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sergiy2304 [10]
3 years ago
8

What are the coordinates of one of the vertices of a rectangle when two sides are given by the lines x - 3y = -8 and 3x + y = 6?

Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
5 0

Answer:

(1, 3)

Step-by-step explanation:

x - 3y = -8

3x + y = 6

Isolate a variable in one of the equations:

y = 6 - 3x

Substitute the value of y into the other equation:

x - 3(6 - 3x) = -8

Use distributive property:

x - 18 + 9x = -8

Combine like terms:

10x - 18 = -8

Isolate the variable:

10x = 10

x = 1

Substitute the value of x into any equation:

3(1) + y = 6

3 + y = 6

Isolate the variable:

y = 3

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If F(x)=9x which of the following is the inverse of F(x)
user100 [1]

Answer:

Inverse of F(x)=9x = 1/9x

Step-by-step explanation:

If F(x)=9x

which of the following is the inverse of F(x)

When talking about inverse of a function, we are talking about reversal. Therefore, an inverse function is the inverse of another function. In order to get the inverse of a particular function, we reverse the denominator to become the numerator and the numerator to become the denominator.

So for the function,

F(x)=9x, the numerator is 9x and the denominator is 1

Reversing the numerator and denominator, .

Inverse of F(x)=9x = 1/9x

8 0
3 years ago
Read 2 more answers
Describe the graph of the functions y=|x+2|
inn [45]

To obtain the graph of the function y = |x+2| we have to make a table of values of x to find the values of y. The absolute value or modulus of a real number is its numerical value without care its sign. For example, the absolute value of |4| and |-4| is 4.

In order to make a graph we are going to use the values (-3, -2, -1, 0, 1, 2, 3) for x.

x = -3

y = |-3 + 2| = |-1| = 1

x = -2

y = |-2 + 2| = |0| = 0

x = -1

y = |-1 + 2| = |1| = 1

x = 0

y = |0 + 2| = |2| = 2

x = 1

y = |1 + 2| = |3| = 3

x = 2

y = |2 + 2| = |4| = 4

x = 3

y = |3 + 2| = |5| = 5

<u>  x   ║   y</u>

-3        1

-2        0

-1         1

 0        2

 1         3

 2        4

 3        5

Obtaining the graph shown in the image attached.

.

7 0
3 years ago
What is the slope of the equation-3=-4(x-5)
scZoUnD [109]
You need to simplify it first. 
-3=-4(x-5)
Use distribution
-3=-4x+20
y=mx+b
m=slope
your slope is -4 :)
5 0
3 years ago
WORTH 19 POINTS!!
marta [7]
You have to make a cos graph that starts its minimum and of -2, has an amplitude of 10, a period of 10 and  a maximum of 18.
I decided to use a cos graph since cos graphs start at their minimum or maximum unlike a sine graph that starts halfway between the minimum and maximum.  You also know the amplitude has to be 10 since 18+2=20 and 20/2=10.  We were also told that the water wheel completels a rotation every 10 minutes which means the period is 10 minutes.

lets start of with a regular cos(x) graph.  This starts on its maximum instead of minimum so we have to multiply it by -1 to get -cos(x) which does start on its minimum.

-cos(x) has an amplitude of 1 instead of 10, to fix that we multiply it by 10 to get -10cos(x) which has an amplitude of 10.
 
-10cos(x) has a period of 2π instead of 10, to fix this we multiply the x by 2π/10 to get -10cos((π/5)x) which now has a period of 10.

-10cos((π/5)x) has a minimum of -10 and maximum of 10 instead of a minimum of -2 and maximum of 18, to fix this we add 8 to -10cos((π/5)x) to get -10cos((π/5)x)+8 which does have a minimum of -2 and maximum of 18.

Therefore the answer is y=-10cos((π/5)x)+8. x being time in minutes and and y being the height in feet.  

I hope this helps.  Let me know if anything is unclear.
8 0
3 years ago
5. In one year, there were 125 major new automobile types available. If you look at the miles per gallon (MPG) for these vehicle
ziro4ka [17]

Answer:

The answer is "99.82% and 86.99%".

Step-by-step explanation:

In point a:

=P(X < 45)\\\\= P(Z < \frac{45-29.09}{5.46}) \\\\=P(Z < 2.9139)\\\\=0.9982\\\\=99.82\%

In point b:

=P(X >17)\\\\= P(Z > \frac{17-22.37}{4.77}) \\\\=P(Z > -1.1258)\\\\=0.8699\\\\=86.99\% \\\\

5 0
3 years ago
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