An aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Answer:

k)  x = 2

l)  x = 6

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\\Equality Law:\; If $\log_ax=\log_ay$ then $x=y$\\\\Same base as number:\;\;\;$\log_aa=1$\\$\end{minipage}}[/tex]

[tex]\begin{aligned}\log_7(x + 12) + \log_7(x + 1) &= \log_7(42)\\\log_7\left[(x + 12)(x+1)\right]&= \log_7(42)\\(x + 12)(x+1)&=42\\x^2+13x+12&=42\\x^2+13x-30&=0\\x^2+15x-2x-30&=0\\x(x+15)-2(x+15)&=0\\(x-2)(x+15)&=0\\\\\implies x&=2\\\implies x&=-15\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -15 is an extraneous solution.  Therefore, the only valid solution is x = 2.

[tex]\begin{aligned}\log_4(x + 3) + 1 &= 2\log_4(x)\\\log_4(x + 3) + \log_44 &= \log_4(x^2)\\\log_4\left[4(x + 3)\right] &= \log_4(x^2)\\4(x + 3)&=x^2\\4x+12&=x^2\\x^2-4x-12&=0\\x^2-6x+2x-12&=0\\x(x-6)+2(x-6)&=0\\(x+2)(x-6)&=0\\\\\implies x&=-2\\\implies x&=6\end{aligned}[/tex]

As logs of negative numbers cannot be taken, x = -2 is an extraneous solution.  Therefore, the only valid solution is x = 6.

The oscillations have an amplitude of 0.129 m. The block is positioned at 0m and moving at 0m/s at time t=0s.

The maximum deflection of a simple harmonic oscillator from its equilibrium position is its amplitude. Since this is the displacement at time t=1.00s, the oscillations in this instance have an amplitude of 0.129m. The oscillator is in equilibrium at time t=0 s, therefore the block is located at location 0 m. Additionally, since the oscillator has not yet begun to move, these values can be determined by examining the oscillator's equation of motion. According to this equation, the oscillator's position is determined by the expression x=A*cos(t), where A stands for amplitude and for angular frequency. The equation becomes simpler to x=0m for A=0.129m and t=0s. Similar to that, v=-Asin(t) gives the velocity. The equation is again simplified to v=0m/s as A=0.129m and t=0s.

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The measure of a different interior angle of the triangle is 52 degrees.

A right angled triangle is a triangle with one of the angles as 90 degrees.

The sum of the interior angle of a triangle is 180 degrees.

Given the data in the question;

Since the sum of the interior angle of a triangle is 180 degrees.

Angle a + Angle b + Angle c = 180

38 + Angle b + 90 = 180

Angle b + 128 = 180

Angle b = 180 - 128

Angle b = 52 degrees.

Therefore, the measure of the second angle is 52 degrees.

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The order of the numbers from the smallest to the largest is: 0.04, 25%

It can be said that the ascending or increasing order is the one where the values, elements or numbers of a group or set are ordered starting from the one with the smallest value to the one with the highest value of all.

Ordering the numbers from the smallest to the largest , we have:

25% is equal to 25/100 = 0.25, so 0.25 is largest than 0.04

0.04 < 0.25

0.04 < 25%

The correct option is:

0.04, 25% = correct order

25%, 0.04 = incorrect order

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You should distinguish elements of your data visualization by discriminating data the foreground and background and using contrasting colors and shapes. This makes the content more accessible.

The term shapes in math is known as the process of define the outline or the boundary of an object.

Here we have given that should distinguish elements of your data visualization and the content more accessible.

Here we have given that distinguishing elements of your data visualization by separating the foreground and background and using contrasting colors and shapes makes the content easier to see.

While we looking into this one than we have identified that this can help make data visualizations more accessible for audience members with low vision.

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The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

Marcus makes $3,000 each month. He pays a total of 28% in taxes and 5% for

It's rather easy to figure out net income. Simply deduct expenses like taxes, insurance, and retirement contributions from your gross income, which is the entire amount of money you have made. Deductions from gross income equal net income.

Gross income – deductions = net income.

3000 - 840 - 150 = 2010.

The amount you make each month before taxes and other deductions is known as your monthly gross income. In other words, it is your annual income divided by 12.

monthly gross income = 3000.

The amount you make each month before taxes and other deductions is known as your monthly gross income so monthly gross income is 3000.

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Answer: b is the coefficient of the x term. In the standard form f(x) = ax^2 + bx + c, b is the value of the coefficient of the x term. So the value of b is 0.

Step-by-step explanation:

The value of b in the given function is 12.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

For example, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Given that, a table defining the function, we need to form an equation and compare with the standard form of a quadratic function,

We can use the vertex form of a quadratic function, which is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Since, we know the vertex of this parabola from the table, we can use that information to write the equation in vertex form: f(x) = a(x + 6)^2 + 8

Expanding this, we get f(x) = a(x² + 12x + 36) + 8

Comparing this with the standard form, we see that a = 1, b = 12, and c = 8.

Therefore, the value of b is 12.

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The complete question is :-

The table represents a quadratic function f(x). x f(x) −10 24 −9 17 −8 12 −7 9 −6 8 −5 9 −4 12 If the equation of the function f(x) is written in standard form f(x) = ax2 + bx + c, what is the value of b?

The length of sides a,b and c of triangle are 2, 4 and 5 respectively whereas the perimeter is 11ft.

A one-dimensional length, a two-dimensional shape, or both can have perimeters that are closed paths that contain, surround, or define them. A circle's or an ellipse's perimeter is measured by its circumference.

The perimeter calculation has a lot of useful applications. Calculated perimeter is the term used to describe the size of fence required to completely surround a yard or garden. How far a wheel or circle can go in one spin is determined by its circumference, which measures its perimeter. Similar to this, a spool's circumference is inversely related to the length of thread that is wound around it; if the string were exactly the same length, the circumference would be equal.

Given that

b = 2a

c = 3 +a

We know that the perimeter is equal to the sum of all the sides

Perimeter = a+b +c

11 = a +2a + a+3

8 = 4a

a = 2

Hence, sides a ,b and c are 2, 4, 5 respectively.

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The charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.

The electric force between two objects is given by Coulomb's law: F = k[tex]q_1[/tex][tex]q_2[/tex] /[tex]r^2[/tex], where k is the Coulomb constant, [tex]q_1[/tex]and [tex]q_2[/tex]  are the charges of the two objects, and r is the distance between them.

We have , [tex]q_2[/tex] = b

r = 50cm = 0.5m

k = 9 x [tex]10^9[/tex] [tex]Nm^2/C^2[/tex]

We know that b has a mass of 300 g and that a has twice the charge of b. So we can substitute these values and solve for [tex]q_1[/tex]:

[tex]q_1[/tex]= 2 * [tex]q_2[/tex]

[tex]q_2[/tex] = 0.38 N * [tex]0.5^2[/tex] / k

Substituting the values in Coulomb's law we get,

[tex]F = k q_1 q_2/r^2[/tex]

0.38 N = k * [tex]q_1[/tex] * [tex]q_2[/tex] /  [tex]0.5^2[/tex]

[tex]q_2[/tex]  = 0.38 N * [tex]0.5^2[/tex] / (9 x      [tex]10^9[/tex])

[tex]q_2[/tex]  = 0.00085 *  [tex]10^{-6}[/tex]

then we can multiply [tex]q_2[/tex]  by 2 to find the charge on object a:

[tex]q_1[/tex] = 2 * [tex]q_2[/tex]

[tex]q_1[/tex]= 0.00017 x [tex]10^{-6}[/tex] C

So, the charge on the object a is 0.00017 micro Coulombs (0.00017 μC) to two significant figures.

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The given function has

x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative:  The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.

What is a function?

A function is a mathematical relationship between a set of inputs (referred to as the domain) and a set of outputs (referred to as the range). In other words, a function assigns a unique output to each input value in the domain.

Given the function f(x) = x(x − 4)³(x+4)²

x-intercepts: The x-intercepts are the points at which the function crosses the x-axis, meaning the y value is equal to zero. To find the x-intercepts we need to set f(x) = 0 and solve for x.

x(x - 4)^3(x+4)^2 = 0

the x-intercepts of the function f(x) = x(x - 4)^3(x+4)^2 are x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative: The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End Behavior: The end behavior of this function is that as x approaches positive or negative infinity the value of f(x) approaches positive infinity.

Hence, the given function has

x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative:  The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.

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Answer:

34.94

Step-by-step explanation:

Answer: 34.94

Step-by-step explanation:

Answer:

19.8

Step-by-step explanation:

Answer:

Do 99 divided by 5

Step-by-step explanation:

Use cross multiplication

Step-by-step explanation:

the easiest way might be the approach to calculate the area of the whole rectangle and then subtract the area of the triangle.

the area of the whole rectangle is

18×16 = 288 m²

the area of a triangle is

baseline × height / 2

in a case like this (right-angled triangle) we can use one leg as baseline, and the other leg (90°) as height.

so, the height is the same as the width of the rectangle : 16 m.

how long is the baseline ?

it is on the 18 m length of the rectangle, and there are two 3 m "gaps", one left, and one right.

so, what's left for the baseline of the triangle itself ?

baseline = 18 - 3 - 3 = 12 m

therefore the area of the triangle is

12×16/2 = 12×8 = 96 m²

so, the total area of the shaded region is

288 - 96 = 192 m²

y = $40 is the equation of the line that represents the information. The line has no slope.

A linear equation can be used to represent the equation that represents Mr. Williams' total payment for city water. A linear equation is one that is composed of a single variable raised to the power of one.

A linear equation takes the following form:

y = ax + b

Where: a = slope = which measures the equation's rate of change

b = the intercept

y = $40 + (x × 0)

y = $40

A linear equation can have an upward, downward, or zero slope when plotted on a graph.

The equation of the line that represents the information is y = $40. There is no slope to the line.

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If a bus company usually transports 12 000 people per day at a ticket price of $1. The ticket price that will maximize revenue is $2 per ticket.

Equation to find the ticket price is:

y = (12000 - 400x)(1 + .1x)

Take the derivative of the function by product rule

y' = (12000 - 400x)(.1) + (-400)(1 + .1x)

y' = 1200 - 40x - 400 - 40x

y' = 800 - 80x

Let y' = 0

0 = 800 - 80x

Solving for x

80x = 800

Divide both side by 80x

x = 800/80

x = 10

Point at x = 10

Substitute x with 10 for 1 + .1x

1 + .1(10)

= 1 + 1

= $2 per ticket

Therefore the ticket price is  $2 per ticket.

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The reflection preserves the side lengths and angles of the triangle. The dilation preserves angles but not side lengths. Therefore, option B is the correct answer.

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

Given that, triangle is reflected across the y-axis and then dilated by a factor of centered at the origin.

The triangle ABC in a graph with vertices A (-4, -2), B (4, -2), and C (4, 4)

A reflection across the y-axis changes the coordinates of the triangle from (x, y) to (-x, y) without changing the side lengths and angles.

The dilation of the triangle by a factor an then centered at the origin increases the side length of the triangle but the angles in the triangle remain the same since the ratio of the sides before and after dilation are the same.

Therefore, option B is the correct answer.

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Answer:

See below

Step-by-step explanation:

As 0 is included in the first part, this means that there is a jump discontinuity at x=0 for the second part of the function as you can see in the graph.

The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that corporate and special interest influence in elections should be limited to prevent corruption and maintain a fair and level playing field for all candidates.

The opponent to Citizens United v. Federal Elections Commission (2010) would most likely argue that the decision to allow unrestricted corporate and special interest spending in elections has had a negative impact on the integrity of the democratic process. They would point to the increased influence of money in politics and the dangers of corruption that come with it. They would argue that the decision has allowed wealthy entities to have an outsized influence in elections, creating an unfair and unequal playing field for candidates. Furthermore, they would argue that the decision has weakened the regulation of campaign spending and has allowed for the creation of so-called "dark money" groups, which can spend money on elections with little to no transparency. In short, the opponent to Citizens United v. Federal Elections Commission (2010) would argue that allowing unlimited corporate and special interest spending in elections has created an unequal playing field and should be limited in order to protect the integrity of the democratic process.

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Declare a vector of doubles named swimming logs with size of num students. Initialize first element to first student and last element to last student. Fill the middle elements with zeros.

Firstly, declare a vector of doubles named swimming logs with a size of num students. This is done by writing "vector swimming logs(num students);". This creates a vector with the size specified by num students, which can be read from input.

Next, initialize the first element of the vector to first student. This is done by writing "swimming logs[0] = first student;". This sets the first element of the vector to the value of first student, which can be read from input.

Then, initialize the last element of the vector to last student. This is done by writing "swimming logs[num students - 1] = last student;". This sets the last element of the vector to the value of last student, which can be read from input.

Finally, fill the middle elements of the vector with zeros. This is done by writing "for (int i = 1; i < num students - 1; i++) { swimming logs[i] = 0; }". This loop iterates from the second element to the second last element of the vector, setting each element to 0. This completes the initialization of swimming logs with the specified values.

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The table is completed as follows:

The situation is modeled by a linear function, in slope-intercept format, as follows:

y = mx + b.

In which:

The initial capacity is of 770 liters, decaying by 14 liters each minute, hence the parameters are given as follows:

b = 770, m = -14.

The function for this problem is defined as follows:

y = -14x + 770.

The numeric values are given as follows:

The table is given by the image presented at the end of the answer.

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If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

If y fluctuates inversely of x, then y = kx, where k is a fixed value. According to the expressions "y varies inversely as x" and "y is inversely proportionate to x," y decreases as x increases or vice versa. There are two translations for this idea. For some constant k, referred to as the constant of proportionality, yx = k.

According to the expression "y varies inversely as x," y drops by the same amount that x grows. In other terms, xy = k means that the equation xy is constant.

Let the equation be x = k/y, then k be a constant

[tex]$$\begin{aligned}& x=k \times \frac{1}{y} \\& \Rightarrow k=x y=9 \times 7=63 \\& \Rightarrow x=\frac{63}{y}\end{aligned}$$[/tex]

So [tex]$y=\frac{63}{x}$[/tex]

At x = 6 we have

[tex]$y=\frac{63}{6}=10.5$$[/tex]

If y varies inversely as x and y = 9 when x = 7, then the value of y = 10.5 when x = 6.

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The space taken up by the table is 24 feet².

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Kitchen table = 6 feet by 4 feet

This means,

The table is a rectangle.

The area of the table.

= 6 x 4

= 24 feet²

Thus,

The area of the rectangle is 24 feet².

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Payoff matrix: R (row player) receives payoff if total number of fingers shown is even, C (column player) receives payoff if total number of fingers shown is odd.

Two-finger morra is a game in which two players take turns holding up either one or two fingers. The payoff for the game is the total number of fingers shown, with the player whose total is even (R) receiving the payoff, and the player whose total is odd (C) receiving the payoff. This game can be represented in a payoff matrix, which is a table that shows the payoffs for each player in each possible situation. For two-finger morra, the payoff matrix would have two rows and two columns, representing the two players, R and C. The top row would show the payoffs for R when the total number of fingers is even, and the bottom row would show the payoffs for R when the total number of fingers is odd. Similarly, the left column would show the payoffs for C when the total number of fingers is even and the right column would show the payoffs for C when the total number of fingers is odd.

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When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.

A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.

Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.

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Los ángulos de mayor y menor medida son 85° y 35°, respectivamente.

En esta pregunta tenemos dos ángulos, cuyas medidas deben ser determinadas a partir de las ecuaciones matemáticas derivadas del enunciado. Primero, escriba la relación de las sumas de las medidas de los ángulos:

x + y = 120°

Donde:

Segundo, establezca la ecuación que relaciona las medidas de los ángulos:

x = 3 · y - 20°

Tercero, se resuelve el sistema de ecuaciones lineales:

(3 · y - 20°) + y = 120°

4 · y = 140°

y = 35°

x = 3 · 35° - 20°

x = 85°

No existen preguntas verificadas en español sobre el tema, de modo que se añade una pregunta en inglés.

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Answer:

The answer would be B

Step-by-step explanation:

By taking a quotient, we will see that the first number is 3×10¹³ times larger than the second one.

Here we have two numbers written on scientific notation, and we want to see how many times is the first number larger than the second one.

To see that, we need to take the quotient between the two numbers, so we will get:

(9 × 10⁹)/(3 × 10⁻⁴) = (9/3)× (10⁹/ 10⁻⁴)

Remember that the in the quotient of powers with a same base we just need to take the difference between the exponents, then we will get:

(9/3)*(10⁹/ 10⁻⁴) = 3*10⁽⁹⁺⁴⁾ = 3×10¹³

The first number is 3×10¹³ larger than the second.

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Answer: Please provide me with more details regarding the issue, such as an expression or equation that x is a component of. Could you kindly provide me with additional background or details regarding the issue you're seeking to resolve?

Step-by-step explanation:

Give me more details about the answer and I will solve it for you.

Using Angle Sum property, the measure of 3 angles is ∠Q = 35°, ∠R = 19°, ∠S = 126°.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180o, regardless of whether it is acute, obtuse, or right.

One of the most commonly applied properties in geometry is the triangle's angle sum property. Most often, the unknown angles are calculated using this attribute.

As given the measure of 3 angles is -

∠Q = 4x - 17

∠R = x + 6

∠S = 10x - 4

We know that by angle - sum property,

The sum of 3 angles of triangle = 180°

⇒ 4x - 17 + x + 6 + 10x - 4 = 180

⇒ 15x -15 = 180

⇒ 15x = 180 + 15

⇒ 15x = 195

⇒ x = 13

∠Q = 4x - 17 = 4 × 13 - 17 = 35°

∠R = x + 6 = 13 + 6 = 19°

∠S = 10x - 4 = 10 × 13 - 4 = 126°

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Complete question -