<span>Triangle PQR is a right triangle. First we have to find the length of each side of the triangle. This can be done using the points provided, along with the Pythagorean theorem, which is a^2+b^2=c^2.
PR^2 = (7- -2)^2+(3-5)^2 = 85 => PR = sqrt(85)
QR^2 = (7- -1)^2+(3-1)^2 = 68 => QR = sqrt(68)
QP^2 = (1-5)^2+(-1 - -2)^2 =17 => QP = sqrt(17)
Now that we have the sides of the triangle, we can put them into the Pythagorean theorem again to see that it works out:
(Sqrt(17))^2 + (sqrt(68))^2 = (sqrt(85))^2
17 + 68 = 85
85 = 85
Since the Pythagorean theorem works for right triangles, the triangle is indeed a right triangle.</span>
Answer:
Step-by-step explanation:
1 quart = 32 fluid ounces
4 quart = 32 x 4 = 128 ounces
Rate of 128 ounces = 128 ÷ 5.12 = 25
Rate of 79 ounces = 79 ÷ 3.95 = 20
4 quart jug is a better buy
Step 1 :
Equation at the end of step 1 :
((6x + 3) - 2 • (x + 1)) + 5
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
4x + 6 = 2 • (2x + 3)
Final result :
2 • (2x + 3)
Answer:
x > 2
Step-by-step explanation:
Given
- 8x + 2x - 16 < - 5x + 7x ← simplify both sides
- 6x - 16 < 2x ( subtract 2x from both sides )
- 8x - 16 < 0 ( add 16 to both sides )
- 8x < - 16 ( divide both sides by - 8 )
Remembering to reverse the symbol as a consequence of dividing by a negative value.
x > 2
Answer:
7. 8125 l
Step-by-step explanation:
256 km ....... 20l
100 km ...........x l
x = 100×20/256
= 7. 8125 l
