Carl’s Cable Company charges $55 for monthly service plus $4 for each pay-per-view movie. Teleview Cable Company charges $110 per month with no fee for movies. For what number of movies is the cost of Carl’s Cable Company less than the cost of Teleview?

Answer:

Inverse function, [tex]f^{-1}=2^x[/tex]

Step-by-step explanation:

We are given a function [tex]f(x)=\log_2x[/tex]

We need to find the inverse of f(x)

Step 1: Set f(x)=y

[tex]y=\log_2x[/tex]

Step 2: Switch x and y

[tex]x=\log_2y[/tex]

Step 3: Solve for y (isolate y)

[tex]y=2^x[/tex]              [tex]\because \log_ab=x\Rightarrow b=a^x[/tex]

Inverse of function [tex]f(x)\rightarrow f^{-1}(x)=2^x[/tex]

The inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

The logarithmic expression is given as:

[tex]f(x) = \log_2(x)[/tex]

Replace f(x) with y

[tex]y = \log_2(x)[/tex]

Swap the positions of x and y

[tex]x = \log_2(y)[/tex]

Apply the change of base rule of logarithm

[tex]2^x = y[/tex]

Rewrite as:

[tex]y = 2^x[/tex]

Express y as an inverse function

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

Hence, the inverse of the logarithmic function is [tex]f^{-1}(x) = 2^x[/tex]

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To find the length of cable remaining on the spool, subtract the weight of the empty spool from the total weight, and then divide the result by the weight of cable per metre.

The question involves the process of subtracting, conversion and division. First, we need to subtract the weight of the empty spool from the total weight of the partly-used spool and the remaining cable to find the weight of the remaining cable alone. This means 1540 grams - 260 grams = 1280 grams. Then, we convert the weight of the remaining cable (which is in grams) to metres by dividing it by the weight of one metre of cable (which is 85 grams). So, 1280 grams ÷ 85 grams/metre = approximately 15 metres. Therefore, this is the quantity of cable that Ted has left on the spool.

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The width of the given rectangle is 33  inches.

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Let's say the width of the rectangle is W while the length is L.

Given that,

A rectangle has a width that is 3 more than twice the length.

So,

W = 2L + 3

And,

Perimeter = 2(L + W) = 96

L + W = 48

By substitution,

L + 2L + 3 = 48

3L = 45

L = 15

So,

W = 2(15) + 3 = 33

Hence "The width of the given rectangle is 33  inches".

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The value of the solution of expression is, r = 7

We have to give that,

An expression to simplify,

r + 15 = 4r - 6

Now, Simplify the expression by combining like terms as,

r + 15 = 4r - 6

Subtract r on both sides,

r + 15 - r = 4r - r - 6

15 = 3r - 6

Add 6 into both sides,

15 + 6 = 3r

21 = 3r

Divide 3 on both sides,

r = 21/3

r = 7

Therefore, the solution is, r = 7

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Answer:

3.50p>(or equal to) 140; p>(or equal to)40

Step-by-step explanation:

The diving and swimming lessons will occur on the same day after 15 days because 15 is the smallest common multiple of 3 and 5.

The question pertains to finding a common multiple of the numbers 3 and 5. These numbers represent the intervals at which you have swimming and diving lessons respectively. The first common multiple of 3 and 5, other than 1, is 15. Therefore, you will have both lessons on the same day again after 15 days.

This comes from the idea that a number's multiples are the set of numbers formed by multiplying that number by any of the whole numbers. So, the multiples of 3 are 3, 6, 9, 12, 15, 18, etc., while the multiples of 5 are 5, 10, 15, 20, etc. The number 15 is a multiple of both 3 and 5, therefore, it is a common multiple of 3 and 5.

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Answer:

11 bags

Step-by-step explanation:

Let x bags of fertilizer should be purchased.

The dimension of rectangular lawn is 410 feet by 65 feet.

The area of rectangle is given by

Area = length × width

Thus, the area of rectangular lawn is

Area = 410 × 65

Area = 26650

Now, one bag of fertilizer covers 2500 square feet of lawn.

Thus, we have

[tex]\frac{1}{2500}=\frac{x}{26650}\\\\2500x=26650\\\\\x=\frac{26650}{2500}\\\\x=10.66[/tex]

Hence, the required number of bags = 11.

Final answer:

To find (g x h)(5), calculate h(5) first, then substitute the result into g(x) and calculate. The equivalent expression is (5)^2 - 7.

Explanation:

To solve (g x h)(5), we need to find g(h(5)). Given h(x) = x - 7 and g(x) = x^2, we first find h(5) = 5 - 7 = -2. Then, we evaluate g(-2) = (-2)^2 = 4. So, (g x h)(5) = g(h(5)) = g(-2) = 4, which corresponds to the option (5)^2 - 7.

Final answer:

To find where the tangent line is horizontal on the curve y = 2x^3 + 3x^2 - 12x + 8, set its derivative to zero and solve for x, resulting in points (-2, 8) and (1, 1) where the tangent lines are horizontal.

