Answer:
1:3
Step-by-step explanation:
The difference of the squares of two distinct positive numbers is equal to twice the square of their difference. What is the ratio of the smaller number to the larger? I'll call the numbers a and b.
a² - b² = 2(a-b)²
a² - b² = 2(a-b)(a-b) First Outside Inside Last (a-b)(a-b)
a² - b² = 2(a²-ab-ab+b²) = 2(a²-2ab+b²) = 2a² - 4ab + 2b²
a² - b² = 2a² - 4ab + 2b² subtract a² - b² from both sides
<u>-a² + b² -a² + b²</u>
0 = a² -4ab +3b² factor into multiplication of two binomials. What factors (two
numbers multiply) to 3 add up to -4? The only two numbers
are -3 and -1.
0 = (a-3b)(a-1b) set each binomial equal to zero and solve
0 = a-3b or 0 = a-1b
<u>+3b +3b</u> or <u>+1b +1b</u>
3b = a or 1b = a
1:3 or 1:1 (but 1:1 says they are the same number, so if there is a smaller number, only 1:3 is correct)
one is an Honors course, while the other is not.
Answer:
12/5
Step-by-step explanation:
Remember SOH CAH TOA
Simplify both sides of the equation
3x+1/10 = x+ -1/7
Subtract x from both sides
3x+1/10 -x = x+ -1/7 -x
2x+1/10 = -1/7
Subtract 1/10 from both sides
2x+1/10 - 1/10 = -1/7 -1/10
2x= -17/70
Divide both sides by 2
2x/2 = -17/70/2
x= -17/140
decimal x will equal -0.121
Ask any questions you want and I hope that's help !
Let's assume the laptop is opened at 90 degrees (this is done for the sake of simplicity, is actually irrelevant) then each plane would be analogous to the 'x' and 'y' planes you see in a Cartesian Plane, which only intersect at one point called the Origin. Any two lines with different slopes will intersect only one time (if they're parallel they have the same slope)
