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For the set of triangle vertices, find the coordinates of the vertices of the image after a dilation by the given scale
factor and center of dilation.
D(2,-2), E(4, -2), F(1, -4)
k = 1.5,, E(4,-2), centered at E
Answers
The image of the triangle DEF are formed by the following coordinates: D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5).
How to dilate a triangle centered at a given point
In this problem we need to apply a rigid transformation known as dilation, whose definition is introduced below:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]
Where:
O(x, y) - Center of dilationP(x, y) - Original pointP'(x, y) - Resulting pointk - Dilation factorWe need to determine the image of triangle DEF. If we know that D(x, y) = (2, - 2), E(x, y) = (4, - 2), F(x, y) = (1, - 4) and k = 1.5, then the images of the vertices of the triangle:
D'(x, y) = (4, - 2) + 1.5 · [(2, - 2) - (4, - 2)]
D'(x, y) = (4, - 2) + 1.5 · (- 2, 0)
D'(x, y) = (4, - 2) + (- 3, 0)
D'(x, y) = (1, - 2)
E'(x, y) = (4, - 2) + 1.5 · [(4, - 2) - (4, - 2)]
E'(x, y) = (4, - 2)
F'(x, y) = (4, - 2) + 1.5 · [(1, - 4) - (4, - 2)]
F'(x, y) = (4, - 2) + 1.5 · (- 3, - 2)
F'(x, y) = (4, - 2) + (- 4.5, - 3)
F'(x, y) = (- 0.5, - 5)
The coordinates of the image of triangle DEF are D'(x, y) = (1, - 2), E'(x, y) = (4, - 2) and F'(x, y) = (- 0.5, - 5)
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Related Questions
Solve for EG. Enter your answer in the box.
Answers
Answer:
EG = 44
Step-by-step explanation:
EG, the whole thing, is 10x - 16. It says that at the top of the image. But also, under the segment, we can put together two small pieces, EF and FG. So, the whole thing could also be 4x + 20.
The two expressions both describe EG. They are equal to each other. Write an equation.
10x - 16 = 4x + 20
subtract 4x
6x - 16 = 20
add 16
6x = 36
divide by 6
x = 6
They are asking for EG. Use either expression.
EG = 4x + 20
= 4(6) + 20
= 24 + 20
= 44
or,
EG = 10x - 16
= 10(6) - 16
= 60 - 16
= 44
Actually, its a neat check to do both ways bc it should come out the same.
EG = 44
$4700 accumulating to $5994.76, compounded monthly for 5 years. What is the interest rate %
Answers
48.76%
Step-by-step explanation:Compound interest describes interest on the principal plus interest.
Compound Interest Formula
The formula to find compound interest is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]. In the formula:
A is the total amount, P is the principal, r is the rate as a decimal, n is how often interest is compounded,t is time.We can plug in our information to find the rate.
Solving For Interest Rate
First, let's rewrite the equation with our information. Note that for simplicity I will write rounded values for each step, but in reality, no rounding should be done until the last step.
[tex]5994.76 = 4700(1+\frac{r}{12})^{12*5}[/tex]Then, simplify the exponent and divide both sides by 4700.
[tex]1.275=(1+\frac{r}{12} )^{60}[/tex]Take the 60th root of both sides.
[tex]1.004=(1+\frac{r}{12} )[/tex]Subtract 1 from both sides.
[tex]0.004063=\frac{r}{12}[/tex]Finally, multiply both sides by 12.
r = 0.04876This means that the rate is 0.04876. We can multiply this by 100 to get the rate as a percentage. The interest rate is 48.76%.
A coffee shop sells bags of coffee for
$9.90 per kilogram. Each bag holds 0.5 kilogram of coffee.
How many bags of coffee do they sell if they earn $702.90?
Explain your answer.
Answers
Answer:
142 bags
Step-by-step explanation:
0.5KG is half of a KG, so we can start by finding half of $9.90
$9.90/2 being $4.95
So each bag is $4.95
The total is $702.90
Dividing $702.90/$4.95 will equal the number of bags
702.9/4.95=142 bags
Solve for t
18,000=9000(1.003)^12t
Answers
Answer:
t=1.92938456
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
if m< is 28 degrees, what is m< DAC
Answers
We can write the measurement of ∠DAC as -
∠DAC = ∠ADB - ∠DCA
What is a triangle?A triangle is a polygon with three edges and three vertices.
