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svet-max [94.6K]
3 years ago
9

Simplify: 3(4x – 2) + 9 + 2

Mathematics
1 answer:
kirill [66]3 years ago
6 0

Answer:

-6x+5y+8

Step-by-step explanation: subtract 9xfrom 3x

Subtract 2 from 10

-6x+5y+10-2

-6x+5y+8

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Solve using algebraic equation: <br> 5sin2x=3cosx<br><br> (No exponents)
DaniilM [7]
5\sin2x=3\cos x\iff10\sin x\cos x=3\cos x

by the double angle identity for sine. Move everything to one side and factor out the cosine term.

10\sin x\cos x=3\cos x\iff10\sin x\cos x-3\cos x=\cos x(10\sin x-3)=0

Now the zero product property tells us that there are two cases where this is true,

\begin{cases}\cos x=0\\10\sin x-3=0\end{cases}

In the first equation, cosine becomes zero whenever its argument is an odd integer multiple of \dfrac\pi2, so x=\dfrac{(2n+1)\pi}2 where n[/tex ]is any integer.\\Meanwhile,\\[tex]10\sin x-3=0\implies\sin x=\dfrac3{10}

which occurs twice in the interval [0,2\pi) for x=\arcsin\dfrac3{10} and x=\pi-\arcsin\dfrac3{10}. More generally, if you think of x as a point on the unit circle, this occurs whenever x also completes a full revolution about the origin. This means for any integer n, the general solution in this case would be x=\arcsin\dfrac3{10}+2n\pi and x=\pi-\arcsin\dfrac3{10}+2n\pi.
6 0
3 years ago
Which of the following is an extraneous solution of square root 4x+41 = x+5?
saw5 [17]
The answer is
4(2)+41=2+5
49
X=2
5 0
2 years ago
Solve x^2 + 4x + 8 = 0
Mkey [24]

Answer:

x = -2 + 2 i or x = -2 - 2 i

Step-by-step explanation:

Solve for x:

x^2 + 4 x + 8 = 0

Subtract 8 from both sides:

x^2 + 4 x = -8

Add 4 to both sides:

x^2 + 4 x + 4 = -4

Write the left hand side as a square:

(x + 2)^2 = -4

Take the square root of both sides:

x + 2 = 2 i or x + 2 = -2 i

Subtract 2 from both sides:

x = -2 + 2 i or x + 2 = -2 i

Subtract 2 from both sides:

Answer:  x = -2 + 2 i or x = -2 - 2 i

8 0
2 years ago
What is 2 5/12 - 1 7/12 =
castortr0y [4]

Answer:

Divide: 7/12  : 3/10  = 7/12  · 10/3= 7 · 10  /12 · 3  = 70/36  = 35/18

To divide one fraction by another, invert (turn upside-down) the second fraction, then multiply.

Hope this helps:)sorry if it doesnt

4 0
3 years ago
A(x) = -0.015x^3+1.05xA ( x ) = − 0.015 x 3 + 1.05 x gives the alcohol level in an average person's blood x hrs after drinking 8
goldfiish [28.3K]

Answer:

Yes

Step-by-step explanation:

the function that gives the alcohol level is:

A ( x ) = - 0.015 x^3 + 1.05 x

where x is the number of hours.

we need to know if after 4 hours an average person is legally drunk, thus:

x=4

and we substitute this in the function:

A ( 4 ) = - 0.015 (4)^ 3 + 1.05(4)

solving these operations we obtain:

A(4)=-0.015(64)+4.2\\A(4)=-0.96+4.2

A(4)=3.24

the alcohol level after 4 hours is 3.24.

Since a person is considered to be legally drunk if the level exceeds 1.5, and we obtained 3.24 which is greater than 1.5, a person who has been drinking for 4 hours under the conditions indicated by the problem would be considered legally drunk.

5 0
2 years ago
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