(a) Answer: One solution.
Explanation: two lines that have same slope with opposite sign will necessarily cross each other at a single point, as one is "pointing uphill" and the other "downhill."
(b) Answer: Infinitely many solutions.
Explanation:
2x + 3y = 5.5
4x + 6y = 11 | divide by 2
-->
2x + 3y = 5.5
2x + 3y = 5.5
--> equations are identical.
2x + 3y = 2x + 3y
so any (x,y) will satisfy this equation. This means infinitely many solutions.
(c) Answer: One solution
Explanation:
Continuing the two lines it becomes obvious they will cross at one point (the solution)
(d) Answer: No solution
Explanation: If the two lines are parallel, they will never cross (by definition of "parallel"). Therefore there will be no solution to the corresponding linear system.
Answer:
x=20
3x= 3(20)=60
4x= 4(20)=80
Step-by-step explanation:
The angles CD is 90 degrees because the small square indicates
it. Angles AD are a straight angle, therefore all the other angles within A to D, must equal 180 degree. (straight line/angle=180 degrees).
so AB + 70+ 90= 180 degrees
AB= 180 -70-90
AB=20
x=20
3x= 3(20)=60
4x= 4(20)=80
The correct answer is Choice B: 720.
To solve this, you have to use the Fundamental Counting Principal. You find the total number of options for each of the digits, then multiply them together.
For the first one, there are 10 options, then 9 options and finally 8 options.
10 x 9 x 8 = 720
Answer:
<h2>$ 22200 in higher yielding bank and $ 44400 in lower yielding bank</h2>
Step-by-step explanation:
Jolene invests in two bank accounts. The first account gives a 4% interest per year and the second bank gives a 10% interest rate per year.
She puts twice as much in the lower yielding bank account. Let us denote the amount put in high yielding bank account by
. Lower yielding bank account will have
.

Interest from lower yielding bank = 
Interest from higher yielding bank = 
Total Interest per year = $ 3996 = 

∴ Jolene invested $ 22200 in higher yielding bank and $ 44400 in lower yielding bank.
Answer:
9 inches
Step-by-step explanation:
Do the question algebraically, represented by this equation:
let x be the shorter piece
x + (x + 8) = 26 (longer piece is 8 units longer)
Remove brackets
x + x + 8 = 26 Combine like terms
2x + 8 = 26 Start isolating "x"
2x + 8 - 8 = 26 - 8 Subtract 8 from both sides
2x = 18
2x/2 = 18/2 Divide both sides by 2
x = 9 shorter piece
The shorter piece would be 9 inches.
If you needed the longer piece too:
longer piece = x + 8
x + 8
= 9 + 8
= 17
The longer piece would be 17 inches.
Check your answer:
Longer + Shorter = 26 Substitute the lengths
17 + 9 = 26 Add
26 = 26 same number
LS = RS left side equals right side
The answer is correct.