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2 years ago

Find a so the function be continuous Function

Mathematics

1 answer:

gladu [14]2 years ago

5 0

The limit as x approaches 1 from either side should match, so that

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}(-2x+a)=a-2$

$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}x=1$

==> a - 2 = 1 ==> a = 3

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Apply Crammer's Rule to find the solution to the following quations .2x + 3y = 1, 3x + y = 5

Bond [772]

Answer:

The solution to the equation system given is:

x = 2
y = -1

Step-by-step explanation:

First, we must know the equations given:

2x + 3y = 1
3x + y = 5

Following Crammer's Rule, we have the matrix form:

$\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] =\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Now we solve using the determinants:

$x=\frac{\left[\begin{array}{ccc}1&3\\5&1\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(1*1)-(5*3)}{(2*1)-(3*3)} = \frac{1-15}{2-9} =\frac{-14}{-7} = 2$

$y=\frac{\left[\begin{array}{ccc}2&1\\3&5\end{array}\right]}{\left[\begin{array}{ccc}2&3\\3&1\end{array}\right] } =\frac{(2*5)-(3*1)}{(2*1)-(3*3)}=\frac{10-3}{2-9} =\frac{7}{-7}=-1$

Now, we can find the answer which is x= 2 and y= -1, we can replace these values in the equation to confirm the results are right, with the first equation:

2x + 3y = 1
2(2) + 3(-1)= 1
4 - 3 = 1
1 = 1

And, with the second equation:

3x + y = 5
3(2) + (-1) = 5
6 - 1 = 5
5 = 5

4 0

2 years ago

What is the answer to 7^3 x 7^-5? I need it for an important test that I can’t fail. Please help.

Vilka [71]

The answer fir sure is 1/49

4 0

1 year ago

Rick bought a car for $17,500. Each year, the car's value decreases by 20%. At this rate, what can Rick expect the value of his

Arada [10]

Answer:

His car would be worth $15,502.24

Step-by-step explanation:

20% of 17,500 is 350. 350 x 6 = 2,100. 17,500 - 2,100 = 15,400. But that is not an answer choice so be go to the closest number which is $15,502.24

5 0

2 years ago

The equation 50=36.50+0.10m represent the additional number of messages roboerto can send with a budget of $50 .solve the equati

charle [14.2K]

Answer :
M = 135

Step by Step Explanation :
See the photo attached :) it’s kinda hard to explain in words but you cancel out the 36.50 by subtracting it on both sides, and then the equation becomes 13.50 = 0.10m. Since we have to get the m by itself, you cancel out the 0.10 by subtracting on both sides, and it leaves you with 135 = m

(Ignore my messy handwriting on a post it :3)

I hope this helped! If u have any questions feel free to comment on this!

4 0

2 years ago

Please Help ASAP PLEASE !!!!!!!

saul85 [17]

Answer:

transitive property of equality

Step-by-step explanation:

I know cus i took the test also sorry it took so long dude

6 0

3 years ago