factorize Factor 25x² - 16y²
​

A cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.

We can determine how much interior room a cylinder has by measuring its volume. The volume would be the same as how much material would fill the full can if you had one.

Volume of cylinder = π*r²*h

r is the radius and h is the height.

For given cylinder:

r = 4 ft and h = 9 ft

Volume of given cylinder = π*4²*9

Volume of given cylinder = 144π cu. ft.

Now, from the options:

As, its is clear from  formula of cylinder that there is a square of radius.

Thus,

take radius r = 3 ft  such that r² = 9 ft and height h = 4 ft.

These are the same dimensions as the given cylinder.

Thus, a cylinder with a radius of 3 ft and a height of 4 ft has the same volume as one with a radius of 4 ft and a height of 9 ft.

Know more about the cylinders

https://brainly.com/question/23935577

#SPJ1

Answer:

Equation: 7x + 8x = 180

x = 12

∠CBA = 84

∠CFH = 96

Step-by-step explanation:

We can see that ∠CBA = ∠CFE and ∠CBD = ∠CFH.

We know that the sums of two angles on a straight line are going to be equal to 180.

∠CBA = 7x

∠CFH = 8x

To find the value of x, we must do the following:

7x + 8x = 180

15x = 180

15x/15 = 180/15

x = 12

Now we just substitute to find the angle measures:

∠CBA = 7 · 12 = 84

∠ CFH = 8 · 12 = 96

Answer:

how u love me and u dont even kno me

Answer:

Thank you.

Step-by-step explanation:

I'll press thank you on your account. I'm 14 btw too. 15 in Jan.

Answer:

Step-by-step explanation:

Hello,

(a) Peter cycle at an average speed of x km/h

it means that he is doing x km in 1 hour

so to do 40 km he needs 40/x hour

(b) it means that he was doing x-5 km/h

so it took 40/(x-5) hour

(c) 1 hour 20 minutes correspond to 1+20/60=1+1/3=4/3 hour as 1 hour is 60 minutes

so we can write

40/(x-5)=40/x+4/3

\(<=> 3*40x=3*40(x-5)+4x(x-5) \ \ \ \text{multiply by 3x(x-5) both sides}\\<=> 120x =120x-600+4x^2-20x\\<=>4x^2-20x-600 = 0\ \ \ \text{divide by 4} \\<=> x^2-5x-150=0\)

(d)

\(x^2-5x-150=0\\<=> x^2+10x-15x-150=0\\<=> x(x+10)-15(x+10)=0\\<=> (x-15)(x+10)=0\\\\<=> x = 15 \ \ or \ \ x=-10\)

the speed is positive so we take the positive solution which is 15

the speed is 15 km/h

hope this helps

do not hesitate if you need more information

If this exact question is repeatedly deleted, it's probably because of the ambiguity of the given equation. I see two likely interpretations, for instance:

\(\dfrac{(5\times5)^k}{5^{-8}} = 5^3\)

or

\(\dfrac{5\times 5^k}{5^{-8}} = 5^3\)

If the first one is what you intended, then

\(\dfrac{(5\times5)^k}{5^{-8}} = \dfrac{(5^2)^k}{5^{-8}} = \dfrac{5^{2k}}{5^{-8}} = 5^{2k-(-8)} = 5^{2k+8} = 5^3\)

and it follows that

2k + 8 = 3   ==>   2k = -5   ==>   k = -5/2

If you meant the second one, then

\(\dfrac{5\times 5^k}{5^{-8}} = \dfrac{5^1\times5^k}{5^{-8}} = \dfrac{5^{k+1}}{5^{-8}} = 5^{k+1-(-8)} = 5^{k+9} = 5^3\)

which would give

k + 9 = 3   ==>   k = -6

And for all I know, you might have meant some other alternative... When you can, you should include a picture of your problem.

Answer:

15% 15%

Step-by-step explanation:

it was correct for me

The percent error of Li’s guess is 15%

"It is the absolute difference between an observed value and the actual value."

"It is the ratio of the absolute error of the measurement to the actual value."

"It is the relative error multiplied by 100."

For given example,

Li’s guess is 345 jelly beans.

observed value (E) = 345

The actual number of jelly beans is 300

actual value (A) = 300

So, the absolute error is,

Absolute error = |E - A|

                        = | 345 - 300|

                        = 45

Now, we find the relative error of Li's guess.

Relative error = 45 ÷ 300

Relative error = 0.15

The percent error is,

0.15 × 100 = 15%

Therefore, the percent error of Li’s guess is 15%

Learn more about the percent error here:

brainly.com/question/3670306

#SPJ2

Answer:

a. 45 b. 44  c. 30  d. 50 and e. 65

Step-by-step explanation:

divide. when you divide a fraction, flip it.  ex. 22 ÷ 1/2 would be 22× 2/1

Answer:

the first one is the answer is 45 miles , because 135 miles divided by 3 hours [180 minutes] equals to 0.75 , 180 minutes times 0.75 equals to 135 miles , 2 hours [120 minutes] times 0.75 equals to 90 miles and 1 hour [60minutes] times 0.75 equals to 45 miles.

Step-by-step explanation:

b. 44  c. 30  d. 50 and e. 65

Based on the given frequency distribution in the histogram, the shape of the distribution of water bills can be described as skewed right. Option C

In a skewed right distribution, the tail of the distribution extends to the right side, indicating that there are some higher values or outliers on that end.

In this case, we can observe that there are more residents with higher water bills (e.g., 13 residents with bills in the range of 200 to 225) compared to the lower bills (e.g., 1 resident with a bill in the range of 100 to 125). This indicates a right-skewed pattern.

Therefore, the correct answer is "skewed right."

Learn more about observation at https://brainly.com/question/2419635

#SPJ1

The equation r^2 = sin(2θ) can be rewritten as: r = ± √(sin(2θ))

Since r is always non-negative, we only need to consider the positive square root:

r = √(sin(2θ))

The shaded region is given by the area inside the curve r = √(sin(2θ)) and outside the curve r = 0. This region is symmetric about the polar axis, so we can find the area of one half and multiply by 2.

Using the formula for the area of a polar region, we have:

A = 2∫[0,π/4] 1/2 (r(θ))^2 dθ

Substituting r = √(sin(2θ)), we get:

A = 2∫[0,π/4] 1/2 sin(2θ) dθ

Using the identity sin(2θ) = 2sin(θ)cos(θ), we can simplify the integral:

A = 2∫[0,π/4] 1/2 (2sin(θ)cos(θ)) dθ

A = ∫[0,π/4] sin(θ)cos(θ) dθ

Using the double angle formula, we have:

A = 1/2 ∫[0,π/4] sin(2θ) dθ

Integrating with respect to θ, we get:

A = 1/4 [-cos(2θ)]|[0,π/4]

A = 1/4 (-cos(π/2) + cos(0))

A = 1/4 (0 + 1)

A = 1/4

Therefore, the area of the shaded region is 1/4 square units.

Learn more about Trigonometry here:- brainly.com/question/13729598

#SPJ11

To calculate the area of a shaded region defined by a polar curve, use the formula Area = 1/2 ∫ (from α to β) (\(r(\theta)^2\)) dθ. The polar function is the square root of the given function, and the boundaries of the shaded region mark limits of integration. Without those values, we can't provide a numerical answer.

The question asks us to calculate the area of a shaded region defined by the polar equation \(r^2\)=sin 2(theta). This equation falls under the category of a polar curve. To find the area of a region defined by a polar curve, we use the formula Area = 1/2 ∫ (from α to β) (\(r(\theta)^2\)) dθ. Here, r(θ) is the polar function (in this case, since \(r^2\) =\(sin^2(theta)\), r(θ) = sqrt(\(sin^2(theta)\))), and α and β are the boundaries of the shaded region.

Without knowing the exact values for α and β, we can't provide a numerical answer, but you would integrate the resulting equation from the lower bound to the upper bound. Before integrating, it is vital to ensure that the function is only taking positive values, otherwise, it could lead to miscalculations. Hence, it's important that when you square root sin2(theta), you use the absolute value of sin(theta).

https://brainly.com/question/32287400

#SPJ6

You can make a maximum of two tomato-cheese sandwiches. because you can only make as many tomato-cheese sandwiches as the number of cheese slices you have

To make a tomato-cheese sandwich, you need one tomato slice and one cheese slice. Since you have three tomato slices and two cheese slices, you are limited by the availability of cheese slices.

Therefore, you can only make as many tomato-cheese sandwiches as the number of cheese slices you have, which in this case is two.

The ingredient that limits the number of sandwiches you can make is the cheese slice. You have more tomato slices than cheese slices, so you cannot make more than two tomato-cheese sandwiches.

Even if you have extra tomato slices, you cannot make additional sandwiches because you do not have enough cheese slices to pair with them.

In summary, the number of tomato-cheese sandwiches you can make is determined by the ingredient with the lowest quantity,

which in this case is the cheese slice. Therefore, you can make a maximum of two tomato-cheese sandwiches.

To know more about number click here

brainly.com/question/28210925

#SPJ11

Answer:

34, 35, 36

Step-by-step explanation:

1st number = x

2nd number = x+1

3rd number = x+2

So the equation would be:

x+2(x+1)+(x+2)-7=133

x+2x+2+x+2-7=133

4x-3=133

4x=136

x=34

      Three consecutive numbers justifying the condition given in the statement will be 34, 35, 36.

Let three consecutive number are,

n, (n + 1), (n + 2)

First statement given,

" The sum of first number, twice the second number"

Expression for the statement → [n + 2(n + 1)]

Second statement → " 7 less than the third number"

Expression for the statement → (n + 2) - 7

Combine the expressions,

"The sum of first number, twice the second number and 7 less than the third number is 133"

Form the equation and simplify,

n + 2(n + 1) + (n + 2) - 7 = 133

n + 2n + 2 + n + 2 - 7 = 133

(n + 2n + n) + (2 + 2 - 7) = 133

4n - 3 = 144

4n = 136

n = 34

         Therefore, the numbers are,

                            1st number → n = 34

                            2nd number → (n + 1) = 35

                            3rd number → (n + 2) = 36

Learn more about the solution of equations here,

https://brainly.com/question/864749?referrer=searchResults

Answer:

yes

when the point is pugged into the equality, it works

Answer:

2/5

Step-by-step explanation:

3/5 + 1/9

= 12+6/45

= 18/45 which is 2/5

Answer:

it is D

Step-by-step explanation:

The sum of the first 200 multiples of 3 is 60,300(B).

To find the sum of the first 200 multiples of 3, we need to calculate the arithmetic series. The formula for the sum of an arithmetic series is Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. In this case, the first term (a) is 3, and the last term (l) is 3 * 200 = 600.

Plugging these values into the formula, we get Sn = (200/2)(3 + 600) = 100 * 603 = 60,300. Thus, the sum of the first 200 multiples of 3 is 60,300(C).

For more questions like Series click the link below:

https://brainly.com/question/28167344

#SPJ11

Answer:

\(x^{2}\) - 2x - 24

Step-by-step explanation:

(x + 9)(x - 2) - 9x - 6

\(x^{2}\) - 2x + 9x - 18 - 9x - 6          Multiply.

\(x^{2}\) - 2x - 24                              Combine the like terms.

By applying the binomial distribution formula, it can be concluded that the probability of seeing at least one albino squirrel is 0.095.

Combination is the number of ways to choose a sample of r elements from a set of n distinct objects where order does not matter and replacements are not allowed.

C(n,r) = n! / (r! (n-r)!)   where

n = number of samples

r = number of selected samples

The binomial distribution formula is used to find the probability of the specific outcome in a discrete distribution.

P(X) = C(n,r) * \(p^{r}\) * \(q^{n-r}\) where:

C = combination value

p = probability of success on a single trial

q = probability of failure on a single trial

If n is the number of the squirrel, p is the probability of seeing albino squirrels and q is the probability of seeing non-albino squirrels, then:

n = 10000

p = 1/100000

q = 1 - 1/100000 = 99999/100000

The probability of seeing at least one albino squirrel:

= P (X ≥ 1)

= 1 - P(X< 1)

= 1 - P(X=0)

= 1 - C(10000,0) * (1/10000)⁰ * (99999/100000)¹⁰⁰⁰⁰⁻⁰

= 1 - (1 * 1 * (99999/100000)¹⁰⁰⁰⁰)

= 1 - 0.904836

= 0. 095164

≈ 0.095

Thus the probability of seeing at least one albino squirrel is 0.095.

To learn more about binomial distribution formula click here: brainly.com/question/29125646

#SPJ4

The points that lies on the same line are (-3, 12), and, (-1, 4).

Here, we have,

The given coordinate points are (-2, 8) and (5,-20).

Here, slope (m)= 8+20/-2-5

= 28/-7

=-4

Substitute m= -4 and (x, y)=(-2,8) in y=mx+c, we get

8 = 8+c

or, c = 0

So, the equation of a line is y= -4 x

Now,

(-6, -2) in the given equation is -2=-4 (-6)

-2≠ 24

(-3, 12)  in the given equation is y= -4 x

12 = 12

(4, 16) in the given equation is y= -4 x

16 ≠ -16

(0, 6) in the given equation is y= -4 x

6 ≠ 0

(-1, 4) in the given equation is y= -4 x

4 = 4

(7,5) in the given equation is y= -4 x

5 ≠ -28

Therefore, the points that lies on the same line are (-3, 12), and, (-1, 4).

To learn more about the equation of a line visit:

brainly.com/question/2564656.

#SPJ1

Answer:

C

Step-by-step explanation:

Answer:

(a/b)*(b/a)=1.

Step-by-step explanation:

Answer:

\(\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}\)

Step-by-step explanation:

Given equation:

\(y=y^2x+2 \cos(x)\)

To find the derivative of the given equation, use implicit differentiation.

Add d/dx in front of each term:

\(\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x+\dfrac{d}{dx}\:2 \cos(x)\)

Differentiate terms in x only (and constant terms) with respect to x:

\(\dfrac{d}{dx}\:y =\dfrac{d}{dx}\:y^2x-2 \sin(x)\)

Use the chain rule to differentiate terms in y only:

(in practice this means to differentiate with respect to y then place dy/dx on the end)

\(\dfrac{dy}{dx}\: =\dfrac{d}{dx}\:y^2x-2 \sin(x)\)

Use the product rule on the term in x and y:

\(\textsf{let }u=y^2 \implies \dfrac{du}{dx}=2y \dfrac{dy}{dx}\)

\(\textsf{let }v=x \implies \dfrac{dv}{dx}=1\)

\(\implies u\dfrac{dv}{dx}+v\dfrac{du}{dx}=y^2+2xy \dfrac{dy}{dx}\)

Therefore:

\(\dfrac{dy}{dx} =y^2+2xy \dfrac{dy}{dx}-2 \sin(x)\)

Rearrange to make dy/dx the subject:

\(\dfrac{dy}{dx}-2xy \dfrac{dy}{dx} =y^2-2 \sin(x)\)

\(\dfrac{dy}{dx}(1-2xy)=y^2-2 \sin(x)\)

\(\dfrac{dy}{dx}=\dfrac{y^2-2 \sin(x)}{1-2xy}\)

If d represents how many dozens of eggs were ordered, then the expression that represents the number of eggs that were ordered is 12d. Therefore, if we order d dozen of eggs, we will have 12 * d eggs.

For such more question on dozens

https://brainly.com/question/1344677

#SPJ8

The functions in ascending order of asymptotic growth are 2 log(n + 1000), n log3 27, 256log16 n, n.

The function 2 log(n + 1000) has the slowest growth as its growth rate is logarithmic, meaning it increases very slowly.

The function n log3 27 has a slightly faster growth rate as it is a logarithmic function with a larger base than the first function.

The function 256log16 n has an even faster growth rate as it is a logarithmic function with a larger base than the previous two functions. Finally, the function n has the fastest growth rate as it is a linear function, meaning it grows at a constant rate.

To understand why the growth rates of these functions differ, we need to look at their mathematical definitions. The function 2 log(n + 1000) grows very slowly because logarithmic functions grow very slowly as the input variable increases. The function n log3 27 has a slightly faster growth rate as it is a logarithmic function with a larger base than the first function. The function 256log16 n grows faster than the previous two functions because it has a larger base in its logarithm. Finally, the function n grows at a constant rate, meaning its growth rate is the fastest among the four functions.

Learn more about logarithmic function here:

https://brainly.com/question/30339782

#SPJ11

Y=4x-1

The equation of a line is:

Y=mx+c

We are told that the slope is 4 which is also gradient, meaning that M=4

Now we are left with:

Y=4x+c

There are two ways to get C:

1. We know that C represents the y-intercept so immediately we can conclude that C=-1

2. You can work it out by substituting the coordinate for the X and Y value:

-1=4(0)+c

-1=C

So in conclusion, the equation of the line is:

Y=4x-1

We are given the 95% confidence interval for the population mean of the change in AHE between 1992 and 2008 as [4.393, 9227].

This means that if we were to take multiple random samples and compute the confidence intervals for the change in AHE using the same method, approximately 95% of those intervals would contain the true population mean.

CI = X ± z* (s/√n)

where X is the sample mean, s is the sample standard deviation, n is the sample size, and z* is the critical value of the standard normal distribution for the desired confidence level.

However, we can conclude that the confidence interval has a lower bound of 4.393 and an upper bound of 9227, which means that we are 95% confident that the population mean of the change in AHE between 1992 and 2008 falls between these two values.

To learn more about “mean” refer to the https://brainly.com/question/1136789

#SPJ11

Answer:

(233.8436 ; 271.0564)

Yes

Step-by-step explanation:

Given :

Sample mean, xbar = 252.45

Sample standard deviation, s = 74.50

Sample size, n = 64

α = 0.05

The confidence interval :

Mean ± margin of error

Margin of Error = tα/2 * s/√n

df = n - 1 = 64 - 1 = 63

t(α/2, df = 63) = 1.998

Margin of Error = 1.998 * 74.50/√64

Margin of Error = 18.6064

The confidence interval :

252.45 ± 18.6064

(233.8436 ; 271.0564)

Comparing the confidence interval value and the mean value reported by the American Automobile Association ;it can be concluded that the mean reported by the American Automobile Association differ from the mean spent at Niagara Fall as 215.60 falls below the confidence interval.

The confidence interval  is (233.8436 ; 271.0564).

We have given that the,

Sample mean, x bar = 252.45

Sample standard deviation, s = 74.50

Sample size, n = 64

α = 0.05

The confidance interval is Mean ± margin of error.

\(Margin of Error = t\alpha /2 \times s/\sqrt{n}\)

\(df = n - 1 \\df= 64 - 1 \\df= 63\)

\(t(\alpha/2, df = 63) = 1.998\)

\(Margin of Error = 1.998 \times 74.50/\sqrt64\)

Margin of Error = 18.6064

The confidence interval  is given by,

252.45 ± 18.6064

Therefore we get the confidence interval  is (233.8436 ; 271.0564)

Comparing the confidence interval value and the mean value reported by the American Automobile Association ;it can be concluded that the mean reported by the American Automobile Association differ from the mean spent at Niagara Fall as 215.60 falls below the confidence interval.

To learn more about the confidence interval visit:

https://brainly.com/question/15712887

The multiplication using Tape Diagram is $44.8

A tape diagram is a pictorial model resembling a tape, that is used to assist with the calculation of addition, subtraction, multiplication, etc.

Given: 7 × $6.4

7 × $6.4 means $6.4 in 7 places. Thus, we can write that:

7 × $6.4 = $6.4 + $6.4 + $6.4 + $6.4 + $6.4 + $6.4 + $6.4 = $44.8

Check the attached picture for the Tape Diagram

Therefore, the multiplication 7×$6.4 gives $44.8

Learn more about Tape Diagram on:

https://brainly.com/question/2604125

#SPJ1

===================================================

Explanation:

The combination of angle x and the 93 degree angle forms x+93. This obtuse angle is congruent to 130 because these two angles are alternate interior angles and because line L is parallel to line M.

So,

x+93 = 130

x+93-93 = 130-93 .... subtracting 93 from both sides

x = 37

Answer:

true

Step-by-step explanation:

have a good day

Answer:

true? i don't kn ow the question