Answer:
- The y-intercept is (0, -37/7).
Explanation:
When you have one point and the slope of a line you can find its equation by using the point-slope form of the linear function:
- m = slope
- point = (a, b)
- point-slope equation: (y - b) = m (x - a).
Now substitute m = -1/7 and (a,b) = (5, - 6)
Solve for y:
- y = -(1/7)x - 37/7 ← this is the slope-intercept form of the equation.
The y-intercept is the point when x = 0. So, the corresponding y-coordinate is the constant term in the last equation:
And the y-intercept is the point (0, -37/7).
Rewrite the root expressions as fractional exponents:
![\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = \dfrac{7^{1/3}}{7^{1/5}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7B7%7D%7D%7B%5Csqrt%5B5%5D%7B7%7D%7D%20%3D%20%5Cdfrac%7B7%5E%7B1%2F3%7D%7D%7B7%5E%7B1%2F5%7D%7D)
Recall that 
, so that
Simplify the exponent:
Then you end up with
![\dfrac{\sqrt[3]{7}}{\sqrt[5]{7}} = 7^{2/15}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7B7%7D%7D%7B%5Csqrt%5B5%5D%7B7%7D%7D%20%3D%207%5E%7B2%2F15%7D)
Answer:
ABCD is not a parallelogram
Step-by-step explanation:
Use the distance formula to determine whether ABCD below is a parallelogram. A(-3,2) B(-3,3) C (5,-3) D (-1.-5)
We have to find the length of the sides of the parallelogram using the formula below
= √(x2 - x1)² + (y2 - y1)² when given vertices (x1, y1) and (x2, y2)
For side AB
A(-3,2) B(-3,3)
= √(-3 -(-3))² + (3 -2)²
= √0² + 1²
= √1
= 1 unit
For side BC
B(-3,3) C (5,-3)
= √(5 -(-3))² + (-3 -3)²
= √8² + -6²
= √64 + 36
= √100
= 10 units
For side CD
C (5,-3) D (-1.-5)
= √(-1 - 5)² + (-5 - (-3))²
= √-6² + -2²
= √36 + 4
= √40 units
For sides AD
A(-3,2) D (-1.-5)
= √(-1 - (-3))² + (-5 -2)²
= √(2² + -7²)
= √(4 + 49)
= √53 units
A parallelogram is a quadrilateral with it's opposite sides equal
From the above calculation
Side AB ≠ CD
BC ≠ AD
Therefore, ABCD is not a parallelogram
