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xenn [34]
3 years ago
7

from 1970 to 1980 the consumer price index increased from 38.8 to 82.4. If a container of onion dip cost $0.48 in 1970 and the p

rice of onion dip increased at the same rate as the CPI from 1970 to 1980, by approximately how much did the price of a container of onion dip increase from 1970 to 1980
Mathematics
2 answers:
Vikki [24]3 years ago
5 0
We need to find the percent increase from 38.8 to 82.4, so

x * 38.8 = 82.4
x = 82.4/38.8
x = 2.1237

Multiply by 100 to convert to percentage (move decimal 2 places to the right)

2.1237 = 212.37%

Now we can apply this percentage increase to the onion dip...

0.48 x 212.37% =
0.48 x 2.1237 = 1.019 
 
Round to the nearest cent $1.02 is the amount of increase.  Now add it to the original price to get today's price...

$1.02 + .48 = $1.50
 
gregori [183]3 years ago
4 0

Answer:

C.

$0.54

Step-by-step explanation:


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Answer:

The x-intercepts are x = 1 , x = 2 , x = 3

The y-intercept is -6

Step-by-step explanation:

* Lets explain how to solve the problem

- To find the x-intercept of a function substitute f(x) by 0

- To find the y-intercept of a function substitute x by 0

- To find the factors of quadratic function use the long division

* Lets solve the problem

∵ f(x) = x³ - 6x² + 11x - 6

∵ (x - 3) is one of its factors

- Use the long division to find the other factors

∵ x³ - 6x² + 11x - 6 ⇒ dividend

∵ x - 3 ⇒ divisor

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ x³ ÷ x = x²

# Multiply x² by the divisor (x - 3)

∵ x²(x - 3) = x³ - 3x²

# subtract it from the dividend

∵ (x³ - 6x² + 11x - 6) - (x³ - 3x²) = (x³ - x³) + (-6x² + 3x²) +11x - 6

∴ The dividend is -3x² + 11x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ -3x² ÷ x = -3x

# Multiply -3x by the divisor (x - 3)

∴ -3x(x - 3) = -3x² + 9x

# subtract it from the dividend

∵ (-3x² + 11x - 6) - (-3x² + 9x) = (-3x² - 3x²) + (11x - 9x) - 6

∴ The dividend is 2x - 6

# Divide the 1st term in the dividend by the 1st term of the divisor

∵ 2x ÷ x = 2

# Multiply 2 by the divisor (x - 3)

∴ 2(x - 3) = 2x - 6

# subtract it from the dividend

∴ (2x - 6) - (2x - 6) = (2x - 2x) + (-6 + 6) = 0

∴ (x³ - 6x² + 11x - 6) ÷ (x - 3) = x² - 3x + 2

∴ The factors of f(x) are (x - 3)( x² - 3x + 2)

- The factor (x² - 3x + 2) can factorize into two bracket

∵ The last term is positive and the middle term is negative than the

   two brackets have the middle sign (-)

∵ x × x = x² ⇒ 1st terms in the two brackets

∵ 2 × 1 = 2 ⇒ 2nd terms in the two brackets

∵ 2 × x = 2x

∵ 1 × x = x

∵ 2x + x = 3x

∴  (x² - 3x + 2) = (x - 2)(x - 1)

∴ f(x) = (x - 3)(x - 2)(x - 1)

- To find the x-intercept put f(x) = 0

∴ (x - 3)(x - 2)(x - 1) = 0

- That means each bracket = 0

∵ x - 3 = 0 ⇒ add 3 for both sides

∴ x = 3

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∴ x = 2

∵ x - 1 = 0 ⇒ add 1 for both sides

∴ x = 1

∴ The x-intercepts are x = 1 , x = 2 , x = 3

- To find the y-intercept put x = 0

∵ f(x) = x³ - 6x² + 11x - 6

∵ x = 0

∴ f(0) = 0 - 0 + 0 - 6 = -6

∴ The y-intercept is -6

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