MATHEMATICS COLLEGE

In the right triangle, if a = 3 and b = 6, what is the value of c?a 3 times the square root of 5
b 9
c 9 times the square root of 5
d 45

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Using the pythagorean theorem, $a^(2) +b^(2) =c^(2)$

we plug the numbers in; $3^(2) + 6^(2) =c^(2)$

9+36=c^2

45=c^2

sqr root of 45 is $√(45)$

next find the positive perfect sqr root of 45 which will be 9.

9 goes into 45 5 times so it will be $√(9x5)$

Sqr root of 9 is 3 so it will be $3 √(5)$

Answer 2

Answer: A I had took the quiz

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Which expression can be used to determine the product of -4 and 3 1/4

Answers

Answer:

Possible options:

= -4 * 3 1/4

= -4 * 13/4

= -4 * 3.25

Step-by-step explanation:

Without the options that seemed to go along with this question, it will be difficult to give the exact expression, but here are a few options.

-4 * 3 1/4 = -13

-4 * 13/4 = -13

-4 * 3.25 = -13

Each of these expressions will give the product of -4 and 3 1/4.

Cheers

The sum of the squares of two consecutive odd positive integers is 74. Find the integers.

Answers

Let first odd number be x

Then that would be $x^2 + (x+2)^2=74$ . We need to solve for x.

$x^2 + (x+2)^2=74\n\ \nx^2 + x^2 + 4x+4 = 74\n\ \n2x^2 + 4x +4=74\n\ \n2x^2+4x-70 = 0\n\ \n2(x^2+2x-35)=0\n\ \n2(x+7)(x-5)=0\n\ \nx=-7\text{ or }5$

But we need positive integers so we would have $\boxed{x=5}$ , so then our integers would be x, x+2 = 5, 7

Check work:

5² + 7² = 25 + 49 = 74.

So our integers would be 5 and 7.

Hope this helps.

Let’s use a sample set.
Let’s use 5 and 7.
5•5=25
7•7=49
49+25=74
The integers are 5 and 7. The way I found this was by thinking of 9 and 11 at first. I knew that it would be entirely way too much, but 3 and 1 would be too little. 5 and 7 fit in the middle of those two samples.

Your answer is 5 and 7.

A total of 600 advertisements were sold for a certain magazine. If 30 percent of the first 200 sold were in color, 20 percent of the next 300 sold were in color, and 90 percent of the last 100 sold were in color, what percent of the 600 advertisements were in color?

Answers

Answer:

%35 of them were in color

Step-by-step explanation:

Since 30 percent of the first 200 sold were in color, 200x30/100 = 60 of them were in color.

Since 20 percent of the next 300 sold were in color, 300x20/100 = 60 of them were in color.

Since 90 percent of the last 100 sold were in color, 100x90/100 = 90 of them were in color.

In total, 60 + 60 + 90 = 210 out of 600 were in color.

The percentage is: $(600)/(100)$ = $(210)/(x)$ → x = $(21000)/(600)$ = 35

Final answer:

To find the percentage of advertisements that were sold in color, divide the number of color ads by the total number of ads and multiply by 100. We get answer 35.

Explanation:

To find the percentage of advertisements that were sold in color, we need to find the number of color advertisements in each group and then calculate the percentage.

For the first 200 ads, 30% were in color, so the number of color ads is 0.3 * 200 = 60.
For the next 300 ads, 20% were in color, so the number of color ads is 0.2 * 300 = 60.
For the last 100 ads, 90% were in color, so the number of color ads is 0.9 * 100 = 90.

The total number of color ads is 60 + 60 + 90 = 210. To find the percentage, we divide 210 by 600 and multiply by 100.

So, the percentage of advertisements that were in color is 35%.

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14 over 15 rounded to the nearest tenth

Answers

Answer:

0.9

Step-by-step explanation:

14/15 = 0.933333333 IF:

1. You first change it into a decimal by dividing the numerator by the denominator.

14 ÷ 15

2.You will get a recurring decimal.

0.933333333

3. The first digit after the decimal is in the position of the 'tenths'

0.9

4. You should use only two digits after the decimal to calculate

0.93

5. Since the number 3 is less than five, it will change into a zero and get eliminated.

∴ The answer will be = 0.9

Which fraction is closer to 1/2 than to 0 or 1

Answers

The fraction is closer to 1/2 than to 0 or 1 is 8/12.

What is Fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.
How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

First Fraction

2/12 = 1/6 = 0.1667

Second Fraction

3/12

= 0.25

Third Fraction

8/12

= 0.6667

Fourth Fraction

10/12

= 0.83333

So, Fraction closer to 1/2 or 0.5 is 8/12.

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In this situation I would convert the 1/2 into a fraction that has a common denominator. 1/2 will now be 6/12.

I think the best answer here is 8/12 because 6/12 is only two lines away from 8/12 where as everything else is either closer to 1 or 0.

I hope this helps. Good luck.

Which is true about the polynomial –8m3 + 11m?It is a trinomial with a degree of 3.
It is a trinomial with a degree of 3.

It is a trinomial with a degree of 2.
It is a trinomial with a degree of 2.

It is a binomial with a degree of 3.
It is a binomial with a degree of 3.

It is a binomial with a degree of 2.

Answers

The correct answer is: "It is a binomial with a degree of 3."

What is a polynomial?

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

The polynomial -8m³ + 11m is a binomial with a degree of 3.

A polynomial is an expression consisting of variables and coefficients, where the variables are raised to non-negative integer powers and the coefficients are constants.

The degree of a polynomial is the highest power of the variable in the polynomial.

In this case,

The polynomial has two terms, or it is a binomial.

The highest power of "m" in the polynomial is 3, which means that the degree of the polynomial is 3.

Therefore,

The correct answer is: "It is a binomial with a degree of 3."

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Answer:

Binomial with a degree of 3

Step-by-step explanation:

-8m^3 + 11m....notice that it has 2 terms....(-8m^3) and (11m). Having 2 terms makes it a binomial...if it would have had 3 terms, it would have been a trinomial. If it has only one variable, the degree is the highest exponent...so this has a degree of 3 since ^3 is the highest exponent.

so the answer is : binomial with a degree of 3

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