Prime number definition
Answers
A prime number is a number that has no factors other than ' 1 ' and itself.
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Laura is the fund-raising manager for a local charity. She is ordering caps for an upcoming charity walk. The company that makes the caps charges $6 per cap plus a $25 shipping fee. Laura has a budget of $1,000. What is the greatest number of caps she can buy?
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Answer:
Hope it helps you............
Final answer:
To find the remaining area of the paperboard, calculate the area of the rectangle, subtract the area of the semicircle. The area of the rectangle is 336 square inches, and the area of the semicircle is 32π square inches. The remaining area is approximately 236.05 square inches.
Explanation:
To answer this question, we first need to calculate the area of the entire paperboard, and then calculate the area of the semi-circle that was cut out. We then subtract the area of the semi-circle from the area of the paperboard to get the remaining area.
The area of a rectangle is calculated by multiplying its length by its width. For the paperboard, we find the area by multiplying 21 inches (length) by 16 inches (width), which gives us 336 square inches.
Next, we have to calculate the area of the semi-circle that was cut out. Assuming the cut was made along the width of the paperboard, the diameter of the semi-circle would be 16 inches. The radius, therefore, is 8 inches. The area of a circle is given by the formula πr², where r is the radius. For a semi-circle, we simply take half of this. This gives us an area of half of π(8)² = 32π square inches.
So, to find the remaining area of the paperboard, we subtract the area of the semi-circle from the area of the rectangle: 336 square inches - 32π square inches = approximately 236.05 square inches.
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Answer:
The best option is;
A triangle with three equal sides all longer than 12 inches
Step-by-step explanation:
The cross sectional area of the square prism that passes through points A, B and C is found as follows;
Shape of cross section ABC = Triangle
Base, AB of the triangle is given by;
AB = √(8² + 8²) = √128 = 8·√2
Side, AC of the triangle is given by AC = √(8² + 12²) = 4√13
Therefore, the height of the triangle is given as follows;
Height, h = √(4·√13)²-(4·√2)² = 4·√11
The area of the cross section then is 0.5 × Base × Height
= 0.5 × 8·√2 × 4·√11 = 16·√22
A triangle with 3 equal sides of 8 inches has an area of 4×8×sin(60) = 16√3
A triangle with 2 equal sides of 12 inches and one side of 8 inches has an area of 4×12×sin(60) = 24√3
Therefore since 16·√22 > 24√3 > 16√3, the best option is a triangle with three equal sides of all longer than 12 inches.
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The answer is: 3(s + 9t).
A.) 6x^3+7x^2-x-5
B.) -6x^3+7x^2-x+1
C.) -x^3-x-5
D.) x^2-x+1
2.) f^2*f^4
A.) (2f)^8
B.) (2f)^6
C.) f^8
D.) f^6
Please explain how you got the last one.
I would appreciate it.
And i will thank you if its easy to understand
:)
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You can consider the subtraction similiar to a -1(-6x^3+3). The 1 is implied. So to distribute that negative, we multiply this out.
-6x^3+3 becomes 6x^3 - 3
Our problem is now: 7x^2-x-2 + 6x^3 - 3
Now we add together like items. Let's rearrange for our sanity.
+ 6x^3 + 7x^2 - x - 2 - 3
Simplify: 6x^3 + 7x^2 - x - 5
Unfortionately, outside of factoring or something along those lines, that's as simple as we can get it. So the answer is A.
Problem B: f^2*f^4
Math rules tell us when we multiply the same bases with exponents, we add the exponents together. But the base doesn't change.
4+2 = 6. So: f^6 (D)
That's the easy answer: Math rules say so.
To expand on that specific rule, consider x^2 * x^3. What at the root are these saying? Multiply 2 copies of X, and then multiply 3 copies of x.
We can rewrite this same equation as x*x * x*x*x.
Remember that since all of these are multiplication, there is no order of operations that needs to be followed.
If we were simplifying that version of the equation, we would write x ^ 5.
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Answer:
1,807.2
Step-by-step explanation:
Using the formula for hexagon.
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Answer:
you cant solve it, since we need and = sign and other numbers on that side,
but you can simplify it to (x^2+4x+4)
Step-by-step explanation:
x^3+6x^2+12x+8/x+2
=(x+2)(x+2)(x+2)/x+2
=x^2+4x+4, since you cancel out one of the numerators(x+2) with the denominator