The smaller triangle is dilated to create the larger triangle. The center of dilation is plotted, but not labeled. Describe this dilation. Be sure to include all of the information someone would need to perform the dilation.The smaller triangle is dilated to create the larger triangle. The center of dilation is plotted, but not labeled. Describe this dilation. Be sure to include all of the information someone would need to perform the dilation.
Answers
To dilate of the small triangle to get the large triangle the center of dilation is required
The description of the dilation is as follows;
Location of the center of dilation;
The coordinate of the center of dilation is given as follows;
[tex]\left( x_0 = \dfrac{k \cdot x_1 - x_2}{k - 1}, \ y_0 = \dfrac{k \cdot y_1 - y_2}{k - 1} \right)[/tex]
Where;
k = The scale factor of dilation
(x₁, y₁) = A coordinate point on the preimage
(x₂, y₂) = A coordinate point on the image
From the given drawing, we have;
Two vertices on the preimage are; (2, 0), and (5, 1)
Two corresponding vertices on the image are; (0, 0), and (9, 3)
Using the formula for length, l, we have;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
[tex]l_{small} = \sqrt{\left (1 -0 \right )^{2}+\left (5-2 \right )^{2}} = \sqrt{10}[/tex]
[tex]l_{large} = \sqrt{\left (9 -0 \right )^{2}+\left (3-0 \right )^{2}} = \sqrt{90} = 3 \cdot \sqrt{10}[/tex]
[tex]The \ scale \ factor, \ k = \dfrac{l_{large}}{l_{small}} = \dfrac{3 \cdot \sqrt{10} }{\sqrt{10} } = 3[/tex][tex]\left( x_0 = \dfrac{3 \times 2 -0}{3 - 1}, \ y_0 = \dfrac{3 \times 0 - 0}{3 - 1} \right)[/tex]
[tex]\left( x_0 = 3, \ y_0 = 0\right)[/tex]
The center of dilation is the point (3, 0)The steps to create the larger triangle from the center of dilation are as follows;
From the center of dilation, draw lines passing through the vertices of the small triangleWith the ruler mark points on the radial lines that are three times the distances from the vertices of the small triangle from the center of dilationJoin the marked points to create the larger triangleAlternatively larger triangle can also be created using the vertices as follows;
The coordinates of the third vertex of the small triangle are; (4, -2)
To obtain the coordinates of the large triangle, the coordinates of
the small triangle are multiplied by the scale factor, followed by adding the
coordinates of the center of dilation, we have that the coordinates of the
image are;
[tex](k \times x_{ai} + x_0, \ k \times y_{ai} + y_0)[/tex]
Where;
[tex](x_{ai}, \ y_{ai})[/tex] = The difference between the coordinate values of the vertices of
the small triangle and the center of dilation, we have;
(2 - 3, 0 - 0) = (-1, 0)
(5 - 3, 1 - 0) = (2, 1)
(4 - 3, -2 - 0) = (1, -2)
We have [tex](k \times x_{ai} + x_0, \ k \times y_{ai} + y_0)[/tex] are;
(3 ×(-1) + 3, 3× 0 + 3) = (-3 + 3, 0) = (0, 0)
(3 × 2 + 3, 3 × 1 + 0) = (6 + 3, 3) = (9, 3)
(3 × 1, 3 × (-2) + 0) = (3 + 3, -6) = (6, -6)
The vertices of the larger triangle are found as (0, 0), (9, 3), (6, -6)
By drawing lines joining derived vertices the larger triangle can be created
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Related Questions
100 points and brainlyest
Part 2 - Writing Equivalent Expressions - You will now use mathematical properties to create two expressions that are equivalent to Sara’s expression.
Property Used
Original/Changed Expression
New expression with property used
Commutative Property of Addition (rearrange the added terms in the parentheses to group like terms together.)
