find the missing side of each triangle.Leave your answers in simplest radical form.A 3√39B√619C2√14D√563E√394

The inverse of the equation is determined as \(y = \log_{6}(-3x)\).

option D is the correct answer.

The inverse of the equation is calculated by applying the following method;

The given equation;

y = - 6ˣ/3

The inverse of the equation is calculated as;

multiply through by 3

\(-3x = 6^y\)

Take the logarithm of both sides of the equation with base -6:

\(\log_{6}(-3x) = y\)

Finally, replace y with x to obtain the inverse equation as follows;

\(y = \log_{6}(-3x)\)

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Answer: log(2) 512= 9

Step-by-step explanation:

A P E X ;)

In logarithmic form, the expression \(2^9 = 512\) can be rewritten as follows:

\(log_{(2)}\ 512 = 9\)

As we know that the logarithmic form allows us to express the exponent as the logarithm of the base to a certain value, which in this case is 9.

To understand this, let's break down the expression.

The base of the logarithm is 2, and the result of raising 2 to the power of 9 is 512.

By taking the logarithm of 512 to the base 2, we get the exponent, which is 9.

So, in logarithmic form can be written as:

\(log_{(2)}\ 512 = 9\)

Therefore, in logarithmic form, the expression \(2^9 = 512\) can be rewritten as follows:

\(log_{(2)}\ 512 = 9\)

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Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

The constant of​ proportionality of the equation y = 5/7x is 5/7

The equation that describes a proportional relationship between x and y is given as

y = 5/7x

A proportional equation is represented as

y = kx

Where k represents the constant of​ proportionality

By comparing the equations y = kx and y = 5/7x, we have the following equations

y = y

k = 5/7

x = x

The above equations mean that the constant of​ proportionality of the equation k

This can also be rewritten as the constant of​ proportionality of the equation y = 5/7x is 5/7

Hence, the constant of​ proportionality of the equation y = 5/7x is 5/7

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To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

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

To simplify this expression, we can expand the square:

\(f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20\)

Therefore, f(g(x)) simplifies to\(x^2 - 8x + 20.\)

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

\(g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2\)

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to\(x^2 - 8x + 20\), and g(f(x)) simplifies to 1/x^2.

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The sum of the infinite geometric sequence is 3 3/4

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

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

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Feet long bricks - 0.75

No of bricks she added

is 15

So now we will multi plied

0.75× 19

Se solution 0.75

× 15

________

11 . 25

So the Answer is 11 . 25 is the final

answer

hope this Answer will help you

The normal range using a compound inequality is 1.5 < x < 4

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

pH values less than 4

pH values greater than 1.5

Represent the pH values with x

Using the above as a guide, we have the following:

x is less than 4

x is greater than 1.5

When represented as inequality, we have

x < 4 and x > 1.5

Combine the inequalities

1.5 < x < 4

Hence, the normal range is 1.5 < x < 4

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The smallest possible value of the number that is an integer is -21

From the question, we are to determine the smallest possible value of the number

From the given information, we have that

"Twenty less than a number is more than twice the same number"
Let the number be x

Then,

we can write that

x - 20 > 2x

Now, we will solve for x

x - 20 > 2x

-20 > 2x - x

-20 > x

Therefore,

x < -20

The possible integers are -21, -22, -23, -24, -25, -26, ...

Then,

The smallest integer is -21

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Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

The value of the test statistic is given as follows:

z = 4.47.

The equation to calculate the test statistic using the z-distribution is given as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

In which:

The parameters for this problem are given as follows:

\(\overline{p} = 0.59, p = 0.5, n = 618\)

p = 0.5 as the most term means that we are testing if the proportion is either less than or greater than 0.5.

Then the test statistic is obtained as follows:

\(z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}\)

\(z = \frac{0.59 - 0.5}{\sqrt{\frac{0.5(0.5)}{618}}}\)

z = 4.47.

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Answer:

Steps

-x/3 >5

Multiply both sides by 3

3(-x/3)>5.3

Simplify

-X> 15

Multiply both sides by - 1 (reverse the inequality)

(-x)(-1)<15(-1)

Simplify

X< -15

so C is the answer

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

you have it correct

because when you are talking about negative the smaller number it the greater number

The inequality - 8 < - 4 is true among all the other given options.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two points on the number line one at - 8 and one at - 4.

We know 8 > 4 therefore - 4 > - 8 Or - 8 < - 4.

The more we go toward the left of the number line the numbers are smaller and smaller.

