<h2>
Answer:</h2>
First, we must determine the slope, then we find the y-intercept using slope formula and slope-intercept form.
<u>For slope:</u>
<u />
<u />
Slope (m) = 7
<u>For y-intercept:</u>
<u />
<u />
Y-intercept (b) = 26
Using this information, we can now create the equations for this line.
Formulas:
Slope formula: <em>y₂ - y₁/x₂ - x₁</em>
Slope-intercept form: <em>y = mx + b</em>
Point-slope form: <em>y - y₁ = m(x - x₁)</em>
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*Note: (x₁, y₁), (x₂, y₂) = <em>2 points on the line</em>
Answer:
The ship is located at (3,5)
Explanation:
In the first test, the equation of the position was:
5x² - y² = 20 ...........> equation I
In the second test, the equation of the position was:
y² - 2x² = 7 ..............> equation II
This equation can be rewritten as:
y² = 2x² + 7 ............> equation III
Since the ship did not move in the duration between the two tests, therefore, the position of the ship is the same in the two tests which means that:
equation I = equation II
To get the position of the ship, we will simply need to solve equation I and equation II simultaneously and get their solution.
Substitute with equation III in equation I to solve for x as follows:
5x²-y² = 20
5x² - (2x²+7) = 20
5x² - 2y² - 7 = 20
3x² = 27
x² = 9
x = <span>± </span>√9
We are given that the ship lies in the first quadrant. This means that both its x and y coordinates are positive. This means that:
x = √9 = 3
Substitute with x in equation III to get y as follows:
y² = 2x² + 7
y² = 2(3)² + 7
y = 18 + 7
y = 25
y = +√25
y = 5
Based on the above, the position of the ship is (3,5).
Hope this helps :)
Answer: No, your friend is not correct. You cannot use a similarity transformation to turn a square into a rectangle. Here's why:
1) If you used a similarity transformation, the size and position of the shape would change, but the shape itself remains the same.
2) Squares and rectangles are NOT similar.* Referring to the first point I listed, if the shapes are not similar, then a similarity transformation cannot be used to turn one shape into another.
<em>*Similar means that the edges are proportional to one another, such as a square with sides of 4 meters vs a square with sides of 2 meters: the sides are different lengths, but the shape is the same.</em>
I hope this helps! Please feel free to comment below if you need any clarification. Have a good day, and good luck on your assignment. :)
Answer:
x = -2.
Step-by-step explanation:
In this case, a is 1, b is 4 and c is 4.
-4 plus or minus the square root of 4^2 - 4 * 1 * 4 divided by 2 * 1 = -4 plus or minus the square root of 16 - 16 / 2 = -4 plus or minus the square root of 0 / 2 = -4 / 2 = -2.
x = -2.
Hope this helps!
