Graph the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and its image after a dilation with scale factor k=3
Answers
The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.
Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)
Y(2, 3)→3(2, 3)→Y'(6, 9)
Z(1,-1)→3(1, -1)→Z'(3, -3)
Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).
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Related Questions
Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x, y)(x,y).
\def\arraystretch{2} \begin{alignedat}{1}3 x-2 y&=4\\5 x+10 y&=-60\end{alignedat}
3x−2y
5x+10y
=4
=−60
Answers
The value of ordered pair of (x,y) is (-2, -3)
How to solve the equation by substitution method ?x - 5y = 13
4x - 3y = 1
Solve the equation for x
x - 5y = 13
Move '5y' to R.H.S and change it's sign
x=13+5y
Substitute the given value of X into the equation
4x - 3y = 1
4(13+5y)-3y = 1
Solve the equation for y
distribute 4 through the parentheses
52+20y -3y =1
Collect like terms
52+17y = 1
Move constant to R.H.S and change it's sign
17y = 1 - 52
Calculate
17y = - 51
Divide both sides of the equation by 17
17y/17 = -51/17
Calculate
y = -3
Now, substitute the given value of y into the equation
x = 13 + 5y
x= =13+5x(-3)
Solve the equation for x
Multiply the numbers
= 13 - 15
Calculate the difference
= -2
The possible solution of the system is the ordered pair
( x , y )
( x , y ) = ( - 2 , - 3 )
-----------------------------------------------------------------------
Check if the given ordered pair is the solution of the system of equation
-2-5×(-3)=15
4×(-2)-3×(-3)=1
Simplify the equalities
13 = 13
1=1
Since all of the equalities are true, the ordered pair is the solution of the system
( x , y ) = ( - 2 , - 3 )
Therefore the value of ordered pair of (x,y) is (-2, -3)
The complete question is : Solve the system by substitution. x−5y=13 4x−3y=1 Enter your answer as an ordered pair (x,y).
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solve
2(2.1z+4.5)<21.6
Answers
Answer:
Z< 3
Step-by-step explanation:
Hope this helps :)
Which value best estimates the value for the correlation coefficient of the scatter plot below: 1, -0.8, -0.2, 0.2, 0.8, or 1?
Answers
An Imaginary Poll in June 2021 asked KHS students to list their favorite Marvel comic
character. The responses are shown below.
Spiderman - 45
Hulk - 30
Black panther - 28
Black widow - 17
Rocket raccoon - 5
Total = 125
If we randomly select two different people from this sample, what is the probability that both
chose Black Panther as their favorite character?
a. 2/125
b. 1/250
c. 189/3875
d. 1/15500
e. 756/15625
Answers
The probability that both choose Black Panther as their favourite character is 189/3875.
How is the probability calculated?KHS students' list of their favourite Marvel comic character:
Spiderman - 45
Hulk - 30
Black panther - 28
Black widow - 17
Rocket raccoon - 5
Total = 125
The chances that two people can be drawn from a sample of 125 playing cards in 125[tex]C_{2}[/tex] ways.
[tex]125C_{2}=\frac{125*124}{1*2} \\\\125C_{2}=\frac{15500}{2}\\\\125C_{2}= 7750[/tex]
The event of choosing 2 Black Panthers from 28 can happen in 28 [tex]C_{2}[/tex] ways.[tex]28C_{2}=\frac{28* 27}{1*2} \\\\28C_{2}=\frac{756}{2}\\\\28C_{2}= 378[/tex]
The probability that both choose Black Panther as their favourite character is:[tex]P(BP) = \frac{28 C _{2}}{125C_{2}} \\\\P(BP) = \frac{378}{7750} \\\\P(BP) = \frac{189}{3875}[/tex] or 0.04877
So, option c is correct.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The likelihood that an event will occur increases with its probability. Probability informs us of the likelihood that an event will occur given enough trials.Probabilities can be expressed numerically by the number of desired outcomes, divided by the total number of outcomes, when dealing with experiments that are random and well-defined in a purely theoretical context (like flipping a coin).To learn more about probability, refer:
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Martin and three of his friends take turns driving on a trip. The gas mileage for their car ranges from 28.94 to 24.68 miles per gallon. Each friend drives between 63 and 69 miles, so Martin estimates they will need about 7 gallons of fuel for their trip. Is this a reasonable estimate?
A.
Yes, the estimate given is reasonable.
B.
No, the estimate should be higher.
C.
No, the estimate should be lower.
Answers
No, the estimate should be higher
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
As, Maximum miles driven=highest consumption per gallon × Maximum
gallons
where;
Maximum miles driven per person=64 mile
Maximum miles driven = 64×4
=256 miles
So, highest consumption =24.56 miles per gallon
let the Maximum gallons needed be x
256=24.56 x
24.56 x=256
x ≥ 256/24.56
x ≥10.42 gallons
Hence, No, the estimate should be higher
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CC wants to buy online tickets for a concert. two options are given here. option 1: $85 for each ticket plus a shipping fee of $15 option 2: $95 for each ticket and free shipping. select the equation for option 2.
a. y=85x+15
b. y=-95x
c. y=15x+85
d. y=95x
Answers
Answer:
Step-by-step explanation:
i want to know too:((
The equation for the second plan is y = 95x, therefore, option (d) is correct.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, the second plan costs $95 for each ticket and free shipping.
The total cost, y, for x tickets are:
y = 95x.
Hence. the equation for the second plan is y = 95x, therefore, option (d) is correct.
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what is the probability of having the first head at the k-th trial? what is the name of this random variable?
Answers
The probability of having the first head at the k-th trial is 1/2.
The formula for the binomial distribution of probability is shown below. It can be used to determine the likelihood of getting K heads out of N coin tosses.
[nC k]* [pk]* [qn-k]
p= probability of receiving a head and
q= probability of having a tail.
Both p and q are 1/2.
As a result, the equation is [f12n! * f! r! * (n-r)!]
If you obtain exactly r successes, you also get (n - r) failures at the same time.
qn - rpr = P(getting r successes and n - r failures) (since the n trials are independent) Using the product theorem
There is no mention of the challenges from which the results were attained. There are nCr methods for selecting successful trials among r trials. The remaining (n - r) trials should be failures once the r trials that were picked for successes have been chosen. These nCr methods are incompatible. P(obtaining exactly r successes) in each of these nCr methods equals qn - rpr.
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Hello please solve this with steps Factor
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor.
Answers
f(x)=x^3-12x^2+36x-32 completely given that (x-2) is a factor is [tex](x-2)^2(x-8)[/tex].
What is factor?
In mathematics, an integer m that can be multiplied by another integer to produce n is known as a divisor of an integer n, also known as a factor of n. One can also state that n is a multiple of m in this situation.
Knowing that (x−2) is a factor you can divide the polynomial:
2.....|.......1.........-12.........+36.........-32
........|...................2..........-20.........+32
........|.......1.........-10..........+16...........0
and find:
[tex]x^3-12 x^2+36 x-32=(x-2)\left(x^2-10 x+16\right)[/tex]
We could use the quadratic formula to find the factors of [tex]$q(x)=\left(x^2-10 x+16\right)$[/tex]
or go simply by inspection:
1) q(x) has two changes in sign, so it has two positive real roots.
2) The product of the roots is 16
3) the sum of the roots is 10
It's easy to see that x=2 and x=8 are such roots, and thus:
[tex]x^3-12 x^2+36 x-32=(x-2)^2(x-8)[/tex]
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This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blank question. PARKS Rachelle wants to determine the best state park for hiking and fishing. She has developed a metric based on the information she has gathered and the best catch from her previous fishing trips to the parks. Part A Use the metric to calculate a score for each park. Round to the nearest tenth. Park Score = 100[0.2(online rating5)+0.4(miles of trails25)+0.4(fish weight10)] State Park Online Star Rating Hiking Trails (mi) Best Fish (lb) Park Score Gooseberry Falls 4.8 20 9.8 Lake Maria 4.3 14 8.2 Maplewood 4.9 25 7.3 Camden 4.3 15.8 10.1 Part B Part B How might someone who enjoys hiking much more than fishing change this metric? 100 words remaining Tools are not currently accessible
Answers
Answer:
Step-by-step explanation:
PLEASE HELP I BEG I NEED JUST THIS ONE PROBLEM:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN.
Please give Statement/Reasoning proof as well. THANK YOU PLEASEE
Answers
For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
What is Trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid's parallel sides are referred to as its bases.
Given:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.
Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.
We have to find BC:BN
ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line "l" parallel to AB intersects the diagonal AC at p and BD at N.
Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
But, BC= BN+NC
Therefore, BC:BN = (BN + NC): BN
⇒ BC:BN = (3 + 5): 3
⇒ BC:BN = 8:3
Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
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How many ounces of iodine worth 30 cents an ounce must be mixed with 50 ounces of iodine worth 18 cents an ounce so that the mixture can be sold for 20 cents an ounce?
Answers
Find the distance of a line with endpoints (1, 2) and (7, 4). Round to the nearest tenth.
Distance Formula:
d=√√(x₂-x₁)² + (y₁ - y₁)²
Answers
The distance between the two points is 2√10
Distance between two points:
The formula for the distance between two points (x₁, y₁) and (x₂, y₂) is given by Distance = √ [(x₂-x₁)² + (y₁ - y₁)²]
This formula can be used to find the length of a line whose endpoints are (x₁, y₁) and (x₂, y₂)
Here we have
The endpoints of the line are (1, 2) and (7, 4)
As we know d =√ [(x₂-x₁)² + (y₁ - y₁)²]
Take (x₁, y₁) = (1, 2) and (x₂, y₂) = (7, 4)
By the given formula,
Distance of line = √ [(7 - 1)² + (4 - 2)²]
= √[(6)² + (2)²]
= √(36 + 4)
= √40
= 2√10
Therefore,
The distance between the two points is 2√10
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Find the total cost to the nearest cent.
