The dimensions of triangle ΔDEF can be obtained from ΔABC by applying a scale factor of dilation of [tex]\displaystyle \frac{1}{2}[/tex].
The conclusion which is true about the triangles is D. They are similar by the definition of similarity in terms of dilation.Reasons:
The given vertices of the triangles are;
ΔABC: A(1, 5), B(3, 9), C(5, 3)
ΔDEF: D(-3, 3), E(-2, 5), and F(-1, 2)
The lengths of the sides of ΔABC are
AB = √((1 - 3)² + (5 - 9)²) = √20 = 2·√5
BC = √((5 - 3)² + (3 - 9)²) = √40 = 2·√10
AC = √((1 - 5)² + (5 - 3)²) = √20 = 2·√10
The lengths of the sides of ΔDEF are;
DE = √((-3 - (-2))² + (3 - 5)²) = √5
EF = FE = √((-1 - (-2))² + (2 - 5)²) = √10
DF = √((-3 - (-1))² + (3 - 2)²) = √5
Therefore;
[tex]\displaystyle The \ dilation \ that \ gives \ \Delta ABC = \frac{\overline {EF}}{\overline {BC}} = \frac{\overline {DE}}{\overline {AB}} = \frac{\overline {DF}}{\overline {AC}} = \frac{\sqrt{10} }{2\cdot \sqrt{10} } = \frac{1}{2}[/tex]
The ratio of the sides of ΔABC to the corresponding sides of ΔDEF are equal to [tex]\displaystyle \frac{1}{2}[/tex].
Which gives;
ΔDEF is a dilation of ΔABC, and ΔDEF and ΔABC are similar by the
definition of similarity in terms of a dilation.
Learn more here:
https://brainly.com/question/14380197
Answer:
Step-by-step explanation:
They are congruent by the definition of congruence in terms of rigid motions.
16.73L is how much to cl
Answer:
1673
Step-by-step explanation:
multiply the volume value by 100
Answer:
1673
Step-by-step explanation:
since your liter to centiliter you just multiple you number by 100 for example:
10.30l x 100 = 1030
[WILL GIVE BRAINLIEST]
The price of milk is tripled, and then rose another $0.75 per gallon. If the price now is AT LEAST $4.50, which inequality expresses this situation?
A. 3x + 0.75 ≤ 4.5
B. 3x + 0.75 ≥ 4.5
C. 3x - 0.75 ≥ 4.5
D. 3(x + 0.75) ≤ 4.5
I’ll give brainliest to someone with a correct answer along with an explanation :)
Answer:
D
Step-by-step explanation:
Hello!
The answer is D because, the 1st part triples which is part of the question and is atleast 4.5
Please brainly if I helped you
How many solutions does this
system have?
(24x - 9y = 3
8x - 3y = 1
-
A. None
B. One
C. Infinite
Answer:
C) Infinitely many solutions
Step-by-step explanation:
Given the systems of linear equations in standard form:
Equation 1: 24x - 9y = 3
Equation 2: 8x - 3y = 1
Transform both equations into slope-intercept form, y = mx + b:
Equation 1: 24x - 9y = 3Subtract 24x from both sides:
24x - 24x - 9y = -24x + 3
-9y = -24x + 3
Divide both sides by -9 to isolate y:
[tex]\mathsf{\frac{-9y}{-9}\:=\:\frac{-24x + 3}{-9} }[/tex]
[tex]\mathsf{y\:=\:\frac{8}{3}x\:-\frac{1}{3}}[/tex] ⇒ This is the slope-intercept form of Equation 1, 24x - 9y = 3.
Equation 2: 8x - 3y = 1Subtract 8x from both sides:
8x - 8x - 3y = - 8x + 1
-3y = -8x + 1
Divide both sides by -3 to isolate y:
[tex]\mathsf{\frac{-3y}{-3}\:=\:\frac{-8x + 1}{-3} }[/tex]
[tex]\mathsf{y\:=\:\frac{8}{3}x\:-\frac{1}{3}}[/tex] ⇒ This is the slope-intercept form of Equation 2, 8x - 3y = 1.
It turns out that both equations in the given system are equivalent, and their graphs will coincide on top of one another. In this case, the equations are said to be dependent, both equations will have the same solutions.
Hence, there are infinitely many solutions to the given systems of linear equations, making Option C the correct answer.
12.An online bookstore ships boxes with a copy
of the new bestseller in each box. The total
weight of the shipment is 1,200 pounds. If
each box weighs 1.2 pounds, how many boxes
are shipped?
A)10
B)10,000
C)1,000
D) 100
Answer:1000
Step-by-step explanation:
1200 divided by 1.2
Pls Help Me With This Question
Answer:
first solution is correct
Step-by-step explanation:
because line (GA) is out of the circle
Look at picture below
Answer:
10,250
Step-by-step explanation:
Correct me if I am wrong But,
Sara says “if you subtract 17 from my number and multiply the difference by -4, the result is -24” what is Sara’s number? I’ll give brain
3x+10+x solve for x thank you :)
Answer:
4x + 10
Step-by-step explanation:
help anybody please?
Answer:
2t= ½
Step-by-step explanation:
2t = ½
divide both sides by 2 to get t on its own.
t = ¼
A department store buys 300 shirts at a cost of $5,400 and sells them at a selling price of $20
each. Find the percent markup.
The percent markup is %. (Round to the nearest whole number as needed.)
