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3 years ago

Three times a number increased by ten is equal to twenty less than six times the number. Find the number

Mathematics

1 answer:

AysviL [449]3 years ago

4 0

Let the number be x. "Three times a number increased by 10" is mathematically translated as

3x + 10

"is equal" is mathematically translated as twenty less than six times the number" is mathematically translated as

6x - 20

The whole sentence "Three times a number increased by ten is equal to twenty less than six times the number" is translated as

3x + 10 = 6x - 20

We now solve the above linear equation to find the number x

3x - 6x = - 20 - 10

- 3x = - 30

x = 10

Check answer

Three times a number increased by ten : 3 × 10 + 10 = 40

Twenty less than six times the number : 6 × 10 - 20 = 40

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Read 2 more answers

Twenty times y is at most 100 in interval notation

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Answer:

$y\in (-\infty ,5]$

Step-by-step explanation:

In this problem, we need to write "Twenty times y is at most 100 in interval notation ".

20 times y means, 20y

Atmost means an inequality which is $\le$

ATQ,

$20\times y\le 100$

i.e.

$20y\le 100\\\\y\le 5$

We can also write it as :

$y\in (-\infty ,5]$

Hence, the required interval notation is $y\in (-\infty ,5]$ .

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3 years ago

Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years af

Leno4ka [110]

The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

<h3>What is compound interest?</h3>

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

$A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\$

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate<em> r </em>of in the time period of <em>t.</em>

Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.

Put the values in the above formula as,

$5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29$