Answer:
To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 and with the center of dilation at the origin (0, 0), we need to apply the dilation formula:
(x', y') = (2 * (x - 0) + 0, 2 * (y - 0) + 0) = (2x, 2y)
For point A, the original coordinates are (-4, 1), so we substitute these values into the dilation formula:
(x', y') = (2 * (-4 - 0) + 0, 2 * (1 - 0) + 0) = (-8, 2)
So, after the dilation, the new coordinates of point A are (-8, 2).
For point B, the original coordinates are (-1, 3), so we substitute these values into the dilation formula:
(x', y') = (2 * (-1 - 0) + 0, 2 * (3 - 0) + 0) = (-2, 6)
So, after the dilation, the new coordinates of point B are (-2, 6).
Answer:
Step-by-step explanation:
Step 1: Understanding the Dilation
A dilation with a scale factor of 2 and a center of dilation at the origin is a transformation that enlarges or shrinks an object by a factor of 2, with the origin (0, 0) as the center of the dilation.
Step 2: Using the Formula
To find the coordinates of the dilated points, we use the formula:
(x', y') = (2 * x, 2 * y)
Where (x, y) are the original coordinates of the points, and (x', y') are the coordinates of the dilated points.
Step 3: Finding the Coordinates of A′
We are given that the original coordinates of point A are (-4, 1), so we substitute these values into the formula:
A′ = (2 * -4, 2 * 1) = (-8, 2)
Step 4: Finding the Coordinates of B′
We are given that the original coordinates of point B are (-1, 3), so we substitute these values into the formula:
B′ = (2 * -1, 2 * 3) = (-2, 6)
Step 5: Conclusion
So, after a dilation with a scale factor of 2 and a center of dilation at the origin, the new coordinates of A′ and B′ are (-8, 2) and (-2, 6) respectively.
It takes Mrs. Ritts 3 hours to mow her back yard. This is 2 hours less than twice the time it takes her to mow the front yard. Write an equation that will show the time it takes her to mow the front yard. (use x as the variable)
Answer:
5/2 hours or 2 hours and 30 minutes
Step-by-step explanation:
The x represents the time it took Mrs. Ritts to mow the front yard. We don't know this time so put it as a variable. We also know that the time to mow her backyard is equal to 2 times the variable and then minus 2.
Equation: 3 = (2x) - 2
Now we just isolate the x. First, start by adding 2 to both sides.
5 = 2x
Now just divide both sides by 2.
5/2 = x
5/2 as a mixed number would be 2 and 1/2 so that means the time would be 2 and a half hours.
Find R. Round to the nearest tenth.
Answer:
letter R rounded off to the nearest tenth is 40
15 is the answer because this is the nearest
37
B
12
35
Find cos(o) in the triangle.
A
Answer:
cos α = 35/37-------------------------------
Definition:
cosine = adjacent leg / hypotenuseSubstitute for cos α:
cos α = 35/37(Hari Bahadur sold a watch after allowing 20% discount and then adding 13% VAT. If the discount amount is Rs.192 more than VAT amount then find the marked price and selling price of the watch.)
Answer: Let's assume that the marked price of the watch is M.
The discount amount would be 20% of M, which can be calculated as:
0.2 * M = 0.2M
The selling price after the discount would be:
M - 0.2M = 0.8M
The VAT amount would be 13% of the selling price after the discount, which can be calculated as:
0.13 * 0.8M = 0.104M
Now, as the discount amount is Rs.192 more than the VAT amount, we can write an equation:
0.2M = 0.104M + 192
0.096M = 192
M = 192 / 0.096 = 2000
So, the marked price of the watch is Rs.2000 and the selling price after the discount and VAT is 0.8M = 0.8 * 2000 = 1600.
Step-by-step explanation:
If 15 + 3x is 10 more than 17, what is the value of 6x?
