we have that the midpoint is (-2,-7)
and the endpoint is (12,-9)
We remember the midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where (x1,y1) are the coordinates of one endpoint and
(x2,y2) are the coordinates for the other endpoint.
Here, we are trying to find (x2,y2) given that
(x1, y1) ---> (12, -9)
[tex]\begin{gathered} x_1=12 \\ y_1=-9 \end{gathered}[/tex]And since we also know the midpoint M(-2, -7), making a comparison with this and the midpoint formula, we get two equations, the first one is:
[tex]\frac{x_1+x_2}{2}=-2[/tex]substituting x1 and solving for x2:
[tex]\frac{12+x_2}{2}=-2[/tex][tex]\begin{gathered} 12+x_2=4 \\ x_2=4-12 \\ x_2=-8 \end{gathered}[/tex]And now, with the second equation which is:
[tex]\frac{y_1+y_2}{2}=-7[/tex]we substitute y1 and solve for y2:
[tex]\frac{-9+y_2}{2}=-7_{}[/tex]solving for y2:
[tex]\begin{gathered} -9+y_2=-14_{} \\ y_2=-14+9 \\ y_2=-5 \end{gathered}[/tex]This the other endpoint (x2,y2) is at (-8,-5)
Write a polynomial f (x) that satisfies the given conditions.
Polynomial of lowest degree with zeros of -4 (multiplicity 3), 3 (multiplicity 1), and with f (0) =960.
f (x)=
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1). The polynomial is f(x)=-5(x+4)³(x-3).
Given that,
Lowest degree polynomial with f(0) = 960 with zeros of -4 (multiplicity 3), 3(multiplicity 1)
We have to find the polynomial of f(x) which satisfy the conditions.
Here,
We have the zeros of the polynomial are -4 (multiplicity 3), 3(multiplicity 1)
Which we can write as -4,-4,-4,3 are the zeros.
Then we can write the polynomial as
f(x)=ω(x+4)³(x-3)
We have to first find the value of ω.
So,
We have f(0)=960
ω(0+4)³(0-3)=960
ω(4)³(-3)=960
64ω(-3)=960
-192ω=960
ω=960/-192
ω=-5
We got the ω as -5.
The polynomial f(x)=-5(x+4)³(x-3)
Therefore, the polynomial is f(x)=-5(x+4)³(x-3).
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Which figure is a line?
Answer:
Bottom left
Step-by-step explanation:
The figure that looks like <-------------------------> is a line
Top left *------------------------* is a segment
Bottom right is a ray *---------------->
Top right is a * point or dot
I hope this helps!
Please help me with this!!!
Answer:
Is this correct??
if yes reply
Which relation is a function?
Responses
A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
Image with alt text: A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
Coordinate grid with graph of a vertical line at x equals 3.
Image with alt text: Coordinate grid with graph of a vertical line at x equals 3.
A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.
Image with alt text: A coordinate grid with the graph of a circle centered at the origin and passing through the point begin ordered pair 2 comma 1 end ordered pair.
A coordinate grid with graph of a curve that increases through the third quadrant through the origin and exits the first quadrant
The relation which is a function among the answer choices is; A coordinate grid containing a U shape with arrows on both ends that opens to the right. The bottom portion of the U passes through the origin.
What is a function?A function is a relation in which each element of the domain is associated with exactly one element of the codomain.
A relation can be tagged a function if it describes that there should be only one output (y - value) for each input ( x - value). Put simply, a function is a kind of relation (defined by a set of ordered pairs) in which case, it ensures that every x-value is associated with only one y-value.
On this note, since the relation described in the first answer choice is such that every x-value is associated with only one y-value as it is a parabola (quadratic function), it is termed a function.
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The histogram shows the distribution of hurricanes that have hit a country from 1851 through 2015, where 1 is the weakest level and 5 is the strongest level.
(a) Find the mean, variance, and standard deviation of the probability distribution.
(b) Interpret the results.
