A kayak rental company charges $25.00 to rent a kayak and $3.50 for each half hour it is used.

Which linear function best represents the total cost of renting a kayak for 4 hours?


r (t) = 3.50t + 25
r(4) = 39



r (t) = 25t +3.5
R(8) = 203.5



r(t) = 25t + 3.5
r(4) = 103.5



r(t) = 3.50t +25
r(8) = 53

Answer:

x∈ (11, +∞)

x∈ (-∞, 7)

Step-by-step explanation:

6|x-9|>12 :Split into possible cases

6(x-9)>12, x-9≥0 : solve the inequalities

x>11, x≥9

x<7, x<9 : find the intersections

x∈ (11, +∞)

x∈ (-∞, 7)

Answer:

-3

Step-by-step explanation:

-9+6

=6-9

=-3

Answer:

-3

Step-by-step explanation:

-9+6

- + = -

So this expression will be subtracted.

-9+6 = -3

The answer is negative because greater value has a negative sign....

Answer:

Isaac traveled 12.8 miles by taxi for $27.46.

Step-by-step explanation:

The formula required here is

$2.50 + ($1.95/mile)x = $27.46.

We need to solve this for x, the number of miles traveled:

Subtract $2.50 from both sides, obtaining:

($1.95/mile)x = $24.96

Now divide both sides by ($1.95/mile):

   $24.96

------------------ = 12.8 miles

($1.95/mile)

Isaac traveled 12.8 miles by taxi for $27.46.

Answer:

Answer:

B.

Step-by-step explanation:

If f(-x)=f(x), then f is even.

If f(-x)=-f(x), then f is odd.

To determine if f(x)=3x^4+5x^2+1 is even or odd plug in -x like so:

f(x)=3x^4+5x^2+1

f(-x)=3(-x)^4+5(-x)^2+1

f(-x)=3x^4+5x^2+1

f(-x)=f(x)

So f is even.

You should keep in mind the following:

(-x)^odd=-(x^odd)

(-x)^even=x^even

Examples:

(-x)^81=-(x^81) since 81 is odd

(-x)^10=x^10 since 10 is even

Anyways, the student is right and f(-x)=f(x).

Answer:

The student's claim is true, because for any input of x, f(x)=f(−x).

Step-by-step explanation:

If a student says that the function f(x)=3x^4+5x^2+1 is an even function, the student's statement true  because for any input of x, f(x)=f(−x).

f(-x)=f(x) is even.

f(-x)=-f(x) is odd

Answer:

The angles do not have the same reference angle.  

Step-by-step explanation:

We can answer this question by referring to the unit circle.

The reference angle of 5π/6 is π/6, and the reference angle of 5π/3 is π/3.

B, C, and D are wrong. Tangent is negative in both quadrants

Tan(5pi/6) and tan(5pi/3) are both equal to -sqrt(3), so they are equal.

Tan is a trigonometric function that represents the ratio of the opposite side to the adjacent side of a right triangle. Tan(x) is equal to sin(x) / cos(x).

When we evaluate tan(5pi/6), we find that it is equal to -sqrt(3).

When we evaluate tan(5pi/3), we find that it is equal to -sqrt(3).

Therefore, both tan(5pi/6) and tan(5pi/3) are equal to -sqrt(3), so they are equal.

Answer:

-2

Step-by-step explanation:

Let's plug your functions f(x)=x^2-2x and g(x)=6x+4 into (f+g)(x)=0 and then solve your equation for x.

So (f+g)(x) means f(x)+g(x).

So (f+g)(x)=x^2+4x+4

Now we are solving (f+g)(x)=0 which means we are solve x^2+4x+4=0.

x^2+4x+4 is actually a perfect square and is equal to (x+2)^2.

So our equation is equivalent to solving (x+2)^2=0.

(x+2)^2=0 when x+2=0.

Subtracting 2 on both sides gives us x=-2.

Answer:

x=-2

Step-by-step explanation:

f(x) = x^2 - 2x

g(x) = 6x + 4

Add them together

f(x) = x^2 - 2x

g(x) =       6x + 4

-----------------------

f(x) + g(x) =x^2 +4x+4

We want to find when this equals 0

0 =x^2 +4x+4

Factor

What two numbers multiply together to give us 4 and add together to give us 4

2*2 =4

2+2=4

0=(x+2) (x+2)

Using the zero product property

x+2 =0    x+2=0

x+2-2=0-2

x=-2

Answer:

x=48

Step-by-step explanation:

Answer:

The quotient is 1/4

Step-by-step explanation:

1/3 ÷ 4/3

The first step you have to do is change the division sign into multiplication. So that the denominator of 2nd term will become numerator and the numerator will become denominator.

