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3 years ago

Find the values of x and y.

Mathematics

1 answer:

vova2212 [387]3 years ago

4 0

Look at the picture.

We have the equation (1) 12x + 4y = 40.

We know, the sum of the acute angles in a right triangle is 90°.

Therefore we have the equation (2) (12x + 4y) + (17x - y) = 90

Substitute (1) to (2):

40 + 17x - y = 90 <em>subtract 40 from both sides</em>

17x - y = 50 (3)

We have the system of equations:

$\left\{\begin{array}{ccc}12x + 4y = 40&|:4\\17x-y=50\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x + y = 10\\17x-y=50\end{array}\right}\ \text{add both side of equations}\\.\qquad20x=60\qquad|:20\\.\qquad x=3$

Substitute the value of x to (3)

$17(3)-y=50\\51-y=50\qquad|-51\\-y=-1\to y=1$

Answer: x = 3 and y = 1.

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Let g be the function given by g(x)=x^2*e^(kx) , where k is a constant. For what value of k does g have a critical point at x=2/

ArbitrLikvidat [17]

G `( x ) = $2x * e^{kx} + k x^{2} *e^{kx} = \\ = xe^{kx}(2 + kx )$
2 + k x = 0
k x = -2
k = -2: x = - 2 : 2/3 = - 2 * 3/2
k = - 3
Answer: for k= - 3, the function g ( x ) have a critical point at x = 2/3.

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3 years ago

Rationalize the expression. Write it in simplest form.<br><br> 9x/√-2x-11

GenaCL600 [577]

This appears to be just an expression we are simplifying, not an equation we are solving. I THINK you are saying that the expression looks like this:
$\frac{9x}{ \sqrt{-2x-11} }$
If you rationalize the denominator, you would get this expression:
$\frac{9x}{ \sqrt{-2x-11} } * \frac{ \sqrt{-2x-11} }{ \sqrt{-2x-11} }$
which, after simplifying, looks like this:
$\frac{9x \sqrt{-2x-11} }{-2x-11}$
and that's as simple as I can see that one getting. You can't factor anything out of the denominator to cancel with the numerator, so I think you're as simple as you can get there!

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3 years ago

Jennifer scores a 77 on her algebra 2 test. The mean on the test was 73. The standard deviation on the test was 5. What was her

MA_775_DIABLO [31]

Answer:

0.80

Step-by-step explanation:

The z-score is found from the formula ...

Z = (X -μ)/σ

Z = (77 -73)/5 = 4/5 = 0.80

Jennifer's Z-score was 0.80.

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NNADVOKAT [17]

The second one should be correct

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vladimir2022 [97]

If you are looking for the square root, which I’m assuming. It’s 4 square root of 17, or 16.492

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