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Rudiy27
3 years ago
14

Find the equation of the straight line through (–2, 3) perpendicular to 2x + y =8

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
8 0

Answer:

y = \dfrac{1}{2}x + 4

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

We need to find the slope, m, and the y-intercept, b.

The line we need is perpendicular to the line 2x + y = 8.

<em>The slopes of perpendicular lines are negative reciprocals.</em>

We solve the given equation for y to find the slope of the given line.

2x + y = 8

y = -2x + 8

The given line has slope -2.

The negative reciprocal of -2 is 1/2.

Our line has slope, m = 1/2.

Now we have

y = 1/2 x + b

Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.

y = 1/2 x + b

3 = 1/2 * (-2) + b

3 = -1 + b

4 = b

b = 4

Now we have

y = 1/2 x + 4

Answer: y = \dfrac{1}{2}x + 4

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There is a 30 percent chance that A can fix her busted computer. If A cannot, then there is a 40 percent chance that her friend
Solnce55 [7]

Answer:

(a) 0.70

(b) 0.40

Step-by-step explanation:

Mutually-exclusive events are those events which cannot occur together.

Consider that events X and Y are mutually exclusive.

P (X and Y) = 0

Here the two events can be defined as follows:

A = A can fix the busted computer

B = B can fix the busted computer

The information provided are as follows:

P (A) = 0.30

P (B) = 0.40

If A cannot, then there is a chance that her friend B can fix it.

The above statement suggest that the events A and B are mutually exclusive, i.e. if A can fix the computer then B does not have to and if cannot then only B will fix it.

That is, P (A and B) = 0.

(a)

Compute the probability it will be fixed by either A or B as follows:

P (A or B) = P (A) + P (B) - P (A and B)

                = 0.30 + 0.40 - 0

                = 0.70

Thus, the probability it will be fixed by either A or B is 0.70.

(b)

Compute the probability that if it is fixed it will be fixed by B as follows:

P (not A and B) = P (B) - P (A and B)

                         = 0.40 - 0

                         = 0.40

Thus, the probability that if it is fixed it will be fixed by B is 0.40.

8 0
3 years ago
Two cylinders are shown below. Find the volume of each cylinder. Use 3.14 for π. Round your answers to the nearest hundredth. a.
Katena32 [7]

Answer:

3-8I am right or wrong and the answer is 5

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3 years ago
If a polynomial is divided by a binomial and the remainder is zero, what does that tell you about the relationship between the b
OleMash [197]

Answer:

Step-by-step explanation:

The binomial is a factor of the polynomial.

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Graph the function y = x3 + 6x2 + 2x – 11. Based on the graph, what is the largest possible x-value if y = 0?
professor190 [17]

Answer:

Step-by-step explanation:

The graph is done using Desmos. Just by substitution x = 1 will force the graph to go to y = 0, but graphs are not always that good. This one gets 1.111

to get y = 0. I'd use 1 if you had to answer it and a computer will mark it.

5 0
3 years ago
Read 2 more answers
Thirty elves would like to build a skating ring so they can all use it at the same time. Santa tells them, they need at least 40
Delicious77 [7]

Answer:

The Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Step-by-step explanation:

Given:

Number of skaters = 30

Area for each skater = 40 sq ft

We need to find the dimension of rectangular ring the are going to build.

Now we know that they building the skating ring such that they all can use at same time.

Hence if the all use at same time then we will find the total area first.

Total area can be calculated by multiplying Number of skaters with area required for each skaters.

Framing the equation we get;

Total area = 30\times 40 = 1200 \ ft^2

Hence The total area of the rectangular ring would be 1200 sq. ft.

Now we know that Total area is equal to product of length and width.

length\times width =1200ft^2

1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30

Hence the Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

3 0
2 years ago
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