Step-by-step explanation:
pythagoras theorem: c²=a²+b²
Where c= longest side of a right angle triangle
AB= 6+r = c
AD= 12 =a
CD= r =b
(6+r)² = 12²+ r²
36+12r+r² =144 +r²
12r+r²-r²=144-36
12r=108
r= 108/12
r=9
Part 1:the answer is 1/36
each time we roll the dice, the whole probabilities are 6
if we roll it two times
6*6=36
part 2
it's 1/8
each time we flip a coin, the whole probabilities are 2
if we flip it 3 times
2*2*2=8
good luck
The first thing I'll do is solve "5y = 2x + 20" for "<span>y=</span>", so that I can find my reference slope:
y = (2/5)x + 4;
So the reference slope from the reference line is <span>m = 2/5;</span>.
Now I need to find two new slopes, and use them with the point they've given me; namely, with the point (-1, 3). They want me to find the line through (4, –1) that is parallel to 5y = 2x + 20; that is, through the given point, they want me to find a line that has the same slope as the reference line.
Since a parallel line has an identical slope, then the parallel line through (-1, 3) will have slope <span>m = 2/5</span>. Now I have a point and a slope! So I'll use the point-slope form to find the line: y - 3 = (2/5)( x + 1);
Finally, y = (2/5)x + 17/5;
In order to find the y-intercept, replace x by 0.
So, for first option:
f(0) = 7(1) - 2 = 5
For second option:
f(0) = -3(1) - 5 = -8
For third option:
f(0) = 5(1)-1=4
For Fourth option:
f(0) = -5(1) + 10 = 5
For Fifth Option:
f(0) = 2(1) + 5 = 7
So, option 1 and 4 have the y-intercept (0,5)
3.) D
4.) A
Hope this helps
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