What are two ways in which humans can cause coral reef bleaching ​

Alternatively, we could also restrict the domain of f(x) to a range that excludes the values of x that produce non-unique values of y, such as x = -3, which produces a value of y = 2 for f(x).

what is domain ?

In mathematics, the domain of a function is the set of all possible input values (also called independent variables) for which the function is defined and produces a valid output. It is the set of values that we are allowed to input into the function.

In the given question,

For the inverse of f(x) = x² + 6x + 5 to be a function, we need to ensure that it passes the vertical line test. In other words, for every value of x, the inverse function should produce only one unique value of y.

To ensure that the inverse of f(x) is a function, we need to restrict the domain of f(x) to a range that produces only one value of y for each value of x. This means that we need to make sure that f(x) is one-to-one, or injective, meaning that no two distinct values of x can produce the same value of y.

To check if f(x) is injective, we can use the discriminant of the quadratic equation x² + 6x + 5 = y, which is b² - 4ac, where a = 1, b = 6, and c = 5. The discriminant is:

b² - 4ac = 6² - 4(1)(5) = 16

Since the discriminant is positive, there are two distinct real roots of the quadratic equation, which means that f(x) is not injective and therefore does not have an inverse that is a function.

To ensure that the inverse of f(x) is a function, we need to restrict the domain of f(x) to a range that produces only one value of y for each value of x. One way to do this is to restrict the domain of f(x) to only include the values of x for which the discriminant is non-negative, meaning that the quadratic equation x² + 6x + 5 = y has real roots. This can be expressed as:

b² - 4ac >= 0

6² - 4(1)(5) >= 0

16 >= 0

This inequality is true for all values of x, which means that we can restrict the domain of f(x) to the entire real line to ensure that the inverse of f(x) is a function. Alternatively, we could also restrict the domain of f(x) to a range that excludes the values of x that produce non-unique values of y, such as x = -3, which produces a value of y = 2 for f(x).

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Answer:

first calculate the area of the two triangles and add them up...calculate the area of the three rectangles on each side add them up...finally add the sum of the rectangles together with the triangle

Step-by-step explanation:

The expected number of gumballs of each color, if all five colors were equally likely to be put in the bag, would be 10 gumballs of each color.

If all five colors were equally likely to be put in the bag, then each color would have a 1/5 probability of being selected for each gumball. Since there are a total of 50 gumballs in the bag, we can calculate the expected number of gumballs for each color by multiplying the total number of gumballs (50) by the probability of each color (1/5).

Expected number of red gumballs = (1/5) * 50 = 10

Expected number of green gumballs = (1/5) * 50 = 10

Expected number of orange gumballs = (1/5) * 50 = 10

Expected number of yellow gumballs = (1/5) * 50 = 10

Expected number of blue gumballs = (1/5) * 50 = 10

Therefore, if all colors were equally likely, we would expect to have 10 gumballs of each color in the bag.

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Answer:

Option (3). x < 3

Step-by-step explanation:

Given function is a logarithmic function,

\(y=\text{ln}[\frac{(-x+3)}{2}]\)

We know that logarithm is defined for all positive real numbers except zero.

\(\frac{(-x+3)}{2}>0\)

(-x + 3) > 0

-x > -3

x < 3

That means the given logarithmic function is defined for all real values lees than 3.

And the domain of the function will be x < 3

Option (3) will be the answer.

Answer:

x < 3        Option C on E2020.

Step-by-step explanation:

Answer:  10

Step-by-step explanation:

20% is 10% of 50 % because you /   100 in half and 20 in half and it's the same thing the answer is 10, my guy.

Answer:

Volume of the counter = Length × Width × Height

                                      = 19 1/2 × 8 3/4 × 2

                                      = 341 1/4 cubic metres

The percentage increase in the price of petrol is approximately 5.56%.

Percentages are used to compare and express parts of a whole, and to express changes or differences in values. For instance, we can use percentages to express:

A discount or a markup in prices

The increase or decrease in a quantity or value

The proportion of a quantity compared to a whole

The probability of an event occurring.

In the given question,

To determine the percentage increase in the price of petrol, we need to calculate the difference between the old price and the new price, divide that by the old price, and then multiply by 100 to convert to a percentage.

The difference between the old price and the new price is:

R 13.28 - R 12.58 = R 0.70

Dividing the difference by the old price:

R 0.70 ÷ R 12.58 ≈ 0.0556

Multiplying by 100 to convert to a percentage:

0.0556 × 100 ≈ 5.56%

Therefore, the percentage increase in the price of petrol is approximately 5.56%.

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Answer:

0.286

Step-by-step explanation:

2/7 as a decimal is 0.28571429

0.28571429 rounded to thousandths place = 0.286

hope this helps!!!

The decimal form of the number will be 0.286

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the fractional number is 2/7. The decimal form of the number will be,

2/7 as a decimal is 0.28571429 by dividing the number 2 by 7.

Rounded to the thousandths place,

0.28571429 = 0.286

Hence, the decimal form of the number will be 0.286

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Answer:

2√3π cm

Step-by-step explanation:

area of circle: πr²

area = A²

A =√ 12π

therefore, A = 2 √ 3π

Answer:

answer: 2* pi * sqrt(3)

Step-by-step explanation:

Area = pi * r^2

12*pi = pi * r^2

sqrt(12) = r

r = 2*sqrt(3)

The diameter of the circle is twice as larger.

d = 2(2sqrt(3))

d = 4 sqrt(3)

the circumference of a circle is d*pi

1/2 the circumference is pi*d/2

The arc length =  1/2 the circumference

The arc length = pi*d/2 = pi * 4*sqrt(3)/2 = 2* pi * sqrt(3)

Use the equations for the circumference and the area of a circle

For the circumference:

The circumference is 37.68 ft.

For the area

The area is 113.04 ft.

The solution of the system of equations f(x) = 2^x + 1 and g(x) = 3^x is x = 1

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

f(x) = 2^x + 1

g(x) = 3^x

The above expression is a system of exponential equations

We are required to solve by graph

That implies that we graph the equations in the system on the same plane and write out ordered pairs from the point of intersection of the equations in the system

Next, we plot the graph

See attachment for the graph of the equations

The ordered pairs of the intersection point is (1, 3)

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Answer:

none

Step-by-step explanation:

\(one \: fifth = \frac{1}{5} \\ from \: the \: options \: no \: fraction \: is \: equivalent \: to \: one \: fifth \: and \: non \: of \: the \: fracrions \: can \: be \: reduced \: to \: give \: one \: fifth \\ so \: the \: answer \: is \: none\)

y = (2x + 1)/(3x + 4)

y(3x + 4) = (2x + 1)

3xy + 4y = 2x + 1

4y - 1 = 2x - 3xy

4y - 1 = x(2 - 3y)

x = (4y - 1)/(2 - 3y) , answer = E

The solutions of the system of equations are 8 and -4.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

-4x - y = -28 _____(1)

x + y = 4 _____(2)

x = 4 - y _____(3)

Substituting (3) in (1) we get,

-4(4 - y) - y = -28

-16 + 4y - y = -28

-16 + 3y = -28

3y = -28 + 16

3y = -12

y = -4

Substituting y = -4 in (3) we get,

x = 4 - (-4)

x = 4 + 4

x = 8

Thus,

The value of x is 8.

The value of y is -4.

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Answer:

The teenager will travel 9 miles in one hour

Step-by-step explanation:

54 miles in 6 hours --> x miles in one hour

54 miles/6 hours --> x miles/1 hour

nine miles in one hour

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Answer:

1/3600

Step-by-step explanation:

10^-2=1/100

6^-2=1/36

(1/100)*(1/36)=1/3600

We can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

A 95% confidence interval for the population mean can be constructed using the t-distribution when the sample size is small (<30) or the population standard deviation is unknown.

In this case, we have a random sample of 46 people with a mean body mass index (BMI) of 27.2 and a standard deviation of 6.0.

Thus, we need to use the t-distribution to construct the confidence interval.

The formula for the confidence interval is as follows:

Upper limit of the confidence interval:27.2 + (2.013) (6.0/√46) = 29.032Lower limit of the confidence interval:27.2 - (2.013) (6.0/√46) = 25.368

Therefore, the 95% confidence interval for the population mean BMI is (25.368, 29.032).

This means that we can be 95% confident that the true population mean BMI is between 25.368 and 29.032.

