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2 years ago

Find the solution of y=x+3 and y=2x+6

Mathematics

2 answers:

lisabon 2012 [21]2 years ago

3 0

Answer:

x = 3 and y = 0

Step-by-step explanation:

To find the solution where you have two equations is called a System of Equations.

What you do is you notice there are two equations and the let both equations equal each other. We can do this because both equations start with a y. These "y" work like puzzles and you can connect the "x+3" and "2x + 6" together. Then solve for it. Here's what i mean,

y = x+3

y = 2x+6

Now connecting them,

x+3 = 2x+6

Subtract x from both sides

3 = x + 6

Subtract 6 from both sides,

x = -3

Now solve for y,

y = -3 + 3 = 0

So our solution is x = 3 and y = 0.

olasank [31]2 years ago

3 0

Answer:

(x, y) = (-3, 0)

Step-by-step explanation:

Substitution or elimination work well for solving this system of equations.

<h3>Elimination</h3>

Subtract the first equation from the second.

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

0 = x +3

-3 = x . . . . . . . subtract 3

y = (-3) +3 = 0 . . . . use the first equation to find y

(x, y) = (-3, 0)

<h3>Substitution</h3>

Use the second equation to substitute for y in the first.

2x +6 = x +3

x = -3 . . . . . . . . . subtract x+6 from both sides

y = (-3) +3 = 0 . . . . find y using the first equation

(x, y) = (-3, 0)

A graphing calculator answers these quickly.

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Answer:

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Step-by-step explanation:

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3 years ago

The volume of the pyramid shown in the figure is cubic centimeters. If the slant height of the pyramid increases by 4 centimeter

Nostrana [21]

Answer:

Part a) The volume of the original pyramid is $15\ cm^{3}$

Part b) The volume of the pyramid increases by $6\ cm^{3}$

Step-by-step explanation:

<u><em>The complete question is</em></u>

Part 1) The volume of the pyramid shown in the figure is 9,15,21, or 63 cubic centimeters?. Part 2) If the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by 6,9,12 or 21 cubic centimeters?

we know that

The volume of the pyramid is equal to

$V=\frac{1}{3}Bh$

where

B is the area of the base

h is the height of pyramid

see the attached figure to better understand the problem

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

$B=3^{2}=9\ cm^{2}\\h=5\ cm$

substitute

$V=\frac{1}{3}(9)(5)=15\ cm^{3}$

Step 2

Find the volume of the new pyramid

$B=9\ cm^{2}$ -------> the area of the base is the same

$h=5+2=7\ cm$ ------> the height increase by

substitute

$V=\frac{1}{3}(9)(7)=21\ cm^{3}$

Subtract the original volume from the new volume

$21\ cm^{3}-15\ cm^{3}=6\ cm^{3}$

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3 years ago

What can you say about the sum of consecutive odd numbers starting with 1? that is, evaluate 1, 1c3, 1c3c5, 1c3c5c7, and so on,

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1. 1

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3. 1+3+5 = 9 ( $3^{2}$ )

4. 1+3+5+7 = 16 ( $4^{2}$ )

5. 1+3+5+7+9 = 25 ( $5^{2}$ )

6. 1+3+5+7+9+11 = 36 ( $6^{2}$ )

7. 1+3+5+7+9+11+13 = 49 ( $7^{2}$ )

If we notice, the sum of the consecutive odd integers in each case is equal to the square of the place where it lies. For example, the sum of numbers in seventh place is equal to $7^{2}$ . The sum of the numbers in the fifth line is equal to $5^{2}$ .

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