Sam can rent a canoe for $3 an hour. if he rents the canoe , he would also have to pay $15 for a non-refundable deposit. he has $30 to spend on canoeing. write an equationto find out how many hours sam can canoe?

we have

[tex]y=16x^{2} +1[/tex]

Step 1

exchange variables x for y and y for x

[tex]x=16y^{2} +1[/tex]

Step 2

Isolate the variable y

Subtract [tex]1[/tex] both sides

[tex]x-1=16y^{2}+1-1[/tex]

[tex]16y^{2}=x-1[/tex]

Divide by [tex]16[/tex] both sides

[tex]16y^{2}/16=(x-1)/16[/tex]

[tex]y^{2}=\frac{x-1}{16}[/tex]

Square root both sides

[tex]y=(+/-)\sqrt{\frac{x-1}{16}}[/tex]

[tex]y=(+/-)\frac{\sqrt{x-1}}{4}[/tex]

Step 3

Let

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

[tex]f(x)^{-1}=(+/-)\frac{\sqrt{x-1}}{4}[/tex]

therefore

the answer is

The inverse is equal to

[tex]f(x)^{-1}=(+/-)\frac{\sqrt{x-1}}{4}[/tex]

The inverse of the function is y = \sqrt{x+1/16}

Given the expression

y = 16x² + 1

We see to find the inverse of the function

Replace y with x to have;

x = 16y² - 1

Make y the subject of the formula

16y² = x + 1

Divide both sides by 16

16y²/16 = x+1/16

y² = x+1/16

Take the square root of both sides

y = \sqrt{x+1/16}

Hence the inverse of the function is y = \sqrt{x+1/16}

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By substituting the values x=2 and y=4 into the given equation, we get a result of 70 which does not match with any of the provided options.

The value of the expression 4x + y-2y−x when x = 2 and y = 4 can be determined by substituting these values into the expression. By doing so, we get:

4 * 2 + 4^2 * 4 - 2 = 8 + 64 - 2 = 70

So, the correct value is 70, which is not present in the provided options (a. 2 b. 3 c.4 d.6). Maybe there is a misunderstanding or typo in the question or options. The way it's presented right now, the correct answer would be none of the above.

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Let us say that x is the real height of the original hut, therefore we can establish the equation:

5 : x = 1.5 : 8

5 / x = 1.5 / 8

Solving for x:

x = 5 * 8 / 1.5

x = 40 / 1.5

x = 26.67 ft

An infinite number of line segments can have the midpoint (2, -3) in the coordinate plane, because you can have infinite pairs of points such that their midpoint is (2, -3).

In the coordinate plane, an infinite number of line segments can have the midpoint (2, -3). The reasoning behind this is that a midpoint is the point that is equidistant from the end points of a line segment. You can have infinite pairs of points in a coordinate plane such that their midpoint is (2, -3). For instance, the points (4, -1) and (0, -5) have the midpoint (2, -3), and so do the points (2, 7) and (2, -13). This can similarly be done for an infinite number of other sets of points.

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The answer is that there are infinitely many line segments that have the midpoint (2, -3).

A midpoint of a line segment is the point that divides the segment into two equal parts.

Let's consider a Cartesian coordinate system where the midpoint is given as (2, -3).

Any line segment with the midpoint (2, -3) would have a segment bisecting it.

So, it's not just one line segment that has this midpoint, but an infinite number of line segments.

To explain this, consider any line segment in the coordinate plane.

The midpoint of AB will always be (2, -3) if the segment is positioned such that it's equally distant from (2, -3).

We can slide and rotate this line segment around the midpoint (2, -3) while keeping it the same length, and the midpoint will always remain (2, -3).

So, the answer is that there are infinitely many line segments that have the midpoint (2, -3).

There are 20 twentieths in five halves. This conversion is achieved by first converting halves to tenths (5 halves = 10 tenths) and then further converting tenths to twentieths by doubling the numerator, resulting in 20 twentieths in total.

To determine how many twentieths are in five halves, we need to convert both fractions to a common denominator. Since twentieths have a denominator of 20 and halves have a denominator of 2, we can make them compatible by expressing halves as tenths (which have a denominator of 10) and then further converting them to twentieths.

First, we can rewrite five halves as ten tenths (5/2 = 10/10). Now, we need to express tenths as twentieths, which is done by doubling the numerator. So, 10 tenths are equivalent to 20 twentieths.

Therefore, there are 20 twentieths in five halves.

In summary, when converting from halves to twentieths, we first turn halves into tenths by multiplying by 10, and then we further convert tenths to twentieths by doubling the numerator. Thus, five halves equal 20 twentieths.]

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The question does not provide enough specifics to calculate the area of the rectangle. Generally, you find a rectangle's area by multiplying its length by its width.

Unfortunately, the question seems to have provided the potential answers for the area of the rectangle, but no specifics about the rectangle itself are given. Typically, you would find the area of a rectangle by multiplying the length by the width. For example, if a rectangle had a length of 10 units and a width of 7 units, you would calculate the area by multiplying together these two figures (10 units * 7 units), which equals 70 units².

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The correct mathematical expression for the elevator's movement of up 4, down 4, up 8, and down 2 floors is option c: (+4) + (-4) + (+8) + (-2).

The correct expression that matches the scenario where an elevator went up 4 floors, down 4 floors, up 8 floors, and then down 2 floors is (+4) + (-4) + (+8) + (-2). Let's break it down step by step:

By combining these, the expression becomes c= (+4) + (-4) + (+8) + (-2). This expression correctly reflects the elevator's movements up and down the floors.

There is about 1129 feet per second on the speed of sound in the stormy day.

Find the distance in feet:

1129 * 5 = 5645 ft

Change to miles: 1 mile is equal to 5280 foot

5645 / 5280 = 1 mile

Answer:

Step-by-step explanation:

from the graph, y=0 when x=3

so that eliminates:

g(x) = (x + 3)3

g(x) = x3 + 3

g(x) = x3 − 3

ans is g(x) = (x-3)^3

Answer:

g(x) = (x - 3)3

Step-by-step explanation:

Compare to the parent function of f(x) = x3, the displayed graph is shifted to the "left" by 3 units so it is a translation in the x-direction.

The answer is g(x) = (x - 3)3

original point is (7,13)

 with translation (4,-8)

 add 4 to 7 = 11

subtract 8 from 13 = 5

 new point = (11,5)

Answer:

5 offices had fewer than 5 desks

Step-by-step explanation:

Clearly from the scatter plot we could see that 5 offices have lesser than 5 desks.

The number of desks are represented by the horizontal axis and the number of computers are represented by the vertical axis.

so by looking at the scatter plot we could see that the five points are before 5 on the horizontal axis i.e. we have to count all those points such that the desk are less than 5 i.e. ( when the desks are 0,1,2,3 and 4).