please help!!!!!!!!!!!!

The function represents the total number of seats will be 80x² + 560x. The correct option is B.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

Given that the number of rows in an auditorium can be represented by the function f(x) = 80x. The number of seats in each row can be represented by the function g(x) = x + 7.

The total number of seats will be:-

h(x)  = f(x)  x g(x)

h(x) = 80x ( x + 7 )

h(x) = 80x² + 560x

Therefore, the function represents the total number of seats will be 80x² + 560x. The correct option is B.

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Answer

368

Step-by-step explanation:

1840÷5=368

Answer:

170,

Step-by-step explanation:

my explanation is commented on the other persons answer

The sum log 4(11) + log 8(11) + log 64(11) can be expressed in the form log b(n), where b and n are positive integers, and b is as small as possible.The sum of b and n is 13.

1. Use the change of base formula to convert each logarithm to the same base (in this case, base 2):

- log 4(11) = log 2(11) / log 2(4) = log 2(11) / 2

- log 8(11) = log 2(11) / log 2(8) = log 2(11) / 3

- log 64(11) = log 2(11) / log 2(64) = log 2(11) / 6

2. Find the common denominator for the fractions, which is 6:

- (log 2(11) / 2) × (3/3) = 3 × log 2(11) / 6

- (log 2(11) / 3) × (2/2) = 2 × log 2(11) / 6

- log 2(11) / 6 stays the same

3. Add the numerators together:

- (3 × log 2(11) + 2 × log 2(11) + log 2(11)) / 6

- (3 + 2 + 1) × log 2(11) / 6

- 6 × log 2(11) / 6

4. Cancel out the 6 in the numerator and denominator, resulting in log 2(11).

5. The sum is expressed as log b(n) = log 2(11), so b = 2 and n = 11.

6. Finally, find b + n: 2 + 11 = 13.

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Answer:

Answer: 91 3/8 ft^2

Step-by-step explanation:

i assume is a width of 8 1/2 ft

we have a rectangle and the area is A=L*W

we have 8 1/2 x  10 3/4= 17/2  x 43/4= 731/8= 91 3/8 ft62

The prove to show that ΔABC is similar to ΔMNC is explained below.

Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Considering the given diagram, we can say:

AM = MC    (Given)

BN = NC     (Given)

BC = BN + NC (addition property of a line segment)

AC = AM + MC (addition property of a line segment)

NC/ BC = MC/ AC = constant

∠ACB = ∠MCN  (Reflexive property)

Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)

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Answer:

B

Step-by-step explanation:

None of the provided options are irrational. Irrational numbers are those which cannot be expressed as the ratio of two integers. In other words, if represented in decimal form, they would continue indefinitely after the decimal point, such as the value of π. This also means, by definition, they cannot be both irrational and an integer.

They are all real numbers as they can represent a distance along a line (they could all be plotted on a number line or graph, for instance).

Only 0 and 4 out of the provided options are integers (whole numbers). As mentioned above, all integers are rational by definition.

All the identifiers that are included when identifying significant digits are-

Each of the digits of a number starting with the digit farthest to a left that is not zero as well as ending with the digit farthest to a right that is neither zero or is a zero but is considered exact.

For the given options.

Except option 1 every option is correct.

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Answer:

Umbrella insurance is a type of personal liability coverage the goes above and beyond the amount the a regular home or vehicle insurance offers.

Step-by-step explanation:   I just looked it up hope that answers your question.

Answer:

x = 5

Step-by-step explanation:

All linear pairs are supplementary which means the angles add up to 180:

8x + 63 + 6x + 47 = 180

14x + 110 = 180

14x = 180 - 110

14x = 70

x = 5

Step-by-step explanation:

The circumference of a WHOLE circle = pi * d

   you have 1/2 of this  and d = 10 ft

     so   1/2 pi * 10      PLUS the two straight sides + 8+6

       1/2 pi * 10   + 8 + 6

         5 pi + 8 + 6

        5 * 3.14   + 14 = 29.7 ft

The temperature at 8:00 A.M. was 15°C.

Using the given information:
1. At 7:00 P.M., the temperature was 16°C.
2. This temperature was 9°C less than the temperature at 2:00 P.M.

We can use this information to find the temperature at 2:00 P.M.:
Temperature at 2:00 P.M. = 16°C (temperature at 7:00 P.M.) + 9°C
Temperature at 2:00 P.M. = 25°C

3. The temperature at 2:00 P.M. was 10°C higher than the temperature at 8:00 A.M.

Now, we can find the temperature at 8:00 A.M.:
Temperature at 8:00 A.M. = 25°C (temperature at 2:00 P.M.) - 10°C
Temperature at 8:00 A.M. = 15°C

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Answer:

In a right triangle, the mid–point of the hypotenuse is equidistant from the three vertices of triangle.

Therefore , the solution of the given problem of function comes out to be f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].

The mathematics programme covers a wide range of topics, including mathematics, numbers, but also their subsets, along with building, construction, and the both real and fictional geographic locations. A work covers the connections between different variable elements that all work together to produce the same result. A utility is made up of several distinctive components that, when combined, produce specific results for each input.

Here,

We must first assess g(x) in order to determine f[g(x)], and then we can use the outcome to determine f[g(x)].

