Answer:
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Algebra Examples
Popular Problems Algebra Solve by Substitution 3x-4y=9 , -3x+2y=9
3
x
−
4
y
=
9
,
−
3
x
+
2
y
=
9
Solve for
x
in the first equation.
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x
=
3
+
4
y
3
−
3
x
+
2
y
=
9
Replace all occurrences of
x
in
−
3
x
+
2
y
=
9
with
3
+
4
y
3
.
x
=
3
+
4
y
3
−
3
(
3
+
4
y
3
)
+
2
y
=
9
Simplify
−
3
(
3
+
4
y
3
)
+
2
y
.
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x
=
3
+
4
y
3
−
9
−
2
y
=
9
Solve for
y
in the second equation.
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Move all terms not containing
y
to the right side of the equation.
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x
=
3
+
4
y
3
−
2
y
=
18
Divide each term by
−
2
and simplify.
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x
=
3
+
4
y
3
y
=
−
9
Replace all occurrences of
y
in
x
=
3
+
4
y
3
with
−
9
.
x
=
3
+
4
(
−
9
)
3
y
=
−
9
Simplify
3
+
4
(
−
9
)
3
.
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x
=
−
9
y
=
−
9
The solution to the system of equations can be represented as a point.
(
−
9
,
−
9
)
The result can be shown in multiple forms.
Point Form:
(
−
9
,
−
9
)
Equation Form:
x
=
−
9
,
y
=
−
9
image of graph
Step-by-step explanation:
The sum of all inner angles in the shape should be 540°
(180° for triangles, 360° for squares and other simple 4-corner-shapes, the pattern is the number of corners minus 2 multiplied by 180°)
we can calculate
540-106-94-135=205
so we got 205 degrees for the two unclear corners and one of them has to be 5° greater.
x is 100°
x is 100°x+5 is 105°
(note that in the subtraction part we could have subtracted 5 more and would be left with 2x=200)
<h3>
Answers:</h3>
- A. T <-> U is a <u>biconditional</u>
- B. (A & B) v (C & D) is a <u>disjunction</u>
- C. R -> ~S is a <u>conditional</u>
- D. P & Q is a <u>conjunction</u>
- E. ~(R v P) is a <u>negation</u>
========================================
Explanations:
- A biconditional is anything in the form A <-> B. This is a compact way of saying (A -> B) & (B -> A). We replace A and B with logical statements.
- Disjunctions are of the basic form A v B. The "v" basically means "or".
- Any conditional is of the form "if... then...". For example, "if it rains, then it gets wet outside" is a conditional. In terms of logic symbols, we write A -> B to mean "if A, then B".
- Conjunctions are whenever we combine two logical statements with an "and" or an ampersand symbol. The basic form is A & B
- Negations are the complete opposite of the original. If the original is P, then the negation is ~P, which is read as "not P".
It is probably A. A is the most reasonable answer.