5(2j + 3 + j)
Combine Like terms after rearranging them
(put your answer from the previous row here)
Distributive Property of multiplication over addition (multiply the number outside the parentheses)
(put your answer from the previous row here)
(Use this final expression that you write in this box on the next slide.)
Answers
Answer:
Commutative Property of Addition: to change the order of numbers in an addition or multiplication operation does not change the sum or the product.
New expression with property used: 5(2j + j + 3)
Combine like terms: when combining like terms, add their coefficients
The like terms are 2j and j. Add their coefficients: 2 + 1 = 3, which means that the combination of like terms is 3j.
New expression with property used: 5(3j + 3)
Distributive Property of multiplication over addition: multiplying a sum by a number gives the same result as multiplying each added term by the number and then adding the products together.
So 5(3j + 3) = 5 · 3j + 5 · 3 = 15j + 15
New expression with property used: 15j + 15
A line contains the points (-6, -4) and (0,4). What is the equation of this
line in slope-intercept form?
4
OA) y=3*+
x+4
(
4
OB) y=
3
ОВ)
X-4
OC) y=x-4
OD) y=x+4
Answers
As y=4x−2 can be written as y=4x+(−2) . Hence, it's slope is 4 and intercept on y -axis is −2
A) [tex]y=\frac{4}{3}x+4[/tex]
Step-by-step explanation:Write the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
________________________________________________________
Substitute and calculate
[tex]Substitute:[/tex] [tex]x_1=-6\\ x_2=0\\ y_1=-4\\ y_2=4[/tex] [tex]into\ m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute
[tex]m=\frac{4-(-4)}{-(-6)}[/tex]
Determine the sign
[tex]m=\frac{4+4}{6}[/tex]
Calculate the sum or difference
[tex]m=\frac{8}{6}[/tex]
Cross out the common factor
[tex]m=\frac{4}{3}[/tex]
________________________________________________________
Substitute and calculate
[tex]Substitute[/tex] [tex]m=\frac{4}{3}\\ x=-6\\ y=-4[/tex] [tex]into\ y=mx+b[/tex]
Substitute
[tex]-4=\frac{4}{3}\times(-6)+b[/tex]
Reduce the expression to the lowest term
[tex]-4=-4\times2+b[/tex]
Calculate the product or quotient
[tex]-4=-8+b[/tex]
Rearrange variables to the left side of the equation
[tex]-b=-8+4[/tex]
Calculate the sum or difference
[tex]-b=-4[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]b=4[/tex]
________________________________________________________
Substitute
[tex]Substitute[/tex] [tex]y=\frac{4}{3}x+4\\ m=\frac{4}{3}[/tex] [tex]into\ y=mx+b:[/tex]
[tex]y=\frac{4}{3}x+4[/tex]
________________________________________________________
Rewrite the equation of the line
[tex]Rewrite\ y=\frac{4}{3}x+4\ in\ slope-intercept\ form:[/tex]
[tex]y=\frac{4x}{3}+4[/tex]
I hope this helps you
:)
Which expression can represent 70% of x?
3 ( x Over 4 ) minus one-half ( x Over 10 )
3 ( x Over 4 ) minus ( x Over 10 )
(x Over 2) + (x Over 10)
( x Over 2 ) + one-half ( x Over 4 )
Answers
Answer:
its b
Step-by-step explanation:
cuz
HELP!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
126 Degrees
Step-by-step explanation:
Angel Z is going to be 42 degrees so 3*42 is 126
A castle has to be guarded 24 hours a day. 7 knights are ordered to split each day's guard duty equally. How long will each knight spend on duty? Record your answer in minutes
Answers
Answer:
≈206 Minutes
Step-by-step explanation:
We know that the castle has to be guarded for 24 hours a day. Since there are 60 minutes in an hour, that means it must be guarded for 1,440 minutes (60 * 24 = 1,440). If we split this evenly between each of the 7 knights, through division, we know that they must each be on guard for 205.714285714 minutes, or approximately 206 minutes.
