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SOVA2 [1]
3 years ago
15

The first angle of a triangle is 13 degrees more than the second angle the third angle of a triangle is 2 times the second angle

use x to represent the unknown value write an algebraic expression for each of the quantities being compared what is the first angle the second angle and the third angle
Mathematics
1 answer:
MissTica3 years ago
5 0
<span>Second angle = x
First angle = 2x
Third angle = x + 68
x + 2x + (x + 68) = 180
4x + 68 = 180
4x = 112

x = 28.
First angle = 56 degrees
Second angle = 28 degrees
Third angle = 96 degrees
Total = 180 degrees.</span>
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6 0
4 years ago
A rectangle has a perimeter of 30 feet and an area of 50 square feet. What are the dimensions of the rectangle?
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Perimeter (p) = 2×length (l) + 2×width (w)
p = 2l+2w
area (a) = l×w, so solve for one (I'll use l):
a = l \times w \\ l =  a \div w \\ p = 2l + 2w = 2(l + w)
since p = 30, and a = 50, substitute the "a÷w" in for l in the perimeter equation:
p = 2(l + w) = 2((a \div w) + w) \\  = 2((a \div w) + ( {w}^{2} \div w)) \\  p= 2((a +  {w}^{2}) \div w
Now plug in p and a values:
p= 2((a +  {w}^{2}) \div w) \\ 30 = 2((50 +  {w}^{2}) \div w)  \\ 30 \div 2 = (50 +  {w}^{2}) \div w \\ 15w = 50 +  {w}^{2}
15w = 50 +  {w}^{2}  \\  {w}^{2}  - 15w + 50 = 0 \\ (w - 5)(w - 10) = 0
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