Line 1:
Expanding the vertex form, we have
x² + 2·1.5x + 1.5² - 0.25 = x² +3x +2
Expanding the factored form, we have
x² +(1+2)x +1·2 = x² +3x +2
Comparing these to x² +3x +2, we find ...
• the three expressions are equivalent on Line 1
Line 2:
Expanding the vertex form, we have
x² +2·2.5x +2.5² +6.25 = x² +5x +12.5
Expanding the factored form, we have
x² +(2+3)x +2·3 = x² +5x +6
Comparing these to x² +5x +6, we find ...
• the three expressions are NOT equivalent on Line 2
The appropriate choice is
Line 1 only
Answer:
I can't seem to solve these but hope this information helps :)
Step-by-step explanation:
Remove any grouping symbol such as brackets and parentheses by multiplying factors.
Use the exponent rule to remove grouping if the terms are containing exponents.
Combine the like terms by addition or subtraction.
Combine the constants.
Answer:
56
Step-by-step explanation:
Keep the order of opperations in mind when doing this (PEMDAS). First, solve what is inside the parentheses (6-1). Then, solve the exponent and the multiplication (6² and 5×5). Finally, finish adding and subtracting to get the answer.
1, a.) The two specific conjectures are in the first image.
1, b.) The two general conjectures are in the second image.
2, a.) Two specific conjectures for this pattern are:
- The common difference between two consecutive terms is 3.
- And the given difference is A.P.
2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.
For finding its nth term we can use the formula: a(n) = a + (n-1) x d.
2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.
Combine like terms
8x+24=x+5
subtract x from both sides
8x+24=x+5
-x -x
7x+24=5
subtract 24 from both sides
7x+24=5
-24 -24
7x = -19
divide 7 from both sides
7x = -19
7x/7 = -19/7
x= -19/7
