∠ROT=160°
∠SOT=100°
Now we calculate ∠SOR as follows: ∠SOR = ∠ROT - ∠SOT
∠SOR = 160° - 100°
∠SOR = 60°
It is stated that the angles ROQ, QOS, and POT all have the same measure.
Thus, ∠SOQ + ∠QOR = 60°
Since ∠SOQ equals ∠QOR, we can express this as:
2∠SOQ = 60°
From which we find ∠SOQ = 60° ÷ 2
∠SOQ = 30°
Also, ∠POT = ∠SOQ = ∠ROQ = 30°
Answer:
Red paint will cover 262 square feet
of the ramp.
Step-by-step explanation:
The lateral surface area represents the surface area of the sides of the ramp without including the top and bottom surfaces
This ramp has three surfaces
The two sides are triangular with dimensions of length 20 and height 8.5
The back consists of a rectangular shape with length 12 and height 8.5
Step 1: Calculating the Area of Triangle
The area of the triangular side = 
The area of the triangle = 
The area of the triangle = 
Thus, the area of the triangle = 85 square feet
Area of both triangles = 
= 170
Step 2: Finding the Area of Rectangle
Area of rectangle = 
therefore,
Area of the rectangular back = 
= 102 square feet
Step 3: Calculating the total lateral surface area
Overall Lateral Surface Area
= Area of triangles + Area of Rectangle
= 272 square feet
This question is quite lengthy, so I will offer a brief overview. To find your x-value, set y to 0 in the given equation.
2x + 3y = 1470
2x + 3(0) = 1470
2x = 1470
x = 735
Thus, your farthest point on the x-axis is (735,0).
Now, repeat for y.
2x + 3y = 1470.
2(0) + 3y = 1470
3y= 1470
y= 490
Your highest point thus is (0,490).
After plotting both points, connect them with a straight line to illustrate your graph.
Check
Initially, we need to determine how fast he skis in a minute without considering any speed increase.
To do that, we'll divide the total distance by the time.
960 divided by 5 equals 192.
Therefore, his speed is 192 meters per second.
Now, let's add 20 to this figure.
192 plus 20 equals 212.
Now, to calculate how far he can travel in 10 minutes, we multiply 212 by 10.
212 times 10 equals 2120.
Thus, Alex can cover 2120 meters in 10 minutes.
Answer:
7 years
Step-by-step explanation:
Suri is 17 years old.
Her cousin's age is c.
Suri's age is stated to be 4 less than 3 times her cousin’s age.
This means we take 3 times her cousin’s age and subtract 4.
17 = 3c - 4
We now need to solve for c, which represents her cousin's age.
Add 4 to each side:
17 + 4 = 3c - 4 + 4
17 + 4 = 3c
21 = 3c
Now divide both sides by 3:
21/3 = 3c/3
7 = c
Thus,
Her cousin is 7 years old.
