Plot the image of point B under a dilation about point P
with a scale factor of
Answers
Please find the attached file.
We have been given am image of point B on coordinate plane. We are asked to plot the mage of point B under a dilation about point P with a scale factor of [tex]\frac{1}{2}[/tex].
To solve our given problem, we need to find vertical distance and horizontal distance between point B and point P.
We can see that vertical distance is 4 units as shown in the attachment and horizontal distance is 6 units.
Since the scale of dilation is [tex]\frac{1}{2}[/tex], so the vertical distance between point P and B' would be [tex]\frac{1}{2}[/tex] of 4 that is [tex]\frac{1}{2}(4)=2[/tex].
The horizontal distance between point P and B' would be [tex]\frac{1}{2}[/tex] of 6 that is [tex]\frac{1}{2}(6)=3[/tex].
Now we will count 3 units to left of point P and 2 units upwards. That will be the position of point B'.
The below-attached graph represents the image of point B under a dilation about point P with a scale factor of 1/2.
To plot the image of point B under a dilation about point P with a scale factor of 1/2, follow these steps:
Draw point P on the coordinate plane at any location.From point P, move vertically 6 units up and label the new point as B.From point P, move horizontally 4 units to the left and label the new point as B'.The point where this line intersects the vertical line through point C will be the image of point B under the dilation with a scale factor of 1/2.
Thus, the image of point B will be half as far away from point P as point B.
Hence, the below-attached graph represents the image of point B under a dilation about point P with a scale factor of 1/2.
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Related Questions
What is the area of triangle MNO?
Answers
Answer:
30 [tex]ft^2[/tex]
Step-by-step explanation:
To find the area of a triangle, you must use the formula:
[tex]\frac{1}{2} bh[/tex]
The "[tex]b[/tex]," is the base (12), and the "[tex]h[/tex]," is the height (5).
Plug in the numbers accordingly:
[tex]\frac{1}{2} (12)(5)[/tex]
[tex]\frac{1}{2} (60)[/tex]
30
Misha solves the equation 3 x minus 2 (x + 3) = 4 (x minus 2) minus 7 by applying the distributive property to each side of the equation. The result is 3 x minus 2 x minus 6 = 4 x minus 8 minus 7. Misha then wants to combine like terms. Which are the terms Misha should combine?
Answers
Answer:
2(x+3)=4
2x+6=4
2x=4-6
2x=-2
2x÷2
x=1
Answer:
The terms that Misha should combine are 3x – 2x and –8 – 7
Step-by-step explanation:
Misha have the equation : 3x-2(x+3) = 4(x-2)-7
After applying distributive property, a(b+c) = ab+ac
3x - 2x - 6 = 4x - 8- 7 ..............(1)
Now, we need to combine the like terms, like terms are the terms having the same coefficient and combining them means to combine their coefficients.
In equation (1), 3x and -2x are like terms as it have the same coefficient x
Hence we will solve them and get (3-2)x = x
Similarly, -8 and -7 can be solved and we get -7-8 = -15
Now, the equation becomes, x-6 = 4x-15
Then, again collecting the like terms on L.H.S and R.h.s and then solving, we get
4x - x = 15-6
3x = 9
x = 3
At McCain Middle School, approximately 10 out of every 14 students ride the bus to school each morning.McCain Middle School has 147 students.How many students can be expected to ride the bus to school?
Answers
Answer:
105
Step-by-step explanation:
set a ratio so
10/14=?/147
cross multiply
10*147=?*14
1470=14*?
divide 1470 by 14 and get 105
An
Step-by-step explanation:
Please help me in these simple equations
Answers
Answer:
1. [tex]225cm^2[/tex]
2. [tex]544mm^2[/tex]
3. [tex]405mm^2[/tex]
4. [tex]67.50cm^2[/tex]
5. [tex]495mm^2[/tex]
6. [tex]480cm^2[/tex]
Step-by-step explanation:
1. Square
[tex]A=s^2[/tex]
s = 15 cm
[tex]A=(15cm)^2\\A=225cm^2[/tex]
------------------------------------------------------------------------------
2. Rectangle
[tex]A=l*w\\A=(32mm)(17mm)\\A=544mm^2[/tex]
------------------------------------------------------------------------------
3. Rectangle
[tex]A=l*w\\A=(45mm)(9mm)\\A=405mm^2[/tex]
------------------------------------------------------------------------------
4. Triangle
[tex]A=\frac{hb}{2}\\ A=\frac{(9cm)(15cm)}{2}\\ A=\frac{135cm^2}{2}\\ A=67.50cm^2[/tex]
------------------------------------------------------------------------------
5. Triangle
[tex]A=\frac{hb}{2}\\ A=\frac{(30mm)(33mm)}{2}\\ A=\frac{990mm^2}{2}\\ A=495mm^2[/tex]
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6. Rectangle
[tex]A=l*w\\A=(34cm)(20cm)\\A=480cm^2[/tex]
probability: There are 11 shirts
in your closet, 6 blue and 5
green. You randomly select
one to wear on Monday and
then a different one on
Tuesday. You wear blue shirts
both days.
