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3 years ago

What is the answer and plz explain

Mathematics

1 answer:

bagirrra123 [75]3 years ago

7 0

Answer:

36 squared units

Step-by-step explanation:

So you can draw "made up lines" or I guess lines you draw yourself to create 2 rectangles. Check attachment.

The first rectangle is a square and has sides 3 and 3, so you get the area of 9.

The second, has sides 9 and 3, so you get the area of 27

Since you are trying to find the entire thing, you add 27 and 9 to get 36

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Raina must choose a number between 55 and 101 that is a multiple of 2, 8 and 10. Write all the numbers that she could choose. If

Aleonysh [2.5K]

Answer:

The only possible number is $80$ .

Step-by-step explanation:

The number in question needs to be a multiple of all three of $2$ , $8$ , and $10$ . As a result, it must also be a multiple of the least common multiplier (lcm) of the three number.

Start by finding the least common multiplier of the three numbers.

Factor each number into its prime components:

$2$ is a prime number itself.
$8 = 2^3$ .
$10 = 2 \times 5$ .

The only prime factors are $2$ and $5$ .

The greatest power of $2$ among the three numbers is $3$ .
The greatest power of $5$ among the three numbers is $1$ .

Therefore, the least common multiplier of the three number should be the product of $2^3$ and $5$ . That's equal to $2^3 \times 5 = 8 \times 5 = 40$ .

In other words, the number (or numbers) in question could be written in the form $40\, k$ , where $k$ is an integer.

The question requires that this number be between $55$ and $101$ . In other words,

$55 \le 40\, k \le 101$ .

The goal is to find the possible values of $k$ . Note that from integer division by $40$ ,

$55 = 1 \times 40 + 15$ , and
$101 = 2 \times 40 + 21$ .

The inequality becomes:

$1 \times 40 + 15 \le 40\, k \le 2 \times 40 + 21$ .

However,

$1 \times 40 < 55 = 1 \times 40 + 15$ , and
$2 \times 40 + 21 = 101 < 3 \times 40$ .

Hence,

$1 \times 40 < 1\times 40 + 15 \le 40\, k \le 2 \times 40 + 21 < 3 \times 40$ .

$1 \times 40 < 40\, k < 3 \times 40$ .

Divide by the positive number $40$ to obtain:

$1 < k < 3$ .

Since $k$ is an integers, $k = 2$ .

Indeed, $40 \, k = 80$ is between $55$ and $101$ .

Therefore, $80$ is the number in question.

5 0

4 years ago

Read 2 more answers

Robby ate 5 potato chips. Jimmy ate p times as many potato chips as Robby. Which expression shows how many potato chips Jimmy at

mario62 [17]

Answer:

Step-by-step explanation:

Since Robby ate 5 potato chips and Jimmy ate p times that then you have to multiply them together.

Our final expression is 5p.

Hope this helped :)

8 0

3 years ago

the annual interest on 17,000 investment exceeds the interest on an 11,000 investment by 308 . the 17,000is invested at a 0.4% h

solmaris [256]

keeping in mind that

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}$

x = percent rate for the 17000 investment.

y = percent rate for the 11000 investment.

so the amount for the 17000 interest will just be (x/100) * 17000, or namely 170x.

and the amount of interest earned for the 11000 is (y/100) * 11000, or just 110y.

now, regardless of what "x" and "y" are, we know that the interest from the 17000 is higher by 308 bucks, therefore 170x = 110y + 308.

we also know that the rate of <u>x</u> is higher as well than <u>y</u> by 0.4%, so then x = y + 0.4.

$\bf \begin{cases} 170x=110y+308\\ \boxed{x}= y +0.4\\[-0.5em] \hrulefill\\ 170\left( \boxed{y+0.4} \right)=110y+308 \end{cases} \\\\\\ 170y+68=110y+308\implies 60y=240\implies y=\cfrac{240}{60}\implies \blacktriangleright y=\stackrel{\%}{4} \blacktriangleleft \\\\\\ x=y+0.4\implies \blacktriangleright x=\stackrel{\%}{4.4} \blacktriangleleft$