7. water in an open bowl evaporates at a rate proportional to the area of the surface of the water. (this means that the rate of decrease of the volume is proportional to the area of the surface.) show that the depth of the water decreases at a constant rate, regardless of the shape of the bowl.

Answer:

B

Step-by-step explanation:

Answer:

B. \(\frac{x^2}{3^2} +\frac{y^3}{2^2} =1\)

Step-by-step explanation:

The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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Answer: all the different form of 4 like 2 squared or 8/2

Step-by-step explanation: i’m going to have to go with one bc i don’t think they are including fractions and squares

Answer:

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

Answer:

630/49

Step-by-step explanation:

Answer:

the first option : The area of each square is equal to the square of the length of the side to which it is adjacent.

Answer:

22

Step-by-step explanation:

f(-6) = -3(-6) + 4  Negative times a negative is a positive.

f(-6) = 18 + 4

f(-6) = 22

The answer for f(x) = -3x + 4 when x = -6 is 22.

Given equation is f(x) = -3x + 4

We have to put x = -6

f(-6) = -3 (-6) +4

       = 18 + 4

       = 22

Hence, the answer is 22.

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We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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24 minutes.

Let me explain.

The lawn can be any size, but for the purpose of simplicity, let's say it's 240 square meters.

Peter mows 6 square meters per minute if he mows 240 square meters in 40 minutes.

John mows 4 square metres each minute if he mows 240 square metres in 60 minutes.

They'll mow 10 square meters per minute if they work together.

As a result, mowing the entire lawn will take them 24 minutes.

(Note that the location is irrelevant as long as we know how long each man takes to complete the task separately.) The answer would be the same if the field was 1 million hectares in size.)

I hope this helps.

The required values of given functions are:

(fog)(x) : x² -4x + 2

(gof)(x) : 3x² - 60

Domain of (gof)(x) : x ∈ [ 4.47 , ∞) .

Domain of (fog)(x) : x = 2±√2.

Given,

f(x)=x²-18

g(x)= 3x-6

Now,

Firstly (fog)(x),

f(x)=x²-18

g(x)= 3x-6

Substitute g(x) in f(x),

(fog)(x) = (3x-6)² -18

(fog)(x) = 9x² -36x +18

(fog)(x) = x² -4x + 2

Next step to find domain,

x² -4x + 2 ≥ 0

x = 2±√2.

Secondly, (gof)(x)

f(x)=x²-18

g(x)= 3x-6

Substitute f(x) in g(x)

gof(x) = 3(x² - 18) - 6

gof(x) = 3x² - 60

Next step to find domain,

3x² - 60 ≥ 0

x ≥ 4.47

x ∈ [ 4.47 , ∞) .

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Given:

In a right angle triangle ABC, \(\angle B=90^\circ,x=8.7\ m\), and \(\theta = 45^\circ\)

To find:

The value of AC.

Solution:

In a right angle triangle,

\(\cos \theta =\dfrac{Adjacent}{Hypotenuse}\)

\(\cos \theta =\dfrac{BC}{AC}\)

\(\cos (45^\circ) =\dfrac{8.7}{AC}\)

\(\dfrac{1}{\sqrt{2}}=\dfrac{8.7}{AC}\)

On cross multiplication, we get

\(AC=8.7\times \sqrt{2}\)

\(AC=12.30365799\)

\(AC\approx 12.304\)

Therefore, the measure of AC is 12.304 m.

The root of the equation e^-2x + 4x² - 36 = 0 is 2.28668 (correct to four decimal places).

The equation is e^-2x + 4x² - 36 = 0.

We need to find the roots of this equation by using the Secant method.

Secant method is used to find the roots of nonlinear equations.

The Secant method is an open root-finding method that utilizes a sequence of approximations to the roots of a function.

It is less time-consuming than other techniques for obtaining roots since it does not need derivatives.

Given the equation is e^-2x + 4x² - 36 = 0 with two initial guesses, x₁ = 1 and x₂ = 4, and a pre-specified relative error tolerance ε = 0.05.

Applying the Secant method to the equation e^-2x + 4x² - 36 = 0, we get the following results:

\begin{array}{|c|c|c|c|} \hline x_{n-1} & x_n & x_{n+1} & \text{Error}\\ \h

line 1 & 4 & 2.41332 & 0.3922\\ 4 & 2.41332 & 2.31278 & 0.0436\\ 2.41332 & 2.31278 & 2.28822 & 0.0107\\ 2.31278 & 2.28822 & 2.28667 & 0.0007\\ 2.28822 & 2.28667 & 2.28668 & 0.0000\\ \hline \end{array}

Therefore, the root of the equation e^-2x + 4x² - 36 = 0 is 2.28668 (correct to four decimal places).

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Answer:

1.283.5

2.34.56

3.92.96

4.39.9

5.34

6.18.7

Step-by-step explanation:

Answer:45%

Step-by-step explanation:

:))))

Answer:

45%

Step-by-step explanation:

99/180 = 55%

100% - 55% = 45% decrease

Answer: 45%

The unknown angle x in the triangle is 80 degrees

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

The triangle

The unknown angle x is calculated using the sum of angles in a triangle theorem

So, we have

x + 60 + 40 = 180

Evaluate the like terms

x + 100 = 180

So, we have

x = 80

Hence, the unknown angle x is 80 degrees

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The total number of registered doctors is roughly 183,156 + 52,600 = 235,756 when rounded to the nearest whole number.

In a recent year, 52,600 female registered doctors accounted for 28.7 percent of all registered doctors. The total number of registered physicians, rounded to the nearest whole number,

To begin, calculate the percentage of male registered doctors: 100 percent - 28.7 percent = 71.3 percent, which represents the percentage of male registered doctors.

