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schepotkina [342]
3 years ago
10

Solve for x 3^(x-2)=-2^(x-1)+3

Mathematics
1 answer:
Lisa [10]3 years ago
8 0
3(x - 2) = -2(x - 1) + 3
 3x - 6 = -2x + 1 + 3
 3x - 6 = -2x + 4
<u>+2x        +2x      </u>
5x - 6 = 4
<u>     +6  +6</u>
     <u>5x</u> = <u>10</u>
      5      5
       x = 2
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Please help !! what’s the answer? i don’t understand !!
dedylja [7]

Answer:

992

Step-by-step explanation:

You must convert the meter the kilometer by miltiplying by 1000

and when you do it you must multiply 0.992 by 1000 since it is a fraction .

or you can work it this way :

  • 0.992⇒1m
  • x(the new rate) ⇒1000m
  • x= 0.992*1000= 992

7 0
3 years ago
Our answer should be a complex number in the form a +bi where a and b are real numbers.
Otrada [13]

Answer:

16 +88i

Step-by-step explanation:

8 x (11i + 2 ) =

Distribute

8*11i + 8*2

88i +16

Writing in the proper form

16 +88i

6 0
2 years ago
If 13cos theta -5=0 find sin theta +cos theta / sin theta -cos theta​
Ivahew [28]

Step-by-step explanation:

<h3>Need to FinD :</h3>

  • We have to find the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0.

\red{\frak{Given}} \begin{cases} & \sf {13\ cos \theta\ -\ 5\ =\ 0\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \big\lgroup Can\ also\ be\ written\ as \big\rgroup} \\ & \sf {cos \theta\ =\ {\footnotesize{\dfrac{5}{13}}}} \end{cases}

Here, we're asked to find out the value of (sinθ + cosθ)/(sinθ - cosθ), when 13 cosθ - 5 = 0. In order to find the solution we're gonna use trigonometric ratios to find the value of sinθ and cosθ. Let us consider, a right angled triangle, say PQR.

Where,

  • PQ = Opposite side
  • QR = Adjacent side
  • RP = Hypotenuse
  • ∠Q = 90°
  • ∠C = θ

As we know that, 13 cosθ - 5 = 0 which is stated in the question. So, it can also be written as cosθ = 5/13. As per the cosine ratio, we know that,

\rightarrow {\underline{\boxed{\red{\sf{cos \theta\ =\ \dfrac{Adjacent\ side}{Hypotenuse}}}}}}

Since, we know that,

  • cosθ = 5/13
  • QR (Adjacent side) = 5
  • RP (Hypotenuse) = 13

So, we will find the PQ (Opposite side) in order to estimate the value of sinθ. So, by using the Pythagoras Theorem, we will find the PQ.

Therefore,

\red \bigstar {\underline{\underline{\pmb{\sf{According\ to\ Question:-}}}}}

\rule{200}{3}

\sf \dashrightarrow {(PQ)^2\ +\ (QR)^2\ =\ (RP)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ (5)^2\ =\ (13)^2} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ +\ 25\ =\ 169} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 169\ -\ 25} \\ \\ \\ \sf \dashrightarrow {(PQ)^2\ =\ 144} \\ \\ \\ \sf \dashrightarrow {PQ\ =\ \sqrt{144}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{PQ\ (Opposite\ side)\ =\ 12}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the value of PQ (Opposite side) is 12. Now, in order to determine it's value, we will use the sine ratio.

\rightarrow {\underline{\boxed{\red{\sf{sin \theta\ =\ \dfrac{Opposite\ side}{Hypotenuse}}}}}}

Where,

  • Opposite side = 12
  • Hypotenuse = 13

Therefore,

\sf \rightarrow {sin \theta\ =\ \dfrac{12}{13}}

Now, we have the values of sinθ and cosθ, that are 12/13 and 5/13 respectively. Now, finally we will find out the value of the following.

\rightarrow {\underline{\boxed{\red{\sf{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}}}}}}

  • By substituting the values, we get,

\rule{200}{3}

\sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\Big( \dfrac{12}{13}\ +\ \dfrac{5}{13} \Big)}{\Big( \dfrac{12}{13}\ -\ \dfrac{5}{13} \Big)}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ {\footnotesize{\dfrac{\dfrac{17}{13}}{\dfrac{7}{13}}}}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{13} \times \dfrac{13}{7}} \\ \\ \\ \sf \dashrightarrow {\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{\cancel{13}} \times \dfrac{\cancel{13}}{7}} \\ \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{\dfrac{sin \theta\ +\ cos \theta}{sin \theta\ -\ cos \theta}\ =\ \dfrac{17}{7}}}}}_{\sf \blue{\tiny{Required\ value}}}}

∴ Hence, the required answer is 17/7.

6 0
2 years ago
Symplify by combining like terms:-17+2x+4x+5
k0ka [10]
6x-12
Combine 2x and 4x = 6x
Combine -17 and 5 = -12
6 0
3 years ago
Read 2 more answers
What simple interest rate is needed for $6,000 to earn $1,000 in 15 months
Mekhanik [1.2K]

let's recall that a year has 12 months, so 15  months is really 15/12 years.

\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$1000\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\to \frac{15}{12}\dotfill &\frac{5}{4} \end{cases}

\bf 1000=(6000)r\left( \cfrac{5}{4} \right)\implies 1000=7500r\implies \cfrac{1000}{7500}=r\implies \cfrac{2}{15}=r \\\\\\ \stackrel{\textit{converting that to a percentage}}{\cfrac{2}{15}\cdot 100 = r\implies \cfrac{40}{3}=r}\implies \stackrel{\%~\hfill }{13.\overline{3}}=r

4 0
3 years ago
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