Find the least number should 2028 be multiplied so that the product is a perfect
square?

The results of the division of polynomials are given as follows:

Considering that x² - 9 is the subtraction of perfect squares, we have that:

x² - 9 = (x - 3)(x + 3)

Hence the division is:

h(x) = (x - 3)(x + 3)/(x - 3) = x + 3.

Considering that x² - 16 is the subtraction of perfect squares, we have that:

x² - 16 = (x - 4)(x + 4)

Hence the division is:

h(x) = (x - 4)(x + 4)/(x - 4) = x + 4.

Considering that the roots of x² - 4x + 3 are x = 1 and x = 3, we have that:

x² - 4x + 3 = (x - 1)(x - 3).

Hence the division is:

h(x) = (x - 1)(x - 3)/(x - 3) = x - 1.

Considering that the roots of x² + 4x - 5 are x = -5 and x = 1, we have that:

x² + 4x - 3 = (x + 5)(x - 1).

Hence the division is:

h(x) = (x + 5)(x - 1)/(x - 1) = x + 5.

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Answer:

I = (PTR)/100

1450=(5000*1*R)/100

1450*100=5000R

145000/50000=R

29=R

Step-by-step explanation:

We know,

[tex] S.I. = \rm\cfrac{P*R*T}{100}[/tex]

Given,

Principal P = 5000

Rate R = R(Assume)

Time T = 1

Interest = 1450

Plug:

[tex]1450 = \frac{5000 \times r \times 1}{100} [/tex]

Solve:

[tex]1450 \times 100 = 5000 \times r[/tex]

[tex]145000 \div 5000 = r[/tex]

[tex]r \: = \: 29 \%[/tex]

Rate = 29

Therefore,the rate of Interest is 29%.

=======================================================

Explanation:

Replace x with 4 and y with 5.

Then use the order of operations (PEMDAS) to simplify until you get a single number.

Something like 9x means "9 times x", and a similar situation happens with the 8y term as well.

---------

Here's what the steps look like:

9x + 8y

9*4 + 8*5

36 + 40

76

Therefore, 9x+8y = 76 when x = 4 and y = 5.

The point (4,5) is located on the line 9x+8y = 76

Answer:

6/25.

Step-by-step explanation:

They are 19, 29, 59, 79, 89 and 97.

A total of 6.

So the required fraction is 6/25.

The equation for function g is given by using translational ideas:

g(x) = 7x/3 + 1.

According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or stretching vertically or horizontally, and reflecting over the x- or y-axis.

Given that f(x) exists, obtaining f is equal to compressing horizontally by a factor of a. (ax).

The function in this issue is as follows:

f(x) = 7x + 1.

We have the following for a horizontal compression of 1/3:

g(x) = f(1/3x) = 7x/3 + 1.

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The volume of helium inside the balloon decreased at a rate of 0.1 cubic feet per minute. The linear equation that represents the given data is y = -0.1x + 6 and its slope m = -0.1.

The equation of the line passing through the points (x1, y1) and (x2, y2) is

(y - y1) = m(x - x1).

Where m is the slope of the line and is calculated by

m = (y2 - y1)/(x2 - x1)

The given data in the table represents the volume of helium (cu ft), inside a balloon relative to the elapsed time in minutes.

x: 5, 10, 15, 20, 25, 30, 35, 40

y: 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2

From this table, consider two points (5, 5.5) and (10, 5)

So, the equation of the line is

y- y1 = m(x - x1)

Where slope m = (y2 - y1)/(x2 - x1)

⇒ m = (5 - 5.5)/(10 - 5)

⇒ m = -0.5/5

∴ m = -0.1

Thus, the equation is

y - 5.5 = -0.1(x - 5)

⇒ y - 5.5 = -0.1x + 0.5

⇒ y = -0.1x + 0.5 + 5.5

⇒ y = -0.1x + 6.0

∴ y = -0.1x + 6

Since the slope of the line is negative, the volume of the helium inside the balloon decreased at a rate of 0.1 cubic ft per minute.

