Expert Help with High School Geometry

All kites are rhombuses. True or False

What is the center and radius of the circle with equation ${\displaystyle {(x-5)}^2+{(y+3)}^2=16}$?

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.
A.True
B.False

Number of diagonals in a pentagon is...

Write the expression in the form of one angle.
$\sin \left(\frac{\mathrm{\pi }}{2}\right)\cos \left(\frac{\mathrm{\pi }}{7}\right)+\cos \left(\frac{\mathrm{\pi }}{2}\right)\cos \left(\frac{\mathrm{\pi }}{7}\right)$

Stained glass is a semicircle. Its length is $26$. What is the perimeter of the window? Use $3.14$ for $\mathrm{\pi <!--\; \pi \; -->}$

First order logic - why do we need function symbols?
Employing function symbols in first order logic necessitates us to delineate "terms" inductively, which renders many proofs more extensive and considerably more irksome.
Of course, function symbols simplify matters when trying to use first order logic to describe things, but on the surface it seems to me they could be replaced completely by relations: Instead of $f$ use a relation $R_f$ such that instead of writing $\mathrm{\phi <!--\; \phi \; -->}(f(x))$ write ($\mathrm{\forall <!--\; \forall \; -->}x\mathrm{\exists <!--\; \exists \; -->}!y(R(x,y))\wedge <!--\; \wedge \; -->R(x,y)\wedge <!--\; \wedge \; -->\mathrm{\phi <!--\; \phi \; -->}(y)$. Now use $f(x)$ as a shorthand notation, so you can use it in "real life" but avoid it in proofs.
I guess I'm missing some deep neccecity here, but what?
(The same goes for constant symbols, but they don't really complicate things as function symbols do).

The sum of interior angles of a hexagon is
A.3600
B.5400
C.7200
D.9000

Given AB, explain how to construct a square with sides of length AB

Negation of "If ... then" statements
I am just being introduced to how logic is used in mathematics and my lecturer mentioned that $\sim <!--\; \sim \; -->(P\to <!--\; \to \; -->Q)\equiv <!--\; \equiv \; -->p\wedge <!--\; \wedge \; -->\sim <!--\; \sim \; -->q$. This is quite hard to grasp at first glance, so he gave an example: The negation of "if $x\ne <!--\; \ne \; -->0$ then $y=0$" is "$x\ne <!--\; \ne \; -->0\wedge <!--\; \wedge \; -->y\ne <!--\; \ne \; -->0$".
Well, my question is, why should that be the case? Why is the negation of "if $x\ne <!--\; \ne \; -->0$ then $y=0$" not "$x\ne <!--\; \ne \; -->0\wedge <!--\; \wedge \; -->y=0$"?
Any explanations will be greatly appreciated :)

Is displacement greater than distance?

" The simplest way to write 15: 40 is as ?
1) 2 : 3
2) 5 : 4
3) 8 : 3
4) 3 : 8

The mean of sample A is significantly different than the mean of sample B. Sample A: $59,30,74,62,87,73$ Sample B: $53,67,85,57,93,79$ Use a two-tailed $t$-test of independent samples for the above hypothesis and data. What is the $p$-value? (Answer to $3$ decimal places)

A solid cylinder sits on top of a solid cube as shown in the figure. How far above the table's surface is the center of gravity of the combined object?

State whether the given statement is true or false: 9, 40, 41 is a Pythagorean triplet. True or false

5, 12, 13 is a Pythagorean triplet. True or false

Find the measure of interior angle of a regular octagon.
A ${135}^{\circ <!--\; \circ \; -->}$
B ${105}^{\circ <!--\; \circ \; -->}$
C ${145}^{\circ <!--\; \circ \; -->}$
D ${120}^{\circ <!--\; \circ \; -->}$

What's a convex quadrilateral?

How many sides does a circle have?