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garri49 [273]
3 years ago
11

Which theorem or postulate proves that ABC and DEF are similar?

Mathematics
1 answer:
Mrrafil [7]3 years ago
5 0
<h3>Answer: SSS similarity (choice A)</h3>

The SSS stands for "side side side", so saying "SSS similarity" means the three corresponding sides are in the same proportion as each other.

Divide each side of DEF by its corresponding side of ABC

DE/AB = 18/3 = 6

EF/BC = 42/7 = 6

FD/CA = 36/6 = 6

We get 6 each time we divide, so the scale factor is 6. Each side of DEF is 6 times longer compared to its corresponding counterpart back in ABC.

Side note: the area of triangle DEF is 36 times larger since 6^2 = 36.

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An explosion causes debris to rise vertically with an initial speed of 120 feet per second. The formula h equals negative 16 t s
Novay_Z [31]

Answer:

The debris will be at a height of 56 ft when time is <u>0.5 s and 7 s.</u>

Step-by-step explanation:

Given:

Initial speed of debris is, s=120\ ft/s

The height 'h' of the debris above the ground is given as:

h(t)=-16t^2+120t

As per question, h(t)=56\ ft. Therefore,

56=-16t^2+120t

Rewriting the above equation into a standard quadratic equation and solving for 't', we get:

-16t^2+120t-56=0\\\textrm{Dividing by -8 throughout, we get}\\\frac{-16}{-8}t^2+\frac{120}{-8}t-\frac{56}{-8}=0\\2t^2-15t+7=0

Using quadratic formula to solve for 't', we get:

t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\t=\frac{-(-15)\pm \sqrt{(-15)^2-4(2)(7)}}{2(2)}\\\\t=\frac{15\pm \sqrt{225-56}}{4}\\\\t=\frac{15\pm\sqrt{169}}{4}\\\\t=\frac{15\pm 13}{4}\\\\t=\frac{15-13}{4}\ or\ t=\frac{15+13}{4}\\\\t=\frac{2}{4}\ or\ t=\frac{28}{4}\\\\t=0.5\ s\ or\ t=7\ s

Therefore, the debris will reach a height of 56 ft twice.

When time t=0.5\ s during the upward journey, the debris is at height of 56 ft.

Again after reaching maximum height, the debris falls back and at t=7\ s, the height is 56 ft.

5 0
3 years ago
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olga55 [171]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

120 are the residents per year and the 3 represents the years so when you multiply them it would make how many residents that left Planet X in 3 years.

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The correct answer is C
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Answer:

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Step-by-step explanation:

I'm a smart man I would know trust me

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