Answer:
see explanation
Step-by-step explanation:
Since BD bisects ∠ ABC , then
∠ ABD = ∠ DBC , substitute values
3x + 4 = 55 ( subtract 4 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
Answer:
7.5 L of 10% solution and 22.5 L of 30% solution
Step-by-step explanation:
Volume of 10% solution plus volume of 30% solution = total volume of 25% volume.
x + y = 30
Acid in 10% solution plus acid in 30% solution = total acid in 25% solution.
0.10 x + 0.30 y = 30 × 0.25
0.10 x + 0.30 y = 7.5
Solve the system of equations, using either substitution or elimination. I'll use substitution:
x = 30 − y
0.10 (30 − y) + 0.30 y = 7.5
3 − 0.10 y + 0.30 y = 7.5
0.20 y = 4.5
y = 22.5
x = 30 − y
x = 7.5
Sarah needs 7.5 L of 10% solution and 22.5 L of 30% solution.
When you solve proportions, you have to cross multiply.
9 x
--- = --- Multiply each numerator by the opposite denominator.
11 22
(9)(22) = 11x Then, multiply.
198 = 11x Then, divide.
18 = x
9514 1404 393
Answer:
8. C) 24.2
9. A) 8.1
Step-by-step explanation:
8. The radius is shown as being 7.8 +4.3 = 12.1, so the diameter x is ...
d = 2r
x = 2(12.1) = 24.2
__
9. The unknown leg (y) of the right triangle can be found from the Pythagorean theorem.
y² +11.7² = 12.5² . . . . . the radius is half the diameter
y = √(156.25 -136.89) = √19.36 = 4.4
Then the segment of interest is ...
x + y = 12.5
x = 12.5 -4.4 = 8.1
Answer:
6.104 m
Step-by-step explanation:
The length of the bench is 30.52 m.
5 people want to sit down on the bench.
We assume they are seated with equal spacing between themselves.
The length occupied by each person will therefore be:
30.52 / 5 = 6.104 m
