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3 years ago

If

Mathematics

2 answers:

algol [13]3 years ago

6 0

Answer:

Step-by-step explanation:

We have the two functions:

$f(x)=\sqrt{x}+12\text{ and } g(x)=2\sqrt{x}$

And we want to find (f-g)(144).

This is the same thing to f(144)-g(144).

So, let’s determine the value of f(144) and g(144) first:

$\begin{aligned} f(144)&=\sqrt{144}+12 \\ &=12+12 \\ &=24\end{aligned}$

And:

$\begin{aligned} g(144)&=2\sqrt{144} \\ &=2(12) \\ &=24 \end{aligned}$

Hence:

$\begin{aligned} (f-g)(144) &= f(144)-g(144) \\ &=24-24 \\ &=0 \end{aligned}$

Our final answer is 0.

Natalija [7]3 years ago

6 0

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$(f - g)(x) = \sqrt{x} + 12 - 2 \sqrt{x} \\$

$(f - g)(x) = - \sqrt{x} + 12$

$(f - g)(144) = - \sqrt{144} + 12$

$(f - g)(144) = - \sqrt{ {12}^{2} } + 12$

$(f - g)(144) = - (12) + 12$

$(f - g)(144) = - 12 + 12$

$(f - g)(144) = 0$

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

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What is the sum of the roots of the polynomial shown below? f(x) = x^3 + 2x^2 - 11x-12

svp [43]

Answer:

Sum of the roots of the polynomial $x^{3}+2 x^{2}-11 x-12 \text { is }-2$

Solution:

The general form of cubic polynomial is $a x^{3}+b x^{2}+c x+d=0$ ---- (1)

If we have any cubic polynomial $a x^{3}+b x^{2}+c x+d=0$ having roots $\alpha , \beta , \theta$

Sum of roots $\alpha + \beta + \theta$ = $\frac{-b}{a}$ ---(2)

From question given that,

$x^{3}+2 x^{2}-11 x-12$ --- (3)

On comparing equation (1) and (3), we get a = 1, b = 2, c = -11 and d = -12

Hence the sum of roots using eqn 2 is given as,

= $\frac{-2}{1}$

= -2

Hence the sum of the roots of the polynomial $x^{3}+2 x^{2}-11 x-12 \text { is }-2$

4 0

3 years ago

HELP PLEASE I HAVE A COUPLE MORE! Please help and fast would be great! BRAINLEST!!!

Harlamova29_29 [7]

Answer:

b. slope: -5; y-intercept: 7

Step-by-step explanation:

We are given the equation:

y + 5x = 7

To find the slope and y-intercept of the line, it would be helpful to get the equation into slope-intercept form. The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

Lets get the given equation into slope-intercept form.

y + 5x = 7

Subtract 5x from both sides.

y = -5x + 7

Now we have the equation in slope-intercept form. By looking at the equation, we can see that the slope is -5 and that the y-intercept is 7.

The correct answer choice would be b.

I hope you find my answer and explanation to be helpful. Happy studying.

3 0

3 years ago

If 3x^2 + y^2 = 7 then evaluate d^2y/dx^2 when x = 1 and y = 2. Round your answer to 2 decimal places. Use the hyphen symbol, -,

S_A_V [24]

Taking $y=y(x)$ and differentiating both sides with respect to $x$ yields

$\dfrac{\mathrm d}{\mathrm dx}\bigg[3x^2+y^2\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[7\bigg]\implies 6x+2y\dfrac{\mathrm dy}{\mathrm dx}=0$

Solving for the first derivative, we have

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac{3x}y$

Differentiating again gives

$\dfrac{\mathrm d}{\mathrm dx}\bigg[6x+2y\dfrac{\mathrm dy}{\mathrm dx}\bigg]=\dfrac{\mathrm d}{\mathrm dx}\bigg[0\bigg]\implies 6+2\left(\dfrac{\mathrm dy}{\mathrm dx}\right)^2+2y\dfrac{\mathrm d^2y}{\mathrm dx^2}=0$

Solving for the second derivative, we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}=-\dfrac{3+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}y=-\dfrac{3+\frac{9x^2}{y^2}}y=-\dfrac{3y^2+9x^2}{y^3}$

Now, when $x=1$ and $y=2$ , we have

$\dfrac{\mathrm d^2y}{\mathrm dx^2}\bigg|_{x=1,y=2}=-\dfrac{3\cdot2^2+9\cdot1^2}{2^3}=\dfrac{21}8\approx2.63$

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3 years ago

Question 2: You want to donate 30% of the $400 earned at your yard sale to

lilavasa [31]

Answer:

10%= 40$ 30%=120$

Step-by-step explanation:

ok so u earn 400$ at a yard sale. you divide it by 100 400/100=4. ok so then you multiply four by 10=40 and that is 10% multiply it by 30 u get 120 or 30%

sorry for the bad spelling

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Kipish [7]

Answer:

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Step-by-step explanation: hope this helps

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