The area of an isosceles triangular land whose base side length 10 meter is 60 square meter. Find the measure of its remaining sides.
Answers
Answer:
2√30m
Step-by-step explanation:
I hope it will be helpful to youEvaluate the expression :
( 4 \ \times \ 5 )^{2} \ - \ 6 \ + \ 3(4 × 5)
2
− 6 + 3 =
Answers
ANSWER
221
use a calculator
Tutorial
An isosceles triangle has an angle that measures 100°. What measures are possible for the
other two angles? Choose all that apply.
80 100 40 50
Answers
The only measure that is possible for the other two angles is 40 degrees.
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
Let's call the two other angles in the isosceles triangle "x". We know that the sum of the three angles in a triangle is always 180 degrees. Therefore, we can set up an equation:
100 + x + x = 180
Simplifying this equation, we get:
2x + 100 = 180
Subtracting 100 from both sides, we get:
2x = 80
Dividing both sides by 2, we get:
x = 40
So the other two angles must both measure 40 degrees.
None of the other choices (80, 100, or 50 degrees) are possible for the other two angles in an isosceles triangle with one angle measuring 100 degrees.
Therefore, the only measure that is possible for the other two angles is 40 degrees.
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You need to earn at least $300 for a school fundraiser washing cars. You charge $12 for trucks
and SUVs and $8 for cars. Write an inequality that represents how many vehicles need to be washed
to earn your goal.
Answers
12x + 8y > = 300
Put the equals to sign (=) under the greater than sign (>)
if the breadth of rectangle is one-fourth of its length and perimeter in60 CM find the length and breadth of rectangle
Answers
Answer:
Step-by-step explanation:
Let length be x
So breadth will be 1/4x
2(x+1/4x)=60
x+1/4x=60/2=30
find lcm and the lcm would be 4 and make denominators equal and add it
4/4x+1/4x=30
5/4x=30
x=30*4/50=6*4=24
Therefore the length is 24/4=6cm and breadth is 24cm.
which numbers are irrational
Answers
What is the solution of the system of equations shown below?
y = -x + 3
y = 4x - 2
A. (0,3)
B. (1,2)
C. (2,1)
D. (0, -2)
Answers
Answer:
B. (1,2) is the answer to the question
Step-by-step explanation:
i juts take the quiz
~brainliest ??
The solution of the linear equations y = -x + 3 and y = 4x - 2 will be (1, 2). Then the correct option is B.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equations are given below.
y = -x + 3 ...1
y = 4x - 2 ...2
From equations 1 and 2, then we have
4x - 2 = - x + 3
4x + x = 2 + 3
5x = 5
x = 1
Then the value of 'y' is given as,
y = - 1 + 3
y = 2
The solution of the linear equations y = -x + 3 and y = 4x - 2 will be (1, 2). Then the correct option is B.
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Write the equation of a line with slope -1/3 and y-intercept -7
A. y=-7x-1/3
B. y=-1/3x+7
C. y=-1/3x-7
Answers
Explanation: y = slope(x) + y intercept
find the circumference of a circle whose radius is 3 3/4 ft.
Answers
Applying the expression for the circumference of a circle we found the circumference to be 23.565 ft
Mensuration of flat shapesGiven Data
Radius = 3 3/4 ftLet us first convert to proper fraction
Radius = 15/4 ft
We know that the expression for the circumference of circle is given as
Circumference = 2πr
Substituting our given data for radius we have
Circumference = 2*3.142*15/4
Circumference = 94.26/4
Circumference = 23.565 ft
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Who is this you tuber
Answers
Answer:
theodd1sout pretty cool guy
Answer:
the odd ones out
Step-by-step explanation:
Bella was out at a restaurant for dinner when the bill came. Her dinner came to $24. After adding in a tip, before tax, she paid $29.04. Find the percent tip.
