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3 years ago

Rewrite this radicand as two factors, one of which is a perfect square. √60

Mathematics

2 answers:

Sphinxa [80]3 years ago

5 0

Answer:

√4 * √15.

Step-by-step explanation:

√60

=√(4 * 15)

= √4 * √15

Morgarella [4.7K]3 years ago

5 0

Answer:

our answer is $\sqrt{4}*\sqrt{15}$ or in simplified form

as $2*\sqrt{15}$

Step-by-step explanation:

$\sqrt{60}$

We need to solve the above expression

Factors of 60:

1X60, 2X30, 3X20, 4X15, 5X12, 6X10

We need two factors one of which is perfect square

From the above factors only 4X15 full fills our condition as 4 is a perfect square

$\sqrt{60}\\ =\sqrt{4 * 15}\\ We\,\,know\,\, \sqrt{a*b}= \sqrt{a}*\sqrt{b}\\ =\sqrt{4}*\sqrt{15}\\$

Solving, we get

$2*\sqrt{15}$

So, our answer is $\sqrt{4}*\sqrt{15}$ or in simplified form

as $2*\sqrt{15}$

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Suppose that 10 people, including you and a friend, line up for a group picture. How many ways can the photographer rearrange th

slamgirl [31]

Answer:

483 840 ways

Step-by-step explanation:

Let you and your friend be A and B.

With three people always between you two,, we have

Case 1: AxxxBxxxxx

Case 2: xAxxxBxxxx

Case 3: xxAxxxBxxx

Case 4: xxxAxxxBxx

Case 5: xxxxAxxxBx

Case 6: xxxxxAxxxB

So there is 6 ways of arranging you two through the line and for each of the six cases,

If you two remained in your positions, the rest can be arranged in 8! ways

Also for each case, you two can interchange your positions in 2! ways

Therefore,

The photographer can rearranged the line keep three people between you an your friend in

8! * 2! * 6 = 483 840 ways

7 0

2 years ago

Use the drawing tool(s) to form the correct answer on the provided graph.

Kitty [74]

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

$y> \frac{1}{4}x+6$ ------>inequality A

The solution of the inequality A is the shaded area above the dashed line $y=\frac{1}{4}x+6$

The y-intercept of the dashed line is (0,6)

The x-intercept of the dashed line is (-24,0)

The slope of the dashed line is positive m=1/4

$y> 2x-1$ ------>inequality B

The solution of the inequality B is the shaded area above the dashed line $y=2x-1$

The y-intercept of the dashed line is (0,-1)

The x-intercept of the dashed line is (0.5,0)

The slope of the dashed line is positive m=2

The solution of the system of inequalities is the shaded area between the two dashed lines

using a graphing tool

see the attached figure

4 0

2 years ago

Can someone tell me if it’s correct?

mart [117]

Yes yes it is correct

8 0

3 years ago

Read 2 more answers

State which of the following sets of ordered pairs represent a function.

zalisa [80]

Answer:

Option (D) is correct.

Step-by-step explanation:

A function can be termed as a process from a set of x values to a set of possible y-values where each x-value relates to exactly one y-value.

In other words, a relation can only be a function there is no repetition of x-values. It means a relation can not have duplicated inputs.

Given the sets

Set A: (5,2), (4, 3), (3, 4), (2,5)

Set B: (-1,-6), (0, 2), (1, 2), (3, 6)

Set C: (2, 1), (4, 2), (2, 3), (8,4)

It is clear that sets A and B represent the function because, in these sets, each x-value relates to exactly one y-value. In other words, there are no duplicated inputs.

But, set C has duplicated inputs i.e. x = 2 is repeated twice, and a function can not have a repeated input.

Therefore, we conclude that set A and set B represent a function.

Thus, option (D) is correct.

7 0

3 years ago

Aidan has 20 ft of fence with which to build a rectangular dog run. What is the maximum area he can enclose? Enter your answer i

irina1246 [14]

<h2>Maximum area is 25 m²</h2>

Explanation:

Let L be the length and W be the width.

Aidan has 20 ft of fence with which to build a rectangular dog run.

Fencing = 2L + 2W = 20 ft

L + W = 10

W = 10 - L

We need to find what is the largest area that can be enclosed.

Area = Length x Width

A = LW

A = L x (10-L) = 10 L - L²

For maximum area differential is zero

So we have

dA = 0

10 - 2 L = 0

L = 5 m

W = 10 - 5 = 5 m

Area = 5 x 5 = 25 m²

Maximum area is 25 m²

7 0

3 years ago