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nikklg [1K]
3 years ago
6

Find a vector that is parallel to -9x+2y = 10. Please explain step by step

Mathematics
1 answer:
coldgirl [10]3 years ago
4 0

Answer:


Step-by-step explanation:

Step One: Find the slope of the given Line

2y - 9x = 10                   Add 9x to both sides

2y - 9x + 9x = 9x + 10  Combine

2y = 9x + 10

y = 9/2 x + 5

The parallel line has a slope of 9/2

Step Two: Find the magnitude

sqrt(x^2 + y^2) = r                   You don't have a magnitude. Invent one, r

x^2 + y^2 = r^2                        Both sides have been squared

Step Three: Find the change in y / x

y / x = 9/2

Step Four: Find the value of y

y/x = 9/2                 Multiply both sides by x

y = 9/2 * x

Step Five: Solve for x

x^2 + y^2 = r^2

x^2 +(9/2x)^2 = r^2

x^2 + 81x^2 / 4 = r^2                Change the 1 to common denominator 1 = 4/4

4/4 x^2 + 81x^2/ 4 = r^2

85 x^2/ 4 = r^2                        Multiply both sides by 4/85

4/85 * (85 / 4) x^2 = 4/85 r^2  

x^2 = 4/85 r^2                         Take the square root of both sides

x = +/- 2/sqrt(85) r                   Rationalize the denominator  

x = (+/- 2 sqrt(85) ) / 85 *

Step Six: Solve for y

y = 9/2 x

y = 9/2 * 2 sqrt(85) / 85      Cancel the 2s

y = +/- 9* sqrt(85)/85

Answer

<2*sqrt(85)/85 ,  9 sqrt(85)/85>

You can write the minus answer if you need it. I kind of suspect you won't.

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The table below shows the temperature in degrees for eight consecutive days as well as the respective number of ice cream cones
cricket20 [7]

Answer:

We have to find the equation of least squares regression line in order to find the number of ice cream cones that the shopkeeper to sell if the temperature is 106 degrees. We can use excel regression data analysis tool to find the equation of the regression line. The excel output is attached here.

The equation of the least squares regression line is:

\hat{y}=46.587+5.080x

Now, if the temperature is 106 degrees, then the number of cones expected to be sold is given below:

\hat{y}=46.587+5.080 \times 106

         =585.1 \approx 585

Therefore, the number of ice cream cones that the shopkeeper would expect to sell if the temperature is 106 degrees is 585.



6 0
3 years ago
There are eight different jobs in a printer queue. Each job has a distinct tag which is a string of three upper case letters. Th
N76 [4]

Answer:

a. 40320 ways

b. 10080 ways

c. 25200 ways

d. 10080 ways

e. 10080 ways

Step-by-step explanation:

There are 8 different jobs in a printer queue.

a. They can be arranged in the queue in 8! ways.

No. of ways to arrange the 8 jobs = 8!

                                                        = 8*7*6*5*4*3*2*1

No. of ways to arrange the 8 jobs = 40320 ways

b. USU comes immediately before CDP. This means that these two jobs must be one after the other. They can be arranged in 2! ways. Consider both of them as one unit. The remaining 6 together with both these jobs can be arranged in 7! ways. So,

No. of ways to arrange the 8 jobs if USU comes immediately before CDP

= 2! * 7!

= 2*1 * 7*6*5*4*3*2*1

= 10080 ways

c. First consider a gap of 1 space between the two jobs USU and CDP. One case can be that USU comes at the first place and CDP at the third place. The remaining 6 jobs can be arranged in 6! ways. Another case can be when USU comes at the second place and CDP at the fourth. This will go on until CDP is at the last place. So, we will have 5 such cases.

The no. of ways USU and CDP can be arranged with a gap of one space is:

6! * 6 = 4320

Then, with a gap of two spaces, USU can come at the first place and CDP at the fourth.  This will go on until CDP is at the last place and USU at the sixth. So there will be 5 cases. No. of ways the rest of the jobs can be arranged is 6! and the total no. of ways in which USU and CDP can be arranged with a space of two is: 5 * 6! = 3600

Then, with a gap of three spaces, USU will come at the first place and CDP at the fifth. We will have four such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 4 * 6!

Then, with a gap of four spaces, USU will come at the first place and CDP at the sixth. We will have three such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 3 * 6!

Then, with a gap of five spaces, USU will come at the first place and CDP at the seventh. We will have two such cases until CDP comes last. So, total no of ways to arrange the jobs with USU and CDP three spaces apart = 2 * 6!

Finally, with a gap of 6 spaces, USU at first place and CDP at the last, we can arrange the rest of the jobs in 6! ways.

So, total no. of different ways to arrange the jobs such that USU comes before CDP = 10080 + 6*6! + 5*6! + 4*6! + 3*6! + 2*6! + 1*6!

                    = 10080 + 4320 + 3600 + 2880 + 2160 + 1440 + 720

                    = 25200 ways

d. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways. Similarly, if LPW comes last, the remaining 7 jobs can be arranged in 7! ways. so, total no. of different ways in which the eight jobs can be arranged is 7! + 7! = 10080 ways

e. If QKJ comes last then, the remaining 7 jobs can be arranged in 7! ways in the queue. Similarly, if QKJ comes second-to-last then also the jobs can be arranged in the queue in 7! ways. So, total no. of ways to arrange the jobs in the queue is 7! + 7! = 10080 ways

3 0
3 years ago
Five and thirty-nine thousandths in standard decimal form
Nesterboy [21]

Answer:

Five and thirty-nine thousandths in standard decimal form is

5.039

Hope This Helps!!!

7 0
2 years ago
Learning Task 4. Solve the problem by applying the sum and product of roots
Delvig [45]

Answer:

<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>

Step-by-step explanation:

For a quadratic equation:

x^2+bx+c=0

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

x^2-18x+80=0

Factoring by finding two numbers that add up to 18 and have a product of 80:

(x-10)(x-8)=0

The solutions to the equation are:

x=10, x=8

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

6 0
3 years ago
1 4/9 divided by -2/9
Varvara68 [4.7K]

Answer:

6 1/2

Step-by-step explanation:

change 1 4/9 into a improper fraction, which is 13/9, and when dividing fractions flip the second number upside down then multiply. 13/9 times -2/9 is -117/18. simplify, which is 13/2, which is also equal to 6 1/2. hope this helped

7 0
2 years ago
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