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3 years ago

Simplify (write without the absolute value sign) |x+3|, if x>2

Mathematics

1 answer:

kodGreya [7K]3 years ago

6 0

Answer:

Step-by-step explanation

Note that if x>2, then x+3>3+2=5. Then x+3>0. Recall that the absolute value function is defined as

$|x|=x \text{ if } x\geq 0$

$|x|=-x \text{ if } x< 0$

Since x+3>0, we have that |x+3|=x+3

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Find the flaw with the following "proof" that every postage of 3 cents or more can be formed using just 3-cent and 4-cent stamps

Reika [66]

Answer:

The main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

Step-by-step explanation:

From the question we are told that

The proof is

Every postage stamp of three cents or more can be formed using just 3 cent and 4 cent stamps.

Basic Step : We can form postage of 3 cents with a single 3 cent stamp and we can form postage of 4 cents using a single four cents tamp

Inductive Step: Assume that we can form postage of j cents for all non negative integers j with j <= k using just 3 cent and 4-cent stamps. We can then form postage of k+1 cents by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps

FLAW IDENTIFICATION

Looking the inductive step, the statement ''by replacing one 3 cent stamp with a 4-cent or two 4-cent stamps with three 3-cent stamps '' means that it is possible to use a 3-cent stamp for postage that requires a 4 -cent stamp and this is not correct according the statement in the basic step

Generally the main flaw of this proof is that it did not take into consideration the fact a 4 cent postage must be made with a 4 cent stamp and a 3 cent postage must be made with a 3 cent stamp but only looked at allocating the stamps based on the total amount of postage

4 0

3 years ago

I need help, Please hurry, It's timed.

kenny6666 [7]

The answer is
C) 22x^2-x+17

5 0

3 years ago

Read 2 more answers

A car travels 182 miles in 3 hours and 15 minutes. How many miles does it travel per hour?

timofeeve [1]

57 miles about I'm not positive but I think this is right

6 0

4 years ago

Derive a formula to find the perimeter of an isosceles triangle in which one of the equal

Scorpion4ik [409]

Given :

Length of one of the equal sides of an isosceles triangle = 3x+2

Then, length of the other equal side will also be = 3x+2

Length of the unequal side of this isosceles triangle = 14

Formula for finding the perimeter of an isosceles triangle :

$= \tt side + side + side$

A formula for finding the perimeter of this isosceles triangle :

$= \tt3x + 2 + 3x + 2 + 14$

Bringing all like terms together we get :

$=\tt 3x + 3x + 2 + 2 + 14$

$= \tt6x + 4 + 14$

$\color{plum}\tt = 6x + 18$

Thus, the formula = 6x+18

Therefore, a formula to find the perimeter of this isosceles triangle = <u>6x+18</u>

7 0

3 years ago

Your parents have a credit card with a balance of $3,287.90 at an interest rate of 14.5% APR. They pay $1,200.00 each month on t

aleksandrvk [35]

It will take them approximately 3 months to pay off the balance on the credit card

<h3 /><h3>First Month</h3>

To solve this problem, we need to find the interest on 3287.90 at 14.5%

for the first month, we would have

$\frac{x}{3287.90}=\frac{14.5}{100} \\x=476.74$

Now we divide this by 12 to give the interest payable on the first month

$\frac{476.75}{12}=39.73$

So we have

$(3287.90+39.73)-1200=2127.63$

<h3>Second Month</h3>

We would do the same thing for the second month and it will give us

$(\frac{x}{2127.63}=\frac{14.5}{100})/12\\\frac{308.506}{12}=25.71$

For the second month, we have $25.71 as the interest payable

We can calculate how much would be left after the second month.

$(2127.63+25.71)-1200=953.34$

<h3 /><h3>Third Month</h3>

In the third month, since the balance remaining is less than the monthly payment schedule, we can assume they'd pay everything off which is 953.34.

From the calculations above, we can see that it'll take them 3 months to pay off the credit card balance.

The balance at the end of each month are;

$2,127.63
$953.34
$0

Learn more on APR here;

brainly.com/question/11686424

6 0

2 years ago