Looking at the equation, you could see that it is in vertex form. Vertex form looks like this: y=a(x-h)^2+k where a is the slope to find the first point away from the origin and (h,k) is the vertex. So, the vertex is (3,-1). The first point away from the origin is up two, over one, so the slope is 2. This means that a is 2. One way you could check this is by putting 2 in for a. If you put it into standard form, it would be 2x^2-12x+17. To find the x in the vertex when the equation is in standard form we use -b/2a. So it would give us 3 for x. If we put in 3 for x, we get -1 for y, so the vertex is (3,-1). This means that a is 2. Sorry for this lengthy answer, hope it helps.
Answer:
g(x) = 2x + 2
Step-by-step explanation:
f(x) = 6x
g(x)= 1/3*f(x) + 2
g(x) = 2x + 2
Answer:
8 and 9
Step-by-step explanation:
Let the two consecutive integers be x - 1 and x
Smaller = x-1
Largere = x
If the square of the smaller integer is nineteen more than five times the larger integer, then;
(x-1)² = 19 + 5x
Expand
x²-2x+1= 19+5x
x²-2x-5x+1-19 -0
x²-7x-18 =0
Factorize
x²-9x+2x-18 =0
x(x-9)+2(x-9) = 0
(x+2) = 0 and x - 9 = 0
x = -2 and 9
SInce x cannot be negative;
x = 9
Smaller number = 9-1
Smaller number = 8
Hence the two consecutive integers are 8 and 9
The equation t = 10.5(c + a) represents the total money earned by the company from the sale of tickets
<u>Solution:</u>
Given that,
Ticket charged for people of all age groups = $ 10.50 per ticket
Let "c" represents the total number of children who bought tickets
Let "a" represents the total number of adults who bought tickets
Now, let the total money collect be represented by "t"
Number of people bought tickets = number of children bought tickets + number of adults bought tickets
<em><u>Now the total money earned by company is given as:</u></em>
Total money earned = cost per ticket x number of people bought tickets
Total money collected = cost per ticket x (number of children bought tickets + number of adults bought tickets)
Substituting the known values we get,
t = 10.5(c + a)
Hence, the required equation is t = 10.5(c + a)
Answer:
123
304
314
Step-by-step explanation:
38, 79, 84 in base 10 to base 5
5 __ 38
5 __7 r 3
5 __1 r 2
___0 r 1
From bottom to top
38 base 10 = 123 base 5
2.)
5 __ 79
5 __15 r 4
5 __3 r 0
___0 r 3
From bottom to top
38 base 10 = 304 base 5
3.)
5 __ 84
5 __16 r 4
5 __ 3 r 1
____ 0 r 3
From bottom to top
38 base 10 = 314 base 5
