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2 years ago

How many intersections are there of the graphs of the equations below?

Mathematics

1 answer:

kipiarov [429]2 years ago

6 0

Answer:

The number of intersections = ∞

Step-by-step explanation:

Given the system of equations:

0.5 x + 5y = 6

3x + 30y = 36

By multiplying the first equation by 6

∴ 6 (0.5 x + 5y) = 6 * 6

∴ 3x + 30y = 36

So, Those equations are "Dependent", because they are really the same equation, just multiplied the first equation by 6.

So, the two equations are identical

Therefore: They have infinity number of solutions.

See the attached figure.

0.5 x + 5y = 6 ⇒ in black color

3x + 30y = 36 ⇒ in red color

You might be interested in

Which equation represents this number sentence? Two more than one-third of a number is 8

Natali [406]

Answer:

B. $2+\frac{1}{3}n=8$

Step-by-step explanation:

Let n be the number.

We are asked to write an mathematical expression for the given word phrase.

One third of a number, n, would be $\frac{1}{3}n$ .

Two more than one third of a number, n, would be $2+\frac{1}{3}n$ .

We are told that Two more than one-third of a number is 8. We can represent this information in an equation as:

$2+\frac{1}{3}n=8$

Therefore, option B is the correct choice.

8 0

2 years ago

Read 2 more answers

Suppose a continuous probability distribution has an average of μ=35 and a standard deviation of σ=16. Draw 100 times at random

yulyashka [42]

Answer:

To use a Normal distribution to approximate the chance the sum total will be between 3000 and 4000 (inclusive), we use the area from a lower bound of 3000 to an upper bound of 4000 under a Normal curve with its center (average) at 3500 and a spread (standard deviation) of 160 . The estimated probability is 99.82%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For sums, we have that the mean is $\mu*n$ and the standard deviation is $s = \sigma \sqrt{n}$

In this problem, we have that:

$\mu = 100*35 = 3500, \sigma = \sqrt{100}*16 = 160$

This probability is the pvalue of Z when X = 4000 subtracted by the pvalue of Z when X = 3000.

X = 4000

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

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{4000 - 3500}{160}$

$Z = 3.13$

$Z = 3.13$ has a pvalue of 0.9991

X = 3000

$Z = \frac{X - \mu}{s}$

$Z = \frac{3000 - 3500}{160}$

$Z = -3.13$

$Z = -3.13$ has a pvalue of 0.0009

0.9991 - 0.0009 = 0.9982

So the correct answer is:

5 0

2 years ago

The mayor of Brookmarsh is running a campaign to revitalize his city. Currently, the population of Brookmarsh is 10,000 and is i

lisabon 2012 [21]

The equation correctly modeled would be

1000+.02t = 15000

8 0

2 years ago

If Angle 6 is congruent to angle 10 and Angle 5 is congruent to angle 7, which describes all the lines that must be parallel? Li

Nina [5.8K]

Answer:

Third option: Lines "r" and "s" and lines "t" and "u" must be parallel.

Step-by-step explanation:

The missing figure is attached.

You need to remember that:

1- A Transversal is defined as a line that intersects two or more lines.

2- When a transversal cut two parallel lines, several angles are formed, which are grouped in pairs. Some of them are:

a. Vertical angles: are those pairs of angles that share the same vertex and are opposite to each other. These angles are congruent.

b. Corresponding angles: are those pairs of non-adjacent angles located on the same side of the transversal and outside the parallel lines. They are congruent.

In this case, you can identify in the figure that:

$\angle 6$ and $\angle 10$ are Corresponding angles.

$\angle5$ and $\angle 7$ are Vertical angles.

Therefore, based on the explained before, you can conclude that lines "r" and "s" and lines "t" and "u", must be parallel.

7 0

2 years ago

Read 2 more answers

Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1

astra-53 [7]

Answer:

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

Step-by-step explanation:

This case represents a definite integral, in which lower and upper limits are needed, which corresponds to the points where both intersect each other. That is:

$x^{2} - 24 = 1$

Given that resulting expression is a second order polynomial of the form $x^{2} - a^{2}$ , there are two real and distinct solutions. Roots of the expression are:

$x_{1} = -5$ and $x_{2} = 5$ .

Now, it is also required to determine which part of the interval $(x_{1}, x_{2})$ is equal to a number greater than zero (positive). That is:

$x^{2} - 24 > 0$

$x^{2} > 24$

$x < -4.899$ and $x > 4.899$ .

Therefore, exists two sub-intervals: $[-5, -4.899]$ and $\left[4.899,5\right]$ . Besides, $x^{2} - 24 > y = 1$ in each sub-interval. The definite integral of the region between the two curves over the x-axis is:

$A = \int\limits^{-4.899}_{-5} [{1 - (x^{2}-24)]} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} [{1 - (x^{2}-24)]} \, dx$

$A = \int\limits^{-4.899}_{-5} {25-x^{2}} \, dx + \int\limits^{4.899}_{-4.899} \, dx + \int\limits^{5}_{4.899} {25-x^{2}} \, dx$

$A = 25\cdot x \right \left|\limits_{-5}^{-4.899} -\frac{1}{3}\cdot x^{3}\left|\limits_{-5}^{-4.899} + x\left|\limits_{-4.899}^{4.899} + 25\cdot x \right \left|\limits_{4.899}^{5} -\frac{1}{3}\cdot x^{3}\left|\limits_{4.899}^{5}$

$A = 2.525 -2.474+9.798 + 2.525 - 2.474$

$A = 9.9\,units^{2}$

The area of the region between the two curves by integration over the x-axis is 9.9 square units.

4 0

2 years ago