How do you find the remaining side of a 45°-45°-90° triangle if the longest side is 28?

Help please. this doesn't make sense

saveliy_v [14]

Answer:

a = 39.2650873379cm

b = 11.5529459767cm

Step-by-step explanation:

a - Use the area of a triangle equation - 1/2 * a * b * Sin(C)

1/2 * 8 * 10 * Sin(79) = 39.2650873379cm

b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)

64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398

c = square root of 6.9396506484 = 11.5529459767cm

Put to however many significant figures / decimal places required.

:)

5 0

2 years ago

an aquarium tank is 3 feet long, 1 foot wide, and 2 feet high. how many gallons of water would it take to fill the tank two-thir

emmainna [20.7K]

Answer: the answer is 6ft

Step-by-step explanation:

3 times 1 times 2 = 6ft

7 0

3 years ago

Write an equation in slope intercept form for the line that goes through the point (-2,-5) and (3,5)

Orlov [11]

Answer:

Slope intercept form is y=mx+b

Let’s first find the slope, which is y2-y1/x2-x1

Let’s make the point (-2,-5) our x1 and y1 and let’s make the point (3,5) our x2 and y2.

5+5/3+2

10/5

2 = slope

So far, our equation is looking like this:

y=2x + b

To find the y-intercept (b), let’s plug in one of the points.

Let’s use the point (3,5)

(5)=2(3) + b

5=6 + b

What adds to 6 to equal 5? -1

So, our y-intercept is going to be -1

Finally, our equation is going to look like this:

y=2x-1

Hope I helped!

5 0

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:

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

6 0

3 years ago

Show the ratios are equivalent by simplifying any 4 of them.

aliya0001 [1]

When simplified all of them equal 3/1. They are asking you to just chose 4 of them. Hope that helps!

4 0

4 years ago