therefore, probability for picking 2 same color balls:
= (3/10) (2/9) +(03/10) × (04/9) +(03/10) (02/9)
= 0.3
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for her phone service, keisha pays a monthly fee of , and she pays an additional per minute of use. the least she has been charged in a month is . what are the possible numbers of minutes she has used her phone in a month? use for the number of minutes, and solve your inequality for .
Answer:
256
Step-by-step explanation:
What is the best Square-1?
The Square-1 is a Cubic twisty puzzle.
It is similar to the 3x3 Rubik's cube, but due to the way the pieces are cut and designed can shapeshift. It is even governed by the WCA, and uniquely the only shapeshifting puzzle in the WCA.
It's probably the hardest WCA puzzle to learn how to solve due to the restrictions in its turning and its unique design.Square-1 became an official WCA event in 2007. It is a shape-shifting puzzle with a middle slice that you can use to interchange pieces.
X-Man Volt has long been the best square-1 on the market. However, Yu-Xin has rolled out a new budget square-1, which is fully magnetic.
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Please help on this!!
Answer:
4x+14
Step-by-step explanation:
Your welcome! Give me brainiest! :>
The temperature was 42°C this afternoon. If the temperature dropped 9°C, what is the temperature now?
The temperature was 42°C this afternoon. If the temperature dropped 9°C, The temperature is now 33°C.
In order to calibrate thermometers, a variety of temperature scales with distinct reference points and thermometric materials are used.The Celsius scale (°C), formerly known as centigrade, with the unit symbol °C, is the most commonly used scale, followed by the Fahrenheit scale (°F) and the Kelvin scale (K), which is mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).
42°C - 9°C = 33°C
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i need this answer asap
The equation to find the value of x is x² - x - 4 = 0
How to represent the area and perimeter of a sandbox with an equation?The dimension of a sand box can be represented as (x + 2) inches and (x + 1) inches. The value of the area in square inches of the sandbox is equal to the value of the perimeter of the sandbox in inches.
Therefore, the equation that can be used to find the value of x can be express as follows:
Hence,
area of the sandbox = (x + 2)(x + 1)
area of the sandbox = x² + x + 2x + 2
area of the sandbox = x² + 3x + 2
Perimeter of the sandbox = 2(x + 2 + x + 1)
Perimeter of the sandbox =2(2x + 3)
Perimeter of the sandbox = 4x + 6
Therefore,
x² + 3x + 2 = 4x + 6
x² + 3x - 4x + 2 - 6 = 0
Hence, the equation is x² - x - 4 = 0
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The reciprocal of 1 3/13
(Type an integer or a simplified fraction.)
IS
Answer:
[tex]\frac{13}{16}[/tex]
Step-by-step explanation:
1 [tex]\frac{3}{13}[/tex] is the same as [tex]\frac{13}{13}[/tex] + [tex]\frac{3}{13}[/tex] = [tex]\frac{16}{13}[/tex]
The reciprocal is just turning the fraction upside down.
Evaluate this answer
By replacing the value of x by 4 the answer to the given Algebraic Expression is 10
What is an Algebraic Expression?
The concept of algebraic expressions is to represent numbers using letters or alphabets without providing their real values. In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.
Solution:
All we have to do to solve the following problem is to replace x by 4
3(4+4)(4+1)/(4+2)(4-2)
(3*8*5)/(6*2)
10
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What are the 5 different equations of lines?
Various linear equations in different forms are : horizontal and vertical line equations, An equation for a line in point-slope form, Linear equation in two-point form, the line's slope-intercept form equation, intercept form
and standard form.
1) Equation of a Vertical Line : x = k , where k is a constant.
2) Equation of a Horizontal Line: y = k , where k is a constant.
3) Form of a Point Slope: y - y1 = m (x - x1).
If the slope m and a point (x1, y1) through which the line travels are known, the point-slope form is helpful.
4) Form of the slope-intercept, y = mx + b
If the slope m and the y-intercept (0, b) are known, the slope-intercept form is helpful.
5) Standard form: a x + b y = c , where a, b and c are constants.
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An object moving at speed s for time t travels distance st. Dale and his dog walked for 1.25 hours at a speed of 4 miles per hour.
