The width of a rectangular swimming pool is 11 meters less than length, and the perimeter is 62 meters. Find its dimensions in meters. Width=?m Length=?m

The solution of the equations are

x^2 - 36 = 0

x = 6, -6

The equation x2 + 12x + 36 = 0

x = -6, -6

The equation x^2 - 36 = 0 is solved as follows

x^2 - 36 = 0

x = ±√36

x = 6 or -6

The quadratic equation x^2 + 12x + 36 = 0 is solved as follows

x^2 + 6x + 6x + 36 = 0

x(x + 6) + 6(x + 6) = 0

(x + 6)(x + 6) = 0

hence

x = -6 and -6

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The required measure of the unknown side in similar triangles is 4.

Similar triangles are two triangles that have the same shape but are not necessarily the same size. More specifically, two triangles are similar if their corresponding angles are congruent (i.e., have the same measure), and the corresponding sides are proportional (i.e., have the same ratio).

Here,
Two similar triangles are given in the figure,

Let the unknown side be x
For a similar triangle, the ratio of the corresponding sides are equal So,
a / 8 = 6 / 12
a = 8/2
a = 4

Thus, the required measure of the unknown side in similar triangles is 4.

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Answer:

I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.

Step-by-step explanation:

The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.

Answer:

The width of the patio is 15 feet

Step-by-step explanation:

We can start by using the formula for the area of a rectangle:

Area = length x width

In this case, we know that the area of the patio is given by:

16x^2 + 20x square feet

And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:

16x^2 + 20x = (x + 5) x width

Simplifying the right-hand side by multiplying x + 5 by width, we get:

16x^2 + 20x = width x^2 + 5x

To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:

width x^2 - 16x^2 + 20x - 5x = 0

Simplifying the left-hand side by combining like terms, we get:

width x^2 - 16x^2 + 15x = 0

Factoring out x, we get:

x (width x - 16x + 15) = 0

Now we can solve for the width by setting each factor equal to zero and solving for x:

x = 0 or width x - 16x + 15 = 0

Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:

width x - 16x + 15 = 0

We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:

(width x - 1)(x - 15) = 0

Setting each factor equal to zero and solving for x, we get:

width x - 1 = 0 or x - 15 = 0

width x = 1 or x = 15

Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:

width x = 1, x = 15, so we choose x = 15

width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet

Therefore, the width of the patio is 15 feet.

The least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:

Length = 24 feet + 6 inches = 24.5 feet

Width = 4 feet + 6 inches = 4.5 feet

Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)

The volume of the sidewalk is then:

Volume = Length x Width x Depth

= 24.5 feet x 4.5 feet x 1/3 feet

= 3.25 cubic feet

Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:

Number of bags = Volume of sidewalk / Volume per bag

= 3.25 cubic feet / 0.6 cubic feet per bag

= 5.42 bags

Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

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The area of the triangular sail in the sail model is 42 square inches.

The area of a triangular sail is given by the formula:

Area = (1/2)bh

where b is the length of the base and h is the height.

Substituting b = 12 inches and h = 7 inches, we get:

Area = (1/2)(12 inches)(7 inches) = 42 square inches

Therefore, the area of the triangular sail in the sail model is 42 square inches.

The area of a triangle is given by the formula:

Area = (1/2) * base * height

where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.

To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.

Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.

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Answer:

24

Step-by-step explanation:

N/A

Answer:

the perimeter of the rectangle is 26 meters.

Step-by-step explanation:

To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:

width = area / length = 36 / 9 = 4 meters

Now we can use the formula for the perimeter of a rectangle:

perimeter = 2(length + width)

Substituting the given values, we get:

perimeter = 2(9 + 4) = 2(13) = 26 meters

Therefore, the perimeter of the rectangle is 26 meters.

Answer:

Step-by-step explanation: To calculate the total amount of money Jamal made in six months, we need to multiply the number of paintings sold by the price of each painting, and then add the results for the large and small paintings:

7 large paintings * $45.99/large painting = $321.93

4 small paintings * $28.99/small painting = $115.96

Total amount made = $321.93 + $115.96 = $437.89

Therefore, Jamal made $437.89 in six months by selling seven large paintings and four small ones.

The probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

To calculate the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb, we can use the complementary probability. That is, we can calculate the probability that a 23-watt bulb is obtained within the first 5 selections and then subtract this from 1 to get the probability that at least 6 bulbs must be examined.

The probability of obtaining a 23-watt bulb on the first selection is 1/50. If a 23-watt bulb is not obtained on the first selection, the probability of obtaining one on the second selection is 49/50 x 1/49 = 1/50.

Similarly, the probability of obtaining a 23-watt bulb on the third, fourth, or fifth selection is also 1/50.

Therefore, the probability of obtaining a 23-watt bulb within the first 5 selections is:

P(23-watt bulb in first 5 selections) = P(23-watt bulb on first selection) + P(23-watt bulb on second selection) + P(23-watt bulb on third selection) + P(23-watt bulb on fourth selection) + P(23-watt bulb on fifth selection)

= 1/50 + 1/50 + 1/50 + 1/50 + 1/50

= 1/10

The probability of needing to examine at least 6 bulbs before obtaining a 23-watt bulb is therefore:

P(need to examine at least 6 bulbs) = 1 - P(23-watt bulb in first 5 selections)

= 1 - 1/10

= 9/10

Therefore, the probability that it is necessary to examine at least 6 bulbs before obtaining a 23-watt bulb is 9/10 or 0.9 (approximately).

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Answer:

2026 to maximize the present value function.

Step-by-step explanation:

To find the year in which the timber should be harvested to maximize the present value function, we need to find the time t that maximizes the present value function A(t). We can begin by finding A(t):

A(t) = V(t)e^(-0.09t)

A(t) = 140,000e^(0.72√t) * e^(-0.09t)

A(t) = 140,000e^(0.72√t - 0.09t)

To maximize A(t), we need to find the critical points of A(t). We can do this by taking the derivative of A(t) and setting it equal to zero:

A'(t) = 140,000(0.36/√t - 0.09)e^(0.72√t - 0.09t) = 0

Simplifying this equation, we get:

0.36/√t - 0.09 = 0

0.36/√t = 0.09

√t = 4

t = 16

Therefore, the critical point of A(t) occurs at t = 16 years.

We can check that this is a maximum by taking the second derivative of A(t) and evaluating it at t = 16:

A''(t) = 140,000(-0.648/t^3 - 0.243/√t + 0.081)e^(0.72√t - 0.09t)

A''(16) = 140,000(-0.648/16^3 - 0.243/4√16 + 0.081)e^(0.72√16 - 0.09(16))

A''(16) ≈ -4,980.4

Since the second derivative is negative, we can conclude that t = 16 years corresponds to a maximum for the present value function A(t).

Therefore, the timber should be harvested in the year 2010 + 16 = 2026 to maximize the present value function.

Answer:

Step-by-step explanation:

whatb you need

Answer:

Step-by-step explanation:

Here is a more detailed explanation:

We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:

x   f(x)   g(x)

1    3      5

4    9      20

To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.

For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:

y - 3 = 2(x - 1)

y - 3 = 2x - 2

y = 2x + 1

So the equation of f(x) is y = 2x + 1.

Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:

y - 5 = 5(x - 1)

y - 5 = 5x - 5

y = 5x

So the equation of g(x) is y = 5x.

To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:

2x + 1 = 5x

3x = 1

x = 1/3

Substituting this value of x back into either equation, we can find the corresponding value of y:

y = 2(1/3) + 1 = 7/3

So the point of intersection is (1/3, 7/3).

Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.

Answer:

1. volume= 135

2. prism volume in cubic feet is: 21

3. surface area is 294 ft^2

4. surface area is 430 ft^2

Answer:

Step-by-step explanation:

You want to know how long Hoang and Bill have worked at the hospital if Hoang has worked there 5 years longer, and 5 years ago that was twice as long as her friend Bill.

Hoang's longevity will be twice Bills when Bill's is equal to the difference. That is, 5 years ago, Bill had been there 5 years and Hoang had been there 10 years.

Now, each has been there 5 years longer, so ...

If h represents Hoang's time at the hospital, 5 years ago it was (h-5). Currently, Bill's time at the hospital is (h-5), and 5 years ago it was (h-10). The relation between the times 5 years ago is ...

  (h -5) = 2(h -10)

  15 = h . . . . . . . . . . add 20-h to both sides

  h-5 = 15 -5 = 10 . . . . Bill's time at the hospital

Hoang and Bill have been at the hospital 15 years and 10 years, respectively.

a. The angle generated by P in time t is pi radians.

b. The distance traveled by P along the circle in time t is 16pi cm.

c. The linear speed of P is 2pi cm/sec.

What is angular speed ?

Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second and is denoted by the symbol "ω" (omega).

Angular speed is calculated as the change in angle (measured in radians) divided by the time it takes to make that change. In other words, it is the rate at which the angle is changing over time.

Angular speed is an important concept in physics and engineering, as it is used to describe the motion of rotating objects such as wheels, gears, and turbines. It is also used to calculate other important parameters such as linear speed, centripetal force, and torque.

The problem involves finding the properties of a point P that is rotating around a circle with a given radius r and angular speed omega. The problem provides the values of r, omega, and t and asks to find the angle generated by P in time t, the distance traveled by P along the circle in time t, and the linear speed of P.

(a) To find the angle generated by P in time t, we use the formula for angular displacement:

theta = omega * t

Here, omega is given as pi/8 radians per second and t is given as 8 seconds. We substitute these values to get:

theta = (pi/8) * 8 = pi radians

Therefore, the angle generated by P in time t is pi radians.

(b) To find the distance traveled by P along the circle in time t, we use the formula for arc length:

s = r * theta

Here, r is given as 16 cm and theta is calculated in part (a) as pi radians. We substitute these values to get:

s = 16 * pi = 16pi cm

Therefore, the distance traveled by P along the circle in time t is 16pi cm.

(c) To find the linear speed of P, we use the formula for tangential velocity:

v = r * omega

Here, r is given as 16 cm and omega is given as pi/8 radians per second. We substitute these values to get:

v = 16 * (pi/8) = 2pi cm/sec

Therefore, the linear speed of P is 2pi cm/sec.

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.

We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.

According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.

As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.

To figure this out, we can use the formula below:

Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.

Estimated number of influenza patients = 0.04 times 25

Expected number of influenza patients is one.

Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.

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The correct answers are

1)  2x^2 + 12

2) Option C.

3) Option B.

1. You must apply the Distributive property as following:

(-5x^2 - 2x +4) + (8x^2 -x -1) - (x^2 -5x + 2x -10)

2. Now, you must distribute the negative sign, then you have:

3. Finally, you must add the like terms. Then you obtain the polynomial:

2x^2 + 13

4. By definition, a polynomial that has two terms is classified as a binomial. Therefore, the answer is the option C.

5. The degree of a polynomial is determined by highest exponent of the variable. So, it is a polynomial of degree 2 (option B).

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Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:

D = R * T = 20 km/h * 1.6 h = 32 km

Therefore, the bicyclist traveled a total distance of 32 kilometers.

Step-by-step explanation:

The area of the triangle DEF shown in the coordinate plane is 6 units².

Area of a triangle is defined as the total region bounded by the shape of the triangle.

The formula to calculate the area of a triangle if the base length and height is given is,

Area = [tex]\frac{1}{2}[/tex] × base × height

Given is a triangle in a coordinate plane.

Base of the triangle is the side DE.

Length of DE is the length of the points (1, 1) t0 (1, 4), which is 3 units apart.

Length of base = 3 units

Height of the triangle is the perpendicular length from the vertex opposite base to the base.

That is, the distance from F(-3, 3) to (1, 3), which are 4 units apart.

Height = 4 units.

Area of triangle DEF = [tex]\frac{1}{2}[/tex] × 3 × 4

                                  = 6 units²

Hence the area of the triangle is 6 units².

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To find the total distance of Alanah's trip to the arena, we need to add up the distances of each segment of her trip. We can use the distance formula to calculate the distances between the different points.

First, let's calculate the distance between Alanah's house (A) and Mia's house (M). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((4 - 2)^2 + (14 - 10)^2)

distance = sqrt(4 + 16)

distance = sqrt(20)

distance ≈ 4.5

So the distance between A and M is approximately 4.5 miles.

Next, let's calculate the distance between Mia's house (M) and Teresa's house (N). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((14 - 6)^2 + (16 - 12)^2)

distance = sqrt(64 + 16)

distance = sqrt(80)

distance ≈ 8.9

So the distance between M and N is approximately 8.9 miles.

Finally, let's calculate the distance between Teresa's house (N) and the arena. Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((16 - 10)^2 + (8 - 16)^2)

distance = sqrt(36 + 64)

distance = sqrt(100)

distance = 10

So the distance between N and the arena is exactly 10 miles.

Now we can add up the distances of the three segments to get the total distance of Alanah's trip to the arena:

total distance = 4.5 + 8.9 + 10

total distance ≈ 23.4

Therefore, the total distance of Alanah's trip to the arena is approximately 23.4 miles

To find the percent decrease, we first need to find the amount of the decrease, which is the difference between the regular price and the sale price:

$550 - $456.50 = $93.50

So the amount of the decrease is $93.50.

To find the percent decrease, we divide the amount of the decrease by the original price and then multiply by 100:

($93.50 / $550) x 100 ≈ 17.0%

Therefore, the percent decrease of the sale price from the regular price is approximately 17.0%.

The values are Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and range  IQR ≈ 0.5250 months.

The IQR for the average first-time walking age for groups of 33 people can be found as follows:

The standard deviation of the sample mean is given by:

σM = σ/√n = 2.2/√33 ≈ 0.3839

Using the standard normal distribution, the z-scores for the first and third quartiles are:

zQ1 = invNorm(0.25) ≈ -0.6745

zQ3 = invNorm(0.75) ≈ 0.6745

The corresponding sample means can be found using:

M = μ ± z(σM)

Where μ = 12, the population mean.

M1 = 12 - 0.6745(0.3839) ≈ 11.7375

M3 = 12 + 0.6745(0.3839) ≈ 12.2625

Therefore, the first quartile Q1 is approximately equal to 11.7375 months and the third quartile Q3 is approximately equal to 12.2625 months.

The IQR is given by:

IQR = Q3 - Q1 = 12.2625 - 11.7375 ≈ 0.5250 months.

Rounding to 4 decimal places gives Q1 ≈ 11.7375 months, Q3 ≈ 12.2625 months, and IQR ≈ 0.5250 months.

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Sara need 9/4 ounces of chopped nuts

Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces

The recipe feeds 6 people

The number of ounces of chopped nuts that Sara needs can be calculated as follows

13 1/2

= 27/2 ÷ 6

= 27/2 × 1/6

= 27/12

= 9/4

Hence Sara needs 9/4 ounces of chopped nuts for one serving

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The fractional equivalent of the repeating decimal is 15/99

What does division of fractions mean?

A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.

n = 0.1515...-------(1)

multiply n by 100 =10²

The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.

100n=15.15......--------(2)

Subtract (1) from (2)

100n=15.15...

n = 0.1515....

___________

99n=15

=> n=15/99

The fractional equivalent of the repeating decimal is 15/99

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Answer:

3000 x 1.02^10 = 3656.98.. = 3656 people

Answer:

See below

Step-by-step explanation:

The linear function is to be expressed in slope-intercept form:

y = mx + c

where:              

                           m = slope

                               = [tex]\frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]

           Select a pair of x and y coordinates of two points along this graph

e.g (0,1) and (5,0):

                          m = [tex]\frac{(0 - 1)Percent InDecimal}{(5 - 0) hour}[/tex]

                              = [tex]\frac{-1}{5}[/tex]

       ∴ slope = [tex]-\frac{1}{5}[/tex] = [tex]-0.2\frac{PercentInDecimal}{hour}[/tex]

  which means 0.2 × 100%= 20%

∴The slope indicates that the power decreases by 20% per hour

                          c = y-intercept:

   It is the y-value AT which the graph cuts or meets the y-axis. Its corresponding x-coordinate is 0. The y-intercept can be either read directly from the graph or calculated mathematically

       ∴y-intercept = 1

In this scenario, the y-intercept indicates the initial value or the value present in the beginning.
which means 1.0 × 100% = 100%
∴The y-intercept indicates that the battery is at 100% when you turn on the laptop.

∴Linear function relating y to x:

Substituting the values of m and c into the above stated equation:

     [tex]y = -\frac{1}{5}x + 1[/tex]

The x-intercept is the x-value at which the graph crosses or intersects the x-axis. It’s corresponding y-coordinate is zero.

     x-intercept = 5

In this scenario, the x-intercept indicates the point at which the final value is reached or achieved.

∴ The x-intercept indicates that the battery lasts 5 hours.

The battery power is at 75% = [tex]\frac{75}{100}[/tex] = 0.75 (expressed in decimal form. This means y = 0.75, which is to be substituted into the above derived linear function to solve for the corresponding value of x:

[tex]0.75 = -\frac{1}{5}(x) + 1[/tex]

Rearrange the equation to isolate x and make it the subject of the equation:

[tex]\frac{1}{5}x = 1 - 0.75[/tex]

[tex]\frac{1}{5}x = 0.25[/tex]

Cross-multiplication is applied:

[tex](1)(x) = (5)(0.25)[/tex]

x = 1.25 hours

∴The battery power is at 75% after 1.25 hours

The value of z is 27 when the value of w is 5, when w varies inversely with z.

The ratio of two proportional values at a constant value is the proportionality constant. When either the ratio or the product of two variables results in a constant, the connection between the two is proportional. The ratio between the two stated quantities affects the proportionality constant's value. Direct variation and inverse variation are two different sorts of this relationship.

Given that, w is 15 when z is 9, and w varies inversely with z.

This can be represented as:

w = k (1 /z)

where, k is the proportionality constant.

Substituting the value of w = 15 and z = 9 we have:

15 = k(1/9)

k = 15(9)

k = 135

Substituting the value of k and w = 5:

5 = 135(1/z)

z = 135/5

z = 27

Hence, the value of z is 27 when the value of w is 5.

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Answer:

5 = $ 5.25.    10= $ 6.50.   20= $9.00

Step-by-step explanation:

if this is wrong you can completely write me a really rude email or message or something

Answer:

To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.

Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.

Periodic Interest Rate = APR / Number of Billing Periods in a Year

Periodic Interest Rate = 21.99% / 12

Periodic Interest Rate = 1.8325%

Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.

Answer:

12 teams means 6 games each match day. Each team can play all the 11 other teams so 11 match days. So 66 games.