So, option 2 is correct.

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The desired minimum revenue is $130.

What is revenue?

Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.

Let us assume,

charge = b

customer= c

revenue= r

We know that,

r= bc

⇒ [tex]r=16\times 10[/tex]

⇒ [tex]r=\ 160[/tex]

Also,

[tex]b+1[/tex] ⇒ [tex]c-2[/tex]

with a target of [tex]r \geq 130[/tex]

Therefore,

[tex]b=10+x[/tex] ⇒ [tex]c=16-2x[/tex]

[tex](10+x)(16-2x)\geq 130\\160-20x+16x-2x^2 \geq 130\\-2x^2 -4x+30\geq 0\\x^2+2x-15\leq 0\\(x+1)^2 \leq 4^2\\x+1 \leq 4[/tex]

as negative value is not considered.

[tex]x\leq 3[/tex]

We get the result that [tex]\[/tex]3 is the maximum increase amount.

Therefore, revenue will be:

[tex](10+3)(16-3\times2)=13\times 10\\[/tex]

revenue = [tex]\[/tex]130

Full Question: Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.

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Answer:

The desired minimum revenue is $130.

What is revenue?

Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.

Step-by-step explanation:

Worked out for me :)

Using a calculator, the critical value for the t-distribution with a confidence level of 99% and 49 df is of Tc = 2.4049.

It is found using a calculator, with two inputs, which are given by:

In this problem, the inputs are given as follows:

Hence, using a calculator, the critical value for the t-distribution with a confidence level of 99% and 49 df is of Tc = 2.4049.

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The match of solutions with the exponential expressions is

1) [tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}=2[/tex]

2) [tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)=1/2[/tex]

3) [tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} =2[/tex]

4) [tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}=1[/tex]

The base will be multiplied by itself a certain number of times, as indicated by the exponent (also known as a power or degree).

Formulae for solving exponents are referred to as exponents formulas. The exponent of a number is written as [tex]x^{n}[/tex], which means that x has been multiplied by itself n times.

[tex]x^{n}(x^{m})=x^{n+m} \\\frac{x^{n} }{x^{m} }=x^{n-m} \\(x^{n} )^{m} =x^{nm} \\((x)(y))^{n}=x^{n}(y^{n} \\x^{0}=1[/tex]

1) the solution of the first expression will be

[tex]\frac{(2(3^{-2}) )^{3} (5(3^{2}) )^{2} }{(3^{-2})((5)(2))^{2}}[/tex]

[tex](2^3) (3^{-6} ) (5^2) (3^4) / (3^{-2}) (10^2)= (2.2^2.5^2) (3^{-6}.3^4) / (3{^-2}) (10^2)= (2)(10^2) (3^{-2}) / (3^{-2}) (10^2)\\=2[/tex]

2)The solution of the second expression will be

[tex](3^3) (4^0)^2 (3(2))^{-3} (2^2)[/tex]

Any  number with power zero is 1.

So,

[tex](3^3) (1^2) (3^{-3}) (2^{-3}) (2^2)= (2^{(-3+2)})=2^-1\\= 1/2[/tex]

3) The solution of third expression will be

[tex]\frac{(3^74^7) (2(5))^{-3} (5)^2}{(12^7) (5^{-1}) (2^{-4})} \\= \frac{(12^7) (2^{-3}) (5^{-3}) (5^2)}{(12^7) (5^{-1}) (2^{-4})} =\frac{(2^-3) (5^{(-3+2)})}{(5^{-1}) (2^{-4})} = \frac{(2^{-3}) (5^{-1})}{(5^{-1}) (2^{-}4)} = \frac{1}{(2^{-1})} = 2[/tex]

4) The solution to the forth expression will be

[tex]\frac{(2(3))^{-1} (2^0)}{(2(3))^{-1}}\\=2^{0}\\ =1[/tex]

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Answer:

The person above litteraly gave you the answer just reread the first equations and then you will figure it out

Step-by-step explanation:

The number has over positive integer divisors. One of them is chosen at random. If each divisor has the same probability, then the likelihood that a random one will be odd is precisely 1/19. This assumes that all divisors have the same probability. This is further explained below.

