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3 years ago

What is the distance between (8, -3), (4,-7)?

Mathematics

1 answer:

Papessa [141]3 years ago

7 0

Answer:

$4\sqrt{2}$ which is none of your choices....

Did you mean (8,-3) and (4,-7)?

Step-by-step explanation:

We need to first find the distance between the x's.

Then the distance between the y's.

The distance between the x's is 8-4=4.

The distance between the y's is -3-(-7)=4.

So the distance between two points $(x_1,y1)\text{ and }(x_2,y_2)$ is $\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ .

So we already found x1-x2 and y1-y2 so now we have:

$\sqrt{(4)^2+(4)^2}$

$\sqrt{16+16}$

$\sqrt{2(16)$

$\sqrt{16}\sqrt{2}$

$4\sqrt{2}$

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Holly made 12 pair of earrings for each of her girlfriends. To wrap the pairs individually, she creates a simple cardboard gift

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Answer:

3280cm²

Step-by-step explanation:

We are told the gift box is folded into a Pyramid with a square base.

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From the question, we are given:

Length of the base of the square = 10cm

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Step 1

Find the Area of the square

Formula = Side length² this is because all the side of a square is equal.

Length of the base = 10cm

Area of the square = (10cm)²

= 100cm²

Step 2

Find the Area of the triangle. We are told the 4 triangles are equilateral, which means their side are equal.

Hence, for one triangle.

Area of a triangle = 1/2 × base × height

Base = side length = 10cm

Height = 8 2/3 = 8.6666666667cm

Area of a triangle = 1/2 × 10 × 8.6666666667

Area of a triangle = 43.333333333cm²

Since we have 4 triangles

We would have : 4 × 43.333333333cm²

= 173.33333333cm²

The Area of the 4 equilateral triangles =

173.33333333cm²

Step 3

The Surface area of the Square Pyramid

= Sum of the areas of all the faces.

= 100cm² + 173.33333333cm²

= 273.33333333cm²

Therefore, the minimum amount of cardboard needed to make one gift box = 273.33333333cm²

Step 4

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3 years ago

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The augmented matrix of a system of equations has been transformed to an equivalent matrix inâ€‹ row-echelon form. Usingâ€‹ x, y

jenyasd209 [6]

Answer: The system of equations is:

x + 2y + 2 = 4

y - 3z = 9

z = - 2

The solution is: x = -22; y = 15; z = -2;

Step-by-step explanation: ONe way of solving a system of equations is using the Gauss-Jordan Elimination.

The method consists in transforming the system into an augmented matrix, which is writing the system in form of a matrix and then into a Row Echelon Form, which satisfies the following conditions:

There is a row of all zeros at the bottom of the matrix;
The first non-zero element of any row is 1, which called leading role;
The leading row of the first row is to the right of the leading role of the previous row;

For this question, the matrix is a Row Echelon Form and is written as:

$\left[\begin{array}{ccc}1&2&2\\0&1&3\\0&0&1\end{array}\right]$ $\left[\begin{array}{ccc}4\\9\\-2\end{array}\right]$

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z = -2

y + 3(-2) = 9

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x = - 22

The solution is (-22,15,-2).

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