Which of these statements is correct? The system of linear equations 6 x minus 5 y = 8 and 12 x minus 10 y = 16 has no solution. The system of linear equations 7 x + 2 y = 6 and 14 x + 4 y = 16 has an infinite number of solutions. The system of linear equations 8 x minus 3 y = 10 and 16 x minus 6 y = 22 has no solution. The system of linear equations 9 x + 6 y = 14 and 18 x + 12 y = 26 has an infinite number of solutions

Answers

Answer 1

Answer:

The only true statement is:

"The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution."

Step-by-step explanation:

First, some definitions.

A system of linear equations has infinite solutions if both equations define the same line, has no solutions if we have two parallel lines, has one solution in all the other cases.

Where two lines are parallel if we can write them as:

a*x + b*y = c

a*x + b*y = d

where c and d are different numbers.

Now we can analyze the given statements:

a)

6x - 5y = 8

12x - 10y = 16

has no solution?

If we divide both sides of the second equation by 2, we get:

(12x - 10y)/2 = 16/2

6x - 5y = 8

We get the first equation, then both equations define the same line, thus the system has infinite solutions, then the statement is false.

b)

7x + 2y = 6

14x + 4y = 16

has infinite solutions?

Let's divide the second equation by 2, then we get:

(14x + 4y)/2 = 16/2

7x + 2y = 8

If we rewrite our system of equations, we get:

7x + 2y = 6

7x + 2y = 8

These are parallel lines, thus, this system has no solutions.

So the statement is false.

c)

8x - 3y = 10

16x - 6y = 22

has no solution?

Again, let's divide the second equation by 2 to get:

(16x - 6y)/2 = 22/2

8x - 3y = 11

If we rewrite our system:

8x - 3y = 10

8x - 3y = 11

These are parallel lines, thus the system has no solutions, so this statement is correct.

d)

9x + 6y = 14

18x + 12y = 26

Has infinite solutions?

Dividing the second equation by 2 we get:

(18x + 12y)/2 = 26/2

9x + 6y = 13

So the equations are different (are parallel lines again) so this system has not infinite solutions.

Then the statement is false.

Answer 2

Answer:

The answer to your question is the third choice.

Step-by-step explanation:

a)          6x - 5y = 8

          12x - 10y = 16

We observe that these lines are the same so they have infinite solutions.

b)

           7x + 2y = 6

          14x + 4y = 16

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

c)

            8x - 3y = 10

           16x - 6y = 22

These lines are parallel because they have the same slope, so they do not cross, there is no solution.

d)

           9x + 6y = 14

          18x + 12y = 26

These lines are parallel because they have the same slope, so they do not cross, they do not have an infinite number of solutions.


Related Questions

Tell wether x and y show a proportional relationship.

x 1 2 3 4
y 4 8 12 16

Answers

Answer:

They do because y is always 4 times of x.

Step-by-step explanation:

Please answer this, I am confused (5^2)(7^2)(3^2)

Answers

Given:

The expression is:

[tex](5^2)(7^2)(3^2)[/tex]

To find:

The value of the given expression.

Solution:

We have,

[tex](5^2)(7^2)(3^2)[/tex]

On simplification, we get

[tex](5^2)(7^2)(3^2)=(25)(49)(9)[/tex]

[tex](5^2)(7^2)(3^2)=11025[/tex]

Therefore, the value of the given expression is 11025.

Find the equal measures of 1. 28 m = ________ km 2. 3899 ml = ______ l 3. 79 kg = _____ g Show the process of each

Answers

Answer:

1. 0.028 km

2. 3.899 L

3. 79,000 g

Riley's cat has 8 kittens. Of those 8 kittens, 4 are brown, 1 is grey, and the rest are orange. Which of the following could be used to find the probability that the first kitten Riley picks up at random is NOT orange?

Answers

Answer:

5/8 or 62.5 percent

Step-by-step explanation:

Which equation represents the function y - 5 = –2(x+3) in slope-intercept form?
Oy= 2x + 1
Oy = 2x - 1
Oy= -2x - 1
Oy = -2x + 11
Oy = -23 - 11

Answers

Answer:

-2x-1

Step-by-step explanation:

when you graph the equation it gives you a decreasing slope with the y intercept of -1. the slope is 2 and since its decreasing it is -2. therefore its -2x-1

The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

What is a straight line?

A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.

here, we have,

given that,

the function y - 5 = –2(x+3)

now, we have to find  in slope-intercept form.

now, we have,

function has a decreasing slope with the y intercept of -1. the slope is 2

and since its decreasing it is -2.

again, we have,

y - 5 = –2(x+3)

or, y = -2x - 6 + 5

or, y = -2x -1

here, slope = m = -2

and, y-intercept = c = -1

as, we know that,

slope-intercept form is: y = mx+ c

so, we get,  y = -2x -1

Hence, The solution is, the function y - 5 = –2(x+3) in slope-intercept form is y = -2x -1 .

