Water flows from a faucet into a bathtub at a constant rate of 7 gallons of water pouring in every 2 minutes. The bathtub is initially empty and the plug is in. If the tub can hold 50 gallons of water, how long will it take to fill the tub? A. 14.26 minutesB. 14 minutesC. 7.14 minutesD. None of the aboveI would appreciate the help

Answer:

  y = 6x +2

Step-by-step explanation:

It is useful to start with the point-slope form of the equation for a line when you are given a point and a slope.

  y -k = m(x -h) . . . . line with slope m through point (h, k)

  y -(-22) = 6(x -(-4))

  y +22 = 6x +24 . . . simplify

  y = 6x +2 . . . . . . subtract 22

The system of equations which this graph represent include the following:

A. y = x² + 2

   y = x + 4

In Geometry, the point-slope form of a straight line can be calculated by using this equation:

y - y₁ = m(x - x₁)

Where:

First, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (6 - 3)/(2 + 1)

Slope (m) = 3/3

Slope (m) = 1.

At data point (-1, 3) and a slope of 1, an equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3 = -1(x + 1)

y = -x + 4

For the quadratic equation, we have;

y = a(x - h)² + k

6 = a(-2 - 0)² + 2

4 = a4

a = 4/4

a = 1

Therefore, the required quadratic function is given by:

y = a(x - h)² + k

y = (x - 0)² + 2

y = x² + 2

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Missing information:

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

Answer:

\( f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2\)

\(f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2\)

And replacing we got:

\( lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}\)

And if we simplfy we got:

\( lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h \)

And replacing we got:

\(lim_{h \to 0} 6x + 1 +3h = 6x+1\)

And the bet option would be:

C. 6x + 1

Step-by-step explanation:

We have the following function given:

\( f(x) = 3x^2 +x+2\)

And we want to find this limit:

\( lim_{h \to 0} \frac{f(x+h) -f(x)}{h}\)

We can begin finding:

\( f(x+h) = 3(x+h)^2 +(x+h) +2= 3(x^2 +2xh+h^2) +x+h+2\)

\(f(x+h) = 3x^2 +6xh +3h^2 +x+h+2= 3x^2 +6xh +x+h+ 3h^2 +2\)

And replacing we got:

\( lim_{h \to 0} \frac{3x^2 +6xh +x+h+ 3h^2 +2 -3x^2 -x-2}{h}\)

And if we simplfy we got:

\( lim_{h \to 0} \frac{6xh +h+ 3h^2 }{h} =lim_{h \to 0} 6x + 1 +3h \)

And replacing we got:

\(lim_{h \to 0} 6x + 1 +3h = 6x+1\)

And the bet option would be:

C. 6x + 1

Answer:

6x+1

Step-by-step explanation:

Plato :)

Answer:

$85

Step-by-step explanation:

(if you need to explain how the anwer was gotten)

34 ÷ 4 = 8.5

8.5 × 10 = 85

Answer:

y = -3x + 1

Step-by-step explanation:

Perpendicular lines have opposite reciprocal slopes, so the slope will be -3.

Plug in the slope and given point into y = mx + b

y = mx + b

-5 = -3(2) + b

-5 = -6 + b

1 = b

Then, plug in the slope and y intercept into y = mx + b again:

y = -3x + 1 will be the equation of the line

Answer:

$6

Step-by-step explanation:

there was 11 total and 5 went into the soda and 6 went into the pizza so it's 6.

Answer:

10000000 - 6872536 = 3127474

Hence 68,72,536 is 31,27,474 less than 1,00,00,000.

Answer:

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755
0.0755 * 100 = 7.55%

Step-by-step explanation:

To find the percentage of 1 - 3√(5/35), we need to first evaluate the expression.

1 - 3√(5/35) = 1 - 3√(1/7) = 1 - 3*(1/sqrt(7)) ≈ 0.0755

To convert this decimal to a percentage, we simply multiply by 100:

0.0755 * 100 = 7.55%

Answer:

1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Step-by-step explanation:

We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Answer:

expand the square

2(x-6) (x-6)

2(x(x-6)-6(x-6)

2(x²-6x-6(x-6)

2(x²-6x-6x+36)

2(x²-12x+36)

2x²-24x+72

Step-by-step explanation:

hope this helps

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

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Answer:

3 types of polynomials. They are monomial, binomial and trinomial.

-------------->

There can be rational, irrational and imaginary solutions. Irrational and imaginary solutions will always come in pairs. This is due to the fact that to find these types of solutions, you must use the Quadratic Formula and the \begin{align*}\pm\end{align*} sign will give two solutions.

Step-by-step explanation:

The surface area of the complex solid is 530 square yards.

In this problem we need to determine the surface area of the complex solid, that is, the sum of the area of all faces of the solid. The area formulas required to find the surface area is:

A = w · h

Where:

The surface area of the complex solid is:

A = 2 · (11 yd) · (3 yd) + 2 · (4 yd)² + (12 yd) · (11 yd) + (12 yd) · (3 yd) + (12 yd) · (7 yd) + 2 · (4 yd) · (12 yd) + (12 yd) · (7 yd)

A = 66 yd² + 32 yd² + 132 yd² + 36 yd² + 84 yd² + 96 yd² + 84 yd²

A = 530 yd²

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The ratio of number of burgers without onions to the number of burgers with onions is 4:1.

The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.

Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;

ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)

                = 12/ 3

                = 4/ 1

The ratio of number of burgers without onions to burgers with onions = 4:1

Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.

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Answer:

17

Step-by-step explanation:

The value of x from the angles between given parallel line is 17.

Consecutive angles lie along the transversal, both angles will always be on one side of the transversal, and they'll either both be inside the parallel lines or outside the parallel lines (interior or exterior angles, respectively). Consecutive angles are always supplementary if the transversal crosses parallel lines.

From the given figure, we have two angles 2x+5 and 8x+5.

As we know, sum of consecutive angles is 180°

Now, 2x+5+8x+5=180

10x+10=180

10x=170

x=17

So, 2x+5=39° and 8x+5=141°

Therefore, the value of x from the angles between given parallel line is 17.

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Answer:

a: \(f(t)=(t+2)^2-18\)

b: vertex: (-2, -18)

   minimum

c: x = -2

Step-by-step explanation:

Completing the square is difficult to explain in words. but I'll try my best. Let me know if you need any more information.

Part A ===============

Start with the given function in this form:

\(f(x)=ax^2+bx+c\\t^2+4t-14\)

We need an additional number, d, and we'll calculate it like this:

\(d=(\frac{b}{2a})^2 \\\\d=(\frac{4}{2(1)} )^2\\d=2^2\\d=4\)

d needs to be added and subtracted at the same time. That way we do not change the value of the expression:

\(ax^2+bx+d-d+c\\\\t^2+4t+4-4-14\)

And you can separate them like this to make it easier to read:

\((t^2+4t+4) + (-4-14)\\(t^2+4t+4)-18\)

Finally, we need to factor the trinomial in the parenthesis. Because we've completed the square, it's now a perfect square trinomial.  The factored form is just:

\((x+e)^2\)

where e is half of b, or the square root of c. That looks like this in our case, and you can also expand it to make sure.

\((t+2)^2\\\\(t+2)(t+2)\\t^2+2t+2t+4\\t^2+4t+4\)

Put that all together and you get the answer:

\(f(t)=(t+2)^2-18\)

Part B ===============

Vertex form is this:

\(f(x)=a(x-h)^2+k\)

where (h, k) is the vertex and a is the scale factor.

In part A, we converted the given function into vertex form. Looking at that, you can see the vertex is at (-2, -18), and the scale factor is 1. When the scale factor is positive, the parabola faces upwards. When it's negative, the parabola faces downwards.

The scale factor is a positive 1 in this case, and if you picture that in your mind, the vertex is at the very lowest point, or the minimum, of the parabola.

Part C ==============

The axis of symmetry is always on the vertex, and that is because the vertex is the exact point where the parabola changes direction from positive to negative, or negative to positive.

The vertex of this parabola is (-2, -18), so the axis of symmetry is at x = -2.

Sorry if that got too long and hard to follow, I can clarify any part of it if needed.

Answer:

6 inches by 10 1/2 inches by 30 inches

Step-by-step explanation: To find this answer you have to multiply the old dimensions by the scale factor which is 3/4. You would do 8 times 3/4 which is 6 inches. Then 14 inches times 3/4 which is 10 1/2. And then 40 inches times 3/4 and that answer is 30 inches. Those are the new dimensions for the cabinet.

Answer:

A)7L=7000ml C)18L=18000ml

Step-by-step explanation:

The resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

The circumference of a circle or ellipse in geometry is its perimeter.

That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc.

The curve length around any closed figure is more often referred to as the perimeter.

The length of a circle's outline is referred to as its circumference, and the length of a form with straight sides is referred to as its perimeter.

So, since the fence around the circular pool is given, then it will also be the value of the circumference of the pool.

Circumference = 75 ft

Radius:

2πr = 75

r = 75/2π = 75/(2×3.14) ≈ 11.937

radius = 11.94 ft

Diameter:

2r = 2×11 ≈ 23.87 ft

Therefore, the resultant values are as follows:

Radius = 11.94 ft; Diameter: 23.87 ft; Circumference = 75 ft

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Complete question:

The fence around a circular pool is 75 ft long. Find: Radius, Diameter, and Circumference.

Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

Meaning of probability :

Probability is calculation of how likely some event will happen. Whenever we are not sure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are going to happen.

The analysis of events governed by probability is called statistics.

According to the given information :

Red section = \(\frac{2}{5}\)

multiply numerator and denominator by \(2\) we get

Red section = \(\frac{4}{10}\)

 Blue section = \(\frac{1}{2}\)

 multiply numerator and denominator by \(5\) we get

 Blue section = \(\frac{5}{10}\)

 Green section = \(1\)- Red section - Blue section

 Green section =\(1-\frac{4}{10} -\frac{5}{10}\)

  Green section = \(\frac{1}{10}\)

Therefore Probability of red = \(\frac{4}{10}\) , blue = \(\frac{5}{10}\) , green = \(\frac{1}{10}\).

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Answer:

y = -1/6x + 2

Step-by-step explanation:

To find the slope of a perpendicular line, you take the opposite reciprocal

6x -> -1/6x

y = -1/6x + 2

An absolute value is the numerical value of a number without consideration of its sign. It can be represented graphically by a straight line known as a number line. Absolute value equations are equations that include absolute values of variables or unknown quantities. The following are examples of how to write an absolute value equation in the form |x-c|=d to fit the provided solution sets:

Example 1:

Solution set: {x|x≤-3 or x≥1}
Absolute value equation: |x-(-1)|=4
Explanation: -1 is the midpoint of the two ranges (-3 and 1) in the solution set. |x-(-1)|=|x+1| is the absolute value expression for the midpoint -1. The distance d from -1 to the solutions' furthest endpoints, 1 and -3, is four, hence the value of d in the absolute value equation is 4.
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The volume, in cubic in, of a rectangular prism is,

⇒ V = 4,180 inches³

We have to given that;

A rectangular prism has a height of 11 in, a width of 20 in, and a length of 19in.

Now, We know that;

Volume of a rectangular prism is,

V = Length x width x height

Substitute all the values, we get;

V = 11 x 20 x 19

V = 4,180 inches³

Thus, The volume, in cubic in, of a rectangular prism is,

⇒ V = 4,180 inches³

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The total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

In addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms "addends" and "sum" refer to the numbers that are added and the result of the operation, respectively.

To find the total number of atoms represented by Cd(CH₂CICO₂)₂, we need to count the number of atoms of each element in the molecule and add them up.

Cd(CH₂CICO₂)₂ contains:

1 cadmium (Cd) atom

2 carbon (C) atoms

6 hydrogen (H) atoms

4 oxygen (O) atoms

2 chlorine (Cl) atoms

Adding these up, we get:

1 + 2 + 6 + 4 + 2 = 15

Therefore, the total number of atoms represented by Cd(CH₂CICO₂)₂ is 15.

The answer is (D) 15.

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Answer:

If you are asking what 2 divided 2 is its 1

Step-by-step explanation:

Answer:

It equals 1

Step-by-step explanation:

Because 2 divided by 2 is 1

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=\sqrt{c^2 - o^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{MN}\\ o=\stackrel{opposite}{18} \end{cases} \\\\\\ MN=\sqrt{ 30^2 - 18^2} \implies MN=\sqrt{ 576 }\implies MN=24 \\\\[-0.35em] ~\dotfill\\\\ \cos(M )=\cfrac{\stackrel{adjacent}{24}}{\underset{hypotenuse}{30}} \implies \cos(M)=\cfrac{4}{5}\)