# Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________

Question
Equations and inequalities
Fill in the blank/s: When solving x = 3y + 2 and 5x - 15y = 10 by the substitution method, we obtain 10 = 10, so the solution set is ___________ The equations in this system are called ___________ . If you attempt to solve such a system by graphing, you will obtain two lines that ___________

2020-12-29
Given equations are
$$\displaystyle{X}={3}{Y}+{2}$$
$$\displaystyle{X}-{3}{Y}={2}---{\left({1}\right)}$$
$$\displaystyle{5}{X}-{15}{Y}={10}---{\left({2}\right)}$$
$$\displaystyle{\frac{{{a}_{{1}}}}{{{a}_{{2}}}}}={\frac{{{1}}}{{{5}}}},{\frac{{{b}_{{1}}}}{{{b}_{{2}}}}}={\frac{{-{3}}}{{-{15}}}}={\frac{{{1}}}{{{5}}}}{\quad\text{and}\quad}{\frac{{{c}_{{1}}}}{{{c}_{{2}}}}}={\frac{{{2}}}{{{10}}}}={\frac{{{1}}}{{{5}}}}$$
$$\displaystyle{w}{e}{k}{n}{o}{w}{t}\hat{{w}}{h}{e}{n}{\frac{{{a}_{{1}}}}{{{a}_{{2}}}}}={\frac{{{b}_{{1}}}}{{{b}_{{2}}}}}={\frac{{{c}_{{1}}}}{{{c}_{{2}}}}}$$
then given lines have infinite number of solutions
And given line will be coincident lines.
Hence, solution set will be infinite.The equation are in this system are called coincident . And we will draw graph then line will coincide with each other

### Relevant Questions

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
$$\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}$$
where A is the cross-sectional area of the vehicle and $$\displaystyle{C}_{{d}}$$ is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity $$\displaystyle\vec{{{v}}}$$. Find the power dissipated by form drag.
Express your answer in terms of $$\displaystyle{C}_{{d}},{A},$$ and speed v.
Part B:
A certain car has an engine that provides a maximum power $$\displaystyle{P}_{{0}}$$. Suppose that the maximum speed of thee car, $$\displaystyle{v}_{{0}}$$, is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power $$\displaystyle{P}_{{1}}$$ is 10 percent greater than the original power ($$\displaystyle{P}_{{1}}={110}\%{P}_{{0}}$$).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, $$\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}$$, is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
The unstable nucleus uranium-236 can be regarded as auniformly charged sphere of charge Q=+92e and radius $$\displaystyle{R}={7.4}\times{10}^{{-{15}}}$$ m. In nuclear fission, this can divide into twosmaller nuclei, each of 1/2 the charge and 1/2 the voume of theoriginal uranium-236 nucleus. This is one of the reactionsthat occurred n the nuclear weapon that exploded over Hiroshima, Japan in August 1945.
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Solve the following system of linear equations in two variables by Substitution method.
$$5x-2y=-7$$
$$x=-2y+1$$

Fill in the blank/s: When solving $$3x^2 + 2y^2 = 35, 4x^2 + 3y^2 = 48$$ by the addition method, we can eliminate x2 by multiplying the first equation by -4 and the second equation by _________ and then adding the equations.

Fill in the bla?

An equation that expresses a relationship between two or more variables, such as $$H = \frac{9}{10} (20 - a)$$ is called a/an ? The process of finding such equations to describe real-world phenomena is called mathematical ? Such equations, together with the meaning assigned to the variables, are called mathematical ?

4.7 A multiprocessor with eight processors has 20attached tape drives. There is a large number of jobs submitted tothe system that each require a maximum of four tape drives tocomplete execution. Assume that each job starts running with onlythree tape drives for a long period before requiring the fourthtape drive for a short period toward the end of its operation. Alsoassume an endless supply of such jobs.
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b) Suggest an alternative policy to improve tape driveutilization and at the same time avoid system deadlock. What is themaximum number of jobs that can be in progress at once? What arethe bounds on the number of idling tape drives?
Fill in the blank/s: When solving a system of linear equations by graphing, the system’s solution is determined by locating ___________

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
Fill in the bla
so the resulting statement is true.
when solving
$$3x^2+2y^2=35$$
$$4x^2+3y^2=48$$
by the addition method, we can eliminate $$x^2$$ by the multiplying the first equation by -4 and the second equation by __________ and then adding the equations