Answers
Answer:
There was a 54.5% probability of you getting a blue shirt on Monda and a 50% chance on Tuesday.
Solve for x. 5 = − 3 9 x
Answers
Answer:
x = -5/27
Step-by-step explanation:
5 = − 3 · 9x; x = -5/27
The stock of Company A gained 5% today to $34.65. What was the opening price of the stock in the beginning of the day?
Answers
To find the opening price of the stock, we can subtract the 5% gain from the current price. The opening price of the stock in the beginning of the day was approximately $36.47.
Explanation:To find the opening price of the stock, we need to deduct the 5% gain from the current price of $34.65.
Let x be the opening price.
Since the stock gained 5%, the opening price minus 5% of the opening price equals the current price: x - 0.05x = 34.65.
Simplifying the equation, we get 0.95x = 34.65. To solve for x, divide both sides of the equation by 0.95.
The opening price of the stock in the beginning of the day was approximately $36.47.
What is the slope of the line defined by the equation y = -2x + 3?
A)
-2
B)
- 2 / 2
2
D
3
Answers
The answer is A
In the formula for slope intercept it is y= mx+b
The m in the formula is the slope
Answer:
The answer is -2
Step-by-step explanation:
The slope is m.
In an equation, it's shown as y=mx+b, where m is the slope and b is the y intercept.
Help please. Find the value of x in the isosceles triangle shown below
Answers
Answer:
A
Step-by-step explanation:
We need to use some properties of an isosceles triangle and the Pythagorean Theorem.
First, the vertical line down the middle of the triangle is the height, which means the angle is makes with the base is 90 degrees and it bisects the base. So, we have two right triangles, each with a height of 6 and with a base of 4/2 = 2.
We can now use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, a = 6 and b = 2 and x = c, so:
a² + b² = c²
6² + 2² = x²
x² = 36 + 4 = 40
x = √40
Thus, the answer is A.
Answer:
A
Step-by-step explanation:
This triangle contains two congruent right angle triangles
x² = 6² + 2²
x² = 36 + 4
x² = 40
x = sqrt(40)
x = 4sqrt(10)
The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x). How does the graph of g(x) compare to the graph of f(x)? g(x) is stretched horizontally and reflected over the y-axis. g(x) is stretched horizontally and reflected over the x-axis. g(x) is compressed horizontally and reflected over the y-axis. g(x) is compressed horizontally and reflected over the x-axis.
Answers
The correct answer is: g(x) is compressed horizontally and reflected over the y-axis.
To understand how the graph of [tex]\( g(x) = f(-2x) \)[/tex] compares to the graph of the parent function [tex]\( f(x) = x^3 \)[/tex], we need to analyze the effects of the transformations applied to [tex]\( f(x) \)[/tex].
1. The transformation [tex]\( f(-x) \)[/tex] would reflect the graph of [tex]\( f(x) \)[/tex] over the y-axis. This is because for every point [tex]\( (x, y) \)[/tex] on the graph of [tex]\( f(x) \)[/tex], there will now be a corresponding point [tex]\( (-x, y) \)[/tex] on the graph of .
2. The transformation [tex]\( f(2x) \)[/tex] would compress the graph of [tex]\( f(x) \)[/tex] horizontally by a factor of 2. This is because for every point [tex]\( (x, y) \)[/tex] on the graph of [tex]\( f(x) \)[/tex], there will now be a corresponding point [tex]\( \left(\frac{x}{2}, y\right) \)[/tex] on the graph of [tex]\( f(2x) \)[/tex]. The x-values are halved, which means the graph is compressed along the x-axis.
Combining these two transformations, [tex]\( g(x) = f(-2x) \)[/tex] indicates that the graph of [tex]\( f(x) \)[/tex] is first compressed horizontally by a factor of 2 and then reflected over the y-axis.
Therefore, the graph of [tex]\( g(x) \)[/tex] is compressed horizontally and reflected over the y-axis when compared to the graph of the parent function [tex]\( f(x) \)[/tex].