Like:

1/3 * 3/4

Now you can cancel out 3 by 3

1 * 1/4

1/4

Thus the quotient is 1/4 ....

For this case we must find the quotient of the following expression:

[tex]\frac {\frac {1} {3}} {\frac {4} {3}}[/tex]

If we apply double C we have:

[tex]\frac {3 * 1} {3 * 4} =[/tex]

We cancel similar terms in the numerator and denominator and finally we have the quotient is:

[tex]\frac {1} {4}[/tex]

Answer:

[tex]\frac {1} {4}[/tex]

[tex]V=\dfrac{1}{3}\pi r^2h\\\\h=2r\\V=\dfrac{1}{3}\pi r^2\cdot(2r)=\dfrac{2}{3}\pi r^3[/tex]

Answer:

[tex]V=\frac{2}{3}\pi R^{3}[/tex]

Step-by-step explanation:

The Volume of a cone is by definition 1/3 of the volume of a Cylinder. In this question, the height equals to diameter (2R).

So, We have:

[tex]h_{cone}=2R\\V=\frac{1}{3}\pi R^{2}h \Rightarrow V=\frac{1}{3}\pi R^{2}2R \Rightarrow V=\frac{2}{3}\pi R^{3}[/tex]

We conclude that under this circumstance, a cone with a height equal to its diameter will turn its volume to be equal to 2/3 of pi times the radius raised to the third power.

In other words, when the height is equal to the diameter. The relation between radius, height and Volume changes completely.

Answer:

x < -2

Step-by-step explanation:

2|x| > 3x + 10

Divide both sides by 2.

|x| > 1.5x + 5

********************************************************

An absolute value inequality of the form

|X1| > X2

where X1 and X2 are expressions in x is solved by solving the compound inequality

X1 > X2 or X1 < -X2

********************************************************

Back to your problem.

|x| > 1.5x + 5

x > 1.5x + 5   or   x < -(1.5x + 5)

-0.5x > 5     or   x < -1.5x - 5

x < -10   or    2.5x < -5

x < -10    or    x < -2

Since x < -10 is included in x < -2, the solution is

x < -2

Answer:

Discontinuities are created when the denominator of the rational expression equals zero (because division by zero is undefined). Graphically, this is usually represented by a dashed vertical line indicating a vertical asymptote.

The graph of the quadratic parent function, y = x^2, is indeed a parabola and lies in quadrants I and II. It is not a straight line and doesn't occupy quadrants I and III.

The graph of the quadratic parent function, which is y = x^2, has specific characteristics, namely:

https://brainly.com/question/32643207

#SPJ12

Answer:

z=312 if you meant x=26

Step-by-step explanation:

Direct proportional means there is a constant k such that z=kr. k is called the constant of proportionality. The constant k will never change no matter your (x,z).

So using our equation z=kr with point (18,216) we will find k.

216=k(18)

Divide both sides by 18

216/18=k

k=216/18

Simplify

k=12

So we now know the equation fully that satisfies the given conditions of directly proportion and goes through (x,z)=(18,216).

It is z=12x.

Now we want to know the value of z if x=26.

Plug it in. z=12(26)=312

z=312

Answer:

Efficiency is the ratio of output work to input work.

Machine efficiency is the percent ratio of output work to input work, calculated by (Wout / Win) * 100, and accounts for real-world energy losses, making it always less than 100 percent.

The ratio of output work to input work expressed as a percent is known as the efficiency of a machine. This efficiency (Eff) can be calculated using the equation Eff = (Wout / Win) * 100, where Wout is the output work and Win is the input work. In the context of simple machines, work (W) is defined as the force (F) applied over a distance (d), thus W = F * d. While ideal mechanical advantage (IMA) does not consider losses like friction and is calculated using specific equations for each type of machine, efficiency takes into account real-world factors and is always less than 100 percent due to these energy losses.

