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Vlada [557]
3 years ago
13

How many Solutions does this system have? (1 point)

Mathematics
1 answer:
mixas84 [53]3 years ago
5 0

The given system of equation that is 2x+y=3 and 6x=9-3y has infinite number of solutions.

Option -C.

<u>Solution:</u>

Need to determine number of solution given system of equation has.

\begin{array}{l}{2 x+y=3} \\\\ {6 x=9-3 y}\end{array}

Let us first bring the equation in standard form for comparison

\begin{array}{l}{2 x+y-3=0} \\\\ {6 x+3 y-9=0}\end{array}

\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}

To check how many solutions are there for system of equations a_{1} x+b_{1} y+c_{1}=0 \text{ and }a_{2} x+b_{2} y+c_{2}=0, we need to compare ratios of \frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} \text { and } \frac{c_{1}}{c_{2}}

In our case,  

a_{1} = 2, b_{1}= 1\text{ and }c_{1}= -3

a_{2}  = 6, b_{2} = 3,\text{ and }c_{2} = -9

\begin{array}{l}{\Rightarrow \frac{a_{1}}{a_{2}}=\frac{2}{6}=\frac{1}{3}} \\\\ {\Rightarrow \frac{b_{1}}{b_{2}}=\frac{1}{3}} \\\\ {\Rightarrow \frac{c_{1}}{c_{2}}=\frac{-3}{-9}=\frac{1}{3}} \\\\ {\Rightarrow \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}=\frac{1}{3}}\end{array}

As \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}, so given system of equations have infinite number of solutions.

Hence, we can conclude that system has infinite number of solutions.

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Find the slope of the line containing the pair of the points. (-10,9) and (-6,-9)
zlopas [31]

Answer:

-9/4

Step-by-step explanation:

putting these to y/x form it is 9/-10 and -9/-6 which has a difference of -9/4 (hopefully this is correct-)

5 0
2 years ago
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The rabbit population of Springfield, Ohio was 144,000 in 2016. It is expected to decrease by about 7.2% per year. Write an expo
xeze [42]
<h2>Hello!</h2>

The answer is:

In 2036 there will be a population of 32309 rabbits.

<h2>Why?</h2>

We can calculate the exponential decay using the following function:

P(t)=StartAmount*(1-\frac{percent}{100})^{t}

Where,

Start Amount, is the starting value or amount.

Percent, is the decay rate.

t, is the time elapsed.

We are given:

StartAmount=144,000\\x=7.2(percent)\\t=2036-2016=20years

Now, substituting it into the equation, we have:

P(t)=StartAmount(1-\frac{percent}{100})^{t}

P(t)=144000*(1-\frac{7.2}{100})^{20}

P(t)=144000*(1-0.072)^{20}

P(t)=144000*(0.928)^{20}

P(t)=144000*(0.928)^{20}

P(t)=144000*0.861=32308.888=32309

Hence, we have that in 2036 the population of rabbis will be 32309 rabbits.

Have a nice day!

5 0
3 years ago
A parallelogram is a _____. (Choose all that apply)
Mama L [17]

Answer:

Quadrilateral

Step-by-step explanation:

The definition of a parallelogram is a quadrilateral that has two sets of parallel sides.

3 0
2 years ago
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The mass of a tiger at a zoo is 235 kilograms. Randy's cat has a mass of 5,000 grams. How many times greater is the mass of tige
ANTONII [103]
Solutions 

We know that <span>the mass of a tiger at a zoo is 235 kilograms. Randy's cat has a mass of 5,000 grams. To solve the problem we have to convert 235 kilograms into grams. 

</span>235 kilograms = 235000 grams 

<span>Randy's cat has a mass of 5,000 grams 
</span>
Randy's cat = <span>5,000 grams 
</span>
Tiger = <span>235000 grams  
</span>
Our next step is to subtract 5000 from <span>235000 grams  
</span>
235000 grams  - <span>5000 grams = 230000 
</span>
Answer = <span>230000  grams </span>

6 0
3 years ago
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What are the best approximations of the solutions to this system?
Scilla [17]

(-1.2,-2.0) and (1.9,2.2) are the best approximations of the solutions to this system.

Option B

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

Here, we have a graph of two functions from which we need to find the approximate value of common solutions. Let's find this:

First look at where we have intersection points, In first quadrant & in third quadrant.

<u>At first quadrant:</u>

Draw perpendicular lines from x-axis & y-axis from this point . After doing this we can clearly see that the perpendicular lines cut x-axis at x=1.9 and y-axis at y=2.2. So, one point is (1.9,2.2)

<u>At Third quadrant:</u>

Draw perpendicular lines from x-axis & y-axis from this point. After doing this we can clearly see that the perpendicular lines cut x-axis at x=-1.2 and y-axis at y=  -2.0. So, other point is (-1.2,-2.0).

5 0
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