Answer:
x = 13
Step-by-step explanation:
Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:
Cross multiply:
8(x + 2) = 10 (x - 1)
8x + 16 = 10x - 10
Subtract 8x from both sides:
8x - 8x + 16 = 10x - 8x - 10
16 = 2x - 10
Add 10 to both sides:
16 + 10 = 2x - 10 + 10
26 = 2x
Divide both sides by 2:
13 = x
Verify whether x = 13 is the correct value:
This shows the proportional relationship between , and that ΔNML and ΔPST are indeed similar right triangles.
Therefore, the correct answer is x = 13.
X+
=12
5x=36
x=7.2
So, the triangular entrance to the tent is
7.2 feet tall and
4.8 feet wide
Answer:
x=16°
Step-by-step explanation:
tanθ=opposite/adjacent
tan(<CAB)=BC/AB
<CAB=tan⁻¹(21/29)=35.9097308°
tanθ=opposite/adjacent
tan(<DAB)=BD/AB
<DAB=tan⁻¹((21/2)/29)=19.90374954°
<CAB=<DAB+x
x=<CAB-<DAB
=35.9097308-19.90374954
x=16.00598126°
Answer:
-12.8%
Step-by-step explanation:
To calculate the percent decrease, we:
- Find the difference between the new value and the original
- Divide the number by the original
- Multiply by 100 and the % symbol.
The population of the town originally had 25,000. 3,200 people moved away. This means that the new population is 21,800.
- 21,800-25,000=-3,200
- -3,200/25,000=-0.128
- -0.128(100)=-12.8%
The towns population decreased by 12.8%.
The first thing we must do for this case is to define variables:
We have then:
x: liz's age
y: melinda's age
We now write the system of equations:
By solving the system graphically we have that the age of each one is currently:
Next year, the age of liz is:
Answer:
Next year, Liz's age is 11 years.
Note: see attached image for the graphic solution.