Answer: 3 - [tex]\frac{c}{4}[/tex]

Step-by-step explanation:

2c - 8f = 24

2(c - 4f) = 2(12)

c - 4f = 12

4f = 12 - c

F = 3 - [tex]\frac{c}{4}[/tex]

Answer:

[tex]\Large \boxed{Y=5}[/tex]

Step-by-step explanation:

[tex]\textnormal{First, divide by 90 from both sides of the equation.}[/tex]

[tex]\displaystyle \frac{90y}{90}=\frac{450}{90}[/tex]

[tex]\textnormal{Solve to find the answer.}[/tex]

[tex]\displaystyle 450\div90=5[/tex]

[tex]\displaystyle y=5[/tex], which is our answer.

Hope this helps!

The value of Y in the equation '90 x Y = 450' can be found by isolating Y. This is done by dividing both sides of the equation by 90. Hence, Y equals 5.

In the mathematical equation

90 x Y = 450

, we are being asked to solve for Y. To solve for Y, we can use the basic algebraic principle of isolating the variable on one side of the equation. In this case, since we have 90 multiplied by Y equals 450, we want to isolate Y. We can do that by dividing both sides of the equation by 90. The equation now becomes

Y = 450/90

. By performing the division, we find that

Y equals 5

.

https://brainly.com/question/31896359

#SPJ11

Answer:

Step-by-step explanation:

If two lines are parallel, their slopes are equal.

Next time, if you are given possible answer choices, please share them.

Answer:

The slopes of the two lines that are parallel, are equal.

Step-by-step explanation:

In order for two or more lines to be parallel their slopes have to be the same.

Answer:

False

Step-by-step explanation:

It would be at -3,9.

Answer:

6/16 or 0.375 ..

Step-by-step explanation:

Each time the coin has two possible outcomes so tossing the coin four times

The sample space will be: 2^4 = 16

The sample space is: {HHHH, HTHH, THHH, HTHT , HHHT, HTTH, TTHH, THTH, HHTT, HHTH, TTTH, THHT ,HTTT, TTTT, TTHT, THTT}

Let A be the event that there are exactly two heads

A = {HTHT, HTTH, TTHH, THTH, HHTT, THHT}

n(A) = 6

So the probability of exactly two heads is:

P(A) = 6/16 or 0.375 ..

Answer:

3/8

Step-by-step explanation:

The person up there answered it right they just went too high with the numbers.

Answer:

(5,1)

(5,0)

Step-by-step explanation:

Vertical lines contain the same x-coordinate per any point on it's line.

So the x-coordinate of (5,-2) is 5.

We are looking for points that have the x-coordinate being 5.

(5,1)

(5,0)

Actually the equation for this line is x=5.

[tex]\huge{\boxed{\text{(5, 1)}}}\ \huge{\boxed{\text{(5, 0)}}}[/tex]

[tex]\text{A vertical line is a line where all of the x values (the first values) are the same.}[/tex]

[tex]\text{In this case, all answers with an x value of 5 are correct.}[/tex]

Answer:

b = -9

Step-by-step explanation:

As we go from M(4, 3) to N(7, 12), x increases by 3 and y increases by 9.  Thus, the slope of the line segment connecting these two points is m = rise / run = m = 9/3, or just m = 3.

Subbing the coordinates of M into y = mx + b, we get:

3 = 3(4) + b, or 3 = 12 + b, so that b = -9.

Answer:

-9

Step-by-step explanation:

The next step for the evaluation of the given expression is:

         [tex](3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

We are given an arithmetic expression as follows:

      [tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})[/tex]

Now, in order to solve the given arithmetic expression we need to use the distributive property.

i.e.

[tex](a+b)c=a\cdot c+b\cdot c[/tex]

Now, the expression in the next step is written as follows:

[tex](3+\dfrac{1}{3})(5)+(3+\dfracx{1}{3})(\dfrac{1}{4})=(3)(5)+(\dfrac{1}{3})(5)+(3)(\dfrac{1}{4})+(\dfrac{1}{3})(\dfrac{1}{4})[/tex]

Answer:

4√3.

Step-by-step explanation:

√48

= √(16 * 3)

= √16 * √3

= 4√3.

Answer:

please could you send graphics A,B,C. you just sent D.

Answer:

its B It gives the number of the kinds of berries needed for the cost to be the same at both bakeries.

