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AveGali [126]
3 years ago
7

If a b and c satisfy the equation a^2+b^2=c^2, are 2a, 2b, and 2c also possible side lengths of a right triangle? How do you kno

w?
Mathematics
1 answer:
Jlenok [28]3 years ago
8 0

a²+b² = c²

Well we know that a 3-4-5 triangle follows this rule, if a=3, b=4, c=5.

3² + 4² = 5²        ⇒     9 + 16 = 25      ⇒      25 = 25

Now let's multiply all the sides by 2.

(3*2)² + (4*2)² = (5*2)²    

    6²  +   8²    =   10²

        36 + 64  =  100

                100 = 100

Therefore, 2a, 2b, and 2c are also possible length of a right triangle.

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The Marketing Department is deciding which classes to offer over the summer. The classes under consideration are:
svetlana [45]

Answer:

48

Step-by-step explanation:6x8=48

7 0
3 years ago
-x=-y+2 and 3y+4=2x solve using matrices
MissTica

\begin{cases}-x=-y+2\\3y+4=2x\end{cases}\implies\begin{cases}x-y=-2\\2x-3y=4\end{cases}

In matrix form, this is

\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-2\\4\end{bmatrix}

The coefficient matrix has determinant

\begin{vmatrix}1&-1\\2&-3\end{vmatrix}=-3+2=-1\neq0

so it has an inverse, which is

\begin{bmatrix}1&-1\\2&-3\end{bmatrix}^{-1}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}

Multiply both sides by the inverse matrix:

\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}1&-1\\2&-3\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}3&-1\\2&-1\end{bmatrix}\begin{bmatrix}-2\\4\end{bmatrix}

\implies\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-10\\-8\end{bmatrix}

so that x=-10 and y=-8.

8 0
3 years ago
Someone please helpp
umka2103 [35]

Answer:

The two equations are similar because they both end up with the same common value. 0=0 The work you need to show that this is correct will be shown below.

Step-by-step explanation:

2(5m−4)−3(m−5)2=−3m2+40m−83

Add 3m^2 to both sides.

−3m2+40m−83+3m2=−3m2+40m−83+3m2

40m−83=40m−83

Subtract 40m from both sides.

40m−83−40m=40m−83−40m

−83=−83

−83+83=−83+83

0=0

If you have any questions regarding my answer please tell me in the comments, I will come and answer them. Have a good day.

6 0
3 years ago
Divide 1.20m in the ratio 2:3:4 what's the answer
Vikki [24]
2 :3 :4 gives 9 shares  (2 + 3 + 4)

9 shares = 120cm
1 share = 120/9 cm = 13 1/3 cm  ( or 13.333)

2 shares = 26 2/3 cm
3 shares = 40 cm
4 shares = 53 1/3 cm
3 0
3 years ago
A right triangle has a leg of 11 cm and a hypotenuse of 17 cm.
nordsb [41]
A^2 + b^2 = c^2
11^2 + b^2 = 17^2
121 + b^2 = 289
b^2 = 289-121= 168
b = 13.0 cm
3 0
3 years ago
Read 2 more answers
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