How far did Dale and his dog walk?
Write your answer as a whole number or decimal.
how many miles
Dale and his dog walk for 5 miles.
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in common usage.
Given:
Dale and his dog walked for 1.25 hours at a speed of 4 miles per hour.
Since,
Distance = Speed x time
Here, speed = 4 miles per hour and
time is 1.25 hours
So,
Distance = 4 x 1.25
Distance = 5 miles
Hence, Dale and his dog walk for 5 miles.
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the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels. if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean, what is the minimum sample size that should be taken?
If we want to be 90% confident that the sample mean is within 17 kernels of the true population mean then the minimum sample size that should be taken is 83.
Given:
the population standard deviation for the number of corn kernels on an ear of corn is 94 kernels.
if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean
what is the minimum sample size that should be taken = ?
population standard deviation (σ) = 94
margin of error (E) = 17
for 90% confidence interval Zα/2 = 1.645
formula:
sample size (n) = [ zα/2 × σ/E]²
sample size (n) = [1.645×94/17]²
sample size (n) = 82.7
sample size (n) ≈ 83
Hence we get the required answer.
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A point located at (−4, 4) is rotated 180° about the origin. Which of the following shows the coordinates of the point’s new location?
The image of (- 4, 4) by rotation is equal to (4, - 4).
How to find the image of a given point as a result of a rotation
In this problem we get the coordinates of the point and we are asked to find the coordinates of its image by rotation about the origin. The rotation rule is described below:
x' = x · cos θ - y · sin θ
y' = x · sin θ + y · cos θ
Where:
θ - Angle of rotation, in degrees.x, y - Coordinates of the original point.x', y' - Coordinates of the image.First, write the coordinates of the point:
P(x, y) = (- 4, 4)
Second, use the rotation formula to find its image:
x' = - 4 · cos 180° - 4 · sin 180°
x' = 4
y' = - 4 · sin 180° + 4 · cos 180°
y' = - 4
The point (4, - 4) is the image by rotation of the point (- 4, 4).
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What are the 4 types of rational numbers?
Positive Rational Numbers, Negative Rational Numbers, Whole Numbers, Fractions are the 4 types of rational numbers.
1. Positive Rational Numbers: These are numbers that are greater than zero, such as 1/2, 3/4, and 5/6.
2. Negative Rational Numbers: These are numbers that are less than zero, such as -1/2, -3/4, and -5/6.
3. Whole Numbers: These are numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.
4. Fractions: These are numbers that are represented as a ratio of two integers, such as 1/2, 3/4, and 5/6.
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to be considered abnormal height a 20 year old must be 2.1 feet below average or 2.1 feet above average. if the average height is 5.8 feet, at what heights (in interval notation) would a 20 year old be considered abnormal?
A 20 year old has height below 3.7 feet and above 7.9 feet then 20 year old be considered abnormal.
The average height means that the given population determined by the interaction between the environment in which it lives and the resources it commands.
Abnormal means diffrent from what is normal or usual, in a way that worries you or that is unplesant.
We have given that average height is 5.8 feet.
And abnormal height a 20 year old must be 2.1 feet below average height or 2.1 feet above average height.
Therefore 5.8 - 2.1 = 3.7 feet
5.8 + 2.1 = 7.9 feet
Hence height below 3.7 feet abd above 7.9 feet is considered to be abnormal.
That means [-∞ , 3.7] and [7.9,∞] is considered to be abnormal height for 20 year old man.
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WILL GIVE BRAINLIEST
find the slope of the line that passes through the 2 given points.
( -6 , 2 ) and ( -5 , -2 )
Answer:
( -4 , 1 )
Step-by-step explanation:
Answer: -4
(Hope I'm correct :D )
Step-by-step explanation:
Easy, let's start with what we know to find the slope. To find the slope you do:
(y2-y1)/(x2-x1)
For this equation then, we do:
(-2 - 2)/ (-5 - (-6)) Which simplifies to:
-4/1
= -4
So the slope is -4.
Dakota has 128 baseball cards. She wants to put them in an album that has 16 pages.
