a new website didicated to helping users research their ancestry had 200 visitors in the first week. the marketing director beleives that without an advertising compaign, the site will gain 50 new users each week. how many total visitors will they have after 12 weeks?

Final answer:

To solve the system of equations using elimination, multiply one equation by a constant so that the coefficients of one variable will be the same in both equations. Then add or subtract the equations to eliminate that variable. Finally, solve for the remaining variable and substitute back to find the complete solution.

Explanation:

To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the two equations. In this case, we can eliminate the variable y by multiplying the first equation by 3 and the second equation by 4. This will give us:

15x + 12y = 36

12x - 12y = 72

Next, we can add the two equations together to eliminate y:

27x = 108

Dividing both sides by 27, we find that x = 4.

Substituting this value of x back into one of the original equations, we can solve for y:

5x + 4y = 12

5(4) + 4y = 12

20 + 4y = 12

Subtracting 20 from both sides, we get 4y = -8.

Dividing both sides by 4, we find that y = -2.

Therefore, the solution to the system of equations is x = 4 and y = -2.

The average speed in miles per hour is 39mi/hr

Speed is the ratio of distance with respect to time. The formula for calculating speed is expressed as:

Speed = Distance/Time

Given the following

Distance = 312 miles

Time = 8 hours

Substitute

Speed = 312/8

Speed = 39mi/hr

Hence the average speed in miles per hour is 39mi/hr

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Answer:

12(pi)

Step-by-step explanation:

Answer:

y>0

Step-by-step explanation:

To integrate 1 / sqrt(25 - 16x^2) dx, we use trigonometric substitution with x = (5/4)sinθ. After substitution, integration, and back-substitution, the result is arcsin(4x/5) + C, where C is the constant of integration.

The integral to solve is ∑ (1 / sqrt(25 - 16x^2)) dx, which resembles the inverse trigonometric function, specifically the arcsine function. To solve this integral, we can use a trigonometric substitution. Since the integral involves a square root of a difference of squares, we can substitute x with (5/4)sinθ, which simplifies the integral considerably.

After substitution, we can then use the derivative of sinθ, which is cosθ, in order to find the full differential dx to replace in our integral. The resulting integral in terms of θ can be integrated using standard techniques, yielding an arcsine function as the antiderivative. After integrating, we must then convert back from θ to x to express the solution to the original integral in the original variable.

The answer to the integral ∑ (1 / sqrt(25 - 16x^2)) dx is arcsin(4x/5) + C, where C is the constant of integration. The substitution step is crucial in solving this type of problem and is a commonly used method in calculus.

Answer:

The value of the car is 0.94 times the value of the car the previous year.

we need to factor the expression

[tex] x^{2} + 27x + 162 [/tex]

Equate to zero the expression

[tex] x^{2} + 27x + 162=0 [/tex]

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex] x^{2} + 27x =-162 [/tex]

Complete the square. Remember to balance the equation by adding the same constants to each side

[tex] x^{2} + 27x +182.25=-162+182.25 [/tex]

[tex] x^{2} + 27x +182.25=20.25 [/tex]

Rewrite as perfect squares

[tex] (x+13.5)^{2}=20.25 [/tex]

[tex] (x+13.5)=(+/-)4.5 [/tex]

[tex] x1=-13.5+4.5= -9 [/tex]

[tex] x2=-13.5-4.5= -18 [/tex]

Hence

[tex] x^{2} + 27x + 162 =(x+9)*(x+18) [/tex]

Remember that the area of the rectangle is equal to

[tex] A=L*W [/tex]

therefore

the answer is

the dimensions of the rectangular piece of cloth could be

[tex] L=(x+18)\ inches\\ W=(x+9)\ inches [/tex]

The person's body temperature will approach 98.6ºF as time lapses. Option A is correct.

A horizontal asymptote for a function is an imaginary line that is not part of the graph and lies along the x-axis of the graph either to the left or right.

The horizontal asymptote of the given function can be described as the nature of the function T(f) as t approaches infinity.

This is the point where the line y=0 which means that the person's body temperature will approach 0ºF above 98.6ºF as t goes to infinity.

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To find the inverse of a function, switch x and y and solve for y. The inverse of f(x) = (x-1)/5 is f^-1(x) = 5x + 1. Verify that f(f^-1(x)) = x and f^-1(f(x)) = x.

To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation y = (x-1)/5 for x. Let's do that:

Step 1: Replace y with x and x with y: x = (y-1)/5.

Step 2: Solve for y: Multiply both sides by 5: 5x = y - 1. Add 1 to both sides: 5x + 1 = y.

