Write the equations of functions satisfying the given properties, in expanded form. a. Cubic polynomial, x-intercepts at - and -2, y-intercept at 10. 14 b. Rational function, x-intercepts at -2,-2, 1; y-intercept at - %; vertical asymptotes at 2, 3, -4; horizontal asymptote at 1.

Answer:

Step-by-step explanation:

Dbbdhdbjsbsjsbsbns

you can determine the weight of the concrete column in pounds = m * 2.20462 lbs/kg based on the given values of height (h), diameter (d), density (rho), and assuming a weight of 359 lbs (w) is not necessary for this calculation.

To find the weight of the concrete column in pounds, we can use the following steps:

1. Convert the diameter from millimeters to meters:

  d = 300 mm = 0.3 m

2. Calculate the cross-sectional area of the column:

  A = π * (d/2)^2

3. Calculate the volume of the column:

  V = A * h

4. Convert the density from milligrams per cubic meter to pounds per cubic meter:

  rho = 2.3 mg/m^3 = 2.3 * 10^-6 lbs/m^3

5. Calculate the mass of the column:

  m = V * rho

6. Convert the mass from kilograms to pounds:

  Weight (lbs) = m * 2.20462 lbs/kg

Using these calculations, you can determine the weight of the concrete column in pounds based on the given values of height (h), diameter (d), density (rho), and assuming a weight of 359 lbs (w) is not necessary for this calculation.

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Maximum two hours of gaming a day is healthy.

What is meaning of healthy?

Not just the absence of illness or infirmity, but also a complete condition of physical, mental, and social well-being, is what is meant by "health."

Additionally, twice as many parents of teen boys than teen girls report that their son plays video games daily. Teenage guys are also more likely to play video games for three or more hours.

The American Academy of Pediatrics advises limiting screen-based entertainment to no more than two hours each day. According to Radesky, parents should make a "media plan" that specifies how much time a kid can spend playing video games without having an impact on their behavior or their schoolwork.

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Answer:

Hello,

We don't need vw(x) !

\(w^{-1}(x)=\dfrac{x-1}{2}\)

Step-by-step explanation:

\(w(x)=2x+1=y\\\\2y+1=x \ exchanging \ x\ and\ y\\\\y=\dfrac{x-1}{2} \\\\w^{-1}(x)=\dfrac{x-1}{2}\)

Answer: 0.6039

Step-by-step explanation:

Answer:

60.39% = 0.6039

Step-by-step explanation:

To write it as a decimal we have to divide it by 100.

60.39% ÷ 100 = 0.6039

Answer:

39,160

Step-by-step explanation:

20x22=440 x89=39,160

If f(2) = 1 and the tangent line at x has slope (x − 1)ex2 − 2x. f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x).

To find f(x), we'll first integrate the given slope function to obtain the original function. The slope of the tangent line is given as (x - 1)e^(x^2 - 2x).

Let F'(x) = (x - 1)e^(x^2 - 2x). To find f(x), we need to integrate F'(x) with respect to x:

∫(x - 1)e^(x^2 - 2x) dx

Now, we can use substitution. Let u = x^2 - 2x, then du = (2x - 2) dx. Therefore, the integral becomes:

∫((u + 1)/2)e^u du

Now, we can integrate by parts. Let v = e^u, then dv = e^u du. Let w = (u + 1)/2, then dw = 1/2 du. Using integration by parts formula:

∫w dv = wv - ∫v dw

∫(u + 1)/2 * e^u du = ((u + 1)/2)e^u - ∫(1/2)e^u du

Now integrate the remaining part:

∫(1/2)e^u du = (1/2)e^u + C

Substituting back:

f(x) = ((x^2 - 2x + 1)/2)e^(x^2 - 2x) + C

Now, use the given condition f(2) = 1:

1 = ((2^2 - 2*2 + 1)/2)e^(2^2 - 2*2) + C

1 = (1)e^0 + C

C = 0

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Answer:

61 mph consistently

Step-by-step explanation:

4.5/0.5 = 9 = 30 min

274.5/9 = 30.5 = speed in half an hour.

30.5 x 2 = 61 = consistent speed for an hour.

Answer:

102 beads will be used for each necklace.

Step-by-step explanation:

3,264/32=102

Answer:

Total distance:

Step-by-step explanation:

Thus, the total distance can be calculated by adding the miles

i.e.

\(d=\:\frac{2}{5}+\frac{1}{3}\)

LCM of 5,3 is 15

   \(=\frac{6}{15}+\frac{5}{15}\)

\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}\)

  \(=\frac{6+5}{15}\)    

  \(=\frac{11}{15}\)

   \(=\:0.73\)  miles

Thus,

Total distance:

Answer: 1 tablespoon

Step-by-step explanation:

Answer:

63, 15, 90

Step-by-step explanation:

The length of IKE is 2x - 12.

A condition on a variable that is true for just one value of the variable is called an equation.

Since KITE is a kite, we know that KT = IT and KE = IE. Let's call the length of these diagonals d. Then we have:

KT + TI = d

KE + EI = d

Substituting in the given values, we get:

x + 6 + 2x = d

2x + IE = d

Solving for d in the first equation, we get:

3x + 6 = d

Substituting this into the second equation, we get:

2x + IE = 3x + 6

Solving for IE, we get:

IE = x + 6

Therefore, IKE is equal to:

IKE = IT - IE

IKE = (d - KT) - (x + 6)

IKE = (3x + 6 - x - 6) - (x + 6)

IKE = 2x - 12

So, the length of IKE is 2x - 12.

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It was mostly during C . Dry season

The “Cricket Season” is the period of days where cricket is played in a country when the pitches get dry and also this is the period where the domestic matches begin.

And this season varies with countries, in India it starts with the Ranjit Trophy, Sheffield Shield for Australia etc.

Cricket seasons are the times of the year when cricket is played. Because top-class cricket is almost always played outdoors, on uncovered pitches, and rain prevents play, the seasons in each country are geared to coincide with the driest months of the year

    The cricket season starts at the beginning of April and finishes at the end of September. As the time zones move around the planet, the seasons will differ in other countries.

In the UK,

professional games have occasionally taken place at the end of March but the season will normally begin at the start of April.

In India

The cricket season in India will usually begin in mid-September. Often, there are senior women’s games starting things off before men’s tournaments commence in October.

In Australia

Cricketers in Australia may start playing in September, especially in the west of the country which gets the warmer weather first.

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Answer:

5.root730 6.root329 8.root39

Step-by-step explanation:

use pythagoras law because its right angled triangle

hypautnse=root(side^2+side^2)

SORRY I DONT KNOW HOW TO TYPE ROOT SIGN ON HERE

Answer:

5. - 27.02

6. - 18.14

8. - 6.24

Step-by-step explanation:

Hello There!

Because each triangle is a right triangle we can solve for the missing side length using the Pythagorean Theorem

The Pythagorean theorem states that the sum of the two legs squared is equal to the hypotenuse squared

\(a^2+b^2=c^2\)

For number 5 we are given two legs so all we have to do is plug in the values

\(17^2+21^2=c^2\)

now we solve for c

\(17^2=289\\21^2=441\\441+289=730\\c^2=730\\\sqrt{c^2} =c\\\sqrt{730} =27.01851217\)

we're left with c = 27.01851217

are final step is to round to the nearest hundredth

So we can conclude that the missing side length is equal to 27.02

For number 6 we are given the hypotenuse and a leg

So this time we use this equation

\(a^2=c^2-b^2\)

where a^2 = missing leg

now we plug in the values and solve for a

\(a^2=27^2-20^2\\27^2=729\\20^2=400\\729=329\\a^2=329\\\sqrt{a^2} =a\\\sqrt{329} =18.13835715\)

we're left with a = 18.13835715

our final step is to round to the nearest hundredth

So we can conclude that missing side length is equal to 18.14

For number 8 we are given the hypotenuse and a leg

so once again we use this equation:

\(b^2=c^2-a^2\)

now we plug in the values and solve for x

\(b^2=8^2-5^2\\8^2=64\\5^2=25\\64-25=39\\b^2=39\\\sqrt{b^2} =b\\\sqrt{39} =6.244997998\)

we're left with b = 6.244997998

our final step is to round to the nearest hundredth

so we can conclude that the missing side length is equal to 6.24

About 15.87% of the attendance figures would be less than 3500.

About 0.62% of the attendance figures would be greater than 5000.

About 34.13% of the attendance figures would be between 3700 and 4300 each week.

The mean is the average of a set of numbers, while the standard deviation measures the spread of the data around the mean. The normal distribution is fully characterized by its mean and standard deviation. In this case, the mean attendance is 4000, and the standard deviation is 500.

To answer the first question, "What percentage of the attendance figures would be less than 3500?" we need to calculate the area under the curve to the left of 3500. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 15.87%.

To answer the second question, "What percentage of the attendance figures would be greater than 5000?" we need to calculate the area under the curve to the right of 5000. Again, we can use a standard normal distribution table or a calculator to find this area. The result is approximately 0.62%.

To answer the third question, "What percentage of the attendance figures would be between 3700 and 4300 each week?" we need to calculate the area under the curve between 3700 and 4300. We can use a standard normal distribution table or a calculator to find this area. The result is approximately 34.13%.

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Answer:

The radius of the hemisphere is 13.73 in.

Step-by-step explanation:

A hemisphere is exactly half of the sphere.

The volume of the hemisphere is, \(V=\frac{2}{3}\pi r^3\)

Where r is the radius of the hemisphere.

Given the volume of the hemisphere is \(V=2712.3\ in^3\)

Therefore, \(2712.3=\frac{2}{3}\pi r^3\)

⇒\(r^3=\frac{2712.3*3}{2\pi}\)

\(r=13.73\ in\)

Answer:

2.75 feet

Step-by-step explanation:

I did the problem with the given instructions, but it really should be 2.74 feet. Instead of dividing the circumference by 6.28, you should divide the circumference by pi, then by two.

Hope this helps! :)

Answer:

D

Step-by-step explanation:

pretty sure 360 is a complete turn so it would end up in the same spot

Answer:

-4,4

Step-by-step explanation:

PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction. The solution to the Expression (3^0 * 8^2)^-2 is 1/4096.

The expression (3^0 * 8^2)^-2, the order of operations, which is typically referred to as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Step 1: Simplify the exponent expressions within the parentheses:

(3^0 * 8^2) = (1 * 64) = 64

Step 2: Rewrite the expression with the simplified value:

(64)^-2

Step 3: Apply the exponent rule for a negative exponent:

(64)^-2 = 1 / (64)^2

Step 4: Evaluate the expression within the parentheses:

(64)^2 = 64 * 64 = 4096

Step 5: Rewrite the expression with the simplified value:

1 / 4096

Therefore, the solution to the expression (3^0 * 8^2)^-2 is 1/4096.

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James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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Answer:

None of them, 3x + 15 is correct.

Step-by-step explanation:

In order to apply the distributive properly correctively, we need to multiply everything in the parentheses. For an example, lets look at the given expression:

\(3(x+5)\)

We multiply everything in the parentheses by 3

\(3x+15\)

Looking at out choices, none of them uses the distributive property correctly.

Answer:

B. y = -1/3x + 1

Step-by-step explanation:

(look at attached picture)

The integral ∫ \((4x^6)^3\) dx, evaluated by making the appropriate substitution, is (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

To evaluate the integral ∫ \((4x^6)^3\) dx, we can make the appropriate substitution u = 4\(x^6\).

First, we need to find the derivative of u with respect to x, du/dx.

Taking the derivative of both sides, we get du/dx = 24\(x^5\).

Next, we rearrange the equation to solve for dx: dx = du / (24\(x^5\)).

Now, we substitute u = 4\(x^6\) and dx = du / (24\(x^5\)) into the integral:

∫ \((4x^6)^3\) dx = ∫ \(u^3\) (du / (24\(x^5\))).

Simplifying the integral, we have (1/24) ∫ (\(u^3\) / (\(x^5\))) du.

Since u = 4\(x^6\), we can rewrite the integral in terms of u only:

(1/24) ∫ (\(u^3\) / (\((u/4)^{(5/6)})\)) du.

Simplifying further, we have

(1/24) ∫ (\(u^3\) / (\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du

This becomes

(1/24) ∫ (\(u^3\) / ((\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du = (1/24) ∫ (\(u^3\) / (\(u^{(5/6)}\) × (\(4^{(-5/6)})\))) du

Now, we can integrate with respect to u:

(1/24) × [(\(u^{(4/3 + 1)}\) × \((4^{(-5/6)})\)) / (4/3 + 1)] + C

Simplifying further, we get

(3/168) × \(u^{(7/3)}\) × \((4^{(-5/6)})\) + C

Finally, substituting back u = 4\(x^6\), we have

(3/168) × \((4x^6)^{(7/3)}\) × \((4^{(-5/6)})\) + C.

This simplifies to (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

Therefore, the integral ∫ \((4x^6)^3\) dx, evaluated by making the appropriate substitution, is  (3/168) × \(4^{(11/6)}\) × \(x^{(7/2)}\) + C.

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Answer:

About 11.4

Step-by-step explanation:

There are 3.78541178 liters in a gallon.

Round that up to the nearest 100 and you get 3.8

Multiply 3.8 by 3.

You get 11.4

The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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Answer:

\(\boxed{\sf -14-4i}\)

Step-by-step explanation:

\(\sf (-2i)(2-7i)\)

Multiply -2i * 2-7i:-

\(\sf -2i\times 2-2(-7)i^2\)

i^2 is -1

\(\sf -2i\times 2-2(-7)(-1)\)

Now, do the multiplications.

Reorder the terms.

\(\sf -14-4i\)

____________________________________

The required negative function h(x) with a y-intercept at "-4" with one solution is x + 4

The y-intercept of an equation is the pint where the x-value of the function is 0, that is;

f(-4) = 0

Since the solution has one solution, hence it will be linear in nature

h(x) = x + 4

This gives the required negative function h(x) with a y-intercept at "-4" with one solution

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