Which statement(s) about the line below are true? Select all that apply.
2 answers:
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Answer:
The area of rhombus PQRS is 120 m.
Step-by-step explanation:
Consider the rhombus PQRS.
All the sides of a rhombus are equal.
Hence, PQ = QR = RS = SP = 13 m
The diagonals PR and QS bisect each other.
Let the point at of intersection of the two diagonals be denoted by <em>X</em>.
Consider the triangle QXR.
QR = 13 m
XR = 12 m
The triangle QXR is a right angled triangle.
Using the Pythagorean theorem compute the length of QX as follows:
QR² = XR² + QX²
QX² = QR² - XR²
= 13² - 12²
= 25
QX = √25
= 5 m
The measure of the two diagonals are:
PR = 2 × XR = 2 × 12 = 24 m
QS = 2 × QX = 2 × 5 = 10 m
The area of a rhombus is:
Compute the area of rhombus PQRS as follows:
Thus, the area of rhombus PQRS is 120 m.
The curve has been attached and the answer choices are:
y = 3x² – 2x + 1
y = 3x² – 6x + 3
y = 3x²<span> – 7x + 1
</span>
The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.
Let's start with first equation:
y = 3x² – 2x + 1
using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3
Hence, the vertex would be:
(h,k) = (1/3 , 2/3)
Also, the leading coefficient is positive, so the parabola would be concave up.
Thus the final answer choice will be:
y = 3x² – 2x + 1
y = 3x² – 2x + 1
y = 3x² – 6x + 3
y = 3x²<span> – 7x + 1
</span>
The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.
Let's start with first equation:
y = 3x² – 2x + 1
using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3
Hence, the vertex would be:
(h,k) = (1/3 , 2/3)
Also, the leading coefficient is positive, so the parabola would be concave up.
Thus the final answer choice will be:
y = 3x² – 2x + 1