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wolverine [178]
3 years ago
8

Here is a system of equations. (y=x-6 y=-x-2 Graph the system. Then write its solution. Note that you can also answer "No soluti

on" or "Infinitely many" solutions.​
Mathematics
1 answer:
sladkih [1.3K]3 years ago
7 0

Answer:

Example system with no solution

We're asked to find the number of solutions to this system of equations:

\begin{aligned} y &= -3x+9\\\\ y &= -3x-7 \end{aligned}  

y

y

​  

 

=−3x+9

=−3x−7

​  

 

Without graphing these equations, we can observe that they both have a slope of -3−3minus, 3. This means that the lines must be parallel. And since the yyy-intercepts are different, we know the lines are not on top of each other.

There is no solution to this system of equations.

Example system with infinite solutions

We're asked to find the number of solutions to this system of equations:

\begin{aligned} -6x+4y &= 2\\\\ 3x-2y &= -1 \end{aligned}  

−6x+4y

3x−2y

​  

 

=2

=−1

​  

 

Interestingly, if we multiply the second equation by -2−2minus, 2, we get the first equation:

\begin{aligned} 3x-2y &= -1\\\\ \blueD{-2}(3x-2y)&=\blueD{-2}(-1)\\\\ -6x+4y &= 2 \end{aligned}  

3x−2y

−2(3x−2y)

−6x+4y

​  

 

=−1

=−2(−1)

=2

​  

 

In other words, the equations are equivalent and share the same graph. Any solution that works for one equation will also work for the other equation, so there are infinite solutions to the system.

Step-by-step explanation:

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One light-year equals 5.9 x 1012 miles. How many light-years are in 6.79
inna [77]

Option B

The number of light years in 6.79 \times 10^{16} miles is 11508 light years

<em><u>Solution:</u></em>

Given that,

One light-year equals 5.9 x 10^12 miles

Therefore,

1 \text{ light year } = 5.9 \times 10^{12} \text{ miles }

To find: Number of light years in 6.79 \times 10^{16} miles

Let "x" be the number of light years in 6.79 \times 10^{16} miles

Then number of light years in 6.79 \times 10^{16} miles can be found by dividing 6.79 \times 10^{16} miles by miles in 1 light year

\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79 \times 10^{16}}{5.9 \times 10^{12}}\\\\\text{Use the law of exponent }\\\\\frac{a^m}{a^n} = a^{m-n}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = \frac{6.79}{5.9} \times 10^{16-12}\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 1.1508 \times 10^4\\\\\text{Number of light years in } 6.79 \times 10^{16} miles = 11508

Thus number of light years in 6.79 \times 10^{16} miles is 11508 light years

3 0
3 years ago
A package of 4 pairs of insulated gloves cost 35.96
tino4ka555 [31]

Answer:

You need to add more to this question but I am assuming you want to know how much each pair of gloves is?

Step-by-step explanation:

Divide 35.96 by 4

35.96÷4= $8.99 per pair of insulated gloves

6 0
2 years ago
Let L: R2 --&gt; R2 be a linear operator.If L((1,2)T) = (-2,3)Tand L((1,-1)T) = (5,2)TFind the value of L((7,5)T
devlian [24]

Answer: L((7,5)T)=(7, 18)T

Step-by-step explanation:

The step by step explanation is given in picture.

3 0
2 years ago
What is the surface area
nexus9112 [7]

Answer:

A 1759 sq. units

Step-by-step explanation:

to find the surface area of a closed cylinder the formula is

2πr² + πdh

r = radius = 10

d = diameter = 10 + 10 = 20

2 x 3.14 x 10² + 3.14 x 20 x 18

628.3 + 1130.94 = 1759.24

ans = 1759

5 0
3 years ago
Which statement best describes the function below?
marta [7]
<h2>Answer:</h2>

A. It is a many-to-one function.

<h2>Step-by-step explanation:</h2>

Hello! It will be a pleasure to help to figure out what's the correct answer to this problem. First of all, we have the following function:

f(x) = 2x^3 + 2x^2-x

When plotting this function, we get the red graph of the function shown below. So let's solve this as follows:

<h3>A. It is a many-to-one function.</h3>

True

A function is said to be many-to-one there are values of the dependent variable (y-values) that corresponds to more than one value of the independent variable (x-values). To test this, we need to use the Horizontal Line Test. So let's take the horizontal line y=0.5, and you can see from the first figure below that y=0.5 is mapped onto x=-1.241 \ x=-0.344 \ and \ x=0.585. so this is a many-to-one function.

<h3>B. It is a one-to-one function.</h3><h3>False</h3>

Since this is a many-to-one function, it can't be a one-to-one function.

<h3>C. It is not a function.</h3>

False

Indeed, this is a function

<h3>D. It fails the vertical line test.​</h3>

False

It passes the vertical line test because any vertical line can intersect the graph of the function at most once. An example of this is shown in the second figure below.

6 0
3 years ago
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