What is the distance between –3 and 2 on the number line? A number line going from negative 5 to positive 5. –5 –1 1 5
Answers
Answer:
The distance is 5.
Step-by-step explanation:
As you want distance, the best approach is to subtract.
My advice when you're dealing with a number line, and a negative and a positive number, is to subtract the negative from the positive, so that you get a positive distance.
Therefore:
[tex]2 - ( - 3) = 2 + 3 = 5[/tex]
Simplify x^2+ 5x + 4 over
x+4
Answers
Answer:
x+1
Step-by-step explanation:
Brian has a piece of yarn that 4 centimeters long how many millimeters long is his piece of yarn
Answers
Answer:
40mm.
there are 10 mm. in a cm, so if there are 4 cm, then there are 40 mm.
Hope this helps :)
The value of the expression 2x + x(100 – 15x) when x = 5 is
119
129
135
145
Answers
Answer:
[tex]135[/tex]
Step-by-step explanation:
[tex]2(5) + 5(100 - 15(5))\\10 + 500-375\\135[/tex]
The value of the expression 2x + x(100 – 15x) when x = 5 is 135.
What is an expression?An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
The given expression is,
2x + x(100 – 15x)
Now we have to find the value of expression when x = 5
Put the value of x in the given expression we get,
2(5) + 5(100 – 15*5)
solving the brackets we get,
10 + 5( 100 - 75)
10 + 5*25
10 + 125
135
hence, the value of the expression 2x + x(100 – 15x) when x = 5 is 135.
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Find the equation of the line that has a slope of 11 and passes through the point (-5,8). Help me please please do it right
Answers
Answer:
y=11x-47
Step-by-step explanation:
The formula for the volume of a cone is V= 1/3pir^2h where V represents the volume, r represents the radius of the base, h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
Answers
The height of the cone is approximately 7.01 centimeters.
We know the volume (V) is 66 cubic centimeters and the radius (r) is 3 centimeters. Substitute these values into the formula:
V = 1/3πr²h
66 = 1/3 × π × 3² × h
Simplify the equation:
Multiply both sides by 3:
200 = π × 9 × h
Cancel out the common factor of 9:
200/9 = π × h
Solve for the height (h):
Divide both sides by π:
h = 200/9π
Then, we have that;
h ≈ 7.01 cm
Therefore, the height of the cone is approximately 7.01 centimeters.
Find the volume of the regular hexagonal prism with side lengths of 4 ft, height of 3ft and apothem of approximately 3.5 ft
Answers
Answer:
A(p) = 84 ft³
Step-by-step explanation:
Volume of regular prism is equal to V(p):
V(p) = Area of the face * h
we know h = 3 ft
A regular hexagonal prism has 6 equal sides forming its face.
Finding the area (A₂) of a triangle formed by center of the prism, straight lines between the center and two adjacents vertex and side between these two vertex, and then multiply that area by 6 (number of equal triangles inside hexagonal prism) we get the area of the face, but we need further consideration, the triangle described above, has doble area of (A₁), the triangle formed by apothem, half side, and straight line between center of the face and the vertex, therefore.
Area of small triangle = base * height
A₁ = (1/2) * 4 * 3,5
A₁ = 2*3,5
A₁ = 7 ft²
A₂ = 2* 7
A₂ = 14 ft²
Finally volume of the hexagonal prism is:
V(p) = 6 * 14
A(p) = 84 ft³
Consider the system of equations.
y=-2x + 4
3y + x=-3
Which statement is true of this system of equations?
Both equations are in slope-intercept form.
The first equation converted to slope-intercept form is y + 2x = 4.
The second equation converted to slope-intercept form is.y =
Neither equation is in slope-intercept form.
Answers
Answer:
the second equation converted to slope-intercept form is y = -1/3x -1
Step-by-step explanation:
what is the volume of a cylinder with a height of 6 cm and a radius of 3 cm
Answers
Answer: 169.65 cm
Step-by-step explanation: I just put this into a calculator, hope this helps!
Answer:
169.64600329385
Step-by-step explanation:
pls help with this asap
Answers
Answer:
B
Step-by-step explanation:
Answer:
C. 540
Step-by-step explanation:
A=2(wl+hl+hw)
You are asked to draw a triangle with side lengths of 10 inches, 7 inches, and 2 inches. How many triangles like this can you draw?
A- One
B- Three
C- Two
D- Zero
Answers
Bette has a life insurance policy that will pay her family $40,000 per year if
she dies. Bette's insurance company expects that it would have to put
$2,500,000 into a bank account so that it could make the payments. What
does Bette's insurance company expect the interest rate to be?
