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4 years ago

When 18 is subtracted from six times a certain number ,the result is -42 what is the number

Mathematics

1 answer:

Effectus [21]4 years ago

3 0

Answer:

The value for such given number is -4.

Step-by-step explanation:

Let the given number = m

So, according to the question: 6 m - 18 = -42

Now, solving for the value of m,

6m - 18 = -42 ⇒ 6m = -42 + 18

⇒ 6m = -24

or, m= -24/ 6 = -4

So, m = -4

Hence the value for such number is -4.

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3 years ago

Corinne bought 5 bags of chips and 4 jars of dipping sauce for $21.82. At the same prices, Ginger bought 4 bags of chips and 3 j

AURORKA [14]

Step-by-step explanation:

5 bags of chips and 4 jars of dipping sauce cost $21.82. Also, 4 bags of chips and 3 jars of dipping sauce cost $16.86.

This problem can be modeled using linear equations in two variables.

Let $c$ be the cost of a bag of chip and $s$ be the cost of a jar of dipping sauce.

The information yields the equations

$5c+4s=21.82,4c+3s=16.86\\\textrm{Multiply first equation by 4 and second equation by 5}\\20c+16s=87.28,20c+15s=84.3\\\textrm{Subtracting second equation from the first one}\\s=\$2.98$

∴ A jar of dipping sauce costs $\$2.98$ .

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4 years ago

Solve using algebraic equation: <br> 5sin2x=3cosx<br><br> (No exponents)

DaniilM [7]

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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 $x=\pi-\arcsin\dfrac3{10}+2n\pi$ .

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