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I would really appreciate if someone could answer this:)

Answers

Answer:

first you need to know that the the sum of the co-interior angle is  180 degree and the sum of the opposite side of  parallelogram is always equal.

now x+140=180(being co - interior angle)

or, x= 180-140

therefore, x =40 degree

y= 140 degree because sum of the opposite side of  parallelogram is always equal.

x= z=40 degree (sum of the opposite side of  parallelogram is always equal.

when you are again confused go in this link

 ----> https://www.scholr.com/ncert-solutions/consider-the-following-parallelograms-fi/40087/

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I neeed the answer plssss

Answers

Answer:

300km

Step-by-step explanation:

if 1 hr=80

then take 80 and multiply it by 3.75

hope this helps!

please give brainiest if you want<3

Answer:

300km

Step-by-step explanation:

Please, I'm desperate need of help I will mark Brainliest to the one who answers with the full process! Gold will Bless You!

Two angles of a triangle are 85° and 65°, and the longest side of the triangle is 34 cm. How long is the shortest side? Include a labelled diagram.

Answers

Add 65 and 85

65+85= 150

Next subtract 180-150

The answer is 30, so that is the missing angle is 30.

The side opposite to 30 is the shortest side

Here I added the picture!

plz it's do to day HELP PLZ​

Answers

Answer:

9 units^3

Step-by-step explanation:

V = l*w*h

   = 1 1/2 * 4 * 1 1/2

Change to improper fractions

  = 3/2 * 4 * 3/2

   = 36/4

   = 9 units^3

A grocery store chain uses loyalty cards that offer discounts on sale attheir store. The probability that a randomly chosen shopper has a loyaltycard is 0.8. A group of shoppers have been selected at random to completea customer satisfaction survey. Let Xi be a random variable that equals 1 when a customer has a loyalty card and 0 otherwise.

Required:
a. Construct a joint probability table for the random variables X, and X.
b. Define the event that the first four customers sampled have loyalty cards in terms of the random variables X, X2, X3, and Xd. Then compute the probability of this event.

Answers

The answer is a cause

What is half of 3/4 in fraction?

Answers

Answer:

3/8

Step-by-step explanation:

1/2 times 3/4= 3/8

Select the correct answer.
Which expression is equivalent to the glven expression?
(3m-4)^3(3m^5)
A. 81/m^2 B.27/m^7 C. 27/m^2 D.81/m^7

Answers

The answer for this question is D

The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (3m⁻⁴)³ (3m⁵)

Now, We can simplify as;

⇒ (3m⁻⁴)³ (3m⁵)

⇒ (3³m⁻¹²) (3m⁵)

⇒ (27m⁻¹²) (3m⁵)

⇒ 81 m⁻¹²⁺⁵

⇒ 81 m⁻⁷

⇒ 81 / m⁷

Thus, The correct expression which is equivalent to the given expression is,

⇒ 81 / m⁷

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The club with an occupancy of 100 will sell out at $25 per ticket. If the owner decides to increase the price by $5, then 2 less tickets will be sold. Determine the revenue function if x is the number of $5 increases.

Answers

Answer:

100 + (5X) = -2X

Step-by-step explanation:

Since the club with an occupancy of 100 will sell out at $ 25 per ticket, and if the owner decides to increase the price by $ 5, then 2 less tickets will be sold, to determine the revenue function if X is the number of $ 5 increases the following calculation must be performed:

100 + (5X) = -2X

So, for example, if the price were increased by $ 15, the equation would apply as follows:

15/5 = 3

100 + (5x3) = -2 x 3

100 + 15 = -6

115 = -6

WILL MARK BRAINLIEST!!
Which is the graph of g(x)

Answers

Answer:

the second one after first

Step-by-step explanation:

it strictly obeys the rules of boundary

If using the method of completing the square to solve the quadratic equation
x^2 + 8x – 4 = 0, which number would have to be added to "complete the square"?

Answers

Step-by-step explanation:

everything can be found in the picture

Which of the following functions has a rate of change that stays the same?
A. y=-4+10
B. y=1/2x^2
C. y=3^x
D. y=x^2+2

Answers

Answer:

The answer is A because the rest are parabolas

Simplify the fraction to lowest terms.
56/
182

Answers

the answer to your question is 4/13.

A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 1.5 hours

Answers

Answer:

The Sample Size Need To be at least 114

Step-by-step explanation:

According to the Question,

Given, A university dean of students wishes to estimate the average number of hours students spend doing homework per week. The standard deviation from a previous study is 6.2 hours.

The Maximum Error(E) is given as 1.5 hours and the standard deviation(σ) is 6.2 hours.

Now, For 99% Confident the level of value α is 0.01.

α/2 = 0.01/2 ⇒ 0.005

Thus, From The table, We get that the value of [tex]Z_{alpha/2}[/tex] is 2.58.

Hence, the sample size n can be found as

n = {[tex]\frac{(Z_{alpha/2} * Standard Deviation)}{E}[/tex]}²

n = {2.58 × 6.2}² / 1.5²

n = 113.72 .

So, The Sample Size Need To be at least 114.

