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ss7ja [257]
2 years ago
9

Solve the system (x-1)²+(y-2)²=2² and y=2x+2.

Mathematics
1 answer:
Likurg_2 [28]2 years ago
3 0

Answer:

  (x, y) = (-0.6, 0.8)  or  (1, 4)

Step-by-step explanation:

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

 (x -1)² +((2x +2) -2)² = 4

  x -2x +1 + 4x² = 4 . . . . . . . eliminate parentheses

  5x² -2x -3 = 0 . . . . . . . . . . subtract 4, collect terms

Now we can rearrange the middle term to ease factoring by grouping.

  (5x² -5x) +(3x -3) = 0

  5x(x -1) +3(x -1) = 0

  (5x +3)(x -1) = 0

The values of x that make these factors zero are ...

  x = -3/5, x = 1

The corresponding values of y are ...

  y = 2(-3/5)+2 = 4/5 . . . . for x = -3/5

  y = 2(1) +2 = 4 . . . . . . . . for x = 1

The solutions are: (x, y) = (-3/5, 4/5) or (1, 4).

___

A graphing calculator verifies these solutions.

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What is the equation of the line perpendicular to y=2x+3.14 going through the points (2,4)?
inessss [21]

Answer:

x+2y-10=0

Step-by-step explanation:

Consider an equation: y=mx+c

Here, m is the slope of the line and c is the y-intercept.

Given equation is y=2x+3.14

Here, slope is m=2

As product of slopes of two perpendicular lines is equal to -1, slope of the required line is m_1=\frac{-1}{m}=\frac{-1}{2}.

Let (x_1,y_1)=(2,4)

Equation of the required line is y-y_1=m_1(x-x_1)

y-4=\frac{-1}{2}(x-2)\\2(y-4)=-1(x-2)\\2y-8=-x+2\\x+2y-8-2=0\\x+2y-10=0

8 0
3 years ago
Factor 1.2 out of <br><br> 1.2x - 7.2
tatyana61 [14]

Answer:

6/5 x (x-6)

Step-by-step explanation:

convert the decimal into a fraction

1.2x -7.2

6/5x - 36/5

factor 6/5 from the expression

6/5x (x-6)

5 0
2 years ago
What is the probability that a randomly selected camper likes swimming or having a cookout, but not both?
emmainna [20.7K]
I would think 0.10 would be the answer
3 0
2 years ago
What is 5000x 600000 pls help
lukranit [14]

Answer:

= 3,000,000,000

Step-by-step explanation:

Step 1- Multiply

5×6= 30

Once you've multiplied, you can just add the 0's to 30.

There are a total of eight 0's.

Once you've added all the 0's, you'll get 3,000,000,000.

3 0
3 years ago
Read 2 more answers
Finding Side Lengths
zheka24 [161]

Answer:

  • x = 2.5
  • y = 5

Step-by-step explanation:

As the two figure are the image and pre-image of a dilation.

Considering the left sided triangle is original and right sided triangle ( smaller one) is the image.

As one of the sides of the left triangle (original figure) is 4 in. And the corresponding length of the side on the right triangle (image of the figure) is 2 in.

It means the image of the side (2 in) is obtained when the side (4 in) of the original object is dilated by a scale factor of 1/2. In other words, the side of the image (2 in) is obtained multiplying the side (4 in) of original figure by 1/2. i.e. 4/2 = 2 in

Lets determine the missing side of the right side triangle by the same rule.

As the original object has one of the sides is 5 in and the corresponding side of the image has x in. As the original figure is dilated by a scale factor of 1/2. so the missing side of x will be: x = 5/2 = 2.5

So, the value of x will be 2.5

Similarly, the original object has one of the sides with length (y + 1 in). As the As the original figure is dilated by a scale factor of 1/2. As the corresponding length of the side of the image triangle is 3 in.

so

y + 1 = 2(3)         ∵ 3 in (image side) is multiplied by 2

y + 1 = 6

y = 6 - 1

y = 5

So, the value of y = 5

Therefore,

  • x = 2.5
  • y = 5
6 0
3 years ago
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