1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
9966 [12]
3 years ago
14

How many solutions does an equation have when the variable adds out and the final sentence is true?

Mathematics
2 answers:
salantis [7]3 years ago
7 0

Answer:

Infinitely many solutions

Step-by-step explanation:

If we have a system of equation like:

2x+y=4

6x+3y=12

If we make y the subject in the first equation and substitute into the second equation, we get:

6x+3(4-2x)=12

We expand to get:

6x+12-6x=12

6x-6x+12=12

Now the variable adds out to give:

12=12

This statement is true so the equation has infinitely many solution.

azamat3 years ago
7 0

Answer:

  • <u>infinite solutions</u>

Explanation:

When <em>the variable adds out</em> means that after all the simplifications, at the end, it will not appear in the final sentence or expression.

Then, if the <em>final sentence is true,</em> and not variable appears, but only constants, the sentence is always true, no matter what value the variable takes.

That means that you can put any value for the variable in the original equation and the equation will be true; hence there are infinite solutions.

This is an example:

<u>1. Equation</u>:

  • 3x + 5+ x² = 2 - ( - 4x - x²) + (3 - x)

<u>2. Remove the parenthesis</u>:

  • 3x + 5+ x² = 2 +  4x + x² + 3 - x

<u>3. Add like terms on the right side and transpose the variables to the left side</u>:

  • 3x + 5 + x² = 5 + 3x + x²
  • 3x + x² - 3x -x² + 5 = 5

<u>4. Combine like terms on the left side</u>:

  • 5 = 5

Thus, <em>the variable added out and the final sentence is true</em>. Hence, this equation has infinite solutions, which you can prove substituting the variable with any value.

You might be interested in
What type of triangle is formed by joining the points D(7, 3), E(8, 1), and
KiRa [710]

D(7, 3), E(8, 1), and  F(4, -1)

We calculate the squared distances between the points:

DE^2 = 1^2 + 2^2 = 5

EF^2=4^2+2^2=20

DF^2=3^2+4^2=25

Since DF^2=DE^2+EF^2 we have a right triangle with hypotenuse DF.

7 0
3 years ago
The goal of a nutritional study was to compare the caloric intake of adolescents living in rural areas of the US with the calori
stiks02 [169]

Answer:

To give more clarity to the question, lets examine the attached back-to-back stem plot.

A)

Having examined the stem plot, we can using quick calculations, summarize that:

The mean (40.45 cal/kg) and median (41 cal/kg) daily caloric intake of ninth-grade students in the rural school is higher than the corresponding measures of center, mean (32.6 cal/kg) and median (32 cal/kg), for ninth-graders in the urban school.

The median and the mean for the students in the 9th grade in the urban school is lower than that of those of their contemporaries in the rural school. The respective medians and means are stated below:

Urban 9th Grade Students

Median = 32 cal/kg

Mean = 36 cal/kg

Rural 9th Grade Students

Median = 41 cal/kg

Mean = 41 cal/kg

Please note that all figures above have been approximated to the nearest whole number.

B)

It is unreasonable to generalize the findings of this study to all rural and urban 9th-grade students in the United States because the sample is too small compared to the target population size.

To allow for generalization, they would have to collect and analyze more samples say from every state within America.

Cheers!

5 0
3 years ago
Patterns find next 2 numbers 1.) 7,4,1,-2,__,__ <br> 2.) 1,4,9,16,__,__ <br> 3.) 0,1,8,27,__,__
kati45 [8]

Answer:

1. 7, 4, 1, -2, -5, -8

2. 1, 4, 9, 16, 25, 36

3. i'm not sure about this one.


3 0
3 years ago
Cari owns a horse farm and a horse trailer that can transport up to 8,000 pounds of livestock and tack. She travels with 5 horse
const2013 [10]

Answer:

5(1248 lb/horse + t lb) ≤ 8000 lb

Step-by-step explanation:

One way to do this is to find the average weight of the 5 horses:

It is:

6,240 lb

---------------- = 1248 lb/horse

  5 horses

and to this, for each horse, we must add t lbs tack.

Thus, 5(1248 lb/horse + t lb) ≤ 8000 lb

would be an appropriate inequality.

Please note that your question mentions "the following inequalities;" that means you are expected to share them!  Please do so next time.  Thanks.

5 0
3 years ago
Explain why these answers are true.
Dmitry [639]

Answer:

A, i actullay dont know i just want the piont and this was a long time ago so he doesnt need it

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • The number 6 is a member of which four groups of real numbers?
    9·1 answer
  • Simplify the expression: 3x2(x2 - 4x - 2) + (5x3 + 7x2 + 2x + 11) Show and explain your steps.
    7·1 answer
  • Solving inequalities, what is x/18&gt;27
    11·1 answer
  • Vivi is a drummer for a band. She burns 756 calories while drumming for 3hours. She burns the same number of calories per hour.
    7·1 answer
  • NEED HELP!<br><br> Create a table of points from the equation f (x)= 3x^2 -8x + 2
    13·1 answer
  • 1/2 x 1/4 answer then write in simplest form
    15·1 answer
  • Select the equation of a line that is perpendicular to the line on the graph and passes through the point (3, 2). (1 point) y =
    5·1 answer
  • A board that is 4 1/2 feet long weighs 7 1/5 pounds. How much would one foot of the board
    6·1 answer
  • HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
    7·1 answer
  • The perimeter of a triangle is 56. The side lengths are x + 4, 3x + 7, and x + 9. What is the value of x?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!