MATHEMATICS HIGH SCHOOL

What is the square root for √84?
Simplified and the non simplifed one

Answers

Answer 1
Answer:

To simplify the square root, find the prime factorization of the number within the square root:

84 = 7 * 12

7 * 12 = 7 * 4 * 3

7 * 4 * 3 = 7 * 2 * 2 * 3

√(84) = √(2 * 2 * 3 * 7)

Take any number that is repeated twice within the prime factorization, and move it outside of the root:

√(2 * 2) = 2

√(2 * 2 * 3 * 7) = 2 √(3 * 7) = \boxed{2 √(21)}

The simplified form of √84 will be 2√21.

The non-simplified form is found by putting the term into the calculator:

√(84) = \boxed{9.166}

Rounded to the nearest thousandths place, the non-simplified form of √84 will be 9.166.
Answer 2
Answer:

•Simplified Square Root for √84 is 2√21
√4*21=√84.
Now extract and take out the square root √4 * √21. Root of √4=2 which results into 2√21

•Determine the square root.
The square root of eighty-four √84 = 9.16515138991

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Dennis is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party store, string is sold by the yard. If Dennis wants to get 69 balloons, how many yards of string will he need?

Answers

Answer:

207

Step-by-step explanation:

9ft=3yrds

3x69=207

One hundred is multiplied by a number between 0 and 1. the answer has to be ?

Answers

100 * 0.5 = 50
0.5 is between 0 and 1

Andrew has a new 3 ft wide bookcase with two shelves, each 15 in. in high. he plans to store his CD’s on the shelves, using new CD racks. Each CD rack is 17 in. wide and 7 in. high, and holds three stacks of 12 CDsWill Andrew have enough room for his 250 CD’s in the bookcase if he uses the two shelves inside the book case it doesn’t put any CDs on top of it? how many CDs will he be able to store?

Answers

Answer: He will not have enough room

Step-by-step explanation: To determine if Andrew has enough room for his 250 CDs on the two shelves inside the bookcase, we need to calculate how many CD racks can fit on each shelf and how many CDs each of these racks can hold.

The bookcase is 3 ft wide, which is equivalent to 36 inches. Each shelf is 15 inches high. Therefore, the available space for CD racks on each shelf is 36 inches in width and 15 inches in height.

Each CD rack is 17 inches wide and 7 inches high. To calculate how many racks can fit on each shelf, we can use the following formula:

Number of racks on a shelf = (Width of shelf) / (Width of CD rack)

Number of racks on a shelf = 36 inches / 17 inches ≈ 2.12 (round down to 2, as you can't have a fraction of a rack)

Now, let's calculate how many CDs each of these racks can hold. Each CD rack can hold three stacks of 12 CDs each, for a total of 3 x 12 = 36 CDs.

So, on each shelf, Andrew can fit 2 CD racks, and each rack can hold 36 CDs. Therefore, each shelf can store 2 x 36 = 72 CDs.

Since Andrew has two shelves, he can store a total of 2 x 72 = 144 CDs in the bookcase.

So, he will be able to store 144 CDs in the bookcase, which is less than his 250 CDs. Therefore, he won't have enough room for all his 250 CDs in the bookcase, and he will need additional storage for the remaining CDs.

Find the value for x and y

Answers

Answer: x=70, y=30

Step-by-step explanation:

Which of the following is the correct definition of a geometric sequence?

Answers

Geometric sequences use multiplication as the common ratio, whether you are dividing by a fraction or a rational number.  The key thing is that the ratio has to be the same throughout the whole sequence.  Therefore, that makes the last choice above the one you want.

What is the x-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = 2x + 6 and y = 3x + 4 intersect?Can you please explain with some details?

Answers

Answer:

The x-coordinate of the point in the standard (x,y) coordinate plane at which the 2 lines y = 2x + 6 and y = 3x + 4 intersect is:

                            x=2

Step-by-step explanation:

The point of intersection of the two lines is the point where the y-value of the two lines are equal.

Now, in order to find the x-coordinate of the point of intersection we equate the equation of two lines in terms of x and by some operation we obtain the value of x.

Here the equation of two lines are:

y = 2x + 6 and y = 3x + 4

Now, on equating the y-value we have:

  2x+6=3x+4

Now,

3x-2x=6-4

i.e.

x=2

Also, on putting the value of x in any of the two equation of lines we have:

y=10

Hence, the point of intersection is: (2,10)
You have to solve equation system:
\left \{ {{y=2x+6}|*(-1) \atop {y=3x+4}} \right. \n \left \{ {{-y=-2x-6} \atop {y=3x+4}} \right. \n 0=x-2\n x=2

Or you can also graph it. Look at enclose.
To graph it you have to draw two lines choosing two points for each one.
For example:
y=2x+6
so if x=0 y = 6
if x = 1 y = 8
You connect this points and you have y=2x+6 line. You do this the same with the second line. 
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