O A. 0.4%
O B. 2%
O C. 2.3%
O D. 1.6%
Answers
Divide the yearly payout by the amount in the bank:
40,000 / 2,500,000 = 0.016
Multiply by 100 to get the percentage:
0.016 x 100 = 1.6%
The answer is D. 1.6%
The insurance company expects an interest rate of 1.6% to provide the yearly payment of $40,000, calculated by dividing the annual payment by the principal amount deposited.
The student's question asks to calculate the interest rate expected by Bette's insurance company in order to provide a yearly payment of $40,000 to her family, given that the company needs to deposit $2,500,000 into a bank account.
To find the interest rate, we can use the formula for simple interest: Interest = Principal times Rate times Time. Since we are looking for the rate and are given the annual interest (the yearly payment) and the principal (the amount deposited), we can rearrange the formula to solve for the rate: Rate = Interest / Principal / Time. Here, Interest is $40,000, Principal is $2,500,000, and Time is 1 year.
Plugging in the values gives us: Rate = $40,000 / $2,500,000 / 1 = 0.016 or 1.6%. Therefore, the expected interest rate is 1.6%, which corresponds to option D.
Please help I am stuck
Answers
2+2= ???
pleaae herp houme whork
Answers
Answer:
Goodness, hard question... I believe it is, uh 4?
2+2=4
for eg: if u buy 2 pencils and 2 erasers then,you have total 4 stationery items
hope it will help you
The area of a square is (4x2 − 12x + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work
Answers
Answer:
Length of each side 3/2 or 1.5 square units
Step-by-step explanation:
(4^2 − 12x + 9)
=(2x-3)(2x-3)
2x-3=0
2x=3
x=3/2
The length of each side of the square by factoring in the area expression completely is 3/2.
We have given that,
The area of a square is (4x^2 − 12x + 9) square units.
We have to determine the,
Determine the length of each side of the square by factoring in the area expression completely.
Length of each side 3/2 or 1.5 square units
(4^2 − 12x + 9)
=(2x-3)(2x-3)
2x-3=0
2x=3
x=3/2
The length of each side of the square by factoring in the area expression completely is 3/2.
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Solve 65x = 20.
Round to the nearest ten-thousandth.
Answers
Answer: 0.3076
Step-by-step explanation:
Answer:
0.307
Step-by-step explanation:
To get rid of the 65, simply divide both sides of the equation by 65. Thus, rounded to the nearest ten-thousandth, x = 0.307.
The ratio of red fish to yellow fish in the pond is 2:3. If there are 24 yellow fish, how many red fish are in the pond?
Answers
Answer:
16
Step-by-step explanation:
Since there are 24 yellow fish and the ratio of the yellow fish to the red fish is 3:2. Then we know that 24/3=8. This means that 1 is equal to 8 fish. Since there are 2 ones for the red fish, we times 8 by 2 to get 16.
A 6-pack of dish towels costs $21.42. What is the unit price?
Answers
Answer:
3.57
Step-by-step explanation:
Answer:
$3.57 for each towel
Step-by-step explanation:
It is $21.42 for a 6-pack of towels, so take $21.42 and divide it by 6. Therefore, you will get $3.57 for each towel. I hope this helps! Stay safe and have a wonderful day! Peace! ✌
Water has a “bent” geometry. Which explanation does not explain why? Water’s oxygen has unbonded electron pairs that repel each other. Water can form hydrogen bonds. Electrons are evenly distributed in the water molecule.
Answers
Answer: c, electrons are eventlyg distributed in the water molecules.
Step-by-step explanation:
Answer:
its c on edge
Step-by-step explanation:
did the assignment
5,8,11,7? If the mean of the data set is 8 points, find the missing number of points.
Answers
Answer:
9
Step-by-step explanation:
if you add 5,8,9,11,and 7 you get 40 then you need to divide it by 5 because their are 5 numbers so then 40 divided by 5 is 8 so the number is 9
Final answer:
To determine the missing number in the data set with a mean of 8, we set up the equation 8 = (5 + 8 + 11 + x) / 4. Solving for x, we find that the missing number is 8.
Explanation:
To find the missing number in the data set 5, 8, 11, ?, where the mean is 8 points, we can use the formula for the mean of a data set. The mean is the sum of all data points divided by the number of points. Since we know the mean and three of the four numbers, we can create an equation to solve for the missing number:
Mean = (Sum of all data points) / (Number of data points)
8 = (5 + 8 + 11 + x) / 4
Now, solve for x:
8 * 4 = 5 + 8 + 11 + x
32 = 24 + x
x = 32 - 24
x = 8
Therefore, the missing number is 8.