Hurricanes
1
2
3
4
5
0.0
0.1
0.2
0.3
0.4
0.5
Category
Probability
0.419
0.276
0.225
0.068
0.012
The mean = 0.2, variance = 0.03226 and Standard deviation = 0.1796
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given:
level x
1 0.419
2 0.276
3 0.225
4 0.068
5 0.012
So, mean = (0.419+ 0.276 + 0.225+ 0.068 + 0.012)/5
mean = 0.2
level x (x- mean) (x- mean)²
1 0.419 0.219 0.0479
2 0.276 0.076 0.0057
3 0.225 0.025 0.000625
4 0.068 -0.268 0 .0718
5 0.012 -0.188 0.0353
So, variance = 0.032265
standard deviation = √(variance)
Standard deviation = √(0.032265)
Standard deviation = 0.1796
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75+25x=300 situation
write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
an equation of the line in point-slope form is
An equation of the line in point-slope form is y = 6x + 50.
Define point slope form.y = y₁ = m(x -x₁) is the equation of a straight line, where m is the slope and (x₁, y₁) are the coordinates at a given point on the line (see slope-intercept form). When you know the slope and another point on the line, the point-slope form of a linear equation is most helpful for locating a point on a line. When two other points are known, it can also be used to locate a point on a line.
Given,
y₂ = 200
y₁ = 230
x₂ = 30
x₁ = 25
Slope = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Slope = [tex]\frac{230-200}{30-25}[/tex]
Slope = [tex]\frac{30}{5}[/tex]
Slope = 6
Equation:
y - y₁ = m(x - x₁)
y - 200 = 6(x - 25)
y - 200 = 6x - 150
y = 6x + 50
An equation of the line in point-slope form is y = 6x + 50.
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Use the figure to answer the following question.
If AC||DE, which of the following justifies ΔABC ~ ΔDBE?
A. Definition of Similar Triangles
B. SAS Similarity Theorem
C. SSS Similarity Theorem
D. AA Similarity Postulate
The statement that justifies the triangles' similarity is (c) SSS similarity theorem
How to determine the statement that justifies the triangles?The triangles are given as
Triangle ABC and Triangle DBE
From the figure, we can see that the corresponding vertical lines of either triangle are parallel (but not equal)
This means that, the triangles are similar triangles
This is so because the other two sides of the smaller triangle lie completely on the bigger triangle
As a general rule, the corresponding sides of similar triangles are in proportions
So, we can say that the corresponding side lengths of the triangles are similar
The statement that justifies this is the Side-Side-Side similarity theorem
Hence, the true statement is (c) SSS similarity theorem
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suppose you are35 years old and would like to retire at age65 . Furthermore, you would like to have a retirement fund from which you can draw an income of $150000 per yearforever! How much would you need to deposit each month to do this? Assume a constant APR of8 % and that the compounding and payment periods are the same.
Answer:
$1258.09
Step-by-step explanation:
You want the monthly annuity payment that will let you withdraw $150,000 per year forever from an account earning 8% after 30 years.
Account balanceIn order to withdraw an amount "forever," the withdrawal amount must be equal to the interest earned by the account.
I = Prt
150,000 = P(0.08)(1)
P = 150,000/0.08 = 1,875,000
Annuity paymentThe value of an ordinary annuity is given by the formula ...
A = P(12/r)((1 +r/12)^(12t) -1) . . . . . where P is the monthly payment, and r is the annual interest rate earned over a period of t years.
Using the values we know, we can find P:
1875000 = P(12/0.08)((1 +0.08/12)^(12·30) -1) = 1490.359449P
P ≈ 1258.09
You would need to deposit $1258.09 each month.
__
Additional comment
The formulas used here assume that the deposits and withdrawals occur at the end of the month.
U.S. growers harvested 11 billion bushels of corn in 2005. About 1.9 billion bushels were exported, and 1.6 billion bushels were used for ethanol. Choose one bushel of corn at random. What is the probability that it was used either for export or for ethanol?
Answer:
32% or 31.82%
Step-by-step explanation:
so total = 11 billion and export + ethanol = about 3.5 billion so the probability is 3.5/11 or 35/110 which, as a percent, can be written as 32% or more accurate, 31.82% so this is answer
Simplify the fraction
36
84
as much as possible.
36
84
3
7
5
12
Answer:
3/7
Hope this helps!
Have a good day :).
Jasmine paid $17.60 for a blender that was originally $22. What percent discount did she receive?