Answers
Answer:
21%
Step-by-step explanation:
So we have to use percent change
The formula is subtracted/original multiply 100=percent change
so she added a $5.04 tip
5.04/24=0.21, then multiplied by 100=21
so she tipped 21%
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
go 3 forward make a dot. and 8 down make a dot. then connect dots.
Answer:
all u do is get your mouse and move it and then do it TA-DA boom the answer XD
Step-by-step explanation:
comment below what u would say
5 units 2 units 2 units 3 units 2 units the area of the figure is blank square units
Answers
Answer:
Your answer is 8 Square Units
Step-by-step explanation:
3 x 2 = 6
2 x 2 = 4 / 2 = 2
6 + 2 = 8
Hope this Helps!
Answer this pls!!
-7k - 4k = 8 - 2k - 8k
Answers
Answer:
Step-by-step explanation:
Using the equation, first move all of the k to the left side, then, you'll get as what I write in the attachment, minus when move to the other side will be positive, and vice versa.
Solve for X Show and explain your work Please
Answers
x=8.385
Step-by-step explanation:
Angle EBD is a right angle since it's facing the diameter ED
Hence triangle BED is a right isosceles triangle since we also know that EB=BD
so A is the midpoint of ED since it's the center of the circle and ED is a diameter
which implies ED=2×AD=2×6=12
Using the Pythagorean theorem on a right isosceles triangle which states:
a²+b²=c²
x²+x²=12²
2x²=144
x²=72
x=√72=8.485
What is the constant of proportionality from the following equation: s = 0.75u
u
A
0.75
u
S
Answers
Answer:
0.75
Step-by-step explanation:
The equation representing direct proportion is
y = kx ← k is the constant of proportionality
s = 0.75u ← is in this form
with k = 0.75
A hotel has a rectangular-shaped meeting room that is 13.4 yds. wide and 15.1
yds. long. If carpet costs $1.71 per ft^2
, what would be the cost of carpeting the
meeting room?
Answers
A hotel has a rectangular shaped meeting room that is 13.4 yards wide and 15.1 yards long. If the carpenter cost $ 1.71 per feet² what would be the cost of carpenting the room ?
✯ Explanation -Given :
Length of the meeting room = 15.1 yardBreadth of the meeting room = 13.4 yardRate of carpenting per feet² = $ 1.71Need to find :
Cost of carpenting the room.Solution :
THIS QUESTION IS BASED ON MEANSURATION TO SOLVE THIS QUESTION FIRST WE WILL CALCULATE THE AREA OF THE MEETING ROOM AND THEN WE WILL CALCULATE THE COST OF CARPENTING THE MEETING ROOM.
Calculating the area of the meeting room
[tex] \star \: \large \boxed{\sf{ Area_{(rectangle)} = Length × Breadth }}[/tex]
[tex] \large\rm{ Area_{(rectangle)} = (15.1 × 13.4) yard² = 202.34 \: yards²}[/tex]
Area of the meeting room = 202.34 yard²
Calculating the cost of carpenting the meeting room
First we will convert yards into feet
We know,
1 yard = 3 feet
202.34 yard = 202.34 × 3 = 607.02 feet
Now calculating the cost of carpenting the meeting room
Rate of carpenting = $ 17.1 per feet²
Cost of carpenting = $ ( 17.1 × 607.02) = $10,380.04
Final Answer -
Cost of carpenting the meeting room = $10,380.04.[tex] \rule{180pt}{3pt}[/tex]
(-4,1); perpendicular to y= -5/6x +3
Answers
Answer:
y = (6/5)x + 29/5
Step-by-step explanation:
To avoid confusion please enclose the fractional exponent inside parentheses: y= -5/6x +3 => y= (-5/6)x +3
The new line is to be perpendicular to the given line (above). The slope of this new line must be the negative reciprocal of (-5/6), which is (6/5).
