9514 1404 393
Answer:
15
Step-by-step explanation:
In vector form, the equation of point p on the line can be written as ...
p = (-3, -4) +t(25 -(-3), 38 -(-4)) . . . . . for some scalar t
p = (-3, -4) +t(28, 42)
p = (-3, -4) +14t(2, 3)
where t takes on any value between 0 and 1.
If we let t = n/14 for some integer 0 ≤ n ≤ 14, then the coordinates of point p will be integers.
There are 15 values that n can have in the allowed range.
The caterpillar touches 15 points with integer coordinates.
Question 1:This is a 45-45-90 right triangle. If the leg length is

, then the hypotenuse length will be

.
The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get

. Thus, the last choice is your answer.
Question 2:This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of

.
Then, the longer leg will have a length of

.
Also, the hypotenuse will have a length of

This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.
Hope this helps! :)
C. e
Step-by-step explanation:

Answer:

Step-by-step explanation:
<u>Key skills: Exponents + Fractions</u>
Use the negative exponent property. If your number is x^-y then it would be the same as 1/x^y
3^-4 is the same as 
3^4 is 81, so your answer would be 1/81.
Hope you have a nice day and understood this!
Answer:
B: y = 2x² - 16x + 40
Step-by-step explanation:
You can find this simply by expanding the given function:
y = 2(x - 4)² + 8
y = 2(x² - 8x + 16) + 8
y = 2x² - 16x + 32 + 8
y = 2x² - 16x + 40