$ 15 lunch
tip: 20%
Answers
15.00 x2= 300 = 3.00
a triangle undergoes a dilation with a scale factor of 9/5. the resulting triangle is _[blank]_ the original triangle.
Answers
The resulting triangle is 9/5 the original triangle.
How triangle dilated with scale factor?
The focuses in the direction planes are A(0, 2), B(2, 1), C(- 2, - 2). In the event that the scale factor is 2, each direction point of the first triangle is duplicated by the scale factor 2. Subsequently, the expanded triangle will be A'B'C' and the direction focuses got are A'(0, 4), B'(4, 2), C'(- 4, - 4).
According to question:Let we have a triangle ABC,If this triangle undergoes a dilation with a scale factor of 9/5,
Then changed triangle is A'B'C'
So, relation between them is A'B'C' = 9/5(ABC)
Thus, the resulting triangle is 9/5 multiple of triangle ABC.
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0) The sum of the first and second of three
consecutive even integers is 126. Find the
three even integers.
Answers
Answer:
The three consecutive even integers are 40, 42 and 44.
Step-by-step explanation:
Let the consecutive even integers be
x, (x + 2) and (x + 4)The sum of the first and second of three consecutive even integers is 126.
So,
x + (x + 2) + (x + 4) = 126
Open the brackets
x + x + 2 + x + 4 = 126
Combine like terms we get,
3x + 6 = 126
Subtract 6 from both sides we get,
3x + 6 - 6 = 126 - 6
3x = 120
Divide 3 from both sides we get,
3x/3 = 120/3
x = 40
The value of x is 40 and the the consecutive even integers are
x = 40
x + 2 = 40 + 2 = 42
x + 4 = 40 + 4 = 44
Thus, The three consecutive even integers are 40, 42 and 44.
Solve for the following
Answers
A rocket is fired with an initial vertical velocity of 40 m/s from a launch pad 45 m high. Its height is given by the formula , where h is in meters and t is in seconds. How high does the rocket go? How much time is the rocket in flight?
Answers
The maximum height which the rocket attains is 80 m and the time taken by the rocket is 8 sec.
Given,
the following formula yields the height h,
h= -5t² + 40t +45
45m is the height of the launch pad.
We take the first derivative of the function h and then set it to zero to determine the height the rocket reaches.
h' = 0
-10t + 40 =0
-10t = -40
t = 4
Therefore, height reached by the rocket in time t = 4 is,
h= -5t² + 40t +45
= -5(4)² + 40(4) + 45
=125 m
As a result, the rocket can reach:
125- 45
= 80 m
(To determine the real height the rocket travels, we have subtracted the height of the launch pad.)
The rocket takes twice as long to launch as it does to reach the peak.
t = 2*4 = 8 sec
Therefore,
the rocket goes 80 meters in height
the rocket's flight time is 8 seconds.
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Let y = (5 +b)x-c be perpendicular to 8x + 12y = 40. What is the value of b?
Answers
The value of b is -11/2.
What is the slope of the equation?
The slope of a line is a measure of its steepness. Mathematically, the slope is calculated as "rise over run" (change in y divided by change in x).
To find the value of b, we need to find the slope of the given line and the line that is perpendicular to it.
The slope of the line 8x + 12y = 40 is -8/12 = -2/3.
The slope of a line that is perpendicular to this line is the negative reciprocal of -2/3, which is 3/-2 = -3/2.
The slope of the line y = (5 + b)x - c is 5 + b. Therefore, to find the value of b, we need to set 5 + b equal to -3/2:
5 + b = -3/2
b = -3/2 - 5
b = -11/2
Therefore, the value of b is -11/2.
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Evaluate the expression.
5+ [4•3(2 + 1)]
Answers
Answer:
41
Step-by-step explanation:
A square garden is surrounded by a concrete walkway of width x. The length of the walkway is 15 feet long
a) Write an expression for the area of the garden.
The formula for the area of a square is A = s^2, where s is
a side length of the square.
A(x) = (15 + 2x)
b) Consider the information given above and discuss the maximum and minimum size of the concrete walkway. Be sure to explain your estimates.
Answers
Considering the information, the minimum and maximum size of the concrete walkway is is -900 and -450 units respectively
How to determine the minimum and maximum values?Minimum and maximum values of the area of the square garden is the area the square garden can occupy.