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, The number may be divided into more than positive integers. A selection is made at random from among them. If each divisor has the same probability, then the chance that a random one would be odd is exactly 1/19. This assumes that each divisor has the same probability. This makes the assumption that the probability of each divisor is the same.

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Answer:

No,

Step-by-step explanation:

X^-2 is equal to 1/X^2. so any number or letter to negative power, is the same as 1 divided by that number or letter to the positive power..(power remains with denominator

Answer is Healthclub A costs $33 less in monthly fees than Healthclub B

The number next to the “x” is your rate.

So Healthclub A charges $33 less than B

A charges 27 monthly fee

B charges 60 monthly fee

60-27=33

Considering the definition of an inequality, the number of people who can go to the amusement park is 3.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is

$9.75 + $16.25×p ≤$65

Solving:

$16.25×p ≤$65 - $9.75

$16.25×p ≤$55.25

p ≤$55.25÷ $16.25

p≤ 3.4

Finally, the number of people who can go to the amusement park is 3.

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Answer:

it helps you control your spending, track your expenses, and save more money.

Answer:

x = -1, x = -2 , x= 2

Step-by-step explanation:

First we factorise this cubic function :

(x+1)(x+2)(x-2) = 0

Using the law a×b×0 = 0

We know that to find the zeros we have to set each bracket equal to 0 :

x+1 = 0    OR   x+2 = 0    OR   x-2 = 0  

x = -1                x = -2               x = 2

Hope this helped and have a good day

Using linear functions, it is found that both people are paid the same.

A linear function is modeled by:

y = mx + b

In which:

For Bob, we have that that the intercept is of 30000, with a slope of $600, hence his salary after x years is given by:

B(x) = 30,000 + 600x.

For Sue, we have that that the intercept is of 2 x 15000 = 30000, which is the fixed yearly salary with a slope of 2 x 300 = $600, hence her salary after x years is given by:

S(x) = 30,000 + 600x.

The salaries are equal, that is, both people are paid the same.

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Using the z-distribution, the estimate for how much the drug will lower a typical patient's systolic blood pressure is:

[tex]46.6 \leq \mu \leq 48[/tex]

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

In this problem, we have a 80% confidence level, hence[tex]\alpha = 0.8[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.8}{2} = 0.9[/tex], so the critical value is z = 1.28.

The other parameters are given by:

[tex]\overline{x} = 47.3, \sigma = 15.9, n = 878[/tex]

Then the bounds of the interval are:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 47.3 - 1.28\frac{15.9}{\sqrt{878}} = 46.6[/tex]

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 47.3 + 1.28\frac{15.9}{\sqrt{878}} = 48[/tex]

Hence the interval is:

[tex]46.6 \leq \mu \leq 48[/tex]

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[tex](x-1) ^ { 3 } -(x-2) ^ { 2 } =1[/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x-2\right)^{2}=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-\left(x^{2}-4x+4\right)=1 [/tex]

[tex]x^{3}-3x^{2}+3x-1-x^{2}+4x-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-1-4=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5=1 [/tex]

[tex]x^{3}-4x^{2}+7x-5-1=0 [/tex]

[tex]x^{3}-4x^{2}+7x-6=0 [/tex]

[tex]±6,±3,±2,±1 [/tex]

Slope can be found from two points using the equation [tex]\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex].

Take any two points to substitute in. In this example, I'll use the first two points, (-4, 15), and (-2, 9). Put these into the equation and you'll get

[tex]\frac{(9-15)}{(-2-(-4))}[/tex]. Simplify further to get [tex]\frac{-6}{2}[/tex]. Divide this and you'll get the slope, -3!

hope this helps!

Integrate both sides.

