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creativ13 [48]
2 years ago
9

Write the converse of the following statement and determine its truth value.

Mathematics
1 answer:
Tanya [424]2 years ago
3 0

Answer:

1) The convers of the conditional statement is;

If the ratio of lefties to righties is 1:8,  then a class has 3 left-handed people and 24 right-handed people

2) The convers of the conditional statement is true

Step-by-step explanation:

1) The given statement is presented as follows;

"If a class has 3 left-handed people and 24 right-handed people, then the ratio of lefties to righties is 1:8"

The hypothesis = A class has 3 left-handed people and 24 right-handed people = p

The conclusion = The ratio of lefties to righties is 1:8 = q

We have;

If p, then q which is p → q

The converse statement = If q, then p which is q → p

Then the converse of the conditional statement can be written as follows;

If the ratio of lefties to righties is 1:8,  then a class has 3 left-handed people and 24 right-handed people

2) Given that the ratio of 3:24 = 1:8, we have that both the hypothesis and the conclusion are true, therefore, the converse of the conditional statement is true.

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In ∆PQR, ∠P = 90degrees , PQ= 12 cm, PR=16cm. Find ∠Q
siniylev [52]

Answer:

∠Q  = 53.13 degrees

Step-by-step explanation:

Given that ∆PQR, ∠P = 90degrees , this means that the triangle is a right angled triangle

Hence using the notation

SOH CAH TOA

where S is sine, C is cosine, T is tangent and O, A and H represents the size of the opposite, adjacent and hypotenuse sides

Considering  ∠Q and the given sides

PR=16cm is the opposite side,

PQ= 12 cm is the adjacent side hence we use TOA

Tan Q = 16/12 =

Q = Arc tan 16/12

= 53.13 degrees

5 0
2 years ago
Find two consecutive integers such that the smaller integer is six more than twice the larger integer
ZanzabumX [31]
Let the integers be x and x+1.

x = 6 + 2(x + 1)

x = 6 + 2x + 2

x = -8

Hence, the integers are -8 and -7.
8 0
3 years ago
What is the length of AC
meriva
Hi!
This is a fun one, as it delves into basic trigonometry.

We're going to use the Pythagorean theorem here, which says that for right triangles where "c" is the hypotenuse,

a² + b² = c²

We have to split this large triangle into two parts, both of which are right triangles. (This is why they drew a line in the middle to tell you that the larger triangle is composed of two right triangles.)

Let's do the one on the right first.

We know that the length of the hypotenuse is 10, and that the length of one of the legs is 6.5. If we plug this into our equation, we'll get the length of the other leg. I'm choosing "b" to be 6.5, but it really doesn't matter if you pick "a" or "b", so long as you reserve "c" for the hypotenuse (longest side).

a² + 6.5² = 10²
a² + 42.25 = 100
a² = 57.75
√a² = √57.75
a ≈ 7.6

Therefore, the length of DC is about 7.6.

Find the length of AD using the same method (7.5 is the hypotenuse "c", and 6.5 is one of the legs "a" or "b"). Then, once you have AD, add the lengths of AD and DC to get AC.

Have a great one!
7 0
2 years ago
How do I solve this??
WITCHER [35]

v + 9 / 3 = 8

v + 9 = 24

v = 24 - 9

v = 15

If you have any questions on how I got to this solution, please ask. :)

6 0
3 years ago
Read 2 more answers
9(-6X-2) -7 (-10X-2)
Maksim231197 [3]
9(-6x-2)-7(-10x-2)
Simplify, by distributing the 9 and the -7
-54x-18+70x+14
Combine like terms
16x-4 is the simplified expression

Hope this helped!
3 0
2 years ago
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