All categories

2 years ago

Given the values of the linear functions f (x) and g(x) in the tables, where is (f – g)(x) positive?

Mathematics

1 answer:

alexandr402 [8]2 years ago

4 0

Comparing the functions, from the tables, it is found that (f - g)(x) is positive in the interval (–∞, 9) .

----------------------

For the subtraction function, we simply subtract both functions, thus:

$(f - g)(x) = f(x) - g(x)$

It is positive if f is greater than g, that is: f(x) > g(x).
It is a linear function, so one function is greater before the equality, one after.
They are equal at x = 9.
If x < 9, f(x) > g(x), and thus, (f - g)(x) is positive, which means that the desired interval is:

(–∞, 9)

A similar problem is given at brainly.com/question/24610273

You might be interested in

John has $4000 in his savings account.each month he withdraws $70 from his account which is the type of function that models thi

r-ruslan [8.4K]

Answer:

y = 4000 - 70x

Linear function.

Step-by-step explanation:

Let x = number of weeks.

In 1 week, he withdraws $70.

That means -70 in 1 week.

After the second week, he will have withdrawn 2 times $70, or

-70 × 2

After 3 week, he will have withdrawn -70 × 3

After x weeks, he will have withdrawn $70 × x,or simply -70x.

He starts with 4000, so after x weeks, he has 4000 - 7x.

Let y = the amount of money at week x.

The equation is

y = 4000 - 70x

This is a linear function.

6 0

2 years ago

On Mars the acceleration due to gravity is 12 ft/sec^2. (On Earth, gravity is much stronger at 32 ft/sec^2.) In the movie, John

insens350 [35]

Solution :

Given initial velocity, v= 48 ft/s

Acceleration due to gravity, g = $12\ ft/s^2$

a). Therefore the maximum height he can jump on Mars is

$H_{max}=\frac{v^2}{2g}$

$H_{max} = \frac{(48)^2}{2 \times 12}$

= 96 ft

b). Time he can stay in the air before hitting the ground is

$T=\frac{2v}{g}$

$T=\frac{2 \times 48}{12}$

= 8 seconds

c). Considering upward motion as positive direction.

v = u + at

We find the time taken to reach the maximum height by taking v = 0.

v = u + at

0 = 16 + (12) t

$t=\frac{16}{12}$

$=\frac{4}{3} \ s$

We know that, $S=ut + \frac{1}{2}at^2$

Taking t = $=\frac{4}{3} \ s$ , we get

$S=16 \times\frac{4}{3} + \frac{1}{2}\times(-12) \times \left(\frac{4}{3}\right)^2$

$S=\frac{32}{3}$ feet

Thus he can't reach to 100 ft as it is shown in the movie.

d). For any jump whose final landing position will be same of the take off level, the final velocity will be the initial velocity.

Therefore final velocity is = -16 ft/s

3 0

2 years ago

An oil painting has a price of

Debora [2.8K]

Answer:

i think it $3.20

Step-by-step explanation:i think you got to check it in caculator

3 0

3 years ago

You need to wrap a present that you will put inside a cylindrical container. You’ll need to know how much will fit in the conta

nirvana33 [79]

Answer:

149.28 sq. inches

137.5 cubic inches.

Step-by-step explanation:

The cylindrical container has length or height (h) 7 inches and has a diameter of 5 inches i.e. radius (r) 2.5 inches.

Now, total surface area of the container = $2\pi r^{2} + 2\pi rh$

= $\frac{2 \times 22 \times (2.5)^{2} }{7} + \frac{2 \times 22 \times 2.5 \times 7}{7}$

= 39.28 + 110

= 149.28 sq. inches (Answer)

Again the volume of the container will be $\pi r^{2}h$

= $\frac{22 \times (2.5)^{2} \times 7}{7}$

= 137.5 cubic inches. (Answer)

6 0

3 years ago

- Find the mean, median, mode, and range of the<br> data set.<br> {7, 3, 5, 4, 5}

noname [10]

Answer:

The range is 2

Step-by-step explanation:

The median is 5. The mode is 5. The mean is 5.

6 0

2 years ago