The map shows air travel distances from Minneapolis to four other cities. Use the triangle
inequality to find the range of possible distances between:
Minneapolis
1584
San Francisco
355
1056
1018
Chicago
Houston
New York
Chicago and Houston
San Francisco and Chicago
New York and San Francisco
Houston and New York
The triangle inequality states that the sum of any two sides of a triangle must be greater than the third side.
Using this principle, we can calculate the range of possible distances between each of the following cities:
Minneapolis and San Francisco: The sum of the distances from Minneapolis to Chicago and from Chicago to San Francisco is 1584 + 355 = 1939. Therefore, the minimum distance between Minneapolis and San Francisco is 1939 - 1584 = 355. The maximum distance between Minneapolis and San Francisco is 1939.
Minneapolis and Houston: The sum of the distances from Minneapolis to Chicago and from Chicago to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Minneapolis and Houston is 2640 - 1584 = 1056. The maximum distance between Minneapolis and Houston is 2640.
Minneapolis and New York: The sum of the distances from Minneapolis to Chicago and from Chicago to New York is 1584 + 1018 = 2602. Therefore, the minimum distance between Minneapolis and New York is 2602 - 1584 = 1018. The maximum distance between Minneapolis and New York is 2602.
Chicago and Houston: The sum of the distances from Chicago to Minneapolis and from Minneapolis to Houston is 1584 + 1056 = 2640. Therefore, the minimum distance between Chicago and Houston is 2640 - 1056 = 1584. The maximum distance between Chicago and Houston is 2640.
San Francisco and Chicago: The sum of the distances from San Francisco to Minneapolis and from Minneapolis to Chicago is 355 + 1584 = 1939. Therefore, the minimum distance between San Francisco and Chicago is 1939 - 355 = 1584. The maximum distance between San Francisco and Chicago is 1939.
New York and San Francisco: The sum of the distances from New York to Minneapolis and from Minneapolis to San Francisco is 1018 + 355 = 1373. Therefore, the minimum distance between New York and San Francisco is 1373 - 1018 = 355. The maximum distance between New York and San Francisco is 1373.
Houston and New York: The sum of the distances from Houston to Minneapolis and from Minneapolis to New York is 1056 + 1018 = 2074. Therefore, the minimum distance between Houston and New York is 2074 - 1056 = 1018. The maximum distance between Houston and New York is 2074.
Cory is a bird-watcher. He estimates that 30% of the birds he sees are
American robins, 20% are dark-eyed juncos, and 20% are song sparrows. He
designs a simulation.
Let 0, 1, and 2 represent American robins.
Let 3 and 4 represent dark-eyed juncos.
Let 5 and 6 represent song sparrows.
Let 7, 8, and 9 represent other birds.
The table shows the simulation results.
05716
16803
96568
32177
33855
76635
92290
88864
72794
14333
79019
05943
77510
74051
87238
97895
86481
94036
12749
24005
According to this simulation, what is the probability that at least one of the
next five birds he sees is a song sparrow?
The probability that at least one of the next five birds he sees is a song sparrow is 0.65
How to determine the probability from the simulationFrom the question, we have the following parameters that can be used in our computation:
05716 16803 96568 32177 33855
76635 92290 88864 72794 14333
79019 05943 77510 74051 87238
97895 86481 94036 12749 24005
Also, we have:
Let 0, 1, and 2 represent American robins.Let 3 and 4 represent dark-eyed juncos.Let 5 and 6 represent song sparrows.Let 7, 8, and 9 represent other birds.Using the above as a guide, we have the following individual representations of at least one sparrow bird
Yes Yes Yes No Yes
Yes No Yes No No
No Yes Yes Yes No
Yes Yes Yes No Yes
So, we have
At least one sparrow bird = 13
Total = 20
So, the probability is
P = 13/20
Evaluate
P = 0.65
Hence, the probability is 0.65
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David's phone has about 10,000 songs. The distribution of play time for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time i of these songs.
a) Calculate the mean and standard deviation of the sampling distribution.
b) Interpret the standard deviation from part (a)
On solving the provided question, we can say that The following are the mean and standard deviation of the sample distribution of x: Average: 225 sec. 19 second standard deviation.
What is standard deviation?Standard deviation is a statistic that expresses the variability οr variance of a grοup of numbers. While a high standard deviation suggests that the values are mοre dispersed, a low standard deviation suggests that the values tend tο be closer to the established mean.
A measure of hοw dispersed the data are frοm the mean is the standard deviation (οr ). When the standard deviation is lοw, the data tend to be grouped around the mean, and when it is large, the data are mοre dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each scοre from the mean.
The median matches the median οf the population.
The pοpulation standard deviation is divided by the square root of the sample size tο produce the standard deviation.
The following are the criteria fοr this issue:
average population of 225 seconds.
60 second population standard deviatiοn.
10 second sample size.
Consequently, the following is the standard deviation fοr the sample distributiοn of x:
19 seconds are equal to 60/√(10).
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Determine if the point (-6, 3) is a solution to the system.
y =1/2x+6
2y = -x-3
The point (-6, 3)
is a solution to the system of equations.
is not a solution to the system of equations.
Answer:
is not a solution to the system of equations.
Step-by-step explanation:
Sure! Here's a step-by-step solution to determine if the point (-6, 3) is a solution to the system:
Substitute the x and y values into the first equation:
y = 1/2x + 6
3 = 1/2(-6) + 6
Simplify the right side of the equation:
3 = -3 + 6
Solve for the value of y:
3 = 3
The first equation is satisfied, so now let's substitute the x and y values into the second equation:
2y = -x - 3
2 * 3 = -(-6) - 3
6 = +6 - 3
Simplify the right side of the equation:
6 = -3
The second equation is not satisfied, so the point (-6, 3) is a not solution to the system.
Examine the figure below, find the length of b, round to the nearest whole
number.
32°
L
b
M
The length of the side using cosine rule and approximating to a whole number gives 23
How to use Cosine Rule?The law of cosines is used to find the missing parts of an oblique triangle when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.
This is expressed as;
b² = a² + c² - 2ac cos b
Plugging in the relevant values gives;
b² = 28² + 41² - 2(28 * 41) cos 32
b² = 2465 - 1947.118
b² = 517.882
b = √517.882
b = 22.757 ≈ 23
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11311 rounded off to the nearest 100
Answer:
11300
Step-by-step explanation:
The closest 100 to 11311 is 11300
If the number was 11351 you would round up to 11400
Rayna and Desi are building a fence together. It takes Rayna $3$ hours to make $10$ feet of fence line. It takes Desi $1$ hour to make $2$ feet of fence line. How many hours will it take them to build $80$ feet of fence line together?
Answer: Let's call the number of hours it takes for Rayna and Desi to build the fence together as "h". During this time, Rayna will build 10h feet of fence line, and Desi will build 2h feet of fence line.
Together, they will build 10h + 2h = 12h feet of fence line in h hours.
To build 80 feet of fence line, they will need h hours such that:
12h = 80
So,
h = 80 / 12 = 6.67 hours
So it will take Rayna and Desi 6.67 hours to build 80 feet of fence line together.
Step-by-step explanation:
Please, answer the question shown below.
D. $402 Million.
Using fitted curve, a similar new blockbuster would expect
C. 290 millionWhat is fitted curve?A fitted curve is a curve that is created to model a set of data points, such that the curve passes as closely as possible to the points. The process of finding a fitted curve is called curve fitting or regression analysis.
Tracing the fitted curve, we have that
week 1 = 150 million
Week 2 = 75 million
Week 3 = 40 million
Week 4 = 25 million
Adding up the amounts
= 150 + 75 + 40 + 25
= 290 million
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Examine the figure below, find each angle’s measure.PLEASE HELPP ANYONEEE?
