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3 years ago

Which triangle must be a right triangle and why?

Mathematics

2 answers:

Lapatulllka [165]3 years ago

8 0

Of your answers, the first one is correct. There are two right triangles in the graph, ABC and A'B'C'. However, only A'B'C' is listed.

Ipatiy [6.2K]3 years ago

4 0

Answer:

Option 4 is correct: ΔBGC is right angle because line EG ⊥ line segment CC'.

Step-by-step explanation:

Right Angled triangle is triangle with measure of one angle 90°.

Option A:

ΔA'B'C' is not right traingle because no angle if of 90° and image has no role in it. It only work if ΔABC is also a right angle traingle but it is not.

Option B:

Intersection of line/line segment has no role in right triangle if it does not intersect at right angle. ∴ ΔADC is not right angled triangle.

Option C:

ΔBCC' is not right angled triangle because thee is not right angle and point B lies on line of reflection has no role in it.

Option D:

ΔBGC is right angle triangle because m∠BGC = 90°.

m∠BGC = 90° as line EG is perpendicular to CC' at G.

Option D is correct.

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The length of a rectangle is eight more than twice its width. The perimeter is 96 feet. Find the dimensions of the rectangle

Debora [2.8K]

Answer:

The width of the rectangle is 14'8", and the length is 33'4"

Step-by-step explanation:

We're given two pieces of information:

The length is eight more than twice the width:

$l = 2w + 4$

The perimeter is 96 feet:

$p = 96$

We also need to apply one more piece of information that is not provided here, and that is the relationship between the perimeter of a rectangle, and it's length and width:

$p = 2l + 2w$

We can solve for w by plugging the other two values into the last:

$p = 2w + 2l\\96 = 2w + 2(2w + 4)\\96 = 2w + 4w + 8\\88 = 6w\\3w = 44\\w = \frac{44}{3}\\w = 14\frac{2}{3}$

Now we can find the length by plugging w into the first equation:

$l = 2w + 4\\l = 2(14\frac{2}{3}) + 4\\l = 29\frac{1}{3} + 4\\l = 33\frac{1}{3}$

One third of a foot is four inches, so the width is 14'8" and the length is 33'4"

To make sure our answer is correct, we should plug those numbers back into the area equation and see if we're right:

$p = 2l + 2w\\p = 2(33\frac{1}{3}) + 2(14\frac{2}{3})\\p = 66\frac{2}{3} + 29\frac{1}{3}\\p = 96$

So we know our answer's correct

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3 years ago

Can someone like do my homeowkr for me? im lazy and it was due yesterday

sweet [91]

Answer:

you can just look it up

Step-by-step explanation:

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3 years ago

what the equation is to this word problem. Famous Chef Fanzo puts 2 ostrich eggs and 14 duck eggs into his famous scramble. One

Svetach [21]

We are given with the combination ratio of ostrich eggs and duck eggs to produce a scramble and equivalently another ratio to make one. In this case, the algebraic expression would be:

2 + 14 x = 5
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The ratio thus of duck egg to ostrich egg is 3 duck eggs/14 ostrich eggs
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3 years ago

Find two consecutive positive integers such that the square of the first decreased by 17 equals 4 times the second.

Zina [86]

Answer:

The two consecutive positive integers are 7 and 8

Step-by-step explanation:

Let

x ----> the first positive integer

x+1 ----> the second consecutive positive integer

we know that

$x^{2} -17=4(x+1)$

Solve for x

$x^{2} -17=4x+4\\ \\x^{2}-4x-21=0$

Solve the quadratic equation by graphing

The solution is x=7

see the attached figure

Find the value of x+1

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therefore

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