Answer:
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Step-by-step explanation:
Answer:
BZ = 64/23 = 2 18/23
Step-by-step explanation:
The angle bisectors divide the triangle into proportional parts, so we have ...
CB/CY = AB/AY
CB = CY(AB/AY) = 4(8/6) = 16/3 . . . . multiply by CY and evaluate
and ...
BZ/CB = AZ/AC
BZ = AZ(CB/AC) . . . . multiply by CB
But we have ...
AZ = 8 -BZ, so this becomes ...
BZ = (8 -BZ)(16/3)/(10)
BZ(1 +8/15) = 64/15 . . . . add the BZ term on the right to both sides
BZ = (64/15)(15/23) = 64/23 . . . . divide by the coefficient of BZ
BZ = 64/23 = 2 18/23
The solution to the system of equations are (2, 5).
Solution:
The system of equations are
x + y = 7 – – – – (1)
2x – y = –1 – – – – (2)
To find x from equation (1):
x + y = 7
Subtract y from both sides of the equation, we get
⇒ x + y – y = 7 – y
⇒ x = 7 – y – – – (3)
Substitute (3) in (2) we get,
2(7 – y) – y = –1
14 – 2y – y = –1
14 – 3y = –1
Subtract 14 from both sides,
–3y = –15
Divide by –5 on both sides,
y = 5
Substitute y = 5 in equation (3)
x = 7 – 5
x = 2
The solution to the system of equations are (2, 5).
Answer: it will cost $280
Step-by-step explanation:
The diagonal of the rectangular garden divides it into two equal right angle triangles. The diagonal represents the hypotenuse of each right angle triangle. The length and width of the rectangle represents the adjacent and opposite sides of the right angle triangle. To determine the length of the diagonal, d, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore
d² = 24² + 32²
d² = 576 + 1024 = 1600
d = √1600
d = 40 feet
If the path is 2 feet wide, then the area of the path is
Area = 40 × 2 = 80 ft²
If gravel costs $3.50 a square foot, then the cost to install the gravel path is
3.5 × 80 = $280