The measures of all the angles D, C, E and F are 90 degrees
How to determine the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The circle
On the circle, we have the angles D, C, E and F to be angles in a semicircle
As a general rule:
Angles in a semicircle are right angle
This means that
Angle in a semicircle = 90 degrees
Using the above as a guide, we have the following:
D, C, E and F = 90 degrees
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Consider a function f(x) = x ^2 . A second function h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).
Answer:
So the equation of the transformed function h(x) is h(x) = -x^2 + 3.
Step-by-step explanation:
Since h(x) is the result of reflecting f(x) across the x axis and translating it 3 units in the positive y-direction, we know that:
The x-coordinates of f(x) and h(x) are the same, so x is unchanged.
The y-coordinates of f(x) and h(x) are reflected across the x axis, so we need to negate the y-coordinate.
The y-coordinate of h(x) is shifted up by 3 units, so we need to add 3 to the y-coordinate.
Given the equation of f(x) = x^2, the equation of h(x) can be written as:
h(x) = -x^2 + 3
So the equation of the transformed function h(x) is h(x) = -x^2 + 3.
Find the surface area of the pyramid. The side lengths of the base are equal.
The surface area of the pyramid is 116.4 sq. ft.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.
The area of the triangle is given as:
A = 1/2 (b)(h)
For the face of the pyramid:
b = 12 and h = 9
Substituting the values we have:
A = 1/2 (12)(9)
A = 54 sq. ft
The pyramid consists of three faces thus,
A = 3(54) = 162 sq ft
For the base of the pyramid:
b = 12 and h = 10.4 ft
A = 1/2(12)(10.4)
A = (6)(10.4)
A = 62.4 sq ft
The surface area of the pyramid is:
SA = 54 + 62.4
SA = 116.4 sq. ft
Hence, the surface area of the pyramid is 116.4 sq. ft.
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Combine the sum of the exterior angles and the sum of the interior angles of a triangle. Find the sum.
Answer:
Step-by-step explanation:
The sum of the exterior angles of a triangle is equal to 360 degrees, while the sum of the interior angles of a triangle is equal to 180 degrees.
When you combine the sum of the exterior angles and the sum of the interior angles of a triangle, you get:
360 degrees + 180 degrees = 540 degrees
So, the sum of the exterior angles and the sum of the interior angles of a triangle is equal to 540 degrees.
After birth, a baby's weight increased at a steady rate for several weeks.
A linear model of this situation contains the values (1, 7.3) and (9, 9.7), where x represents the number of weeks, and y represents the baby's weight, in pounds.
Q.What was the baby's weight at birth?
A.0.3 of a pound
B.8 pounds
C.7.3 pounds
D.7 pounds
Answer:
The correct answer is D. 7 pounds.
Step-by-step explanation:
The weight of the baby when its born is 7 pounds.
(a) In the figure below, m AB = 54° and m CD = 66°. Find m ZAEB.
A
B
E
C
D
m 2 AEB =
The measure of the angle m∠AEB, found using the angle of intersecting secant theorem, where the measure of the arcs intercepted by the secants are m[tex]\widehat{AB}[/tex] = 54°, and m[tex]\widehat{CD}[/tex] = 66° is; m∠AEB = 6°
What is the angle of intersecting secant theorem?The angle of intersecting secant theorem states that the measure of the angle formed by the intersection of two secant is half the positive difference of the arcs intercepted by the secants.
Please find attached the possible drawing in the question, obtained based on the specified parameters and on similar questions on the internet, created with MS Word.
The parameters indicates that we get;
m[tex]\widehat{AB}[/tex] = 54°
m[tex]\widehat{CD}[/tex] = 66°
The angle of intersecting secants theorem indicates that we get;
m∠AEB = (1/2) × (m[tex]\widehat{CD}[/tex] - m[tex]\widehat{AB}[/tex])
Therefore;
m∠AEB = (1/2) × (66° - 54°) = 6°
m∠AEB = 6°
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Which statement best describes the functions represented here?
