Let s represent the measure of the second angle.
The measure of the first angle is 15° less than the second, so we can represent the first angle by (s-15).
The measure of the third angle is 45° more than half the second, so we can represent the third angle by (45+(s/2)).
The sum of these angles is 180°, so we can represent the sum as
... (s-15) + s + (45+s/2) = 180
Collecting terms, we have
... 2.5s +30 = 180
... 2.5s = 150 . . . . . . subtract 30
... s = 150/2.5 = 60 . . . . divide by the coefficient of s
The first angle is 60-15 = 45.
The second angle is 60.
The third angle is 45+60/2 = 75.
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<u>Check</u>
The sum of the three angles is 45 +60 +75 = 180.
Answer:
x = {-4, 4}
Step-by-step explanation:
Subtracting 3 gives ...
5x^2 = 80
Dividing by 5, we get ...
x^2 = 16
Taking the square root gives the solutions ...
x = ±4
The smaller value of x is -4; the larger value is 4.
We know that the side lengths of the square base are: x * x. The volume is 12, so for now, let's say that y is the other side length. Then, x * x * y = 12. We can solve for y: y = 12/x^2. Now, we find the surface area of the 5 sides.
Four of the sides have the same area: x * (12/x^2) = 12/x, so we multiply this by 4: 48/x.
The last side is the base: x * x = x^2.
We add 48/x to x^2:
x^2 + 48/x
So, the answer is the fourth choice, (d).
Let's start b writing down coordinates of all points:
A(0,0,0)
B(0,5,0)
C(3,5,0)
D(3,0,0)
E(3,0,4)
F(0,0,4)
G(0,5,4)
H(3,5,4)
a.) When we reflect over xz plane x and z coordinates stay same, y coordinate changes to same numerical value but opposite sign. Moving front-back is moving over x-axis, moving left-right is moving over y-axis, moving up-down is moving over z-axis.
A(0,0,0)
Reflecting
A(0,0,0)
B(0,5,0)
Reflecting
B(0,-5,0)
C(3,5,0)
Reflecting
C(3,-5,0)
D(3,0,0)
Reflecting
D(3,0,0)
b.)
A(0,0,0)
Moving
A(-2,-3,1)
B(0,-5,0)
Moving
B(-2,-8,1)
C(3,-5,0)
Moving
C(1,-8,1)
D(3,0,0)
Moving
D(1,-3,1)