What does the Pythagorean Theorem state about the sides of a right triangle if the legs of triangle have the measurement of a and b and the hypotenuse of the triangle measures c?

Answer:

21

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given is a sample with 4 items as

12,9,14,21

Mean = average of 4 = 14

s is the square root of sample variance

Sample variance is the sum of squares divided by n-1

But Yuri divided by 4 = n instead of 3 = n-1

That is the only mistake he did and all other steps are right.

The approximate solution of the equation log₂(3·x - 1) = log₄(x + 8), obtained algebraically is about x = 1.353. The solution cain be verified using the attached graph created with MS Excel

The steps used to find the solution of the logarithm equation can be presented as follows;

The logarithm equation is;  [tex]\log_2(3\cdot x - 1) = \log_4(x + 8)[/tex]

Converting the logarithm to the same base, we get;

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{\log_2 4}[/tex]

[tex]\log_4(x + 8) = \frac{\log_2(x + 8)}{2}[/tex]

[tex]\log_2(3\cdot x - 1) = \frac{\log_2(x + 8)}{2}[/tex]

2 × log₂(3·x - 1) = log₂(x + 8)

log₂(3·x - 1)² = log₂(x + 8)

(3·x - 1)² = (x + 8)

(3·x - 1)² - (x + 8) = 0
9·x² - 7·x - 7 = 0

Solving using technology, we get; x ≈ 1.353 and x ≈ -0.575

Plugging in the value of x = 1.353, we get;

log₂(3 × 1.353 - 1) ≈ 1.613

log₄(1.353 + 8) ≈ 1.613

The value of the logarithm are much different when x ≈ -0.575, the expression log₂(3·x - 1) have no solution. The solution is therefore; x ≈ 1.353

Please find the attached the graph of the equation log₂(3·x - 1) = log₄(x + 8), showing the solution as x ≈ 1.353

Final answer:

To solve the equation log2(3x-1) = log4(x+8), we can rewrite the equation and simplify it to calculate the approximate solution as x = 4.5.

Explanation:

To solve the equation log2(3x-1) = log4(x+8), we can start by using the property of logarithms that states log(a) = log(b) if and only if a = b. Based on this property, we can rewrite the equation as 3x - 1 = x + 8. Simplifying this equation, we get 2x = 9. Finally, by dividing both sides by 2, we find that x = 4.5. Therefore, the approximate solution to the equation is x = 4.5.

The two consecutive numbers are 7 and 8.

Consecutive numbers are numbers that follow each other. For example, 1,2,3,4 are consecutive numbers.

Let:

x = first number

(x + 1) = second number

From the question, this expression can be derived:

[(x) + (x + 1)] ²

This can be simplified to (2x +1)²

The second expression is : x² + (x +1)²

(2x +1)² -  [x² + (x +1)²] = 112

expanding the bracket gives:

(4x²  + 4x + 1) - [x² + (x² + 2x +1) = 112

4x²  + 4x + 1 - 2x² - 2x - 1 = 112

Add like terms

2x² + 2x = 112

Divide both sides by 2

x² + x = 56

x² + x - 56 = 0

Factorise the equation

The factors of -56x² that add up to x are : 8x and -7x

(x² - 7x) (8x - 56)  = 0

x(x - 7) 8(x -7) = 0

x = 7

or

x = -8

Since x cannot be a negative number, x is 7 and (x + 1) = 8

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Answer:

It is one.

Step-by-step explanation:

If you didn't get 1 re read the problem

Answer

A = 24.96 yd^2

Step-by-step explanation:

We need to find the area of the room

Area is length times width

A = lw

We know the length is 5.2 yds and the width is 4.8

A = 5.2 * 4.8

A = 24.96 yd^2

This one helps too.

Ur welcome.

The width of the garden is 12 feet and the length of the garden is 20 feet.

Let's denote the width of the garden as 'w'. The length will then be 'w + 8'. Measurements are in feet. The garden is surrounded by a 4-foot sidewalk. Therefore, the total length of the garden including the sidewalk is 'w + 8 + 4 + 4 = w + 16', and the total width is 'w + 4 + 4 = w + 8'.

The area of the sidewalk surrounding the garden is the area of the large rectangle minus the area of the garden. So, we set up the following equation:
(w + 16)(w + 8) - (w)(w + 8) = 320.

After simplifying, we can get a quadratic equation: w² + 8w - 320 = 0 and then solve this equation, which gives us w = 12 or w = -28. We ignore the negative solution as the width cannot be negative. So, the dimensions of the garden are:
Width: 12 feet
Length: 20 feet.

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Laura started with $60.00 before purchasing a shirt for $16.80 and a sweater for $24.75, and then had $18.45 remaining.

Calculating Laura's Starting Amount

To find out how much money Laura started with, we need to add the amount she spent on the shirt and sweater to the amount she had left over. Laura spent $16.80 on a shirt and $24.75 on a sweater. After these purchases, she had $18.45 remaining.

We calculate the total amount spent by adding the costs of the shirt and sweater together:

Cost of the shirt: $16.80

Cost of the sweater: $24.75

Total spent: $16.80 + $24.75 = $41.55

We now add the amount left after the purchases to find the total amount Laura started with:

Total spent: $41.55

Amount left: $18.45

Total amount Laura started with: $41.55 + $18.45 = $60.00

Answer:

A.) They are easier to get than both car loans and credit cards.

Step-by-step explanation:

Payday loans are also called cash advance loans or check advance loans.

These loans are comparatively very easy loans for a person to get. These are short term loans that come with high interest rates. The rates are based on the borrower's income and credit profile.

In this loan the principal amount is typically a small portion of the borrower's next paycheck.

The slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)

To determine the slope and y-intercept of the equation, we will rewrite the equation in the form of the slope-intercept form of the equation of a straight line.

The slope-intercept form equation of a straight line is

y = mx + c

Where m is the gradient

and c is the y-intercept

From the question, the given equation is  y − 3(x − 1) = 0

This can be rewritten in form of the equation of a straight line as

y -3x +3 = 0

Then,

y = 3x - 3

Now, compare this to y = mx + c  (the slope-intercept form of the equation of a straight line)

Then,

m = 3 and c = -3

That is,

slope = 3 and y-intercept = -3

Hence, the slope and the y-intercept of the equation y − 3(x − 1) = 0 are: slope = 3 and y-intercept = -3. The correct option is the fourth option (slope = 3 and y-intercept = -3)

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