Answer:
15 units
Step-by-step explanation:
The distance between two points can be found using the following formula:
Given points:
(-7, 5) and (2, -7)
<u>where:</u>
- x₁ = -7
- x₂ = 2
- y₁ = 5
- y₂ = -7
Substitute these points into the formula and simplify:
![\sf d=\sqrt{(2-(-7))^2+((-7)-5)^2} \ \textsf{[simplify the radicand]}\\\\ d=\sqrt{(2+7)^2+(-12)^2} \ \textsf{[simplify]}\\\\d=\sqrt{(9)^2+(-12)^2} \ \textsf{[evaluate the power]}\\\\d=\sqrt{81+144} \ \textsf{[add]}\\\\d=\sqrt{225}\ \textsf{[simplify]}\\\\d=15](https://tex.z-dn.net/?f=%5Csf%20d%3D%5Csqrt%7B%282-%28-7%29%29%5E2%2B%28%28-7%29-5%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bsimplify%20the%20radicand%5D%7D%5C%5C%5C%5C%20d%3D%5Csqrt%7B%282%2B7%29%5E2%2B%28-12%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bsimplify%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B%289%29%5E2%2B%28-12%29%5E2%7D%20%5C%20%5Ctextsf%7B%5Bevaluate%20the%20power%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B81%2B144%7D%20%5C%20%5Ctextsf%7B%5Badd%5D%7D%5C%5C%5C%5Cd%3D%5Csqrt%7B225%7D%5C%20%5Ctextsf%7B%5Bsimplify%5D%7D%5C%5C%5C%5Cd%3D15)
The distance between the two points is 15 units.
Learn more here:
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Actually, the answer is not A, if you're saying A is the first choice above. That's incorrect. You will need to use the Geometric mean for right triangles here to figure out what the value of a is. We will use this form:
. We have a value for YZ of 3; side a is XZ. That means in order to solve this we need WZ, which we can find using pythagorean's theorem. 3^2 + 4^2 = c^2 and 9 + 16 = c^2 and c = 5. Now we fill in accordingly:
. Cross-multiply to get 3XZ=25 and side XZ is
. XZ is 25/3 and YZ is 3, so 25/3 - 3 = XY. That means that XY (side a) = 16/3 or 5 1/3, choice B, or the second one down.
Answer:
Step-by-step explanation:
x-intercepts are SOLUTIONS to a quadratic whereas when you put those solutions into factor form (in a set of parenthesis), you have the FACTORS of the quadratic. They are the same thing generally, they are just written in different forms. For example, if a solution to a quadratic is x = 3, it has been understood that x = 3 when y = 0. Therefore, if x - 3 = y and y = 0, then x - 3 = 0. Solving that for x, you get x = 3. That factor of x = 3 is (x - 3).
Following that logic, for a:
If the x intercepts are x = 0 and x = 3, it is understood that x + 0 = 0 so x = 0 and the factor is (x + 0) (it could also be x - 0 since adding 0 is the same as subtracting 0); if x = 3 it is understood that x - 3 = 0 and the factor is (x - 3).
For b:
If the x-intercepts are x = -1 and x = 1, then originally the factors were (x + 1) and (x - 1). Again, set each of those equal to 0 and solve for x (THE X-INTERCEPT EXISTS WHERE Y = 0!)
For c:
If the x-intercepts are x = -5 and x = 10, then originally the factors were (x + 5) and (x - 10).
For d:
If the x-intercept is a fraction, do the same thing:
x = 1/2 so
x - 1/2 = 0 Now multiply both the x and the 1/2 by a 2 to get the factor (2x - 1) and the other factor from x = 4 is (x - 4)
Answer:
19. parallel
20. corresponding
21. exterior
22. corresponding exterior angles
if not for the points i wouldve left u to suffer on ur own so yor welcome
