MATHEMATICS COLLEGE

Help pls with answer!!!Rewrite the function in the given form.

Answers

Answer 1

Answer:

Answer:

$g(x) = (-2)/(x-1)+5\n\n$

The graph is shown below.

=========================================================

Explanation:

Notice that if we multiplied the denominator (x-1) by 5, then we get 5(x-1) = 5x-5.

This is close to 5x-7, except we're off by 2 units.

In other words,

5x-7 = (5x-5)-2

since -7 = -5-2

Based on that, we can then say,

$g(x) = (5x-7)/(x-1)\n\ng(x) = (5x-5-2)/(x-1)\n\ng(x) = ((5x-5)-2)/(x-1)\n\ng(x) = (5(x-1)-2)/(x-1)\n\ng(x) = (5(x-1))/(x-1)+(-2)/(x-1)\n\ng(x) = 5+(-2)/(x-1)\n\ng(x) = (-2)/(x-1)+5$

This answer can be reached through alternative methods of polynomial long division or synthetic division (two related yet slightly different methods).

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

Compare the equation $g(x) = (-2)/(x-1)+5\n\n$ to the form $g(x) = (a)/(x-h)+k\n\n$

We can see that

a = -2
h = 1
k = 5

The vertical asymptote is x = 1, which is directly from the h = 1 value. If we tried plugging x = 1 into g(x), then we'll get a division by zero error. So this is why the vertical asymptote is located here.

The horizontal asymptote is y = 5, which is directly tied to the k = 5 value. As x gets infinitely large, then y = g(x) slowly approaches y = 5. We never actually arrive to this exact y value. Try plugging in g(x) = 5 and solving for x. You'll find that no solution for x exists.

The point (h,k) is the intersection of the horizontal and vertical asymptote. It's effectively the "center" of the hyperbola, so to speak.

The graph is shown below. Some points of interest on the hyperbola are

(-1,6)
(0,7) .... y intercept
(1.4, 0) .... x intercept
(2, 3)
(3, 4)

Another thing to notice is that this function is always increasing. This means as we move from left to right, the function curve goes uphill.

Related Questions

What is the quotient of 10?
Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.y = e^x^2 ln 4x^3
State if the two triangles are congruent. If they are, state how you know.1) SSS2) SAS3) ASA4) AAS5) NOT CONGRUENTPic is up right answer = brainliest
What is The greatest common factor of 42 and 96 I’ll give you brainliest
The parabola y=x2 is scaled vertically by a factor of 7. What if the equation of the new parabola

Sanjay attempts a 49-yard field goal in a football game. For his attempt to be a success, the football needs to pass through the uprights and over the crossbar that is 10 feet above the ground.Sanjay kicks the ball from the ground with an initial velocity of 73 feet per second, at an angle of 34° with the horizontal.

What is true of Sanjay's attempt?

Responses

The kick is not successful. The ball is approximately 5 feet too low.

The kick is not successful. The ball is approximately 8 feet too low.

The kick is not successful. The ball is approximately 2 feet too low

The kick is good! The football clears the crossbar by approximately 5 feet.

Answers

In the above prompt involving a trajectory calculation, the correct option is: "The kick is not successful. The ball is approximately 5 feet too low." (Option A)

What is the rationale for the above response?

x component of trajectory = 73 cos 34 f/s

Now how long will it take to travel 49 yards (= 147 feet) ?

147 / (73 cos 34) = 2.43 seconds

Initial y component of trajectory = 73 sin 34 f/s = 40.82 f/s

but this velocity is acted upon by gravity

y = y0 + vot - 1/2 a t^2

y0 = 0

Now we need to know the y value at 2.43 seconds to see if it will clear the uprights.

y = 40.82 (2.43) - 1/2 (32.174)(2.43)2

= 4.2 Feet
Thus, it is correct to state that the "The kick is not successful. The ball is approximately 5 feet too low."

Learn more about Trajectory:
brainly.com/question/28164318
#SPJ1

A man flies a small airplane from Fargo to Bismarck, North Dakota --- a distance of 180 miles. Because he is flying into a head wind, the trip takes him 2 hours. On the way back, the wind is still blowing at the same speed, so the return trip takes only .9 hours. What is the plane's speed in still air, and how fast is the wind blowing?

Answers

Answer:

90 mi/h

Step-by-step explanation:

Calculate speed, distance, or time using the formula d = st, distance equals speed times time. The Speed Distance Time Calculator can solve for the unknown sdt value given two known values.

Time can be entered or solved for in units of seconds (s), minutes (min), hours (hr), or hours and minutes and seconds (hh:mm:ss).

To solve for distance use the formula for distance d = st, or distance equals speed times time.

distance = speed x time

Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour. If rate r is the same as speed s, r = s = d/t. You can use the equivalent formula d = rt which means distance equals rate times time.

distance = rate x time

To solve for speed or rate use the formula for speed, s = d/t which means speed equals distance divided by time.

speed = distance/time

To solve for time use the formula for time, t = d/s which means time equals distance divided by speed.

time = distance/speed

Plane speed in still air: 120mph

Wind speed: 30pmh

Speed of plane to Bismarck: 90mph

Speed of plane to Fargo: 150mph

A truck weighs 16,000 pounds. What is the weight range in tons?

Answers

Answer:

Step-by-step explanation:

uh idrk all ik is that 16,000 punds = 8 tons

8
16,000 pounds equals 8 tons

Catherine's employer matches 25% of her 401(k) contributions — up to $2000. Catherine's salary is $50,000, and last year she contributed $10,000 to her 401(k) plan. What was her employer's contribution to the 401(k)?

Answers

We have been given that Catherine's employer matches 25% of her 401(k) contributions or a maximum of $2000. Further we are given that Catherine's salary is $50,000 and she contributed $10,000 to her 401(k) plan.

Let the contribution form her employer be $x. We are given that her employer matches 25% of Catherine's contribution under 401(k) plan. Therefore, contribution made by employer would be either 25% of 10,000 or 2000, whichever is lesser.

Let us find 25% of 10,000.

$25\% \text{ of 10000 } = 10,000 * (25)/(100) = \$2500$

Since 25% of 10,000 is more than 2000, therefore, Catherine's employer would make a contribution of $2000.

25% of $10,000 is $2,500

But because they only match "up to $2,000," her employers contribution was $2,000

Need help pleaseeee!

Answers

Answer:

I don't know the answer but I know the formula. Its I=prt

Step-by-step explanation:

Intrerest= principle amount, rate, and time.

Hope this helps!! :)

A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and standard deviation 7 ml. The fillvolumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL?
1.0000
0.8810
0.8413
0.9987

Answers

The required probability that a bottle has a volume greater than 992 mL is 0.84134. Option C is correct

Given that,
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (ml) and a standard deviation of 7 ml. The fill volumes are normally distributed. What is the probability that a bottle has a volume greater than 992 mL, is to be determined