Answer:
they mark up the price by 11 percent
Step-by-step explanation:
first you do 5400/300 and you get 18
than you find out how much percent of 18 is 2
than you have how much percent they market up the price
Find the slope of the line passing through the points (5, 1) and (5, "-6)"
NEED HELP FAST
Answer:
m = 0
Step-by-step explanation:
(5,1) and (5,-6)
(-6-1)/(5/5)
= -7/0 = 0 (horizontal line)
Please awnser iodijeiodweoijoewideejoidejoiwjiiowjiojiowjd
Answer: B
Step-by-step explanation:
5² + x² = 6²
25 + x² = 36
36 - 25 = 11
√x² = √ 11
x = √11
Answer my math question I asked so many times I lost most of points by
At PetSmart, zebra fish cost $1.85 each and neon tetras cost $2.10 each. Nicolas bought 11
fish for a total of $21.60 (not including tax). How many of each fish did he buy?
Separate your answer list with a comma, for example: 30 neon tetras, 20 zebra fish.
Answer:
5 Neon tetras
6 Zebra Fish
Step-by-step explanation:
21.60/2=10.80
Neon Tetras: 2.10*5=10.50
Zebra fish: 1.85*6=11.10
10.50+11.10= 21.60
What is the length of the indicated arc ?
A.
3π
B.
(
3π
⁄
4
)
C.
(
3π
⁄
2
)
D.
(
1π
⁄
4
)
E.
None of the above
Answer:
none of the above
Step-by-step explanation:
but I'm not sure
Use the graph to write a linear function that relates y to x
Answer:
y=2
Step-by-step explanation:
y is the y-intercept which is what ever is on the y axis and has a dot
3x-(2x-1)=7x-(3-5x)+(-x+24)
Answer:
x=-2
Step-by-step explanation:
first, remove the parenthesis.
3x-2x+1=7x-3+5x-x+24
collect like terms
x+1=11x+21
subtract x from both sides
1=10x+21
subtract 21 from both sides
-20=10x
divide both sides by 10
-2=x
What is the equation of the line in slope-intercept form?
Please help me find the slope!!!
Answer:
-3/2
Step-by-step explanation:
yall help me please.
Help plssssssss asap
Answer:
it's 110° reason (interior angles of triangle are equal to exterior angle)
-7(3x + 5) + 20 = 5(3 - 5x) + 4x
Is it no solution/ many solutions or infinite
Answer:
0= 30
Step-by-step explanation:
-7(3x+5) +20=5)3-5x)+4x
-21x-35+20=5)3-5x)+4x
Add the numbers
-21x-35+20=5)3-5x)+4x
-21x-15=5)3-5x)+4x
Rearrange terms
-21x-15=5)3-5x)+4x
-21x-15=5(-5x+3)+4x
Distribute
-21x-15=-25x+15+4x
Combine like terms
-21x-15=-21x+15
Add 15 to both sides of the equation
-21x-15+15=-21x+15+15
Simplify
Add the numbers
-21x=-21x+30
add 21 to both sides of the equation
-21x+21x= 21x+30+21x
Simplify
combine like terms
0=30
What do you know to be true about the values of p and q.
A. p = q
B. p < q
C. p > q
D. Can't be determined
Answer:
A. p = q
Step-by-step explanation:
For each triangle, add the angles together and then subtract the sum from 180°.
First triangle:
60° + 50° = 110°
180° - 110° = 70°
Missing angle = 70°
Second triangle:
80° + 30° = 110°
180° - 110° = 70°
Missing angle = 70°
Hope this helps :)
Which is equivalent to 4(x – 1)?
Answer:
=4*x-4*1
= 4x - 4 is equivalent to 4(x-1)
Is 12/6 an integer??????
NO 12/6 IS NOT A INTEGER
Step-by-step explanation:
A INTEGER IS A NUMBER WITH A SUBTRACTION SIGN IN FORNT OF IT LIKE -5
what is 10 times 643 rounded to the nearest hundered
Answer:
6400
Step-by-step explanation:
643 × 10 = 6430
Nearest hundredth is the third last digit so it should be the number 4
Since the digit after 4 is less than 5, we keep the number the same
The answer you should get is 6400
A bakery can make 63 cookies in 9 minutes. At this rate, how many cookies can the bakery make in 20 minutes?
Answer:
Step-by-step explanation:
First, we need to calculate how many cookies can the Bakery make in one minute.
So we use [tex]\dfrac{63}{9} = \dfrac{21}{3} = 7[/tex] to find out that the rate is 7 cookies per minute.
So in 20 minutes, the bakery can make [tex]20*7=140[/tex] cookies.
Step-by-step explanation:
First, we need to calculate how many cookies can the Bakery make in one minute.
So we use to find out that the rate is 7 cookies per minute.
So in 20 minutes, the bakery can make cookies.
Answer:
140 cookies in 20 minutes
Please help asap im trying to not stress over late work <3
Answer:
Part A) $202.50=9
Part B) $292.50=11
Step-by-step explanation:
Part A) y is the total cost, x is the total number of students. Therefore, y=x.
Which makes $202.50=9
Part B) since $202.50= 9 students,
1 student= $202.50÷9 = $22.50
Since 4 students joined,
4 students= $22.5 × 4= $90.00
4+9= 11 students
So 11 students= $202.50+$90.00 =$292.50
the total cost will now be $292.50
Alex wrote the expanded form for the number 165.038 as “100 + 60 + 5 + 30 + 8.” Was he correct? If not, give the correct expanded form. (PLEASE HELP)
hehehe please help ASAP
Answer: 6 because 60 divided by 10 = 6 36 divided 6 = 6 etc..
Step-by-step explanation:
