Two water tanks are being filled. The water in Tank A is 3 inches deep, and the depth of the water increases 4
inches every hour. The water in Tank B is 10 inches deep, and the depth is increasing by 2 inches every hour.
Write an inequality to determine when the water in Tank A will be deeper than the water in Tank B.

I need an inequality written for what is written above please!!!

Answer:↓↓↓

Step-by-step explanation:

We are given that side AB is congruent to BD. We are also given that side AC is congruent to CD.

We know that side BC and side CB are congruent because of the Reflexive property.

Therefore, ΔABC and ΔDBC are congruent because of SSS Postulate.

Hope this helped!

Answer:

x > -2

Step-by-step explanation:

x + 3 > -1 - x

x + x + 3 > -1 - x + x

2x + 3 > -1

2x + 3 - 3 > -1 - 3

2x > -4

2x/2 > -4/2

x > -2

Comparison or relational operations, such as <, >, =, allow for comparing numbers. They determine if a number is less than, greater than, equal to, or not equal to another number, enabling decision-making and comparisons within arithmetic and programming operations.

When comparing numbers, you can use various relational operators to determine the relationship between them. Here are the commonly used comparison operators:

Less than (<): This operator compares two numbers and returns true if the first number is smaller than the second number. For example, 5 < 10 is true.

Greater than (>): This operator compares two numbers and returns true if the first number is larger than the second number. For example, 10 > 5 is true.

Less than or equal to (<=): This operator compares two numbers and returns true if the first number is smaller than or equal to the second number. For example, 5 <= 5 is true.

Greater than or equal to (>=): This operator compares two numbers and returns true if the first number is larger than or equal to the second number. For example, 10 >= 10 is true.

Equal to (==): This operator compares two numbers and returns true if they are equal. For example, 5 == 5 is true.

Not equal to (!=): This operator compares two numbers and returns true if they are not equal. For example, 5 != 10 is true.

These comparison operators allow you to compare numbers and make decisions based on their relationships within arithmetic or programming operations.

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The rate of change of the volume of the sphere is 100,530.96 mm^3/s

How to calculate rate of change of the volume of the sphere?

Given,

radius = r = 80 / 2 = 40 mm

rate of change radius = \(\frac{dr}{dt}\) = 5 mm/s

Formula to calculate volume of the sphere is

\(V = \frac{4}{3}\pi r^{3}\)

Differentiating the volume formula and we get new formula to calculate rate of change of the volume.

\(\frac{dV}{dt} = \frac{4}{3}\pi 3r^{2}\frac{dr}{dt}\)

Simplify to

\(\frac{dV}{dt} = 4\pi r^{2}\frac{dr}{dt}\)

Now, we put the given value to formula and calculate it

\(\frac{dV}{dt} = 4\pi (40)^{2}(5)\)

\(\frac{dV}{dt} = 100,530.96\) mm^3/s

Thus, the rate of change of the volume of the sphere is 100,530.96 mm^3/s

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Answer:

3k

Step-by-step explanation:

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Answer:

91-t

Step-by-step explanation:

Well this is a subtraction problem, so therefore it is pretty simple to make an equation. All you do is subtract T from 90

The given differential equation is

22y" + 4y' + 5y = 1 + 2x.

To use variation of parameters solution is:

y(x) = e^(-0.09091x)(c1 cos(0.84577x) + c2 sin(0.84577x)) - (1/12)(4x² - 9x + 6)

Given equation is:

22y'' + 4y' + 5y = 1+ 2x

We have to use variation of parameters method to solve it.The characteristic equation is:

22m² + 4m + 5 = 0

Solving the above equation,

we get:

m = -0.09091 ± 0.6145i

Now,

we can take

y1(x) = e^(-0.09091x)cos(0.6145x) and

y2(x) = e^(-0.09091x)sin(0.6145x)

Particular integral

y(x) = u1(x)y1(x) + u2(x)y2(x)

where u1(x) and u2(x) are functions to be determined by using below equations:

u1'(x)y1(x) + u2'(x)y2(x)

= 0u1'(x)y1'(x) + u2'(x)y2'(x)

= 1+ 2x

Differentiating y1(x) and y2(x), we get:

y1'(x) = -0.09091e^(-0.09091x)cos(0.6145x) - 0.6145e^(-0.09091x)sin(0.6145x)y2'(x)

= -0.09091e^(-0.09091x)sin(0.6145x) + 0.6145e^(-0.09091x)cos(0.6145x)

