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3 years ago

2x + 3y = 15 and x - 3y = 3 What's the ordered pair

Mathematics

1 answer:

Ganezh [65]3 years ago

4 0

Answer:

x = 6

y = 1

Step-by-step explanation:

to solve this system of equation we say let

2x + 3y = 15 .......................... equation 1

x - 3y = 3.................................. equation 2

from equation 2

x - 3y = 3.................................. equation 2

x = 3 + 3y.................................... equation3

substitute for x in equation 1

2x + 3y = 15 .......................... equation 1

2(3+3y) + 3y = 15

6 + 6y + 3y = 15

9y = 15 -6 ................................... combining the like terms

9y = 9

divide both sides by the coefficient of y

9y/9 = 9/9

y =1

put y = 1 in equation 3

x = 3 + 3y.................................... equation3

x = 3 + 3(1)

x = 3 +3

x = 6

therefore the value of x is 6 and y is 1 respectively

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What transformations are needed to change the parent cosine function to y=3cos(10(x-pi))?

LUCKY_DIMON [66]

Answer:

The graph of $y=cos(x)$ is:

*Stretched vertically by a factor of 3

*Compressed horizontally by a factor $\frac{1}{10}$ .

*Moves horizontally $\pi$ units to the rigth

The transformation is:

$y=3f(10(x-\pi))$

Step-by-step explanation:

If the function $y=cf(h(x+b))$ represents the transformations made to the graph of $y= f(x)$ then, by definition:

If $0$ then the graph is compressed vertically by a factor c.

If $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$ then the graph is reflected on the x axis.

If $b> 0$ The graph moves horizontally b units to the left

If $b$ The graph moves horizontally b units to the rigth

If $0$ the graph is stretched horizontally by a factor $\frac{1}{h}$

If $h> 1$ the graph is compressed horizontally by a factor $\frac{1}{h}$

In this problem we have the function $y=3cos(10(x-pi))$ and our parent function is $y = cos(x)$

The transformation is:

$y=3f(10(x-\pi))$

Then $c =3>1$ and $b =-\pi < 0$ and $h=10 > 1$

Therefore the graph of $y=cos(x)$ is:

Stretched vertically by a factor of 3.

Also as $h=10$ the graph is compressed horizontally by a factor $\frac{1}{10}$ .

Also, as $b =-\pi < 0$ The graph moves horizontally $\pi$ units to the rigth

6 0

3 years ago

What is the perimeter of triangle UVW

lara [203]

Count how much spaces from one point on the end of the line to the other.

Line VU has 9 units
Line VW has 12 units
Line UW has:

a² + b² = c²
9² + 12² = c²
81 + 144 = c²
c² = 225
√c² = √225
c = 15
Line UW has: 15 units

Now add all the units together to get the perimeter:

9 + 12 + 15 =
21 + 15 =
36

36 is your answer

hope this helps

8 0

3 years ago

How do you write 26.2 as a mixed number in simplest form

Arte-miy333 [17]

To write 26.2 as a mixed number in the simplest form, do the following:
26.2 = 26 + 0.2
= 26 + 2/10

Note that
$\frac{2}{10}= \frac{2 \times 1}{2 \times 5} = \frac{1}{5}$

Therefore
$26.2 = 26 \, \frac{1}{5} \\$

Answer: $26 \, \frac{1}{5}$

7 0

3 years ago

Anyone know the answer?

Stolb23 [73]

Answer:

y-intercept = 1

Step-by-step explanation:

Here 1 grids crossing means increasing or decreasing by 1 grid. Here we are seeing the line crosses 1 grid above 0. So its positive 1. From here we find the y intercept is +1. Line crosses at coordinate ( 0 , 1 )

8 0

2 years ago

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2p - 6 = 8 + 5(p +9)<br> How do you solve it

Marat540 [252]

Step-by-step explanation:

2p-6=8+5p+45

2p-6=53+5p

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p=59/-3

p= -19.67

let me know if this helps :)

3 0

3 years ago

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