Step-by-step explanation:

Answer:

Graph 1 has two solutions

Graph 2 has one solution

Graph 3 has no solution

Graph 4 has two solutions

Step-by-step explanation:

* Lets explain the solution of the quadratic equation

- The quadratic equation represented graphically by a parabola

- The solution of the quadratic equation is the intersection point

  between the parabola and the x-axis

- At the x-axis y coordinate of any point is zero, then the solution is

 the value of x-coordinate of this point

- If the parabola cuts the x-axis at 2 points then there are 2 solutions

- If the parabola cuts the x-axis at 1 point then there is 1 solutions

- If the parabola doesn't cut the x-axis then there is no solution

* Lets solve the problem

# Graph 1:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

# Graph 2:

∵ The parabola cuts the x-axis at one point

∴ There is one solution

# Graph 3:

∵ The parabola doesn't cut the x-axis

∴ There is no solution

# Graph 4:

∵ The parabola cuts the x-axis at two points

∴ There are two solutions

A quadratic function is given in the general form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0.
The solutions of a quadratic function are found using the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
The number of solutions is determined by the discriminant, which is the expression inside the square root: b² - 4ac.
Here's how the discriminant determines the number of solutions:
1. If the discriminant is positive (b² - 4ac > 0), there are two distinct real solutions.
2. If the discriminant is zero (b² - 4ac = 0), there is exactly one real solution.
3. If the discriminant is negative (b² - 4ac < 0), there are no real solutions (but there are two complex solutions).
Now, let's apply this to the quadratic functions that you've been given. Unfortunately, you haven't provided the specific functions, so I'll give you a generic example for each case. You will be able to use this method to determine the number of solutions for any given quadratic function.
Example 1: One Solution
Consider the equation x^2 - 4x + 4 = 0.
Here, a = 1, b = -4, c = 4.
Discriminant = (-4)² - 4(1)(4) = 16 - 16 = 0.
Since the discriminant is zero, there is exactly one solution.
Example 2: Two Solutions
Consider the equation x^2 - 4x + 3 = 0.
Here, a = 1, b = -4, c = 3.
Discriminant = (-4)² - 4(1)(3) = 16 - 12 = 4.
Since the discriminant is positive, there are two distinct real solutions.
Example 3: No Real Solutions
Consider the equation x^2 + 2x + 5 = 0.
Here, a = 1, b = 2, c = 5.
Discriminant = (2)² - 4(1)(5) = 4 - 20 = -16.
Since the discriminant is negative, there are no real solutions.
Drag and label each quadratic function with the number of solutions based on your calculation of the discriminant:
- If the discriminant is zero, label it "one solution."
- If the discriminant is positive, label it "two solutions."
- If the discriminant is negative, label it "no real solutions."
Remember to apply this method to each of the quadratic functions that you have by calculating their discriminants.

Multiply the total number of slices by the fraction he ate:

12 slices x 1/6 = 12/6 = 2

He ate 2 slices.

Answer:

2

Step-by-step explanation:

1/6 of 12 =

= 1/6 * 12

= 1/6 * 12/1

= (1 * 12)/(6 * 1)

= 12/6

= 2

Answer:

First part:

Set h(t) = 17and solve for t.

-16t²+ 58t + 7= 17

-16t² + 58t - 10 = 0

Solve this quadratic equation for t. You should get 2 positive solutions. The lower value is the time to reach 17 on the way up, and the higher value is the time to reach 17 again, on the way down.

Second part:

Set h(t) = 0 and solve the resulting quadratic equation for t. You should get a negative solution (which you can discard), and a positive solution. The latter is your answer.

Answer:

C. There are infinitely many solutions.  

Step-by-step explanation:

3x – 6 < 3x + 13

Subtract 3x from each side

-6 < -13

This inequality is always true.

There are infinitely many solutions.

After simplifying the inequality, it becomes apparent that it holds true for all values of x. Therefore, there are infinitely many solutions to this inequality.

To solve the inequality 3x – 6 < 3x + 13, we need to isolate the variable x on one side. However, when we attempt to subtract 3x from both sides to move the terms involving x to one side, we are left with – 6 < 13 which is a true statement, but no longer contains the variable x. This means that the inequality holds true for all values of x. Therefore, the solution to the inequality is that there are infinitely many solutions. No matter what value of x you choose, the inequality will always be true.