What is the equation of thr function y=6/x translated 5 units to the left and 4 units up

Answer:

1- The sum is: 2m + 2n + 7 = 2(m+n) + 7

2- The difference is: 3m - 2

3- The difference is: -2m - 2n + 2 = -2(m+n-1)

Explanation:

Before we begin, remember the following:

+ve * +ve = +ve

-ve * -ve = -ve

+ve * -ve = -ve

-ve * +ve = -ve

Also, remember that, we only add/subtract like terms. There are terms which have the same variable(s) raised to the same degree

Now, let's check the problems:

Problem 1:

Adding two polynomials:

(m + n + 3) + (m + n + 4)

We first start by getting rid of the brackets:

m + n + 3 + m + n + 4

Now, we add like terms:

2m + 2n + 7

As an additional step, we can take 2 as a common factor from the first two terms:

2(m+n) + 7

Problem 2:

Subtracting two polynomials:

(10m - 6) - (7m - 4)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

10m - 6 - 7m + 4

Now, we add/subtract like terms:

3m - 2

Problem 3:

Subtracting two polynomials:

(4m - 5) - (6m - 7 + 2n)

We first start by getting rid of the brackets. Take care of the different signs while doing so:

4m - 5 - 6m + 7 - 2n

Now, we add/subtract like terms:

-2m - 2n + 2

As an additional step, we can take -2 as a common factor from the above expression:

-2(m+n-1)

Hope this helps :)

Answer:

Guy above is correct

Step-by-step explanation:

Answer:

2x+y=20 and -5y=6x+12 are your equations.

You can turn 2x+y=20 into y=-2x+20

Substitute this value of y into the other equation.

-5(-2x+20)=-6x+12

10x-100=-6x+12

16x=112

x=7

Substitute this value of x into the other equation.

2(7)+y=20

y=6

Your answer is x=7 and y=6.

The range of f(x) = (4/5)^x is {y| y > 0}, and the range of g(x) = (4/5)^x + 6 is {y| y > 6}.

The range of a function refers to the set of all possible output values of the function. To determine the range of f(x) = (4/5)^x, we need to consider that any positive real number raised to any power will yield a positive result. Therefore, the range of f(x) is {y | y > 0}.

For g(x) = (4/5)^x + 6, we can see that adding a constant term of 6 to the function will shift the entire graph upwards by 6 units. Consequently, the range of g(x) is {y | y > 6}.

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The solution is: a can of tomatoes for 53 cents, is the best buy available.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Here, we have,

So, we have two options:

option 1: a can of tomatoes for 53 cents.

option 2: a can of tomatoes for 70 cents with a 20% discount.

First we have to determine the price of the 2nd option.

10 % of 70 cents is 7 cents

20 % of 70 cents is 14 cents.

So, we have 14 cents of discount, which makes the new price (70-14=) 56 cents.

Now our two options are either 53 or 56 cents.

Therefore option 1 is the best buy available.

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Answer:

9.25%

Step-by-step explanation:

We have the price book of $40 but karen pais $43.70 then the $3.70 extra that she paid it's the value of taxes. Then to know the tax rate we have to do the next procediment:

[tex]$40\longrightarrow 100\%[\text]

[tex]$3.70\longrightarrow x\%[/tex]

Where x is the tax rate, then:

[tex]x=\dfrac{\$3.70\cdot 100\%}{\$40}[/tex]

[tex]x=\dfrac{370\%}{40}=9.25\%[/tex]

Answer:

Hence, the sum of the geometric series is:

                                      259

Step-by-step explanation:

We are given a geometric series as:

[tex]\sum_{i=1}^4 6^{i-1}[/tex]

i.e. we are asked to fnd the sum of first four terms of the geometric series with first term as 1

Since, the series is:

[tex]6^0+6^1+6^2+6^3[/tex]

Also, the common ratio of the series is: r=6

Since, each of the term of the series is 6 times it's preceding term.

Also we know that sum of a finite geometric series with n-terms and common ratio r is calculated by the formula:

[tex]S_n=a(\dfrac{r^n-1}{r-1})[/tex]

Here we have: a=1 and r=6 and n=4

Hence,

[tex]S_4=1(\dfrac{6^4-1}{6-1})\\\\\\S_4=\dfrac{1295}{5}\\\\\\S_4=259[/tex]

                        Hence, the sum of the series is:

                                     259

Answer:

1. Two planes intersect to ALWAYS form a line. If two planes intersect, they intersect in a line. The two planes that do not intersect, they form parallel lines.

2. The true statement is :

All quadrilaterals are polygons with four sides. A quadrilateral is a geometrical shape that has four sides and four angles. These are also called polygons. There are many types of quadrilaterals like - the parallelogram, the rectangle, the square, rhombus etc.

Answer:

its b!

Step-by-step explanation:

discount is $8 = 40/100 to find that discout

is $3.20

sale price : $8.00 - $3.20 which is $4.80!

Your welcome! :D

The area of the sector rounded to the nearest hundredth is  [tex]$37.02 \, \text{mm}^2$[/tex].

To find the area of a sector, we use the formula:

[tex]\[ \text{Area of sector} = \frac{\text{Central angle}}{2\pi} \times \pi r^2 \][/tex]

Given that the central angle is [tex]\( \frac{2\pi}{9} \)[/tex] radians and the diameter (which is twice the radius) is [tex]$20.6 \, \text{mm}$[/tex], the radius is [tex]\( \frac{20.6 \, \text{mm}}{2} = 10.3 \, \text{mm} \)[/tex].

Now, substituting these values into the formula:

[tex]\[ \text{Area of sector} = \frac{\frac{2\pi}{9}}{2\pi} \times \pi (10.3)^2 \][/tex]

[tex]\[ = \frac{1}{9} \times \pi \times 10.3^2 \][/tex]

[tex]\[ = \frac{1}{9} \times 3.14 \times 106.09 \][/tex]

[tex]\[ = \frac{1}{9} \times 333.2086 \][/tex]

[tex]\[ \approx 37.02 \, \text{mm}^2 \][/tex]

Rounded to the nearest hundredth, the area of the sector is approximately [tex]$37.02 \, \text{mm}^2$[/tex].

The sequence in this scenario is arithmetic, with the patient increasing their distance walked by 3 km each week. Using the formula for the nth term of an arithmetic sequence, the patient will walk a distance of 32 km during the 10th week.

The sequence in this case is arithmetic. This can be determined by observing that the difference between the distances walked each week is consistent. In this case, the difference is 3 km, as the patient increases their distance by 3 km each week.

To find out how far the patient will walk during the 10th week, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n-1)d

Where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.

Given that the first term is 5 km, the common difference is 3 km, and we want to find the 10th term, we can substitute the values into the formula:

a10 = 5 + (10-1)3

a10 = 5 + 9 * 3

a10 = 5 + 27

a10 = 32

Therefore, the patient will walk a distance of 32 km during the 10th week.