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3 years ago

1. Sort the numbers into 2 groups, rational or irrational. Write the numbers in the appropriate bubble.

Mathematics

1 answer:

rodikova [14]3 years ago

6 0

Answer:

[see below]

Step-by-step explanation:

All natural numbers, whole numbers, integers, fractions (with integers), and numbers with terminating or repeating decimals are rational.
Irrational numbers cannot be written as fractions with integers. This includes non-germinating and non-repeating decimals.

Rational Numbers:

0.8
64
0 (it can be written as $\frac{0}{1}$ )
32
-19
-100
3
7
175
2
6
12.67
1121
12
5
3/7

Irrational Numbers:

2.343443444...
π

Hope this helps.

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8 times of the eight term of an arithmetic progression is equal to 12 times of the twelfth term. find its first term if the comm

Ilya [14]

Answer:

a₁ = 38

Step-by-step explanation:

Given AP, where:

8a₈ = 12a₁₂
d = -2,
a₁ = ?

=============

<h3>Solution</h3>

aₙ = a₁ + (n-1)d

a₈ = a₁ + 7d = a₁ + 7*(-2) = a₁ - 14
a₁₂ = a₁ + 11d = a₁ + 11*(-2) = a₁ - 22

8a₈ = 12a₁₂

8(a₁ - 14) = 12(a₁ - 22)
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6 0

3 years ago

here are some numbers: 8, 11, 13, 18, 25, 37 8, 13 , 18 is an arithmetic progression and the rule is to add 5 use three of the n

Yuliya22 [10]

Answer:

Progression: 11, 18, 25

Rule: Add 7

Step-by-step explanation:

Given

List of numbers: 8, 11, 13, 18, 25, 37

Sample Progression: 8, 13, 18; with common difference of 5

Required

Form a different progression using any three listed numbers

To solve this; we'll make use of trial and error methods;

<em>NB: I've tried several numbers; So, I'll just stick to the one that works</em>

To start with;

Select ->11

Add 7 to 11: 11 + 7 - > 18

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With the above illustration, we've successfully used three numbers (11, 18 and 25) to form a new progression and the rule is to add 7

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3 years ago

Triangle J K L is shown. Angle J L K is 105 degrees. The length of J K is 4.7 and the length of J L is 2.7.

cluponka [151]

Answer:

The approximate measure of angle K is 34°

Step-by-step explanation:

In ΔJKL

∠L = 105°

JK = 4.7

JL = 2.7

Sine Rule:

$\frac{SinA}{a} = \frac{SinB}{b}= \frac{SinC}{c}$

So, $\frac{SinL}{JK} = \frac{SinK}{JL}\\\frac{SinL}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105}{4.7} = \frac{SinK}{2.7}\\\frac{Sin 105 \times 2.7}{4.7} = SinK\\\frac{(0.9659 \times 2.7)}{4.7} = Sin K\\\frac{2.60793}{4.7} = Sin K\\0.5549 = Sin K\\Sin^{-1}(0.5549)= K\\K = 33.70$

K ≈ 34°

So, Option B is true

Hence The approximate measure of angle K is 34°

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