Answer:
20% off
Step-by-step explanation:
22-17.60=4.4
(5)4.4=22
please help me solve this
Answer:
bottom right
Step-by-step explanation:
bottom right
Consider a population that begins growing exponentially at a base rate of 4.3% per year and then follows a logistic growth pattern. If the carrying capacity is 62 million, find the actual fractional growth when the population is at 10 million, 30 million, and 50 million.
The actual fraction of growth-
a) population = 10 million; growth rate = 559/155.
b) population = 30 million; growth rate = 344/155
c) population = 50 million; growth rate = 126/155
What is defined as the exponential population growth?In exponential growth, the per capita (per person) growth rate of a population remains constant regardless of population size, causing the population to grow faster and faster as it grows larger.The logistic growth rate of a population decreases as population size approaches a maximum imposition by limited resources available in the environment, recognised as the carrying capacity (K).The base growth rate = 4.3%.
The current carrying capacity = 62 million.
The actual fractional growth for the given values are-
growth rate = r * (1 - population/carrying capacity)
a) population = 10 million,
Put the values;
growth rate = 4.3 × (1 - 10/62)
growth rate = 559/155 is the actual fraction of growth.
b) population = 30 million,
Put the values;
growth rate = 4.3 × (1 - 30/62)
growth rate = 344/155 is the actual fraction of growth.
c) population = 50 million,
Put the values;
growth rate = 4.3 × (1 - 50/62)
growth rate = 126/155 is the actual fraction of growth.
Thus, the actual fraction of growth is estimated.
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help with the first one ?
The solution of the equation is x = 5.
How to solve equation?The equation is written as follows:
- 94 = -2 (8x + 7)
The variable to be found as variable x.
A variable is a number represented with a letter in an equation.
Hence,
- 94 = -2 (8x + 7)
open the bracket on the right side of the equation
-94 = - 16x - 14
add 14 to both sides of the equation
-94 = - 16x - 14
-94 + 14 = - 16x - 14 + 14
-80 = - 16x
divide both sides by -16
x = -80 / -16
x = 5
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c(x)=(x-5)^3, what is c(3)
Answer:
-8
Step-by-step explanation:
You want the value of c(3) when c(x) = (x -5)^3.
Function valueThe value of a function is found by substituting the argument for the variable and doing the arithmetic.
c(x) = (x -5)^3
c(3) = (3 -5)^3 = (-2)^3
c(3) = -8
The parent function f(x) = square root of x is transformed to g(x) = f(-x) - 2
Answer:
A
Step-by-step explanation:
below is the parent function graphed and according to the chart we move the graph down 2 units and reflect it over the x axis and a is the only option
If you spend 1.5 hours a week studying for English and 6.5 hours studying for math what is the ratio
of time spent studying in math to studying for English?
Question Help: please break it down because I don’t understand
Answer:
the ratio is 6.5 : 1.5
Step-by-step explanation:
it asks "what is the ratio of time spent studying in math to studying for English?"
ratio uses the ":" mark. also you put the parts like this:
first part : second part
the parts can be found by looking for the "to" as indicated bold in the question
the first part of the ratio it asks is the "time spent studying in math" in hours which is 6.5
the second part of the ratio it asks is the "time spent studying in English" in hours which is 1.5
so the answer is:
6.5 : 1.5
Answer:
Ratio of time spent studying in math to studying for English
[tex]\large \text{$=\dfrac{13}{3}$ }[/tex]
Step-by-step explanation:
What is a ratio?
We use ratios to compare two numeric quantities or quantities with the same units
Basically a ratio of one quantity x to another quantity y can be expressed in the following ways, all read as the ratio of x to y
x/ y
x to y
x : y
The most useful way of representing a ratio is by using the fractional form because it can be used in determining other quantities
In this problem you spend 6.5 hours/week studying for math and 1.5 hours/week studying for English
Since both units are the same (hours/week) we can compute the ratio as
[tex]{\dfrac{\text{Number of hours studying math}}{\text{Number of hours studying English}}\\\\= \dfrac{6.5}{1.5}\\\\[/tex]
We can simply this fraction as follows
Multiply both numerator and denominator by 10
[tex]= \dfrac{65}{15}\\\\[/tex]
Divide both sides by 5
[tex]\dfrac{65 \div 5}{15 \div 5}\\\\= \boxed{\bold{\dfrac{13}{3}\\\\}}[/tex]
This is the same as 13:3 or 13 to 3
(Be careful what is the numerator and what is the denominator.