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\(\cfrac{2y}{3}-\cfrac{3}{4}=\cfrac{1}{12}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{12}}{12\left( \cfrac{2y}{3}-\cfrac{3}{4} \right)=12\left( \cfrac{1}{12} \right)}\implies 8y-9=1 \\\\\\ 8y=10\implies y=\cfrac{10}{8}\implies y=\cfrac{5}{4}\)

Answer:

well, starting by adding all the amount first. we will add 2.5 + .75, which equals 3.25 then, dividing 13 by 3.25 equals four. so within 4 days you will run out of milk.

Research Report:

Title: The Number of Coins Carried by Teachers

Introduction:

This research report aims to investigate the number of coins carried by teachers. The study seeks to understand the reasons behind carrying coins and whether there are any patterns or correlations between the number of coins and certain factors such as age, gender, and occupation.

The data was collected through a survey distributed among teachers from various educational institutions. The findings of this study provide insights into teachers' habits and preferences when it comes to carrying coins.

Results and Analysis:

A total of 300 teachers participated in the survey. The data revealed that the majority of teachers (60%) carry less than 5 coins, while 25% carry between 5 and 10 coins. Only a small percentage (15%) reported carrying more than 10 coins.

Further analysis based on demographic factors indicated that age and occupation had a significant influence on the number of coins carried. Older teachers were more likely to carry fewer coins, with 70% of teachers above the age of 50 carrying less than 5 coins.

Additionally, primary school teachers tended to carry more coins compared to secondary school teachers.

Discussion and Interpretation:

The findings suggest that the number of coins carried by teachers is influenced by various factors.

Teachers may carry coins for a range of reasons, such as purchasing small items, providing change for students, or utilizing vending machines.

The lower number of coins carried by older teachers could be attributed to a shift towards digital payment methods or a preference for carrying minimal cash.

The discrepancy between primary and secondary school teachers could be due to differences in daily activities and responsibilities.

This research provides valuable insights into the habits and preferences of teachers regarding the number of coins they carry.

Understanding these patterns can assist in designing more efficient payment systems within educational institutions and potentially guide the development of tailored financial solutions for teachers.

Further research could explore the reasons behind carrying coins in more depth and investigate how the digitalization of payments affects teachers' behavior in different educational contexts.

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Answer:

Step-by-step explanation:

Given,

Radius ( r ) = 10

Height ( h ) = 6

pi ( π ) = 3.14

now, let's find the volume of given cone:

\(\pi {r}^{2} \frac{h}{3} \)

Plug the values

\( = 3.14 \times {10}^{2} \times \frac{6}{3} \)

Evaluate the power

\( = 3.14 \times 100 \times \frac{6}{3} \)

Calculate

\( = 628 \: {units}^{3} \)

Hope this helps..

Best regards!!

Answer:

The answer is 200π units³ .

Step-by-step explanation:

Given that the formula of volume of cone is V = 1/3×π×r²×h where r represents radius and h is height. Then, you have to substitute the value of radius and height into the formula :

\(v = \frac{1}{3} \times \pi \times {r}^{2} \times h\)

\(let \: r = 10 \: , \: h = 6\)

\(v = \frac{1}{3} \times \pi \times {10}^{2} \times 6\)

\(v = \frac{1}{3} \times \pi \times 600\)

\(v = 200\pi \: {units}^{3} \)

a) At least 75% of the home buyers' age is between 25 years old and 69 years old.

b) At least 84% of the home buyer's age are between 19.5 years old and  74.5 years old.

When the distribution is not normal, Chebyshev's Theorem is used. It states that:

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Answer:

7.447 × 10(to the power of 6.)

Step-by-step explanation:

Answer:

7.447 × 106

Step-by-step explanation:

ye

Answer:

78

Step-by-step explanation:

you know how

Answer:

A. 15

Step-by-step explanation:

Answer:

31

Step-by-step explanation:

Projectile B begins its descent 1 seconds before Projectile A does.

In Mathematics and Geometry, the y-intercept of any graph or table such as a quadratic equation or function, generally occurs at the point where the value of "x" is equal to zero (x = 0).

By critically observing the table shown in the image attached above, we can reasonably infer and logically deduce the following y-intercept of Projectile A:

y-intercept = (0, 44).

Maximum height = (4, 300).

When t = 0, the y-intercept of Projectile B can be calculated as follows;

h(t) = -16t² + 96t

h(0) = -16(0)² + 96(0)

h(0) = 0.

For the maximum height, we have:

h(t) = -16t² + 96t

h'(t) = -32t + 96

32t = 96

t = 96/32

t = 3

Difference in time = 4 - 3

Difference in time = 1 seconds.

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation: