See the attachment to answer the question

Answer:

L = 9

Step-by-step explanation:

Translating this into symbols, we get L = W + 1 and A = 72 = W * L.

Substituting W + 1 for L in the latter equation, we get:

72 = W(W + 1), or:

W^2 + 1W - 72 = 0

This factors into (W + 9)(W - 8) = 0, so that W must be either -9 or +8.

Since W represents width, a physical measurement, we eliminate the negative result and conclude that W = 8 units.  Then L = W + 1 = 9 units.

Note that (8)(9) = 72, as we already know.

The length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Let's denote the width of the rectangle as \( w \) and the length of the rectangle as \( l \).

According to the problem, the length \( l \) is given by:
[tex]\[ l = w + 1 \][/tex]

The area of the rectangle is given by:
[tex]\[ \text{Area} = l \times w = 72 \][/tex]

Substituting the expression for \( l \) into the area formula:
[tex]\[ (w + 1) \times w = 72 \][/tex]

This can be rewritten as:
[tex]\[ w^2 + w - 72 = 0 \][/tex]

We now have a quadratic equation. To solve this, we can use the quadratic formula:
[tex]\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]\\where \( a = 1 \), \( b = 1 \), and \( c = -72 \).\\[/tex]
Plugging in these values:
[tex]\[ w = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot (-72)}}{2 \cdot 1} \]\[ w = \frac{-1 \pm \sqrt{1 + 288}}{2} \]\[ w = \frac{-1 \pm \sqrt{289}}{2} \]\[ w = \frac{-1 \pm 17}{2} \][/tex]

This gives us two potential solutions for \( w \):
[tex]\[ w = \frac{16}{2} = 8 \]\[ w = \frac{-18}{2} = -9 \][/tex]

Since a width cannot be negative, we discard \( w = -9 \) and take \( w = 8 \).

Therefore, the width \( w \) is 8 units. Using the relationship \( l = w + 1 \), we find:
[tex]\[ l = 8 + 1 = 9 \][/tex]

So, the length of the rectangle is: [tex]\[ {9} \] units.[/tex]

Answer:

10,50,250

Step-by-step explanation:

multiply by 5 each time

Answer: 2, 10, 50, 250, 1250

Step-by-step explanation:

The given sequence is a geometric sequence. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence.

r represents the common ratio.

n represents the number of terms.

From the information given,

a = 2

n = 5

T5 = 1250

The 5th term, T5 is expressed as

1250 = 2 × r^(5 - 1)

1250/2 = r^4

625 = r^4

5^4 = r^4

r = 5

The second term is

2 × 5 = 10

The third term is

10× 5 = 50

The fourth term is

50 × 5 = 250

The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. Here are two key characteristics of the polar coordinate system:

1. Radial Distance (Radius): In the polar coordinate system, the location of a point is determined first by its distance from a fixed point, called the pole, analogous to the origin in the Cartesian coordinate system. This distance is often denoted as \( r \), and it can be thought of as the radius of a circle centered at the pole, with the point lying on the circumference of this circle.

2. Angular Coordinate (Angle): The second characteristic of a point's location in the polar coordinate system is the angle [tex]\( \theta \)[/tex] (theta), which is measured from a fixed direction, typically the positive x-axis of the corresponding Cartesian coordinate system. This angle, usually measured in degrees or radians, determines the direction of the line from the pole to the point.

These two values, [tex]\( r \)[/tex] and [tex]\( \theta \)[/tex], are called polar coordinates, and they provide an alternative to the Cartesian (rectangular) coordinate system for representing points on a plane, particularly useful in scenarios where the geometry or the nature of the problem is radially symmetric, such as in the cases of circular motion or fields (gravitational, electric, etc.).

Answer:

Je pense que la réponse est 15 jours

Step-by-step explanation:

Answer: B. 2.5 in

Step-by-step explanation:

From the given right angle triangle,

the hypotenuse of the right angle triangle is the unknown side.

With m∠32 as the reference angle,

the adjacent side of the right angle triangle is 4 in

the opposite side of the right angle triangle is w

To determine w, we would apply

the tangent trigonometric ratio which is expressed as

Tan θ = opposite side/adjacent side. Therefore,

Tan 32 = w/4

w = 4tan32 = 4 × 0.625

w = 2.5 in

Answer:

There is an average of approximately 1 sheep per square mile.

Step-by-step explanation:

Given there are 9.54 sheep spread across 18.52 square miles of land.

The average number of sheep per square mile is given as

A = 9.54/18.52

Without using a calculator, this is by inspection, about 9/18 = 0.5.

Using a calculator, we have

A = 9.54/18.52 = 0.51511879

Approximately 1 sheep per square mile.

Answer:

a subscript n=4.3(n-1)+3.9

Step-by-step explanation:

Answer:

The correct answer is a) R = = - [tex]\frac{1}{5}[/tex] [tex]x^{2}[/tex] + 30x; b) $ 1120; c) Maximum quantity is 75 units with maximum revenue being $1125; d) p = $15.

Step-by-step explanation:

Demand equation: p = - [tex]\frac{1}{5}[/tex]x + 30 , 0 [tex]\leq[/tex] x [tex]\leq[/tex] 150 ; where p is the price of the product and x is the quantity sold.

a) Revenue function by the problem is given to be R= p × x = - [tex]\frac{1}{5}[/tex] [tex]x^{2}[/tex] + 30x.

b) Revenue at x = 70 is given by 2100 - 980 = $ 1120.

c) For maximizing the R we differentiate it with respect to x and equate it to zero.

⇒ - [tex]\frac{2}{5}[/tex] x + 30 =0

⇒ x = 75.

As the second order derivative is negative at this point, this is the value of x that maximizes the revenue.

Maximum Revenue is at x = 75 and is equal to $1125.

d) Price charged by the company for maximum revenue is $15.

0.8‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎

Answer:

o.8

Step-by-step explanation:

trust me im doing it

Answer:

slow hiker rate= 1.1mph and fast hiker rate= 5.5 mph

Step-by-step explanation:

lets consider the Speed of the slow hiker =x

Then Speed of fast hiker =x+4.4

As we know that distance is the product of speed and time

therefore,

Distance covered by slow hiker in 5 hours = 5x km

Distance covered by fast hiker in 5 hours=5 (x+4.4)=5x+22 km

As they are are 33 miles apart , therefore

5x + 5x+22 = 33

10x = 33-22

10x = 11

x =11/10 => 1.1

Rate of slow hiker is x i.e 1.1mph

Rate of fast hiker = x+4.4 => 5.5 mph

Answer:

slower hiker's speed = 1.1 mph

faster hiker's speed = 5.5 mph

Step-by-step explanation:

Extracting the key information from the question:

*** Two hikers are 33 miles apart and are walking towards each other.

*** One of them walks 4.4 mph faster than the other and later met themselves in 5 hours.

*** We are required to find the speed of each of the hikers.

  Speed = distance/time

 Let us use "x" to represent the slower speed. Since one of the hikers was 4.4 mph faster than the other hiker, we can represent the faster speed with x+4. Now, if they met themselves in 5 hours, even though they were 33 miles apart initially, then we can represent the situation with the given equation:-

  (x mph × 5hours) + [(x+4.4)×5] = 33 miles

5x  +  (5x + 22) = 33

5x + 5x + 22= 33

10x + 22 = 33

 10x = 33-22

  10x = 11

    x = 11/10

    x = 1.1mph (speed of slower hiker)

 The speed of the faster hiker = x + 4.4

 = 1.1 + 4.5

 = 5.5mph

Answer:false

Step-by-step explanation: Then you would get rid of the x

The correct option is Class A had the higher median score. Class A scored better on the test.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two whiskers that represents the maximum and minimum numbers.

On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

The median of class A = 9

The median of class B = 8.2

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Answer:

It will hold 200 Litres  of water

Step-by-step explanation:

To find the number of litres of water the fish tank can hold, we will follow the steps below;

Write down the formula for calculating its volume

V = l×w×h

where v = volume of the tank

w=width of the tank  

l = length of the tank

From the question given;

w= 50 cm = 0.5 m

height h = 20 cm = 0.2 m

l = 2 m

V= l×w×h

  =  2×0.5×0.2

  =0.2 m³

we can now change it to liters

V = 0.2 m³ × 1000 = 200 L

It will hold 200 Litres  of water

Answer:

8 units

Step-by-step explanation:

[tex] {(x + 6)}^{2} + {(y - 4)}^{2} = 16 \\ {(x + 6)}^{2} + {(y - 4)}^{2} = {4}^{2} \\ equating \: it \: with \\ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\ {r}^{2} = {4}^{2} \implies \: r = 4 \\ d = 2r = 2 \times 4 = 8 \: units[/tex]

Hence, diameter of the circle is 8 units.

Answer: [tex]32009355.90cm^3[/tex]

Step-by-step explanation:

Formula: [tex]V=Bh\\[/tex]

Since the base is a circumference, we can replace B for the area of a circumference formula.

[tex]V=\pi r^2h[/tex]

What we have here is 12 ft as the diameter of the circumference. A diameter is twice the radius, therefore we can conclude that if we take the diameter and divide it by 2, it will give us the radius.

[tex]12/2=6ft[/tex] this is the radius.

Now plug all this information into your formula.

[tex]V=(3.14)(6ft)^2(10ft)\\V=(3.14)(36ft^2)(10ft)\\V=1130.40ft^3[/tex]

Our values are in feet but the question requires cm. Let's convert from [tex]ft^3[/tex] to [tex]cm^3[/tex].

Normally, our conversion factors are raised to the power of 1, but in this case it's raised to the power of 3. So, first let's see how many cm are 1 ft.

[tex]1ft=30.48cm[/tex]

Here is where magic comes. We can raise both to the power of 3, in order to find the cubic ft and cm that we need as our conversion factors.

[tex](1ft)^3=(30.48cm)^3\\1ft^3=28316.8cm^3[/tex]

Now we have our conversion factors.

[tex]1130.40ft^3(\frac{28316.84cm^3}{1ft^3})=32009355.90cm^3[/tex]

Answer:

  4.8 or 4 4/5

Step-by-step explanation:

Put the given value into the equation and solve for the missing one.

  (3/5)(6) -(1/3)y = 2

  3.6 -y/3 = 2 . . . simplify to decimal form

  -y/3 = -1.6 . . . . subtract 3.6

  y = 4.8 . . . . . . . multiply by -3

The missing number is ...

  4.8 = 4 4/5

_____

The coefficients are given as fractions, so the answer may be expected in mixed-number form.

Steps to solve:

-3x - 8 = 10

~Add 8 to both sides

-3x - 8 + 8 = 10 + 8

~Simplify

-3x = 18

~Divide -3 to both sides

-3x/-3 = 18/-3

~Simplify

x = -6

Best of Luck!

The solution of the equation -3x - 8 = 10 is,

⇒ x = -6

The given algebraic equation is,

-3x - 8 = 10

Now since its degree is 1

Therefore it is nothing but a linear equation.

By simple operation we can solve it

Now to solve it proceed the following steps:

Add 8 both sides, we get

⇒ -3x - 8 + 8 = 10 + 8

⇒            -3x  = 18

Divide by -3 both sides we get

⇒            x  = 18/-3

⇒            x  = 6

Hence,

The solution is x = -6

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Answer:

that is the solution to the question

Final answer:

To calculate the principal with an interest of $119.88, an interest rate of 3.6%, and a time of 3 years, use the simple interest formula. By rearranging the formula and doing the math, the principal amount is found to be $1,110.

Explanation:

To find the principal amount when you know the interest earned, the interest rate, and the time, you can use the formula for simple interest which is Interest = Principal × rate × time. Our goal is to rearrange the formula to solve for the principal.

Given that the Interest earned is $119.88, the interest rate is 3.6% (or 0.036 when converted to a decimal), and the time is 3 years, we can plug these values into the formula:

Interest = Principal × rate × time
$119.88 = Principal × 0.036 × 3
$119.88 = Principal × 0.108

To find the Principal, divide the interest earned by the product of the rate and time:

Principal = $119.88 / 0.108
Principal = $1,110

The principal amount is $1,110.

Given:

To find out:

If it runs into a wall what force will be exerted by the cat?

Formula used:

Force = mass × acceleration

Solution:

Force = mass × acceleration

Now, Putting these values of m and a in the above equation.

we get:

F = 10 × 10

= 100 N

Thus, the force will be exerted by the cat is 100 N.

The force exerted by the cat when it runs into a wall can be calculated using Newton's Second Law of Motion, resulting in a force of 100 Newtons.

The subject of this question pertains to the concept of Newton's Second Law of Motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. Here, the cat is considered the object in motion. The cat's mass is 10kg, and its acceleration is given as 10 m/s².

By substituting these values into Newton's second law (Force = mass x acceleration), we can calculate the force exerted by the cat as it runs against a wall: Force = 10kg x 10 m/s² = 100 N (Newtons). Therefore, the cat will exert a force of 100 Newtons when it runs into the wall.

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Answer: 24 miles

Step-by-step explanation: 12 mph is two times as fast as 6 mph so 6 hours round trip is 2 hours for bike and 4 hours for jogging. You can either plug 2 for 12 (bike) or 4 for 6 (jog) either way you get 24

Answer:

24 miles

Step-by-step explanation:

Answer:

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg

the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

Hexagon is a two-dimensional geometrical shape that is made of six sides, having the same or different dimensions of length. Some real-life examples of the hexagon shape are a hexagonal floor tile, pencil cross-section, clock, a honeycomb, etc. It can be either regular (with 6 equal side lengths and equal angles) or irregular (with 6 unequal side lengths and angles).

According to the question,

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2)

                                             = 180(6 - 2)

                                             = 180 × 4

                                             = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 × 240/13 = 2160/13

[tex]\frac{2160}{13}[/tex]  = [tex]166\frac{2}{13}[/tex]

Hence, the size of largest angle is  [tex]166\frac{2}{13}[/tex] degree

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Answer:

(-8, -1)

Step-by-step explanation:

The problem tell us that y = -1.  Plug in this y-value to wherever you see a y in the first equation.  You should be able to solve from there.  Your solution will be (-8,-1).

-2x - 3(-1) = 19

-2x + 3 = 19

-2x = 16

x = -8

For this particular problem, you could have also looked at the answer choices and seen that there was only one answer with the correct y-value.

Answer:

One centimeter is equal to 10 millimeters. It is also equal to 0.1 decimeter and 0.01 meter. One kilometer contains 100,000 centimeters.

Step-by-step explanation:

thank me and rate me!!!plz thank you :)

Answer: 100x centimeters

Step-by-step explanation:

We know that 100 centimeters are in every meter. To find the number of centimeters in X amount of meters, we multiply X by 100. Take for example 4 meters. 4 times 100 equals 400. We then know that there are 400 centimeters in 4 meters.

Answer:

240 people

Step-by-step explanation:

According to the given data,

In each bus,there are total number of 36 students and 4 adults

So, total 40 people are in one bus so...

As, there are six Fields buses

=>40 x 6

=240

Answer: Total 240 people are going on the field trip.

To calculate the total number of people going on the field trip, multiply the number of students and adults by the number of buses and sum the result, resulting in 240 people.

The question relates to the calculation of the total number of people going on a field trip with a given number of students and adults per bus and a total number of buses. To find out how many people in total are going on the field trip, we need to multiply the number of students and adults by the number of buses and add up the results.

Each bus holds 36 students and 4 adults. With 6 buses on the field trip, we calculate the total number of people by multiplying the number of buses by the total capacity per bus (students plus adults): (36 students + 4 adults) × 6 buses.

So, the calculation is as follows:

40 people per bus × 6 buses = 240 people going on the field trip.

Answer:

There are a total of  

✔ 12

strawberries.

There are a total of  

✔ 2

people.

The expression to find the mean, or balance point, is  

✔ 12/2

✔ Ona

should give 2 strawberries to  

✔ Barton

for the number of strawberries to be balanced.

Step-by-step explanation:

Barton only has four strawberries and needs two more, while Ona has eight and will share two.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Barton has 4 strawberries and Ona has 8 and they want to redistribute their strawberries so they each have an equal number.

We'll apply division by splitting into equal halves or groups, the division may be used to decide how to distribute a dish of cookies evenly among a group.

In order for Ona and Barton to have the same number of strawberries, the total number of strawberries must be divided in two.

=(8 + 4) / 2

= 12 /2

= 6

Thus, Barton only has four strawberries and needs two more, while Ona has eight and will share two.

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Answer:

1.25 cm

Step-by-step explanation:

Draw a radius line from the center to one of the top corners.  This forms a right triangle where the hypotenuse is r, the width is 1, and the height is 2−r.  Using Pythagorean theorem:

(2−r)² + 1² = r²

4 − 4r + r² + 1 = r²

5 − 4r = 0

r = 5/4

r = 1.25