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iVinArrow [24]
3 years ago
10

What is the equation of the line that passes through (4, 2) and is parallel to 3x – 2y = -6?

Mathematics
1 answer:
Dmitrij [34]3 years ago
3 0

Answer:

y = \frac{3}{2} x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 2y = - 6 into this form

Subtract 3x from both sides

- 2y = - 3x - 6 ( divide all terms by - 2 )

y = \frac{3}{2} x + 3 ← in slope- intercept form

with slope m = \frac{3}{2}

• Parallel lines have equal slopes, hence

y = \frac{3}{2} x + c ← partial equation of parallel line

To find c substitute (4, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = \frac{3}{2} x - 4 ← equation of parallel line

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A city has a population of 310,000 people. Suppose that each year the population grows by 9%. What will the population be after
Leno4ka [110]

Answer: 644,800

Step-by-step explanation:

This can also be solved using the terms of Arithmetic Progressions.

Let the 13 years be number of terms of the sequences (n)

Therefore ;

T₁₃              = a + ( n - 1 )d , where a = 310,000 and d = 9% of 310,000

9% of 310,000 = 9/100 x 310,000

                        = 27,900

so the common difference (d)

                     d = 27,900

Now substitute for the values  in the formula above and calculate

T₁₃              = 310,000 + ( 13 - 1 ) x 27,900

                  = 310,000 + 12 x 27,900

                  = 310,000 + 334,800

                  = 644,800.

The population after 13 years = 644,800.

 

3 0
2 years ago
A warehouse has 784 barrels of a chemical. You require 98 barrels for one run of your process. How many barrels will be left aft
sergejj [24]
686 barrels left. If I'm not mistaken this should just be simple subtraction
4 0
3 years ago
The City Zoo has different admission prices for adults and children. When three adults and two children went to the​ zoo, the bi
Anna11 [10]

Let a and c represent, respectively, the price of an adult and a child ticket. We know that

\begin{cases}3a+2c=78.94\\2a+3c=75.86\end{cases}

Multiply the first equation by 3 and the second equation by 2 to get

\begin{cases}9a+6c=236.82\\4a+6c=151.72\end{cases}

Subtract the two equations to have

5a=85.1 \iff a=17.02

Plug this value in the first equation to get

3\cdot 17.02+2c=78.94\iff 2c=27.88\iff c=13.94

7 0
3 years ago
What is the slope of this equation? <br> 5y = -4 + 3x
BigorU [14]

Answer:

3/5

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 ce
julsineya [31]

Answer:

The proportion of students whose height are lower than Darnell's height is 71.57%

Step-by-step explanation:

The complete question is:

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Darnel is a middle school student with a height of 161.4cm.

What proportion of proportion of students height are lower than Darnell's height.

Answer:

We first calculate the z-score corresponding to Darnell's height using:

Z=\frac{X-\mu}{\sigma}

We substitute x=161.4 , \mu=150, and \sigma=20 to get:

Z=\frac{161.4-150}{20} \\Z=0.57

From the normal distribution table, we read 0.5 under 7.

The corresponding area is 0.7157

Therefore the proportion of students whose height are lower than Darnell's height is 71.57%

8 0
3 years ago
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