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polet [3.4K]
3 years ago
10

Find the length of side AB in the right triangle shown.

Mathematics
1 answer:
Bogdan [553]3 years ago
5 0
Side AB is 72 cm long.



Explanation:

To find the length of side AB you have to use this formula:

{a}^{2}  +  {b}^{2}  =  {c}^{2}

*Remember there are two legs (a and b) and a hypotenuse (c) on a triangle. The longest side will be the hypotenuse and the other two will be the legs. For this triangle the hypotenuse is side BC while the legs are sides CA and side AB.

Plug in the numbers into the equation.


{65}^{2}  +  {b}^{2}  =  {97}^{2}
For this triangle, you were given the hypotenuse (c) and one leg (a). To find the last length solve the equation and balance it so only b is left, like this:

4225 +  {b}^{2}  = 9409

9409 - 4225 = 5184

Soo...

{b}^{2}  = 5184

Then to get the side length, square root 5184.

\sqrt{5184}  = 72

So the length of the last side is 72 cm.
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Suppose that 18 inches of wire costs 72 cents.
NeX [460]

Answer:

41 inches of wire will cost 164 cents.

Step-by-step explanation:

1st Method

Use proportions!

18/ 72 = 41/ c

Cross multiply

18 * c = 72 * 41

18c = 2952 divide both sides by 18

<em>c = 164</em>

2nd Method.

Find the rate of the costs. r = rate

18*r = 72

r = 4 cents/inch

Now that you've found the rate you can multiply it by 41 inches to find the cents the wire costs!

41 inch * r (cents/inch)          inches cancels out.

41 * 4 = 164

<em>164 cents</em>

7 0
2 years ago
Find d for the arithmetic series with S17=-170 and a1=2
Irina18 [472]
So, we know the sum of the first 17 terms is -170, thus S₁₇ = -170, and we also know the first term is 2, well

\bf \textit{ sum of a finite arithmetic sequence}\\\\&#10;S_n=\cfrac{n(a_1+a_n)}{2}\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;----------\\&#10;n=17\\&#10;S_{17}=-170\\&#10;a_1=2&#10;\end{cases}&#10;\\\\\\&#10;-170=\cfrac{17(2+a_{17})}{2}\implies \cfrac{-170}{17}=\cfrac{(2+a_{17})}{2}&#10;\\\\\\&#10;-10=\cfrac{(2+a_{17})}{2}\implies -20=2+a_{17}\implies -22=a_{17}

well, since the 17th term is that much, let's check what "d" is then anyway,

\bf n^{th}\textit{ term of an arithmetic sequence}\\\\&#10;a_n=a_1+(n-1)d\qquad &#10;\begin{cases}&#10;n=n^{th}\ term\\&#10;a_1=\textit{first term's value}\\&#10;d=\textit{common difference}\\&#10;----------\\&#10;n=17\\&#10;a_{17}=-22\\&#10;a_1=2&#10;\end{cases}&#10;\\\\\\&#10;-22=2+(17-1)d\implies -22=2+16d\implies -24=16d&#10;\\\\\\&#10;\cfrac{-24}{16}=d\implies -\cfrac{3}{2}=d
6 0
3 years ago
What’s the equation when the line is (6,5) and slope is 2/3
Vsevolod [243]

Answer:

y=2/3x+1

Step-by-step explanation:

using the slope intercept formula, y=mx+b, where m is the slope, and b is the y intercept. So we get the equation y=2/3x+b, because the slope is given, then you use the given point and substitute it into the equation, 5=2/3(6)+b which you can solve and you will get 5=4+b, b =1, then you add 1 to your original equation to get your answer, y=2/3x+1

4 0
3 years ago
An account earns simple interest.<br> $1675 at 4.6% for 4 years
Paul [167]

Answer:

$308.20

Step-by-step explanation:

The simple interest formula i = p·r·t applies here:

($1675)(0.046)(4) = $308.20

5 0
3 years ago
A container can hold five orange slices.If a company has 737 orange slices to put in containers how many more slices would they
Phantasy [73]
Answer:2
You need 2 more orange slices to fill up the last container.
5 0
3 years ago
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