What is the value of y in the equation 3y - 8 = 22?
7.3
8
10
14

Answers

The answer to your question is ten

Simplify (2 1/6 - 1 2/3) - 2 2/3​

Answers

Answer:

[tex]- 2\frac{1}{6}[/tex]

Step-by-step explanation:

[tex](2\frac{1}{6} -1\frac{2}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{5}{3}) - 2 \frac{2}{3}[/tex]

[tex](\frac{13}{6} -\frac{10}{6}) - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - 2 \frac{2}{3}[/tex]

[tex]\frac{3}{6} - \frac{8}{3}[/tex]

[tex]\frac{3}{6} - \frac{16}{6}[/tex]

[tex]- \frac{13}{6}[/tex]

[tex]- 2\frac{1}{6}[/tex]

An aeroplane descended 1.4 miles to an elevation of 0.6 miles as shown by the equation below.
Solve the equation to find the elevation of the plane before its descent.
x-1.4 = 0.6
A 0.8
B 1.0
C 2.0
D 1.2
Quick

Answers

Answer:

C 2.0

Step-by-step explanation:

x-1.4 =0.6

add 1.4 to both sides

x=2.0

I would appreciate if someone could answer this

Answers

Answer:

x = 15

LN and MO both equal 43

Step-by-step explanation:

LN and MO are diagonals in rectangle

Diagonals of a rectangle are congruent Hence, 4x - 17 = 2x + 13

Now we solve for x

4x - 17 = 2x + 13

Add 17 to both sides

4x = 2x + 30

Subtract 2x from both sides

2x = 30

Divide both sides by 2

x = 15

Now we want to find the values of LN and MO

To do so we substitute 15 for x in it's given expression ( note: because LN = MO we only need to do this process once )

LN = 4x - 17

Substitute 15 for x

4(15) - 17

Multiply

60 - 17

Subtract

LN and MO = 43

In general, half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers, how many will qualify for the discount

Answers

Answer:60

Step-by-step explanation:

300 of 20% is 60

The number of qualified customers for the discount will be 60.

What is the percentage?

The Percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

It is given that half of all the customers you speak to will ask about any upcoming pricing discounts or promotions. Of those who do ask, only 20% qualify for the discount. So that means if I speak to 300 customers.

The number of qualified customers will be calculated as below:-

The qualified customers are 20% of 300.

Number = 300 x (20/100)

Number = 300 x 0.2

Multiply the number 330 with 0.2 to get the final value.

Number = 60

Therefore, the number of qualified customers for the discount will be 60.

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A student is taking a multiple-choice exam in which each question has four choices.

Assume that the student has no knowledge of the correct answers to any of the questions.

She has decided on a strategy in which she will place four balls (marked A, B, C, and D) into a box.

She randomly selects one ball for each question and replaces the ball in the box.

The marking on the ball will determine her answer to the question.

There are five multiple choice questions on the exam.

What is the probability that she will get

a. Five questions correct?

b. At least four questions correct?

c. No questions correct?

d. No more than two questions correct?


Answers

Answer:

d no more than two questions correct

Use slopes and y-intercepts to determine if the lines y=−2/3x+2 and −3x+2y=−4 are parallel.

Answers

Answer:

the answer is no

Step-by-step explanation:

y = -2/3x+2

2y = 3y-4

y = 3/2y-2

but here's a comment: it is perpendicular because it is it's opposite reciprocol

0.36% as a fraction in simplest form

Answers

Answer: 9/2500

Step-by-step explanation:

We start with turning it into a fraction:

0.36/100

Then, we turn every number into a whole number by multiplying by whatever the last decimal place is called (hundreth= x100)

36/10000

Lastly, we simplify as much as we can by finding the least common denominator. In this case, the smallest whole number both 36 and 10000 can be divided by is 4:

(36/4)/(10000/4)

= 9/25000

Identify the x-intercept points of the parabola

Answers

Answer:

(3,0) and (-1,0)

Step-by-step explanation:

The X intercept are the point(s) where the line croses the X axis (the horizontal/leftright line). the points for this graphing system are always listed (x,y) so to find a certain point you find the X value then the Y value

Triangle ABC IS dilated using the origin as the center of dllation to create triangle A'B'C'. What rule best represents the dilation applied to triangle ABC to ​

Answers

The scale factor is 3 so B would be your answer because all coordinates are multiplied by 3

11. f(x) = x + 3, g(x) = -x + 2. Find (f + g)(x)

Answers

Answer:

(f + g)(x) = 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = x + 3

g(x) = -x + 2

(f + g)(x) is f(x) + g(x)

Step 2: Find

Substitute in function values:                                                                          (f + g)(x) = x + 3 - x + 2[Subtraction] Combine like terms (x):                                                              (f + g)(x) = 3 + 2Add:                                                                                                                   (f + g)(x) = 5

Which expression is equivalent to 5^15 x 5^5

Answers

Answer:

[tex]5^{15} * 5^{5}[/tex]

= [tex]25^{20\\}[/tex]

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