Problem 1
<h3>Answers:</h3><h3>angle 6 = 50</h3><h3>angle 7 = 50</h3><h3>angle 8 = 40</h3>
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Work Shown:
point E = intersection point of diagonals.
x = measure of angle 6
y = measure of angle 8
angle 7 is also x because triangle AED is isosceles (AE = ED)
Focus on triangle AED, the three angles A, E, D add to 180
A+E+D = 180
x+80+x = 180
2x+80 = 180
2x = 180-80
2x = 100
x = 100/2
x = 50
So both angles 6 and 7 are 50 degrees.
Turn to angle 8. This is adjacent to angle 7. The two angles form a 90 degree angle at point A. This is because a rectangle has 4 right angles.
(angle7)+(angle8) = 90
50+y = 90
y = 90-50
y = 40
angle 8 = 40 degrees
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Problem 2
<h3>Answers:</h3><h3>angle 2 = 61</h3><h3>angle 3 = 61</h3>
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Work Shown:
Angle 5 is 29 degrees (given). So is angle 4 because these are the base angles of isosceles triangle DEC (segment DE = segment EC)
angle 3 and angle 4 form a 90 degree angle
x = measure of angle 3
(angle 3)+(angle 4) = 90
x+29 = 90
x = 90-29
x = 61
Angle 2 is congruent to angle 3 since triangle BEC is isosceles (BE = EC), so both angle 2 and angle 3 are 61 degrees each.
Answer: x > 5
Explanation: First we want to look at our variable and ask ourselves what's happening to it. Since 2 is being subtracted from 9x, we always undo addition and subtraction first so we add 2 to both sides.
That gives us 9x > 45.
Now we need to undo multiplication and division. Since 9 is being multiplied by <em>x</em>, to get <em>x</em> by itself, we need to divide by 9 on the left side of the inequality. If we divide by 9 on the left side, we must also divide by 9 on the right side.
This leaves us with <em>x > 5</em> which is the solution to this inequality.
Answer:
1.) The quotient of a number and 2 = x ÷ 2
2.) A number decreased by 2 = x - 2
3.) 2 times a number = 2x
4.) 2 increased by a number = 2 + x
Step-by-step explanation:
Let's look for key words hidden in these sentences:
1.) The <u>quotient</u> of a number and 2 = The word quotient refers to division
2.) A number <u>decreased</u> by 2 = The word decreased refers to subtraction
3.) 2 <u>times</u> a number = the word times refers to multiplication
4.) 2 <u>increased</u> by a number = the word increased refers to addition
Hope this helps!
Answer:
Since the perimeter is 56 inches we can solve for the lenght with this equation:
And solving for the length we got:
So then the lenght = 16 inhes and the width of 12 inches
Step-by-step explanation:
For a rectangle of width 12 inches and lenght y inches we know that the perimeter is given by:
Since the perimeter is 56 inches we can solve for the lenght with this equation:
And solving for the length we got:
So then the lenght = 16 inhes and the width of 12 inches
A + 2b + 6c = -9
Multiply the equation by 2,
2a + 4b + 12c = -18
In short, Your Answer would be -18
Hope this helps!