So, the inverse of f(x) = (x-1)/5 is f-1(x) = 5x + 1.

To verify that f(f-1(x)) = x, substitute f-1(x) into f(x) and simplify:

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

Similarly, to verify that f-1(f(x)) = x, substitute f(x) into f-1(x) and simplify:

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

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The number of hamburgers will be 348.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that On Saturday, a local hamburger shop sold a combined total of 464 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold.

The number of hamburgers will be calculated as below:-

Cheeseburgers= x

Hamburgers= 3x

3x+x=464

4x=464

x=116

Substitute the value of x in expression.

Hamburgers= 3x

Hamburgers= 3 x 116 = 348

Therefore, the number of hamburgers will be 348.

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The local hamburger shop sold 116 hamburgers on Saturday. We determined this by setting up an equation where the number of hamburgers (H) plus three times the hamburgers (3H) equaled the total sales of 464 burgers, and then solving for H.

The question asks us to solve a basic algebra problem involving hamburgers and cheeseburgers. Let's define the number of hamburgers sold as H. Since the number of cheeseburgers sold was three times the number of hamburgers sold, we can represent the number of cheeseburgers as 3H. The total number of burgers sold was 464. Now, we can write down the equation:

H + 3H = 464

This simplifies to:

4H = 464

Now, we divide both sides by 4 to find the value of H:

H = 464 / 4

H = 116

So, the local hamburger shop sold 116 hamburgers on Saturday.

Answer:

Yes. Ratios of miles to minutes for Samuel and Beverly are proportional

Step-by-step explanation:

Samuel's speed can be calculated as following:

[tex]28/32=0,875[/tex]

0,875 miles per minute.

On the other hand Beverly's speed can be calculated as following:

[tex]42/48=0,875[/tex]

0,875 miles per minute

If we convert the speed to mile per hour:

[tex]0,875*60=52,5[/tex]

It can be easily seen that both Samuel and Beverly drove at the same speed at 52,5 miles per hour.

Answer: [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.

Step-by-step explanation:

Given: The dimensions for the carpet is  15 ft. by 20 ft.

We know that area ( in square units ) of a rectangle is given by :-

[tex]Area=length\times width[/tex]

Therefore, area of the required carpet is given by :-

[tex]Area=20\times15=300\text{ square feet}[/tex]

We know that 1 feet =1/3 yard

Now,

[tex]300\text{ square feet}=300\times\frac{1}{3}\times\frac{1}{3}\\=\frac{100}{3} \text{square yards}=33\frac{1}{3}\text{ square yards}[/tex]

Hence, [tex]33\frac{1}{3}[/tex] square yards of carpet is needed.

Answer: a horizontal translation and a 180 rotation

Step-by-step explanation:

Answer:

B-  [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)=14.966[/tex]

Step-by-step explanation:

Given equation : square root of 56 − the square root of 14 + the square root of 126    or     [tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]

Solution of the equation :

[tex]\sqrt(56)-\sqrt(14)+\sqrt(126)[/tex]

= [tex]2\sqrt(14)-\sqrt(14)+3\sqrt(14)[/tex]

= [tex]\sqrt(14)(2-1+3)[/tex]

= [tex]4\sqrt(14)[/tex]

=14.966

Now,

Therefore, Option B is correct

Answer:

$77.72

Step-by-step explanation:

This is the total cost of the book with tax.

Answer:

d the answer is d

Final answer:

The mixed number of 158/4 simplified is 39 1/2. A proportion comparing the ratios 1/48 and w/16 is solved by cross-multiplication resulting in w = 1/3 as the solution.

Explanation:

To write 158/4 as a mixed number in simplest terms, we first divide 158 by 4. When we do this division, 4 goes into 158, 39 times completely, since 4 * 39 = 156, and we get a remainder of 2. Therefore, the mixed number form of 158/4 is 39 2/4. To simplify this fraction further, we divide the numerator and the denominator by their greatest common divisor, which in this case is 2. Simplifying 2/4 by dividing both the numerator and denominator by 2, we get 1/2. Hence, the mixed number in its simplest terms is 39 1/2.

To set up a proportion using the given ratios, we start with the ratio 1/48 and set it equal to w/16, which can be represented as:

1/48 = w/16

When solving for w, we cross-multiply to get:

1 * 16 = 48 * w

Which simplifies to:

16 = 48w

Finally, to find the value of w, we divide both sides of the equation by 48, which gives us w = 16/48. Simplifying by dividing both numerator and denominator by the greatest common divisor, 16, we get:

w = 1/3