To find the equation of a line knowing two points it passes through, we must first find the slope and then substitute the x and y values to figure out the y intercept.
First thing is to find the slope using the formula m = Δy ÷ Δx
m = 5 - (-2) ÷ 4 - (-5)
Now we simplify
m = 7 ÷ 9
Our equation so far is y = 7/9x + b. Now we can substitute the values of x and y from a point to figure out the answer. The equation here uses the point (4,5)
5 = 7/9 · 4 + b
Get b on one side
5 - 28/9 = b
Simplify
b = 1 + 8/9
That makes the equation of the line y = 7/9x + (1 + 8/9)
Answer:
A. 5 ft, 4 ft, 3 ft
Step-by-step explanation:
When you use the Pythagorean theorem with the numbers of the first choice, you find that these could be the sides of a right triangle:
3² + 4² = 9 + 16 = 25 = 5²
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You have found the correct answer at this point.
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If you want to check, you can examine the other choices:
C: 6² +10² = 136 ≠ 11²
B: 2² +4² = 20 ≠ 6²
D: 5² +10² = 125 ≠ 15²
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<em>Comment on 3-4-5 triangle</em>
As you can see from the above, side measures of 3, 4, and 5 will form a right triangle. This is the smallest set of integers that will do so. It is also the ratios of the only set of side lengths in arithmetic progression that will do so.
This latter fact can help you rule out choices B and D in this problem, because each of those has sides in the progression 1 : 2 : 3.
(3, 4, 5) triangles come up often in algebra and geometry problems. This is a useful "Pythagorean triple" to remember.
Answer:
80 ft
Step-by-step explanation:
Perimeter is adding the lengths of all the sides.
The answer should be 4. Take note of the pattern of unit digits of 2^n.
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
Every 4 powers, it rotates 2, 8, 6, 4. Since 2020 is divisible by 4, the answer is 4.
If you would like to calculate 4 * 1 1/5, you can do this using the following steps:
1 1/5 = 6/5
4 * 1 1/5 = 4 * 6/5 = 24/5 = 4 4/5
The correct result would be 4 4/5.
If that was not your question, please ask differently and I will try and answer your question. :)
