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2 years ago

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Mathematics

1 answer:

viktelen [127]2 years ago

8 0

Answer:

The inverse is 5x+3

Step-by-step explanation:

y = (x-3) /5

Exchange x and y

x = (y-3)/5

Solve for y

Multiply each side by 5

5x =(y-3)/5 *5

5x = y-3

Add 3 to each side

5x+3 =y-3+3

5x+3 =y

The inverse is 5x+3

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You use a gift card to buy a pair of shorts for $8. There is $32 left on the gift card after your purchase. What was the origina

Olenka [21]

Answer:

Step-by-step explanation:

32+8=40

6 0

2 years ago

Does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?

stiv31 [10]

Given equation of the Circle is ,

$\sf\implies x^2 + y^2 = 25$

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

$\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2$

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

$\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }$

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

5 0

2 years ago

Read 2 more answers

The length of a rectangle is 22 feet longer than the width. the perimeter is 1616 feet. find the dimensions of the rectangle.

NemiM [27]

So we can setup variable equations for this:
so we're given that the length is 22feet longer than the width!
so as an expression length is equal to 22+w
and width as an expression is just w
so the formula for the perimeter for a rectangle is 2l+2w=perimeter
so fill it in now!
1616=2(22+w)+2w
1616=44+2w+2w
1616=44+4w
1572=4w
divide by four..
w=393
and length is simply 22 more than that as stated in the question!
so length is 415
dimensions are: 415x393

7 0

3 years ago

Let xy=1 and let dy/dt=5 Find dx/dt when x=5

madreJ [45]

So the first step is to take the derivative of xy=1. Don't forget the product chain rule!

 $xy=1
\\x=5
\\y= \frac{1}{x}=\frac{1}{5}
\\ 
\\\frac{dy}{dt}=5
\\
\\x\frac{dy}{dt}+y\frac{dx}{dt}=0
\\
\\5\times5+ \frac{1}{5} \frac{dx}{dt}=0
\\
\\\frac{1}{5} \frac{dx}{dt}=-25
\\
\\ \frac{dx}{dt}=-125
$

3 0

2 years ago

Systems of equations with different slopes and different y-intercepts have more than one solution.

FrozenT [24]

Answer: OPTION C.

Step-by-step explanation:

The systems of linear equations can have:

1. No solution: When the lines have the same slope but different y-intercept. This means that the lines are parallel and never intersect, therefore, the system of equations has no solution.

2. One solution: When the lines have different slopes and intersect at one point in the plane. The point of intersection will be the solution of the system

3. Infinitely many solutions: When the lines have the same slope and the y-intercepts are equal. This means that the equations represents the same line and there are infinite number of solution.

Therefore, based on the explained above, the conclusion is: Systems of equations with different slopes and different y-intercepts never have more than one solution.

7 0

2 years ago