Evaluate the expression (27÷3) x (5+9)

Final answer:

A rational function with vertical asymptotes at x = 3 and x = -4, x-intercepts at x = -1 and x = 5, and a horizontal asymptote at y = 6 is constructed by using factors that make the denominator zero at the vertical asymptotes and the numerator zero at the x-intercepts, with a constant ratio to define the horizontal asymptote.

Explanation:

To construct a rational function that meets the specified criteria, we need to ensure that the function has the correct vertical and horizontal asymptotes as well as the specified x-intercepts. A vertical asymptote occurs where the denominator of the rational function is equal to zero, whereas x-intercepts occur where the numerator is equal to zero.

The horizontal asymptote represents the end behavior of the function as x approaches infinity.

Step-by-step construction of the rational function

For vertical asymptotes at x = 3 and x = -4, the denominator must be zero at these points. So, we can use factors (x - 3) and (x + 4) in the denominator.

For x-intercepts at x = -1 and x = 5, the numerator must be zero at these points. Thus, we can use factors (x + 1) and (x - 5) in the numerator.

To incorporate a horizontal asymptote at y = 6, we need the degrees of the numerator and denominator to be the same, and the leading coefficients must have a ratio that equals 6. To achieve this, we introduce the constant 6 in the numerator.

The resulting rational function, considering all the conditions above, is:

f(x) = ​6(x + 1)(x - 5) / ((x - 3)(x + 4))

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have the point (-1, 6) and the slope m = -3. Substitute:

[tex]y-6=-3(x-(-1))\\\\\boxed{y-6=-3(x+1)}\to\boxed{B)}[/tex]

The number of pots required to plant 24 seeds will be 8.

The mathematical expression is the combination of 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 be used to denote the logical syntax's operation order and other properties.

Given that Anna buys 24 seeds and plants 3 in each pot. She has 5 pots.

The number of the pots will be calculated as Anna needs 3 more pots. 3 times 5 is 15 seeds. And she has 24 seeds. so 24 divided by 3 is 8. 8 minus 5 is 3.

Number = 24 / 3 = 8 pots

Therefore, the number of pots required to plant 24 seeds will be 8.

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Answer:

Step-by-step explanation:

The math thinking refers to the process you did to solve the sum 9 + 7.

To solve this we could think the following process:

1. We complete the first number to 10.

2. The completion subtracted one unit from 7, so now it's 6.

3. Then we sum the ten and the six, it's easier to operate with tens.

Therefore, the answer is 16.

Remember that not everyone solve math problems and exercises the same way, because we all are different from each other.

Answer:

x = 55°

Step-by-step explanation:

<4 = 105

<4 + <3 = 180 (supplementary angles, form a line)

180-105= 75

<3 = 75

The interior angles of a triangle always equal 180 degrees.

<3 = 75 degrees, <6 = 50, <2 = x

75+50+x = 180

125 + x = 180

x = 55°

Answer:

[tex]\log _3\left(81\right)=4[/tex]

Step-by-step explanation:

Given : [tex]\log _3\left(81\right)[/tex]

We have to find the value of [tex]\log _3\left(81\right)[/tex]

Consider [tex]\log _3\left(81\right)[/tex]

Rewrite 81 in base power form, [tex]81=3^4[/tex]

[tex]=\log _3\left(3^4\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)[/tex]

We have,

[tex]\log _3\left(3^4\right)=4\log _3\left(3\right)[/tex]

[tex]=4\log _3\left(3\right)[/tex]

[tex]\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1[/tex]

[tex]\log _3\left(3\right)=1[/tex]

[tex]=4\log _3\left(3\right)=4[/tex]

Thus,  [tex]\log _3\left(81\right)=4[/tex]

4

Now, we will solve the problem of the logarithm.

