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3 years ago

What is the solution to this system of equations?

Mathematics

1 answer:

Maurinko [17]3 years ago

3 0

Answer:

(x, y) = (5, -2)

Step-by-step explanation:

A graphing calculator provides a quick and easy way to find the solution.

_____

There are several other ways to solve these equations. Or you can estimate where the answer might be using logic like this:

The intercepts of the first equation are ...

x-intercept = 26/4 = 6 1/2
y-intercept = -26/3 = -8 2/3

So the graph of it will form a triangle with the axes in the 4th quadrant.

The intercepts of the second equation are ...

x-intercept = 11/3 = 3 2/3
y-intercept = 11/2 = 5 1/2

So the graph of it will form a triangle with the axes in the 1st quadrant. The x-intercept of this one is less than the x-intercept of the first equation, so the two lines must cross in the 4th quadrant.

The only 4th-quadrant answer choice is (5, -2).

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Find the Circumference of the circle. Use 3.14 for π. Round your answer to the nearest tenth.

kotykmax [81]

Answer:

28.3 cm

Step-by-step explanation:

The formula to find the circumference is 2•π•radius. The diameter is 9 cm, so the radius is 9/2 = 4.5 cm. So, the circumference is:

2•4.5•3.14 = 28.26 ≈ 28.3 cm

8 0

3 years ago

Write an expression to represent:One more than the quotient of a number X and 4

astra-53 [7]

Answer:

X/4 +1

Step-by-step explanation:

The word "quotient" tells us that we'll be dividing X and 4.

This can be modeled as X/4

To this quantity, we will be adding 1.

We now get X/4 +1

7 0

3 years ago

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54 boo . Divide 189 by 7 then multiply by 2 which is 54

3 0

3 years ago

Read 2 more answers

The length of a rectangle is six times its width. If the area of the rectangle is 384^2, find its perimeter.

Leno4ka [110]

Answer:

Perimeter, P = 112 meters

Step-by-step explanation:

Let the length of the rectangle be L.
Let the width of the rectangle be W.

Translating the word problem into an algebraic expression, we have;

L = 6W ...... equation 1

<u>Given the following data;</u>

Area of rectangle = 384 m²

To find the perimeter of the rectangle;

First of all, we would determine the dimensions of the rectangle using its area.

Mathematically, the area of a rectangle is given by the formula;

Area of rectangle = LW ..... equation 2

Substituting eqn 1 into eqn 2, we have;

384 = 6W(W)

384 = 6W²

Dividing both sides by 6, we have;

W² = 384/6

W² = 64

Taking the square root of both sides, we have;

W = √64

Width, W = 8 meters

Next, we would find the length;

L = 6W

L = 6 * 8

Length, L = 48 meters

Lastly, we would determine the perimeter of the rectangle using the above dimensions;

Mathematically, the perimeter of a rectangle is given by the formula;

Perimeter = 2(L + W)

Substituting the values into the formula, we have;

Perimeter, P = 2(48 + 8)

Perimeter, P = 2(56)

<em>Perimeter, P = 112 meters</em>

4 0

3 years ago

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

Artist 52 [7]

Answer:

This system of equations has infinite points of intersection

Step-by-step explanation:

* To know the point of intersection of the system of equations,

you will solve the graphically or algebraically

- Graphically by drawing two lines on the coordinate plane

- Algebraically by substitution method or elimination method

* Lets use the substitution method

∵ y = 4 - x

∵ 2y = 8 - 2x

- Substitute y in the second equation by its value in the

first equation

∴ 2(4 - x) = 8 - 2x ⇒ open the bracket

∴ 8 - 2x = 8 - 2x

* The two sides equal each other, that means we can use any

vales of x, and on the graph they will be the same line for

the two equations

∴ This system of equations has infinite points of intersection

3 0

3 years ago