Answer:
Step-by-step explanation:
In order to find the measure of each angle, it is important to remember that the sum of the interior angles of a triangle is 180 degrees. Knowing this, you can write the following equation:
[Equation 1]
Based on the information given in the exercise, you know that:
[Equation 2]
[Equation 3]
Then, you can substitute the Equations 2 and 3 into the Equation 1 and then solve for "M" in order to find the measure of the angle "M" in degrees:
Substituting this value into the Equations 2 and 3, you can find the measure of the angle "N" in degrees and the mesure of the angle "O" in degrees. These are:
Therefore:
The value of y is 110 degrees. Since the two lines are parallel, hence x is equivalent to 70 according to alternate theorem rule.
<h3>Line Geometry</h3>
The given line geometry is made up of lines and an isosceles triangle. The triangle has equal base angles
Determine the value of y
70 + y = 180 (supplementary)
y = 180 - 70
y = 110 degrees
Since the two lines are parallel, hence x is equivalent to 70 according to alternate theorem rule.
Learn more on line geometry here: brainly.com/question/1655368
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You can write three equations in the numbers of nickels (n), dime (d), and quarters (q).
n + d + q = 23 . . . . . . . there are 23 coins total
0n +d -q = 2 . . . . . . . . .there are 2 more dimes than quarters
5n +10d +25q = 250 . .the total value is $2.50
The collection includes 11 nickels, 7 dimes, and 5 quarters.
_____
I used the matrix function of my calculator to solve these equations. You can find q by subtracting from the last equation five times the sum of the first two equations.
(5n +10d +25q) -5((n +d +q) +(d -q)) = (250) -5(23 +2)
25q = 125 . . . . . . . simplify
q = 5
From the second equation,
d = q +2 = 7
And from the first,
n = 23 -5 -7 = 11
Answer:
Shorts = 112 and t shirts = 165
Step-by-step explanation:
Let S = shorts
Let T = t shirts
T + S = 277
$2T + $3S = $656
-2(T + S) = 277 so -2T -2S = -544
2T + 3S = 656 so 2T + 3S = 656
------------------------
SO: (subtract T's cancel out) 1S = 112
divide by 1 so S = 112
Plug S into the top equation: T + s = 277 T + 112 = 277 so T = 165
The option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7], and the range is R: [–5, 1]
<h3>What is an ellipse?</h3>
An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have an ellipse equation:
We can write the above equation as:
The domain will be:
D: [–5, 7]
The range will be:
R: [–5, 1]
Thus, the option second D: [–5, 7]; R: [–5, 1] is correct the domain is D: [–5, 7] and the range is R: [–5, 1]
Learn more about the ellipse here:
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