In the diagram, ABC ~ DEF. The area of ABC is 72 square cm. Find the area of DEF.
А
6 cm
B
20 cm
m
Area of DEF
cm
Answers
Answer:
120
Step-by-step explanation:
just do 20x 6 and you get 120
Similar triangles may or may not be congruent
The area of triangle DEF is 800 square cm
The given parameters is
[tex]\triangle ABC \sim \triangle D EF[/tex]
This means that the triangles are similar.
The corresponding sides of the triangles are:
[tex]AC = 6[/tex]
[tex]DF = 20[/tex]
So, the scale factor (k) from ABC to DEF is:
[tex]k = \frac{D EF}{ABC}[/tex]
[tex]k = \frac{20}{6}[/tex]
Simplify
[tex]k = \frac{10}{3}[/tex]
The area of triangle DEF is then calculated as follows:
Area = Area of triangle ABC * k^2
So, we have:
[tex]A =72 \times \frac{10}{3} \times \frac{10}{3}[/tex]
[tex]A = 800[/tex]
Hence, the area of triangle DEF is 800 square cm
Read more about similar triangles at:
https://brainly.com/question/14285697
Related Questions
divide 18 by 3, then add 9
Answers
Answer:
15
Step-by-step explanation:
18 ÷ 3 = 6
6+3 =15
hope this helps
given the function f(x)=x^3 +x^2-2x+1 what is the resulting function f(x) is shifted to the left one unit
Answers
Answer:
The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
Step-by-step explanation:
Suppose we have a function f(x). If we want to shift the function 1 unit to the left, we find f(x+1).
In this question, we have:
[tex]f(x) = x^3 + x^2 - 2x + 1[/tex]
Shifting 1 unit to the left:
[tex]f(x+1) = (x+1)^3 + (x+1)^2 - 2(x+1) + 1[/tex]
[tex]f(x+1) = (x^3 + 3x^2 + 3x + 1) + (x^2 + 2x + 1) - 2x - 2 + 1[/tex]
[tex]f(x+1) = x^3 + (3+1)x^2 + (3+2-2)x + 1 + 1 - 2 + 1[/tex]
[tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
The resulting function is [tex]f(x+1) = x^3 + 4x^2 + 3x + 1[/tex]
how do you create a graph for linear equation? I need to graph 3x=4
Answers
Answer:
Look at the graph below, hope this helped.
Step-by-step explanation:
Casandra earned 520$ this month by walking her neighbors dog . This is a 30% increase from amount she earned last month
Answers
Answer: last week she earned $364.
Step-by-step explanation:
Specify the set of B by giving a written description of It’s element where B={ 0,1,4,9,16,25}
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the set B
B={ 0,1,4,9,16,25}Analysis of the elements in the set B
[tex]m = 0 = 0^{2}[/tex][tex]m\:=\:1\:=\:1^2[/tex][tex]m\:=\:4\:=\:2^2[/tex][tex]m\:=\:9\:=\:3^2[/tex][tex]m\:=\:16\:=\:4^2[/tex][tex]m\:=\:25\:=\:5^2[/tex]We can check that each element in set B is a square of a whole number.
Therefore, we conclude that:
B = { square numbers less than 30 }.
or
B = {m/m is square of a whole number; [tex]0 \leq m \leq 5[/tex] }
Four sisters are all 2 years apart in age. The
total of their ages is equal to 36 years. How
old is the youngest sister
Answers
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The four sisters are all 2 years apart in age. The total of their ages is equal to 36 years.
Let x be the age of the youngest sister. Then the age of other sister will be x + 2, x + 4, and x + 6. Then the equation is given as,
x + x + 2 + x + 4 + x + 6 = 36
4x + 12 = 36
4x = 36 - 12
4x = 24
x = 24 / 4
x = 6
The equation that represents the age of the youngest sister is 4x + 12 = 36. Then the age of youngest sister will be 6 years old.
More about the Algebra link is given below.
https://brainly.com/question/953809
#SPJ5
A way to remember corresponding angles is to remember: *
Answers
i need help plz
State the coordinates of the point.
Answers
Answer:
(-5,8)
Step-by-step explanation:
Hope this helps ;)
Shannon, Oscar, and Ella contribute the same amount to their father’s gift. Their older sister Moriah contributes $12. How much does Oscar contribute if the total for the gift is $36? Write and solve an equation.
Answers
Answer:
Amount contributed by Oscar = $8
Step-by-step explanation:
Given that:
Amount spent on gift = $36
Amount contributed by Moriah = $12
Let,
x be the amount contributed by each of them.
Thus,
Gift total = Contribution of all
36 = x+x+x+12
36 = 3x+12
3x+12 = 36
3x=36-12
3x=24
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{24}{3}\\x=8[/tex]
Hence,
Amount contributed by Oscar = $8
Help plz:)))I’ll mark u Brainliest
Answers
Answer:
ST = 8 m
Step-by-step explanation:
Since both triangles are congruent to each other, therefore their corresponding angles and corresponding side lengths would be equal to each other accordingly.