Given is a triangle ABC.
The external angle is the sum of two interior opposite angles.
We can write -
∠ADB = ∠DAC + ∠DCA
So, we can write -
∠DAC = ∠ADB - ∠DCA
Therefore, we can write the measurement of ∠DAC as -
∠DAC = ∠ADB - ∠DCA.
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Use your formula to determine the height of a trapezoid with an area of
24 cubic centimeters and base lengths of 9 cm and 7 cm
Formula: 1/2(a+b)h
Answers
The height of a trapezoid is 3cm
How to use the formula for area to determine the height of a trapezoid?The formula for the area of a trapezoid is:
A = 1/2(base1 + base2) × height
Where base1 and base2 are the lengths of the parallel sides of the trapezoid, and height is the distance between the bases.
That is:
A = 1/2(a+b)h
To determine the height of a trapezoid using the formula substituting the given values and solve for h. That is:
A = 1/2(a+b)h
where A = 24 cubic centimeters, a = 9 cm and b = 7cm
24 = 1/2(9+7)h
24 = 1/2(16)h
24 = 8h
8h = 24
h = 24/8
h = 3 cm
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How much interest will you pay over the life of a $220,000 30-year loan at 8 percent with monthly payments of $1,614.28?
Answers
The total interest that will be paid over the life is $5,28,000. The solution has been obtained using arithmetic operations.
What are arithmetic operations?
For all the real numbers, there are four basic mathematical operations which are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
We are given 30 year loan amounting $220,000 at interest rate of 8 percent with monthly payments of $1,614.28.
The annual interest comes out to be
8% of $220,000 = $17,600
The total interest = $17,600 * 30 = $5,28,000
Hence, the total interest that will be paid over the life is $5,28,000.
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in the given figure,AB is parallel to CD and angle EAB =50°,angle ECD =100°,find angle AEC
Answers
If AB is parallel to CD and angle EAB =50°,angle ECD =100° then Angle AEC is 112∘
Since AB∥CD
∴∠CAB+∠DCA=180 ∘ (Co-interior angles)
The inside angles total 180 degrees and are known as co-interior angles. It indicates that two internal angles that are on the same side of the transversal have a sum that is additional.
∴22 ∘ +∠DCA=180 ∘
⇒∠DCA=180 ∘ −22 ∘ =158 ∘
Also, ∠ECD+∠DCA+∠y=360 ∘ (Angles about a point)
Angles around a point refer to the total number of angles that can be combined to produce a complete turn. A point's surrounding angles add up to 360°. The angles circling a point add up to 360° since they have completed a full turn and are identical in magnitude.
⇒90 ∘ +158 ∘ +∠y=360 ∘
⇒∠y=360 ∘ −(90 ∘ +158 ∘ )
⇒∠AEC=y=360 ∘ −248 ∘ =112∘
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Solve the problem by entering and solving an equation.
A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 14 inches. What is the width of the frame?
The solution is Blank (blank + w)= blank The width of the frame is blank inches.
Answers
The width of the given rectangular frame of perimeter of 52 inches is; 12 inches.
How to find the perimeter of a rectangle?The formula for perimeter of rectangle is;
Perimeter = 2(Length + width)
Now, we have the parameters as;
Perimeter = 52 inches
Length = 14 inches
Thus, plugging in the relevant values into the perimeter equation gives;
52 = 2(14 + width)
52/2 = 14 + width
14 + width = 26
Width = 26 - 14 = 12 inches
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Greta is looking for a new fishing pole for an upcoming trip to the Grand Canyon. She found the model she likes at a local sporting goods store. The price of the pole is $59,50 with a sales tax of 6%. However, she can purchase the pole on a website for $62.50 with no sales tax added on to the price. What is the difference in price between the store and the website? Which is more expensive?
Answers
To find the total cost of the pole at the store including sales tax, we need to multiply the price of the pole by the sales tax rate (expressed as a decimal).
$59.50 x 0.06 = $3.57
So the total cost of the pole at the store is $59.50 + $3.57 = $63.07.
