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3 years ago

What is the equation of the line that is perpendicular to y = -2/3x + 4 and that passes through (–2,–2)?

Mathematics

1 answer:

Rama09 [41]3 years ago

6 0

Answer: y = 3/2x + 1

Step-by-step explanation: For a perpendicular line, take the reciprocal of "m" and reverse the sign.

- 2/3 becomes +3/2

Then substitute the y and x values of the given coordinate into the equation and solve for "b"

y = mx + b

-2 = 3/2(-2) + b

-2 = -3 + b

-2 +3 = b

+1 = b Substitute for b in y = (3/2)x + 1

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When (3,-2) is reflected across the x-axis the resulting image point is:

tankabanditka [31]

Step-by-step explanation:

Reflection across the x-axis:

(x,y) -> (x,-y)

In other words, you want to <u>change the sign of the y</u>.

(3,-2) -> (3,2)

4 0

3 years ago

Miguel's teacher instructed him to graph the linear equation y = (3/5)x + 1. He

gladu [14]

I think it is C.) (3,6)

5 0

3 years ago

Find an equation in standard form for the hyperbola with vertices at (0, ±9) and foci at (0, ±11)

Katen [24]

Answer:

$\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1$ is standard equation of hyperbola with vertices at (0, ±9) and foci at (0, ±11).

Step-by-step explanation:

We have given the vertices at (0, ±9) and foci at (0, ±11).

Let (0,±a) = (0,±9) and (0,±c) = (0,±11)

The standard equation of parabola is:

$\frac{y^{2} }{a^{2} } -\frac{x^{2} }{b^{2} }=1$

From statement, a = 9

c² = a²+b²

(11)² = (9)²+b²

121-81 = b²

40 = b²

Putting the value of a² and b² in standard equation of parabola, we have

$\frac{y^{2} }{81} -\frac{x^{2} }{40} }=1$ which is the answer.

3 0

3 years ago

Lucy rolls 2 fair dice and adds the results from each.

Daniel [21]

Answer:

Answer:

The probability of obtaining the sum of 10 is 1/12 or 0.0833

Step-by-step explanation:

Given

2 fair dice

Required

Probability of obtaining the sum of 10

To solve this, we have to list out the sample space.

Sample space is the total possible sum that can be obtained when she rolls the dice.

Let the first die be represented with S1 and the second be represented with S2.

S1 = {1,2,3,4,5,6}

S2 = {1,2,3,4,5,6}

To get the sample space, we have to add individual elements of S1 and S2.

This is done as follows.

When S1 = 1 and S2 = {1,2,3,4,5,6}

Sum = 1+1, 1+2, 1+3, 1+4, 1+5, 1+6

Sum = 2, 3, 4, 5, 6, 7

When S1 = 2 and S2 = {1,2,3,4,5,6}

Sum = 2+1, 2+2, 2+3, 2+4, 2+5, 2+6

Sum = 3,4,5,6,7,8

Using the same pattern as used above

When S1 = 3 and S2 = {1,2,3,4,5,6}

Sum = 4,5,6,7,8,9

When S1 = 4 and S2 = {1,2,3,4,5,6}

Sum = 5,6,7,8,9,10

When S1 = 5 and S2 = {1,2,3,4,5,6}

Sum = 6,7,8,9,10,11

When S1 = 6 and S2 = {1,2,3,4,5,6}

Sum = 7,8,9,10,11,12

Writing out the Sum, will give us the sample space.

Sample Space = {2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12}

The sample space has a total of 36 elements

To calculate the probability of obtaining the sum of 10,

We have to count the number of 10's in the sample space

Number of 10 = 3

Probability = Number of 10 / Number of Sample Space

Probability = 3 / 36

Probability = 1/12

Probability = 0.0833

Hence, the probability of obtaining the sum of 10 is 1/12 or 0.0833

5 0

3 years ago

Carol went on a holiday to Bristol.

Leviafan [203]

Answer:

658.91$

Step-by-step explanation:

Find the total cost

flight cost 397$

staying at the hotel for 6 night cost 6 x 28.43£

= 170.58£ = 233.69$

breakfast for 4 morning cost 4 x 5.15£= 20.6£

= 28.22$

Total cost is 397$+233.69$+28.22=658.91$

5 0

2 years ago