The number that is 10 more than 64 is 74. We find this by adding 10 to 64.
The question is asking for the number that is 10 more than 64. In mathematics, when we say 'more than', we are asking to add the numbers together. So, to find the number that is 10 more than 64, we simply add 10 to 64.
Here's how to do it:
So 64 + 10 = 74. Therefore, the number that is 10 more than 64 is 74.
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Some of the possible options of the questions are;
A)
B)
C)
D)
The difference of two perfect cubes has a binomial factor and a trinomial factor
The option that gives the long division problem that can be used to prove the difference of two perfect cubes is option D
D)
Reason:
The formula for factoring the difference of twoperfect cubes is presented as follows;
a³ - b³ = (a - b)·(a² + a·b + b²)
Given that a factor of the difference of two cubes is (a - b), and that we
have; (a³ + 0·a·b² + 0·a²·b - b³) = (a³ - b³), both of which are present in
option D, by long division of option D, we have;
By the above long division, we have;
= a² + a·b + b²
Which gives;
= (a³ + 0·a·b² + 0·a·b² - b³)/(a - b)
We get;
(a³ + 0·a·b² + 0·a·b² - b³)/(a - b) = a² + a·b + b²
(a - b)·(a² + a·b + b²) = (a³ + 0·a·b² + 0·a·b² - b³) = (a³ - b³)
(a - b)·(a² + a·b + b²) = (a³ - b³)
(a³ - b³) = (a - b)·(a² + a·b + b²)
Therefore;
The long division problem that can be used to prove the formula for
factoring the difference of two perfect cubes is
, which is option D
D)
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Answer:
The correct options, rearranged, are:
Options:
And the asnwer is the last option (D).
Explanation:
You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.
The difference of two perfect cubes may be represented by:
And it is, as a very well known special case:
Then, to prove, it you must divide the left side, , by the first factor of the right side,
Note that, to preserve the places of each term, you can write:
Then, you have:
By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:
That is the last option (D).
Answer: 9 boys remained in the choir.
Step-by-step explanation:
Let x be the number of of boys and y be the number of girls.
In a school choir, 1/2(half) of the members were girls.
i.e (1)
At the end of the year, 3 boys left the choir, and the ratio of boys to girls became 3:4.
Put y= x from (1), we get
Thus , the number of boys : x= 12
Boys remained in the choir = 12-3=9
Answer:
The coordinates (3,0), (-3,0), (0,3) ,and (0,-3) helps us to draw the graph of the circle. Below is the explanation
Step-by-step explanation:
Given:
The equation of a circle is .
To find:
Graph the given equation.
Let's find the center and radius by comparing the given equation with the standard form.
We can rewrite our equation as
Now, compare them
Center (h,k)=(0,0)
Radius r=3
Now, draw the graph of the circle by placing the center and radius.
So, the coordinates which are 3 units exactly from the center (0,0) help us to find the graph of the circle. So, (0,3), (0,-3), (3,0) ,and (-3,0) would help us to graph the circle.
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