11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.
Make them equal to each other in an equation.
5x = x + 20
Subtract x from both sides.
4x = 20
Divide both sides by 4.
x = 5
12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:
x + x + 50 = 180
Combine like terms.
2x + 50 = 180
Subtract 50 from both sides.
2x = 130
Divide both sides by 2.
x = 65
Now make the base angle plus x equal 180, because they form a straight line.
65 + x = 180
Subtract 65 from both sides.
x = 115
13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.
x + x + 90 = 180
Combine like terms.
2x + 90 = 180
Subtract 90 from both sides.
2x = 90
Divide both sides by 2.
x = 45
The linear equation represents y = mx + b describes several real world situations such as
- Relation between printer and ink cartridges,
- Relationship between number of songs and how much is left on the card.
<u>Step-by-step explanation</u>:
Linear equations y = mx + b.
m is your rate of change.
b is your constant. This is the initial value of y. The value of y when x is 0.
Finally, y is the thing that depends on x.
Oh right, examples:
- I buy a printer for $100 and the ink cartridges cost $25 each. The relationship between ink cartridges and total cost.
total cost = 25(cartridges I buy) + 100 or y = 25x + 100
-
I get a $100 iTunes gift card for my birthday and then start buying $1 songs. The relationship between the number of songs I buy and how much is left on the card
amount left on card = -$1(songs bought) + 100 or y = -x +100
Three to the power of negative four is 81
