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3 years ago

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Jordan received 30 text messages from his friends and 18 text messages from his parents. Write the radio that compares the numbe

r of text messages from his friends to the number of text messages from his parents.

1 answer:

maksim [4K]3 years ago

6 0

Answer:

The answer is 5:3 if I'm correct

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Find all solutions of the equation: 2cos^2x-cosx=1

Art [367]

If you're using the app, try seeing this answer through your browser: brainly.com/question/3166243

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Solve the trigonometric equation:

$\mathsf{2\,cos^2\,x-cos\,x=1}\\\\ \mathsf{2\,cos^2\,x-cos\,x-1=0}$

Make a substitution:

$\mathsf{cos\,x=t\qquad (-1\le t\le 1)}$

and the equation becomes

$\mathsf{2t^2-t-1=0}$

Rewrite conveniently – t as + t – 2t, and then factor the left-hand side by grouping:

$\mathsf{2t^2+t-2t-1=0}\\\\ \mathsf{t\cdot (2t+1)-1\cdot (2t+1)=0}$

Factor out 2t + 1:

$\mathsf{(2t+1)\cdot (t-1)=0}\\\\ \begin{array}{rcl} \mathsf{2t+1=0}&~\textsf{ or }~&\mathsf{t-1=0}\\\\ \mathsf{2t=1}&~\textsf{ or }~&\mathsf{t=1}\\\\ \mathsf{t=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{t=1} \end{array}$

Substitute back for t = cos x:

$\begin{array}{rcl}\mathsf{cos\,x=\dfrac{\,1\,}{2}}&~\textsf{ or }~&\mathsf{cos\,x=1}\\\\ \mathsf{cos\,x=cos\,60^\circ}&~\textsf{ or }~&\mathsf{cos\,x=cos\,0} \end{array}$

Therefore,

$\begin{array}{rcl} \mathsf{x=\pm\,60^\circ+k\cdot 360^\circ}&~\textsf{ or }~&\mathsf{cos\,x=0+k\cdot 360^\circ} \end{array}$

where k is an integer.

Solution set:

$\mathsf{S=\left\{x\in\mathbb{R}:~~x=-\,60^\circ+k\cdot 360^\circ~~or~~x=60^\circ+k\cdot 360^\circ~~or~~x=k\cdot 360^\circ,~~k\in\mathbb{Z}\right\}}$

I hope this helps. =)

3 0

3 years ago

How to simplify this expression

dexar [7]

Answer:

$\dfrac{x+2}{x+1}$

Step-by-step explanation:

Factor the numerator and cancel common factors from numerator and denominator.

$\dfrac{x^2-4}{(x-2)(x+1)}=\dfrac{(x-2)(x+2)}{(x-2)(x+1)}=\dfrac{x+2}{x+1}$

5 0

3 years ago

The expected activity time in PERT analysis is calculated as: the weighted average of a, m, and b, with m weighted 4 times as he

maria [59]

Answer:

$\text{the weighted average of a, m, and b, with m weighted 4 times as heavily as a and b.}$

Step-by-step explanation:

$\text{The expected activity time in PERT analysis is calculated as:}$

$\mathbf{\dfrac{a+4m + b}{6}}$

$where;$

$\text{a = optimistic duration; }$

$\text{m = most likely duration and;}$

$\text{ b = pessimistic duration from the above formula.}$

3 0

2 years ago

Which quadrant does the point (-3, 6) lie in?<br><br> Quadrant IV<br> Quadrant I<br> Quadrant II

elena-14-01-66 [18.8K]

It should be in Quadrant II! <3

6 0

3 years ago

Read 2 more answers

Write -1/2 as a decimal number

Ann [662]

<h2>Answer:</h2>

<u>1/2 is equal to 0.5, so </u><u>-1/2 is -0.5</u><u>.</u>

If you divide -1 by 2, you get -0.5.

5 0

3 years ago

Read 2 more answers