Answer:
- WX =
![\sqrt{74} \approx 8.6023253\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B74%7D%20%5Capprox%208.6023253%5C%5C%5C%5C)
- XY =
![2\sqrt{37} \approx 12.1655251\\\\](https://tex.z-dn.net/?f=2%5Csqrt%7B37%7D%20%5Capprox%2012.1655251%5C%5C%5C%5C)
- WY =
![\sqrt{74} \approx 8.6023253\\\\](https://tex.z-dn.net/?f=%5Csqrt%7B74%7D%20%5Capprox%208.6023253%5C%5C%5C%5C)
- Classify: Isosceles
============================================================
Explanation:
Apply the distance formula to find the length of segment WX
W = (x1,y1) = (-10,4)
X = (x2,y2) = (-3, -1)
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-3))^2 + (4-(-1))^2}\\\\d = \sqrt{(-10+3)^2 + (4+1)^2}\\\\d = \sqrt{(-7)^2 + (5)^2}\\\\d = \sqrt{49 + 25}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-10-%28-3%29%29%5E2%20%2B%20%284-%28-1%29%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-10%2B3%29%5E2%20%2B%20%284%2B1%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-7%29%5E2%20%2B%20%285%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B49%20%2B%2025%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B74%7D%5C%5C%5C%5Cd%20%5Capprox%208.6023253%5C%5C%5C%5C)
Segment WX is exactly
units long which approximates to roughly 8.6023253
-------------------
Now let's find the length of segment XY
X = (x1,y1) = (-3, -1)
Y = (x2,y2) = (-5, 11)
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-5))^2 + (-1-11)^2}\\\\d = \sqrt{(-3+5)^2 + (-1-11)^2}\\\\d = \sqrt{(2)^2 + (-12)^2}\\\\d = \sqrt{4 + 144}\\\\d = \sqrt{148}\\\\d = \sqrt{4*37}\\\\d = \sqrt{4}*\sqrt{37}\\\\d = 2\sqrt{37}\\\\d \approx 12.1655251\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-3-%28-5%29%29%5E2%20%2B%20%28-1-11%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-3%2B5%29%5E2%20%2B%20%28-1-11%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%282%29%5E2%20%2B%20%28-12%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B4%20%2B%20144%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B148%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B4%2A37%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B4%7D%2A%5Csqrt%7B37%7D%5C%5C%5C%5Cd%20%3D%202%5Csqrt%7B37%7D%5C%5C%5C%5Cd%20%5Capprox%2012.1655251%5C%5C%5C%5C)
Segment XY is exactly
units long which approximates to 12.1655251
-------------------
Lastly, let's find the length of segment WY
W = (x1,y1) = (-10,4)
Y = (x2,y2) = (-5, 11)
![d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-5))^2 + (4-11)^2}\\\\d = \sqrt{(-10+5)^2 + (4-11)^2}\\\\d = \sqrt{(-5)^2 + (-7)^2}\\\\d = \sqrt{25 + 49}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\](https://tex.z-dn.net/?f=d%20%3D%20%5Csqrt%7B%28x_1%20-%20x_2%29%5E2%20%2B%20%28y_1%20-%20y_2%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-10-%28-5%29%29%5E2%20%2B%20%284-11%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-10%2B5%29%5E2%20%2B%20%284-11%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28-5%29%5E2%20%2B%20%28-7%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B25%20%2B%2049%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B74%7D%5C%5C%5C%5Cd%20%5Capprox%208.6023253%5C%5C%5C%5C)
We see that segment WY is the same length as WX.
Because we have exactly two sides of the same length, this means triangle WXY is isosceles.
9514 1404 393
Answer:
17 > x+1
Step-by-step explanation:
You can add or subtract any number from both sides to get an equality with the same meaning:
17 > x+1
0 > x-16
You can multiply or divide by any number (except division by 0) to get an equality with the same meaning. If the multiplier (or divisor) is negative, the comparison changes direction.
-16 < -x
48 > 3x
You would need 10 cups since you need 3 cups for every one muffin (24/8=3)
(30/3=10)
For this case, the first thing we must do is define a variable.
We have then:
n: number of days.
We now write the explicit formula that represents the problem.
We have then:
an = 4n + 15
Where,
15: crunches the first day
4: increase the number 4 each day
Answer:
An explicit formula for the number of crunches Abbie will do on day n is:
an = 4n + 15