Answer:
(42.5, 37.5)
Step-by-step explanation:
Given:
Arthur = A(20, 35)
Cameron = C(65, 40)
Jamie = J(45, 20)
Required:
Coordinate of the midpoint of the distance between A and C.
SOLUTION:
Midpoint (M) of AC, is given as:
Let 
Plug the values into the given formula:
Coordinate Jamie should run towards is (42.5, 37.5)
Solution:
<u>Given:</u>
Supplementary angles are a pair of angles that sum up to 180°.
<u>It should be noted:</u>
- If ∠G and ∠H are a pair of supplementary angles, they both sum up to 180°.
Equation formed: ∠G + ∠H = 180
<u>Substitute the values into the equation.</u>
- ∠G + ∠H = 180
- => 65 + ∠H = 180
<u>Subtract 65 both sides.</u>
- => 65 - 65 + ∠H = 180 - 65
- => ∠H = 180 - 65 = 115°
Answer:
(-3, -3)
Step-by-step explanation:
1.) Rewrite the second equation so 3y is on one side of the equation:
3y=6+5x
2.) Substitute the given value of 3y (replacing 3y with 6+5x, since we know they equal each other) into the equation 17x=-60-3y
Should end up with this:
17x=-60-(6+5x)
3.) Solve 17x=-60-(6+5x)
Calculate Difference: 17x=-66-5x
Combine Like Terms: 22x = -66
Divided both sides by 22 to isolate and solve for x: -3
So We know x=-3, now we got to find the y value. We can use either the first or second equation to find y value, so lets use the second.
3y=6+5x
1.) We know that x=-3, so we can simply substitute x in the equation
3y=6+5x with -3
3y=6+5(-3)
2.) Solve 3y=6+5(-3)
Combine Like Term: 3y=6+-15
Combine Like Term Even More: 3y= -9
Divide by 3 on both sides to isolate and solve for y: y=-3
So now we know y=-3 and once again we know x=-3, so if we format that
(-3,-3)
^ ^
x y
Answer: E
Step-by-step explanation: In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. ... Many mathematical theorems are conditional statements.
