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3 years ago

Write an equation of the line that is parallel to 3x + 9y = 7 and passes through the point (6, 4).

1 answer:

Ber [7]3 years ago

4 0

First, rearrange the equation to standard line format
3x + 9y = 7
9y = -3x + 7
y = -3/9x + 7/9
y = -1/3x + 7/9

now we know the slope of the line (both the existing and the new parallel one, since they both have the same slope)

y = -1/3x + b

plug in the new point in and solve for b

4 = -1/3(6) + b
4 = -2 + b
b = 6

y = -1/3x + 6 is the equation for the parallel line

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What equation is represented by the equation on the graph ?

solmaris [256]

Answer: The correct option is D.

Explanation:

From the graph we noticed that the x intercept of the line is (2,0) and the y-intercept is (0,2).

If the line passing through two points then the equation of line is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Since the ien passing through (2,0) and (0,2).

$y-0=\frac{2-0}{0-2}(x-2)$

$y=-1(x-2)$

$y=-x+2$

This equation is represented by option D, therefore the option D is correct.

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3 years ago

Log_{7 }(5 - 3x) Find the derivative

V125BC [204]

Let y be the expression you want to differentiate:

$y=\log_7(5-3x) \implies 7^y=5-3x$

Now,

$7^y=e^{\ln(7^y)}=e^{y\ln(7)}$

Use the chain rule to differentiate both sides with respect to x :

$\ln(7)e^{y\ln(7)}\dfrac{\mathrm dy}{\mathrm dx}=-3$

Solve for dy/dx :

$\ln(7)7^y\dfrac{\mathrm dy}{\mathrm dx}=-3$

$\dfrac{\mathrm dy}{\mathrm dx}=-\dfrac3{\ln(7)7^y}$

$\dfrac{\mathrm dy}{\mathrm dx}=\boxed{-\dfrac3{\ln(7)(5-3x)}}$

6 0

2 years ago

Marian borrowed money to buy a sound system that costs $450. She is charged 5% simple interest for one year what is the total am

yarga [219]

Marian will pay $472.50 for the sound system if she pays the full amount in one year.

Step-by-step explanation:

Given,

Money borrowed for sound system = $450

Interest rate = 5%

Amount of interest = 5% of money borrowed

Amount of interest = $\frac{5}{100}*450$

$Amount\ of\ interest=\frac{2250}{100}\\\\Amount\ of\ interest=\$22.50$

If she pays the amount in one year;

Total amount to be paid = Money borrowed + Amount of interest

Total amount to be paid = $450 + $22.50 = $472.50

Marian will pay $472.50 for the sound system if she pays the full amount in one year.

Keywords: interest, addition

Learn more about addition at:

#LearnwithBrainly

5 0

3 years ago

Read 2 more answers

Christian is throwing a pizza party . he has 1 1/3pounds of cheese available and he needs 1/2 pounds of cheese to make each pizz

Ivanshal [37]

Answer:

Step-by-step explanation:

3 0

3 years ago

Tickets for a choir concert cost $3 for students and $5 for adults. The choir director wants to sell at least $1500 worth of tic

ANEK [815]

Answer: 164.4 or 165

Step-by-step explanation: So, you do 226 x 3 and you get $678. So now that you know that you have $678 worth of student tickets, you want to find how much more you need for the adult tickets, so you do $1500-$678, and you get $822. Divide it by 5 and you get 164.4, so you wanna sell about 165 tickets. Check your work by multiplying 5 by 165 and you get $825, which meets your $1500 minimum

6 0

3 years ago