To find the difference in price between the store and the website, we can subtract the website price from the store price:
$63.07 - $62.50 = $0.57
So the pole is $0.57 more expensive at the store than on the website.
a certain phone company charges $4.50 for the first five minutes of an international phone call. additional time is charged at $.50 per minute. how much would a customer be charged for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day?
Answers
A customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.
Charge for first 5 charged = $ 4.50
Charge for additional time = $ 0.50 per minute
Starting time = 9:35 p.m.
End time = 11:15 p.m.
Total minutes = 100 minutes
Total charge = 4.50 + (95 x 0.50)
= 4.50 + 47.50
= 52.00
Hence, a customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.
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Do you know what 20% of 60 is?
Answers
Answer:1
Step-by-step explanation:
0
A swim club bought a box of c swim caps to split evenly among its 20 members. Write an expression that shows how many swim caps each swimmer will get.
Answers
Answer:
20/C=X
Step-by-step explanation:
C= swim caps
X=How many swim caps each swimmer gets
Label each item as factor by grouping or factor using substitution.
To factor a trinomial of the form
ax 2 + bx + c, find a factor pair of ac
that has the sum of b. Rewrite bx as a
sum of those factors. Then factor out
the GCF from the two groups of terms
to write the original trinomial as the
product of two binomials.
Answers
Answer:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Step-by-step explanation:
To factor a trinomial of the form ax^2 + bx + c, you can use the following steps:
Find a factor pair of ac that has the sum of b. For example, if a = 2, b = -7, and c = -21, then the factor pair for -42 (2 * -21) that has the sum of -7 is (-7, -6).
Rewrite bx as a sum of those factors. In the example, -7x = -7x + (-6x).
Factor out the GCF (greatest common factor) from the two groups of terms. In the example, (2x - 7)(x - 6) = 2x(x - 6) - 7(x - 6) = 2x^2 - 14x + 12x - 42 = 2x^2 - 2x - 42.
Write the original trinomial as the product of two binomials. In the example, the trinomial 2x^2 + -7x + -21 can be factored as (2x - 7)(x - 6)
So the final factorization is (2x - 7)(x - 6)
Someone baked 2 types of pie.
He served 1/2 of the blueberry pie. And he also served 1/4 of the Apple pie, If each pie had 8 pieces to start, what fraction in eights of the Apple did he served?
Answers
The fraction in eights of the Apple pie that the person baked, is 2 / 8 of the apple pie.
How to find the fraction ?The number of pieces that the apple pie had was 8 pieces to start. This means that if the baker served 1 / 4 of this, you can find the fractions in eights by multiplying the fraction served by the number of pieces :
= Fraction served x Number of pieces
= 1 / 4 x 8
= 8 / 4
= 2 pieces
The fraction in eights of the Apple that was served was :
= Number of pieces served / Number of total pieces
= 2 / 8
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The cone in the diagram has the same height and base area as the prism. What is the ratio of the volume of the cone to the volume of the prism?
OA.
OB.
OC.
OD.
OE.
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
volume of cone
volume of prism
-
를
1/02/m
1
N/W
base area = B
h
base area = B
Answers
The ratio of the volume of the cone to the volume of a prism is equal to one.
What is volume?Three-dimensional space is quantified by volume. It is frequently measured quantitatively with SI-derived units (such the cubic metre and litre) or with a variety of imperial or US-standard units (such as the gallon, quart, cubic inch). Volume and height are related in how they are defined (cubed). The volume of a container is typically thought of as its capacity, or the amount of fluid (gas or liquid) that it could hold, as opposed to the amount of space the container occupies. Utilizing naturally occurring containers of a comparable shape and subsequently, standardized containers, volume is measured. Arithmetic formulas make it simple to determine the volume of some basic three-dimensional shapes.
We know that
The volume of the cone = area of the base. height/3
The volume of Prism = area of the base. height
Since the area of the base and height are the same hence the volume will also be . so the ratio will be 1.
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Laura needs 139 programs for the school play on Thursday. How many boxes of programs will she need, given that each box contains 37 programs?
Answers
Match the below functions to their graphs on the right:
Answers
These are functions that almost have to be memorized but can be understood through Desmos for example:
a: W
b: Z
c: X
d: Y
e: V
What term and 12x^2 have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial
Answers
If the GCF of a term and 12x²y is 4xy , then (a) The term is 8xy , The expression is 4xy(2 + 3x) .
The Greatest Common Factor of the two terms is 4xy ,
where , the first term is 12x²y , we have to find the second term ,
Consider Option(a) : where the second term is 8xy ,
So , GCF of 8xy and 12x²y is
= 2(4xy) and 3x(4xy)
= 4xy(2 + 3x ) ....taking 4xy common from both the terms ,
Therefore , Yes , the second term is 8xy and the expression is 4xy(2+3x) .
The given question is incomplete , the complete question is
What term and 12x²y have a GCF of 4xy? Write an expression that shows the monomial factored out of the polynomial , choose the correct answer below :
(a) The term is 8xy , The expression is 4xy(2 + 3x)
(b) The term is 16xy , The expression is 4xy(4xy + 3x)
(c) The term is 3x , The expression is 12x²y(3x + 4xy)
(d) The term is 4x²y , the expression is 4xy(1 + 3x) .
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Let f(x)-3x+5, h(x)-4x-2 and g(x)=x^2. Write an expression for each function.
a. f+g
b. f-g
Answers
Answer:
a. f+g = -3x+5 + x^2
b. f-g = -3x+5 - x^2
Step-by-step explanation:
g(x) = x^2
I'll assume the other two equations were meant to be:
f(x) = -3x+5, and h(x) = -4x-2
a. f+g = -3x+5 + x^2
b. f-g = -3x+5 - x^2
Select True or False for each statement. True False The equation y=3x−5 represents a function. True – The equation , y equals 3 x minus 5, represents a function. False – The equation , y equals 3 x minus 5, represents a function. A function can only be represented by a straight line on the coordinate plane. True – A function can only be represented by a straight line on the coordinate plane. False – A function can only be represented by a straight line on the coordinate plane.
Answers
The statement "The equation y = 3x - 5 represents a function." is; TRUE
The statement "A function can only be represented by a straight line on the coordinate plane." is; FALSE
How to represent Linear Functions?A linear function is one that is formed when a variable y varies directly with a variable x. That is, when y increases, x also increases and the opposite is also true.
The equation y = 3x - 5 represents a function. This statement is said to be true because every value of x gives a different value of y and as such we can say it maps different elements to different images.
A function can only be represented by a straight line on the coordinate plane. This statement is false because a function can also be represented by a circle, ellipse, parabola, etc.
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A certain space shuttle travels at a speed of 3. 6 x
104 miles per hour. How many hours would it take
this space shuttle to travel 7. 2 x 108 miles?
Answers
It would take 2 hours for this space shuttle to travel 7. 2 x 108 miles
As per the given data, a certain space shuttle travels at a speed of 3. 6 x
104 miles per hour.
Here we have to determine that how many hours would it take this space shuttle to travel 7. 2 x 108 miles.
The relation between the speed and the distance is:
Speed = Distance × Time
Speed = 3. 6 x 104 miles per hour
Time = 1 hour
3. 6 x 104 = Distance × 1
Distance = 374.4 miles
The distance to be covered 7. 2 x 108 miles
= 777.6 miles
Hours taken to travel 7. 2 x 108 miles.
Time = [tex]\frac{777.6 }{374.4}[/tex]
≅ 2 hours.
Therefore the time taken to travel 7. 2 x 108 miles is 2 hours.
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Complete the statement about the model.
The model shows that there are 8 groups of
in 3.
Answers
According to the diagram, there are eight fractions of 3/8 in three.
What is a fraction?A fraction is a ratio of two numbers where the numerator and denominator are both integers that can be negative or positive. The numerator can't be zero. Proper fractions and improper fractions are the two types of fractions.A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction's numerator will be less than the denominator.We are shown a diagram of three equal parts divided into eight equal parts.
Divide 3 by 8 to get the value of the equal part.
As a result, the value of each can be given as 3/8.
Therefore There are 8 groups of 3/8 in 3 as per the given diagram.
