Who can help me please I need major help I am just asking for some help
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Answer:
A. (-1, -4)
Step-by-step explanation:
The vertex can be found by converting the equation from standard form to vertex form.
<h3>Vertex</h3>Considering the x-terms, we have ...
y = (x^2 +2x) -3
where the coefficient of x is 2. Adding (and subtracting) the square of half that, we get ...
y = (x^2 +2x +(2/2)^2) -3 -(2/2)^2
y = (x +1)^2 -4
Compare this to the vertex form equation ...
y = a(x -h)^2 +k
which has vertex (h, k).
We see that h=-1 and k=-4. The vertex is (h, k) = (-1, -4).
On the attached graph, the vertex is the turning point, the minimum.
A statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is: option D.
<h3>How to calculate the slope of a line?</h3>Mathematically, the slope of a line is given by the following formula;
For line RP, we have:
Slope RP = 7.
For line SQ, we have:
Slope SQ = negative one-sevenths.
For the midpoint, we have:
In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and divide by two (2).
Midpoint on x-coordinate = (8 + 1)/2 = 9/2 = 4.5.
Midpoint on y-coordinate = (9 + 2)/2 = 11/2 = 5.5.
In conclusion, a statement which proves that the diagonals of square PQRS are perpendicular bisectors of each other is that the midpoint of both diagonals is (4.5, 5.5), the slope of RP is 7, and the slope of SQ is negative one-sevenths.
Read more on squares here: brainly.com/question/2882032
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Answer:
x = 4
Step-by-step explanation:
If you do not want to read the explanation go the the next part in bold
Ok so the shorter leg of the triangle is a radius of the circle. ( This is indicated by the point in the middle of the circle.) for the hypotenuse we are given one part of the length (2) The other part also happens to be a radius ( remember that a radius is a line that starts from the center of the triangle to any point of the circumference. ) Also remember that the radius is equal to 3. That being said the hypotenuse = 2+3 which equals 5.
This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.
Below here is where the work is shown
a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²
5² = 25
3² = 9
we would then have 25 = 9 + b²
Next we subtract 9 from each side
25 - 9 = 16
9 - 9 cancels out
Now we have 16 = b²
finally we want to get rid of the ²
To do so we take the square root of each side
we're left with b = 4 which means that x = 4