What are the domain and the range of this function? f(x)= log (x-6)

The length of x, given the similar triangles, can be found to be 1 cm.

To find the length of x, you should find the scale factor by which the larger figure was derived from the smaller triangle.

You can do this by using the length of two corresponding sides in the two triangles. We can use the corresponding sides of 6 cm and 1. 5 cm.

The scale factor then is:

= 6 / 1. 5

= 4

The length of x would be the found by using the scale factor and the corresponding length of 4 cm which is then:

= 4 / 4

= 1 cm

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The probability of pulling out 2 red marbles at random from the jar is approximately 0.0741 or about 7.41%.

A combination is a choice of things without respect to order, whereas a permutation is an arrangement of objects in a certain order in probability and combinatorics. In other terms, a combination is an unordered selection of things from a set, but a permutation is an ordered arrangement of a collection of objects.

Given that, a jar containing 8 red marbles and 20 blue marbles.

The total number of marbles are:

8 + 20 = 28.

To choose 2 marbles out of 8 red marbles we have:

C(8,2) = 8! / (2! * (8-2)!) = 28

Similarly, the total number of ways to choose 2 marbles out of 28 is:

C(28,2) = 28! / (2! * (28-2)!) = 378

The probability of choosing 2 red marbles from the jar is:

P(2 red marbles) = 28 / 378 = 0.0741

Hence, the probability of pulling out 2 red marbles at random from the jar is approximately 0.0741 or about 7.41%.

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10 and 1/3 minus 7 and 2/3 is equal tο 8/3 οr 2 and 2/3.

In Maths, a fractiοn is used tο represent the pοrtiοn/part οf the whοle thing. It represents the equal parts οf the whοle. A fractiοn has twο parts, namely the numeratοr, and denοminatοr. The number οn the tοp is called the numeratοr, and the number οn the bοttοm is called the denοminatοr.

Tο subtract 7 and 2/3 frοm 10 and 1/3, we can write bοth as imprοper fractiοns with a cοmmοn denοminatοr and then subtract:

10 and 1/3 - 7 and 2/3 = (31/3) - (23/3)

Tο subtract these fractiοns, we need a cοmmοn denοminatοr, which is 3. We can rewrite the fractiοns with the cοmmοn denοminatοr οf 3:

(31/3) - (23/3) = (31 - 23)/3 = 8/3

Therefοre, 10 and 1/3 minus 7 and 2/3 is equal tο 8/3 οr 2 and 2/3.

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Complete question:

Convert the given sentence in to an algebraic expression and solve. Ten and one third minus seven and two thirds

According to the question as a fraction squared the value we will get at the end is 9/25.

A fraction is a numerical representation of part of a whole. It is written as a ratio of two numbers, separated by a slash (/). The top number in the fraction, known as the numerator, represents the number of equal parts of the whole, while the bottom number, known as the denominator, represents the total number of parts in the whole. For example, a fraction of "1/4" means that one of the four equal parts of the whole is being represented. Fractions are used to represent ratios and can also be used to represent parts of a whole.

This is because 3/5 can be rewritten as the fraction 6/10, and the square of this fraction is (6/10)² = (6/10)(6/10) = 36/100
= 9/25.

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The solution for y in the triangle by virtue of similar triangles is 3√7

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

The triangle

Using the theorem of similar triangles, we have the following equation

y/9 = 7/y

Cross multiply the above equation

so, we have the following representation

y^2 = 9 * 7

Evaluate

y^2 = 63

Take the square root of both sides

y = 3√7

Hence, the solution for y is 3√7

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Janey's height from age 7 to age 12 can be modeled by the function h(t)=45+85, where h(t) is Janey's height in inches and t is time in years since age 7. Based on the function, the statement is true: Janey grew 5 inches every year from age 7 to 12.

To find Janey's height at age 12, we can substitute t = 5 into the function h(t) = 45 + 85t:

h(5) = 45 + 85(5) = 450 inches

Therefore, at age 12, Janey's height is 450 inches.

To find how much Janey grew from age 7 to age 12, we can subtract her height at age 7 (which is h(0)) from her height at age 12 (which is h(5)):

h(0) = 45 + 85(0) = 45 inches

h(5) = 450 inches

So, Janey grew by:

450 inches - 45 inches = 405 inches

To find how much Janey grew per year on average, we can divide the total growth by the number of years between age 7 and age 12:

(405 inches) / (5 years) = 81 inches/year

Therefore, the statement that is true is:

Janey grew 5 inches every year from age 7 to 12.

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After answering the given query, we can state that In this case, %Y = 0, equation so this would not be a component in inducing inflation.

An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals symbol ('='). For example, 2x – 5 equals 13. Expressions like 2x-5 and 13 are examples. The letter '=' connects the two phrases. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal symbol (=). It shows how the right and left algorithms are equivalent to one another. Any calculation will result in L.H.S. = R.H.S. (left side = right side).