The diagram is attached below:
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Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
13
12
Answers
Step-by-step explanation:
that is really simple, because the additional half-circle compensates for the missing half-circle on the other side.
so, the area is plain and simple the area of the rectangle, which is
13×12 = 156 = 156.0
A triangle has a perimeter of 9x + 6. The first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. What is the length of the third side of the triangle?
x + 13
x − 1
8x − 7
17x − 1
Answers
The length of the third side of the triangle is x + 13.
What is the length of the third side of the triangle?A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.
The perimeter of a triangle is the sum of the length of all three sides of the triangle.
Given the data in the question;
Perimeter P = 9x + 6Side A = 5xSide B = 3x - 7Side C = ?To find side C, equate the sum of all three sides of the triangle to the perimeter and simplify.
Side A + Side B + Side C = P
5x + ( 3x - 7 ) + Side C = 9x + 6
5x + 3x - 7 + Side C = 9x + 6
8x - 7 + Side C = 9x + 6
Side C = 9x + 6 - ( 8x - 7 )
Side C = 9x + 6 - 8x + 7
Side C = x + 13
Therefore, side C is x + 13.
Option A) x + 13 is the correct answer.
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Answer:
x + 13
Step-by-step explanation:
i took the test xx
Find the equation of the plane passing P(1,2,1) and is orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0.
Answers
The equation of the plane passing P (1,2,1) and orthogonal to the two planes: x-y-z-10 = 0, x-2y + z-2=0 is -3x-2y-z+8=0.
Equation of plane passing through (x1,y1,z1) is given by
A(x-x1)+B(y-y1)+C(z-z1)=0
where, A, B, and C are direction ratios
In the question, it is given that the plane passes through (1,2,1)
So, the equation of the plane will be in the form,
A(x-1)+B(y-2)+C(z-1)=0
It is also given that the plane is perpendicular to give 2 planes.
So, their normal to the plane would be perpendicular to the normal of both planes.
So, the required normal is a cross-product of the normals of planes
x-y-z-10=0 and x-2y+z-2=0
i.e,
-3i-2j-k=0
so, the direction ratios,
A=-3, B=-2, C=-1
putting the direction ratios in the previous equation of the plane,
-3(x-1)-2(y-2)-1(z-1)=0
-3x+3-2y+4-z+1=0
-3x-2y-z+8=0
is the required equation of the plane
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In an experiment with a bag of marbles, P(green) = three fourths. Interpret the likelihood of choosing a green marble.
Likely
Unlikely
Equally likely and unlikely
This value is not possible to represent probability of a chance event.
Answers
The probability of picking a green marble is 3/4 or 0.75. This means it is likely the event would occur. Therefore, option A is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, an experiment with a bag of marbles, P(green)=3/4.
Probability is used to determine how likely it is that a random event would happen. The probability that a random event occurs lie between 0 and 1. The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.
The probability of picking a green marble is 3/4 or 0.75. 0.75 is more than 0.5. This means it is likely the event would occur.
Therefore, option A is the correct answer.
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Question 3 (2 points)
What translation takes the graph of f(x) = 4x - 3 to the graph of g(x) = 4x - 6 ?
Translation of 3 units down
Translation of 6 units left
Translation of 6 units down
Translation of 3 units right
Answers
Answer: The graph of g(x) = 4x - 6 is a translation of the graph of f(x) = 4x - 3.
A translation of a function results in a shift of the graph of the function, either horizontally (left or right) or vertically (up or down).
When the graph of a function is shifted down, the y-coordinates of all the points on the graph decrease. When it's shifted to the left, the x-coordinates of all the points on the graph decrease.
In this case, the graph of g(x) = 4x - 6 is a vertical translation of 3 units down from the graph of f(x) = 4x - 3.
The y-coordinates of all the points on the graph of g(x) = 4x - 6 are 3 units less than the y-coordinates of the corresponding points on the graph of f(x) = 4x - 3.
Therefore, the correct answer is:
Translation of 3 units down.
Step-by-step explanation:
Prove the Pythagorean Theorem with Similar Triangles using a two-column proof.
Answers
Answer:
u
Step-by-step explanation
Please Help Me!!!!! Sorry about the small picture!
Answers
Answer:
1:12, then 1 :11
wait unless its like in the same thing
wait sorry im confused
if its that then i think it would be 2:12
Step-by-step explanation:
sorry not too sure!!!