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3 years ago

Simplity -12c^8 divided by 6c^5

Mathematics

1 answer:

Ratling [72]3 years ago

7 0

Answer:

-2c^13

<em><u>hopefully i helped :)</u></em>

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The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.

solong [7]

Answer:

$20$ .

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are $a$ , $b$ , and $c$ :

$a + b > c$ ,

$a + c > b$ , and

$b + c > a$ .

In this question, the length of the sides are $10$ , $24$ , and $x$ . The length of these sides should satisfty the following inequalities:

$10 + 24 > x$ ,

$10 + x > 24$ , and

$24 + x > 10$ .

Since $x > 0$ , the inequality $24 + x > 10$ is guarenteed to be satisfied.

Simplify $10 + 24 > x$ to obtain the inequality $x < 35$ .

Similarly, simplify $10 + x > 24$ to obtain the inequality $x > 14$ .

Since $x$ needs to be a whole number, the greatest $x$ that satisfies $x < 35$ would be $34$ . Similarly, the least $x\!$ that satisfies $x > 14$ would be $15$ . Thus, $x\!\!$ could be any whole number between $15\!$ and $34\!$ (inclusive.)

There are a total of $34 - 15 + 1 = 20$ distinct whole numbers between $15$ and $34$ (inclusive.) Thus, the number of possible whole number values for $x$ would be $20$ .

5 0

3 years ago

Torri had $20 to buy a birthday present for her dad. She decided to buy a DVD for $18. The sales tax is 7 percent. Does she have

vesna_86 [32]

First, we need to calculate the cost of the sale tax. To do it, we are going to convert the sale tax from percentage to fraction by dividing it by 100, and then we are going to multiply the cost of the DVD by the sale tax:

$Sale.Tax=\frac{7}{100}$

Now, we can multiply the cost of the DVD by the sale tax to find the cost of the sale tax:

$Cost.Sale.Tax=18(\frac{7}{100)} )=9(\frac{7}{50} )=\frac{63}{50} =1.26$

Now that we know that the sale tax is $1.26, we are going to add the cost of the sale tax to the cost of the DVD and check if that sum is less or equal than Torri's money (20$):

$Total.Cost=18+1.26=19.26$

Since $19.26 $\leq$ $20, we can conclude that Torri has enough money to buy the DVD. In fact, Torri will end with a change of $0.74 after buying the DVD.