What is the solution of the system of equations?

-3x-4y-3z=-7
2x-6y+2z=3
5x-2y+5z=9

The distance formula is simply a variation of the theorem. The method is the same with the Pythagorean however we are now dealing with 2 sets of points instead of 2 lengths. 

In the distance formula, the lengths are derived from the (x1,y1)->(x2,y2) coordinate points and the formula simplified. We still square the difference of x’s and difference of y’s to get our two squares then square root the sum to give our length. While the Pythagorean theorem is directly the sum of the square of the other two sides. 

Nevertheless, both formulas work on the same principle.

Answer:

Both formulas can be used to find the distance between two points on the coordinate plane. The vertical leg of the right triangle represents the difference in the y values of the two points. The horizontal leg of the right triangle represents the difference in the x values of the two points. The hypotenuse of the right triangle represents the distance between the two points.

Step-by-step explanation:

Answer:

Find out the what percentage discount is seller offering you .

To prove

Formula

[tex]Discouunt\ percentage = \frac{Discount\times 100}{Marked\ price}[/tex]

Discount = Marked price - Selling price

As given

You are offered an item for $17.85. If the seller states he normally sells the same item for $19.95 .

Here

Marked price = $19.95

Selling price = $17.85

Discount = 19.95 - 17.85

               = $2.1

Put in the formula

[tex]Discouunt\ percentage = \frac{2.1\times 100}{19.95}[/tex]

[tex]Discouunt\ percentage = \frac{210}{19.95}[/tex]

Discount percentage = 10.5% (Approx)

Therefore the discount is seller offering you is 10.5 % .

x = 3 weeks

Growth: 5(2)(3) = 30 flies in 3 weeks

eaten: 3(3) +2 = 9+2 =11 flies eaten in 3 weeks

30-11 = 19 flies ( population after 3 weeks)

Answer:

Given inequality,

[tex]x+y<1[/tex]

For graphing the inequality :

The related equation of the given inequality,

x + y = 1

Having the x-intercept = (1,0),

y-intercept = (0,1),

Also, at (0,0),

0 + 0 < 1 ( True )

⇒ The area of the given inequality x + y < 1 must contain the origin.

Now, '<' show the dotted line.

Thus, by the above explanation we can plot the graph of the given inequality.

The figure that shows how a shape can be rotated about an axis to form a disc is (c) rectangle

The shapes in the figures are given as:

A. Rectangle

B. Semicircle

C. Inscribed semicircle

D. Another Rectangle

When the first rectangle is rotated about the axis, it forms a spiral shape

Rotating a semi-circle and the inscribed semi-circle about its axis would form a hemisphere

However, when a rectangle that has one of it sides on the axis is rotated, it forms a cylinder or disc

Hence, the figure is (d) rectangle

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Answer:

x = 5

Step-by-step explanation:

We need to remember that vertical angles are opposite to each other when two lines cross. The vertical angles that result from two lines crossing have the same measure.

In this problem we have angle E which measures 8x + 8 and angle F which measure 2x + 38.

Since they are vertical angles, we know that they have the same measure and therefore we can equal them both and solve for x:

[tex]8x+8=2x+38\\8x-2x=38-8\\6x=30\\x=5[/tex]

Therefore, x = 5 (and ∠E = ∠F = 48)

To calculate the map distance between Austin and Dallas with a scale of 1 inch representing 20 miles, and an actual distance of 195 miles, set up a proportion and solve to find that Austin and Dallas would be 9.75 inches apart on the map.

To find out how many inches Austin is from Dallas on the map, we need to set up a proportion. The scale given on the map is 1 inch represents 20 miles. We know the actual distance between Austin and Dallas is 195 miles. To calculate the distance on the map, we use the proportion 1 inch / 20 miles = x inches / 195 miles.

Cross-multiply to solve for x:

(1 inch) * (195 miles) = (20 miles) * (x inches)

195 inch-miles = 20x inch-miles

Now, divide both sides by 20 miles to solve for x:

x = 195 inch-miles / 20 miles

x = 9.75 inches

So, on the map, Austin and Dallas would be 9.75 inches apart.

The regular polygon with an interior angle of 140 degrees has 9 sides. This conclusion can be reached by using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides.

The number of sides in a regular polygon can be determined using the formula for the interior angle of a polygon, which is (n-2)*180/n, where 'n' represents the number of sides. This formula comes from the fact that a polygon can be divided into (n-2) triangles, each of which has angles summing up to 180 degrees.

In this particular case, an interior angle of 140 degrees is given. So we will set up an equation: 140 = (n-2)*180/n. Solving for 'n', we get a value of 9.

Therefore, the regular polygon with an interior angle of 140 degrees has 9 sides.

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The number of beads used to make 7 bracelets will be equal to 56 beads.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data given in the question,

Three bracelets have 24 beads, so start with the lowest number. Finding out how often beads are on a single bracelet will help you locate the solution the quickest. We shall know the answer on 24/3.

24/3=8.

Then multiplying 56 by 7 to get.

Then confirm that your response still makes sense.

3 x 8 = 24

5 x 8 = 40

7 x 8 = 56

9 x 8 = 72

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