3e≤6 a e=1 b e=2 c e=3

1 answer:

7 0

A and b are both accurate

For a:
$3(1) \leqslant 6 = 3 \leqslant 6$
which is true

For b:
$3(2) \leqslant 6 = 6 \leqslant 6$
which is also true

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The contrapositive of a conditional statement is "If an item is not worth five dimes, then it is not worth two quarters.”

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Example of use of terms:
Statement: If it is far, we take a bus.
Inverse: If it is not far, we do not take a bus.
Converse: If we take a bus, it is far.
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We also know that
1. The inverse of the inverse is the statement itself, and similarly for converse and contrapositive.
2. Only the contrapositive is logically equivalent to the original statement.
This means that the converse and inverse are logically different from the original statement.

Now back to the given statement.
To find the original statement, we find the contrapositive of the contrapositive.
We then find the converse from the original statement, as in the example above.

Original statement
(note that in English, if it is not worth X dollars, means if it is not worth AT LEAST X dollars")
contrapositive of

"If an item is not worth five dimes, then it is not worth two quarters.”
is the negation of the converse, which become
"If an item is worth two quarters, then it is worth (at least) five dimes."

The converse of the previous statement is therefore
"If an item is worth (at least) five dimes then it is worth two quarters"

In this particular case, we can also take advantage of the fact that the contrapositive is the negation of the converse. So all we have to do is the provide the negation of each component of the contrapositive to get the converse:
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as before.

Note that the converse does NOT logically mean the same as the original statement.

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Find the value of the variable if P is between J & K. A) JP = 8z - 17 B) PK = 5z + 37 C) JK = 17z - 4

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We cannot deduce about the exact location of P between J and K. But we can conclude: segment JP + segment PK = line JK.
JP + PK = JK.
Substitute first each.
(8z - 17) + (5z + 37) = 17z - 4
Combine like terms.
13z + 20 = 17z - 4
Isolate the variable z.
4z = 24
z = 6
The value of the variable z is then 6 units.

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Read 2 more answers

The figure the Floor Plan of a balcony ,it consists of △ABC and semi-circle ,

ivanzaharov [21]

Step-by-step explanation:

(a) In right triangle ABC,

$AC^2 =AB^2 +BC^2 \\ = {12}^{2} + {5}^{2} \\ = 144 + 25 \\ = 169 \\ AC = \sqrt{169} \\ \therefore \: AC = 13\: m \\ \\ AC \: is \: the \: diameter \: of \: semicircle \\ \therefore \: r = \frac{1}{2} \times AC = \frac{1}{2} \times 13 = 6.5 \: m \\ Circumference \:of \:semi-circle \\ C = \pi \: r = 3.14 \times 6.5 = 20.41 \:m\:$

Perimeter of Balcony = 12 + 5 + 20.41 = 37.41 m

(b) Area of balcony

$=\frac{1}{2}\times 12\times 5+\frac{1}{2} \pi r^2 \\\\=\times 6\times 5+\frac{1}{2} \times 3.14\times (6.5)^2 \\\\=30+\frac{1}{2} \times 3.14\times42.25\\\\= 30+\frac{1}{2} \times 132.665\\\\= 30 + 66.3325\\\\= 96.3325 \:m^2 \\\\\approx 96. 33\:m^2$

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3 years ago