MATHEMATICS HIGH SCHOOL

The graph below shows the distance, y, in feet, of a mouse from its hole, for a certain amount of time, x, in minutes:Graph titled Distance Vs Time is shown with Time in minutes along the x-axis and Distance from Hole in feet along the y-axis. The scale on the x-axis shows the numbers 0 to 45 at increments of 9, and the scale on the y-axis shows the numbers 3 to 24 at increments of 3. A straight line joins the ordered pairs 0, 9 and 9, 12 and 18, 15 and 27, 18 and 36, 21.

Based on the graph, what is the initial value of the graph and what does it represent?

0.23 foot per minute; it represents the speed of the mouse
9 feet; it represents the original distance of the mouse from its hole
0.23 foot; it represents the original distance of the mouse from its hole
9 feet per minute; it represents the speed of the mouse

Answers

Answer 1

Answer:

Answer:

The initial value is (0,9).

Hence option B is correct.

Step-by-step explanation:

Based on the graph, the initial value of the graph is (0,9)

where x=0 and y=9

where for the coordinate (x,y) ; x represents the time in minutes and y denotes the distance of the mouse from the hole in feet.

That means initially(i.e. at time t=0) the mouse is 9 feet away from the hole.

Hence the answer is 9 feet; it represents the original distance of the mouse from its hole.

Hence option B is correct.

Answer 2

Answer: Based on the graph, what is the initial value of the graph and what does it represent 0.23 foot; it represents the original distance of the mouse from its hole

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What is the inverse of the function f(x) = 4x + 8?h(x) = x – 2
h(x) = x + 2
h(x) = x – 2
h(x) = x + 2

Answers

we have

$f(x)=4x+8$

Step 1

Let

$y=f(x)$

$y=4x+8$

Step 2

exchanges the variable x for y and the variable y for x

$x=4y+8$

Step 3

Isolate the variable y

$4y=x-8$

$y=(1)/(4)x-2$

Step 4

Let

$h^(-1)(x)=y$

$h^(-1)(x)=(1)/(4)x-2$ ------> the inverse function

therefore

the answer is

$h^(-1)(x)=(1)/(4)x-2$

Final answer:

The inverse of the function f(x) = 4x + 8 is h(x) = (x - 8) / 4.

Explanation:

The inverse of the function f(x) = 4x + 8 can be found by switching the x and y variables and solving for y. So, we have:

x = 4y + 8

Now, we rearrange the equation to isolate y:

x - 8 = 4y

y = (x - 8) / 4

Therefore, the inverse function is h(x) = (x - 8) / 4.

What is the 9th term in the addition pattern with formula 7n – 3? A.13

B.42

C.60

D.76

Answers

replace n with 9 :
7 × 9 - 3 = 60
the answer is C.60

What is the number in the following sequence 101,112,131,415,161

Answers

The sequence is not geometric or arithmetic because there is no common difference or common ratio between each term.

101,112,131,415,161,718... Is basically formed using the 2 digit numbers 10,11,12,13,14,15,16,17,18...(placement of commas is different there) So the next two numbers will be formed using 19,20 & 21
Thus next three numbers are 718 & 192 & 021

What is the 4th tearm to this?
b(n)=4−6(n−1)

Answers

Answer:

If you wish to find any term (also known as the {n^{th}}n

term) in the arithmetic sequence, the arithmetic sequence formula should help you to do so. The critical step is to be able to identify or extract known values from the problem that will eventually be substituted into the formula itself.

Step-by-step explanation:

The function f(x) = –2(x – 10)(x – 200) represents a company's monthly profit as a function of the number of items sold, x. What is the maximum monthly profit?

Answers

expand
f(x)=-2x^2+420x-4000
in form
f(x)=ax^2+bx+c
vertex (highest or lowest point, depending on graph)
vertex is -b/2a that is the x value
to find the profit, plug that x value back in

f(x)=-2x^2+420x-4000
-b/2a=-420/(2)(-2)=-420/-4=105

x min valu is 105
input to find profit
f(105)=-2(105-10)(105-200)
f(105)=-2(95)(-95)
f(105)=18050

max profit is $18050

Answer:

$18050 Is your answer

Step-by-step explanation:

Two men decide to drive to a distant town, taking the same route. The first leaves 2 hours ahead of the second and drives at 60 km per hour, while the second man drives at 90 km per hour. How many hours will it take the second man to catch up with the first man?