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3 years ago

Simplify the expression

Mathematics

2 answers:

hjlf3 years ago

8 0

Hi, I took a while

The answer is c Have a good day

Sergeu [11.5K]3 years ago

7 0

Would be the answer

I had to do this 3x b/c I do virtual school and figured it, out the hard way of course

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What is the initial value, and what does it represent?

inn [45]

Answer:

A. The initial value is 100; it represents money left over from last year's fundraiser

Step-by-step explanation:

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3 years ago

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Show that every triangle formed by the coordinate axes and a tangent line to y = 1/x ( for x > 0)

vfiekz [6]

Answer:

Step-by-step explanation:

given a point $(x_0,y_0)$ the equation of a line with slope m that passes through the given point is

$y-y_0 = m(x-x_0)$ or equivalently

$y = mx+(y_0-mx_0)$ .

Recall that a line of the form $y=mx+b$ , the y intercept is b and the x intercept is $\frac{-b}{m}$ .

So, in our case, the y intercept is $(y_0-mx_0)$ and the x intercept is $\frac{mx_0-y_0}{m}$ .

In our case, we know that the line is tangent to the graph of 1/x. So consider a point over the graph $(x_0,\frac{1}{x_0})$ . Which means that $y_0=\frac{1}{x_0}$

The slope of the tangent line is given by the derivative of the function evaluated at $x_0$ . Using the properties of derivatives, we get

$y' = \frac{-1}{x^2}$ . So evaluated at $x_0$ we get $m = \frac{-1}{x_0^2}$

Replacing the values in our previous findings we get that the y intercept is

$(y_0-mx_0) = (\frac{1}{x_0}-(\frac{-1}{x_0^2}x_0)) = \frac{2}{x_0}$

The x intercept is

$\frac{mx_0-y_0}{m} = \frac{\frac{-1}{x_0^2}x_0-\frac{1}{x_0}}{\frac{-1}{x_0^2}} = 2x_0$

The triangle in consideration has height $\frac{2}{x_0}$ and base $2x_0$ . So the area is

$\frac{1}{2}\frac{2}{x_0}\cdot 2x_0=2$

So regardless of the point we take on the graph, the area of the triangle is always 2.

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3 years ago

Cone A has a radius of 2 inches and a height of 3 inches. In cone B, the height is the same, but the radius is doubled. Calculat

wlad13 [49]

Answer: Option C.

Step-by-step explanation:

Use the formula for calculate the volume of a cone:

$V=\frac{1}{3}\pi r^2h$

Where r is the radius and h is the height.

Volume of the cone A:

$V_A=\frac{1}{3}\pi (2in)^2(3in)=12.56in^3$

Volume of the cone B:

If the height of the cone B and the height of the cone A are the same , but the radius of the cone B is doubled, then its radius is:

$r_B=2r_A\\r_B=2*2in\\r_B=4in$

Then:

$V_B=\frac{1}{3}\pi (4in)^2(3in)=50.26in^3$

Divide $V_B$ by $V_A$ :

$\frac{V_B}{V_A}=\frac{50.26in^3}{12.56in^3}=4$

Therefore: When the radius is doubled, the resulting volume is 4 times that of the original cone.

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3 years ago

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Help!! <br>2x+3 (x-4)=x-20

prohojiy [21]

Remember you can do anything to an equation as long as you do it to both sides

2x+3(x-4)=x-20
first distribute
2x+3(x)+3(-4)=x-20
2x+3x-12=x-20
5x-12=x-20
minus x both sides
4x-12=-20
add 12 to both sides
4x=-8
divide both sides by 4
x=-2

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3 years ago

What must be a factor of the polynomial function f(x) graphed on the coordinate plane below?

vesna_86 [32]

Answer:

x+2

Step-by-step explanation:

we know that

To find out the factors of a polynomial, determine the x-intercepts or zeros of the polynomial

Remember that

The x-intercepts of a polynomial are the values of x when the value of the polynomial is equal to zero

In this problem

Looking at the graph

For x=-2, f(x)=0

x=-2 is an x-intercept or zero of the polynomial

To find out the factor move the constant to the left side and equate to zero

$x=-2$

adds 2 both sides

$x+2=-2+2\\x+2=0$

therefore

The factor is (x+2)

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3 years ago

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