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4 years ago

If the hypotenuse of a right triangle is 10 inches and the side opposite to aq equals 5 inches, what is the measurement of aq ?

Mathematics

1 answer:

amid [387]4 years ago

5 0

I hope this helps you

10^2=|aq|^2+5^2

100-25= |aq|^2

75= |aq|^2

aq= 5 square root of 3

this triangle 30-60-90

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What is the simplified form of 4r + 5s – 16r + 3s?

irakobra [83]

Hello!

You can only combine numbers with the same variable

4r - 16r = -12r
5s + 3s = 8s

The answer is -12r + 8s

Hope this helps!

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Carli has 42 tacos to put in 7 boxes. Each box has the same number of tacos. How many tacos are in each box?

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3 years ago

The graph of y=tan(x) is vertically stretched by a factor of 7, shifted a distance of 12 units to the left, reflected across the

Mekhanik [1.2K]

Step-by-step explanation:

A transformation(s) of a parent function is

$f(x) = a(bx - c) + d$

where a is vertical compression/stretched or reflection

B is horinzotnal compression/stretch or reflection

C is horinzontal translation

D is vertical translation.

The parent function is

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First, we stretched this by 7

so we have

$y = 7 \tan(x)$

We need to shift this 12 units to the left so we have

$y = 7 \tan(x + 12)$

We need to reflect this across x axis so we get

$y = - 7 \tan(x + 12)$

We need to shift this downwards 15 so we get

$y = - 7 \tan(x + 12) - 15$

or because tan is a odd function you could say

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3 years ago

Prove the divisibility of the following numbers:

Brut [27]

Answer:

Step-by-step explanation:

To prove divisibility, we need to factor the divident such that one of its factors matches the divisor.

(I use the notation x|y to denote that x divides y)

(A)

$75^{30}|45^{45}\cdot15^{15}\\45^{45}\cdot15^{15}=3^{45}\cdot 15^{45}\cdot 15^{15}=\\=3^{45}\cdot 15^{60}=3^{45}\cdot 15^{30}\cdot 15^{30}=3^{45}\cdot (3\cdot5)^{30}\cdot 15^{30}=\\=3^{45}\cdot 3^{30}\cdot(5\cdot 15)^{30}=3^{45}\cdot 3^{30}\cdot(75)^{30}\\\implies\\75^{30}|3^{45}\cdot 3^{30}\cdot75^{30}$

(B)

$72^{63}|24^{54}\cdot 54^{24}\cdot2^{10}\\24^{54}\cdot 54^{24}\cdot2^{10}=(2^{162}\cdot 3^{54})\cdot(2^{24}\cdot 3^{72}) \cdot 2^{10}\\=2^{196}\cdot 3^{126}$

In this case, it is easier to also factor the divisor to primes:

$72^{63}=2^{189}\cdot 3^{126}$

Both of these factor must be matched in the dividend in order to prove divisibility, and that indeed turns out to be true:

$2^{189}\cdot 3^{126}|2^{196}\cdot 3^{126}\implies\\2^{189}|2^{196}\,\,\mbox{and}\,\,3^{126}|3^{126}$

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3 years ago

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