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3 years ago

F(x) = 2x + 3 Find f(1 - x) in its simplest form.

Mathematics

1 answer:

Romashka [77]3 years ago

5 0

Answer: f(1 - x) = 2x + 1

<u>Step-by-step explanation:</u>

f(x) = 2x + 3

f(1 - x) = 2(1 - x) + 3 <em>replaced x with 1 - x</em>

= 2 - 2x + 3 <em>distributed the 2</em>

= 5 - 2x <em>simplified</em>

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A merchant wishes to blend 200 pounds of coffee worth $3.20 a pound from two mixtures: one at $3.00 a pound and the other at $3.

Fofino [41]

X pounds of $3
y pounds of $3.25

x+y = 200

300x + 325y = 320*200
300x + 325y = 64000

x+y =200
300x +325y =64000

Solve by eliminating

Multiply top one w/-300

-300y =60000
325y=64000
25y = 4000

y= 160 then

x + 160= 200

x = 40

So the mixture has;

40 pounds of $3 coffee
160 pounds of $3.25 coffee

8 0

4 years ago

27 divided by 53 minus 6 plus 53 times -2 squared

mamaluj [8]

Answer:

$\left(\left(\frac{27}{53}\right)-6\right)+\left(53\left(-\left(2^2\right)\right)\right)=-\frac{11527}{53}\quad \left(\mathrm{Decimal:\quad }\:-217.49056\dots \right)$

Step-by-step explanation:

Considering the expression

27 divided by 53 minus 6 plus 53 times -2 squared

Which can be written as

$\left(\left(\frac{27}{53}\right)-6\right)+\left(53\cdot \left(-\left(2^2\right)\right)\right)$

So, solving the expression

$\left(\left(\frac{27}{53}\right)-6\right)+\left(53\cdot \left(-\left(2^2\right)\right)\right)$

$\mathrm{Remove\:parentheses}:\quad \left(a\right)=a$

$=\frac{27}{53}-6-53\cdot \:2^2$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:6=\frac{6\cdot \:53}{53}$

$=-\frac{6\cdot \:53}{53}+\frac{27}{53}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-6\cdot \:53+27}{53}$

$=\frac{-291}{53}$ ∵ $-6\cdot \:53+27=-291$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-2^2\cdot \:53-\frac{291}{53}$

$=-212-\frac{291}{53}$ ∵ $53\cdot \:2^2=212$

$\mathrm{Convert\:element\:to\:fraction}:\quad \:212=\frac{212\cdot \:53}{53}$

$=-\frac{212\cdot \:53}{53}-\frac{291}{53}$

$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}$

$=\frac{-212\cdot \:53-291}{53}$

$=\frac{-11527}{53}$ ∵ $-212\cdot \:53-291=-11527$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

$=-\frac{11527}{53}$

Therefore,

$\left(\left(\frac{27}{53}\right)-6\right)+\left(53\left(-\left(2^2\right)\right)\right)=-\frac{11527}{53}\quad \left(\mathrm{Decimal:\quad }\:-217.49056\dots \right)$

Keywords: algebraic expression

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8 0

4 years ago

Esme earns a net salary of $2,400 per month. She already has a savings account that has $100 in it. After paying her expenses ev

Mademuasel [1]

Answer:

D. 49.75 months

Step-by-step explanation:

Esme earns a net salary of $2400 per month.

In her saving account she already have a balance of $100.

She saves $100 every month after her monthly expenses.

She plans to buy a car of $20000 using a no interest loan .

She usually make a $300 payment on the loan every month.

The number of months she will save enough money to pay off her loan completely can be calculated below.

let

x = number of months

The amount she saved altogether every month is $300 + $100 = $400.

Recall she already has $100 in her account

Amount of loan to be repaid = 100 + 400x

20000 = 100 + 400x

20000 - 100 = 400x

19900 = 400x

divide both sides by 400

x = 19900/400

x = 49.75 months

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3 years ago

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neonofarm [45]

Answer:

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3 years ago

How has the Roaring Twenties been portrayed in modern media?

Alexus [3.1K]

Answer:

The nation's total wealth more than doubled between 1920 and 1929, and this economic growth swept many Americans into an affluent but unfamiliar “consumer society.” People from coast to coast bought the same goods (thanks to nationwide advertising and the spread of chain stores), listened to the same music

6 0

2 years ago