=> g(x) = x² + 1

When we substitute g(x) for f(x), we obtain:

=> f[g(x)] = f(x² + 1)

=> 3(x² + 1) - 5 = 3x² + 3 - 5

=> 3x² - 2

Therefore, f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].

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Answer:

6

Step-by-step explanation:

Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6.

Answer:

The graph of the parent function y = 2^x can be transformed to create the graph of y = 2^(3x) by horizontally compressing by a factor of 3. Therefore, the correct answer is C.

To answer this question, we can use the Pythagorean Theorem to find three numbers that follow it. Then, we can proceed as follows:

1. We have that the hypotenuse has the greatest length in a right triangle. Then, we have:

• Legs of the right triangle: 11, 60.

• Hypotenuse: 62

Therefore:

This set does not represent the three sides of a right triangle.

Second Case: {45, 60, 74}

Answer:

45 fish

Step-by-step explanation:

If the population decreased 25%, you would subtract a fourth of 60 which is 15, 60 - 15 is 45.

Answer:

45

Step-by-step explanation:

25%x60=15

15-60=45 fish

The sum of p and q corresponds to the coefficient of the x-term in the quadratic trinomial. (C)

There is no specific part of the trinomial that equals the sum of p and q. (None)

The part of the quadratic trinomial that will equal the sum of p and q is the coefficient of the x-term.

To see why this is the case, let's expand the given binomials:

\((x + p)(x + q) = x^2 + px + qx + pq = x^2 + (p + q)x + pq\)

From the expansion, we can see that the coefficient of the x-term is p + q, which is the sum of p and q.

Therefore, the answer is C: The coefficient of the x-term.

This makes intuitive sense because when we multiply the binomials, we add the individual terms involving x, which are px and qx.

The sum of these terms, p + q, gives us the coefficient of the x-term in the resulting quadratic trinomial.

It's important to note that the degree refers to the highest power of x in the trinomial, the constant term is the term with no x, and the coefficient of the x-term is the coefficient attached to the x.

In this case, the sum of p and q corresponds to the coefficient of the x-term.

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It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Answer:

the answer is 10

Step-by-step explanation:

sorry but I don't have the working for this

Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

We take the inverses of the function and get the results as follows:

\(f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1\),  \(f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2\), \(f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3\)

What are the inverses of a function?

A function that can change into another function is referred to as being inverse or anti. In other words, the inverse of any function "f" will take y to x if it takes x to y in the first place. The inverse function is indicated by  F^-1 if the function is denoted by F.

Given C={1,2,3}, and

\(f(x)=x^{2} +1\\ f^{-1}(x)=\sqrt{x-1} \\f^{-1}(f(x))=\frac{\sqrt{\sqrt{4(x)+1} -3}}{\sqrt{2} } \\f(f^{-1} (x))=x\)

Now,

For C=1,

\(f(1)=1+1=2\\f^{-1}(1)=\sqrt{1-1}=0\\f^{-1}(f(1))=\frac{\sqrt{\sqrt{4(1)+1} -3}}{\sqrt{2} } \\f(f^{-1} (1))=1\)

For C=2

\(f(2)=4+1=5\\f^{-1}(2)=\sqrt{2-1}=1\\f^{-1}(f(2))=\frac{\sqrt{\sqrt{4(2)+1} -3}}{\sqrt{2} } \\f(f^{-1} (2))=2\)

For C=3

\(f(3)=9+1=\sqrt{10} \\f^{-1}(3)=\sqrt{3-1}=\sqrt{2} \\f^{-1}(f(3))=\frac{\sqrt{\sqrt{4(3)+1} -3}}{\sqrt{2} } \\f(f^{-1} (3))=3\)

Hence, the solution is provided.

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Answer:

31, the five halves of is 6.2

Step-by-step explanation:

Answer:

n = 4

Step-by-step explanation:

We are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.

To do this, we need to isolate n one one side.

Let's start by adding 2 to both sides.

7n - 2 = 5n + 6

   +2           +2

_______________

7n = 5n + 8

Now, subtract 5n from both sides.

7n = 5n + 8

-5n   -5n

_______________

2n = 8

Divide both sides by 8 to get the value of n.

2n = 8

÷2   ÷2

________

n = 4

Answer:

\( \dfrac{4m^2n}{3p} \)

second choice

Step-by-step explanation:

Deal with the numbers first, then with each set of equal variables.

Use the rule a^m/a^n = a^(m - n)

4/3 cannot be reduced, so the number part remains 4/3.

m^4/m^2 = m^2

n^3/n^2 = n^1 = n

p^3/p^4 = p^-1 = 1/p

Now put it all together:

\( \dfrac{4m^2n}{3p} \)

second choice

\(\\ \sf{:}\longrightarrow \dfrac{4m^4n^3p^3}{3m^2n^2p^4}\)

\(\\ \sf{:}\longrightarrow \dfrac{4}{3}m^{4-2}n^{3-2}p^{3-4}\)

\(\\ \sf{:}\longrightarrow \dfrac{4m^2np^{-1}}3}\)

\(\\ \sf{:}\longrightarrow \dfrac{4m^2n}{3p}\)