We need Pythagoras theorem here
a^2+b^2 = c^2
a, b = legs of a right-triangle
c = length of hypotenuse
Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate]
2S^2+4S = 100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0 means (S+8)=0, S=-8
or (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm
We solve the equation (1/6)x + 14 = (3/4)x, where x is the number of gallons;
We have 2x/12 + 168/12 = 9x/12;
2x + 168 = 9x;
168 = 7x;
x = 168 ÷ 7;
x = 24 gallons;
Answer:
Step-by-step explanation:
The diameter of a circle is twice the radius, so the statement is false.
Answer:
Step-by-step explanation:
2x^2-6x+10=0
2(x^2-3x)+10=0
2(x-(3/2))^2-9/4)+10=0
2(x-(3/2))^2+10-9/2=0
2(x-(3/2))^2+(20-9)/2=0
2(x-(3/2))^2+11/2=0
2(x-(3/2))^2=-11/2
square is always positive so there is no solution
Tan x degrees = 31
To find X use arctan.
x = arctan(31)
x = 88.15
x = 88.2 (rounded to the nearest tenth)
