What is the area of the trapezoid shown? (1) angle a = 120 degrees (2) the perimeter of trapezoid abcd = 36?

stellarik [79]

Answer:

$a = \frac{w + 4 - 3b}{6}$

Step-by-step explanation:

$w = 3(2a + b) - 4 \\ w + 4 = 6a + 3b \\ w + 4 - 3b = 6a \\ \frac{w + 4 - 3b}{6} = \frac{6a}{6} \\ a = \frac{w + 4 - 3b}{6}$

Thanks

hope this helps!!

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5 0

3 years ago

PLEASE HELP THANK YOU!!!

Paul [167]

Answer:

Only C is a function

Step-by-step explanation:

To test whether a graph is a function you use the vertical line test.

If you can place a vertical line anywhere on the plane (in the domain of the "function" to be tested) and it intersects the curve at more than one point, the curve is not a function.

We see with A, wherever we put the vertical line it intersects twice.

With B, it intersects infinitely many times.

C is a function because wherever we put the vertical line, it only intersects once.

D is a function because it intersects twice providing we do not put it on the "tip" of the parabola.

The mathematical reasoning behind this is that a function must be well-defined, that is it must send every x-value to one specific y-value. There can be no confusion about where the function's input is going. If you look at graph B and I ask you what is f(3)? Is it 1? 2? 3? ... Who knows, it's not well-defined and so it's not a function. However if I ask you about C, whichever input value for x I give you, you can tell me to which y-value it gets mapped/sent to.

7 0

3 years ago

Café Noir charges a 1% levy on the bill for trading on Sundays. If the final bill is $55.55, what was the original price, taking

svetoff [14.1K]

As I guess I think its 5

7 0

3 years ago

Find the volume r:7 h:7

sweet-ann [11.9K]

Answer:

V = 1077.566 units²

Step-by-step explanation:

Assuming this is a cylinder, the formula is (area of base) × (height)

or (πr²)(h), simply plug-in the given values:

= (π(7)²)(7)

= (153.938)(7)

V = 1077.566 units²

3 0

3 years ago

In the figure below, points M, P, H, J, and K lie in plane Z.

marishachu [46]

Answers:

(a) LN
(b) PHJ
(c) K
(d) HK

===================================================

Explanation:

Part (a)

Lines LN and PN have the point N in common. This is the intersection point.

-----------------

Part (b)

To name a plane, pick any three non-collinear points that are inside it. We cannot pick points H, J, K together because infinitely many planes pass through it. Imagine the piece of flat paper able to rotate around this axis (like a propeller). Having the points not all on the same line guarantees we form exactly one unique plane.

I'll pick the non-collinear points P, H and J to get the name Plane PHJ. Other answers are possible.

------------------

Part (c)

Points H, J and K are collinear as they are on the same line. Pick either H or K to fill out the answer box. I'll go with point K

------------------

Part (d)

Point P and line HK are coplanar. They exist in the same flat plane, or on the same sheet of flat paper together.

We can think of that flat plane as the ground level while something like point N is underground somewhere. So point N and anything on that ground plane wouldn't be coplanar.

Note: there are other possible names for line HK such as line JH or line JK. The order doesn't matter when it comes to naming lines.

4 0

3 years ago