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9514 1404 393
Answer:
A, C
Step-by-step explanation:
The attached graph shows which lines go through the given point. They are ...
y = 1/2x -1 . . . . 1st selection
y = -1/6x +3 . . . 3rd selection
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The equations can be found algebraically by substituting the given point in the equation and seeing if the result is a true statement.
a) 2 = (1/2)(6) -1 = 3 -1 . . . true
b) 2 = -3(6) . . . . false
c) 2 = -1/6(6) +3 = -1 +3 . . . true
d) 2 = 2/3(6) -1 = 4 -1 . . . . false
e) 2 = 4(6) -2 = 24 -2 . . . . false
f) 2 = -3/2(6) +6 = -9 +6 . . . . false
A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as: p⇒q,
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
.
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that then Triangle ABC is not a right triangle with m(C)=90°
True
and read "if p then q"
Let p be the proposition: Triangle ABC is a right triangle with m(C)=90°.
Let q be the proposition: The sides of triangle ABC are such that
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that
This compound proposition (compound because we formed it using 2 other propositions) is true. So the truth value is True,
the converse, inverse and contrapositive of p⇒q are defined as follows:
converse: q⇒p
inverse: ¬p⇒¬q (if [not p] then [not q])
contrapositive: ¬q⇒¬p
Converse of our statement:
if The sides of triangle ABC are such that
then Triangle ABC is a right triangle with m(C)=90°
True
Inverse of the statement:
if Triangle ABC is not a right triangle with m(C) not =90° then The sides of triangle ABC are not such that
True
Contrapositive statement:
if The sides of triangle ABC are not such that
True
To solve for the longest side, the hypotenuse, you have to use the pythagorean theorem. It will be 10^2 + 9^2 = c^2. 100 + 81 =c^2.
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)
c^2 = 181 so c = sqrt(181).
to find sin of A do opposite/hypotenuse which gives you 9/sqrt(181)
to find cos of A do adjacent/hypotenuse which gives you 10/sqrt(181)