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3 years ago

What is the greatest common factor of 44c^5, 22c^3 and 11c^4

Mathematics

1 answer:

Alexxandr [17]3 years ago

8 0

$\text{ GCF of } 44c^5, 22c^3 , 11c^4 \text{ is } 11c^3$

Solution:

Given that, we have to find the greatest common factor of $44c^5, 22c^3 , 11c^4$

The greatest number that is a factor of two (or more) other numbers.

When we find all the factors of two or more numbers, and some factors are the same ("common"), then the largest of those common factors is the Greatest Common Factor

$\underline{\text{ GCF of } 44c^5, 22c^3 , 11c^4 :}$

First find the GCF of numbers and then find the GCF of variables and then multiply them together

Step 1: GCF of 44, 22 and 11

The factors of 11 are: 1, 11

The factors of 22 are: 1, 2, 11, 22

The factors of 44 are: 1, 2, 4, 11, 22, 44

11 is the greatest factor that is common in above three list

Then the greatest common factor is 11

$\text{ Step 2: GCF of }c^5, c^3 , c^4$

$c^5 = c^3 \times c^2\\\\c^3 = c^2 \times c^1 \text{ or } c^3\\\\c^4 = c^3 \times c^1$

Thus the greatest common factor is $c^3$

Step 3: Multiply the GCF of 44, 22, 11 and GCF of $c^5, c^3 , c^4$

$\text{ GCF of } 44c^5, 22c^3 , 11c^4 = 11 \times c^3 = 11c^3$

Thus $\text{ GCF of } 44c^5, 22c^3 , 11c^4 \text{ is } 11c^3$

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3 years ago

The sum of three numbers is 85. The second is 7 more than the first. The third is 2 more than four times the second. Find the nu

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Let x=the first number
Then x+7=second number
And 4(x+7)+2=third number (2 more than 4 times the second)
Now we are told that:
x+(x+7)+(4(x+7)+2)=85 get rid of parentheses
x+x+7+4x+28+2=85 simplify
6x+37=85 subtract 37 from each side
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3 years ago

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How do you find the height of a triangle (to calculate area)?

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Answer:

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Height of the triangle = 10.392

And the area of the triangle is:

Area of the triangle = 31.176 units^2

Step-by-step explanation:

When you have two measurements of a triangle, as the case in the picture, you can find the third with the Pythagoras theorem, which is:

(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2

As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:

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Now, we can replace the values in the formula obtained:

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(adjacent leg)^2 = 12^2 - 6^2
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Now, as we just need the adjacent leg, we take the square root of both sides:

adjacent leg = $\sqrt{108}$
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Now, with these data, we can find the area of the triangle with the next formula:

Area of a triangle = (base * height) / 2
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