Answer:
They will have the same amount of sugar in their canisters in 15 days
Step-by-step explanation:
Here in this question, we are concerned with knowing the number of days in which the amount of sugar in both canisters will be the same.
Since we do not know the number of days it will
take, we have to represent it using a variable.
Let the number of days be x days
Now, we are told Li uses 8.4 g per day.
So in x days, the amount user will be 8.4 * x = 8.4x g
Thus, the amount of sugar remaining in her canister after x days will be 128 - 8.4x
For Sue, she uses 12.6 grams each day. So in x days, the amount of sugar used will be 12.6 * x = 12.6x g
So the amount of sugar left in her canister will be 191-12.6x
Since on the xth day , the amount of sugar remaining is same, we can equate the amount of sugar remaining in both canisters. That would be;
128-8.4x =191-12.6x
Collect like terms;
12.6x-8.4x = 191-128
4.2x = 63
x = 63/4.2
x = 15 days
Given the expression:
-x^2+18x-99
to solve by completing squares we proceed as follows:
-x^2+18x-99=0
this can be written as:
-x^2+18x=99
x^2-18x=-99.......i
but
c=(-b/2)²
Hence:
c=(-(-18)/2)²=81
adding 81 in both sides of i we get:
x^2-18x+81=-99+81
factorizing the quadratic we obtain:
(x-9)(x-9)=-18
thus
(x-9)²+18=0
the above takes the vertex form of :
y=(x-k)²+h
where (k,x) is the vertex:
the vertex of our expression is:
(9,18)
hence the maximum point is at (9,18)
NOTE: The vertex gives the maximum point because, from the expression we see that the coefficient of the term that has the highest degree is a negative, and since our polynomial is a quadratic expression then our graph will face down, and this will make the vertex the maximum point.
Answer:
g(x) = |x+3| - 5
Step-by-step explanation:
Let y = f(x)
⇒y = |x+3|
When y is replaced by Y + k, the graph of y = f(x) shifts k units down
⇒ y replaced by Y + 5 translates the graph of y = f(x) 5 units down
∴ Y = g(x) is represented by Y + 5 = |x+3|
⇒ Y = |x+3| - 5
or <u>g(x) = |x+3| - 5</u>
Answer:
$3800
Step-by-step explanation:
When simple interest is added to the principal amount, the sum increases linearly with time. Essentially, you are asked for the y-intercept of a line that goes through the points (2, 6200) and (3, 7400). You can use the 2-point form of the equation of a line to find it:
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (7400 -6200)/(3 -2)(x -2) +6200 . . . . fill in given points
y = 1200(x -2) +6200 . . . . . . . . . simplify some
y = 1200x -2400 +6200 . . . . . . simplify more
y = 1200x +3800 . . . . . . . . . . . . . completely simplify
When the number of years (x) is zero, the amount is 3800. The principal is $3800.
_____
The account is earning $1200 per year on a principal of $3800. The interest rate is about 31.6%, an unusually high value.
_____
<em>Alternate solution</em>
You can recognize that the interest earned in one year is 7400 -6200 = 1200. Since this is simple interest, the amount of interest earned each year is the same, so in 3 years, the account has earned 3×$1200 = $3600 in interest. Then the original principal amount must be ...
$7400 -3600 = $3800 . . . . . principal amount
Answer:
Step-by-step explanation:
The general form of a quadratic polynomial is given by:
(1)
You have the following polynomial:
(2)
In order to complete the factorization you can use the quadratic formula, to obtain the roost of the polynomial. The quadratic formula is given by:
(3)
By comparing the equation (1) with the equation (2) you obtain:
a = 3
b = -10
c = 8
Then, you replace these values in the equation (3):
Then, the factorization of the polynomial is:
