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3 years ago

Answers for both boxes please

Mathematics

1 answer:

andre [41]3 years ago

6 0

Step-by-step explanation:

4x + y = 6 => 8x + 2y = 12.

8x + 2y = 12

+ (-5x - 2y = -3)

=> 3x = 9, x = 3.

Therefore 4(3) + y = 6, 12 + y = 6, y = -6.

The solutions are x = 3 and y = -6.

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Write an equation in point-slope form and slope- intercept form for the line.

MAXImum [283]

Answer:

Step-by-step explanation:

8 0

3 years ago

in a certain game, a fair die is rolled and a player gains 20 points if the die shows a 6. if the die does not show a 6, the pla

BaLLatris [955]

The expected gain or loss is an illustration of mean and expected values.

The expected total gain is 83 points

The given parameters are:

Addition of 20 points for rolling a 6
Removal of 3 points for not rolling a 6

The probability of rolling a 6 in a fair die is 1/6.

The probability of not rolling a 6 in a fair die is 5/6.

So, the expected gain in each game is:

$\mathbf{E(x) = 20 \times \frac 16 - 3 \times \frac 56}$

$\mathbf{E(x) = \frac{20}6 - \frac{15}6}$

Take LCM

$\mathbf{E(x) = \frac{5}6}$

$\mathbf{E(x) = 0.83}$

The number of games is 100.

So, the expected gain is:

$\mathbf{Gain = 100 \times 0.83}$

$\mathbf{Gain = 83}$

Hence, the expected total gain is 83 points

Read more about expected value at:

brainly.com/question/13499496

5 0

3 years ago

Find the measure of the angle indicated. ? 82 A) 77° C) 82 B) 75 D) 127°

Naddik [55]

Answer:

c) 82

Step-by-step explanation:

It's 82 degrees because of the opposite interior angle theorem, which means that those two angles are the same, as well as any pair of opposite interior angles.

8 0

3 years ago

If f(x)=2x-5, find a. f(4) b. f(-3)

Vladimir [108]

Replace x in the given equation with each value:

a. f(4) = 2(4) -5

= 8-5

b. (f-3) = 2(-3) - 5

= -6 -5

= -11

8 0

3 years ago

a 16 inch wire is to be cut. one piece is to be bent into the shape of a square, whereas the other piece is to be bent into the

Lyrx [107]

1. Let x be a length of square side, then the square perimeter is 4x (you need to cut 4x from 16 in. to make a square with side x in.). Then 16-4x is remained length of wire and you have to make form this piece a rectangle with sides one of which is twice bigger than another. If y is length of the smaller side, then 2y is length of the bigger side and rectangle perimeter is y+2y+y+2y=6y. You have 16-4x in. of wire left, so 6y=16-4x and $y= \frac{16-4x}{6}$ .

2.
$A_{square}=x^2 \\ A_{rectangle}=y\cdot 2y=\frac{16-4x}{6}\cdot2\cdot\frac{16-4x}{6}= \frac{(16-4x)^2}{18} \\ A(x)=A_{square}+A_{rectangle}=x^2+\frac{(16-4x)^2}{18}$ .

3. Find the derivative of the function A(x):
$A'(x)=2x+ \dfrac{2(16-4x)\cdot(-4)}{18} =2x- \dfrac{4(16-4x )}{9}$ .

4. Solve the equation A'(x)=0:
$2x- \dfrac{4(16-4x )}{9}=0 \\ 18x-64+16x=0 \\ 34x=64 \\ x= \frac{32}{17}$

5. Since $y= \frac{16-4x}{6}$ you have

$y= \dfrac{16-4 \frac{32}{17} }{6} = \dfrac{16\cdot17-4\cdot32}{6\cdot 17} = \dfrac{24}{17}$ .

Answer: the width of the rectangle is $\frac{24}{17}$

6 0

3 years ago

Answers for both boxes please ​

Answers for both boxes please