Solving above equations, we get:

u1'(x) = (2x - 5e^(0.18181x))/(2e^(0.18181x)cos(0.6145x))

u2'(x) = (5e^(0.18181x) - 1)/(2e^(0.18181x)sin(0.6145x))

Integrating above equations, we get:

u1(x) = 0.5(x - 3.6822sin(0.6145x) + 1.346cos(0.6145x))

u2(x) = 0.5(-3.6822cos(0.6145x) - x + 1.346sin(0.6145x))

Thus, the general solution is:

y(x) = c1e^(-0.09091x)cos(0.6145x) + c2e^(-0.09091x)sin(0.6145x) + 0.5(x - 3.6822sin(0.6145x) + 1.346cos(0.6145x))

[-(3.6822cos(0.6145x) + x + 1.346sin(0.6145x))]/(2e^(0.18181x)sin(0.6145x))

Therefore, the solution of the given differential equation is

y(x) = c1e^(-0.09091x)cos(0.6145x) + c2e^(-0.09091x)sin(0.6145x) + 0.5(x - 3.6822sin(0.6145x) + 1.346cos(0.6145x))

[-(3.6822cos(0.6145x) + x + 1.346sin(0.6145x))]/(2e^(0.18181x)sin(0.6145x)).

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Answer:

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Step-by-step explanation:

Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.

Answer:\(g(x)=\frac{3}{7}(21(x+5))^{1/2}\)

Step-by-step explanation:

Transformation rule:

Shifting by k units left : \(f(x)\to f(x+5)\)

Dilation by a factor of h units: \(f(x)\to hf(x)\)

Let g be a horizontal shrink by a factor of 3/7, followed by a translation 5 units left  of the graph of \(f(x)=(21x)^{1/2}\)

The rule for g described by the transformations of the graph of f. : \(g(x)=\frac{3}{7}(21(x+5))^{1/2}\)

The expression that represents the volume of the pyramid is V = (n³-n²)/3

A pyramid is a three-dimensional figure. It has a flat polygon base.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a pyramid is expressed as;

V = 1/3 base area × height.

base area = n× n = n²

height = n-1

Therefore the expression for the volume of a pyramid is

V = n² ( n-1) /3

V = (n³-n²)/3

therefore the expression is V = (n³-n²)/3

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The expansion of ((2x+1)²) is 4x² + 4x + 1 using distributive property.

As we can see in the question that the contraction "don't" is expanded as  "do not.", similarly we can use this technique to expand math phrases. This technique is known as distributive property to multiply it out. In this technique, we multiply a math equation by itself to get the final expansion.

To expand the expression ((2x+1)²), we can use the concept of the distributive property and perform the multiplication as follows: ((2x+1)²) = (2x+1)(2x+1). To expand this expression, we'll multiply each term of the first binomial by each term of the second binomial. Using the FOIL method (First, Outer, Inner, Last), we get:

((2x+1)(2x+1)) = (2x × 2x) + (2x × 1) + (1 × 2x) + (1 × 1)

Simplifying further:

= 4x² + 2x + 2x + 1

= 4x² + 4x + 1

Therefore, the expansion of ((2x+1)²) is 4x² + 4x + 1  using distributive property.

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Answer:

3p - 145w ≥ 50

Step-by-step explanation:

w = number of winners

p = number of plays of carnival game

Profits = 3p - 145w

3p - 145w ≥ 50

The measure of angle ∠M is 53.

We have,

We will use the sin function.

Where,

Sin = Perpendicular / Hypotenuse.

Now,

Sin Ф = 48/60

Ф = \(Sin^{-1}\) (48/60)

Ф = \(Sin^{-1}\) 0.8

Ф = 53

Thus,

The measure of angle ∠M is 53.

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Calculate the area of the floor:

Area = 1.6 x 2.3 = 3.68 square meters

Using the given formula: Pressure = force/area

200 = force / 3.68

Solve for force by multiplying both sides by 3.68

Force = 200 x 3.68

Force = 736 N/m^2

Correct to the nearest 5N/m^2 = 735 N/m^2

First of all we need to calculate the area of the floor and then we will find the pressure using the formula for pressure...

\(\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}\)

Area of floor ↯

\( \sf \: area = length \times breadth\)

\( \sf \: area = 1.6 \times 2.3\)

\( \sf \: area = 3.68 \: {m}^{2} \)

\(\purple{ \rule{300pt}{3pt}}\)

Finding force ↯

\( \tt \: pressure = \frac{force}{area} \)

\( \tt \: 200 = \frac{force}{3.68} \)

\( \tt \: force = 200 \times 3.68\)

\( \tt \: force = 736 \: newton\)

Thus, The maximum force is 736 Newton...~

Given:

Equations are given in the roots.

