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3 years ago

8

Which two angles are congruent

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