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jolli1 [7]
3 years ago
8

Which two angles are congruent

Mathematics
1 answer:
Anna35 [415]3 years ago
5 0
Angles FED and angle JKL
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The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its
Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

b = 3 + 2h

Area = 22

Required

Find the length of the base

The area of a triangle is calculated as thus;

Area = \frac{1}{2} * b * h

Substitute 22 for Area and 3 + 2h for b

The formula becomes

22 = \frac{1}{2} * (3 + 2h) * h

Multiply both sides by 2

2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h

44 = (3 + 2h) * h

Open the bracket

44 = 3 * h + 2h * h

44 = 3h + 2h^2

Subtract 44 from both sides

44 - 44 = 3h + 2h^2 - 44

0 = 3h + 2h^2 - 44

Rearrange

0 = 2h^2 +3h - 44

2h^2 +3h - 44 = 0

At this point, we have a quadratic equation; which is solved as follows:

2h^2 +3h - 44 = 0

2h^2 + 11h - 8h - 44 = 0

h(2h + 11) - 4(2h + 11) = 0

(h - 4)(2h + 11) = 0

Split the above

(h - 4) = 0\ or\ (2h + 11) = 0

h - 4 = 0\ or\ 2h + 11 = 0

Solve the above linear equations separately

h - 4 = 0

Add 4 to both sides

h - 4 + 4 = 0 + 4

h = 0 + 4

h = 4 ---- <em>First value of h</em>

2h + 11 = 0

Subtract 11 from both sides

2h + 11 - 11 = 0 - 11

2h  = 0 - 11

2h = -11

Divide both sides by 2

\frac{2h}{2} = -\frac{11}{2}

h = -\frac{11}{2}<em> ------ Second value of h</em>

Since height can be negative, we'll discard h = -\frac{11}{2}

Hence, the usable value of height is h = 4

Recall that b = 3 + 2h

Substitute 4 for h

b = 3 + 2(4)

b = 3 + 8

b = 11

Hence, the length of the base is 11 meters

3 0
3 years ago
moby sold half his toy car collection, and then bought 12 more cars the next day. he now has 48 toy cars . how many cars did he
Zinaida [17]

Answer:

18

Step-by-step explanation:

48-12 = 36

36/2

18

5 0
3 years ago
20 POINTS !!!!!!
Bas_tet [7]
I think the question is asking for the cost (C) when we already know that the sell price (S) is $24
So C+M=S
C+0.45C=24
1.45C=24
C=16.5516
And the answer is $16 and 55 cents
6 0
3 years ago
(x^2+y)(x^4y^3)/xy^2
r-ruslan [8.4K]

Answer:

(x^2+y)x^3 y^5

Step-by-step explanation:

(x^2 + y)x^4 y^3 / x y^2

(x^2 + y)x^4 - 1 y^3 * y^2

(x^2 + 7)x^3 y^3 * y^2

(x^2 + y)x^3 y^3 +^2

(x^2 + y)x^3 y^5

6 0
3 years ago
Can some help with this ​
igomit [66]

Answer:

36

Step-by-step explanation:

multiply the width & the height

3 0
3 years ago
Read 2 more answers
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