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Bond [772]
3 years ago
6

A pair of perpendicular lines intersect at the point (5,9). Write

Mathematics
1 answer:
maw [93]3 years ago
6 0

Answer:

The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18

Step-by-step explanation:

The coordinates of the point of intersection of the two lines = (5, 9)

The coordinates of a point on one of the two lines, line 1 = (-4, 4)

The slope of a line perpendicular to another line with slope, m = -1/m

Therefore, we have;

The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9

Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5

The equation of the line 2 is given as follows;

y - 9 = -9/5×(x - 5)

y - 9 = -9·x/5 + 9

y =  -9·x/5 + 9 + 9

y = -9·x/5 + 18

Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.

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Answer:18

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3 years ago
Makayla is reading a 400 page book for her book club.she reads 32 pages each hour
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Answer:

12.5 hours

Step-by-step explanation:

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A circle with a radius of 5 sits in a 11 X 11 rectangle. What is the area of the shaded region?
Nataly_w [17]
Hi :) I'm guessing the shaded region is the region inside the rectangle but outside the circle.

To solve this problem, you need to find the area of the rectangle and area of the circle. Then subtract the circle's area from the rectangle's.

Area of a rectangle: length × width
The problem already tells you the area of the rectangle, because it says it is an 11 × 11 rectangle.
(11)(11) = 121

Area of rectangle: 121 units²


Area of a circle: \pi r^2
Plug in 5 for the radius r.

\pi 5^2 = 78.5

Area of circle: 78.5 units²


Now subtract 78.5 from 121.
121 - 78.5 = 42.5

The area of the shaded region is 42.5 units².
8 0
4 years ago
The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 114. If state
natima [27]

Answer:

The number of counties in state A   = 56

The number of counties in state B  = 58.

Step-by-step explanation:

Let the number of countries in state A  = k

So, the number of state in state B = ( k+2)

(as he next consecutive even integer after k is k + 2)

Now, according to the question:

k +  ( k+2 )  = 114

or, 2k + 2 = 114

⇒ 2k   = 114 -2 = 112

⇒ k = 112/2 = 56

or,  k = 56

Hence, the number of counties in state A  = k = 56

and the number of counties in state B =  k+ 2 = 56 + 2 = 58.

8 0
3 years ago
I got that E is 43. Is that right?
never [62]

Answer:

Yes, you are right.........

8 0
3 years ago
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