[tex]\displaystyle \int \frac{ds}{dt} \, dt = \int 36t (9t^2 - 7)^3 \, dt[/tex]

On the right side, substitute [tex]u=9t^2-7[/tex] and [tex]du=18t\,dt[/tex], so that

[tex]\displaystyle \int 36t (9t^2 - 7)^3 \, dt = 2 \int u^3 \, du = \frac12 u^4 + C = \frac12 (9t^2 - 7)^4 + C[/tex]

Use the initial value to solve for [tex]C[/tex].

[tex]s(1) = 1 \implies 1 = \dfrac12 (9 - 7)^4 + C \implies 1 = 8 + C \implies C=-7[/tex]

Then the particular solution is

[tex]s(t) = \boxed{\dfrac12 (9t^2 - 7)^4 - 7}[/tex]

Using Chebyshev's Theorem, we are guaranteed to find at least 75% of the people earning hourly wages between $4.15 and $23.23.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

In this problem, we want the values within 2 standard deviations of the mean, hence the values are:

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Answer:

blank = inheritance

Step-by-step explanation:

Hope that helps

Answer: 254,34 mm².

Step-by-step explanation:

[tex]S{circle}=\pi R^2\\S{circle}=3,14*9^2\\S{circle}=3,14*81\\S{circle}=254,34\ mm^2.[/tex]

Hi :)

Let's first find the area of this circle

For finding the area of a circle we use

[tex]\longrightarrow\sf{A_{\circ}=\pi r^2}[/tex], where only r (radius) is squared

[tex]\textit{We know that :}\begin{cases} \sf{Radius = 9 mm} \\ \sf{\pi =3.14} \end{cases}}[/tex]

Thus

[tex]\longrightarrow\sf{A_{\circ}=3.14\cdot9^2}[/tex]

[tex]\longrightarrow\sf{A_{\circ}=3.14\times81}[/tex]

[tex]\longrightarrow\sf{\underline{A_{\circ}=254.34\: mm}}[/tex]

[tex]\tt{Learn\:More;Work\;Harder}[/tex]

:)

Answer:

3

Step-by-step explanation:

[tex]6=2 \times 3 \\ \\ 12=3 \times 2^2 \\ \\ 21=3 \times 7[/tex]

Step-by-step explanation:

I understand this that we need to find a point B for each of a) to f).

remember, the slope is the (y coordinate difference / x coordinate difference) when going from one point on the line to the other.

a)

the slope 2/3 means that when going to B x has to increase by 3, and y has to increase by 2.

so, B = (-2 + 3, 5 + 2) = (1, 7)

b)

-2/3 means that either x or y have to decrease and the other to increase.

e.g. x increases by 3, y decreases by 2.

so, B = (-2 + 3, 5 - 2) = (1, 3)

c)

4 stands for 4/1.

so, x increases by 1, y increases by 4.

B = (-2 + 1, 5 + 4) = (-1, 9)

d)

similar to c) -3 stands for -3/1.

and similar to b) either x or y has to decrease and the other to increase.

e.g. x increases by 1, y decreases by 3.

B = (-2 + 1, 5 - 3) = (-1, 2)

e)

that means the y difference is 0. B has the same y coordinate.

e.g. B = (3, 5)

x can be any value.

the line is a horizontal line going through y = 5 or (0, 5) on the y-axis.

f)

that means the x difference is 0. B has the same x coordinate.

e.g. B = (-2, 9)

y can be any value.

the line is a vertical line going through x = -2 or (-2, 0) on the x-axis.

This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

According to the statement

we have given that the one statement and we have to tell that the those statement is true or false after analyzing it.

So,

In C++ 11 is  a programming language which is used to write the coding. And in this language you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

Because in the coding it is not possible that the you can make loop without declare the random variable in the loop.

Due to this reasons without declare the variable it is not possible.

So, This statement is true that the In c 11 you cannot use a range-based for loop to modify the contents of an array unless you declare the range variable as a reference variable.

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Answer:

(-1,1)

Step-by-step explanation:

look where the two equations intercept that is usually the answer