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Tems11 [23]
3 years ago
6

How do you find the equation for the line that is parallel to the line y=2/3x-7 and passes through the point (3,-1)

Mathematics
1 answer:
Debora [2.8K]3 years ago
3 0

parallel lines have the same exact slope hmmm what's the slope of y = 2/3x-7 anyway? well, low and behold, is already in slope-intercept form, therefore

\bf \stackrel{\textit{slope-intercept form}}{y=\stackrel{slope}{\cfrac{2}{3}}x-7}.


so we're really looking for the equation of a line whose slope is 2/3, and runs through 3, -1.


\bf (\stackrel{x_1}{3}~,~\stackrel{y_1}{-1})~\hspace{7em} slope =  m\implies \cfrac{2}{3} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-1)=\cfrac{2}{3}(x-3) \\\\\\ y+1=\cfrac{2}{3}x-2\implies y=\cfrac{2}{3}x-3

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Alice and Claire go apple picking. When they are done, Claire has 3 times as many apples in her basket as Alice has in hers. (No
ElenaW [278]

Answer:

6 apples, 21 apples, 30 apples respectively

Step-by-step explanation:

Let us first start by writing <u>expressions</u> so that we can easily solve for the problems below.

Let us suppose Alice is x. In this case, Claire has 3 times Alice's apples, so 3x.

1. If Alice has 2 apples (x), then Claire has 3x

3*2=<u>6 apples</u>

Claire has 6 apples.

2. If Alice has 7 apples (x), then Claire has 3x

3*7=<u>21 apples</u>

Claire has 21 apples.

<u />

3. If Alice has 10 apples (x), then Claire has 3x

3*10=<u>30 apples</u>

Claire has 30 apples.

<em>I hope this helps! Please let me know if you have any further questions :)</em>

5 0
3 years ago
11. Kona wants to bake at most 30 loaves of banana bread and nut bread for a bake sale. Each loaf of banana bread sells for $2.5
aliya0001 [1]

Answer:

x + y ≤ 30

2.5x + 2.75y ≥ 44

3 0
2 years ago
The next term in the following sequence is 12. True or False<br><br>2, 4, 8…
Snezhnost [94]
False, every time in the sequence, the numbers are doubling, therefore, the next number in the sequence would be 16.
5 0
3 years ago
a box with a square base and open top must have a volume of 70304 c m 3 cm3 . we wish to find the dimensions of the box that min
Dmitriy789 [7]

The box should have base 52 cm by 52 cm and height 26 cm.

What is volume?

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

The Volume of a box with a square base x by x cm and height h cm is

V = x^2h

Since the surface area directly affects the amount of material used, we can reduce the amount of material by reducing the surface area.

The surface area of the box described is  A = x^2 + 4xh

We need A as a function of x alone, so we'll use the fact that

V = x^2h= 70304 cm^3

⇒ h = \frac{70304}{x^2}

So, the area becomes,

A = x^2+4x(\frac{70304}{x^2})\\ A = x^2 + \frac{281216}{x}

We want to minimize A, so

A' = 2x - \frac{281216}{x^2} =0\\\frac{2x^3-281216}{x^2}=0\\ {2x^3-281216} = 0\\x^3 - 140608=0\\x^3 = 140608\\x = 52

The second derivative test verifies that A has a minimum at this critical number:

A'' = 2+\frac{562432}{x^3}  which is positive at x = 52.

Now,

h = \frac{70304}{x^2}= \frac{70304}{(52)^2}=26

Hence, The box should have base 52 cm by 52 cm and height 26 cm.

To know more about volume, click on the link

brainly.com/question/463363

#SPJ4

8 0
1 year ago
if my goal is 27,729,350 and i get 150 closer every minute and 15 seconds how long is it going to take me to get to my goal
oksano4ka [1.4K]

Answer: 13,864,675 seconds

Step-by-step explanation:

I minute 15 seconds = 75 seconds

That means it takes 75 seconds to achieve 150 , and it takes x seconds to achieve 27,729,350. Interpreting this in proportion form , we have:

150 ------ 75 seconds

27,729,350 ------- x seconds

Then

150x = 27,729,350 X 75

150x = 2,079,701,250

x =  2,079,701,250 / 150

x = 13,864,675

That means it takes 13,864,675 seconds to achieve the goal , converting this to minutes, we have:

231,077.9 minutes

5 0
3 years ago
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