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4 years ago

How do you convert 3x+2y=6 into slope intercept form?

Mathematics

2 answers:

Advocard [28]4 years ago

8 0

Answer:

y = -3/2 x +3

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

3x+2y = 6

Subtract 3x from each side

3x-3x+2y = -3x+6

2y = -3x+6

Divide each side by 2

2y/2 = -3x/2 +6/2

y = -3/2 x +3

This is in slope intercept form where the slope is -3/2 and the y intercept is 3

Semmy [17]4 years ago

3 0

pretty much by simply solving for "y".

$\bf 3x+2y=6\implies 2y=-3x+6\implies y=\cfrac{-3x+6}{2} \\\\\\ \underset{\textit{distributing the denominator}}{y=\cfrac{-3x}{2}+\cfrac{6}{2}~\hfill }\implies y=-\cfrac{3}{2}x+3\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}$

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Which expressions are equivalent to (v^-1)^1/9

Varvara68 [4.7K]

It has to be (V^-0.1)

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3 years ago

Jose can paint an entire house in seven hours and brandon can paint the same house in eight hours. Write an equation that can be

guajiro [1.7K]

Answer:

t/8 + t/7 = 1

Step-by-step explanation:

Given in the question that,

time require for Jose to paint the house = 7 hours

time require for Brandon to paint the house = 8 hours

Suppose t means Full house painted.

<h3>To solve the question we have to figure out how much each of them can paint in ONE hour.</h3>

7 hours----t

1 hour ---- t/7

8 hours----t

1 hour ---- t/8

<h3>Equation</h3>

t/8 + t/7 = 1 (in one hour)

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5 0

3 years ago

Algebra need to solve question

Zigmanuir [339]

Answer:

Step-by-step explanation:

$(3+\sqrt{7})(3-\sqrt{7}) \\$

First do 3 x 3 = 9 - keep this 9 to the side for now

Then do 3 x $-\sqrt{7}$ = $-\sqrt{21}$ - also keep this to the side for now

Then do $\sqrt{7}$ x 3 = $\sqrt{21}$

Then do $-\sqrt{7}$ x $\sqrt{7}$ = -7

So,

9 $-\sqrt{21}$ + $\sqrt{21}$ - 7

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4 0

3 years ago

Find two numbers x and y such that a) 2x+y=100 and A=2x+2xy+y is maximized b) 2x+4y-15=0 and B= √x2+y2is minimized. Note that in

zaharov [31]

Answer:

a) x = 25, y = 50

b) x = 1.5, y = 3

Step-by-step explanation:

We have to use Lagrange Multipliers to solve this problem. The maximum of a differentiable function f with the constraint g(x,y) = b, then we have that there exists a constant $\lambda$ such that

$\nabla f(x,y) = \lambda \, \nabla g(x,y)$

Or, in other words,

$f_x(x,y) = \lambda \, g_x(x,y) \\ f_y(x,y) = \lambda \, g_y(x,y)$

a) Lets compute the partial derivates of f(x,y) = 2x+2xy+y. Recall that, for example, the partial derivate of f respect to the variable x is obtained from derivating f thinking the variable y as a constant.

$f_x(x,y) = 2 + 2y$

On the other hand,

$f_y(x,y) = 2x+1$

The restriction is g(x,y) = 100, with g(x,y) = 2x+y. The partial derivates of g are

$g_x(x,y) = 2; g_y(x,y) = 1$

This means that the Lagrange equations are

$2y + 2 = 2 \, \lambda$
$2x +1 = \lambda$
$2x + y = 100$ (this is the restriction, in other words, g(x,y) = 100)

Note that 2y + 2, which is $2 \, \lambda$ is the double of 2x+1, which is $\lambda$ . Therefore, we can forget $\lambda$ for now and focus on x and y with this relation:

2y+2 = 2 (2x+1) = 4x+2

2y = 4x

y = 2x

If y is equal to 2x, then

g(x,y) = 2x+y = 2x+2x = 4x

Since g(x,y) = 100, we have that

4x = 100

x = 100/4 = 25

And, therefore y = 25*2 = 50

Therefore, x = 25, Y = 50.

b) We will use the suggestion and find the minumum of f(x,y) = B² = x²+y², under the constraing g(x,y) = 0, with g(x,y) = 2x+4y-15. The suggestion is based on the fact that B is positive fon any x and y; and if 2 numbers a, b are positive, and a < b, then a² < b². In other words, if (x,y) is the minimum of B, then (x,y) is also the minimum of B² = f.

Lets apply Lagrange multipliers again. First, we need to compute the partial derivates of f:

$f_x(x,y) = 2x \\f_y(x,y) = 2y$

And now, the partial derivates of g:

$g_x(x,y) = 2 \\ g_y(x,y) = 4$

This gives us the following equations:

$2x = 2 \, \lambda \\ 2y = 4 \, \lambda \\ 2x+4y-15 = 0$

If we compare 2x with 2y, we will find that 2y is the double of 2x, because 2y is equal to $4 \, \lambda$ , while on the other hand, $2x = 2 \, \lambda$ . As a consequence, we have

2y = 2*2x

y = 2x

Now, we replace y with 2x in the equation of g:

0 = g(x,y) = 2x+4y-15 = 2x+4*2x -1x = 10x-15

10 x = 15

x = 15/10 = 1.5

y = 1x5*2 = 3

Then, B is minimized for x 0 1.5, y = 3.

4 0

3 years ago

Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol

Dima020 [189]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$\hat p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$t_{\alpha/2}=-2.58, t_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.025$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume an estimated proportion of $\hat p =0.5$ since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56$

And rounded up we have that n=2663

6 0

4 years ago

How do you convert 3x+2y=6 into slope intercept form?​

How do you convert 3x+2y=6 into slope intercept form?