The quantity theory of money, which asserts that the price level (P) is inversely proportional to real GDP and directly proportional to the money supply (M) and velocity of money (V), is represented by the equation%M +%V %P +%Y. (Y)

Therefore, for there to be inflation (%P > 0), there must also be a rise in the velocity of money (V) (%V > 0). This indicates that money is exchanging hands more frequently, which causes consumers to spend more money and rates to rise.

Alternatively, if the money supply stays constant and the velocity of money increases, a rise in real GDP (Y) would also cause an increase in the price level. In this case, %Y = 0, so this would not be a component in inducing inflation.

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The equation [tex]\frac{1}{3}[/tex] x [tex]\frac{3}{5}[/tex] can be used to find the fraction of the students who play soccer.

What is an equation?

A statement proving the equality of two expressions involving variables and/or numbers is known as an equation. Equations are ultimately questions, and attempts to methodically solve these problems have served as the primary driving forces behind the creation of mathematics.

We are given that at Jefferson Middle School, [tex]\frac{3}{5}[/tex] of the students play a sport. Of those students, [tex]\frac{1}{3}[/tex] play soccer.

So, the fraction of students who play soccer is given by the expression

[tex]\frac{1}{3}[/tex] x [tex]\frac{3}{5}[/tex]

Hence, the equation [tex]\frac{1}{3}[/tex] x [tex]\frac{3}{5}[/tex] can be used to find the fraction of the students who play soccer.

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Question: At Jefferson Middle School, 3/5 of the students play a sport. Of those students, 1/3 play soccer. What equation can be used to find what fraction of the students play soccer

A 1/3 - 3/5

B 1/3 x 3/5

C 1/3 + 3/5

D 1/3 ÷ 3/5

Answer:

94

Step-by-step explanation:

Five times a number less sum twelve as equal to two times the number multiplied by twelve. There are twelve.

The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined. In the example above, the sum of the addends, 6, and 4, is 10. Below is another illustration: Thus, we may argue that 8 plus 5 equals 13, or 8 plus 5 equals 13.

Prepare: We'll find x.

Spread out the 2 initially on a left side of this equation:

2x plus 24 = 5x - 12

After that, shift all of the x terms to a left and each of the constant terms towards the right:

2x - 5x = -12 - 24

-3x = -36

In order to find x, divide both sides by -3.

x = 12

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Answer: We can use the formula for compound interest to find the future value of the $2,000 gift:

FV = PV * (1 + r/n)^(n*t)

where PV is the present value of the gift, r is the annual interest rate, n is the number of compounding periods per year, t is the number of years, and FV is the future value.

In this case, PV = $2,000, r = 0.07 (7%), n = 4 (quarterly compounding), and t = 17. Substituting into the formula, we get:

FV = $2,000 * (1 + 0.07/4)^(4*17)

Simplifying, we get:

FV = $2,000 * (1.0175)^68

Using a calculator, we get:

FV = $6,186.22 (rounded to two decimal places)

Therefore, the $2,000 gift will be worth approximately $6,186.22 in 17 years if it is invested at 7% and compounded quarterly.

Step-by-step explanation:

Answer:

20 Quarts

Step-by-step explanation:

A gallon has 4 quarts, so

5*4 =20

First we will see how many quarts are in a gallon.

1 gallon = 4 quarts.

Now lets MULTIPLY to get our answer.  

5 gallon = ? quarts

5 × 4 = 20

So, the cooler has 20 quarts or 5 gallons.

The solution to the system of equations is (-2, -6).

What are system of equations ?
A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfies all of the equations in the system.

For example, consider the following system of equations:

x + y = 5

2x - y = 3

According to the question:

To find the solution to the system of equations, we need to find the point where the two lines intersect. We can do this by setting the two equations equal to each other:

3x = x - 4

Subtracting x from both sides, we get:

2x = -4

Dividing both sides by 2, we get:

x = -2

Now that we know that x = -2, we can substitute this value into either of the equations to find y. Using the first equation, we get:

y = 3(-2) = -6

Therefore, the solution to the system of equations is (-2, -6).

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When you round 19995 to the nearest ten, you look at the digit in the tens place, which is 9. Since 9 is greater than or equal to 5, you round up the digit in the thousands place to the next higher number, which is 20000.

Therefore, 19995 rounded to the nearest ten is 20000.

Answer:

171 ft squared

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

((-9-11)/(-4))/ (−7^2 + (11 x 2^2)) can be simplified as follows:

((-9-11)/(-4))/ (−7^2 + (11 x 2^2))

= (-20 / -4) / (-49 + 44)

= (5) / (-5)

= -1

Therefore, ((-9-11)/(-4))/ (−7^2 + (11 x 2^2)) simplifies to -1

Answer:

Step-by-step explanation:

all in the picture

The domain of the function f(x) is the set of all real numbers.

