a chinese restaurant has a large goldfish pond. suppose that an inlet pipe and a hose together can fill the pond in 7 hours. the inlet pipe alone can complete the job in one hour less time than the hose alone. find the time that the hose can complete the job alone and the time that the inlet pipe can complete the job alone.

\(\stackrel{ \textit{multiplying the 1st equation by 9} }{\begin{array}{lllllll} 9(~x&+y&=& ~~ 0)\\\\ -9x&-5y&=&-24 \end{array}}\hspace{5em} \begin{array}{llll} ~~ 9x&+9y&=&0\\\\ -9x&-5y&=&-24\\\cline{1-4} ~~0&-4y&=&-24 \end{array} \\\\[-0.35em] ~\dotfill\\\\ -4y=-24\implies y=\cfrac{-24}{-4}\implies \boxed{y=6} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{x+(6)=0\implies \boxed{x=-6}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (-6~~,~~6)~\hfill\)

Answer:

uhhhh... i thinks its D or A

:\(\implies\) perimeter (∆HFM) = HM+FM+HF

:\(\implies\) 51 = 2x+5+x+8+3x+2

:\(\implies\) 51 = 6x+15

:\(\implies\) 36 = 6x

:\(\implies\) x = 6 units.

in ∆HFM,

in ∆KFM,

Since, all the sides of one triangle does not correspond to the other, these traingles are not congruent.

Answer:

.55

Step-by-step explanation:

Divide the 2 numbers

sum of first n even nos =n(n+1)

sum of first n odd nos=n²

So

Simplify the numerator

Simplify the denominator

Sum of first 100 even nos

Sum of first 100 odd nos

So

The equation yields as

Answer:

\(\sf E=\dfrac{x^2 \cdot x^4 \cdot x^6 \cdot x^8 ... 100\:factors}{x \cdot x^3 \cdot x^5 \cdot x^7 ... 100\:factors}=x^{100}\)

Step-by-step explanation:

Given:

\(\sf E=\dfrac{x^2 \cdot x^4 \cdot x^6 \cdot x^8 ...}{x \cdot x^3 \cdot x^5 \cdot x^7 ... }\)

As:

\(\sf E=\dfrac{x^2 \cdot x^4 \cdot x^6 \cdot x^8 \cdot ... }{x \cdot x^3 \cdot x^5 \cdot x^7 \cdot ... }=\dfrac{x^2}{x^1} \cdot \dfrac{x^4}{x^3} \cdot \dfrac{x^6}{x^5} \cdot \dfrac{x^8}{x^7} \cdot ...}\)

Apply the exponent rule  \(\sf \dfrac{a^b}{a^c}=a^{b-c}\)

\(\begin{aligned}\sf \implies \dfrac{x^2}{x^1} \cdot \dfrac{x^4}{x^3} \cdot \dfrac{x^6}{x^5} \cdot \dfrac{x^8}{x^7} \cdot... & = \sf x^{(2-1)} \cdot x^{(4-3)} \cdot x^{(6-5)} \cdot x^{(8-7)} \cdot ...\\ & = \sf x^1 \cdot x^1 \cdot x^1 \cdot x^1 \cdot ...\end{aligned}\)

As there are 100 factors, then \(\sf x^1\) is multiplied by itself 100 times ⇒ \(\sf x^{100}\)

Therefore:

\(\sf E=\dfrac{x^2 \cdot x^4 \cdot x^6 \cdot x^8 ... 100\:factors}{x \cdot x^3 \cdot x^5 \cdot x^7 ... 100\:factors}=x^{100}\)

This question is incomplete because the options are missing. Here are the options:

A. - 4 = 5x

B. -4 = x

C. -4 + x = 0

D. -4 + 5x = 0

The correct next line of the solution is A. -4 = 5x

An equation is:

According to the above, it can be inferred that the correct answer is option A. because it expresses the correct values according to the operations that have been carried out in the previous lines.

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Answer:

so if they walked in the same speed then how does kayla walk 6 feet and daniela walk 12 feet and where is the graph to label your thing so buddy you got to mention these things so we can answer your quest

Step-by-step explanation:

The value of the function f(x) = 2x/(2x + 3).

A function is defined as a relationship between a set of inputs that each have one output.

Now, as per the question, the functions are give as;

h(x) = (2x + 3)/x

g(x) = 2/x

And, g(f (x) ) = h(x) =  (2x + 3)/x  ......(equation 1)

To estimate the value of f (x); Substitute x for f(x)

g(f (x) ) = 2/f (x)     ......(equation 2)

Equation (equation 1 and 2).

2/f (x) =  (2x + 3)/x

f (x) = 2x/ (2x + 3)

Thus, the value of the function f (x) = 2x/ (2x + 3).

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The correct question is-

The function h (x) = StartFraction 2 (x + 3) Over x EndFraction is a result of the composition (g compose f) (x). If g (x) = StartFraction 2 over x EndFraction, what is f(x)?

The solution to the inequality expression is w <= 18.75

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

225 is no less than 12 times a number w.

When this is represented as an expression, we have

225 >= 12w

Divide both sides by 12

So, we have

18.75 >= w

Rewrite as

w <= 18.75

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Answer:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Step-by-step explanation:

Angle 1: Same-side interior angle of Line 1

Angle 2: Same-side interior angle of Line 2

We know that the difference between the angles is 50 degrees. Since the angles are supplementary, we can write the equation:

Angle 1 + Angle 2 = 180

Now, we need to express the difference between the angles in terms of Angle 1 or Angle 2. We can choose either angle, so let's express it in terms of Angle 1:

Angle 1 - Angle 2 = 50

We can rewrite this equation as:

Angle 1 = 50 + Angle 2

Now substitute this expression for Angle 1 into the first equation:

(50 + Angle 2) + Angle 2 = 180

Combine like terms:

2Angle 2 + 50 = 180

Subtract 50 from both sides:

2Angle 2 = 130

Divide by 2:

Angle 2 = 65

Now substitute this value back into the equation for Angle 1:

Angle 1 = 50 + Angle 2

Angle 1 = 50 + 65

Angle 1 = 115

Therefore, the angles are as follows:

Angle 1 = 115 degrees

Angle 2 = 65 degrees

Answer:

Step-by-step explanation:

gnag  dsewhqjhnqrhjwqkhjqrkhwq

In the given solution, we started by calculating LHS of the given equation which is (y)² + 4y². For that, we first squared the term 'y' and got (y)². Next, we multiplied 2 with y and squared it to get (2y)².

The given equation is y = a sin(2x) - b cos(2x) We need to prove that (y)² + 4y² = 4(a² + b²). Now let's calculate LHS(y)² + 4y²=(y)² + (2y)²

= (a sin(2x) - b cos(2x))² + 4[a sin(2x) - b cos(2x)]²
= [(a sin(2x))² + (b cos(2x))² - 2ab sin(2x) cos(2x)] + 4[(a sin(2x))² + (b cos(2x))² - 2ab sin(2x) cos(2x)]

= (a² + b²)(sin²(2x) + cos²(2x)) + 2ab cos(4x) + 4(a² + b²)(sin²(2x) + cos²(2x)) - 8ab sin²(2x)cos²(2x)

= (a² + b²) + 2ab cos(4x) + 4(a² + b²) - 8ab (sin(2x) cos(2x))²

= 5(a² + b²) - 8ab [sin(4x)/2]²= 5(a² + b²) - 2a² sin²(2x) - 2b² cos²(2x) .

Now let's calculate RHS 4(a² + b²) = 4(a² + b²)(sin²(2x) + cos²(2x))

= 4(a² + b²) - 8ab (sin²(2x) cos²(2x))

Now LHS = RHS, Hence Proved! Therefore, (y)² + 4y² = 4(a² + b²) is the required proof. In this problem, we are given a trigonometric equation y = a sin(2x) - b cos(2x).

And we are required to prove that (y)² + 4y² = 4(a² + b²). In the given solution, we started by calculating LHS of the given equation which is (y)² + 4y². For that, we first squared the term 'y' and got (y)². Next, we multiplied 2 with y and squared it to get (2y)². Then we added both of these terms to get (y)² + 4y².Then we substituted y with the given equation a sin(2x) - b cos(2x). After that, we used the identity (a² + b²) (sin²θ + cos²θ) = a² + b² to simplify the equation. Further, we used the identity sin(2θ) cos(2θ) = (sin(4θ))/2 to simplify the equation further. Finally, we got an equation of LHS which was in terms of a, b and trigonometric functions of x. Next, we calculated RHS of the equation which is 4(a² + b²). And by simplifying it using the same identity as LHS, we got an equation of RHS which was also in terms of a, b and trigonometric functions of x.

Thus, we have proved that (y)² + 4y² = 4(a² + b²).

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The missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

Statement 1: line l is parallel to line m

Reason: Given

Statement 2: \(\angle 2 \cong \angle 6\)

Reason: Corresponding Angles (both angles occupy the same corner, hence they correspond to each other. Corresponding angles have the same measure).

Statement 3: \(\angle 4 \cong \angle 2\)

Reason: Vertical angles (both angles are directly opposite each other as they share the same point, which makes them vertical angles. Vertical angles have equal measure).

Statement 4: \(\angle 6\cong \angle 4\)

Reason: Alternate Interior Angles (applying the transitive property which says if a = b, and b = c, then a = c, therefore, since \(\angle 2 \cong \angle 6, $ and $ \angle 4 \cong \angle 2, $ then $ \angle 6 \cong \angle 4\))

In conclusion, the missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

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Answer:

A. yes B. no C. no D. yes

Step-by-step explanation:

ur welcome luv

The height of the oak tree in front of Igor's castle is approximately 57.27 ft. To find the height of the oak tree, we can use the principle of similar triangles.

The height of the tree can be determined by comparing the ratio of the height of Igor to the distance between Igor and the mirror with the ratio of the height of the tree to the distance between the mirror and the tree.

Let's represent the height of the oak tree as 'h'. According to the problem, Igor's eye height is 4.5 ft, and he is 5.5 ft away from the center of the mirror. The mirror is placed 70 ft from the tree.

Using the similar triangles concept, we can set up the following proportion:

(height of Igor) / (distance between Igor and mirror) = (height of tree) / (distance between mirror and tree)

Plugging in the given values, we have:

4.5 ft / 5.5 ft = h / 70 ft

Solving this proportion, we find:

(4.5 ft * 70 ft) / 5.5 ft = h.

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Two samples can have the same mean but different standard deviations due to the spread of data around the mean. Standard deviation is a measure of how much the data values differ from the mean. The greater the deviation of the data points from the mean, the greater the standard deviation.

Two samples can have the same mean but different standard deviations because standard deviation is a measure of the spread of data around the mean. If the data values are tightly clustered around the mean, the standard deviation will be small. If the data values are spread out around the mean, the standard deviation will be large. Therefore, two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample.

Two samples can have the same mean but different standard deviations because the spread of data around the mean can be different for each sample. For example, consider two samples of test scores. Sample A has a mean score of 80 and a standard deviation of 5. Sample B has a mean score of 80 and a standard deviation of 10. The scores in Sample B have more variability than the scores in Sample A.In a bar graph, the means of the two samples can be represented by two bars with the same height. The standard deviations of the two samples can be represented by error bars on each bar. The error bars show the variability of the data in each sample. The length of the error bars for Sample B would be longer than the length of the error bars for Sample A.

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Answer:

answer 105

Step-by-step explanation:

3x5=15

than do 15x7 u will get 105

Answer: 25.6

Step-by-step explanation: Have an Amazing Day :)

Answer:

25.6 this will be the answer

Step-by-step explanation:

Hope it helps

Answer:

\( {x}^{2} = - 20y \\ y = - \frac{1}{20} {x}^{2} \\ { \tt{y = 4a {x}^{2} }} \\ a = - \frac{1}{5} \\ \\ { \tt{focus = (0, \: - 5)}}\)

The requried coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).

A parabola is a cross-section cut out of the cone and represented by an equation y = 4ax².

The standard form of the equation of a parabola is (y - k) = (1 / 4p)(x - h)², where (h, k) is the vertex and p is the distance from the vertex to the focus. We can convert the given equation x² = -20y into this standard form by completing the square:

x² = -20y

x² / (-20) = y

x² / (-20) + 0 = y + 0

(x - 0)² = -20(y - 0)

Comparing this equation to the standard form, we can see that the vertex is at (h, k) = (0, 0), and that 4p = -20, so p = -5/2.

Since the focus is a distance of p below the vertex, the focus is at (h, k - p) = (0, -5/2), which is the same as (0, -2.5).

Therefore, the coordinates of the focus of the parabola x² = -20y are (0, -2.5), which corresponds to the option (0, -5).

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The value of  (x - µ) / σ is the z factor.

We have:

x is the random number

µ is the mean

σ  is the standard deviation,

Now,

we need to evaluate, (x - µ) / σ

(x - µ) / σ = z factor

The Z factor is computed by dividing the dynamic range by the separation band (i.e., the difference between the sample mean and the control mean).

The difference in a value's z-score between it and the set mean is measured in standard deviations. By deducting the value from the mean and dividing the result by the standard deviation, you may determine it.

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The best measure of center to determine which bus typically has the faster travel time is: A. Bus 47, with a median of 16.

In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

For Bus 47, the median is given by;

4,6,14,28,10,10,12,12,18,18,22,22,16,16,16

Median of Bus 47 = 16

Mean of Bus 47 = 15.

For Bus 14, the median is given by;

10,16,20,28,8,8,14,14,18,18,18

Median of Bus 14 = 16.

Mean of Bus 14 = 16

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Answer:

≈ 1.13

Step-by-step explanation:

To solve this equation, we can start by simplifying the left-hand side using the laws of exponents. We have:

2(1/49)^(r-2) = 2^(1-2) * (1/49)^(r-2) = (1/2^2) * (49^-(r-2)) = (1/4) * (49^-(r-2))

Now we can substitute this expression into the original equation and simplify further:

2(1/49)^(r-2) = 14

(1/4) * (49^-(r-2)) = 14

49^-(r-2) = 56

To isolate the variable on one side of the equation, we can take the logarithm of both sides with base 49:

log49(49^-(r-2)) = log49(56)

-(r-2) = log49(56)

r - 2 = -log49(56)

r = 2 - log49(56)

Therefore, the solution to the equation is:

r = 2 - log49(56) ≈ 1.13

Answer:

540 inches per hour!!

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

2- 4x

= *9

If f(x)=2x²-5x-3 g(x)=2x²+5x+2 then (f/g)(x) = (x - 3) / (x + 2).

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find (f/g)(x), we need to divide f(x) by g(x) as follows:

f(x) = 2x² - 5x - 3

g(x) = 2x² + 5x + 2

f(x) / g(x) = (2x² - 5x - 3) / (2x² + 5x + 2)

To simplify this expression, we can factor the numerator and denominator:

f(x) / g(x) = [(2x + 1)(x - 3)] / [(2x + 1)(x + 2)]

Now, we can cancel out the common factor of (2x + 1) from both the numerator and denominator:

f(x) / g(x) = (x - 3) / (x + 2)

Therefore, (f/g)(x) = (x - 3) / (x + 2).

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Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

The solution is given as follows;7. x² - 12x + y² + 6y = - 9.

We start by grouping the x and y terms separately, then completing the square by adding half of the coefficient of the respective variable and squaring the result. x² - 12x + y² + 6y = - 9(x² - 12x + __) + (y² + 6y + __) = - 9 + __ + __

Now, we'll fill in the blanks in the parentheses so that the trinomials are perfect squares: (x² - 12x + 36) + (y² + 6y + 9) = - 9 + 36 + 9.

This simplifies to: (x - 6)² + (y + 3)² = 36.

The center of the circle is (6, −3), and its radius is 6.9. x² + y² + 14x - 20y - 20 = 0.

First, we group the x terms and the y terms separately:x² + 14x + y² - 20y = 20.

Now, we'll complete the square in both x and y. x² + 14x + y² - 20y = 20(x² + 14x + __) + (y² - 20y + __) = 20 + __ + __.

We'll fill in the blanks so that the trinomials are perfect squares.

To find the terms to add, we take half of the coefficient of the variable and square it. (x² + 14x + 49) + (y² - 20y + 100) = 20 + 49 + 100

Simplifying, we get (x + 7)² + (y - 10)² = 169.

The center of the circle is (-7, 10), and its radius is 13.x - 2x + y + 3/2y = -1

We first rearrange the terms. x - 2x + y + 3/2y = -1-x - 1/2y = -1

We then complete the square in x and y as follows. x - 2x + y + 3/2y = -1(x - 1) - (1/2)(y + 2) = -1/2(x - 1)² - 1/4(y + 2)² = 1/2

The center of the circle is (1, -2) and its radius is 1/2.8. - 3x² - 3y² + 27y + 61 = 0

We rearrange and group the terms. - 3x² - 3y² + 27y = -61

We then complete the square. - 3x² - 3(y² - 9y + 81/4) + 27(81/4) = -61 - 3(81/4)(x² + (y - 9/2)² = 405/4

The center of the circle is (0, 9) and its radius is 3/2.10. x² + y² - 7x - 3y - 1 = 0

We rearrange and group the terms. x² - 7x + y² - 3y = 1

We then complete the square. x² - 7x + 49/4 + y² - 3y + 9/4 = 1 + 49/4 + 9/4(x - 7/2)² + (y - 3/2)² = 25/4

The center of the circle is (7/2, 3/2), and its radius is 5/2.12. 4x² - 16x + 4y² + 16 = 0

We rearrange and group the terms. 4x² - 16x + 4y² = -16

We then complete the square. 4(x² - 4x + 4) + 4y² = 0(x - 2)² + y² = 1

The center of the circle is (2, 0), and its radius is 1.

Completing the square is a method used to turn quadratic expressions in standard form into perfect squares. It’s often used to find the center and radius of circles.

Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

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The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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The expression that can be used to convert 80 US dollars (USD) to Australian dollars (AUD) is:

80 USD × 1.0343 AUD / 1 USD

Since 80 USD is the amount of USD we want to convert and (1.0343 AUD / 1 USD) is the exchange rate between USD and AUD.

To convert 80 USD to AUD, we can use the following expression:

80 USD × 1.0343 AUD / 1 USD

Thus, 82.74 AUD is the amount of AUD you will receive after the conversion.

Therefore, the expression that can be used to convert 80 US dollars (USD) to Australian dollars (AUD) is 80 USD × 1.0343 AUD / 1 USD

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