Find the number of male registered doctors: 0.713 × x = (male registered doctors) 0.713 × x = x - 52,600 0.287 × x = 52,600x = 183,156.42 ≈ 183,156 .
In order to calculate the total number of registered doctors, it is necessary to first find the number of male registered doctors.

The number of female registered doctors has already been provided, which is 52,600. Let x be the total number of registered physicians, then the percentage of female registered doctors can be expressed as:

0.287x = 52,600. Solving for x, we get x = 183,156.42, but this is not a whole number.

To round this to the nearest whole number, we add 0.5 to it (since the decimal is greater than or equal to 0.5), and then take the integer part of the result.

This gives us 183,156 + 0.5 = 183,156.5.

Since this is halfway between 183,156 and 183,157, we round up to 183,157.

Adding the number of female registered doctors to this, we get: 183,157 + 52,600 = 235,757.

So the total number of registered doctors is approximately 235,757 when rounded to the nearest whole number.

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The hypothesis I will test is the correlation between study time and academic performance.

In order to investigate the hypothesis, we will collect data on the study time (in hours) of a group of students and their corresponding academic performance scores. We will then analyze the data to determine if there is a statistically significant relationship between these two variables.

Mathematical Expression:

Let x represent the study time (in hours) and y represent the academic performance score. The hypothesis can be expressed as:

H0: There is no significant correlation between study time and academic performance.

H1: There is a significant correlation between study time and academic performance.

We will use statistical methods such as correlation analysis and hypothesis testing to assess the strength and significance of the relationship.

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Answer:

  x = 4

Step-by-step explanation:

The x-coordinate of the vertex of standard form quadratic y=ax²+bx+c is given by x=-b/(2a). This is also the equation of the axis of symmetry, the vertical line through the vertex.

__

The given equation is ...

  y = -x^2 +8x

Comparing this to the standard form quadratic expression, we see that ...

__

Using these values in the equation of the axis of symmetry, we get ...

  x = -8/(2(-1)) = 8/2 = 4

Th equation of the axis of symmetry is x=4.

_____

Additional comment

The x-coordinate of the vertex is also found as the midpoint of the two x-intercepts. Those are the values of x that make y=0:

  0 = -x² +8x

  0 = -x(x -8)

The factors are zero when x=0 and x=8, so the midpoint between them is ...

  x = (0 +8)/2 = 4

The axis of symmetry is x=4.

Answer:

Step-by-step explanation:

it is 100

Answer:

100

Step-by-step explanation:

25 400 10000

----- × ------ = --------- = 100

100 1 100

Hope this helped you- have a good day bro cya)

Answer:

\(\frac{3}{2}\)

Step-by-step explanation:

To find the slope, we use the formula:

M = \(\frac{y2 - y1}{x2-x1}\)

So, plug in our numbers. For reference:

-2 = x1       2 = y1

0 = x2       5 = y2

2 = x3       8 = y3

After plugging in:

\(M = \frac{5 - 2}{0 - - 2} = \frac{3}{2}\)

Thus, your slope is \(\frac{3}{2}\).

Answer:

20

Step-by-step explanation:

Area of trapezoid: average of two bases times height

196 = (4.6 + 15)/2 * s

196 = 9.8s

s = 20

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

x = - 4

Step-by-step explanation:

Given

- x² - 8x - 16 = 0 ( multiply through by - 1 to clear the leading negative )

x² + 8x + 16 = 0 ← this is a perfect square

(x + 4)² = 0 ( take the square root of both sides )

x + 4 = 0 ( subtract 4 from both sides )

x = - 4

Answer:

f(x) = (x + 3)² - 14

Step-by-step explanation:

f(x) = x² + 6x - 5

To complete the square

add/subtract ( half the coefficient of the x- term)² to x² + 6x

f(x) = x² + 2(3)x + 9 - 9 - 5

     = (x + 3)² - 14 ← in vertex form

The function in vertex form is f : x → (x + 3)² - 14.

To convert the equation.

f : x → x² + 6x - 5 into the vertex form, you will need to complete the square.

First, you will need to add and subtract the square of half of the coefficient of the x term, which is (6/2)² = 9.

This will give you the equation.

f : x → x² + 6x - 5 + 9- 9

Next, you will need to factor the left side of the equation,

f : x → (x² + 6x + 9) - 5 - 9

Now, you can see that the left side of the equation is the square of

(x + 3)² so you can rewrite it as:

f : x → -(x + 3 )² - 5 - 9

Finally, you can simplify the right side of the equation to get:

f : x → (x + 3)² - (5 + 9)

f : x → (x + 3)² - 14.

Therefore, the vertex form is f : x → (x + 3)² - 14.

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Answer:

1

Step-by-step explanation:

say you don't have a dog.. your parents get you one dog, and then get you another, you now have 2 :)

Answer:

26 m

Step-by-step explanation:

Find what length is needed for fencing by finding the perimeter of the land.

Use the perimeter formula, P = 2l + 2w

Plug in the length and width:

P = 2l + 2w

P = 2(8) + 2(5)

P = 16 + 10

= 26

So, the length of wire needed is 26 m

Answer:Well logically She opened the fridge door first!

Step-by-step explanation:

Her eyes too

Answer:

To calculate APR, you can follow these 5 steps:

1. Add total interest paid over the duration of the loan to any additional fees.

2. Divide by the amount of the loan.

3. Divide by the total number of days in the loan term.

4. Multiply by 365 to find annual rate.

5. Multiply by 100 to convert annual rate into a percentage.

Don't know if you still need this, but thought I could help!