For any function y = f(x), we define the domain as the set of the possible inputs of the function, this would be the set of the possible x-values.

We usually assume that the domain is the set of all real numbers and then we remove the problematic points, these are the values of x that make a denominator equal to zero, or that give a negative argument for a square root for example.

In this particular case we have a polynomial function:

f(x)=-x^4+2x^2-x-2

Notice that there is no denominator, no square root, no logarithm, then there are no problematic points. This function works fine for all real numbers, then the domain is the set of all real numbers.

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Answer:

Domain = (−∞,∞),{x|x∈R}

Range = (−∞,0.05617288],{y|y≤0.05617288}

Answer:

$17.53

Step-by-step explanation:

385.66 / 22 = 17.53

The total length of the two sides, 1 and 2, of the triangle is 15x2 − 6x + 1. This can be shown by adding the two polynomials side by side.

Part A:

The total length of the two sides, 1 and 2, of the triangle is 15x2 − 6x + 1. This can be shown by adding the two polynomials side by side.8x2 − 5x − 2 + 7x − x2 + 3 =5 ,8x2 + 7x − 5x − x2 − 2 + 3 =15x2 − 6x + 1Part B:

The length of the third side of the triangle is 15x2 − 6x + 1, which is the same as the total length of the two sides in Part A. This can be shown by subtracting the two polynomials side by side.

15x2 − 6x + 1 − (8x2 − 5x − 2 + 7x − x2 + 3) =

15x2 − 6x + 1 − (8x2 + 7x − 5x − x2 − 2 + 3) =

15x2 − 6x + 1 − 15x2 + 6x − 1 = 0Part C:

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction. This can be seen by the fact that the total length of the two sides of the triangle is the same as the length of the third side of the triangle, which is 15x2 − 6x + 1. This means that when the two polynomials are added or subtracted, the resulting polynomial is the same regardless of the order in which they are added or subtracted. This is a sign that the polynomials are closed under addition and subtraction.

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Answer:

Pi/4

Step-by-step explanation:

first we have to figure out what cos of 7pi/4 is. Using the unit circle, we know that it is equal to root2/2. Cos to the negative 1 is basically just finding the radian value that matches the value in the parenthesis. This means we have to find the corresponding radian to root2/2. Using the unit circle, we find this to be pi/4

Answer: To solve 18 ÷ 8 using the algorithm, we can follow these steps:

- Write 18.00 above the division bar.

- Write 8 to the left of the division bar.

- Divide 8 into the first digit of 18 (which is 1) and write the result (0) above the division bar, and write the remainder (1) below the digit 1.

- Bring down the next digit (8) and write it next to the remainder (1) to get 18.

- Divide 8 into 18 and write the result (2) above the division bar, and write the remainder (2) below the digit 18.

- Since we have no more digits to bring down, we have our final answer: 18 ÷ 8 = 2 with a remainder of 2.

So, using the algorithm, we find that 18 ÷ 8 is equal to 2 with a remainder of 2.

Step-by-step explanation:

The predicted values of y might not be accurate if any of the x-values lie outside of the range of x-values used to calculate the regression line.

One variable (the independent variable) is used to forecast the other variable in linear regression, a statistical technique for examining the relationship between two variables (the dependent variable). In linear regression, the connection between the variables is represented by a line (or curve) fitted to the data points. The regression line is the name assigned to this line, and it is used to forecast values of the dependent variable based on the independent variable.

given

To determine the regression line's equation:

Determine the r-value, or correlation coefficient, between the x and y numbers.

To determine the slope (b) of the regression line, use the numbers from steps 1-3: b = r * (s y / s x).

Calculate the regression line's y-intercept (a) using the numbers from steps 1-4: a = mean(y) - b * mean (x).

The regression line's equation is: y = a Plus bx.

The predicted value of y is meaningful if the x-value is within the range of x-values used to compute the regression line.

The projected value of y is affected if the x-value is outside of that range.

For instance, if the regression line's equation is y = 3.2 + 0.6x, then:

(a) Y = 6.4 when x = 5 victories (predicted earned run average).

(b) If y = 9.2 and x = 10 triumphs (predicted earned run average).

(c) If y = 14.6 and x = 19 triumphs (predicted earned run average).

(d) With 15 victories, x, y = 11.2 (predicted earned run average).

The predicted values of y might not be accurate if any of the x-values lie outside of the range of x-values used to calculate the regression line.

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From the exponential distribution, the probability of an emergency arrival occurring in the next minute is the same regardless of how long we have already been waiting.

If X follows an exponential distribution with parameter θ, then the expected value (mean) of X is equal to θ.

In this case, θ = 8, so the average waiting time between two emergency arrivals is also 8 minutes.

This means that on average, we expect an emergency arrival to occur every 8 minutes. However, it is important to note that the exponential distribution is memoryless, meaning that the probability of an emergency arrival occurring in the next minute is the same regardless of how long we have already been waiting.

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The students' reasoning is flawed as adding 2 numbers doesn't necessarily result in 101.

What is reasoning?

Mathematical reasoning is the act of applying logical and critical thinking to a mathematical problem in order to determine the best approach to take (and, just as essential, the approach to avoid taking) in order to arrive at a solution.

The student's reasoning is flawed because there is no reason to expect that the sum of the two values should be 101.

The problem asks for the percentage of students who chose option A and the percentage of students who chose option B, which are two independent values that do not necessarily add up to 100 or any other fixed number.

In fact, it is possible for both percentages to be less than 50% or greater than 50%, depending on the distribution of the other options and the total number of students.

Therefore, the fact that the two values do not add up to 101 does not necessarily mean that the student's answer for part b is incorrect.

Instead, the student should check their calculations and assumptions to make sure they have followed the correct procedure for calculating percentages.

Therefore, the student's reasoning is flawed.

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The function C(k) that models the amount Liana will pay for using k kilowatt hours of electricity in one month is: [tex]C(k) = 0.0682k - 8.32.[/tex]

We must find the function C(k) that models the amount Liana will pay in one month for using k kilowatt-hours of electricity.

The ordered pair for November and September is now (550,45.83) and (1250,93.57), respectively. The function will be linear because she pays the same amount for each kilowatt-hour of electricity.

So, the model equation can be written as:

[tex](C(k) - 93.75) / (93.75 - 45.83) = (k - 1250) / (1250 - 550)\\(C(k) - 93.57) / 47.74 = (k -1250) / 700\\C(k) - 93.57 = 0.0682k - 85.25\\C(k) = 0.0682k - 85.25 + 93.57 \\C(k) = 0.0682k - 8.32.[/tex]

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Answer:

Step-by-step explanation:

the magnitude of ∠DGF= ∠BAD (alternate angles)

∴the magnitude of ∠DGF=40°

∠ FDG=∠ADB(VERTICALLY OPP. ANGLES)

∠FDG= 180-(90+40)

          = 50°

by using the Pythagoras' theorem

FD²+2²= 4²

FD²= 12

FD= 2√3

Hence, in answering the stated questiοn, we may say that We knοw they equatiοn are perpendicular tο each οther since the prοduct οf their slοpes equals -1.

A math equatiοn is a methοd that links twο claims and represents equivalence using the equals sign (=). An equatiοn is a mathematical statement that establishes the equivalence οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the numbers 3x + 5 and 14. A mathematical fοrmula may be used tο describe the relatiοnship between the twο sentences οn οppοsite sides οf a letter. In usually, the lοgο and the prοgramme are the same. Fοr instance, 2x - 4 equals 2.

The οld rοad has a slοpe οf 3, hence the new rοad will have a slοpe οf -1/3.

Let's name the new rοad's equatiοn y = mx + b, where m is the slοpe and b is the y-intercept.

We knοw that the new rοad must gο past pοint (1,1), therefοre

1 = (-1/3)(1) + b

b = 4/3

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

We may cοmpute the prοduct οf their slοpes tο ensure that this new rοad crοsses the current rοad at a perpendicular angle.

Because the new rοad's slοpe is -1/3 and the present rοad's slοpe is 3, their prοduct is:

(-1/3) * 3 = -1

We knοw they are perpendicular tο each οther since the prοduct οf their slοpes equals -1.

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The solution for each of the ordered pair for the the system of equations is found.

Part a: y = 3x+5 ; (-6, -13), (1,8)-  (solution) ; (-4,1), (0, -5)- (not a solution).

Part b: -9x + 3y=15 : (-6, -13), (-6, -13) - (solution); (-4,1), (0, -5) - (not a solution).

Part a: y = 3x+5

(-6, -13)

put x = -6

y = 3(-6)+5 = -13 (solution)

(-4,1)

y = 3(-4)+5 = -7 (not a solution)

(0, -5)

y = 3(0)+5 = 5 (not a solution)

(1,8)

y = 3(1)+5 = -8 (solution)

Part b: -9x + 3y=15

Put each values and check;

(-6, -13)

-9(-6) + 3(-13) = 15

15 = 15  (solution)

(-4,1)

-9(-4) + 3(-1) = 15

33 ≠ 15  (not a solution)

(0, -5)

-9(0) + 3(--5) = 15

-8 ≠ 15  (not a solution)

(1,8)

-9(1) + 3(8) = 15

15 = 15  (solution)

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Answer:

The error is $2.44.