Determine whether the equations are parallel or not for y= 3x-2 and y= 1/3x -11

Firstly, we will find corner points

A=(-2,5)

B=(6,7)

C=(7,4)

the transformation that has the rule (x, y)→(−x, −y)

x---->-x

We will multiply x-values by -1

A=(-2*-1,5)=(2,5)

B=(6*-1,7)=(-6,7)

C=(7*-1,4)=(-7,4)

y---->-y

We will multiply y-values by -1

A=(2,5*-1)=(2,-5)

B=(-6,7*-1)=(-6,-7)

C=(-7,4*-1)=(-7,-4)

now, we can draw points and find graph

we get

Answer:

-12

Step-by-step explanation:

Given, m = 4

solution:

=-48/m

=-48/4

=-12

Answer:

x1=1

x2= -4

x3= (2 + 5i)

x4= (2 - 5i)

Step-by-step explanation:

STEP 1-

Find the roots of the first term.

(x^2 + 3x -4)=0

Then group the terms that contain the same variable, and move the constant to the opposite side of the equation.

(x^2 + 3x)=4

Complete the square. Remember to balance the equation by adding the same constants to each side.

(x^2 + 3x + 1.5^2)=4 + 1.5^2

(x^2 + 3x + 1.5^2)=6.25

Rewrite as perfect squares

(x + 1.5)^2=6.25

Square root both sides.

(x + 1.5) = (+/-)2.5

x= -1.5(+/-)2.5

x= -1.5 + 2.5 = 1

x= -1.5 + 2.5= -4

so the factored form of the first term.

(x^2 + 3x + 4) = (x - 1) (x + 4)

STEP 2-

Find the roots of the second term

(x^2 - 4x + 29)= 0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(x^2 - 4x)= -29

Complete the square. Remember to balance the equation by adding the same constants to each side

(x^2 - 4x + 4) = - 29 + 4

(x^2 -4x + 4) = -25

Rewrite as perfect squares

(x - 2)^2 = -25

Remember that

i = square root of -1

Square root both sides

(x - 2) = (+/-)5i

x= 2 (+/-)5i

x= 2 + 5i

x= 2 - 5i

so the factored form of the second term is

(x^2 - 4x + 29) = (x - (2 + 5i))(x - (2 - 5i))

STEP 3-

Substitute the factored form of the first and second term in g(x)

g(x) = (x-1)(x + 4)(x- (2+ 5i))(x- ( 2-5i)

there for you have your answers

Making a proportion helps solve this problem. Cm on top, km on bottom.

1 9

---- = ----

20 ?

Cross multiply to get 1? = 180

? = 180.

The distance is 180 km.

Final answer:

The conversion of 9 cm on the map to an actual distance, using the given scale of 1 cm for 20 km, results in an actual distance of 180 kilometers.

Explanation:

The question is asking for the actual distance corresponding to 9 cm on the map. According to the given scale on the map, 1 cm corresponds to an actual distance of 20 km. So to find out how many kilometers 9 cm on the map would be in real life, we simply multiply the length measured on the map by the distance each centimeter represents. This gives us:

9 cm * 20 km/cm = 180 km

So, according to the map, 9 cm corresponds to an actual distance of 180 kilometers.

Learn more about Map Scale Conversion here:

brainly.com/question/32219836

#SPJ3

we know that the endpoints of AB are

and the distance formula is given by

By substituying these points, we have that

which is equal to

then

On the other hand, if

similarly to the previous case, the distance between the endpoint for A'B' is

which is equal to

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

Answer:

Explained below.

Step-by-step explanation:

Let the random variable X be defined as the number of Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway.

The probability of the random variable X is: p = 0.40.

A random sample of n =25 Americans who travel by car are selected.

The events are independent of each other, since not everybody look for gas stations and food outlets that are close to or visible from the highway.

The random variable X follows a Binomial distribution with parameters n = 25 and p = 0.40.

(a)

The mean and variance of X are:

Thus, the mean and variance of X are 10 and 6 respectively.

(b)

Compute the values of the interval μ ± 2σ as follows:

Compute the probability of P (5 ≤ X ≤ 15) as follows:

Thus, 97.72% values of the binomial random variable x fall into this interval.

(c)

Compute the value of P (6 ≤ X ≤ 14) as follows:

The value of P (6 ≤ X ≤ 14) is 0.9361.

According to the Tchebysheff's theorem, for any distribution 75% of the data falls within μ ± 2σ values.

The proportion 0.9361 is very large compared to the other distributions.

Whereas for a mound-shaped distributions, 95% of the data falls within μ ± 2σ values. The proportion 0.9361 is slightly less when compared to the mound-shaped distribution.

Final answer:

The mean of x is 10 and the variance is 6. The interval μ ± 2σ is 10 ± 2√6. P(6 ≤ x ≤ 14) can be calculated using the binomial probability formula.

Explanation:

To find the mean of x, we multiply the sample size (n) by the probability of success (p), which is 40% or 0.4. So, the mean (μ) is 0.4 * 25 = 10. To find the variance of x, we multiply the sample size (n) by the probability of success (p) and the probability of failure (1-p), which is 0.6. So, the variance is 25 * 0.4 * 0.6 = 6.

To calculate the interval μ ± 2σ, we need to find the standard deviation (σ) first. The standard deviation is the square root of the variance, so σ = √6. Then, the interval is μ ± 2σ. Plugging in the values, the interval is 10 ± 2√6. To find the values of x that fall into this interval, we can subtract and add 2√6 from the mean, resulting in the range 10 - 2√6 to 10 + 2√6.

To find P(6 ≤ x ≤ 14), we need to find the probability of x being between 6 and 14. We can use the binomial probability formula to calculate this. P(6 ≤ x ≤ 14) = P(x = 6) + P(x = 7) + ... + P(x = 14). Using a binomial probability table or a calculator, we can find the probabilities of each x value and sum them up.

Learn more about Mean, Variance, Binomial Probability here:

brainly.com/question/19052146

#SPJ3