You are given the first point (2, 3) and a line x = 4. If you go ahead and graph these, it makes it a little more clear when they say that point p is symmetric with point Q with respect to the line x = 4.
Line x = 4 is the line of symmetry, so point Q is reflected across it. Point p has an x value of 2 (2 away from the line of symmetry, so point Q's x value has to be 2 away on the other side... 6. The y value is unchanged so your point is
D. (6, 3)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
Step-by-step explanation:
The vertex form of the quadratic equation y = ax² + bx + c is
y = a(x - h)² + k, where
- (h , k) are the coordinates of the vertex point
- a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept
![h=\frac{-b}{2a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-b%7D%7B2a%7D)
- k is the value of y when x = h
∵ y = x² + 16x - 7
∵ y = ax² + bx + c
∴ a = 1 , b = 16 , c = -7
∵ ![h=\frac{-b}{2a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-b%7D%7B2a%7D)
∴ ![h=\frac{-16}{2(1)}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-16%7D%7B2%281%29%7D)
∴ h = -8
To find k substitute y by k and x by -8 in the equation above
∵ k is the value of y when x = h
∵ h = -8
∴ k = (-8)² + 16(-8) - 7 = -71
∵ The vertex form of the quadratic equation is y = a(x - h)² + k
∵ a = 1 , h = -8 , k = -71
∴ y = (1)(x - (-8))² + (-71)
∴ y = (x + 8)² - 71
∵ (h , k) are the coordinates of the vertex point
∵ h = -8 and k = -71
∴ The vertex is (-8 , -71)
The vertex form of the function is y = (x + 8)² - 71
The vertex is (-8 , -71)
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You can learn more about quadratic equation in brainly.com/question/9390381
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Answer:
1. x=20 so 2x=40 3x=60 4x=80
2. I don't know
3. x=42 180-45-93=42
Answer:
<h2>The line that forms the shadow is 10.26 meters long, approximately.</h2>
Step-by-step explanation:
This problem is about a right triangle, becasue the truck and its shadow are perpendicular.
We are gonna call
the distance of the shadow on the ground, as the image attached shows.
To find the answer, we need to use Pythagorean's Theorem, where the hypothenuse is 11.2 meters, and one leg is 4.5 meters.
![(11.2)^{2} =x^{2} +(4.5)^{2} \\x^{2} =125.44-20.25\\x=\sqrt{105.19} \approx 10.26](https://tex.z-dn.net/?f=%2811.2%29%5E%7B2%7D%20%3Dx%5E%7B2%7D%20%2B%284.5%29%5E%7B2%7D%20%5C%5Cx%5E%7B2%7D%20%3D125.44-20.25%5C%5Cx%3D%5Csqrt%7B105.19%7D%20%5Capprox%20%2010.26)
Therefore, the line that forms the shadow is 10.26 meters long, approximately.
Part1:
The answer is "circumcenter".
One of a few centers the triangle can have, the circumcenter is where the perpendicular bisectors of a triangle converge or intersect. The circumcenter is additionally the focal or central point of the triangle's circumcircle - the circle that goes through each of the three of the triangle's vertices.
Part2:
The answer is "centroid".
The centroid of a triangle refers to the intersection point of the three medians of the triangle (every median associating a vertex with the midpoint of the contrary side). It lies on the triangle's Euler line, which additionally experiences different other key focuses including the orthocenter and the circumcenter.
Part3;
The answer is "incenter".
The incenter of a triangle refers to a triangle center, a point characterized for any triangle in a way that is free of the triangle's situation or scale. The incenter might be identically characterized as the point where the interior edge bisectors of the triangle cross, as the point equidistant from the triangle's sides, as the intersection purpose of the average pivot and deepest purpose of the grassfire change of the triangle, and as the inside purpose of the inscribed circle of the triangle.