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arlik [135]
2 years ago
10

Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AC = 5x - 9, what is x? Round to the nearest tenth.

(1 point)
09.0
9.4
10.0
6.4
Mathematics
1 answer:
Aloiza [94]2 years ago
5 0

Similar shapes may or may not be congruent.

The value of x is (a) 9.0

The corresponding sides are:

  • AB and DE
  • BC and EF
  • AC and DF

The side lengths are:

\mathbf{DE = 41}

\mathbf{EF = 23}

\mathbf{DF = 36}

\mathbf{AC = 5x - 9}

Because the shapes are congruent, and AC corresponds to DF.

This means that:

\mathbf{AC = DF}

So, we have:

\mathbf{5x - 9 = 36}

Collect like terms

\mathbf{5x = 9 + 36}

\mathbf{5x = 45}

Divide both sides by 5

\mathbf{x = 9.0}

<em>Hence, the correct option is (a) 9.0</em>

Read more about congruent triangles at:

brainly.com/question/12413243

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What percent of 143 is 95.1?
Aloiza [94]

Answer:

66.5%

Step-by-step explanation:

95.1/143*100=66.5%

4 0
2 years ago
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15x^2 + 41x + 28 <br><br>STEP BY STEP ANSWER PLSSS​
maria [59]

Answer:

(3x+4)(5x+7)

Step-by-step explanation:

15x^2 +41x+28

Factor the expression by grouping. First, the expression needs to be rewritten as 15x^2 +ax+bx+28. To find a and b, set up a system to be solved.

a+b=41

ab=15×28=420

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 420.

1,420

2,210

3,140

4,105

5,84

6,70

7,60

10,42

12,35

14,30

15,28

20,21

Calculate the sum for each pair.

1+420=421

2+210=212

3+140=143

4+105=109

5+84=89

6+70=76

7+60=67

10+42=52

12+35=47

14+30=44

15+28=43

20+21=41

The solution is the pair that gives sum 41.

a=20

b=21

Rewrite 15x^2 +41x+28 as (15x^2 +20x)+(21x+28).

(15x^2 +20x)+(21x+28)

Factor out 5x in the first and 7 in the second group.

5x(3x+4)+7(3x+4)

Factor out common term 3x+4 by using distributive property.

(3x+4)(5x+7)

7 0
3 years ago
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The area of a rectangular concrete patio is 70 square meters. the perimeter is 34 meters. what are the dimensions of the patio?
Finger [1]
A = L * W
A = 70

70 = L * W

P = 2(L + W)
P = 34

34 = 2(L + W)
34/2 = L + W
17 = L + W
17 - W = L

70 = L * W
L = 17 - W

70 = W(17 - W)
70 = -W^2 + 17W
W^2 - 17W + 70 = 0
(W - 10)(W - 7) = 0

W - 10 = 0        L = 17 - 10
W = 10              L = 7

W - 7 = 0          L = 17 - 7
W = 7               L = 10

so either the width is 10 meters and the length is 7 meters OR the width is 7 meters and the length is 10 meters




5 0
3 years ago
The _____ justifies the conclusion that ∆ABD ≅ ∆AEC.
elena55 [62]
It is the AAS Postulate.

Explanation: You’re given two right angles (because perpendicular sides make right angles).

This also means that the angle next to them are also right angles, because they are linear pairs (180-90=90)

The right angles are:
This is your first A.

Both triangles also share a similar angle:
This is your second A.

You’re given side BD is congruent to EC.

This is your S.

It’s AAS and not ASA because the order refers to how they are connected: they are congruent in the order that the first set of congruent angles connect to the next, then to the congruent side.
3 0
3 years ago
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