Answer:
2x+50 and 5x-55 both are congruent or have same measure.
Step-by-step explanation:
Since we want to prove that both lines are parallel, this means no theorems that involve with parallel lines apply here.
First of, we know that AC is a straight line and has a measure as 180° via straight angle.
x+25 and 2x+50 are supplementary which means they both add up to 180°.
Sum of two measures form a straight line which has 180°.
Therefore:-
x+25+2x+50=180
Combine like terms:-
3x+75=180
Subtract 75 both sides:-
3x+75-75=180-75
3x=105
Divide both sides by 3.
x=35°
Thus, x = 35°
Then we substitute x = 35 in every angles/measures.
x+25 = 35°+25° = 60°
2x+50 = 2(35°)+50° = 70°+50° = 120°
5x-55 = 5(35°)-55 = 175°-55° = 120°
Since 2x+50 and 5x-55 have same measure or are congruent, this proves that both lines are parallel.
Answer:
1 7/8 quarts
Step-by-step explanation:
The amount Yuan has left can be found by multiplying the original amount by the fraction he has left.
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<h3>used</h3>
After using 1/2 of the broth for soup, the fraction remaining is ...
1 -1/2 = 1/2
The amount Yuan used for gravy is 1/4 of this, or ...
(1/4)(1/2) = 1/8 . . . of the original amount of broth
The total fraction Yuan used was ...
fraction used = fraction for soup + fraction for broth = 1/2 +1/8 = 5/8
<h3>remaining</h3>
Then the fraction remaining is ...
fraction remaining = 1 - fraction used = 1 - 5/8 = 3/8.
The amount remaining is this fraction of the original amount:
(3/8)(5 quarts) = 15/8 quarts = 1 7/8 quarts . . . . remaining
Answer:
a¹⁰
Step-by-step explanation:
So here we have (a⁵)², meaning we need to multiply the exponents to get a¹⁰
Answer:
Step-by-step explanation:
First of all, I drawed this graph and uploaded it for you...
We know that a line equation is y = ax + b and I want to know which equation goes through the points (-1, -5) and (1, -1).
Let's put these points in the algebreac expression of line to find the correct equation:
-5 = a. (-1) + b
-1 = a.(1) + b
solving this system of equation by elimination, we find 2b = -6 and b = -3.
Then, -5 = -a + (-3)
-a = -5 + 3
a = 2
Finally, our line equation is y = 2x - 3
The slope also is represented by a. So, the slope is 2.