If the question had asked for the ratio of hours studying English to hours studying Math then the ratio would be 1.5/65 = 15/65 = 3/13)
Find the mode or modes (if any).5, 9, 96, 3, 2, 8, 79, 1, 4, 16
Given:
5, 9, 96, 3, 2, 8, 79, 1, 4, 16
To determine the mode based on the given data set, we note first that mode is the number in a data set that occurs most frequently. Since each value occurs only once, there is no mode of this data set.
Therefore, the answer is: no mode or none.
The data in this table represents a linear function
What is the slope of this line?
The slope of the line is [tex]\frac{2}{3}[/tex]
What is slope of a line?The increase divided by the run is the slope. By examining the rise and run, you can infer the slope of a line from its graph. A line has the property that its slope remains constant throughout.
Determine the coordinates of two points along the line that you choose. Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run). Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.
The slope of the line is [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]
⇒ [tex]\frac{-7-(-5)}{9-6}[/tex]
⇒ [tex]\frac{-7 + 5}{ 3} = \frac{2 }{3}[/tex]
Thus m = 2/3
Similarly in second case : [tex]\frac{y_{2}-y_{1} }{x_{2}- x_{1} }[/tex]
⇒ [tex]\frac{-15 - (-11)}{ 21 - 15}[/tex]
⇒ [tex]\frac{4}{6}[/tex]
= 2/3
Thus the slope of the given table is 2/3
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The mark scored in a test by ten pupils are as follows: 15, 14, 15, 13, 16, 16, 17, 13, 16, 17. Find the modal mark?
The modal mark is 16.because as we can see there are two 15, two 13,one 14, two 17 and three 16.
Write an equation (a) in slope-intercept form and (b) in standard form for the line passing through (-2,5) and parallel
to x + 3y = 7.
a) The equation of the line in slope-intercept form is
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
b) The equation of the line in standard form is
(Type your answer in standard form.)
The equation of the line passing through points (-2, 5) can be written as follows
slope intercept form: y = -x/3 + 13/3standard form: x + 3y = 13How to write the equation of the line in slope-intercept formEquation of a straight line is an equation of the form y = mx + c, where
m = slopec = interceptThe slope is the gradient which is the ratio of the difference in the y direction to the difference in x direction.
given that the equation of the line is x + 3y = 7
rewriting the equation gives
y = -x/3 + 7/3
hence the slope is -1/3, and this is equated with the formula for slope
[tex]\frac{y-y_{1} }{x-x_{1} }=-\frac{1}{3}[/tex]
substituting the values for points (-2,5) and cross multiplying gives
3 (y - 5) = - ( x - -2)
y - 5 = - (x + 2 ) /3
y - 5 = -x/3 - 2/3
y = -x/3 - 2/3 + 5
y = -x/3 + 13/3
Rewriting the equation of the line in standard form is done as follows
y = -x/3 + 13/3
3y = -x + 13
x + 3y = 13
The equations are gotten from substitution the values to the formula for slope and substituting. Rearranging the equation gives the equation in slope intercept form and in standard form.
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How can you use the Distributive Property to find 11 × 5?
Answer:
You cant use the distributive property because it is when the equation is like this: ax(b+c) so if it was 11x(5+0) you would multiply the 5 by 11 by itself and multiply 0 with 11 then you add them and get 55. I hope that helps :)
Step-by-step explanation:
Consider the incomplete paragraph proof.
Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN
Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.
Because of the unique line postulate, we can draw unique line segment PM. Using the definition of reflection, PM can be reflected over line l. By the definition of reflection, point P is the image of itself and point N is the image of ________. Because reflections preserve length, PM = PN.
Given that P is a point on the perpendicular bisector, l, of MN, we have proved that PM = PN because By the definition of reflection, point P is the image of itself and point N is the image of N.
How to Interpret the Perpendicular Bisector?We are given :
P is a point on the perpendicular bisector, l, of MN.
Now, we want to prove that PM = PN
A Reflection is a transformation in which the figure is the mirror image of the other. Every point is a mirror reflection of itself .
By the definition of reflection, we can deduce that point P is the image of itself , and point N is the image of M .
The line l acts as a Line of symmetry or axis of reflection.