Usig the slope-intercept formula, we get y = mx + b, or
1 = (6/5)(-4) + b
The LCD here is 5. Multiplying all 3 terms by 5, we get:
5 = 6(-4) + 5b, or
5 = -24 + 5b, or
5b = 29
Then b = 29/5, and the desired equation is:
y = (6/5)x + 29/5
The price of a gas increases from 2.20 per gallon on Monday to 2.31 per gallon on Tuesday. What is the percent of increase?
Answers
Answer:
4.9%
But I guess you may round to 5%, just be sure to say that you rounded from 4.9%.
Annete completes a 6.8-mile bike route in 90 minutes. She rides her bike at a constant speed for the entire route. To find how fast she traveled, she solves the equation 6.8=x(90). What does x represent?
Answers
Answer:
Her speed in miles per minute
Step-by-step explanation:
Not sure if that's true but yeah
6. In a set of 10 questions ,4 marks are awarded for every correct answer and -2 marks
every wrong answer. Sunil gets 6 correct answers and 4 wrong answers. What is his
score?
Answer this question right , then I will award u brainlist and points
Answers
16 points
Step-by-step explanation:Hi there !
What is his score?
6×4 - 4×2 =
= 24 - 8
= 16 points
Good luck !
Answer:
marks awarded for each correct answer = 4
marks awarded for each incorrect answer = -2
No.of Sunil's correct answer = 6
therefore, mark of Sunil's correct answer = 6 x 4 = 24
No.of Sunil's incorrect answer = 4
therefore, mark of Sunil's incorrect answer = 4 x -2 = -8 (here + and - is multiplied therefore the final answer will be -)
Sunil's total score = 24(positive marks) - 8(negative marks)
=24-8 = 16
This also is an integer question right? ^_^
Algebra 1
> U.15 Solve a system of equations using any method: word problems GDQ
Tutor
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks
Victor and Susan each want to run for president of their school's student body council. In
order to do so, they must collect a certain number of signatures and get a nomination. So far,
Victor has 23 signatures, and Susan has 19. Victor is collecting signatures at an average rate
of 9 per day, whereas Susan is averaging 11 signatures every day. Assuming that their rate of
collection stays the same, eventually the two will have collected the same number of
signatures. How long will that take? How many signatures will they both have?
In
days, Victor and Susan will each have collected
signatures.
Submit
O
к
Answers
Answer:
cl jsjsjsjnsmamansnsnannananann
The sales team at an electronics store sold 48 computers last month. The manager at the store wants to encourage the sales team to sell more computers and is going to give all the sales team members a bonus if the number of computers sold increases by 30% in the next month. a) What is the amount of increase in computers needed? b)What is the new amount of computers the team must sell?
Answers
Answer: a. 14 Computers
b. 62 Computers
Step-by-step explanation:
a) What is the amount of increase in computers needed?
Number of Computers sold last month = 48
Percentage increase required = 30%
Amount of increase in computers needed= 30% × 48
= 0.3 × 48
= 14.4
= 14 approximately
b)What is the new amount of computers the team must sell?
This will be the amount of Computers sold last month plus the increase.
= 48 + 14
= 62 Computers
A bag has three marbles: one red, one blue, and one yellow. The marbles are pulled from the bag one at a time without replacing them. In how many different orders could the marbles be pulled from the bag?
Answers
The number of different orders that the marbles can be pulled from the bag is 6 ways
Combination and permutation of numbersIf a bag contains one red, one blue, and one yellow, then the total number of marbles contained is 3 marbles.
If the marbles are pulled from the bag one at a time without replacing them, the number of different orders that the marbles can be pulled from the bag is expressed as:
[tex]3C_1=\frac{3!}{(3-2)!} \\3C_1=\frac{3!}{1!}\\ 3C1=3! = 6ways[/tex]
Hence the number of different orders that the marbles can be pulled from the bag is 6 ways
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Solve the equation for x 1/2(12x-10)=1/3(9+6x)
Answers
Answer:
x =
Exact form:
- (63/2)
Decimal Form:
- 31.5
Mixed Numbers Form:
- (31 1/2)