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3 years ago

Which of these statements is correct?

Mathematics

2 answers:

tatuchka [14]3 years ago

8 0

Answer:

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

Step-by-step explanation:

1) The system of linear equations 6x - 5y = 8 and 12x - 10y = 16 has no solution.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

6x - 5y = 8

y = 8 - 6x

-5

Step 2 : Substitute y in terms of x from step 1 in the second equation.

16x - 6y = 22

16x - 6 (8 - 6x) = 22

-5

80x - 48 + 36x = 22 x -5

94x = 43

x = 0.457

This statement is incorrect as it does have a solution.

2) The system of linear equations 7x + 2y = 6 and 14x + 4y = 16 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find y in terms of x from any one equation

7x + 2y = 6

y = 6 - 7x

Step 2 : Substitute y in terms of x from step 1 in the second equation.

14x + 4y = 16

14x + 4(6 - 7x) = 16

14x + 12 - 14x = 16

0 ≠ 4

This statement is not true as there are no solutions.

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

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

8x - 3y = 10

x = 10 + 3y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

16x - 6y = 22

16(10 + 3y) - 6y = 22

20 + 6y - 6y = 2

0 ≠ -18

This statement is true because there are no solutions

4) The system of linear equations 9x + 6y = 14 and 18x + 12y = 26 has an infinite number of solutions.

Solve these linear equations simultaneously

Step 1 : Find x in terms of y from any one equation

9x + 6y = 14

x = 14 - 6y

Step 2 : Substitute x in terms of y from step 1 in the second equation.

18x + 12y = 26

18 (14 - 6y) + 12y = 26

8 - 12y + 12y = 26

0 ≠ 18

This statement is incorrect because there are no solutions. It does not have infinite number of solutions.

!!

klasskru [66]3 years ago

8 0

Answer:

<h2>The system of linear equations 8x - 3y = 10 and 16x - 6y = 22 has no solution.</h2>

Step-by-step explanation:

The true statement is the third one, because that system of equations has no solutions. This is because those lines are parallel, see image attached.

We can demonstrate this by solving the system:

$\left \{ {{8x-3y=10} \atop {16x-6y=22}} \right.$

If we multiply the first equation by -2, we would have

$\left \{ {{-16x+6y=-20} \atop {16x-6y=22}} \right\\0x+0y=2\\0=2$

When this happens, means that the system has no solution, that is, the lines that represents those linear equations, are parallel.

Therefore, the right answer is the third option.

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Find the 11th partial sum of the summation of negative 7i plus 22, from i equals 1 to infinity.

Alinara [238K]

The answer is -220
What you do is take -7 and multiply that by (1+2+3+4+5+6+7+8+9+10+11) and then after that add 11 again and multiply it by 22. It would look like this.

-7 x (1+2+3+4+5+6+7+8+9+10+11) +11 x 22

Simplify that to -7 x 66 +11 x 22

now multiply -7 and 66 to get -462

-462 +11 x 22

multiply 11 and 22

-462 + 242

and your final answer will be -220

4 0

3 years ago

John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.

Mandarinka [93]

Let's first define the variables:
x = width
300 - 2x = long
The area will be:
A = (x) * (300 - 2x)
A = 300x - 2x²
We look for the maximum area, for this, we derive:
A '= 300 - 4x
We match zero:
0 = 300 - 4x
x = 300/4 = 75
Therefore, the width is:
x = 75 feet
The length is:
300 - 2x = 300 - 2 (75) = 300-150
150 feet
Answer:
Part A:
The maximum area will be:
A = (150) * (75) = 11250 square feet
Part B:
The dimensions are:
Length = 150 feet
width = 75 feet

3 0

3 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$