2x2 +11x +5
Answer:
(2x + 1)(x + 5)
Step-by-step explanation:
2x² + 11x + 5 =
= 2x² + 10x + x + 5
= 2x(x + 5) + (x + 5)
= (2x + 1)(x + 5)
B. Dilation centered at P, followed by reflection across the y-axis and then the line y = -x + 5
C. Translation (x,y) -> (x+4, y+2), followed by dilation centered at Q
D. Dilation (x+y) -> (3/5x, 3/5y), followed by dilation centered at P
E. Reflection over x-axis followed by rotation of 270 degrees
Answer:
Step-by-step explanation:
Centerat (-1, 2).
Radius of 3.
Center at (3, 4).
Radius of 5.
To carry one circle onto the other, their centers and radius must be the same.
So, circle P must be shifted from (-1, 2) to (3, 4), that means the translation is 4 units to the right side and two units upside, this is the first transformation.
The second transformation must be about stretching the circle P, from a radius of 3 to a radius of 5.
Therefore, the right answer is B.
Answer: Option b and Option c
She will have to get 6 cases of water.
24 and whose fifth term is 1536
or
The common difference, d , in an arithmetic sequence whose fourth
term is 16 and whose seventh term is 31.
Answer:
The common difference d is larger than the common ratio r
Step-by-step explanation:
Geometric sequence
∵ The second term is 24
∴ = 24
∵
- Equate it by its value
∴ ar = 24 ⇒ (1)
∵ The fifth term is 1536
∴ = 1536
∵
- Equate it by its value
∴ = 1536 ⇒ (2)
Divide (2) by (1)
∴
- Divide up and down by ar
∴ r³ = 64
- Take ∛ for both sides
∴ r = 4
Arithmetic sequence
∵ The fourth term is 16
∴ = 16
∵ = a + (4 - 1)d
∴ = a + 3 d
- Equate it by its value
∴ a + 3d = 16 ⇒ (1)
∵ The seventh term is 31
∴ = 31
∵ = a + (7 - 1)d
∴ = a + 6 d
- Equate it by its value
∴ a + 6 d = 31 ⇒ (2)
Subtract equation (1) from equation (2) to eliminate a and find d
∵ (a - a) + (6 d - 3 d) = (31 - 16)
∴ 3 d = 15
- Divide both sides by 3
∴ d = 5
∵ r = 4 and d = 5
∴ d > r
∴ The common difference d is larger than the common ratio r
Answer: Yes, I agree. $10 will be withdrawn every Friday, resulting in the $100 she deposited being completely gone after 10 withdrawals.
Step-by-step explanation: You will want to find the amount of money being taken from the $100 withdrawal first. Turn the percent into a decimal, which should result to 0.10. Take this decimal and multiply it with 100 to get the amount of money being taken out of the account each week, which should be $10. I would go about answering this by multiplying the $10 by the amount of 10 withdrawals. This would result in 100. This answers the question because we are trying to see if 10 withdrawals will completely deplete the $100 in the account.