The given parameters are
A=S²
S= a side of the square= A(x) = (15+2x)
Now, hence A=S²
This implies that
(15+2x)(15+2x)
Expand the brackets to get
225+60x+4x=0
Solving the equation using the quadratic formula
x=± (√b²-4ac)÷2a
This implies that
x= -60±(√60²-4*4*225)÷2*4
Simplifying the equation we have
(-60±0)÷8
x=-30
Now if x= -3
Therefore (15+2*-30) = -45 and (15*x)
= 15*-30=-450 units
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help please!! involves range
Answers
Answer: D
Step-by-step explanation:
i believe
Consider 3x=y. a. Complete the table for the equation. x: 0 1 2
Answers
The values of y when x is 0 1 2 is 0,3,6
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
To get the values of y, we substitute for the values of x in the equation 3x=y
When x = 0
3(0)=y; y = 0
When x = 1
3(1)=y; y = 3
When x = 2
3(2)=y; y = 6
x | 3x | y | (x, y)
----------------------------------------
0 | 3(0) | 0 | (0, 0)
----------------------------------------
1 | 3(1) | 3 | (1, 3)
----------------------------------------
2 | 3(2) | 6 | (2, 6)
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A cylinder has a height of 5 inches and a radius of 2 inches. What is the volume of the cylinder? use pi ≈ 3.14
Answers
Answer:
Volume= 62.8 cubic inch
Step-by-step explanation:
V=B×h
B=
[tex]\pi {r}^{2} [/tex]
= 3.14×2^2=12.56
V=12.56×5= 62.8 cubic inch
Which system of inequalities is shown in the graph?
y<3 and y>2/3x+1
y<3 and y<2/3x+1
y>3 and y>2/3x+1
y>3 and y<2/3x+1
Answers
Answer: A y<3 and y>2/3x+1
Step-by-step explanation: y<3 shades everything under the line because 3 is greater than all the possible values.
y>2/3x+1 shades everything over the line because 2/3x+1 is less than all the possible values.
A computer store buys a computer system at a cost of $436.80. The selling price was first at 728, but then the store advertised a 20% markdown on the system. Answer part b.
A= 582.40
Members of the store's loyalty club get an additional 20% off their computer purchases. How much do club members pay for the computer with their discount?
The price for club members is $______
please help
Answers
The price that that club members pay for the computer is $465.92.
How to calculate the price?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred.
Since the selling price was first at 728, but then the store advertised a 20% markdown on the system and members of the store's loyalty club get an additional 20% off their computer purchases.
The cost will be calculated thus:
582.40 - (20% × $582.40)
= $582.40 - $116.48
= $465.92
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How many solutions does the equation -2 (4x − 1) = −8x – 1 have?
Answers
Answer:
No Solution
Step-by-step explanation:
[tex]\tt -2\left(4x-1\right)=-8x-1[/tex]
Expand:-
[tex]\tt -8x+2=-8x-1[/tex]
Add 8x to both sides:-
[tex]\tt -8x+2+8x=-8x-1+8x[/tex]
Simplify:-
[tex]\tt 2=-1[/tex]
The sides are not equal, therefore there is No Solution.
_____________________
Hope this helps!
Have a nice day!
Antonio is saving money to buy a CD player that costs
$120. He also wants to buy some CDs to play in it.
New CDs cost $15 and used CDs cost $5. Antonio
wants to buy the same number of new and used CDs.
Write and solve an equation to find the number of each
type of CD Antonio can buy if he spends all of the $200
he has saved.
Answers
Equation : 200 = 15x + 5y + 120
what is the distance between P(9,-5) and Q(-2,3) round to nearest tenth if necessary
Answers
Answer:
3.6
Step-by-step explanation:
Please help! Pleaseeeee
Answers
Answer: (C) or (44in^2 )
Step-by-step explanation:
Answer:
A = 40 in²
Step-by-step explanation:
the figure is composed of a rectangle and a triangle.
then area (A) is calculated as
A = area of rectangle + area of triangle
= (16 × 2) + ( [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 6 - 2 = 4 and h = 20 - 16 = 4 , then
A = 32 + ( [tex]\frac{1}{2}[/tex] × 4 × 4)
= 32 + 8
= 40 in²
the p-value for a hypothesis test turns out to be 0.07702. at a 1% level of significance, what is the proper decision?
Answers
7.702 is the proper decision.
What exactly is a p-value?
The p-value (probability value) indicates how likely the data are to occur under the null hypothesis. To do this, the probability of the test statistic is computed. H. Numbers calculated by statistical tests using your data.The p-value indicates how often you would expect the test statistic to be extreme, or more extreme than the statistic computed by the statistical test, if the null hypothesis for the test were true. The p-value decreases as the test statistic computed from the data moves away from the range of the test statistic predicted by the null hypothesis.To know more about p-value visithttps://brainly.com/question/16754784#SPJ4