<span>Two cars run at constant speeds around a one-mile racetrack. If the cars circle the track in the same direction, the faster car passes the slower car every 10 minutes. If the cars circle the track in opposite directions, the cars meet every 30 seconds.</span>
Answer:2.6
Step-by-step explanation:
For #1 you have one leg of a right triangle measuring 4000 (the height of the mountain) and the other leg is 3000 (the distance that Mario is from Jenna). The angle of elevation is the one on the base of the triangle across from the right angle. To find the measure of the angle, use the tangent ratio: tan(A)=4000/3000, which could be simplified to tanA = 4/3. Do that on your calculator using the inverse tangent function to get that the angle of elevation from Mario to Jenna is 53 degrees.
For #2 you have another right triangle situation where the length of the hypotenuse is 20 and the base leg is 10. You are finding again the base angle across from the right angle. Use the cosA=10/20, aka cosA=.5. Again use the inverse cos function on your calculator to find the angle in question is 60 degrees.
Answer:
because AC and BD bis => AX = XC; BX = XD
ΔAXD ≅ ΔCXB (SAS) because: AX = CX
DX = BX
m∠AXD = m∠BXC ( 2 opposing angles)
because ΔAXD ≅ ΔCXB (SAS)
=> AD = BC and m∠DAX = m∠BCX
because m∠DAX = m∠BCX => AD//BC
ABCD has AD = BC and AD//BC => ABCD is a parallelogram
Step-by-step explanation:
Substitute the first equation into the second equation. You will get:
4x - (2x - 5) = 7
Distribute the negative sign into the parenthesis:
4x - 2x + 5 = 7
Simplify
2x + 5 = 7
Subtract 5 on both sides
2x = 2
x = 1
Now, substitute x = 1 into the first equation:
y = 2(1) - 5
y = 2 - 5
y = -3
The solution to the system of equations is (1, -3).