Some logarithmic properties used this time are as follows:

[tex]\boxed{ \ \log_{a} a = 1 \ }[/tex]

[tex]\boxed{ \ \log_{a}b^c = c \log_a b \ }[/tex]

Let us calculate the value of [tex]\boxed{ \ \log_3 81 \ }[/tex]

Recall that [tex]\boxed{ \ 81 = 3^4. \ }[/tex]

[tex]\boxed{ \ \log_3 81 = \log_3 3^4 \ }[/tex]

[tex]\boxed{ \ \log_3 81 = 4 \log_3 3 \ }[/tex]

[tex]\boxed{ \ \log_3 81 = 4 \times 1 \ }[/tex]

Thus, the result is [tex]\boxed{\boxed{ \ \log_3 81 = 4 \ }}[/tex]

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Alternative problem:

What is the value of [tex]\boxed{ \ \log_{81} 3 \ ? \ }[/tex]

Recall that [tex]\boxed{ \ 3 \rightarrow (3^4)^{\frac{1}{4}} \rightarrow 81^{\frac{1}{4}}. \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \log_{81} 81^{\frac{1}{4}} \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \frac{1}{4} \log_{81} 81 \ }[/tex]

[tex]\boxed{ \ \log_{81} 3 = \frac{1}{4} \times 1 \ }[/tex]

Thus, the result is [tex]\boxed{\boxed{ \ \log_{81} 3 = \frac{1}{4} \ }}[/tex]

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Notes:

The relationship between logarithms and exponents is as follows:

[tex]\boxed{ \ \log_{a}b = c \ } \leftrightarrow \boxed{ \ a^c = b \ }[/tex]

Keywords: what is the value of log3 81, logarithmic properties, base, numerous, exponential functions, inverses each other

Answer:

the boat was sold for $17,250

Step-by-step explanation:

Jimmy made a 15% profit, that means that  the 15% of the cost is going to be his profit, so the 15% of $15,000 is:

$15,000(0.15)= $2,250

If his profit is 2,250, the price of the boat is going to be the initial cost plus the profit. So:

Price=$15,000 + $2,250 = $ 17,250

Then, the boat was sold for $17,250

Using proportions and the profit concept, it is found that the boat sold for $17,250.

The rule of three is:

$15,000 - 1

$x - 1.15

Applying cross multiplication:

[tex]x = 15000(1.15) = 17250[/tex]

The boat sold for $17,250.

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To estimate the value of 98.5*13, you round 98.5 to 100 and 13 to 10, and then multiply to get an estimated product of 1000, which is a simple calculation that provides a close approximation to the precise answer of 1,280.5.

To estimate the value of 98.5*13, you can round 98.5 to the nearest ten and 13 to the nearest ten. So, 98.5 is approximately 100 and 13 is approximately 10. To estimate the product, you multiply these two numbers:

100 * 10 = 1000

The estimated value of 98.5*13 is therefore around 1000. The calculator gives 1,280.5 as the precise answer, but our estimate simplifies the calculation while providing a close approximation.

A better estimate for the length of an ironing board would be 120 inches, or 10 feet. This exercise illustrates the importance of carefully calculated approximations rather than relying on rough 'guesstimates'.

A better estimate for the length of an ironing board would be 120 inches, or 10 feet. This estimate is closer to the final approximate value mentioned in the discussion. However, the early estimate of 3 inches was significantly off. This exercise illustrates the importance of carefully calculated approximations rather than relying on rough 'guesstimates'.

The expression is 8 + n.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

A phrase: “twice the sum of four and a number”.

Let the number is n.

The according to the question:

Twice the sum of the four = 8

And a number 8 + n.

Therefore, the expression is 8 + n.

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The total number of people that attended dan's birthday party is;

30 People

We are told that 5 classmates attended dan's birthday party.

Number of classmates at birthday party = 5

We are told that this 5 people is only half of his summer camp friends that attended the birthday party.

Thus, number of summer camp friends that attended = 5 × 2 = 10

Similarly the 5 people is only a third of his relatives that attended the birthday party.

Thus, number of relatives that attended = 5 × 3 = 15

Therefore,

total number of people that attended dan's birthday party = 5 + 10 + 15 = 30 people

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