Answer:
33.3%
Step-by-step explanation:
Let's say the percent change is x%. Then the equation is:
30 + x% * 30 = 40
Subtract 30 from both sides:
x% * 30 = 10
Divide by 30:
x% = 10/30 = 1/3
Remember that % simply means "out of 100", so:
x/100 = 1/3
Multiply both sides by 100:
x = (1/3) * 100 = 33.3%
Month*
divide 840 with 12
as 1 year has 12 months
and you get 70$
so the family spends $70 every month
The values of x in the triangles and the angles in the rhombus are illustrations of tangent ratios
- The values of x in the triangles are 21.4 units, 58 degrees and 66 degrees
- The angles in the rhombus are 44 and 46 degrees, respectively
<h3>How to determine the values of x?</h3>
<u>Triangle 1</u>
The value of x is calculated using the following tangent ratio
tan(25) = 10/x
Make x the subject
x = 10/tan(25)
Evaluate
x = 21.4
<u>Triangle 2</u>
The value of x is calculated using the following tangent ratio
tan(x) = 8/5
Evaluate the quotient
tan(x) = 1.6
Take the arc tan of both sides
x = arctan(1.6)
Evaluate
x = 58
<u>Triangle 3</u>
The value of x is calculated using the following tangent ratio
tan(x) = 0.34/0.15
Evaluate the quotient
tan(x) = 2.27
Take the arc tan of both sides
x = arctan(2.27)
Evaluate
x = 66
<h3>How to calculate the angles of the rhombus?</h3>
The lengths of the diagonals are:
L1 = 2 in
L2 = 5 in
Represent the angles with x and y.
The measures of the angles are calculated using the following tangent ratios
tan(0.5x) = 2/5 and y = 90 - x
Evaluate the quotient
tan(0.5x) = 0.4
Take the arc tan of both sides
0.5x = arctan(0.4)
Evaluate
0.5x = 22
Divide by 0.5
x = 44
Recall that:
y = 90 - x
This gives
y = 90 - 44
Evaluate
y = 46
Hence, the angles in the rhombus are 44 and 46 degrees, respectively
Read more about tangent ratio at:
brainly.com/question/13347349
Answer:
The equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … Will have:
(a) 6 solutions where there are no other restrictions.
(b) 4 Solutions for xi ≥ 3 for i = 1, 2, 3, 4, 5, 6(x3 + x4 +x5 + x6 = 25)
(c) 4 Solutions for 3 ≤ x1 ≤ 10
( x3 + x4 + x5 + x6 = 25)
(d) 5 Solutions for 2 ≤ x2 ≤ 7
Step-by-step explanation:
The equation have 6 unknown variables . This means it will have 6 solutions when no condition is imposed as in (a) above. The number of unknown variables in the equation will give the numbers of solutions
When the conditions are imposed, the numbers of unknown variables will give the number of solutions.
In (b) and (c), the equation will reduce to x3 + x4 +x5 + x6 = 25) and the unknown variables are 4, giving 4 solutions
In (d), the equation will reduce be 5 unknown variables(x2 + x3 + x4 +x5 + x6 = 25) and the solution is 5
