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4 years ago

A system of 3 linear equations in 3 variables is consistent and independent. How many solutions to the system exist

Mathematics

1 answer:

Nezavi [6.7K]4 years ago

5 0

Answer:

One solution

Step-by-step explanation:

By definition:

A system of linear equations is classified according to the number of solutions such as:

* Consistent: If the system has at least one solution.

* Inconsistent: If the system has no solution

Then, the systems of consistent linear equations are classified as:

* Independent: If the system has only one solution

* Dependents: If the system has endless solutions.

Thus. A consistent and independent system of equations has only one solution

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In a closed box there are 7 blue balls and 5 red balls. Randomly pick one from the box one at a time until the ball is green, th

timofeeve [1]

Answer:

1/7 is the probabiltiy

Step-by-step explanation:

6 0

3 years ago

Carlos needs 2/3 cups of raisins to make one batch of oatmeal bars. How many cups of raisins does Carlos need to make 4 batches

Hitman42 [59]

Answer:

8/3 cups

Step-by-step explanation:

Since he needs 2/3 cups for each batch, and he wants to make 4 batches, we can add 2/3 4 times, or multiply 2/3 times 4.

2/3+2/3+2/3+2/3=8/3

2/3*4=8/3

He needs 8/3 cups for 4 batches.

This can also be written as a mixed number: 2 2/3 cups

4 0

4 years ago

David started across a lake 15 miles wide in his fishing boat at 10 miles per hour. He had to row the rest of the way at only 5

schepotkina [342]

Answer:

Total time = 2hrs

Step-by-step explanation:

Firstly, to outline some variables, with which we can construct some equations:

x = the time taken to cross the river at 10mph (in hrs)

y = the time taken to cross the river at 5mph (in hrs)

t = total time taken to cross the river (in hrs)

a = distance travelled at speed 10mph (in miles)

b = distance travelled at speed 5mph (in miles)

Then,

a + b = 15

t = x + y

y = ¹/₂(t) ∴ t = 2y, so,

x + y = 2y ∴ x = y

Secondly, we know speed = distance/time, so,

10 = a/x ⇒ x = a/10

5 = b/x ⇒ x = b/5

So,

a/10 = b/5 ∴ a = 2b

Thirdly, if a + b = 15, then,

2b + b = 15 ⇒ 3b = 15 ⇒ b = 5

[a = 2b ∴ a = 10]

Fourthly, x = b/5, so,

x = 5/5 = 1,

Since x = y, y = 1 and since t = 2y,

t = 2(1) = 2

The whole trip, therefore, took 2hrs.

5 0

3 years ago

Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 5050 meters.

goblinko [34]

Answer:

The diagonal distance across the plaza is 7141.8 meter. Step-by-step explanation:

Given : Elise walks diagonally from one corner of a square plaza to another. Each side of the plaza is 5050 meters.

To find : What is the diagonal distance across the plaza?

Solution :

We have given the side of a square a=5050 m

The length of the diagonal is multiply the length of square with square root 2.

$D=\sqrt{2} (a)$

Substitute the value of a in the diagonal formula,

$D=\sqrt{2} (5050)$

$D=1.414\times 5050$

$D=7141.77$

Nearest tenth = 7141.8 m

Therefore, The diagonal distance across the plaza is 7141.8 meter.

7 0

3 years ago

Is Noah's work correct? Explain. Yes, Noah's calculations are correct. No, Noah did not simplify correctly. No, Noah used the di

ivolga24 [154]

Answer:

No, Noah used the diameter instead of the radius in the calculations.

V = 91.13π

Step-by-step explanation:

Noah is working on a geometry problem that involves finding the volume of a sphere with a diameter of 9 units. His work is shown below.

V = πr3

V = π(9)3

V = π(729)

V = 972π cubic units

Is Noah’s work correct

Volume of a sphere, V = πr³

radius, r = diameter / 2

Diameter = 9 units

r = 9 / 2

= 4.5 units

Volume of a sphere, V = πr³

= π × 4.5³

= π × 91.125

= 91.125π

Approximately 91.13π

V = 91.13π

No, Noah used the diameter instead of the radius in the calculations.

7 0

3 years ago

Read 2 more answers