Answer:
x = 8, and y = 12
Step-by-step explanation:
There are 2 variables, so you need 2 equations to form a system of equations in two variables.
The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.
First equation:
100 + 2x + y + 5x + y = 180
Simplify:
7x + 2y = 80 (First equation)
Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.
Second equation:
2x + y = 5x - y
Simplify:
3x - 2y = 0 (Second equation)
Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.
7x + 2y = 80
3x - 2y = 0
Solve the second equation for 2x.
3x = 2y
Now replace 2y in the first equation with 3x.
7x + 3x = 80
10x = 80
x = 8
Replace x with 8 in the second equation.
3(8) - 2x = 0
24 = 2x
x = 12
Answer: x = 8, and y = 12
we know that
1 yard=3 feet
Multiply (89 yards 2 feet) by 14
(89 yards 2 feet)*14=89*14 yards 2*14 feet-------> 1,246 yards 28 feet
convert 28 feet to yards
28 ft=(28/3) yards=9.33 yards
9.33 yards=9 yards+0.33 yards
0.33 yards=1 foot
so
9.33 yards=9 yards+1 foot
substitute
1,246 yards 28 feet=1,246 yards +9 yards+1 foot----->1,255 yards + 1 foot
therefore
<u>the answer is the option</u>
C. 1,255 yards 1 foot
Answer:
Step-by-step explanation:
A road is perpendicular to a highway leading to a farmhouse d miles away.
An automobile passes through the point of intersection with a constant speed 
= r mph
Let x be the distance of automobile from the point of intersection and distance between the automobile and farmhouse is 'h' miles.
Then by Pythagoras theorem,
h² = d² + x²
By taking derivative on both the sides of the equation,
When automobile is 30 miles past the intersection,
For x = 30
Since 
Therefore,
Answer:
Angle WZY=31degrees
Step-by-step explanation:
5x+11=8x-1
11+1=8x-5x
12=3x
X=12/3
X=4
Substitute x=4 in 5x+11
5(4)+11=31
