Mathematics, 28.06.2019 08:00 codeyhatch142

5-4. solve each of the following equations for the indicated variable. use your equation mat if it is . write down each of your steps algebraically. solve for y: 2(y − 3) = 4 solve for x: 2x + 5y = 10 solve for y: 6x + 3y = 4y + 11 solve for x: 3(2x + 4) = 2 + 6x + 10 solve for x: y = −3x + 6

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Answer from: swaise3300

QUESTION 1

The given equation is :

2(y - 3) = 4

We want to solve for y. This means we have to isolate y on one side of the equation while all other constants are also on the other side of the equation,

We first divide both sides by 2 to obtain,

$\frac{2(y - 3)}{2} = \frac{4}{2}$

We cancel out the common factors to get,

y - 3 = 2

We now group like terms to get,

y = 3 + 2

We simplify to obtain,

y = 5

QUESTION 2

The given equation is

2x + 5y = 10

We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

This implies that,

2x= 10 - 5y

We now divide through by 2, to obtain,

$\frac{2x}{2} = \frac{10}{2} - \frac{5y}{2}$

This will now give us,

$x = 5 - \frac{5}{2} y$

QUESTION 3

The given equation is
6x + 3y = 4y + 11

We want to solve for y. This means that we need to isolate y on one side of the equation, while all other variables and constants are also on the other side of the equation.

We first of all group all the y terms on one side of the equation to obtain,

6x - 11 = 4y - 3y

We simplify to get,

6x - 11 = y

This implies that,

y = 6x - 11

QUESTION 4

The given equation is,

3(2x + 4) = 2 + 6x + 10

We want to solve for x. This means that we need to isolate x on one side of the equation, while all other variables and constant are also on the other side of the equation.

Let us first expand the brackets to get,

6x + 12 = 2 + 6x + 10

This implies that

6x + 12 = 6x + 12

We group like terms to get,

6x - 6x = 12 - 12

We now simplify both sides to get,

0x = 0

We don't want x to vanish, so let us try to divide both sides by zero to get,

$x = \frac{0}{0}$

This is an indeterminate form, which implies that, x has infinitely many solutions. This means that all the real numbers are solution to the equation.

$\therefore \: x \in \: R$

QUESTION 5

The given equation is,

y = - 3x + 6

We want to solve for x, so we add the additive inverse of 6, which is -6 to both sides of the equation to get,

y - 6 = - 3x

We rewrite this to obtain,

- 3x = y - 6

We divide through by -3 to get,

$\frac{ - 3x}{ - 3} = \frac{y}{ - 3} - \frac{6}{ - 3}$

This will give us,

$x = - \frac{y}{3} + 2$

or

$x= 2 - \frac{1}{3} y$

Answer from: Quest

there is no following? ! lol

Answer from: Quest

the exponential expression to find the value of the cd, in dollars, after t years will be: $a= 1500(1.0231)^t$

step-by-step explanation:

formula of compound interest: $a=p(1+\frac{r}{n})^n^t$ , where $a=$ final value after $t$ years, $p=$ initial value, $r=$ rate of interest in decimal and $n=$ number of compounding in a year.

oliver plans to purchase a $1,500 certificate of deposit (cd) at his bank. that means, $p= 1500$

the cd will earn 2.3% interest, compounded semi-annually.

so, $r= 2.3\%= 0.023$ and $n= 2$

now, plugging these values into the above formula, we will

$a= 1500(1+\frac{0.023}{2})^2^t \\ \\ a=1500(1.0115)^2^t\\ \\ a= 1500[(1.0115)^2]^t\\ \\ a= 1500(1.0231)^t$

(rounded to the nearest ten-thousandth)

so, the exponential expression to find the value of the cd, in dollars, after t years will be: $a= 1500(1.0231)^t$

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