Volume of cone round to the nearest 10th

67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :

$y=\frac{3}{2} x+b$

2) Determine the y-intercept

$y=\frac{3}{2} x+b$

Plug in the given point, (4,0)

$0=\frac{3}{2} (4)+b\\0=6+b$

Subtract both sides by 6

$0-6=6+b-6\\-6=b$

Therefore, -6 is the y-intercept of the line. Plug this into $y=\frac{3}{2} x+b$ as b:

$y=\frac{3}{2} x-6$

I hope this helps!

7 0

3 years ago

Evaluate arccsc square root of 2

leonid [27]

Sin⁻¹ √2 = 1/√2 = 1(√2) / (√2)(√2) = √2/2

8 0

3 years ago

A kangaroo can jump 6 times the length of its body. For a kangaroo that is 5 feet long, how many feet can it jump? *

Sindrei [870]

Answer:

30feet

Step-by-step explanation:

5 x 6 =30

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6 0

3 years ago

Read 2 more answers

A ball is dropped from a height of 100 cm. The rebound heights to the nearest centimeter are 60, 36, 22, .... What is the total

Nataly_w [17]

Answer:

a

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

You paid $44 to a loan company for the use of $1,153 for 119 days, what annual rate of interest did they charge? (Assume a 360-d

Zigmanuir [339]

Answer:

Ans. A) The annual rate that the company charged was 11.996%; B) if they charged you 11.186% annual rate, you would have to pay $41.14

Step-by-step explanation:

Hi, first we have to find out what is the effective 119 days rate and then turn it into an annual rate. This is as follows.

$r(Effective119Days)=\frac{44}{1,153} x100=0.038161$

So the charged rate was 3.816% effective, 119 days, now let´s make it an annual rate.

$r(annual)=(1+0.038161)^{\frac{360}{119} } -1=0.119965$

This means that the equivalent rate to 3.816% effective 119 days ys 11.996% effective annually (or just annual).

Now, if they were to charge you 11.186% annual, you would have to make this rate effective 119 days, and then, multiply it by the principal ($1,153). Let´s change the rate first.

$r(Effective119Days)=(1+0.11186)^{\frac{119}{360} -1}=0.03568$

And the money that you will have to pay in interest is $1,153*0.03568=$41.14

Best of luck

7 0

3 years ago