The answer to this question is B
Answer:
3 daisies.
Step-by-step explanation:
Given that,
Samantha has 32 roses and 96 daisies.
She wants to make all the arrangements identical and have no flowers left over. We need to find the no of daisies in each flower arrangement.
For this, we need to first find the HCF of 32 and 96.
The factors of 32 are: 1, 2, 4, 8, 16, 32
The factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
HCF = 32
No of daisies = 96/32 = 3
Hence, there are 3 daisies in each flower arrangement.
<h3>
Answer: $2400</h3>
========================================================
Explanation:
x = Mason's salary in dollars for that month
x/6 = one-sixth of his salary
x/6+800 = total amount spent (the x/6 dollars and $800 combined)
In total, he spent half his salary. This means he spent x/2 dollars for the month overall.
Set the two items equal to one another. Solve for x.
x/6 + 800 = x/2
6(x/6 + 800) = 6*(x/2) ... see note at the bottom of the page
x+4800 = 3x
4800 = 3x-x
4800 = 2x
2x = 4800
x = 4800/2
x = 2400
His monthly salary is $2400
1/6 of this is (1/6)*2400 = 2400/6 = 400 dollars. Add on the $800 he also spent to get a total of 400+800 = 1200 dollars spent, which is exactly one half of the $2400. The answer is confirmed.
-------
Note: I multiplied both sides by 6 to clear out the fractions. The value 6 is the LCD in this case.
Part A:

The first step of completing the square is writing the expression

as

which expands to

.
We have the first two terms exactly the same with the function we start with:

and

but we need to add/subtract from the last term, 49, to obtain 41.
So the second step is to subtract -8 from the expression

The function in completing the square form is

Part B:
The vertex is obtained by equating the expression in the bracket from part A to zero


It means the curve has a turning point at x = -7
This vertex is a minimum since the function will make a U-shape.
A quadratic function

can either make U-shape or ∩-shape depends on the value of the constant

that goes with

. When

is (+), the curve is U-shape. When

(-), the curve is ∩-shape
Part C:
The symmetry line of the curve will pass through the vertex, hence the symmetry line is

This function is shown in the diagram below
Answer:
The second choice.
Step-by-step explanation:
The length of AC must be equal to 5, since it is horizontally five units. We can rule out the first option.
Length BC cannot be the square root of 16, since that would be exactly 4 units. BC is slanted and does not represent a completely vertical line, so it is not a whole number. We can rule out the fourth option.
Length AB cannot be a whole number, being a slanted line that crosses a total of more than four units. Option three can be ruled out.
Therefore, we are left with the second option.