Now, in transformations, we know that reflections preserve length and as a result, PM = PN.
Therefore, we will conclude that point N is the image of M .
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Answer: Point M
Step-by-step explanation:edge 2023
Describe the transformation that shows Figure A is similar to Figure B
Dilate figure A with center o and scale factor 2
What is transformation?
The transformation, or f: X → X, is the name given to a function, f, that maps to itself. The pre-image X becomes the picture X following the transformation. Any operation, or a combination of operations, such as translation, rotation, reflection, and dilation, can be used in this transformation. A function can be moved in one way or another using translation, rotation, reflection, and dilation. A function can also be scaled using rotation around a point.
Example: A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
We know that re-sizing an item uses a transition called dilation.
In the figure the dimensions of the figures differ by a factor of 2.
Thus, dilation of figure A by a factor of 2 shows figure A is similar to Figure B
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Which linear function has the same slope as the one that is represented by the table?
y = -1/5x +1/2 linear function has the same slope .
What is slope ?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. We shall comprehend the slope-finding method and its applications in this essay.
First solve for the slope
m =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
m=[tex]\frac{0-\frac{3}{5} }{\frac{1}{2} -\frac{1}{5} }[/tex]
m = [tex]\frac{-1}{5}[/tex]
Look for the linear equation with the same value of m after determining the slope (parallel equation).
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Find P(A/B), in S = {10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80), A = 40 or less in S and B = even in S. Use fraction form for the probability
Answer:
P(A|B) = 1/2
Step-by-step explanation:
Sample space for B = {10, 20, 30, 40, 50, 60, 70, 80}
where B is even
Total number of elements in sample space = 8
P(A|B) = Probability of a number being 40 or less from the sample space of 8
Sample space for A|B = {10, 20, 30, 40}
So out of a possible 8 elements in the sample space for B only 4 elements can be chosen for the sample space of A
So P(A|B) = 4/8 = 1/2
Find the equation of the line passing through the points (1.-2) and (-2,7). Write the equation in slope-intercept form. A) y = 3x + 13 B) y = 3x - 5 C) y = -3x -2 D) y = -3x + 1
The equation is of the form y=mx+b, where m = slope and b = y-interset. Therefore, find m and b:
For m
[tex]m=\frac{y2-y1}{x2-x1}=\frac{7-(-2)}{-2-1}=\frac{7+2}{-3}=\frac{9}{-3}=-3[/tex]For b
[tex]\begin{gathered} y=mx+b \\ -2=-3(1)+b \\ -2=-3+b \\ -2+3=-3+b+3 \\ b=1 \end{gathered}[/tex]So, the equation is:
[tex]y=-3x+1[/tex]Answer: D.
What are the zeros of the polynomial function f(x) = x3 + 9x2 + 20x? (5 points)
0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4
The zeros of the function f(x) = x³ + 9x² + 20x is :
0, 5 ,4
Explanation :Steps to solve quadratic equation:
Put all of the terms on one side of the equal sign and zero on the other.Factor.Set each factor to a value of zero.Each of these equations must be solved.Because they are the values of x for which f(x) = 0, the solutions of the quadratic equation ax² + bx + c = 0 correspond to the roots of the function f(x) = ax² + bx + c.Check your answer by plugging it into the original equation.
Given function,
f(x) = x³ + 9x² +20x
take x common from f(x),
=> x(x² + x - 20) = 0
=> x(x² + 5x + 4x + 20) = 0
=> x( x + 5 ) + 4 ( x +5 ) = 0
=> (x + 5) ( x + 4 ) = 0
=> x -5 = 0 or x -4 = 0
=> x = 5 and x = 4 .
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Please help I’ll mark you as brainliest if correct!!
Time can be used to quantify, contrast, or even rank the length of events or the gaps between them. To complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
What is meant by Time?Time can be defined in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present and into the future. The duration of events or the gaps between them can be calculated, compared, or even ordered utilizing time.
Given time needed for each meals are;
Turkey = 70 min
Pumpkin pie = 17 min
Rolls = 30 sec
coffee = 45 sec
Total time = 87 min 75 sec
= 1 hour 27min 75 sec
So in order to complete the cooking at 2:00 PM, George needs to start his cooking at 12:30 PM.
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