A.only function p is nonlinear
B. Neither function is nonlinear
C.only function q is nonlinear
D.both functions are nonlinear
Answer:
D
Step-by-step explanation: for p(x), the slope from 0 to 3 is 30, meaning if linear every time x increases by 3, the y value should as well, meaning that six as an x value to be linear should have been 90, but it was not.
For q(x), the slope from 0 to 3 is 90, and following the same thing from above, this means for every 3 units moved on the x, it should increase by 90 units on the y. This means 6 to be linear should have been 200 but instead was 380 making it also nonlinear
HELP ASAP WILL GIVE BRAINLIEST
Which of the following tables represents a linear relationship that is also proportional?
x 2 34
y -303
O
x 4 20
y-2 -1 0
X-214
У 0 12
x012
y-404
The table that represents a linear relationship that is also proportional is; Table 2
How to find the proportional relationship?A proportional relationship is defined as one where there is multiplying or dividing between the two numbers. A linear relationship can be a proportional one (for example y = 2x is proportional), but usually a linear equation has a proportional component plus some constant number (for example y = 2x + 3).
Table 1:
The proportions are;
-3/2, 0/3, 3/4
They are not equal and so not proportional
Table 2:
The proportions are;
-2/4 and -1/2
They are equal and so are proportional
Table 3:
The proportions are;
0/-2, 1/1 and 2/4
They are not equal and so not proportional.
Table 4:
The proportions are;
-4/0, 0/1 and 4/2
They are not equal and so not proportional.
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d. 6.5
templi friebu
4. Mike can empty his pool with a small or large hose. The large hose can pump
triple as much as the small hose. The small hose pumps 20 gallons of water per
minute. He wants to empty his pool in 2 hrs. The pool holds 1200 gallons of water.
Determine the equation that represent this relationship.
a. 1200-60x=2
b. 30x +1200 = 2
c. 45x-1200=2
d) -1200-20x = 2
The relationship representing the amount of water remaining in the pool when using the large hose to pump out is
a. 1200 - 60x = y
How to determine the equationThe amount of water to be pumped out = 1200 gallons
The rate of pumping out using the small hose 20 gallons of water per minute. = -20x
let each minute be x, hence every minute 20x volume of water leaves the pond
The equation is represented as
water remaining = 1200 - 20x
in 2 hours, we have 120 minutes, when will the water finish
water remaining = 0 = 1200 - 20x
20x = 1200
x = 1200 / 20
x = 60 minutes hence 1 hour
For the large hose the rate of pumping out is tripled hence
water remaining = 1200 - 60x
y = 1200 - 60x
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The table below represents which equation?
x −1 0 1 2
y 1 −2 −5 −8
Find the slope of the line that passes through (-8,-1) and (12,4). Write the answer as a fraction in simplest form
slope:
Now write the equation of the line in slope intercept form:
The slope of the line that passes through (-8,-1) and (12,4) is 1/4.
The equation of the line in slope intercept form is y = x/4 - 31/4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be determined by using this mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Substituting the given data points into the slope formula, we have the following;
Slope, m = (4 + 1)/(12 + 8)
Slope, m = 5/20
Slope, m = 1/4.
At point (-8, -1), a linear equation of this line can be calculated in slope-intercept form as follows:
y - y₁ = m(x - x₁)
y - (-8) = 1/4(x - (-1))
y + 8 = x/4 + 1/4
y = x/4 - 31/4.
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What is the slope of this line?
Answer: look at the image for the answer and the solution
Step-by-step explanation:
Of the apps on Juan’s tablet, 3/4 are gaming apps,and 5/7 of the gaming apps are action games.what fraction of the apps on Juan’s tablet are action games?
On solving the provided question, we can say that By fraction, 3/4 times 5/7 is 15/28 and Action games are 15/28 of the apps.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
By fraction,
3/4 times 5/7 is 15/28.
Action games are 15/28 of the apps.
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12.
Find the equation of the circle which touches the line 3y-4x-24 = 0 at the point
(0,8) and also passes through the point (7,9). Prove that this circle also touches the
x-axis. Find the equation of the tangents to this circle which are perpendicular to the
line 3-4x-24=0.
The equation of the circle is (x-3)^2 + (y-4)^2 = 85.the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.
What is the equation of the circleFirst, we find the center of the circle. Since the circle touches the line 3y-4x-24=0 at the point (0,8), the center must lie on the line perpendicular to this line and passing through (0,8), which has the equation 4y + 3x - 32 = 0. The intersection of this line with the line passing through (7,9) and perpendicular to the line 3y-4x-24=0 gives us the center of the circle:
Solving the equations 3y - 4x - 24 = 0 and 4y + 3x - 32 = 0 gives us the point (3,4), which is the center of the circle.
Now, we can find the radius of the circle by using the distance formula between the center (3,4) and the point (7,9):
r = √((7-3)^2 + (9-4)^2) = √(85)
So the equation of the circle is (x-3)^2 + (y-4)^2 = 85.
To prove that the circle also touches the x-axis, we need to show that the distance from the center (3,4) to the x-axis is equal to the radius. The equation of the x-axis is y=0, so the distance from (3,4) to the x-axis is simply 4. Since the radius is sqrt(85), which is also approximately equal to 9.22, we can see that 4 is indeed equal to the radius, so the circle touches the x-axis.
To find the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0, we first find the slope of this line, which is 3/4. The slope of a line perpendicular to this line is the negative reciprocal, which is -4/3.
To find the points of tangency, we need to find the intersection points of the line passing through (3,4) with slope -4/3 and the circle (x-3)^2 + (y-4)^2 = 85. This gives us two points of tangency: (0,7) and (6,1).
The tangent lines at these two points can be found using the point-slope form of the equation of a line, with the slope equal to the negative reciprocal of the slope of the line 3y-4x-24=0:
At (0,7), the tangent line has the equation y - 7 = (-4/3)(x-0), which simplifies to y = (-4/3)x + 7 + 4 = (-4/3)x + 11.
At (6,1), the tangent line has the equation y - 1 = (-4/3)(x-6), which simplifies to y = (-4/3)x + 9.
Therefore, the equations of the tangents to the circle that are perpendicular to the line 3y-4x-24=0 are y = (-4/3)x + 11 and y = (-4/3)x + 9.
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Look at picture please
Answer:
EF this is the correct answer
Multiple step Fnd the value of X.
8)
(X-745)
560 4x0
(3x+2)
36
The value of x in the diagrams are 14 and 99 respectively
How to determine the valuesNote the following points;
Corresponding angles are equal Sum of angles at a point is equivalent to 360 degreesFrom the information given in the diagram
56 degrees and 4x degrees are corresponding
Then,
4x = 56
Make 'x' the subject
x = 14
From the second image
Add the angles and equate to 360 degrees, we have;
3x + 2 + 36 + x - 74 = 360
collect like terms
4x = 360 + 36
4x = 396
Make 'x' the subject
x = 99
Hence, the values are 14 and 99
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An online company is making $60 profit every week. The company owes the bank 300 dollars for the start-up money. How much does the company need to pay the bank and make a profit of 150
Answer:
The company must make $450.
If the company must pay $300, then you will take 300, and since they want to make a profit, which means 1500 dollars more once they pay the 300, the you will add that to 300.
300 + 150 = 450
Now to find how many weeks it will take, you will divide 450 by 60:
450/60 = 7.5
It will take 7 1/2 (or round it to 8)weeks to gain $450, which is enough money to pay the bank $300, and make a profit of $150.
Step-by-step explanation:
Hope it helps! =D
