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4 years ago

13

Chalene wants to cut her hair but is a little nervous. She decides to cut it off slowly so she can get used to it as it gets sho

rter. Right now, her is is 11.5 inches past her shoulders. She decides to cut an inch and a half off her hair every week. Write an expression to describe the length of her hair in relationship to her shoulders.

2 answers:

Ivahew [28]4 years ago

6 0

11.5x
im actually not 100% sure myself, i have the same homework question

strojnjashka [21]4 years ago

5 0

11.5-1.5v you can use any letter though, not just v.

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Given triangle abc with vertices A(2,-1), B(5,6), C(-1,4) as shown. Find the number of square units in the area of triangle abs

Roman55 [17]

Answer:

The area of the triangle is 18 square units.

Step-by-step explanation:

First, we determine the lengths of segments AB, BC and AC by Pythagorean Theorem:

AB

$AB = \sqrt{(5-2)^{2}+[6-(-1)]^{2}}$

$AB \approx 7.616$

BC

$BC = \sqrt{(-1-5)^{2}+(4-6)^{2}}$

$BC \approx 6.325$

AC

$AC = \sqrt{(-1-2)^{2}+[4-(-1)]^{2}}$

$AC \approx 5.831$

Now we determine the area of the triangle by Heron's formula:

$A = \sqrt{s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC)}$ (1)

$s = \frac{AB+BC + AC}{2}$ (2)

Where:

$A$ - Area of the triangle.

$s$ - Semiparameter.

If we know that $AB \approx 7.616$ , $BC \approx 6.325$ and $AC \approx 5.831$ , then the area of the triangle is:

$s \approx 9.886$

$A = 18$

The area of the triangle is 18 square units.

7 0

3 years ago

Identify the graph of xy=-8 for theta=pi/4 and write and equation of the translated or rotated graph in general form.

eduard

Answer:

B

Step-by-step explanation:

I hope this helps!

4 0

3 years ago

Read 2 more answers

Which of the following is the solution set of x² + 8x + 12 = 0?

raketka [301]

Answer:

$\fbox{\begin{minipage}{9em}x = -2 and x = -6\end{minipage}}$

Step-by-step explanation:

Given:

$x^{2} + 8x + 12 = 0$

Solve for:

$x$

Solution:

Step 1: Select the formula to solve for $x$

There are some ways to solve quadratic equations.

One of the simple way (if possible) is performing the factorization.

Another way is using the quadratic formula.

Here, we are going to use factorization.

Step 2: Perform factorization

$x^{2} + 8x + 12 = 0$

<=> $x^{2} + 2x + 6x + 12 = 0$

<=> $(x^{2} + 2x) + (6x + 12) = 0$

<=> $x(x + 2) + 6(x + 2) = 0$

<=> $(x + 2)(x + 6) = 0$

<=> $x = -2$ or $x = -6$

Hope this helps!

:)

4 0

3 years ago

Let p: x < −3<br> Let q: x > 3<br><br> What is represented by p ∨ q?

I am Lyosha [343]

Amphitrite1040Answer:

Amphitrite1040

Step-by-step explanation:

7 0

3 years ago

Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

8 0

3 years ago