MATHEMATICS HIGH SCHOOL

Solve 2cos2x + cosx − 1 = 0 for x over the interval [0, 2pi ).

Answers

Answer 1

Answer:

The solution of 2cos2x + cosx − 1 = 0 is $x=\pi.$

What is a Trigonometric equation?

A Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles.

How to solve?

2cos2x + cosx − 1 = 0

$-3+\cos \left(x\right)+4\cos ^2\left(x\right)=0$

$\cos \left(x\right)=(3)/(4),\:\cos \left(x\right)=-1$

And now,

$x=\pi +2\pi n$

Which is only $x=\pi$ .

Learn more about Trigonometric equations:

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Answers

Please see the pic, I'd solved your question in it.

Darnell's car used 8 gallons of gasoline to travel 340 miles. after a mechanic worked on the car, it used 7 gallons of gasoline to travel 350 miles. If the price of the gasoline was approximately $4.00 per gallon, how much lest to the nearst cent per mile, did it cost to run the car after the mechanic worked on it?

Answers

so, after the mechanic worked on it, it only does 7 gallons for 350miles, how many gallons will it be at that rate, for 340 miles then?

$\bf \begin{array}{ccll}gallons&miles\n\text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\n7&350\nx&340\end{array}\implies \cfrac{7}{x}=\cfrac{350}{340}\implies \cfrac{7\cdot 340}{350}=x\implies 6.8=x$

well, each gallon is 4 bucks, for 6.8 gallons that'd be 6.8*4.

we already know that before the mechanic worked on it, it was doing 8gallons for the same 340 miles, and at 4 bucks a gallon that'd be 8*4.

how much is her savings?

$\bf \stackrel{\stackrel{\textit{gallons cost}}{\textit{before being fixed}}}{(8\cdot 4)}\qquad -\qquad \stackrel{\stackrel{\textit{gallons cost}}{\textit{after it was fixed}}}{(6.8\cdot 4)}$

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.−b b2 − 4ac 2a

Use the part of the quadratic formula that you chose above and find its value, given the following quadratic equation:

4x2 + 6x + 2 = 0

Numerical Answers Expected!

Answers

Hello,

if b²-4ac>0 then the equation has 2 reals roots
if b²-4ac=0 then the equation has one real root with multiplicity 2
if b²-4ac<0 then no real root.

4x²+6x+2=0

Δ=6²-4*4*2=36-32=4=2² ==> 2 reals roots

==>x=(-6-2)/8=-1 or x=(-6+2)/8=-1/2

One other way is:

4x²+6x+2=0
==>2(2x²+3x+1)=0
==>2x²+3x+1=0
==>2x²+2x+x+1=0
==>2x(x+1)+1(x+1)=0
==>(x+1)(2x+1)=0
==>x=-1 or x=-1/2

Answer B

Rewrite the sum of 12 and 8 as a product of the LCM of the two numbers and another sum.

Answers

Answer:

2 or 4

Step-by-step explanation:

Can someone help me please?

Answers

Answer:

-5, -1, 3

Step-by-step explanation:

x + 4 > -2

-4 -4

x > - 6

so any number larger then -6 satisfy the inequality.

It means integers: -5,-4,-3, -2, -1, 0, 1, 2 3, 4, and so on.

{-6 not because -6 is not >-6}

sarah started her part-time job at the hourly wage of $7.30. After 6 months she got a 10% raise. To the nearest cent, whay was her hourly wage after the raise?

Answers

7.3+7.3*0.1=7.3+0.73 = $8.03

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