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Mademuasel [1]
3 years ago
13

Suppose given △ABC with a line segment DE connecting sides AB and BC so that DE ∥ AC . The lengths of the sides of △DBE are thre

e times shorter than the lengths of the sides of △ABC. What is the area of trapezoid ADEC if the area of △ABC is 27 cm^2?

Mathematics
1 answer:
Amanda [17]3 years ago
5 0

Answer:

24 cm^2

Step-by-step explanation:

See the attached diagram

ABC is a triangle, D, E are points on AB and BC.  DE is parallel to BC>

Also DBE has sides 1/3 times that of ABC

We have triangles ABC and DBE are similar with proportionality of sides as 1:3

Hence area of triangle DBE = 1/9 times area of ABC = 3 sq cm.

Area of trapezium ADEC = Area of triangle ABC - area of triangle DBE

=27-3 = 24 cm^2

Answer is 24 cm^2

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In△XYZ , XY¯¯¯¯¯¯=7in , YZ¯¯¯¯¯=5in , and XZ¯¯¯¯¯=4in . This triangle is reflected across the x-axis to result in △X'Y'Z' . Whic
ki77a [65]

Answer:

B

Step-by-step explanation:

Reflection is a transformation that preserves lengths.

Triangle XYZ, with side lengths XY = 7 in, YZ = 5 in, XZ = 4 in, is reflected across the x-axis to result in △X'Y'Z'.

This means that corresponding sides have the same lengths:

  • XY = X'Y' = 7 in;
  • XZ = X'Z' = 4 in;
  • YZ = Y'Z' = 5 in.

Find the perimeters of both triangles:

P_{XYZ}=XY+XZ+YZ=7+4+5=16\ in\\ \\P_{X'Y'Z'}=X'Y'+X'Z'+Y'Z'=7+4+5=16\ in

Hence, only option B is true.

8 0
3 years ago
Factoring Trinomials (<br> Factor each completely.<br> 1) 3p² – 2p - 5
Maurinko [17]
3p^2 - 2p - 5
3p^2 -5p+3p-5 (5 times 3 equals 15)
p(3p-5) +1(3p-5)
Answer:
(3p - 5)(p + 1)
8 0
3 years ago
Read 2 more answers
Which polygons are congruent?Select each correct answer. Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain o
Mashutka [201]

Answer:

Two trapezoids labeled V R A S and B U W D. Sides B U and V R contain one tick mark. Sides B D, U W, V S, and R A each contain two tick marks. Sides A S and W D each contain three tick marks. The angles represented by vertex letters U, B, R, and V each contain two tick marks. The angles represented by vertex letters D, W, S, and A each contain one tick mark.

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3 years ago
Alana ate breakfast at a restaurant. The bill came to $79.75. If she left 20% tip, how much was the tip?
Lana71 [14]
$79.75*0.2= 15.95
$79.75-15.95= $63.80
63.80+15.95= $79.75

Answer= $15.95
3 0
3 years ago
Find the x coordinate of the point.
Olegator [25]

Answer:

x= -17

Step-by-step explanation:

When we have 2 points, we can find the slope using

m = (y2-y1)/(x2-x1)

Substituting what we know

1/5 = (0-3)/(x--2)

1/5 = -3/(x+2)

Using cross products

1*(x+2) = 5*(-3)

x+2 = -15

Subtract 2 from each side

x+2-2 = -15-2

x=-17

3 0
3 years ago
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