Side ST in ∆STU corresponds to side PQ in ∆PQR. ST = PQ.
Side PQ = 8 m
Therefore, side ST = PQ = 8 m
The dimensions of a cylindrical water tank are shown below.
18 yd
o
58,320 yd
3,240 yd
60 yd
O
19,440 yd
15,270 yd3
Which of the following is the best estimate of the volume of
this water tank?
Answers
Look at the table.
Cars Sold
Annual Bonus
120
$1,800
130
$1,950
150
$2,250
175
$2,625
What is the annual bonus for a salesperson who sells 55 cars?
$150
$825
$1,500
$8,250
Answers
Answer: $825 (B)
Step-by-step explanation:
it’s obvious
Answer: The answer is B!
Step-by-step explanation: It's on edge, hope this helped!
Which of the following is a solution to the system of two equations y = 3x – 7 and 4x – 5y = -20?
Answers
Answer:
x = 5, and y = 8
Step-by-step explanation:
You can solve this system by solving either of the equations for either x or y, and substituting that into the other.
Since the first equation is already defined for y, let's substitute that into the second equation:
4x - 5y = -20
4x - 5(3x - 7) = -20
4x - 15x + 35 = -20
4x - 15x = -20 - 35
-11x = -55
x = 5
We can then plug that into either of the original equations to find y:
y = 3x - 7
y = 3 * 5 - 7
y = 15 - 7
y = 8
We can also verify our answer by plugging one of the values into either of the original equations and seeing what we get:
4x - 5y = -20
4x - 5 * 8 = -20
4x - 40 = -20
4x = 20
x = 5
So we know the answer is correct. x is equal to five, and y is equal to eight.
I need help with this
Answers
Answer:
1/4
Step-by-step explanation:
As 4 units move to the right, 1 unit goes up. Using the formula for slope:
Rise / Run
The gradient of the blue line is 1/4 or 0.25
2. 124 2. 1
tell what theroem you used in each class
Answers
Answer:
Vertical Angles Theorem
Step-by-step explanation:
I'm not sure what you're asking because 2. 124 2. 1 doesn't make mathematical sense, but if angle 1=angle 2, you use the vertical angles theorem.
A 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.
15.69 feet
18.01 feet
27.89 feet
36.72 feet
Answers
Answer:
hope this helps, brainlist? (OwO)
Step-by-step explanation:
I think the answer is 27.89 feet, C
The building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
Lenght of the ladder = 32 foot
The angle formed between the ladder and the ground = 29.37°
The ladder, wall of the building, and the ground are making a right-angle triangle.
Let's suppose the base of the ladder is x feet far from the building.
Applying the Cos ratio to find the value of x:
[tex]\rm Cos29.37\°=\frac{x}{32}[/tex]
x = 27.887 feet or (Cos29.37° = 0.871)
x = 27.89 feet
Thus, the building is 27.89 feet far from the base of the ladder if a 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground.
Know more about trigonometry here:
brainly.com/question/26719838
SPJ2
1. A right triangle LMN is given where: side MN = 8 side NL (the hypotenuse) =
10 What is the length of side LM?*
Answers
Step-by-step explanation:
[tex] \underline{ \underline{ \text{Given}}} : [/tex]
Length of MN ( Base ) = 8 Length of NL ( Hypotenuse ) = 10[tex] \underline{ \underline{ \text{To \: find}}} : [/tex]
Length of LM ( Perpendicular )[tex] \underline{ \underline{ \text{Using \: pythagoras \: theorem}}} : [/tex]
[tex] \boxed{ \sf{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }}[/tex]
⤑ [tex] \sf{ Perpendicular = \sqrt{ {(Hypotenuse)}^{2} - {(Base)}^{2} } }[/tex]
⤑ [tex] \sf{ \sqrt{ {(10)}^{2} - {(8)}^{2} } }[/tex]
⤑ [tex] \sf{ \sqrt{100 - 64}} [/tex]
⤑ [tex] \sf{ \sqrt{36}} [/tex]
⤑ [tex] \boxed{ \sf{6\: units}}[/tex]
[tex] \pink{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline { \tt{6 \: units}}}}}}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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solve for x x−6/9=−5
x=
Answers
Answer:
4 4/9
Step-by-step explanation:
Move all terms not containing x
to the right side of the equation.
Exact Form:
x=−409
Decimal Form:x=−4.¯4
Mixed Number Form:
4 4/9
Answer:
-39
Step-by-step explanation:
x-6/9 = -5
then multiply both sides by 9
9 ° (x-6) / 9 = 9 ° -5
simplify
x-6= -45
add 6 to both sides
x-6+6=-45+6
simplify
x= -39
Solve: 33 + 27 ÷ 9 + (30 ÷ 5)
Answers
Answer:
42
Step-by-step explanation:
You need to follow P--E--M--D--A--S
A X U I A U
R P L V D B
E O T I D T
N N I T I R
T E P I T A
H N L O I C
E T I N O T
S S C N I
I A O
S T N
I
O
N
Sara and Sam are each working on a science project in which they need to research the individual masses of the nine planets (including the dwarf planet Pluto as the ninth planet). Sara completes her data for the planets' masses in kilograms while Sam's data is in milligrams.