In square root, if two terms are in the root means we cn write one term outside the root.

Answer:

5, -1

Step-by-step explanation:

Hope it helps! =D

For right triangle LMN, the required ratio equivalent to tan(L) is 5 /13.

In this case, in order to find the ratio equivalent to tan (L).

tan(L) = opposite / adjacent side

tan(L) = NM /LN

Here given

NM = 5cm

LN = 13cm

We already know that tan(L) = perpendicular / adjacent

from given,

tan (L) = 5 / 13

As a result, the required ratio for triangle LMN is 5/13.

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Therefore, the system of linear equations has no solutions (option c).

To determine the number of solutions for the given system of linear equations:

x + 2y + z = -2 (Equation 1)

-2x - 3y - z = 2 (Equation 2)

x + 3y + 2z = -4 (Equation 3)

We can rearrange the equations into a matrix form:

[1 2 1 | -2]

[-2 -3 -1 | 2]

[1 3 2 | -4]

Performing row operations on the augmented matrix:

R2 = R2 + 2R1

R3 = R3 - R1

The matrix becomes:

[1 2 1 | -2]

[0 1 1 | 2]

[0 1 1 | -2]

Further row operations:

R3 = R3 - R2

The matrix becomes:

[1 2 1 | -2]

[0 1 1 | 2]

[0 0 0 | -4]

From the row-echelon form of the matrix, we can see that the third row represents the equation 0 = -4, which is inconsistent. This indicates that there are no solutions to the system of linear equations.

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Answer:

176

Step-by-step explanation:

Multiply −22by −8.

Answer: +176

Explanation: To multiply (-22)(-8), remember that

a negative times a negative is a positive.

So (-22)(-8) is +176.

Answer:

Step-by-step explanation:

a=36 because 36-5=31

Answer:

1/4

Step-by-step explanation:

You can set up ratios or fractions for the matching sides.

A/B

1/4 = 1/4

1.1/ 4/4= 1/4

1.5/6 = 1/4

1/4 is the correct answer as from figure a to b got smaller

The answer is 10.5, but don't put 10.5 if it's just asking for the number and not the unit only put (10)!!!

The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer:

3/7 (simplified)

Step-by-step explanation:

The original answer would be 6/14 because 6 out of 14 people said tennis. However, you divide both by 2 to get 3/7. The percent would be 42% if that is needed.

Answer:

Option (4)

Step-by-step explanation:

From the graph attached,

Equation of the wave function is a cosine function.

Let the graphed function is, f(x) = -Acos(bx - ∅)

Amplitude of the given function,

A = \(\frac{4-(-4)}{2}\) = 4 units

Period = \(\frac{2\pi }{b}\) = 2π

b = \(\frac{2\pi }{2\pi }\) = 1

Given graph is starting from (0, 0).

Therefore, from the given graph, Phase shift of the cosine curve = ∅ = \(\frac{\pi }{2}\)

Therefore, equation of the given cosine function will be,

f(x) = -4cos(x - \(\frac{\pi }{2}\))

Option (4) will be the answer.

Answer:

They will have the same amount on week 20

Step-by-step explanation:

I posted a picture on how I got my answer

Hope this Helped

Answer:

the one who answered is r ig h t

Step-by-step explanation:

Answer: So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

Step-by-step explanation:

Unfortunately, I cannot see the scatter plot you are referring to. However, I can explain how to use a trend line to predict the number of pages in a book with 19 chapters.

A trend line is a line that represents the general direction or tendency of the data in a scatter plot. To use a trend line to predict the number of pages in a book with 19 chapters, you would first need to determine the equation of the trend line.

This equation usually takes the form y = mx + b, where y is the dependent variable (in this case, the total number of pages), x is the independent variable (in this case, the number of chapters), m is the slope of the line, and b is the y-intercept (the value of y when x is 0).

Once you have the equation of the trend line, you can plug in the value x = 19 and solve for y to get the predicted number of pages in a book with 19 chapters.

For example, if the equation of the trend line is y = 50x + 200, then the predicted number of pages for a book with 19 chapters would be:

y = 50(19) + 200

y = 950

So, according to this prediction, a book with 19 chapters would have approximately 950 pages. However, keep in mind that this is just a prediction based on the trend line, and there may be some variability in the actual number of pages for a book with 19 chapters.

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