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2 years ago

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Give an equation of a line that is parallel to −3x + 7y =4. Explain why your line is parallel to the given line and how you arri

ved at your answer.

1 answer:

koban [17]2 years ago

3 0

Answer:

3x -7y = 0

Step-by-step explanation:

Parallel lines have the same slope.

Changing the constant in a linear equation like this only changes the y-intercept. It has no effect on the slope of the line. So, we can change the constant from 4 to 0 and we will have a line with the same slope, parallel to the original, but with a different y-intercept.

The "standard form" of the equation of a line has the leading coefficient positive. We can make that be the case by using the multiplication property of equality, multiplying both sides of the equation by -1.

Parallel line:

-3x +7y = 0

In standard form:

3x -7y = 0

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If you were to solve the following system by substitution, what would be the best

xxMikexx [17]

To solve the two equations simultaneously using the substitution method we need to rearrange one of the equation to make either $'x'$ or $'y'$ the subject.

We can try in turn rearranging both equations and see which unknown term would have been easier to solve first

Equation $2x+8y=12$

Making $'x'$ the subject
$2x=12-8y$ , dividing each term by 2
$x=6-4y$ ⇒ (Option 1)

Making $'y'$ the subject
$8y=12-2x$ , multiply each term by 8 gives
$y= \frac{12}{8} - \frac{2}{8}x$ ⇒ (Option 2)

Equation $3x-8y=11$
Making $'x'$ the subject
$3x=11+8y$ , divide each term by 3
$x= \frac{11}{3}+ \frac{8}{3}y$ ⇒ (Option 3)

Making $'y'$ the subject
$8y=3x-11$ , divide each term by 8
$y= \frac{3}{8}x- \frac{11}{8}$ ⇒ (Option 4)

From all the possibilities of rearranged term, the most efficient option would have been the first option, from equation $2x+8y=12$ with $'x'$ as the subject, $x=6-4y$

3 0

3 years ago

Read 2 more answers

The quantity, Q, of a drug in the blood stream begins with 250 mg and decays to one-fifth its value over every 90 minute period.

Mazyrski [523]

Answer:

$a=250 \, mg\\\\b=5\\\\T= 90'$

Step-by-step explanation:

We have that $Q(t) = a\cdot b^{-\frac{t}{T}} \\$

Where t is the time (in minutes) and for the sake of dimensional consistency, let's assume that T is also in minutes, b is an adimensional number, and a is in mg. So we will have Q in mg as a consequence.

We now want to find out what values these constants might take. Let's see what happens when $t=0$ , that is, just as we start. At that point, we have that the amount of drug in the bloodstream must be equal to 250mg, thus:

$Q(0)= a\cdot b ^{-\frac{0}{T} }=250\,mg\\Q(0)= a=250\,mg$

We have found the constant $a$ ! It is the initial amount of drug! we have made use of the fact that any number raised to the 0th power is equal to one.

Now, we know that every 90 minutes, the amount of drug decreases to one fifth of its former value. How do we put this in mathematical form? Like so:

$Q(t+90')=Q(t)/5$

That is, 90 minutes after time t the amount of drug will be one fifth of the amount of drug at time t. Let's expand the last equation:

$Q(t+90')=Q(t)/5\\\\a\cdot b^{-\frac{t+90'}{T} }=a\cdot b^{-\frac{t}{T} }/5\\\\ b^{-\frac{t+90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{t}{T} }b^{-\frac{90'}{T} }=b^{-\frac{t}{T} }/5\\\\b^{-\frac{90'}{T} }=\frac{1}{5}$

Now the last expression isn't enough to determine both T and b, but that also means that we have some freedom in how we choose them. What seems most simple is to pick $T=90'$ and thus we will get:

$b^{-1 }=\frac{1}{5}\\\\\frac{1}{b}= \frac{1}{5}\\\\b=5$

And that is our final result.

3 0

3 years ago

An art teacher has a jar containing b buttons to distribute to her class for a project. In order to give each in the class 6 but

Nastasia [14]

Answer:

22

Step-by-step explanation:

Given:

An art teacher has the total number of buttons = $b$

1. In order to give each in the class 6 buttons, she will need 18 more buttons.

2. If she gives each child 5 buttons, she will have 4 left over.

Question asked:

How many children are in the class ?

Solution:

<u>Let total number of children in the class = </u> $x$

<u><em>As given that, 18 more buttons will be needed to give 6 buttons to each.</em></u>

The equation will be:-

$b+18=6x\\b-6x=-18\ (equation\ 1)$

<em><u>Also given that, If she gives 5 buttons to each, she will have 4 left over.</u></em>

The equation will be:-

$b-5x=4\ (equation\ 2)$

Subtraction equation 2 from 1

$b-6x-(b-5x)=-18-4\\b-6x-b+5x=-22\\-6x+5x=-22\\-x=-22\\Minus\ canceled\ by\ minus\\x=22$

Hence, total number of children are 22.

4 0

3 years ago

larisa86 [58]

Answer:

c

Step-by-step explanation:

is the c 100%

4 0

2 years ago

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Write down the angle of the<br>compass bearing shown in w<br>the given figure. Ans: 045°

Talja [164]

Answer:

Figure??

Answer is 45 degrees

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers