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3 years ago

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At summer camp, the duration of a basketball game is 3/4 of an hour. The camp counsellors have set aside 6 hours for basketball

games. They need to determine how many games can be played. James and Raquel both attempted to solve the problem and their work is shown below.
Problem: 6 dived by 3/4

Question 1
POSSIBLE POINTS: 5
Select the camp counselor that correctly solved the problem.

James

Raquel

Question 2
POSSIBLE POINTS: 5
Identify and describe the error in the incorrect counsellor's work. :

2 answers:

guapka [62]3 years ago

8 0

It’s raquel. hope that helped

Pavel [41]3 years ago

3 0

I do believe the answer would be Raquel

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Find the equation of the line of symmetry of y= (x+2)(x-8).

Daniel [21]

Answer:

line of symmetry , x = 3

Step-by-step explanation:

Standard form of quadratic equation is y = ax^2 + bx + c, where a, b, and c equal all real numbers. You can use the formula x = -b / 2a to find the line of symmetry.

$y = (x+ 2)(x-8)\\\\y = (x^2 -8x + 2x -16)\\\\y = x^2 -6x -16$

a = 1, b = -6, c = -16

Line of symmetry is ,

$x = -\frac{b}{2a} = -\frac{-6}{2} = 3$

4 0

3 years ago

H(x)= ⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ 8+6x x+4 10 4x−3 , , , x<−7 −7≤x<−5 x≥−5

motikmotik

Answer:

$h(-6) = -\frac{1}{5}$

Step-by-step explanation:

Given

$h(x) =\left[\begin{array}{cc}8 + 6x\ \ &x < -7\\\frac{x + 4}{10} &-7 \le x$

Required

Determine h(-6)

To do this, we make use of:

$h(x) = \frac{x + 4}{10}$

Because $-7 \le -6$

So, we have:

$h(x) = \frac{x + 4}{10}$

$h(-6) = \frac{-6 + 4}{10}$

$h(-6) = \frac{-2}{10}$

Simplify

$h(-6) = -\frac{1}{5}$

4 0

3 years ago

Simplify the following expression:<br> 9^−53 ⋅ 9^37<br><br> Please also explain your answer. Thanks!

Alexus [3.1K]

Answer: 9^-16

Step-by-step explanation:

a^b*a^c= a^b+c

8 0

3 years ago

What is the slope Of a line that passes through the points (9,8) and (2,3)?

tresset_1 [31]

$(\stackrel{x_1}{9}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{9}}}\implies \cfrac{-5}{-7}\implies \cfrac{5}{7}$

6 0

3 years ago

Read 2 more answers

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago