Karl wants to rent a bike for at most $55. He can rent a bike for $7 per hour plus a $9.50 flat fee. Any portion of an hour is charged as a full hour.
What is the maximum number of hours Karl can Rent the bike?

The solution of the inequality are (iii) and (iv)

The solution of the equality is x = 8.

The solution of the equality is x = 0.

The solutions of the inequalities can be found as follows:

x³ + 3(5 - 2) ≥ 20 - 4

x³+ 3(3) ≥ 16

x³+ 9 ≥ 16

x³ ≥ 16 - 9

x³ ≥  7

x ≥ ∛7

x ≥ 1.9

Therefore, (iii) and (iv) are solution.

4(72 - x²) = 3.12 - 4

288 - 4x² = 36  - 4

288 - 4x²= 32

-4x² = -256

x²=  256 / 4

x²=64

x= √64

x= 8

7(x + 12) = 7.12

7x + 84 = 84

7x= 84 - 84

7x= 0

x = 0

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The point (1,6) belongs to the solution region of the system of inequalities.

The system of inequalities is given as:

y>1.5^x + 4

y< 2/3x + 6

Next, we plot both inequalities on a graph (see attachment)

From the attached graph, the point (1,6) is on the solution region of the inequalities

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The area of the rectangle is equal to 216ft^2.

We have given that,

A flower bed is in the shape of a rectangle.

It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.

The mulch is sold by the square foot.

A yard is equal to 3 feet.

7 yards = 7(3) = 24 feet

3 yards = 3(3) = 9 feet

Area of the rectangle=  Lw

Area of the rectangle= 24(9)

Area of the rectangle= 216 ft^2

Therefore the area of the rectangle is equal to 216ft^2.

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The conclusions that can be drawn about f–1(x) are:

Given:

[tex]f(x) = \frac{-2}{3}x - 24[/tex]

[tex]f(x) + 24 = \frac{-2}{3}x[/tex]

To find x, we would multiply both sides by -2/3

= [tex]x= \frac{-3}{2} (f(x) + 24)[/tex]

[tex]f^-^1(x) = -\frac{3}{2} (0) - 36[/tex]

[tex]f^-^1(x) = -36[/tex]

Therefore, [tex]f^-^1(x)[/tex]  has an x-intercept of (-36, 0)

Furthermore, [tex]f^-^1(x)[/tex] has a range of all real numbers.

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Answer:

a_n = n^2 − 1

Step-by-step explanation:

The numbers can be described as a polynomial with the following formula:

a1 = 1^2 − 1 = 1 - 1 = 0

a2 = 2^2 − 1 = 4 - 1 = 3

a3 = 3^2 − 1 = 9 - 1 = 8

a4 = 4^2 − 1 = 16 - 1 = 15

a5 = 5^2 − 1 = 25 - 1 = 24

The amount of money Conor should save each month for 5 months is £136.

Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number.

The amount of money Conor should save each month = total amount needed / number of month

£680 / 5 = £136

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Answer:

30/48

Step-by-step explanation:

[tex]\sqrt[n]{a^n}=a[/tex], therefore [tex]\sqrt[4]{5^4}=5[/tex].

Answer:

It is 5

Key solutions:

Step-by-step explanation:

Isolate the exponents and remove the square, giving you 5

[tex]\left(\sqrt[4]{5}\right)^4\\=5[/tex]

Answer:

C

Step-by-step explanation:

Two negatives cancel out and turn into a positive.

In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8

So the answer is C

The thing that can be deduced from Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic.

It should be noted that elasticity of demand simply means the responsiveness to demand when there's a change in price.

Gus's elasticity of demand for cupcake is that the demand for cupcakes is perfectly elastic. This is when the percentage change in quantity demanded is infinite due to the price change.

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The graph of the linear equation 6x - 2y = 12 would be option C .

Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

Subtract both sides from 6x, leaving you with the equation:

-2y = -6x + 12

Now, you divide all of the sides by -2,

y = 3x - 6

The graph of the linear equation 6x - 2y = 12 would be option C .

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Answer:

step 2: 8x-4=2(6+x+6)

Step-by-step explanation:

[tex]4(2x - 4) = 8 + 2x + 8 \\ 8x - 16 = 16 + 2x here \\ 8x - 2x = 16 + 16 \\ 6x = 32 \\ \frac{6x}{6} = \frac{32}{6} \\ x = 5[/tex]

Answer:

4(2x-4)=8+2x+8

8x-16=16+2x

8x-2x=16+16

6xboth sides over 6

x=5.3repiting

The x coordinate of point A that is shown on the graph is 3π/16.

From the information given, y = kcos(8x). Also, the axis of symmetry is given as kx.

Therefore, the x coordinate will be:

= π/8 + π/16

The LCM of 8 as 16 is 16.

= 2π/16 + π/16

= 3π/16

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The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).

If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:

a · 0² + b · 0 + c = 0     (1)

a · 1² + b · 1 + c = 16      (2)

a · 3² + b · 3 + c = 0      (3)

The solution to this system is a = - 8, b = 24, c = 0.

The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.

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A function assigns the values. The function of the given graph is y=3(4)ˣ, thus, the correct option is C.

A function assigns the value of each element of one set to the other specific element of another set.

The complete question is:

If the parent function is y = 4ˣ, which is the function of the graph?

y = −2(4)ˣ

y = −3(4)ˣ

y = 3(4)ˣ

y = 2(4)ˣ

Since the graph intersect the y-axis at 3, and the parent function of the function is y=4ˣ, therefore, we can write,

y = A(4)ˣ

3 = A(4)⁰

3 = A × 1

A = 3

Hence, the function of the given graph is y=3(4)ˣ, thus, the correct option is C.

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Answer:

Step-by-step explanation:

NOTE :

the sum of the 4 interior angles of a quadrilateral is 360°.

…………………………………………

Then

h + h + 2h + 2h = 360

Then

6h = 360

Then

h = 360 ÷ 6 = 60

Then

2h = 2 × 60 = 120

Answer:

regular pentagon. 2 irregular. 3 irregular. 4 regular octagon. 5 regular nonagon. remember that regular polygon is a polygon that

Answer:

1) Radius of the cone = 9.5 cm

2) BA = 90.25 π cm²

3) SA = 384.7 π cm²

Step-by-step explanation:

1) Radius of the cone = 9.5 cm

2) Base Area of the cone =

BA = (π)(9.5)²

BA = 90.25 π cm²

3) Surface Area of Cone =

SA = π(9.5)(9.5 + √(29.5)²+(9.5)²)

SA = 9.5π(9.5 + 31)

SA = 9.5π(40.5)

SA = 384.7 π cm²

Edge 2022

Answer:

5 %  

Step-by-step explanation:

3020 *  x    = 151          x is the percentage in decimal form

x = 151 / 3020 = .05    which is 5 %

Answer:

Rose bought 14 packages of granola bars.

Step-by-step explanation:

Total bill = 1 bag of potatoes + x amount of packages of granola bars

Total bill = $74.25

1 bag of potatoes = $6.00

1 package of granola bar = 5.25

We set the equation to:

74.25 = 6.00 + 5.25x

Subtract 6.00 from both sides:

68.25 = 5.25x

Divide both sides by 5.25 to leave x by itself

68.25/5.25 = 5.25x/5.25

13 = x

This means Rose bought 13 packages of granola bars.

Let's recheck our work by inputting x = 13 into the equation:

74.25 = 6.00 + 5.25(13)

74.25 = 6.00 + 68.25

74.25 = 74.25

Answer:

3.375 °C

Step-by-step explanation:

Mean temperature for first 7 days = 4 °C

⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C

Temperature on 8th day = -1 °C

[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]

Therefore, mean temperature for first 8 days:

= [28 - 1] ÷ 8

= 27 ÷ 8

= 3.375 °C

The perimeter and area of the square are 16√5 mm and 80 mm²

Perimeter of a square = 4L

where

Therefore,

Perimeter of a square = 4 × 4√5

Perimeter of a square = 16√5 mm

Area of a square = l²

Area of a square = (4√5)²

Area of a square = 16 × 5

Area of a square = 80 mm²

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Answer:

2 / 36 = 1/18

Step-by-step explanation:

there are 2 ways to get 3

1 then 2 or 2 then 1 , 2 out of a possible 36 outcomes

Answer:

alright well

from what I got x is 29.444 , y is 34 and angle b is 60 degrees

the correct answer is A.

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Answer:

The rate of interest is6.4 %

Step-by-step explanation:

Given : Principal (P) = Rs12500  

         Total amount (A) = Rs16500.

         The time period (t) =5  years

To find : Rate of interest (R) = ?

Solution :

It is given that Principal (P) = Rs. 12500

        Total amount (A) = Rs.   16500

        The time period (t) =5  years  

We have to find rate of interest (R).

We know the formula for simple interest as,

       S.I. = A-P

             = 16500±12500

             = Rs. 4000

Now, to find rate of interest, use the formula for simple interest as

           S.I. =  

          ∴

          ∴ *R

             ∴  

                    ∴  

                       ∴R=6.4  %                          

∴  The rate of interest is6.4 %.

Answer:

well i mean it all depends were you live at

Step-by-step explanation:

in new york it will be $36,198. but in California it would be about $31,682 and  Your average tax rate is 16.51% and your marginal tax rate is 24%.  

Answer:

all real numbers

Step-by-step explanation:

When you factor in the .2 on the left side you are left with 1.4 + .4t which is equal to the other side. And so, no matter what value for t you plug in, they will always be equal to eachother.

The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).

In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).

We must check if the proposition is true for every ordered pair. Let analyze each case:

Case I

[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]

Case II

[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]

Thus, the proposition is false.

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