100 POINTS The vertices of a rectangle are (3, 7), (6, 7), (6, 1), and (3, 1). Find the perimeter of the rectangle.

In order to solve the system of linear equations, the coefficients of one of the variables must be the same number but opposite

Mashutka [201]

Answer:

Step-by-step explanation:

because both equations do not have matching numbers for the x or y variable, and both equations are positive you are going to have to multiply each equation by a number so that there will be at least one variable with the same number but with opposite signs.

it does not matter which variable you choose.

lets use y because 2 and 3 are smaller then 2 and 5.

so lets multiply the first equation by 2 in order to get y equal to 6.

2(2x)+2(3y)=(2)6

(do not forget to multiply what the equation is equal to also)

4x+6y=12

now for the second equation we need y to equal negative 6

-3(5x)+-3(2y)=-3(4)

-15x-6y=-12

now lets put the 2 new equations next to each other and see what we can cancel out

4x+6y=12

-15x-6y=-12

-11x=0

x=0

now plug 0 in for x and solve for y (it does not matter which of the 4 equations you choose to solve.

2(0)+3y=6

3y=6

y=2

so your answer is x=0, y=2

8 0

3 years ago

Given the points (2, 2) and (-1, -7) find the slope.

Softa [21]

Slope is change in y over the change in x.

Slope = (-7 - 2) / (-1 -2)

Slope = -9/-3

Slope = 3

6 0

3 years ago

A figure is made up of one square and one triangle. The square has a side Length of 13 feet. The triangle has a base of 13 feet

Marysya12 [62]

Im pretty sure it’s A because a squares area is base x height which would be 13x13= 169 then add the area of the triangle which would be 53.3, so 169+53.3 = 222.3

6 0

3 years ago

Determine if the statement is always, sometimes or never true.

Romashka-Z-Leto [24]

Let

x--------> the measure of the adjacent interior angle

y--------> the measure of an exterior angle at the vertex of a polygon

we know that

The measure of the adjacent interior angle and the measure of an exterior angle at the vertex of a polygon are supplementary angles

so

$x+y=180$ °

Examples

case 1)

In a square

$x=90$ °

so

$y=180-90=90$ °

$x=y$

In this case

The measure of an exterior angle at the vertex of a polygon equals the measure of the adjacent interior angle

case 2)

an equilateral triangle

$x=60$ °

so

$y=180-60=120$ °

$x\neq y$

In this case

The measure of an exterior angle at the vertex of a polygon is not equals the measure of the adjacent interior angle

therefore

the answer is

sometimes

4 0

3 years ago

Read 2 more answers

The derivative of (x^2 +1)(x^3+ 1) (by definition and basic rule)

dlinn [17]

Answer:

f'(x) = 5x^4 + 2x + 3x^2

Step-by-step explanation:

To find the derivative of this equation we can do two things.

One method is to use the product rule, which states that when f(x) consists of two functions multiplied to each other (meaning f(x) = g(x) * h(x)), the derivative is f'(x) = g'(x)*h(x) + g(x)*h'(x). In simple language, the derivative is found by finding the derivative of x² + 1 and multiplying it with the normal function of x³ + 1, after which you add the product of the nnormal function of x² + 1 and the derivative of x³ + 1.

it might be clearer when I show you:

$f(x) = (x^2 + 1)(x^3 + 1)\\f'(x) = (2x)(x^3 + 1) + (x^2 + 1)(3x^2)\\Simplify:\\f'(x) = 2x^4 + 2x + 3x^4 + 3x^2 = 5x^4 + 3x^2 + 2x\\$

If you are not familiar with this rule you can first write out the function and then use the basic rule:

$f(x) = (x^2 +1)(x^3+1) = x^5 + x^2 + x^3 + 1\\f'(x) = 5x^4 + 2x + 3x^2$

If you need any further help please say so in the comments! I hope this helps! If the steps seem complicated, I suggest you could revise expanding brackets (the first step of the second method) and the basic rules of deriving, but feel free to reach out if you struggle afterwards still

8 0

3 years ago

100 POINTS The vertices of a rectangle are (3, 7), (6, 7), (6, 1), and (3, 1). Find the perimeter of the rectangle. ​

100 POINTS The vertices of a rectangle are (3, 7), (6, 7), (6, 1), and (3, 1). Find the perimeter of the rectangle.