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3 years ago

Find the equation of the line through (-7, -2) that is perpendicular to the line y = x/3+6.

Mathematics

1 answer:

azamat3 years ago

6 0

Answer:

y = −3x − 23

Step-by-step explanation:

The equation of the line in the slope-intercept form is y= x/3 + 6.

The slope of the perpendicular line is negative inverse: m = −3.

So, the equation of the perpendicular line is y = −3x + a.

To find a, we use the fact that the line should pass through the given point:

−2 = (−3) ⋅ (−7) + a.

Thus, a = −23.

Therefore, the equation of the line is y = −3x − 23.

Answer: y =−3x − 23

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3 years ago

On a fraction line 6 friends want to equally share 3 yards of yarn how much yarn does each friend get

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Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t

LiRa [457]

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

$(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

$(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6) $=\dfrac{20}{36}$

The probability distribution of this event is given as follows.

$\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|$

First, we determine the expected Value of this event.

Expected Value

$=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67$

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning $=\dfrac{20}{36}$

If the game is played 100 times

Number of times expected to win

$=\dfrac{20}{36} \times 100\\=56$ times$

Therefore, number of times expected to loose

= 100-56

=44 times

8 0

3 years ago

A square is folded into half to form a rectangle. the perimeter of the rectangle is 36cm. calculate the area of a square

zhannawk [14.2K]

Answer:

Let the measure of each side of the square be " x " cm.

then ,

area of square = x²

After we folded the square into a rectangle ,

length of rectangle = x

breadth of rectangle = x/2

perimeter of rectangle = 36 cm

$x + \frac{x}{2} + x + \frac{x}{2} = 36 \\ \\ \frac{2x + x + 2x + x}{2} = 36 \\ \\ \frac{6x}{2} = 36 \\ \\ 6x = 36 \times 2 \\ \\ 6x = 72 \\ \\ 6x = \cancel{\frac{72}{6} } = 12cm$

hence ,

side of square = 12 cm

therefore ,

area of square = 12 × 12 = 144 cm²

hope helpful~

8 0

3 years ago