Answer:
Step-by-step explanation:
When adding rational numbers, if the denominator is the same you simply keep the denominator (bottom of fraction) as it is and apply the operation given to the numerator ( top of fraction )
So we have
==> remove parenthesis and apply signs
==> simplify numerator by combining like terms
and we are done!
Note:
like terms are terms with the same variable and exponent
An example of like terms are 6x^7 and 3x^7 as they have x as a variable and a power of 7
The like terms being combined here were (6x² and 4x²) and (5 and -2)
Answer:
117.5 ft²
Step-by-step explanation:
To find the area of the shaded area, we can find the area of the square, then subtract the areas of the two semicircles.
First, we will find the area of the given square, by using the formula , multiplying the length and width. The dimensions of this square are 14×14.
14 · 14 = 196
The area of the square is 196 ft².
We can now find the area of the two congruent half-circles. Since they are identical, we can simply find the area of one circle if it was whole. To find the area of a circle, we'll use the formula . With some simple deduction, we can see that the diameter of the circle is 10 ft, so the radius would be 5 ft long. Plug our values into the formula.
A = 5²
We will use 3.14 for .
A = 78.5
The area of both the semicircles is 78.5 ft².
Now, we can subtract.
196 - 78.5 = 117.5
The area of the figure is 117.5 ft².
Good luck ^^
Answer:
12 unit cubes
Step-by-step explanation:
There are 4 unit cubes on each layer, and there are 3 layers as you can see. So 4 × 3 would equal 12.
Answer:
she jogged for 35 hours
Step-by-step explanation:
6×5 6+5=11 11+6=17 17+6=23 23+6=29 29+6=35
<em>Answer:</em>
<em>a is greater than 1, so a−1 is positive.</em>
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<em>The distance between a and 1 appears to be less than the distance between 1 and 0, so it looks like a is less than 2. Thus a−2 is negative.</em>
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<em>b is negative, so −b is positive.</em>
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<em>The distance between a and 0 appears to be less than the distance between b and 0, so it looks like |a| is less than |b|. Since b is negative and a is positive, a+b is negative.</em>
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<em>a−b = a+−b. Since b is negative, −b is positive. a is also positive. Thus, a−b is positive.</em>
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<em>Since |a| and |b| are both greater than 1, |ab| is also greater than 1 (this builds on the intuition students gained in fifth grade as in 5.NF.5). ab is negative since a is positive and b is negative. Thus, ab+1 is negative.</em>