Write the quadratic equation whose roots are 6 and 2 with leading coefficient of 5.

Answer:

A seizure and a half

Step-by-step explanation:

Answer:

495962981439552000

The answer is A, rhombus.

Let \(f(x) = x^2+4x+1\). If \(f^{-1}(x)\) is the inverse of \(f(x)\), then

\(f\left(f^{-1}(x)\right) = x\)

We're told that \(f(x)\) has a domain of x ≥ -2, so the above can only be valid for \(f^{-1}(x)\ge-2\).

Evaluate the left side in this equation and solve for the inverse :

\(f^{-1}(x)^2 + 4f^{-1}(x) + 1 = x \\\\ f^{-1}(x)^2 + 4f^{-1}(x) + 4 = x + 3 \\\\ \left(f^{-1}(x) + 2\right)^2 = x + 3 \\\\\sqrt{\left(f^{-1}(x)+2\right)^2} = \sqrt{x+3} \\\\ \left|f^{-1}(x) + 2\right| = \sqrt{x+3}\)

Since \(f^{-1}(x)\ge-2\), or \(f^{-1}(x)+2\ge0\), by definition of absolute value we have

\(\left|f^{-1}(x)+2\right| = f^{-1}(x)+2\)

Then it follows that

\(f^{-1}(x) + 2 = \sqrt{x+3} \implies \boxed{f^{-1}(x) = \sqrt{x+3}-2}\)

We can integrate this S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

We have,

To find the surface area of the revolution about the x-axis of the function f(x) = 5√x over the interval (1.1 to 4.4), we can use the formula for the surface area of revolution:

S = ∫(a to b) 2πy√(1 + (f'(x))²) dx

In this case,

f(x) = 5√x, so f'(x) = (d/dx)(5√x) = 5/(2√x).

Let's calculate the surface area:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + (5/(2√x)²) dx

Simplifying the expression inside the integral:

S = ∫(1.1 to 4.4) x 2π(5√x)√(1 + 25/(4x)) dx

Next, we can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

To find the surface area of revolution about the x-axis of the function

f(x) = 5√x over the interval (1.1 to 4.4), we need to evaluate the integral:

S = ∫(1.1 to 4.4) 2π(5√x)√(1 + 25/(4x)) dx

Let's calculate the integral:

S = 2π ∫(1.1 to 4.4) (5√x)√(1 + 25/(4x)) dx

To simplify the calculation, let's simplify the expression inside the integral first:

S = 2π ∫(1.1 to 4.4) (5√x)√((4x + 25)/(4x)) dx

Next, we can distribute the square root and simplify further:

S = 2π ∫(1.1 to 4.4) (5√(4x + 25))/(2√x) dx

Thus,

We can integrate this expression over the given interval (1.1 to 4.4) to find the surface area.

We can evaluate the integral using numerical methods or a calculator to find the final answer.

Learn more about the surface area of revolutions here:

https://brainly.com/question/32268747

#SPJ1

Answer:

just a

Step-by-step explanation:

because if you do anything times by zero, it is zero.

Answer:

A^6

Step-by-step explanation:

This is the answer bc A^0 would stay the same so you would adding the exponents when you multiply therefore it's A^6

If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

Learn more about volume here:https://brainly.com/question/27710307

#SPJ1

Answer: y=3/4x + 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope (m) = \(\frac{3}{4}\)

y-intercept (c) = 8

Writing in slope intercept form , y = mx +c

y = \(\frac{3x}{4}\) + 8

Hope it helps:)

Answer:

3

Step-by-step explanation:

Because C is 1 and D is 4, so 4-1=3.

The closest to the maximum number of cups the punch bowl can hold is 30

The given parameters are:

1 cup = 15 cubic inches

Diameter of bowl, d = 12 inches

The radius is the half of the diameter.

So, we have:

r = 6

The volume of the bowl is then calculated using:

\(V = \frac{2}{3}\pi r^3\)

This gives

\(V = \frac{2}{3}\pi * 6^3\)

Evaluate

V = 452.16

The maximum number of cups is then calculated using:

Cups = 452.16/15

Evaluate

Cups = 30.1444

Approximate

Cups = 30

Hence, the closest to the maximum number of cups the punch bowl can hold is 30

Read more about volumes at:

https://brainly.com/question/1972490

#SPJ1

The maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

A special kind οf relatiοn knοwn as a functiοn is οne in which each input has precisely οne οutput. In οther wοrds, the functiοn generates exactly οne value fοr each input value. Because οne is mapped tο twο different values, the abοve graph depicts a relatiοnship rather than a functiοn. Hοwever, if οne were instead mapped tο a single value, the relatiοnship mentiοned abοve wοuld becοme a functiοn.

Additiοnally, οutput values can be equal tο input values. We knοw that the square rοοt functiοn is an increasing functiοn, which means that the value οf the functiοn increases as the input value increases.

Therefοre, tο find the maximum value οf the functiοn, we need tο find the maximum value οf h.

Assuming that the lighthοuse is οn the hοrizοn, which is apprοximately 3 miles away, we can use the Pythagοrean theοrem tο find the height οf the lighthοuse:

\(h^2 = (3)^2 - (15)^2h^2 = 9 - 225h^2 = -216\)

Since we cannοt take the square rοοt οf a negative number, there is nο real height fοr the lighthοuse that wοuld make it visible frοm a ship 15 feet abοve the water level.

Therefοre, the maximum distance that the sailοr can see frοm the deck οf the ship is 0 miles.

Learn more about function, by the following link

https://brainly.com/question/25638609

#SPJ1

The answer is x>−1/5 or x<1/5

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

To find the line equation perpendicular to the line equation y = -5x + 3, we need to know that the product of the slopes of two linear equation must be = -1. Then, the slope of the line perpendicular to y = -5x + 3 is:

m1 = -5x ---> m2 = 1/5, so m1 * m2 = -5 * 1/5 = -1.

As we can see, the new slope is the inverse and the reciprocal of the original slope.

Then, we have that passes through the point (5, 5). For this, we can use the Point-Slope Form of the line:

Where, x1 = 5, and y1 = 5. Hence:

Therefore, the line is:

We will solve as follows:

We have that the interest rate is 6.6%:

Here we have P the monthly payment, Pv is the Present value, R is the periodic interest rate(APR/n) n is the total number of interest periods, so:

So, the monthly payment is approximately $155.09.

And the total interest paid is given by:

Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

Learn more about Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

PLATO

i got it correct :)

Answer:

Step-by-step explanation:

To find the median, we need to find the middle value when the data is arranged in increasing order. We can use the cumulative probability to do this:

Number of Shows Streamed Probability Cumulative Probability

0 0.095 0.095

1 0.203 0.298

2 0.326 0.624

3 0.187 0.811

Since the cumulative probability for 2 is the smallest value greater than 0.5, the median is 2. Therefore, the median number of TV shows streamed is 2.

The histogram appears to have a roughly symmetric shape, which supports the assumption that the distribution is approximately normal.

Answer:

24 : 15 : 20

Step-by-step explanation:

express ratios in fractional form and express b and c in terms of a

\(\frac{a}{b}\) = \(\frac{8}{5}\) ( cross- multiply )

8b = 5a ( divide both sides by 8 )

b = \(\frac{5}{8}\) a

also

\(\frac{b}{c}\) = \(\frac{3}{4}\) ( cross- multiply )

3c = 4b ( divide both sides by 3 )

c = \(\frac{4}{3}\) b = \(\frac{4}{3}\) × \(\frac{5}{8}\) a = \(\frac{5}{6}\) a

Then

a : b : c

= a : \(\frac{5}{8}\) a : \(\frac{5}{6}\) a ( multiply each part by 24, the LCM of 8 and 6 )

= 24a : 15a : 20a ( divide each part by a )

= 24 : 15 : 20 ← in simplest form

Step-by-step explanation:

\(\dfrac{x^2-4}{x-2}\)

Apply identity a²-b² = (a-b)(a+b)

So, it will be

\(\dfrac{(x-2)(x+2)}{x-2}\)

Where x-2 gets cancelled from numerator and denominator.

Hence, x+2 is the answer.

Hope it helps :)

Answer:

-300

Step-by-step explanation:

because is in the negative and is a number bigger than 23 but in negative.

Answer:

Read the steps

Step-by-step explanation:

In the first term: 6x^3

leading coeffecient: 6

exponent: 3

In the second term: -4x

leading coeffecient: -4

exponent: 1

The coefficient and exponents are -

\(6x^{3}\) :   coefficient = 6      exponent = 3

\(-4x\) :  coefficient = 4      exponent = 1

We have -

f(x) = \(6x^{3} - 4x\)

We have identify the coefficient and the exponent in the f(x).

Here, the exponent is \(a\). Then -

a = 2x - 4

For x = 5

a = 2 x 5 - 4

a = 6

According to the question -

f(x) = \(6x^{3} - 4x\)

for \(6x^{3}\) :   coefficient = 6     exponent = 3

for \(-4x\) :  coefficient = 4      exponent = 1

Hence, the coefficient and exponents are -

\(6x^{3}\) :   coefficient = 6      exponent = 3

\(-4x\) :  coefficient = 4      exponent = 1

To solve more questions on identifying coefficients and exponents, visit the link below -

https://brainly.com/question/4322167

#SPJ2

(i) \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

(ii) \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

For λ = 2.5, the function f(x) will be continuous at x = 0.

Given the function is,

f(x) = 1.5, when x = 0

    = 1 -2 sin x, when x < π/4

    = 1 + 2 sin x, when x > π/4

    = 1 + (sin λx/sin 5x)

Now,

\(\lim_{x \to \pi/3}\) f(x) = \(\lim_{x \to \pi/3}\) (1 + 2 sin x) [Since, π/3 > π/4]

                    = 1 + 2 sin (π/3)

                    = 1 + 2√3/2 = 1 + √3

Hence, \(\lim_{x \to \pi/3}\) f(x) = 1 + √3.

Now left hand limit is,

\(\lim_{x \to \frac{\pi^+}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^+}{4}}\) (1 + 2sin x) = 1 +2 sin(π/4) = 1 + 2*(1/√2) = 1 + √2

and right hand limit is,

\(\lim_{x \to \frac{\pi^-}{4}}\) f(x) = \(\lim_{x \to \frac{\pi^-}{4}}\) (1 - 2 sin x) = 1 - 2*(1/√2) = 1 - √2

Since left hand limit and right hand limit are not equal so value of \(\lim_{x \to \frac{\pi}{4}} f(x)\) does not exist.

\(\lim_{x \to 0}\) f(x) = \(\lim_{x \to 0}\) (1 + (sin λx/sin 5x)) = 1 + \(\lim_{x \to 0}\) ((sin λx/λx)/(sin 5x/5x))*(λ/5) = 1 + λ/5

Since f(x) is continuous at x = 0.

So, \(\lim_{x \to 0}\) f(x) = f(0)

1 + λ/5 = 1.5

λ/5 = 1.5 - 1 = 0.5

λ = 2.5

Hence the value of λ will be 2.5.

To know more about continuous here

https://brainly.com/question/27761372

#SPJ1

Solution,

radius=21 cm

Circumference of circle=2 pi r

=2*3.142*21

=131.964 cm

hope it helps

Good luck on your assignment

The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

For more such questions on Adjacent numbers:

https://brainly.com/question/28207765

#SPJ8

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

The 90 % confidence interval estimate for the population mean using the student's t-distribution is [ 87.137 , 92.863 ] .

Given :

Suppose that the times to complete an obstacle course are normally distributed with an unknown mean and standard deviation. A random sample of 33 course times is taken and gives a sample mean of 90 seconds and a sample standard deviation of 10 seconds.

a 90% confidence interval estimate for the population mean using the student's t-distribution.round the final answers to two decimal places.

Confidence interval :

CI = X ± Z * s / √n

= 90  ±  1.6449 * 10 / √33

= 90 ± 2.863

= [ 87.137 , 92.863 ]

Learn more about the confidence interval here:

https://brainly.com/question/24131141

#SPJ4

Full question:

is in the image uploaded.

The only matrix that is certainly symmetric is a)\((a^2 - b^2).\)

We know that a matrix A is symmetric if it is equal to its transpose, that is \(A = A^T.\)

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

We can write the transpose of this matrix as

\((a^2 - b^2)^T = (a^2)^T - (b^2)^T = a^2 - b^2\), which is equal to the original matrix. Therefore, this matrix is symmetric.

b) (A+B)(A-B)

Expanding this expression, we get \((A+B)(A-B) = A^2 - AB + BA - B^2.\)

Taking the transpose of this, we get \((A^2)^T - (AB)^T + (BA)^T - (B^2)^T = A^2 - BA + AB - B^2.\)

Since AB and BA may not be equal, we cannot say for certain that this matrix is symmetric.

c) ABA

Taking the transpose of this matrix, we get\((ABA)^T = A^T B^T A^T\). Since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

d) ABAB

Taking the transpose of this matrix, we get \((ABAB)^T = B^T A^T B^T A^T\). Again, since \(A^T and B^T\) may not commute, we cannot say for certain that this matrix is symmetric.

Therefore, the only matrix that is certainly symmetric is a) \((a^2 - b^2).\)

for such more question on matrix

https://brainly.com/question/25581637

#SPJ11