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3 years ago

If f(x)=3x^2+1 and g(x)=1-x, what is the value of (f-g)(2)?

Mathematics

2 answers:

Sav [38]3 years ago

6 0

Answer:

$(f-g)(2)=28$

Step-by-step explanation:

Given:

$f(x)=3x^2+1$

$g(x)= 1-x$

To find the equivalent expression of $(f-g)(2)$ .

$(f-g)(2) = f(2) - g(2)$

Find g(x)

$g(x)=1-x$

Sub x for 2

$g(2)=1-2$

$g(2)=-1$

Find f(x)

$f(x)=3x^2+1$

Sub x for 2

$f(2)=3(2)^2+1$

$f(2)=12+1$

$f(2)=13$

Solve for the giving value

$(f-g)(2)$

$(13- (-1)) (2)$

$14(2)$

stepladder [879]3 years ago

3 0

The answer should be 14.

You just have to substitute x with the given number and finish the equation.

You might be interested in

What is 2/3 x (9+12)

GalinKa [24]

2/3 x (9+12) is 14. Hope it helps :)

3 0

3 years ago

The force of gravity on Mars is different than on Earth. The function of the same situation on Mars would be represented by the

sweet-ann [11.9K]

Answer:

If thrown up with the same speed, the ball will go highest in Mars, and also it would take the ball longest to reach the maximum and as well to return to the ground.

Step-by-step explanation:

Keep in mind that the gravity on Mars; surface is less (about just 38%) of the acceleration of gravity on Earth's surface. Then when we use the kinematic formulas:

$v=v_0+a\,*\,t\\y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2$

the acceleration (which by the way is a negative number since acts opposite the initial velocity and displacement when we throw an object up on either planet.

Therefore, throwing the ball straight up makes the time for when the object stops going up and starts coming down (at the maximum height the object gets) the following:

$v=v_0+a\,*\,t\\0=v_0-g\,*\,t\\t=\frac{v_0}{t}$

When we use this to replace the 't" in the displacement formula, we et:

$y-y_0=v_0\,* t + \frac{1}{2} a\,\,t^2\\y-y_0=v_0\,(\frac{v_0}{g} )-\frac{g}{2} \,(\frac{v_0}{g} )^2\\y-y_0=\frac{1}{2} \frac{v_0^2}{g}$

This tells us that the smaller the value of "g", the highest the ball will go (g is in the denominator so a small value makes the quotient larger)

And we can also answer the question about time, since given the same initial velocity $v_0$ , the smaller the value of "g", the larger the value for the time to reach the maximum, and similarly to reach the ground when coming back down, since the acceleration is smaller (will take longer in Mars to cover the same distance)

3 0

2 years ago

Lucy wants to be exempt from her semester exam. In order for that to happen, she has to average an 85 over 3 test grades. Her fi

anastassius [24]

Answer:

<em>Grades to be scored in 3rd exam = 88</em>

Step-by-step explanation:

Given that average of 3 numbers is 85.

First two numbers are 81 and 86.

To find:

3rd number so that average is 85

Solution:

Let the third number = $x$

Formula for average is:

$Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}$

Here, sum of numbers = $81+86+x =167+x$

Total count of numbers = 3

$85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}$

<em>Grades to be scored in 3rd exam = 88</em>

8 0

3 years ago

Write an equation of the line through each pair of points in slope-intercept form.

ASHA 777 [7]

Answer:

see below

Step-by-step explanation:

a) (– 3, –2) and (–3, 4)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(4 - (-2) / (-3 - (-3))

Simplify the parentheses.

= (4 + 2) / (-3 + 3)

Simplify the fraction.

(6) / (0)

= undefined

If your slope is undefined, it is a vertical line. The equation of a vertical line is x = #.

In this case, the x-coordinate for both points is -3.

Therefore, your equation is x = -3.

b) (3, 2) and (–4, –5)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(-5 - 2) / (-4 - 3)

Simplify the parentheses.

= (-7) / (-7)

Simplify the fraction.

-7/-7

= 1

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the first point (3, 2). Plug in the x and y values into the x and y of the standard equation.

2 = 1(3) + b

To find b, multiply the slope and the input of x(3)

2 = 3 + b

Now, subtract 3 from both sides to isolate b.

-1 = b

Plug this into your standard equation.

y = x - 1

This is your equation.

Check this by plugging in the other point you have not checked yet (-4, -5).

y = 1x - 1

-5 = 1(-4) - 1

-5 = -4 - 1

-5 = -5

Your equation is correct.

Hope this helps!

7 0

3 years ago

What is the answer to #3?

FrozenT [24]

I think it’s 2 but I’m not sure

5 0

3 years ago