Look at picture.
Approximate how many times greater Saturn's mass is than Mercury's.
A) 200,000
B) 2,000,000
C) 2,000
D) 20,000
Answers
Answer:
2000 times
Step-by-step explanation:
Given
Sara:
[tex]Mercury = 3.302 * 10^{23[/tex]
[tex]Saturn = 5.685 * 10^{26[/tex]
Sam:
[tex]Mercury = 3.302 * 10^{29[/tex]
[tex]Saturn = 5.685 * 10^{32[/tex]
To determine the number of times, the mass of Saturn is greater than the mass of Mercury, we simply do the following:
[tex]Times = \frac{Saturn}{Mercury}[/tex]
Using Sara's measurement; this gives:
[tex]Times = \frac{5.685 * 10^{26}}{3.302 * 10^{23}}[/tex]
Apply law of indices
[tex]Times = \frac{5.685 * 10^{26-23}}{3.302}[/tex]
[tex]Times = \frac{5.685 * 10^3}{3.302}[/tex]
[tex]Times = 5.685/3.302 * 10^3[/tex]
[tex]Times = 1.72 * 10^3[/tex]
Approximate
[tex]Times = 2 * 10^3[/tex]
[tex]Times = 2000[/tex]
Dean purchased a box of cereal Which of these measurements BEST describes the volume of the box?
1.)154 cubic feet
2.)154 cubic inches
3.)154 cubic meters
4.)154 cubic millimeters
Answers
Answer:
2
Step-by-step explanation:
You don't measure cereal in the others because feet, meters and millimeters are too big. Hope this helps.
A dripping faucet leaks 40 gallons of water per day.
How many gallons does the faucet leak in 2 days.
Answers
Answer:
80 gallons and a leaking problem.
Step-by-step explanation:
please mark brainliest, give a thanks, and rate a five stars if this helped! feel free to ask anymore questions if you need any more help! thanks!
(lol optional): add my sc: tealyn337
A scale drawing for a backyard is shown below.
In the drawing, 2 cm represents 5 m.
Assuming the patio is rectangular, find the area of the real patio.
Answers
Answer:
50 m²
Step-by-step explanation:
2 cm for length = 5 m. 4 cm for width = 10 m. Area = width • length. 10•5=50
maurice read 10 pages that is 50 percent of the paper lenght what i the paper lenght
Answers
Answer:
Would it not be 20?
Step-by-step explanation:
Answer:
The answer is 20
Step-by-step explanation:
If 10 pages is 50% of the paper length, to make it equal 100% you just multiply 10X2 or add 10+10 and that equals 20.
Find the solution of these two equations. Y=1/5x-7 and y=-x-1
Answers
Answer:For the first one it would be x=35
And the 2nd one would just be x=-1
Step-by-step explanation:
Pls find this asap I am already late for this pls
Answers
Answer:
Step-by-step explanation:
I'm not sure about number 3, but I have the answer for number. The answer is 1:32.
3: 69
3/69
Then we reduce the fraction to the lowest term
3/69 = 1/32
1:32
Just divide 96/3 and you can see that one bus can hold 32 students
Jane drove 693 miles in 11 hours.
At the same rate, how long would it take her to drive 411 miles?
Answers
Answer:
approx. 6.523809523809524 hours
Step-by-step explanation:
Let us first find how long it takes Jane to drive 1 mile.
11/693 = approx. 0.015873015873016 hours to drive one mile.
She drives 411 miles, so we can multiply that by 411:
0.015873015873016 * 411 = approx. 6.523809523809524 hours
I hope this helps! :)
Answer:
6.52 hours
Step-by-step explanation:
693 miles divided by 11 hours = 63 miles per hour.
411 miles divided by 63 miles = 6.52380952 miles
Round to 2 decimal places: 6.52 hours
Which three types of transformations result in congruent shapes? Question 8 options: A) Reflection, rotation, translation B) Reflection, translation, dilation C) Reflection, dilation, rotation D) Rotation, dilation, translation
Answers
Answer: A
Step-by-step explanation:
Answer:
A. Reflection, rotation, translation
Step-by-step explanation:
Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent. Explore and discuss the examples of transformations below with your child. Examples of Transformations.Nikki dove into a pool and swam underwater. The table shows how her depth changed during a 4-second time period.
Which equation shows the relationship in the table between the time, t, and the depth, d?
Answers
Answer:d
Step-by-step explanation:
What will be the 50th term in the sequence defined by an=11+5(n-1)
Answers
Answer:
234
Step-by-step explanation: