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topjm [15]
3 years ago
8

How many solutions can be found for the system of linear equations represented on the graph?

Mathematics
2 answers:
g100num [7]3 years ago
5 0

Answer:

A) no solution

Step-by-step explanation:

These lines are parallel.  This means they never intersect; since the solution to a system of equations is the point or points of intersection, this means there is no solution to this system.

skelet666 [1.2K]3 years ago
3 0

Answer: A) no solution

Step-by-step explanation:

The equation of first line = y=-\dfrac{1}{2}x+4

which can be written as : 2y=-x+8

x+2y=8  

The equation of second line = y=-\dfrac{1}{2}x-6

which can be written as : x+2y=-12

Since , the ratio of the coefficients of x is equal to the ratio of the coefficients of y but not the ratio of the constants .

\dfrac{1}{1}=\dfrac{2}{2}\neq\dfrac{8}{-12}

Therefore , the lines are parallel and do not have any solution.

So , the correct answer is A) no solution.

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The gym has a total of 25 treadmills and stationary bikes. there are seven more stationary bikes than treadmills.
Rudik [331]

The system of equations is t+b=25\\b=t+7

Step-by-step explanation:

We can answer this question as follows.

First of all, we call:

t = number of treadmills

b = number of stationary bikes

The two conditions that we have can be translated into equations as follows:

- The gym has a total of 25 treadmills and stationary bikes:

t+b=25

- There are seven more stationary bikes than treadmills:

b=t+7

So the system of equations to solve is

t+b=25\\b=t+7

We now solve it in the following way: first, we rewrite the second equation by bringing t on the left side,

t+b=25\\b-t=7

Now we add the 1st equation to the 2nd equation:

(t+b)+(b-t)=25+7\\t+b+b-t=32\\2b=32\\b=\frac{32}{2}=16

And therefore,

t+b=25\\t+16=25\\t=25-16=9

So, there are 16 stationary bikes and 9 treadmills.

Learn more about systems of equations:

brainly.com/question/13168205

brainly.com/question/3739260

#LearnwithBrainly

3 0
3 years ago
Which fraction is not equivalent to 7 /30
dybincka [34]
These are the ones that are not equivalent to eachother. 1. 18/30
2. 8/10
3. 4/9
4. 14/18
5. 10/20
6. 20/32
7. 18/30

8 0
3 years ago
Read 2 more answers
3. What is the radius, in centimeters, of a circle that has a circumference of 16 centimeters? ​
ludmilkaskok [199]
Answer: 8cm I think-
3 0
2 years ago
Read 2 more answers
Find the exact length of the curve. 36y2 = (x2 − 4)3, 5 ≤ x ≤ 9, y ≥ 0
IrinaK [193]
We are looking for the length of a curve, also known as the arc length. Before we get to the formula for arc length, it would help if we re-wrote the equation in y = form.

We are given: 36 y^{2} =( x^{2} -4)^3
We divide by 36 and take the root of both sides to obtain: y = \sqrt{ \frac{( x^{2} -4)^3}{36} }

Note that the square root can be written as an exponent of 1/2 and so we can further simplify the above to obtain: y =  \frac{( x^{2} -4)^{3/2}}{6} }=( \frac{1}{6} )(x^{2} -4)^{3/2}}

Let's leave that for the moment and look at the formula for arc length. The formula is L= \int\limits^c_d {ds} where ds is defined differently for equations in rectangular form (which is what we have), polar form or parametric form.

Rectangular form is an equation using x and y where one variable is defined in terms of the other. We have y in terms of x. For this, we define ds as follows: ds= \sqrt{1+( \frac{dy}{dx})^2 } dx

As a note for a function x in terms of y simply switch each dx in the above to dy and vice versa.

As you can see from the formula we need to find dy/dx and square it. Let's do that now.

We can use the chain rule: bring down the 3/2, keep the parenthesis, raise it to the 3/2 - 1 and then take the derivative of what's inside (here x^2-4). More formally, we can let u=x^{2} -4 and then consider the derivative of u^{3/2}du. Either way, we obtain,

\frac{dy}{dx}=( \frac{1}{6})( x^{2} -4)^{1/2}(2x)=( \frac{x}{2})( x^{2} -4)^{1/2}

Looking at the formula for ds you see that dy/dx is squared so let's square the dy/dx we just found.
( \frac{dy}{dx}^2)=( \frac{x^2}{4})( x^{2} -4)= \frac{x^4-4 x^{2} }{4}

This means that in our case:
ds= \sqrt{1+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{4}{4}+\frac{x^4-4 x^{2} }{4}} dx
ds= \sqrt{\frac{x^4-4 x^{2}+4 }{4}} dx
ds= \sqrt{\frac{( x^{2} -2)^2 }{4}} dx
ds=  \frac{x^2-2}{2}dx =( \frac{1}{2} x^{2} -1)dx

Recall, the formula for arc length: L= \int\limits^c_d {ds}
Here, the limits of integration are given by 5 and 9 from the initial problem (the values of x over which we are computing the length of the curve). Putting it all together we have:

L= \int\limits^9_5 { \frac{1}{2} x^{2} -1 } \, dx = (\frac{1}{2}) ( \frac{x^3}{3}) -x evaluated from 9 to 5 (I cannot seem to get the notation here but usually it is a straight line with the 9 up top and the 5 on the bottom -- just like the integral with the 9 and 5 but a straight line instead). This means we plug 9 into the expression and from that subtract what we get when we plug 5 into the expression.

That is, [(\frac{1}{2}) ( \frac{9^3}{3}) -9]-([(\frac{1}{2}) ( \frac{5^3}{3}) -5]=( \frac{9^3}{6}-9)-( \frac{5^3}{6}-5})=\frac{290}{3}


8 0
3 years ago
Jean needs 1/3 cup of wulnuts for each serving of salad she makes.she has 2 cups of walnuts how many servings can she make
valentina_108 [34]
She can make 6 servings
5 0
2 years ago
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