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Dimas [21]
3 years ago
11

Write the equation of a line that is perpendicular to the given line and that passes through the given point. y= 2/3x + 9; (–6,

5)
Mathematics
1 answer:
kow [346]3 years ago
8 0
Hi!

The equation y = 2/3x + 9 is written in slope intercept, or y = mx + b. The m is the slope, and the b is the y intercept.

When a line is perpendicular to another, it meets it at a 90 degree angle. The slope of the line which is perpendicular to one with a given slope is the negative reciprocal of it, for example, if you had a line with slope 1/2, the slope of the line perpendicular to it would be -2.

So for this line, the negative reciprocal of 2/3 is -3/2. You now have one of the slots of the equation filled in, giving you:

y = -3/2x + b

Now, you just need to find b, as slope intercept leaves x and y as variables. Luckily, you are given a point that lays on the line; (-6, 5).

So to solve for b, you can substitute that point in, using -6 as x and 5 as y. That gives you:

5 = -3/2 (-6) + b

Now, just solve for b.

5 = -3/2 (-6) + b
5 = 9 + b
b = -4

And there's your solution for b, which you can fill in, giving you your final answer of:

y = -3/2x - 4
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Jon is paid $20 to mow his neighbor's yard. It takes three hours to mow and $2 worth of gasoline. How much does Jon earn per hou
noname [10]
Jon earns 6 dollars per hour.

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3 years ago
8/9= blank=3/11=blank<br> find an equivlant fraction
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3 years ago
A seed company planted a floral mosaic of a national flag. The perimeter of flag is 2,340 ft determine the flag’s width and leng
Natali5045456 [20]

Answer:

Width: 450 feet

Length: 720 feet

Step-by-step explanation:

So we start with the equation to find the perimeter -

2l + 2w = p

l = length

w = width

p = perimeter

We insert the 2,340 ft as the perimeter -

2l + 2w = 2,340 ft

Now we find another equation for the "length is 270 ft greater than width" -

l = 270 ft + w

Using substitution, we substitute the y in the first equation with 270 ft + w -

2 (270 ft + w) + 2w = 2,340 ft

540 ft + 2w + 2w = 2,340 ft

540 ft + 4w = 2,340 ft

4w = 2,340 ft - 540 ft

4w = 1,800 ft

w = 1,800 ft / 4

w = 450 ft

Now to find the width we substitute the w with 450 ft -

l = 270 ft + w

l = 270 ft + 450 ft

l = 720 ft

Check -

2 * 720 ft + 2 * 450 ft = 2,340 ft

1,440 ft + 900 ft = 2,340 ft

2,340 ft = 2,340 ft  (Correct)

3 0
3 years ago
In AHIJ, the measure of ZJ=90°, IJ = 5 feet, and JH = 3.2 feet. Find the measure of
Dominik [7]

Answer:

32.6

Step-by-step explanation:

opp/adj = 3.2/5

I= tan -1(3.2/5)

I =32.6192

=32.6

3 0
3 years ago
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