The diagonal of a rectangular swimming pool measures 29 yards. If the length of the pool is

25 yards, which measurement is closest to the width of the pool?

A. 4 yards

B. 14.70 yards

C. 38.29 yards

D. 54 yards

Answer:

scaled up 2 times

Step-by-step explanation:

Answer: pink

Step-by-step explanation:

The content of your cover letter should be brief and structured. Avoid lengthy repetition of information covered in your CV. Unlike a CV, it is acceptable to write a cover letter in the first person. Your letter should address the relevant contact, whose name often appears in the job advertisement

Answer: 45.43%

Step-by-step explanation:

Answer:

  45.43%

Step-by-step explanation:

Any time you want to express a number as a percentage, you can multiply it by 100%.

  0.4543 × 100% = 45.43%

To find the coordinates of the centroid for the region bounded by the curves y=16x, y=9/x, y=0, and x=10, we need to calculate the x-coordinate and y-coordinate of the centroid separately. First, let's find the x-coordinate of the centroid.

We can use the formula: x-bar = (1/A) ∫[a,b] xf(x) dx, where A is the area of the region. The intersection points of the curves y=16x and y=9/x can be found by setting the equations equal to each other: 16x=9/x.

Solving this equation, we get x=±√(9/16)=±3/4. Since the region is bounded by x=10, we take the positive value x=3/4. To find the area A, we integrate the difference between the curves: A=∫[3/4,10] (16x-9/x) dx. Evaluating this integral, we find A=400-9ln(10).

Now we can calculate the x-coordinate of the centroid: x-bar=(1/A) ∫[3/4,10] x(16x-9/x) dx. Simplifying the integral and evaluating it, we get x-bar=(8160-36ln(10))/(400-9ln(10)). Next, let's find the y-coordinate of the centroid.

Since the region is symmetric about the x-axis, the y-coordinate of the centroid will be y-bar=0. Therefore, the exact coordinates of the centroid for the given region are: (x-bar, y-bar)=((8160-36ln(10))/(400-9ln(10)), 0).

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The exponential equation of 4 = ln x is \(e^{4} = x\\\)

The ln equation

ln x = 4

The ln equation is written in the form

\(ln_{b} x = y\)

According to the logarithm rule

\(b^{y} = x\)

condition of the rule are x > 0, b > 0 and b ≠ 0

Here b = e , y = 4 and x = x

Natural log ln have base e  

\(e^{4} = x\)

About logarithm - A logarithm is the opposite of a power. In other words, if we take a logarithm of a number, we undo an exponentiation. The logarithmic function log x is the inverse function of the exponential function .

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The equations is inconsistent and has infinitely many solutions. The solution set can be written as {(x, (33-22z)/11, z) : x, z E R}.

This is a system of three linear equations with three variables, x, y, and z. The system can be represented in matrix form as AX = B where A is the coefficient matrix, X is the variable matrix, and B is the constant matrix.

A = |1 -3 -8| |2 5 6| |3 2 -2|

X = |x| |y| |z|

B = |-10| |13| | 3|

To determine the number of solutions for this system, we can use Gaussian elimination to reduce the augmented matrix [A|B] to row echelon form.

R2 - 2R1 -> R2

R3 - 3R1 -> R3

A = |1 -3 -8| |0 11 22| |0 11 22|

X = |x| |y| |z|

B = |-10| |33| |33|

Now we can see that there are only two non-zero rows in the coefficient matrix A. This means that there are only two leading variables, which are y and z. The variable x is a free variable since it does not lead any row.

We can express the solutions in terms of the free variable x:

y = (33-22z)/11

x = x

z = z

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Answer:

0.125

Step-by-step explanation:

(5 divided by 8) - ((1 divided by 4) x 2) = 0.125

Answer:

1/8

Step-by-step explanation:

Because of BEDMAS, we first multiply, then subtract.

We multiply 1/4 and 2, getting 2/4, or 1/2.

Then, our expression becomes 5/8 - 1/2.

We can evaluate:

5/8 - 1/2 = 5/8 - 4/8 and simplify, getting 1/8.

The answer is A

because its the only table that has the multiples of 4 and 3

Answer:

its number 2

Step-by-step explanation:

Answer:

The inequality that models the situation for her to have money to save is

7L² > 3(200L - L²)

On simplifying and solving,

L > 60 meters

Step-by-step explanation:

The length of her farm = L meters

The farm where she grows avocados is of square dimension

Area of the farm = L × L = L²

The piece of land is 200 m wide.

Total area of the piece of land = 200 × L = (200L) m²

If the area of her farm = L²

Area of the side where she lives will be

(Total area of the land) - (Area of the farm)

= (200L - L²)

= L(200 - L)

Every week, Riley spends $3 per square meter on the area where she lives, and earns $7 per square meter from the area where she grows avocados.

Total amount she earns from the side she grows the avocados = 7 × L² = 7L²

Total amount she spends on the side where she lives = 3 × (200L - L²) = 3(200L - L²)

For her to save money, the amount she earns must be greater than the amount she spends, hence the inequality had to be

(Amount she earns) > (Amount she spends)

7L² > 3(200L - L²)

To simplify,

7L² > 3L(200 - L)

Since L is always positive, we can divide both sides by L

7L > 3(200 - L)

7L > 600 - 3L

10L > 600

L > 60 meters

Hope this Helps!!!

Answer:

Answer is in attached image.

Answer:

11 yards.

Step-by-step explanation:

A cylinder's volume is π r² h

Where π = 3.14

r = 4 (since radius is half of diameter)

v (volume) = 552.64

So in this case we are solving for h, height.

So rewrite:

552.64 = (3.14)(4)^2(h)

So now we solve:

1. Evaluate exponent:

552.64 = (3.14)(16)(h)

2. Multiply

552.64 = 50.24h

3. Divide to get h by itself

552.64 / 50.24 = 50.24 / 50.24 (h)

11 = h

Hence the height of the cylinder is 11 yards.

Also I’ve attached below pictures to help further prove. The 10.99 is rounded up to 11.

The average speed if the airplane when it travels 3850 km in 5.5 hours is 700 km per hours.

To calculate the average speed of the airplane, we can use the formula:

Average Speed = Distance Traveled / Time Taken

In this case, the distance traveled by the airplane is 3850 km, and the time taken is 5.5 hours. Let's substitute these values into the formula

Average Speed = 3850 km / 5.5 hours

Calculating the average speed

Average Speed = 700 km/h

Therefore, the average speed of the airplane from New York to Los Angeles is 700 km per hours.

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The total distance travelled by Lisa in a day is found to be 10.24 miles.

Pythagoras (born 570 BC) developed a theorem known as the Pythagorean Theorem, which is exclusively applicable to right triangles.

According to the Pythagorean Theorem, a right triangle's hypotenuse square is equal to the sum of its other two sides. The side opposite the right angle is known as the hypotenuse.

Pythagoras theorem:

a² + b² = c²

Given case:

Here,

a = b = 3 units

Put the values;

3² + 3² = c²

2*9 = c²

c = 3√2

c = 4.24

Total distance = 4.24+ 3 + 3

Total distance = 10.24 miles

Thus, the total distance travelled by Lisa in a day is found to be 10.24 miles.

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Answer:

1 less

Step-by-step explanation:

3x² − 7x +9 if x=2 would equal 7

2x² + 4x − 8 if x=2 would equal 8

The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear equation or function is given as ;

y = mx + b

The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

The slope associated with (-8,4) and (4,5) will be as,

m = (5 - 4)/(4 + 8) = 1/12

Thus, y = (1/12)x + b

Put (4,5)

5 = (1/12)4 + b

b = 5 - 1/3

b = 14/3

Thus, y = (1/12)x + 14/3

Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".

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Answer:

a

Step-by-step explanation:

agree that AOB + BOC = AOC, right?

AOC = 25 = (4x - 15) + (2x + 10) solve for x first

25 = 6x - 5, now add 5 to both sides

30 = 6x   divide both sides by 6, so x = 5

now substitute: BOC = 2x+10 = 10 + 10 = 20

                          AOB = 4x - 15 = 20 - 15 = 5

The diameter of the circle with the circle equation (x+8)² + (y+4)² = 256 is 32 units

The equation of the circle is given as:

(x+8)² + (y+4)² = 256

As a general rule, a circle equation is represented as:

(x - a)² + (y - b)² = r²

Where r is the radius.

By comparing both equations, we have:

r² = 256

Take the square roots of both sides

r = 16

Multiply by 2 to get the diameter

d = 32

Hence, the diameter of the circle is 32 units

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Answer:

Hi!

I think your answer will have two forms

Point form: (-2,1)

Equation form: x = -2 and y = 1

I hope this helped you :)

The geometric series is divergent and The sum of the series is: S = e/3/(1-1/3) = e/2

The given series is: ∑ (en/(4n-1)), n=1 to infinity

To determine if this series is convergent or divergent, we can use the ratio test:

= lim n→∞ \(|(en+1/(4(n+1)-1))/(en/(4n-1))|\)

= lim n→∞ \(|en+1(4n-1)/en(4n+3)|\)

= lim n→∞ \(|(4n-1)/(4n+3)|\)

Since e is a positive constant, it does not affect the convergence or divergence of the series. Taking the limit, we get:

lim n→∞ \(|(4n-1)/(4n+3)|\)

= 1

Since the limit is equal to 1, the ratio test is inconclusive. We need to use another test to determine the convergence or divergence of the series.

Next, we can try the root test:

= lim n→∞ \((en/(4n-1))^(1/n)\)

= lim n→∞ \(e^(1/n) / (4-1/n)^(1/n)\)

= 1/4

Since the limit is less than 1, the series converges by the root test.

To find the sum of the series, we can use the formula for the sum of a convergent geometric series:

S = a/(1-r)

where a is the first term of the series and r is the common ratio.

The first term is e/(4-1) = e/3. The common ratio is e/(4n-1) multiplied by its inverse, which is (4n-1)/e. Simplifying, we get:

r = \((4n-1)/(3(4n)) = (1-1/(4n))/(3/4)\)

Taking the limit as n approaches infinity, we get:

lim n→∞ r = 1/3

Therefore, the sum of the series is:  S = e/3/(1-1/3) = e/2

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Answer:

The number is 13

Step-by-step explanation:

the equation:

\(2x-6=20\)

The solution.

\(2x=20+6\)

\(x=\frac{26}{2} =13\)

Hope this helps

The Policeman’s rate of change is $10 per hour and the firefighter's rate of change is $10 per hour

The Policeman’s rate of change

From the question, we have the following parameters that can be used in our computation:

The graph

On the line of the policeman, we have the following point

(x, y) = (4, 40)

So, the rate of change is

Rate = y/x

This gives

Rate = 40/4

Evaluate

Rate = 10

The firefighter's rate of change

On the line of the firefighters, we have the following point

(x, y) = (4, 60)

So, the rate of change is

Rate = y/x

This gives

Rate = 60/4

Evaluate

Rate = 15

Hence, the rate is $15 per hour

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The correct answer is: Yes, relation Q is a function,because there is exactly one y-value for every x-value.

To determine whether the given relation Q is a function, we need to check if each x-value is associated with a unique y-value. If there is any x-value that corresponds to multiple y-values, then the relation is not a function.

Let's examine the ordered pairs in relation Q: (3, -2), (-3, 1), (-2, -2), (1, -3).

We can see that each x-value in Q is associated with a unique y-value:

For x = 3, the y-value is -2.

For x = -3, the y-value is 1.

For x = -2, the y-value is -2.

For x = 1, the y-value is -3.

Since each x-value is paired with a unique y-value in relation Q, we can conclude that Q is a function.

In a function, every input (x-value) maps to a single output (y-value). If there were any repeated x-values with different y-values in the relation, it would indicate a violation of this rule and Q would not be a function. However, in this case, all the x-values have distinct y-values, satisfying the criteria for a function.

It's worth noting that we can also visualize this relation on a coordinate plane and check if there are any vertical lines that intersect the graph at more than one point. If there are no such lines, it confirms that the relation is a function.

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Answer:

1.71539657854

Step-by-step explanation:

Answer:

C for part a                  D for part b

Step-by-step explanation:

Pretty sure this is correct. Sorry if wrong. Brainliest always appreciated

Answer:

Stretches vertically by 2, shifts right by 1

Step-by-step explanation:

changes to y are direct, but you have to take the inverse for changes to x. This is because for a given value of y, with x-1, you would have to add one to x to make it the same value(to get the same point before the transformation)

The final value of x when (x = 1 ; x<10; x ),in this case will be 9.

This is because the initial value of x is set to 1, and the condition for the loop is that x must be less than 10.

Therefore, the loop will continue to execute as long as x is less than 10, and will stop when x is equal to 10. However, since the final value of x is not included in the loop, the final value of x will be one less than the stopping value, or 9.

Steps include:-
1. Set the initial value of x to 1: x = 1
2. Check if x is less than 10: x<10
3. If x is less than 10, execute the loop and increase the value of x by 1: x++
4. Repeat steps 2 and 3 until x is no longer less than 10
5. The final value of x will be one less than the stopping value, or 9.

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Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

To simplify 1 + sec(t) / 1 + cos(t), we need to use the identity sec(t) = 1 / cos(t).
So, 1 + sec(t) / 1 + cos(t) becomes 1 + 1/cos(t) / 1 + cos(t).
Next, we'll simplify the expression by multiplying the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).
Finally, we can simplify this expression further by factoring out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)).
The cos(t) + 1 in the numerator cancels with the cos(t) + 1 in the denominator, leaving us with 1/cos(t) or sec(t).
To simplify 1 + sec(t) / 1 + cos(t), we use the identity sec(t) = 1 / cos(t). Then, we multiply the numerator and denominator by cos(t), which gives us (cos(t) + 1) / (cos^2(t) + cos(t)).

Therefore, Finally, we factor out a cos(t) from the denominator to get (cos(t) + 1) / (cos(t)(cos(t) + 1)), which simplifies to 1/cos(t) or sec(t).

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The number of gummy bears that Ella started with is equal to 24 gummy bears.

The number of candy that Maggie bought is equal to $6.

The statement "A number is at most six" is x ≤ 6.

The statement "Twenty is no less than a number" is 20 ≥ x.

The solution to the inequality b - 6 > -8 is equal to b > -2.

The solution to the inequality 3 ≤ x/-6 is equal to x ≥ -18.

The solution to the inequality -180 < -12r is equal to r > 15.

The solution to the inequality b - 6 > -8 is equal to y ≥ 3.

All values of m that make the inequality true are:

C. -14

D. -12.

E. -10.

Assuming the number of gummy bears that Ella started with is represented by the variable x, a linear equation which model this situation is given by:

1/2 × x + 13 = 25

x/2 = 25 - 13

x/2 = 12

x = 12 × 2

x = 24 gummy bears.

For the number of candy that Maggie bought, we have the following:

5.50 + 1.75x = 16

1.75x = 16 - 5.50

1.75x = 10.5

x = 10.5/1.75

x = $6.

Next, we would evaluate the given inequality:

-2m + 7 ≤ 35

-2(-18) + 7 ≤ 35

43 ≤ 35 (False).

-2(-16) + 7 ≤ 35

39 ≤ 35 (False).

-2(-14) + 7 ≤ 35

35 ≤ 35 (True).

-2(-12) + 7 ≤ 35

31 ≤ 35 (True).

-2(-10) + 7 ≤ 35

27 ≤ 35 (True).

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