The carrying capacity of a drain pipe is directly proportional to the area of its cross- section. If a cylindrical drain pipe can carry 36 litres per second, determine the percentage increase in the diameter of the drain pipe necessary to enable it to carry 60 litres per second.​

The value of slope of line is,

⇒ m = - 1

We have to given that,

Two points on the line are (- 4, 5) and (- 7, 8).

Now, We know that,

Slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is,

m = (y₂ - y₁) / (x₂ - x₁)

Here, Two points on the line are (- 4, 5) and (- 7, 8).

Hence, Slope is,

m = (8 - 5) / (- 7 + 4)

m = 3 / - 3

m = - 1

Therefore, The value of slope of line is,

⇒ m = - 1

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Answer:x = {-4, 4}

explanation:

Line AB is congruent to line CD , proved.

The proof that line AB is congruent to line CD is determined as follows;

If line AB ≅ CD, then will have the following to be true;

Let angle A = x

The value of angle C will be equal to x (alternate angles are equal)

Let angle B = y

The value of angle D will be equal to y (alternate angles are equal)

Let angle m∠AEB = z

The value of m∠DEC will be equal to z (vertical opposite angles are equal).

So line AB is congruent to line CD , proved.

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Answer:

To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.

One way to do this is to use the formula for the future value of an annuity, which is:

FV = Pmt x ((1 + r)^n - 1) / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.

First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:

r = 7% / 12 = 0.00583

Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.

Finally, we can plug in the values into the formula for the future value of an annuity:

FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583

FV ≈ $141,535.15

Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.

Step-by-step explanation:

To calculate the cost of the mortgage, we need to find the total amount that Sonya will pay back over the 25-year period.

One way to do this is to use the formula for the future value of an annuity, which is:

FV = Pmt x ((1 + r)^n - 1) / r

where FV is the future value, Pmt is the periodic payment, r is the interest rate per period, and n is the number of periods. In this case, we want to find the total future value of the mortgage payments over 25 years, so we can set Pmt equal to the monthly mortgage payment, r equal to the monthly interest rate, and n equal to the total number of months in 25 years.

First, let's convert the annual interest rate to a monthly interest rate by dividing by 12:

r = 7% / 12 = 0.00583

Next, we can use an online mortgage calculator or a spreadsheet to find the monthly mortgage payment based on the loan amount, interest rate, and term. For a $65,000 mortgage at 7% for 25 years, the monthly payment is approximately $471.78.

Finally, we can plug in the values into the formula for the future value of an annuity:

FV = $471.78 x ((1 + 0.00583)^300 - 1) / 0.00583

FV ≈ $141,535.15

Therefore, the total cost of the mortgage over 25 years is approximately $141,535.15. This includes the original loan amount of $65,000 plus the interest that accumulates over the 25-year period.

The two figures are congruent because a reflection and a translation are used to map Figure 1 onto Figure 2.

The angle corresponding to angle M is given as follows: <S.

Examples of transformations are given as follows:

For this problem, the two transformations are:

These two are rigid motions, keeping the side lengths constant, hence the figures are congruent.

Angle S is corresponding to angle M, as they are the angles at the "pointed" vertex of the figure.

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3/5 is the fraction between the numbers 1/3 and 87/100

A number line is a graphical representation of numbers that can be used to understand and visualize numerical relationships. It is a straight line that extends infinitely in both directions and is usually drawn horizontally.

Writing the fractions as percentage:

1/3 * 100 = 33.3%

87/100 = 87%

This shows that the required number must be between 33.3% and 87%

From the given options:

3/5 * 100 = 3 * 20

3/5 * 100 = 60%

Hence the value in between the numbers 1/3 and 87/100 is 3/5

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Answer: -5/4

Step-by-step explanation:

To solve this problem, we need to use Charles's law, which states that, at constant pressure, the volume of a sample of gas is directly proportional to its temperature.

The law can be expressed mathematically as:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{ \frac{V_1}{T_1}=\frac{V_2}{T_2} } \end{gathered}$} }[/tex]

Where:

Now we obtain the data to continue solving:

Now, we will convert the temperatures to Kelvin:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_1=220 \ ^{\circ}C+273=493 \ Kelvin} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{T_2=40 \ ^{\circ}C+273= 313 \ Kelvin} \end{gathered}$} }[/tex]

Now we solve for V₂:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{V_1T_2}{T_1 } } \end{gathered}$} }[/tex]

Where:

Now, we substitute the values in the formula:

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2=\frac{(0.5 \ L\times313\not{k} )}{493\not{k} } } \end{gathered}$} }[/tex]

[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{V_2\approx0.32 \ Liters } \end{gathered}$} }}[/tex]

Answer:

a)

Step-by-step explanation:

the function is 11x6=66+13=79x¹=79

hope it helps

Answer:

sin( 3pi/4 ) = -√2/2

So, B.

Answer: when the value of the dollar decreases, also when demand is high.

Step-by-step explanation: economics

The values of Composite function are:

f(g(-1)) = 20

h[g(4)] = 40

g[f(5)] = -37

f[h(-4)] = -44

g[g(7)] = 35

h[f(1/2)] = -8

We have, f(x) = -2x, g(x) = 3x-7 and h(x)= 2x² -10

f(g(-1)):

First, substitute -1 into g(x): g(-1) = 3(-1) - 7 = -3 - 7 = -10.

Next, substitute the result into f(x): f(-10) = -2(-10) = 20.

Therefore, f(g(-1)) = 20.

h[g(4)]:

First, substitute 4 into g(x): g(4) = 3(4) - 7 = 12 - 7 = 5.

Next, substitute the result into h(x): h(5) = 2(5^2) - 10 = 2(25) - 10 = 50 - 10 = 40.

Therefore, h[g(4)] = 40.

g[f(5)]:

First, substitute 5 into f(x): f(5) = -2(5) = -10.

Next, substitute the result into g(x): g(-10) = 3(-10) - 7 = -30 - 7 = -37.

Therefore, g[f(5)] = -37.

f[h(-4)]:

First, substitute -4 into h(x): h(-4) = 2(-4²) - 10 = 2(16) - 10 = 32 - 10 = 22.

Next, substitute the result into f(x): f(22) = -2(22) = -44.

Therefore, f[h(-4)] = -44.

g[g(7)]:

First, substitute 7 into g(x): g(7) = 3(7) - 7 = 21 - 7 = 14.

Next, substitute the result into g(x) again: g(14) = 3(14) - 7 = 42 - 7 = 35.

Therefore, g[g(7)] = 35.

h[f(1/2)]:

First, substitute 1/2 into f(x): f(1/2) = -2(1/2) = -1.

Next, substitute the result into h(x): h(-1) = 2(-1²) - 10 = 2(1) - 10 = 2 - 10 = -8.

Therefore, h[f(1/2)] = -8.

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Answer: 6 years

Step-by-step explanation:

75,000*15% = 11,250

11,250*6 = 67,500

75,000-67,500 = 7500

7500 is worth less than 15,000

5 years would have been 18,750; more than 15,000

I did some research and found that for quadratic equations in the form of [tex]y = ax^2 + bx + c[/tex], you can find the minimum value using the equation [tex]$\text{minimum} = c - \frac{b^2}{4a}[/tex] .

We can substitute our given values in the formula and get the following: [tex]$37 = 118 - \frac{b^2}{4}$[/tex] .

We can go ahead and solve it, and get the following:

[tex]-81 = -\frac{b^{2}}{4}[/tex]

[tex]324 = b^2[/tex]

[tex]\pm{18} = b[/tex]

Now we know that the equation is either [tex]$f(x)=x^2+18x+118$[/tex]  or [tex]$f(x)=x^2-18x+118$[/tex] .

We will solve using both equations, but we will solve the one with a positive b-value first. Substituting [tex]f(x)[/tex] for [tex]$37$[/tex], the minimum or y-value of the vertex, we can now solve for the x-value of the vertex.

We have:

[tex]37 = x^2+18x+118[/tex]

[tex]0=x^2+18x+81[/tex]

[tex]0=(x+9)^2[/tex]

[tex]x+9=0\\x=-9[/tex]

Doing the same thing with the second equation, we get:

[tex]37 = x^2-18x+118[/tex]

[tex]0=x^2-18x+81[/tex]

[tex]0=(x-9)^2[/tex]

[tex]x-9=0\\x=9[/tex]

After all of this, we know our vertex's x-values are either [tex]9[/tex] or [tex]-9[/tex], and that our y-value is [tex]37\\[/tex].

We can conclude that our k-value (y-value of the vertex in vertex form) is [tex]37[/tex], and our h-value (x-value of the vertex in vertex form) is [tex]9[/tex] or [tex]-9[/tex].

Conclusion:         [tex]h = -9, 9[/tex]

                            [tex]k=37[/tex]

Answer:

The length of the third side is 1 unit.

Step-by-step explanation:

Because this is a right triangle, we can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean theorem: a² + b² = c², where variables a and b are the legs of the triangle and c is the hypotenuse

We are going to let a = (12/13) and b = (5/13), though the order does not particularly matter in this case. We are going to plug and play with the theorem, and then simplify as we go.

[tex](\frac{12}{13})^{2} + (\frac{5}{13})^{2} = c^{2}\\\\\frac{144}{169} + \frac{25}{169} = c^{2}\\\\\frac{144 + 25}{169} = c^{2}\\ \\ \frac{169}{169} = c^{2}\\\\1 = c^{2}\\\\\sqrt{1} = \sqrt{c^{2}} \\\\c = 1[/tex]

The expression 2log(5) can be rewritten as log(25) in the form log(c), representing the Logarithm to the base 10 that yields the value 25.

The expression 2log(5) in the form log(c), we can use the logarithmic property that states:

nlog(b) = log(b^n)

Applying this property, we can rewrite 2log(5) as:

2log(5) = log(5^2)

Simplifying further, we have:

2log(5) = log(25)

Therefore, the expression 2log(5) can be written in the form log(c) as log(25).

The logarithmic function log(c) represents the exponent to which a given base must be raised to obtain the value c. In this case, log(25) represents the exponent to which the base 10 must be raised to obtain the value 25.

In summary, the expression 2log(5) can be rewritten as log(25) in the form log(c), representing the logarithm to the base 10 that yields the value 25.

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no it dose not

your right whats the question

Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

Answer:

(−∞,∞)

Step-by-step explanation:

Since |x−5| is always positive and −2 is negative, |x−5| is always greater than −2, so the inequality is always true.

All real numbers

So, the answer is (−∞,∞)

Answer:

Step-by-step explanation:

A = 10 cm - 4cm = 6cm

B =

[tex]\sqrt{4^2+7^2}\\ = \sqrt{16+49}\\ = \sqrt{65}[/tex]

C  =  [tex]\sqrt{10^2+3^2}\\ = \sqrt{109}[/tex]

D = [tex]\sqrt{10^2+6^2}\\ = \sqrt{136}[/tex]

The slope of the line is,

m = - 1

Given that;

Two points on the line are (0, 5) and (5, 0).

Now,

Since, The equation of line passes through the points ((0, 5) and (5, 0).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (0 - 5) / (5 - 0)

m = - 5 / 5

m = - 1

Thus, The slope of the line is,

m = - 1

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The area of the sector is 30.375 ft squared.

The  sector of a circle has a diameter of 18 feet and an angle of 3/4π radians.

Therefore, the area of the sector can be found as follows:

area of the sector = ∅ / 2 r²

where

∅ = central angle in radian

r = radius of the circle

Therefore,

∅ = 3 / 4 π

r = 18 / 2 = 9 ft

area of the sector = 3 / 4 π ÷ 2 × 9²

area of the sector = 3 / 8π × 81

area of the sector = 243 / 8π

area of the sector = 30.375 ft²

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The area of the sector is 95.43 square feet.

The area of sector when the angle is given in radians is given by the formula:

Area of sector = (1/2) × r²θ

where θ is the angle subtended at the center and r is the radius of the circle.

We have:

θ = 3π/4

r = 18/2 = 9 feet

Substituting into the formula:

Area of sector = (1/2) × 9² × 3π/4

Area of sector = 95.43 square feet

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1/4 or 0.25 is the probability that the coin shows heads and the die shows an odd number.

To find the probability that the coin shows heads and the die shows an odd number, we need to consider the possible outcomes for each event and calculate the probability of their intersection.

For the coin toss, there are two possible outcomes: heads (H) or tails (T). Each outcome has an equal chance of occurring, so the probability of the coin showing heads is 1/2.

For the die roll, there are six possible outcomes: 1, 2, 3, 4, 5, or 6. Out of these outcomes, three numbers (1, 3, and 5) are odd. Again, each outcome has an equal chance of occurring, so the probability of rolling an odd number is 3/6 or 1/2.

To find the probability of both events occurring, we multiply the individual probabilities:

Probability of coin showing heads = 1/2

Probability of die showing an odd number = 1/2

Probability of both events occurring = (1/2) * (1/2) = 1/4

Therefore, the probability that the coin shows heads and the die shows an odd number is 1/4 or 0.25.

This means that out of all possible outcomes from tossing a coin and rolling a die, there is a 1 in 4 chance that the coin shows heads and the die shows an odd number. It's important to note that this calculation assumes fair and unbiased coin and die, where the probabilities of each outcome are equally likely.

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The number that belongs in the green box is given as follows:

D.  2.

A quadratic function is given according to the following rule:

y = ax² + bx + c

The solutions are given as follows:

In which the discriminant is given as follows:

[tex]\Delta = b^2 - 4ac[/tex]

The number that goes into the green box is then given as follows:

2a = 2(1) = 2.

Meaning that option D is the correct option in the context of this problem.

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The three statements about the measures of center that are true include the following:

A. The mean for Group A is less than the mean for Group B.

B. The median for Group A is less than the median for Group B.

C. The mode for Group A is less than the mode for Group B.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Group A

Mean for Group A = [(1 × 5) + (2 × 4) + (3 × 1)]/(5 + 4 + 1)

Mean for Group A = (5 + 8 + 3)/10

Mean for Group A = 16/10

Mean for Group A = 1.6

Mode for Group A = 1

Median for Group A = (1 + 2)/2

Median for Group A = 3/2

Median for Group A = 1.5

Group B

Mean for Group A = [(1 × 3) + (2 × 2) + (3 × 4) + (5 × 1)]/(3 + 2 + 4 + 1)

Mean for Group A = (3 + 4 + 12 + 5)/10

Mean for Group A = 24/10

Mean for Group A = 2.4

Mode for Group B = 3

Median for Group B = (2 + 3)/2

Median for Group B = 5/2

Median for Group B = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A,B,C

Step-by-step explanation:

The equation of the circle with a center at (-4, 6) and a point on the circumference at (-2, 9) is (x + 4)² + (y - 6)² = 13.

Given:

Center of the circle: (-4, 6)

Point on the circumference: (-2, 9)

The center of the circle (h, k) is given as (-4, 6), which means h = -4 and k = 6.

The formula for the distance between the center and the point on the circumference can be used to determine the radius (r).

The formula for distance is provided by:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

where (x₁, y₁) is the center (-4, 6), and (x₂, y₂) is the point on the circumference (-2, 9).

Putting in the values:

d = √((-2 - (-4))² + (9 - 6)²)

= √((2)² + (3)²)

= √(4 + 9)

= √13

So, the radius (r) is √13.

Now, we can substitute the values of h, k, and r into the general equation of the circle:

(x - h)² + (y - k)² = r²

(x - (-4))² + (y - 6)² = (√13)²

(x + 4)² + (y - 6)² = 13

Therefore, the equation of the circle is (x + 4)² + (y - 6)² = 13.

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Answer:

9:30

Step-by-step explanation:

Graph is attach below for this question and the equation of this graph is

A(x) = 400(1.25)ˣ +0

We have,

In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" indicates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).

Given that the boat's value increasing at a rate of 25% per year.

So after each year the value becomes = 1 + 25% = 1 + 0.25 = 1.25 of the previous year.

So the equation becomes: A(x) = 400(1.25)ˣ +0

Since, b = 1.25 > 1, so A(x) is a increasing function. And for every value of x, A(x) < 0.

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Answer: Bryan drove the fastest.

Step-by-step explanation: To find out who drove the fastest, we need to calculate the speed of each person. Speed is given by the formula distance/time.

For Doug:

Speed = 28 miles / 2.3 hours = 12.17 miles/hour

For Primo:

Speed = 34 miles / 2.1 hours = 16.19 miles/hour

For Camillo:

Speed = 57 miles / 1.4 hours = 40.71 miles/hour

For Bryan:

Speed = 49 miles / 1.2 hours = 40.83 miles/hour

Angles in each quadrant with common reference angle as 311° are :

First quadrant = 49°, second quadrant = 131°, third quadrant = 229° and fourth quadrant = 311°.

Given that,

Reference angle = 311°

We have to find an angle in each quadrant with this reference angle.

311° is in the fourth quadrant.

The equivalent angle on the first quadrant is,

360° - 311° = 49°

Equivalent angle on second quadrant is,

180° - 49° = 131°

Equivalent angle on third quadrant is,

360° - 131° = 229°

Hence the angles are found.

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