Explanation:

To find the points on the curve y = 2x^3 + 3x^2 − 12x + 8 where the tangent line is horizontal, we look for where the derivative of the curve equals zero because horizontal tangent lines have a slope of zero. The derivative of the given function is y' = 6x^2 + 6x - 12. This derivative represents the slope of the tangent at any point on the curve.

Setting the derivative equal to zero gives us the quadratic equation 6x^2 + 6x - 12 = 0, which can be simplified to x^2 + x - 2 = 0. Factoring this quadratic equation, we get (x + 2)(x - 1) = 0, leading to two solutions for x: x = -2 and x = 1. Substituting these x-values back into the original equation gives us the y-coordinates and therefore the points on the curve where the tangent line is horizontal: (-2, 8) and (1, 1).

Answer:

The simplified product has a degree of 2.

The simplified product, in standard form has exactly 2 negative terms.

Step-by-step explanation:

[tex](b - 2c)(-3b + c)[/tex]

LEts multiply it using FOIL method

[tex]b* -3b= -3b^2[/tex]

[tex]b*c= bc[/tex]

[tex](-2c) * (-3b)= 6bc[/tex]

[tex](-2c) * c= -2c^2[/tex]

The product is [tex]-3b^2 +bc+6bc-2c^2[/tex]

[tex]-3b^2+7bc-2c^2[/tex]

The simplified product has a degree of 2.

It has two negative terms

Answer: The correct options are,

The simplified product has a degree of 2,

The simplified product, in standard form, has exactly 2 negative terms.

Step-by-step explanation:

Here, the given expression,

[tex](b-2c)(-3b+c)[/tex]

By distributive property,

[tex]=(b-2c)(-3b)+(b-2c)(c)[/tex]

Again by distributive property,

[tex]=b(-3b)-2c(-3b)+bc-2c(c)[/tex]

[tex]=-3b^2+6bc+bc-2c^2[/tex]

[tex]=-3b^2+7bc-2c^2[/tex]

Which is the simplified form of the given expression,

That having three terms in which two terms are negative and the degree ( The highest sum of the exponents of the variables) is 2,

Hence, the correct options are,

The simplified product has a degree of 2,

The simplified product, in standard form, has exactly 2 negative terms.

The number of different coloured crayons is 76.

Given that, Henry wants to see how many different coloured crayons are in the crayons box. There are 4 rows of 19 crayons.

We need to find how many different coloured crayons are there, assuming no duplicate colours.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of different coloured crayons be x.

Now, x=4×19

⇒x=76

Therefore, the number of different coloured crayons is 76.

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I am sure the answer is |10.5−(−6.1)| hope this helps and if correct give me the brainliest please

the correct answer is

|10.5-(6.1)|

I took the test

Answer:

[tex](4x+9)[/tex]

Step-by-step explanation:

we know that

The perimeter of triangle is equal to the sum of the three length sides

therefore

[tex]P=(x+4)+(x+8)+(2x-3)\\ \\P=(x+x+2x)+(4+8-3)\\ \\P=(4x+9)\ units[/tex]

Maria and her family drove 885 miles, and the first '8' in this number represents the hundreds place, meaning it has a value of 800 miles.

The student's question is related to place value in numbers. Maria and her family drove 885 miles on their summer vacation, and the query specifically asks about the value represented by the first digit '8' on the left side of this three-digit number. In this case, the digit '8' is in the hundreds place, which means it represents the hundreds component of the overall number. Therefore, the first '8' has a value of 800. This is because in the number 885, the first '8' represents 8 hundreds, the second '8' represents 8 tens (or eighty), and the '5' represents 5 ones.

Let us say that:

x = the time it take for the new pump to drain the pool alone

4x = the time it take for the older pump

And we are given that together they drain the pool in 4 hours, therefore:

1/x + 1/4x = ¼

Multiply everything by x:

1 + ¼ = ¼ x

1.25 = 0.25 x

x = 5 hours

So, 4x = 20 hours

Hence it take the older pump 20 hours draining alone.

Final answer:

The older pump would take 3.2 hours, or 3 hours and 12 minutes, to drain the pool on its own, since it takes 4 times as long as the newer pump which takes 48 minutes alone.

Explanation:

If an older pump takes 4 times as long to drain a pool as a newer pump, and together they take 4 hours to drain the pool, we can find out how long it would take for the older pump to drain the pool on its own by setting up an equation based on their rates of work.

Let's denote the time it takes for the newer pump to drain the pool alone as t hours. This means that the older pump would take 4t hours to do the job on its own.

Working together for one hour, they would collectively drain 1/t + 1/4t of the pool. Since they can drain the entire pool in 4 hours working together, we can write the equation:

1/t + 1/4t = 1/4

Now, solving for t:

4 + 1 = t

4t + t = 4t

5t = 4t

5t = 4

t = 4/5

So, the newer pump takes 4/5 of an hour (which is 48 minutes) to drain the pool alone. Then the older pump, taking 4 times as long, would take 4 * 4/5, which is 16/5 or 3.2 hours (which is 3 hours and 12 minutes) to drain the pool on its own.