ΔABC is similar to ΔDEF. The ratio of the length of AB to the length of DE is 2:1. Which ratio is also equal to 2:1?
Answers
Answer:
4)
Step-by-step explanation:
When triangles are similar, their corresponding angles are congruent. So, it is not 1) and 2).
Areas ratio is squared to ratio of their sides, so it is not 3).
Perimeter is sum of the sides. All corresponding sides in similar triangles have the same ratio. So, answer is 4).
The ratio [tex]\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}[/tex] is also equal to 2:1
What are similar triangles?"Two triangles are similar when their corresponding sides are in proportion to each other and corresponding angles are equal."
What is ratio?"It is the comparison of two quantities of the same kind."
For given question,
ΔABC is similar to ΔDEF.
⇒ [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]
And ∠A = ∠D, ∠B = ∠E, ∠C = ∠F
We know, if two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.
⇒ [tex]\frac{area~of~\Delta {ABC}}{area~of~\Delta DE F} =(\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{AC}{DF})^2[/tex]
We know, the perimeters of the similar triangles are in the same ratio as the sides.
[tex]\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]
The ratio of the length of AB to the length of DE is 2:1
[tex]\Rightarrow \frac{AB}{DE} = \frac{2}{1}[/tex]
[tex]\Rightarrow \frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F} = \frac{2}{1}[/tex]
Therefore, the ratio [tex]\frac{perimeter~of~\Delta ABC}{perimeter~of~\Delta DE F}[/tex] is also equal to 2:1
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Related Questions
Sydney bikes 32 miles in 2 hours and 64 miles in 4 hours. He bikes at a constant rate. Which function gives the distance d that he travels in t hours?
A. d= 64 t
B. d= 32 t
C. d= 16 t
D. d = 8 t
Answers
Answer:
C. d = 16t
Step-by-step explanation:
Since she is biking at a constant rate, then you would just have to divide 32 by 2 to get 16, which would be the speed Sydney would ride in the matter of one hour. So for how many hours she bikes, multiplied by 16, would be the distance that she travels in said time.
Which expression gives the length of the transverse axis of the hyperbola
shown below?
Answers
Explanation:
Length of transverse axis of hyperbola means distance between both the vertices of hyperbola which is constant given by 2a.
As definition of hyperbola:
Difference in distance of any point (x,y) from both focus is a positive constant equals to length of transverse axis.
So, distance of (x,y) from foci 1)-( distance of (x,y) from foci 2)=2a
x-y=2a
Length of transverse axis is x-y.
hope it helps....
Good luck on your assignment
The length of the transverse axis is x - y if point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length option (C) x - y is correct.
What is hyperbola?It's a two-dimensional geometry curve with two components that are both symmetric. In other words, the number of points in two-dimensional geometry that have a constant difference between them and two fixed points in the plane can be defined.
We have given a hyperbola shown in the picture.
The green line indicates the transverse axis of the hyperbola.
As we know,
The distance between the two vertices of the hyperbola, which is always given by 2a, is referred to as the length of the transverse axis.
Any point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length.
x-y=2a
The length of the transverse axis = x - y
Thus, the length of the transverse axis is x - y if point (x, y) is separated from either focus by a positive constant equal to the transverse axis' length option (C) x - y is correct.
Learn more about the hyperbola here:
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Help Plz
A small bar of gold measures 20 mm by 100 mm by 2 mm. One cubic millimeter of gold weighs about 0.0005 ounces. Find the volume in cubic millimeters and the weight in ounces of this small bar of gold.
The volume of the bar is ___ cubic millimeters and the weight of the bar is ___ ounce(s).
Answers
Answer:
volume=1,000 cubic millimeters
weight=1 ounce
Step-by-step explanation:
40x25x2=1,000
volume=1,000 cubic millimeters
1,000x0.0005=1
weight=1 ounce
Answer:
Volume = 1000 cubic millimeters
weight = 1 ounce
Step-by-step explanation:
40 x 25 x 2 = 1000
volume= 1000 cubic millimeters
1000 x 0.0005 = 1
weight = 1 ounce
hope it works out !!
brainliest please !!
The graphs below have the same shape. What is the equation of the red
graph?
Answers
Answer:
A
Step-by-step explanation:
Since the shape of both graphs is the parent parabola form, and g(x) is just shifted up 2 instead of 5, its equation is [tex]2-x^2[/tex], or answer choice A. Hope this helps!
3(c+2)=36 what is c=?
Answers
Answer:
3(c + 2) = 36
c + 2 = 12
c = 10
Answer:
10
Step-by-step explanation:
3(c+2)=36
- Use distributive property
3c+6=36
- subtract 6 from both sides
3c=30
- divide by 3
c = 10
HELP ASAP PLEASE
Are the bases of the prism equilateral triangles? Why or why not? Note: The bases of a triangular prism are triangles.
For this prism to be a right prism, all the lateral faces must be rectangles. Is enough information given to prove the lateral faces are rectangles? Why or why not?
Answers
Answer:
Step-by-step explanation:
The bases of a triangular prism are equilateral triangles, since they have equal sides: 5, 5, and 5
yes, since if all lateral faces are rectangles, rectangles are formed from 4 perpendicular segments, thus, if all edges of the lateral faces are perpendicular, then they are rectangles
Answer:
yes
Step-by-step explanation:
i tried explaining it in a way that it wouldn't sound like I'm copying the answer above, but really, the answer above is correct and explains it well, refer to the answer above please
This mapping represents a function named f .
Which of the chices also represents the function, f?
Answers
Answer:
Last option (the drawn)
Step-by-step explanation:
The following points correspond to f:
(3, -2), (9, 2)
The slope of the line (m) is:
m = (2 - (-2))/(9 - 3) = 4/6 = 2/3
Therefore, the first option is incorrect (its slope is 3/2).
To find the y-intercept (b) of the line, we replace a known point and the slope into the general equation:
y = mx + b
2 = 2/3(9) + b
b = 2 - 6
b = -4
Therefore, the third option is incorrect (it add 4 instead of subtracting 4).
Replacing x = 6 into the equation we get:
y = 2/3(6) - 4
y = 0
then, point (6, 0) belongs to the line. Therefore, the second option is incorrect (it has the point (6, 1) instead); and the fourth option is correct (it is a line that includes points (0, -4) and (6, 0)).
Answer: the 4th answer is correct
HELP ME ASAP IT IS DUE TODAY!!!!!!!! WHOEVER ANSWER THIS WILL BE REWARDED
Answers
Answer:
Large Pizza
Step-by-step explanation:
Rewarded with what? :P
Anyway,
The area of a circle is pi*r^2. Additionally, the radius is half the diameter.
The first pizza(s) have diameter 12, which means they have radius 6. The area of one is 6*6*pi=36pi, and since there are two we multiply by 2 to get 72pi.
The second pizza has diameter 18, so radius 9. The area of it is 9*9*pi=81pi.
Clearly 72pi is less than 81pi, so the Large Pizza is biggest.
Hope that helped,
-sirswagger21
(oh yeah and btw give me a million bucks for the reward ty :v)
Kelli wants to buy one pound of blueberries and several pounds of grapes. She has $15 to spend. Write an inequality to represent this situation. Then solve the inequality and graph the solutions. What do the solutions represent in the context of the problem?
Answers
Step-by-step explanation:
daddy want some more dior
URGENT!!! HELP
Gina has purchased 100 songs from the internet. She plans to download an equal number of songs on her music player each week for 5 weeks. The graph shows the number of songs left to download, y, for a certain number of weeks, x:
(Graph attached below)
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario? Show your work to find the rate of change and initial value. (6 points)
Part B: Write an equation in slope-intercept form to model the relationship between x and y. (4 points)
Answers
Answer:
Initial value is 100
Step-by-step explanation:
A) rate of change would be dividing the number of songs wanted (100) by the number of weeks downloading (5)
100/5 = 20
since the total quantity wanted is becoming less every week the rate of change would be negative so it becomes -20
Initial value is 100, which is the total number of songs they want
Answer:
Part A:
initial value = 100 (total amount of songs to download)
rate of change = -20 songs/week (100-80 and so on)
Part B:
y = -20x + 100
Please help me solve this puzzle.
Answers
Step-by-step explanation:
marmiad=10
trident=6
pearls =4
10+6×4
=16×4
=64
hey!!
Answer:34
Step by step explanation:
4+4+4=12
4+4+10=18
6+10+10=26
10+6*4=34
hope it helps..
Za and Zb are complementary angles. Za measures 22º.
What is the measure of Zb?
Answers
Answer:
b = 68
Step-by-step explanation:
Complementary angles add to 90 degrees
a+b = 90
22+b = 90
Subtract 22 from each side
b = 90-22
b = 68
Answer:
68 degrees
Step-by-step explanation:
Complementary Angles: The sum of the angles is 90 degrees.
If angle a is 22 degrees, then...
a + b = 90
22 + b = 90
22 - 22 + b = 90 - 22
b = 68
That means that the measure of angle b is 68 degrees.
I hope this helps! Have a great day!
Please help. 10 points and brainliest
Answers
Answer: C
Step-by-step explanation:
Since you are multiplying the two scientific notations, you would multiply 8.1 and 2.2. After, you would multiply the 10³ and 10^6. When you multiply 2 exponents with the same base, you add the exponents. Therefore, C is your correct answer.
Answer:
(8.1*2.2)*10^3+6
Step-by-step explanation:
The equation = 1.782*10^10=17820000000
The top equation = 10.3*1001000
The second equation = 17.82*10^18=17820000000000000000
The third equation = 17.82* 1000000000= 17820000000
A student at a university makes money by buying and selling used cars. Charles bought a used car and later sold it for a 20% profit. If he sold it for $4560, how much did Charles pay for the car? Charles paid $? for the car.
Answers
Answer:
He paid $3648
Step-by-step explanation:
If you subtract 20% from 4560 which he sold it for you will get how much he paid for it.
4560 - 20% = $3648
find the slope of the line that passses thruogh 7.7 and 2,1
Answers
Answer:
6/5
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(1-7)/(2-7)
m=-6/-5
m=6/5
11) Omar is flying a kite on a 50-foot string at a diagonal distance. The kite gets stuck at the top
of a 40-foot tree. How far is Omar from the tree?
Answers
Answer:
30 ft
Step-by-step explanation:
We have a right triangle.
Hypotenuse = c = 50 ft
Leg #1 = a = 40 ft
Leg#2 = b = ?
We need to use Pythagorean Theorem
c² = a² + b²
50² = 40² + b²
b² = 2500 -1600 = 900
b = 30
Can the two triangles be proven congruent by SAS? Explain. answers: A) Yes. The shared side, image, provides enough information for SAS. B) No. There's only enough information provided for ASA. C) Yes. Angle B and angle D can be assumed to be right angles. D) No. The shared side, image, would provide enough information for SSA, but this is not a congruence theorem.
Answers
Answer:
A) Yes. The shared side, image, provides enough information for SAS.
Step-by-step explanation:
Whats the radius of this?
Answers
Answer:
Its trying to trick you, you dont need any fancy shmancy formula. If you see the 8 its trying to make you think of a formula but if there is a formula and you get it wrong then you get it wrong. Its easy the 8 is there but a circle has a radius no matter where you measure it. 8/2 = 4. Radius is 4 Diameter is 8
Think outside the box 4 is radius 8 is diamaterwrite a^4*a^2 without exponents
Answers
Answer:
a x a x a x a x a x a
Step-by-step explanation:
a^4 x a^2
a x a x a x a times a x a
= a^6 or a x a x a x a x a x a
20 POINTS !!! Write 5 true statements for this picture and then After those 5 statements add a becuase and tell why is it true
Answers
MHL is an obtuse angle, 160>90
HPK is an acute angle, 20<90
LHK is an acute angle, it looks smaller than 90
MHJ is an acute angle, it looks smaller than 90
JL intersects MK
what is the standard form of 7+3i/2-5i
Answers
Answer:
-1/29+41/29*i
Step-by-step explanation:
(7+3i)/(2-5i)=(7+3i)(2+5i)/(2-5i)(2+5i)=(14+35i+6i+15i^2)/(4-25i^2)=
(14+41i-15)/(4+25)=(-1+41i)/29=-1/29+41/29*i
Colton is painting a set of figurines a solid color. It takes him 15 minutes and 5 milliliters of paint to finish a small figurine. It takes him 30 minutes and 8 milliliters of paint to complete a large figurine. Colton plans to paint for at least 360 minutes, and he can use a maximum of 100 milliliters of paint.
This graph and system of inequalities represent this situation, where x represents the number of completed small figurines and y represents the number of completed large figurines.
15x + 30 ≥ 360
5x + 8y ≤ 100
Which solution is valid within the context of the situation?
A.
(4,10)
B.
(-2,13)
C.
(1,11.75)
D.
(6,9)
Answers
Answer:
A
Step-by-step explanation:
B,C,D are not in the pink/purplish area when you plot them on the graph
Brainliest plzDear some moderators,
read before you delete no brainers!
From, a brainly user
Answer:
A. (4,10)
Step-by-step explanation:
What problem can be solved by the equation ? 2.50x-2.00=10.50
Answers
Answer:
Joe earns $2.50 for every dog he walks. He also owes $2 to his mom. How many dogs does he need to walk in order for him to get $10.50
Answer:
5.004
Step-by-step explanation:
You have to add 2.00 to the other side of 10.50 and add them both because they are positive and u should get you number 12.50 and brin down 2.50 and divide and u should get ur answer.
Work this out for meee
Answers
Answer:
87.5cm²
Step-by-step explanation:
area of trapezium = 1/2 (a+b)h
1/2 × (10 + 15) ×7
1/2 × 25 × 7
1/2 × 175 = 87.5
Answer:
87,5 cm²
Step-by-step explanation:
A = (b + B)×h/2
= (10cm + 15cm)×7cm/2
= 25cm×3,5cm
= 87,5 cm²
8-2x<4 solve inequality
Answers
Answer:
x > 2
x ∈ ( +2 ; + oo )
Step-by-step explanation:
8 - 2x < 4
8 - 4 < 2x
4 < 2x | : 2
2 < x
x > 2
x ∈ ( +2 ; + oo )
The slope of the fuction on the left is multiplied by p, and q is added to the y intercept to arrive at the function on the right. Which of the following are the values for p and q?
A. p=1/4 and q=3
B.p=1/4 and q=5
C.p=1/4 and q=4
D.p=4 and q=4
Answers
Answer:
C. 1/4 and q=4.
Step-by-step explanation:
I just got it correct on my test.
p=1/4 and q=4 which is correct option(c)
What is slope of line?Slope of line is defined as the angle of line.
Let us get the equation of the two graphs
General equation form is;
y = mx + b
m is slope and b is the y-intercept
For the first one;
y intercept is -3
So the equation is;
y = mx -3
The x-intercept is 3/4
the value of y at the x-intercept is 0
0 = 3/4m -3
3/4m =3
m = 4
so, 4 × p
4p
q added to y-intercept;
q -3
Let us get the equation of the second plot
y-intercept is 1
Equation is;
y = mx +1
We can get slope using x-intercept
x-intercept is -1
0 = -1m +1
m = 1
So;
4p = 1
p = 1/4
For the value of q;
q -3 = 1
q = 1+3 = 4
Hence, p=1/4 and q=4
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I will give the brainliest answer
Answers
Answer:
82units²
Step-by-step explanation:
=2(3*7)+2(3*2)+2(7*2)
=82 units²
Answer:
[tex]82 {units}^{2} [/tex]
Step-by-step
explanation
explanation is attached to the picture
hope this helps
brainliest appreciated
good luck! have a nice day!
please be neat when answering
Answers
Answer:
In fig. 9, angle Y = angle 110° (vertically opposite angles )
Angle x = angle z = 180 - 110 = 70° (angles on a straight line)
In fig 10, angle y = 78°
Angle x = angle z = 180-78 = 102°
In fig 11, angle x = 83°
Angle y = angle z = 180-83 = 97°
In fig 12, angle y = 37°
Angle x = angle z = 180-37 = 143°
HELP ME PLEASEEE thanks
Answers
Answer:
47°
Step-by-step explanation:
Since x and 133° are supplementary (meaning they add up to 180°), x + 133 = 180 so that means x = 47°.
There are 30 dogs at the park. 56 of the dogs are large.
Which method is a way to find the number of large dogs at the park?
Answers
Answer:
30-56
Step-by-step explanation:
It would be to Multiply 30 and [tex]\frac{1}{6}[/tex].