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Answer:

8

Step-by-step explanation:

−6−(−8)+6

=2+6

=8

Answer:

x=4\(\sqrt{5}\),y=8\(\sqrt{5}\)

Step-by-step explanation:

sin∠SRT = sin∠TSV,

SO  \(\frac{x}{20} =\frac{4}{x}\), \(x^{2}\)=80,x=\(\sqrt{80} =4\sqrt{5}\);

In the same way:

sin∠RSV = sin∠RTS,

SO \(\frac{16}{y} =\frac{y}{20}\)，\(y^{2}\)=320,y=8\(\sqrt{5}\)

When the following equations are solved with elimination method, the values of X and y are as follows:

1.)X= 2; y = 9

2.) X= 2 ; y = 1

3.) X = 38.8; y =-6.7

For question 1;

y = 6x-3

5x = 2y-8

Rewrite each equation in the form Ax + y = C.

3 = 6x-y ---> equation 1

8 = -5x+2y----> equation 2

Multiply the first equation by 2 so that the coefficients of y in each equation will be opposites with a sum of 0.

2(3) = 2(6x-y)

6 = 12x -2y

Add the two equations to eliminate the variable y. Then solve for x.

12x -2y = 6

+ -5x+2y = 8

7x = 14

X = 14/7 = 2

Substitute x into the first equations and solve for y.

y = 6(2) -3

y = 12-3

y = 9.

For question 2;

12x+4y= 28

y = 3x-5

Rewrite each equation in the form Ax + y = C.

28 = 12x+4y

5 = 3x-y

Multiply the second equation by 4 so that the coefficients of y in each equation will be opposites with a sum of 0.

4(5) = 4(3x-y)

20 = 12x- 4y

Add the two equations to eliminate the variable y. Then solve for x.

12x+4y= 28

+ 12x- 4y = 20

24x = 48

X = 48/24 = 2

Substitute x into the first equations and solve for y.

Y = 3(2)-5

y = 6-5 = 1

For question 3;

4x = 2y + 12

4y = 12-x

Rewrite each equation in the form Ax + y = C.

12 = 4x -2y

13 = X + 4y

Multiply the second equation by -4 so that the coefficients of x in each equation will be opposites with a sum of 0.

-4(13) = -4(x+4y)

-52 = -4x-4y

Add the two equations to eliminate the variable x. Then solve for y.

4x -2y = 12

+ -4x-4y = -52

-6Y = 40

y = -40/6 = -6.7

Substitute y into the first equations and solve for X.

4(-6.7) = 12-x

-26.8 = 12-X

X = 12+26.8

X = 38.8

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Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

Answer:

-n-2

Step-by-step explanation:

First, you need to distribute the 2 on the -2n and -1. So multiply the 2 by -2n and -1. You get = -4n-2.

You still have the 3n, so the equation will now look like: 3n-4n-2.

Combine like terms. 3n-4n= -1n or just -n.

Now you have -n-2.

Answer:

p = -15

Step-by-step explanation:

-2 = (p+9)/3 multiply both sides by 3 to get rid of fraction

-6 = p + 9 subtract 9 from both sides

-15 = p

The equation is separable. The solution to the initial value problem is y(t) = y(0) = -3.

A. The equation is separable. The solution to the initial value problem is y(t) = ___

To determine whether the given differential equation is separable, we need to check if it can be written in the form dy/dt = g(t) * h(y), where g(t) is a function of t only and h(y) is a function of y only.

In this case, the equation is dy/dt = 2ty + 1. We can rearrange it as:

dy = (2ty + 1) dt

Now, we can see that we have both y and t terms on the right-hand side, indicating that the equation is not yet separable.

Therefore, the correct choice is B. The equation is not separable.

Unfortunately, no solution can be provided for the initial value problem y(0) = -3 since the equation is not separable.

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Answer:

The slope is -2. The y intercept is 4.

Step-by-step explanation:

The trigonometric function can be used to calculate the distance (4124966.128 AU) between the star and also the sun.

d = 4124966.128

Given:

Step 1: To calculate the distance in astronomical units here between star and the Sun, apply the trigonometric function.

The sine function is used to calculate the distance in step two.

sin Ф = P/ H

where H is the hypotenuse and P is the perpendicular.

Step 3: Replace the above expression with the known terms.

sin (0.00001389 ) = 1/d

Step 4: Condense the previous expression.

d = 4124966.128

Thus, the distance of star from the sun is found as d = 4124966.128.

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