Answer:
Problem #1: x = 2.5
Problem #2: x = 10/7
Step-by-step explanation:
Step 1: Find the value of x in (8x - 20)
8x - 20 = 0
<u>Add 20 to both sides</u>
8x - 20 + 20 = 0 + 20
<em>8x = 20</em>
<em />
<u>Divide both sides by 8</u>
8x / 8 = 20 / 8
<em>x = 2.5</em>
<em />
Answer: x = 2.5
<em />
Step 2: Find the value of x in (14x - 20)
14x - 20 = 0
<u>Add 20 to both sides</u>
14x - 20 + 20 = 0 + 20
<em>14x = 20</em>
<em />
<u>Divide both sides by 14</u>
14x / 14 = 20 / 14
<em>x = 10/7</em>
<em />
Answer: x = 10/7
Answer:
n = 59
Step-by-step explanation:
Since the difference between consecutive terms is constant, then the sequence is arithmetic.
The n th term of an arithmetic sequence is
= a₁ + (n - 1)d
Given
= 40, then
a₁ + 9d = 40 → (1)
Given
= 20, then
a₁ + 19d = 20 → (2)
Subtract (1) from (2) term by term
10d = - 20 ( divide both sides by 10 )
d = - 2
Substitute d = - 2 in (1)
a₁ - 18 = 40 ( add 18 to both sides )
a₁ = 58
The sum to n terms of an arithmetic sequence is
= 
[2a₁ + (n - 1)d ]
Here a₁ = 58, d = - 2 and = 0, thus
[ ( 2 × 58) - 2(n - 1)] = 0
( 116 - 2n + 2) = 0
Multiply through by 2
n(118 - 2n) = 0
Equate each factor to zero and solve for n
n = 0
118 - 2n = 0 ⇒ - 2n = - 118 ⇒ n = 59
However, n > 0 ⇒ n = 59
Answer:
12
Step-by-step explanation:
Total CD's Lisa bought = 15
Jazz music = 3
World music = x
Find x
Total CD's Lisa bought = Jazz music + World music
15 = 3 + x
Subtract 3 from both sides of the equation
15 - 3 = 3 + x - 3
12 = x
x = 12
Therefore,
World music = x = 12
N - the number
9 more than a number
n + 9
A change in the scale factor is to occur when an enlargement or a reduction in the dimensions of a building occurs to preserve the relationship between actual and mapped dimensions.
<h3>What is scale factor?</h3>
Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures. An enlargement or a reduction in the dimensions of a building would cause a change in the scale factor.
This can be understood with the following points:
- Scale factor is the proportion between the actual and mapped dimensions of a construction.
- The change in dimensions of the building lead to the change in scale factor.
- This is happened to preserve their relationship.
Thus, a change in the scale factor is to occur when an enlargement or a reduction in the dimensions of a building occurs to preserve the relationship between actual and mapped dimensions.
Learn more about the scale factor here;
brainly.com/question/10253650
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