All categories

3 years ago

1. Is the following pair of linear equations consistent? Justify your answer.

Mathematics

2 answers:

qaws [65]3 years ago

5 0

<h3>Answer:</h3>

<u>Given equation</u>:– 2ax + by = a, 4ax + 2by - 2a = 0

a1 = 2a; b1 = b; c1 = - a & a2 = 4a; b2 = 2b; c2 = - 2a.

<u>For consistence, a1/a2 = b1/b2 = c1/c2 must be equal</u>

2a/4a = b/2b = -a/-2a
1/2 = 1/2 = 1/2

<u>So, The given equation is consistence</u>.

atroni [7]3 years ago

3 0

Yes.

<h3>Justification:</h3>

Here,

a1/a2 = 2a/4a = 1/2,
b1/b2 = b/2b = 1/2,
c1/c2 = - a/- 2a = 1/2.

∵ a1/a2 = b1/b2 = c1/c2

∴ <u>The given system of equations is consistent</u>.

You might be interested in

Someone please help me out I rlly need help

Anit [1.1K]

The equation that could be used to solve for x is (3x-1) = 140 and the value of x is 47°.

According to the question,

We have the following information:

We have two lines that are intersecting each other at a point. The angles made on this point are given.

Now, we know that these two angles are vertically opposite angles. And we also know that vertically opposite angles are equal.

So, we will have the following equation:

3x-1 = 140

Now, we can easily find the value of x from this equation:

Adding 1 on both sides of the equation:

3x = 140+1

3x = 141

Dividing by 3 on both sides:

x = 141/3

x = 47°

Hence, the equation that could be used to solve for x is (3x-1) = 140 and the value of x is 47°.

To know more about equation here

brainly.com/question/18067015

#SPJ1

5 0

1 year ago

Distribute: -3 (2x-4)

kari74 [83]

-6x+12 because you are multiplying -3 and 2x and -3 and -4

8 0

3 years ago

Read 2 more answers

Suppose that the times required for a cable company to fix cable problems in its customers’ homes are uniformly distributed betw

vampirchik [111]

Answer:

a) 60% probability that a randomly selected cable repair visit will take at least 50 minutes

b) 60% probability that a randomly selected cable repair visit will take at most 55 minutes.

c) The expected length of the repair visit is 52.5 minutes.

d) The standard deviation is 7.22 minutes.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

$P(X \leq x) = \frac{x - a}{b-a}$

For this problem, we have that:

Uniformly distributed between 40 and 65 minutes, so $a = 40, b = 65$

(a) What is the probability that a randomly selected cable repair visit will take at least 50 minutes?

Either it takes less than 50 minutes, or it takes at least 50 minutes. The sum of the probabilities of these events is decimal 1. So

$P(X < 50) + P(X \geq 50) = 1$

The intervals can be open or closed, so

$P(X < 50) = P(X \leq 50)$

We have that

$P(X \geq 50) = 1 - P(X < 50)$

$P(X < x) = \frac{50 - 40}{65 - 40} = 0.4$

$P(X \geq 50) = 1 - P(X < 50) = 1 - 0.4 = 0.6$

60% probability that a randomly selected cable repair visit will take at least 50 minutes

(b) What is the probability that a randomly selected cable repair visit will take at most 55 minutes?

This is $P(X \leq 55)$

$P(X \leq 55) = \frac{55 - 40}{65 - 40} = 0.6$

60% probability that a randomly selected cable repair visit will take at most 55 minutes.

(c) What is the expected length of the repair visit?

The mean of the uniform distribution is:

$M = \frac{a+b}{2}$

$M = \frac{40+65}{2} = 52.5$

The expected length of the repair visit is 52.5 minutes.

(d) What is the standard deviation?

The standard deviation of the uniform distribution is

$S = \sqrt{\frac{(b-a)^{2}}{12}}$

$S = \sqrt{\frac{(65-40)^{2}}{12}}$

$S = 7.22$

The standard deviation is 7.22 minutes.

5 0

3 years ago

What you find the area of the following parallelogram, what units should you use?

Dahasolnce [82]

I believe the answer D

5 0

4 years ago

Fill in the blank.

Amiraneli [1.4K]

Answer: x ≈ 18 ft

Step-by-step explanation:

We will use our trig knowledge to solve this.

The man is standing 10 ft away, but we also need to add the 5 ft shadow as well as that is a point on our triangle.

We can set up a simple trig equation of: tan(50) = x/15

x being the height of the lamppost.

Now we solve.

tan(50) = 1.1918

1.1918 *15 = x

x = 17.876

Now round to the nearest foot.

x ≈ 18 ft

4 0

3 years ago