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3 years ago

Identifying the equivalent expression

Mathematics

1 answer:

iragen [17]3 years ago

6 0

Answer:

$\large\boxed{\sqrt{x+3}=(x+3)^\frac{1}{2}}$

Step-by-step explanation:

$\text{Use}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\\sqrt{x+3}=\sqrt[2]{x+3}=(x+3)^\frac{1}{2}$

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We are planning a reception for our daughter. The hall that we are renting charges $55 clean up fee. In addition to the cleanup

elena55 [62]

Answer:

89 is the maximum number of guests that can be invited within budget .

Step-by-step explanation:

The cleaning charges = $55

Total budget available = $3350

Cost per guest = $37

Now, actual budget available for guest = Total budget - Cleaning Fee

= $3350 - $ 55 = $3,295

Now, cost per head =$ 37

So, number of guests (n) possible in the budget

⇒ n = (Total guest Budget)/ Cost per head

= $3,295 / $37 = $89.05

or, n = $89.05

So, 89 is the maximum number of guests that can be invited within budget .

8 0

3 years ago

The slope, m, of a linear equation can be found using the formula m = , where the x- and y-values come from two ordered pairs,

Westkost [7]

The formula is y=mx + b, or rearranged would be m= y/x -b/x.

7 0

3 years ago

Use technology to find the line of best fit for the following data.

likoan [24]

Given:

The data points are:

(1, 0), (2, 3), (3,1), (4,4), (5,5)

To find:

The equation of best fit line in the form of $y=mx+b$ and then find the value of b.

Solution:

The general form of best fit line is:

$y=mx+b$ ...(i)

Where, m is the slope of best fit line and b is the y-intercept of the line.

Using the graphing calculator, we get the equation for the best fit line and the equation is

$y=1.1x-0.7$ ...(ii)

On comparing (i) and (ii), we get

$b=-0.7$

Therefore, the value of b is equal to -0.7.

3 0

3 years ago

<img src="https://tex.z-dn.net/?f=2x%5E%7B2%7D%20-4x%20%2B2" id="TexFormula1" title="2x^{2} -4x +2" alt="2x^{2} -4x +2" align="a

Lostsunrise [7]

$2 {x}^{2} - 4x + 2 \\ \\ 2(x {}^{2} - 2x + 1 )\\ \\ 2(x - 1) {}^{2}$

7 0

3 years ago

Read 2 more answers

Two Social Security numbers (see Exercise 8.12) match zeros if a digit of one number is zero iff the corresponding digit of the

Roman55 [17]

Answer:

Proved

Step-by-step explanation:

From the given parameters, we have:

$n = 9$ i.e. the length of each security numbers

$r = 2$ i.e. 2 security numbers

Required

In 513 security numbers, 2 must have matching zeros

To do this, we make use of Pigeonhole principle.

First, we calculate the number of all security numbers not having matching zeros.

Each of the 9 digits can be selected in 2 ways.

2 ways implies that each digit is either 0 or not

So, total selection is:

$Total = 2^9$

$Total = 512$

Apply Pigeonhole principle

The principle states that: suppose there are n items in m containers, where $n>m$ , then there is at least one container that contains more than 1 item.

This means that if there are 512 security number without matching zeros, then there is 1 (i.e. 512 + 1) with matching zeros.

$512 + 1 = 513$

8 0

3 years ago