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
21 hundreds would be 2100
3/4…
To simplify a fraction, you have to find a similar factor between the numerator and denominator. In this case, it would be 4.
You would divide both numbers by this common factor and create a new fraction.
So… 9/3=3, and 12/3=4. When combined, the answer becomes 3/4.
Answer:
X + Y + Z = 32
X2 = Y
X3 + 2 = Z
X + X2 + X3 + 2 = 32
Make X alone
There is a 2 so we subtract 2 from both sides
X + X2 + X3 = 30
Add the X's up
X + X2 + X3 = X6
X6 = 30
Divide by 6
30 / 6 = 5
You are left with X=5
The first piece of wood has a length of 5
5 x 2 = 10
The second piece has a value of 10
5 x 3 + 2 = 17
The third piece is 17
Hope this helps. If you have any questions you may ask.
Step-by-step explanation:
Solve the area of the whole circle since in an hour, the minute hand covers the whole clock
assuming that the minute hand reaches all the way out to the edge of the clock
the minute hand is the radius
area=pi times r^2
r=5
5^2=25
area=pi times 25
area=25pi
aprox pi=3.14
25 times 2.14=78.5
area=78.5 in^2
