3x - 5 1/2 is the expression
Answer:
36 km
Step-by-step explanation:
This is a right triangle so we can use Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
27^2+ b^2 = 45^2
729+b^2 =2025
Subtract 729 from each side
729-729+b^2 =2025-729
b^2 =1296
Take the square root of each side
b =sqrt(1296)
b=36
Answer:
36
Step-by-step explanation:
a2+b2=c2
a2+27^2=45^2
a2+729=2025
a2=1296
then square root that number to get
a=36
No , the y-values of a data set cannot have both a common difference and a common ratio at the same time.
An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"
Thus nth term of an AP series is Tn = a + (n - 1) d
d = common difference = Tₙ - Tₙ₋₁
Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]
A geometric progression is a sequence in which each term is derived by multiplying or dividing the preceding term by a fixed number called the common ratio.
The nth term of a GP is aₙ = arⁿ⁻¹
Given data ,
A common difference means that the difference between any two consecutive y-values in the data set is the same. For example, if the first y-value is 3 and the common difference is 2, then the second y-value would be 5 (3 + 2), the third y-value would be 7 (5 + 2), and so on. This creates a linear relationship between the y-values.
And , a common ratio means that the ratio between any two consecutive y-values in the data set is the same. For example, if the first y-value is 3 and the common ratio is 2, then the second y-value would be 6 (3 x 2), the third y-value would be 12 (6 x 2), and so on. This creates an exponential relationship between the y-values.
Hence , a linear relationship and an exponential relationship are different, it is not possible for the y-values of a data set to have both a common difference and a common ratio at the same time.
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Answer:
Part a) The linear model that shows the salesperson’s total income is equal to
Part b) The total income is
Step-by-step explanation:
Part a)
Let
k-------> the total sales for the year
y-----> the total income for the year
we know that
The linear equation that represent the situation is
Part b) we have
substitute the value of k in the linear model to find the total income
The salesperson's income is represented by the linear model y = 35000 + 0.10k. If they sell $250,000 of merchandise, their total income, including salary and commission, would be $60,000.
A) The total income of the salesperson can be represented by the linear equation y = 35000 + 0.10k, where y represents the total income including the base salary and commission, and k represents the total sales.
B) To calculate the total income for a certain amount of sales, you would substitute the total sales amount into the equation. If the salesperson sold $250,000 worth of merchandise, the total income would be y = 35000 + 0.10*250000 = 35000 + 25000 = $60,000.
The salesperson would earn a total of $60,000 including base salary and commission for the year for the sales of $250,000 worth of merchandise.
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