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3 years ago

Solve the system of equations. 3x – 4y = 8 18x – 5y = 10 x= y =

Mathematics

1 answer:

Zepler [3.9K]3 years ago

5 0

Answer:

Step-by-step explanation:

Solution by substitution method

3x-4y=8

and 18x-5y=10

Suppose,

3x-4y=8→(1)

and 18x-5y=10→(2)

Taking equation (1), we have

3x-4y=8

⇒3x=4y+8

⇒x=( 4y+8)/ 3 →(3)

Putting x= (4y+8 )/3 in equation (2), we get

18x-5y=10

18( (4y+8) /3) -5y=10

⇒24y+48-5y=10

⇒19y+48=10

⇒19y=10-48

⇒19y= -38

⇒y=- 38 /19

⇒y= -2→(4)

Now, Putting y=-2 in equation (3), we get

x=4y+8

x= (4(-2)+8) /3

⇒x= (-8+8)/ 3

⇒x= 0/ 3

⇒x=0

∴x=0 and y= -2

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What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

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3 years ago

katie bought 4 sweaters that each cost the same amount and 1 skirt that costs 20$. The items she bought cost a total of 160$ bef

Alika [10]

Hello, in order to solve this you first need to take $20 subtracted from 160 that leaves you with 140 next because she bought 4 sweaters you need to divide your remaining cash spent by 4 to get a total of $35 a sweater.

I hope this is what you were looking for, have a great day!

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