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3 years ago

Maria needs to buy 12 wine glasses. write an expression of the cost of 12 glasses at p dollars each.

Mathematics

1 answer:

irinina [24]3 years ago

5 0

12p thats it because you are buying 12 glasses a the cost of p example 12 glasses for 5 dollars would be 12(5)=60

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FEE

frozen [14]

Answer:

The equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

$3x - 4y = -4$

Step-by-step explanation:

The slope-intercept form of the line equation

$y = mx+b$

where

m is the slope

b is the y-intercept

Given the line

3x - 4y = 7

writing in the slope-intercept form

4y = 3x - 7

dividing both sides by 4

4y/4 = 3/4x - 7/4

y = 3/4x - 7/4

Now, comparing with the slope-intercept form of the line equation

y = 3/4x - 7/4

The slope of the line m = 3/4

We know that parallel lines have the same slopes.

Therefore, the slope of the parallel line is: 3/4

now we have,

The point (-4, -2)

The slope m of parallel line = 3/4

Given the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting (-4, -2) and m = 3/4 in the point-slope form of line equation

$\:y-\left(-2\right)=\frac{3}{4}\left(x-\left(-4\right)\right)$

$y+2=\frac{3}{4}\left(x+4\right)$

Thus, the equation in the point-slope form of the line equation is:

$y+2=\frac{3}{4}\left(x+4\right)$

Simplifying the equation

$y+2=\frac{3}{4}\left(x+4\right)$

Subtract 3 from both sides

$y+2-2=\frac{3}{4}\left(x+4\right)-2$

$y=\frac{3}{4}x+1$

Multiplying the equation by 4

$4y = 3x + 4$

$3x - 4y = -4$

Therefore, the equations represent the line that is parallel to 3x - 4y = 7 and pass through the point (-4,-2) are:

$y+2=\frac{3}{4}\left(x+4\right)$

$3x - 4y = -4$

7 0

3 years ago

Initially a tank contains 10 liters of pure water. Brine of unknown (but constant) concentration of salt is flowing in at 1 lite

zhenek [66]

Answer:

Therefore the concentration of salt in the incoming brine is 1.73 g/L.

Step-by-step explanation:

Here the amount of incoming and outgoing of water are equal. Then the amount of water in the tank remain same = 10 liters.

Let the concentration of salt be a gram/L

Let the amount salt in the tank at any time t be Q(t).

$\frac{dQ}{dt} =\textrm {incoming rate - outgoing rate}$

Incoming rate = (a g/L)×(1 L/min)

=a g/min

The concentration of salt in the tank at any time t is = $\frac{Q(t)}{10}$ g/L

Outgoing rate = $(\frac{Q(t)}{10} g/L)(1 L/ min)$ $\frac{Q(t)}{10} g/min$

$\frac{dQ}{dt} = a- \frac{Q(t)}{10}$

$\Rightarrow \frac{dQ}{10a-Q(t)} =\frac{1}{10} dt$

Integrating both sides

$\Rightarrow \int \frac{dQ}{10a-Q(t)} =\int\frac{1}{10} dt$

$\Rightarrow -log|10a-Q(t)|=\frac{1}{10} t +c$ [ where c arbitrary constant]

Initial condition when t= 20 , Q(t)= 15 gram

$\Rightarrow -log|10a-15|=\frac{1}{10}\times 20 +c$

$\Rightarrow -log|10a-15|-2=c$

Therefore ,

$-log|10a-Q(t)|=\frac{1}{10} t -log|10a-15|-2$ .......(1)

In the starting time t=0 and Q(t)=0

Putting t=0 and Q(t)=0 in equation (1) we get

$- log|10a|= -log|10a-15| -2$

$\Rightarrow- log|10a|+log|10a-15|= -2$

$\Rightarrow log|\frac{10a-15}{10a}|= -2$

$\Rightarrow |\frac{10a-15}{10a}|=e ^{-2}$

$\Rightarrow 1-\frac{15}{10a} =e^{-2}$

$\Rightarrow \frac{15}{10a} =1-e^{-2}$

$\Rightarrow \frac{3}{2a} =1-e^{-2}$

$\Rightarrow2a= \frac{3}{1-e^{-2}}$

$\Rightarrow a = 1.73$

Therefore the concentration of salt in the incoming brine is 1.73 g/L

8 0

3 years ago

Consider the expression 20-(4^2/2). How many terms does the expression have?

natali 33 [55]

Answer:

huh

Step-by-step explanation:

7 0

3 years ago

19-x is greater than or equal to 21

Sedaia [141]

Could you possibly add to this post what your goal is? Are you supposed to graph this inequality?

19-x≥21 can be solved for x. Please do that now. If you have the skill and the interest, please graph your solution.

8 0

4 years ago

There are 5 green balls, 2 orange balls, 4 purple balls, and 1 pink ball in a bucket. You pick 1 ball from

bagirrra123 [75]

B
The purple balls constitute 1/3 of the amount of balls there, so you’re that likely to pluck one out.

8 0

3 years ago