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ELEN [110]
3 years ago
12

In the circle above, FH and GJ are chords which intersect at point K. If FK = 3 mm, HK = 4 mm, and GK = 2 mm, what is the length

of JK?
Mathematics
1 answer:
Svetach [21]3 years ago
6 0
We have a formula for that( according to the Intersecting chords theorem)
fk \times hk = gk \times jk
3×4=2×jk
6=jk
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PLEASE HELP ILL DO THE SAME PLEASE AND I NEED STEP BY STEP IM TRYING TO LEARN :(
son4ous [18]

Answer:

5)

Line 1: y=-x+3

Line 2: y=3x-3

6)

Line 1: y=\frac{1}{2}x-2

Line 2: y=-\frac{5}{2}x+6

7)

See below

Step-by-step explanation:

To write the system of equations on the graph, you just need to write the 2 equations of the 2 lines.

5)

The first thing to do is find the slope of the lines. Pick one of them, and start by finding 2 points on that line that land perfectly on the grid.

It's pretty hard to read that top graph in the photo, but I think I see these ones marked:

Line 1: (0, 3) and (3, 0)

Line 2: (0, -3) and (2, 3)

Make sure I got them correct, because the equations will be wrong otherwise. Same for problem 6. To find the slope, divide the change in y by the change in x. Starting with line 1, y went from 3 to 0, so a change of -3. x went from 0 to 3, so a change of 3.

Divide the change in y by the change in x:

m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0-3}{3-0}\\\\m=\frac{-3}{3}\\\\m=-1

The slope of line 1 is -1. That means every time x increases by 1, y decreases by 1. You can see that on the line.

Now for line 2:

m=\frac{3--3}{2-0}\\\\m=\frac{6}{2}\\\\m=3

When x increases by 1, y increases by 3.

The last thing to do is find the y-intercept of both lines. That's just where the line intersects the y-axis, at x = 0, and it's clearly visible on the graph so there isn't much to do.

Line 1: 3

Line 2: -3

Now, you can write the equations for these lines in slope intercept form:

y=mx+b

where m is the slope and b is the y-intercept we found above.

Line 1: y=-x+3

Line 2: y=3x-3

In line 1, -1x can be simplified to just -x.

6)

I'll do the exact same process here, but with less explaining. Let me know if you have any questions.

Find 2 points:

Line 1: (0, -2) and (4, 0)

Line 2: (0, 6) and (4, -4)

Find the slope of line 1:

m=\frac{y2-y1}{x2-x1}\\\\m=\frac{0--2}{4-0}\\\\m=\frac{1}{2}

and line 2:

m=\frac{-4-6}{4-0}\\\\m=\frac{-10}{4}\\\\m=-\frac{5}{2}

Now, the y-intercepts:

Line 1: -2

Line 2: 6

Write the equations:

Line 1: y=\frac{1}{2}x-2

Line 2: y=-\frac{5}{2}x+6

7)

A system with 1 solution means 2 lines that intersect at 1 point. Problems 5 and 6 are both examples of this. A system with no solution means lines that never intersect, meaning that they have the same slope, they're parallel.

Example:

y=2x+1\\y=2x+2

Those both have a slope of 2, and if you graph them, you'll see that they never intersect.

A system with infinitely many solutions means they intersect at every possible point. These would just be the same line.

Example:

y=2x+1\\y=2x+1

That's what they are, graph them however you like.

3 0
2 years ago
I need help pls pls pls
serg [7]

Answer:

e. 55 miles hope that helped

6 0
3 years ago
Read 2 more answers
Write the slope-intercept form of the line with a slope of 2 and a y-intercept of -4. Include your work in your final answer. Ty
kakasveta [241]
Y=mx+b m=slope b=y intercept
y=2x-4
7 0
3 years ago
Read 2 more answers
Picture Added Triangles <br> AA <br> SSS<br> SAS<br> Not Similar
rewona [7]

Answer:

Not Similer

Step-by-step explanation:

we can use the process of elimination, first AA isn't it because the corresponding angles arn't equal, next SSS itsn't it because we don't know the side lengths, and lastly SAS isn't it because we still don't know the side lengths.

5 0
3 years ago
Juan made a design with polygons. which polygon in juan's design is pentagon
larisa86 [58]
The pentagon is the one with 5 sides. Good Luck!

6 0
3 years ago
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