We know that
The triangle inequality<span> states that for any </span>triangle, t<span>he sum of the lengths of any two sides of a </span>triangle<span> is greater than the length of the third side
</span>so
case <span>A. 81 mm, 7 mm, 6 mm
6+7 is not > 81
case </span><span>B. 81 mm, 7 mm, 72 mm
72+7 is not > 81
case </span><span>C. 81 mm, 7 mm, 88 mm
81+7 is not > 88
case </span><span>D. 81 mm, 7 mm, 77 mm
81+7 is > 77------> ok
77+7 is > 81-----> ok
81+77 is > 7-----> is ok
the answer is the option
</span>D. 81 mm, 7 mm, 77 mm
In the parallelogram PQRS
<h3>What is defined as the parallelogram?</h3>
- A parallelogram is a type of quadrilateral created by parallel lines.
- A parallelogram's angle between adjacent sides can vary, however the opposite sides must be parallel in order to be a parallelogram.
- A parallelogram is formed when the opposite sides of a quadrilateral are parallel as well as congruent.
For the given question;
In the parallelogram PQRS,
QR = PS = 5 (opposite side of parallelogram are parallel and equal).
Sum of all angles is 360.
∠Q = ∠S (opposite angles of parallelogram are equal)
∠P + ∠Q + ∠R + ∠S = 360
2∠P + 2∠Q = 360
2∠Q = 360 - 2∠P
2∠Q = 210
∠Q = 105
Thus, the angle Q is found as 105 degrees.
To know more about the parallelogram, here
brainly.com/question/970600
#SPJ1
Answer:
9) a = 8, b = 4√2
10) x = 7√2, y = 7
11) x = 5√2, y = 5
12) a = 10, b = 5√2
Step-by-step explanation:
You can notice all these triangles are special as 45° - 45° - 90° triangles. In 45° - 45° - 90° triangles, the hypotenuse is √2 times the sides. We can set up these equations and solve:
9)
a = 4√2 * √2
a = 8
Since the triangle is isosceles, the legs are the same length, so:
b = 4√2
10)
x = 7 * √2
x = 7√2
Since the triangle is isosceles, the legs are the same length, so:
y = 7
11)
x = 5 * √2
x = 5√2
Since the triangle is isosceles, the legs are the same length, so:
y = 5
12)
a = 5√2 * √2
a = 10
Since the triangle is isosceles, the legs are the same length, so:
b = 5√2
Answer:
Step-by-step explanation:
This question is asking for slope-intercept form which is y=mx+b, where m is the slope and b is the y-intercept. First, find the slope; this can be done in two ways, counting change in y and x then dividing, or using the formula 
. Either way for this graph the slope comes out as -1/3. Next, find the y-intercept, this is where the line intersects with the y-axis. In this case, the line touches the axis at 5, therefore 5 is the value of b.