Dakota can put ________ baseball cards on each page.
Answer: 8
Step-by-step explanation:
128 divided by 16 = 8 baseball cards on each page
8 Baseball card if the page takes the same number of baseball cards
Step-by-step explanation:
If the album as 16pages, and there are 128 baseball cards to share in each pages "equally", then it's going to be 128/16 which equals 8 in each pages
PLEASE HELP ME WITH THIS!! I’ve stuck on this question for a past hour.
Answer:
[tex]\sf a. \quad Scale\;factor=\dfrac{10}{9}[/tex]
b. Enlargement.
Step-by-step explanation:
The original figure is called the "pre-image".
The new, transformed figure is called the "image" and is usually indicated by the addition of ' after the name.
Therefore:
CP is the pre-image.CP' is the image.To find the scale factor of dilation, divide the dimension of the image by the dimension of the pre-image.
[tex]\implies \sf Scale\;factor=\dfrac{CP'}{CP}=\dfrac{20}{18}=\dfrac{10}{9}[/tex]
As the image is larger than the pre-image (and the scale factor is larger than 1), the dilation is an enlargement.
52
Find the volume of the figure
(2 Points)
24 ft
9 ft
15 ft
12 ft
10 ft
Answer: the volume of the figure is 792 ft³
Step-by-step explanation:
The volume of a shape V consists of the volume of a prism V1 and
the volume of the pyramid V2
9²+12²=15²
81+144=225
225≡225
Hence, figure base is а right triangle
So, V=V1+V2
[tex]\displaystyle\\V1=\frac{12*9}{2} *10\\\\V1=6(9)(10)\\\\V1=540\ ft^3\\[/tex]
[tex]\displaystyle\\V2=\frac{1}{3}(\frac{12*9}{2} )(24-10) \\\\V2=\frac{12(9)(14)}{6} \\\\V2=252\ ft^3[/tex]
[tex]V=540+252\\\\V=792\ ft^3[/tex]
Which expression represents the number -2i(5- i) + (17- 8i) rewritten in a + bi
form?
O 15-18i
O 15-2i
O 19 - 18i
O 11 + 8i
Answer:
(a) 15 -18i
Step-by-step explanation:
You want the simplified form of the expression -2i(5- i) + (17- 8i).
Complex numbersFor many purposes, the value i in a complex number can be treated in the same way a variable would be treated. When simplifying an expression involving i, any instances of i² can be replaced with the real value -1.
-2i(5- i) + (17- 8i) = -10i +2i² +17 -8i
= -2 +17 +(-10 -8)i
= 15 -18i
__
Additional comment
Your scientific or graphing calculator can probably help you evaluate such expressions.
Solve the following system of equations. Show your work.
−2x+5y=−2
4x−10y=4
Solution:
There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.
What does a system of equations' graphical solution look like ?The intersection locations of all the aforementioned equations can be found using graphic solutions to a system of equations.
Only when the equations have an intersection point can a system of two or more equations be solved.
According to the given information
A set of equations including
4x - 10y = 4 and 2x + 5y = - 2... (ii).
Now, when we multiply equation(i) by 2, we get
- 4x + 10y = - 4. (iii).
Adding (ii) and (iii) now gives us,
0x + 0y = 0.
Since 0 = 0, these coincident lines have an infinite number of solutions.
There are an infinite number of solutions to the system of equations 2x + 5y = - 2 and 4x - 10y = 4.
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Write an equation perpendicular to 2x + y = −5 and passing through (1,1)
The vertices of a triangle are A(2,5) B(1,2) and C(3,1). Find the coordinates of the image after a rotation 90° clockwise about the origin.
Answer:
A’ (5,2) B’ (2,1) and C’ (1,3)
Step-by-step explanation:
When we reflect a point (x,y) over x-axis, we get (x,-y)
A ( 2,5) becomes (2,-5)
B (1,2) becomes (1,-2)
C ( 3,1) becomes (3,-1)
Then we proceed to rotate 90 degrees counterclockwise about the origin
(x,y) becomes (-y,x)
(2,-5) becomes (5,2)
(1,-2) becomes (2,1)
(3,-1) becomes (1,3)