What’s he hypotenuse, x, if ( 20, 21,x) is a Pythagorean triple?

B= 2a/ h - a

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The solutions to the equation [tex]p^2+4p=1[/tex] using completing the square method are  [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]

The given equation is:

[tex]p^2+4p=1[/tex]

Add [tex](\frac{4}{2})^2[/tex] to both sides of the equation

[tex]p^2+4p+(\frac{4}{2})^2= 1 + (\frac{4}{2})^2\\\\p^2+4p+2^2=1+2^2\\\\(p+2)^2=1+4\\\\(p+2)^2=5\\\\[/tex]

Find the square root of both sides

[tex]p+2 = \pm\sqrt{5}\\\\p=-2\pm sqrt{5} \\\\p = -2 - sqrt{5}\\\\p=-2+ \sqrt{5}[/tex]

The roots of the equation are [tex]-2- \sqrt{5}[/tex] and [tex]-2+ \sqrt{5}[/tex]

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The equation p² + 4p = 1 can be solved by first rearranging to p² + 4p - 1 = 0, completing the square, simplifying and taking square roots. The solutions are p = -2 + sqrt(5) and p = -2 - sqrt(5).

To solve the quadratic equation p² + 4p = 1 by completing the square, we first arrange the equation with the quadratic and linear terms on one side and the constant on the other:

p²+ 4p - 1 = 0.

Next, we complete the square by adding the square of half the coefficient of p to both sides of the equation. The coefficient of p is 4, so half of it is 2, and squaring it gives 4. So, we have:

p² + 4p + 4 = 1 + 4

This simplifies to:

(p + 2)² = 5

Then, we take square roots of both sides:

p + 2 = ± sqrt(5)

Which further simplifies to:

p = -2 ± sqrt(5)

So, the solutions for this quadratic equation are p = -2 + sqrt(5) and p = -2 - sqrt(5).

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Answer:

Percy earns a greater hourly wage of $7.50 at the library.

Step-by-step explanation:

Final answer:

The value of an investment of $4500 at a 7.25% annual interest rate, compounded continuously, is calculated using the compound interest formula [tex]P = P_0e^{rt}[/tex], where P0 is the initial amount, r is the rate as a decimal, and t is the time in years.

Explanation:

The subject of this question is Mathematics, and it falls under the High School grade level. To find the value of an investment compounded continuously, we use the formula:

[tex]P = P_0e^{rt}[/tex]

Where:

Given a $4500 investment at a 7.25% annual interest rate, compounded continuously, we can calculate the future value of the investment after t years. Convert the percentage to a decimal by dividing by 100:

r = 7.25 / 100 = 0.0725

So the formula becomes:

[tex]P = $4500e^{0.0725t}[/tex]

Plug in the number of years into 't' to calculate the future value for that specific duration.

After 2, 4, and 6 years of continuous compounding, the investment values are approximately $5198.85, $6014.70, and $6953.85 respectively.

To find the value of the investment after a certain number of years with continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

Given:

-  P = $4500

-  r = 7.25% = 0.0725  (as a decimal)

We need to calculate the value of the investment after 2, 4, and 6 years.

(a) For 2 years:

[tex]\( A = 4500 \times e^{0.0725 \times 2} \)\\\( A = 4500 \times e^{0.145} \)\\\( A \approx 4500 \times 1.1553 \)\\\( A \approx \$5198.85 \)[/tex]

(b) For 4 years:

[tex]\( A = 4500 \times e^{0.0725 \times 4} \)\\\( A = 4500 \times e^{0.29} \)\\\( A \approx 4500 \times 1.3366 \)\\\( A \approx \$6014.70 \)[/tex]

(c) For 6 years:

[tex]\( A = 4500 \times e^{0.0725 \times 6} \)\\\(A = 4500 \times e^{0.435} \)\\\(A \approx 4500 \times 1.5453 \)\\\( A \approx \$6953.85 \)[/tex]

So, the values of the investment after 2, 4, and 6 years respectively are approximately:

(a) $5198.85

(b) $6014.70

(c) $6953.85

Complete Question:
If $ 4500 is invested at an interest rate of 7.25% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)

(a) 2 years

(b) 4 years

(c) 6 years

Answer:

The cost of the cd is at most 10$

Step-by-step explanation:

Answer:

5-2

28 - 5²

17 - 7 × 2

[tex]\frac{28}{4}-4[/tex]

5 × 3 - 4 × 3

Step-by-step explanation:

Let x and y be any two numbers,

Such that,

y - x = 3,

⇒ y = 3 + x

Where, x is any positive real number.

Thus, we can find such equation by using this,

Such equations could be,

5 - 2, 28 - 25, 17 - 14, 7 - 4, 15 - 12

or

5-2, 28 - 5², 17 - 7 × 2, [tex]\frac{28}{4}-4[/tex], 5 × 3 - 4 × 3

Five equations where the difference is equal to 3 are, respectively:

(i) [tex]y - x = 3[/tex]

(ii) [tex]y + 9\cdot x = 3[/tex]

(iii) [tex]y -5\cdot x = 3[/tex]

(iv) [tex]y +2\cdot x = 3[/tex]

(v) [tex]y -11\cdot x = 3[/tex]

Reminder - Statement is incomplete. After some research, we determine that complete form is: "Write 5 linear equations where the difference is equal to 3".

From Analytical Geometry, a Linear Equation is an expression of the form:

[tex]y = m\cdot x + b[/tex] (1)

Where:

Based on the question, we need to write 5 expressions so that:

[tex]y - m\cdot x = b[/tex]

If we know that [tex]b = 3[/tex], then we get the following expressions:

(i) [tex]y - x = 3[/tex]

(ii) [tex]y + 9\cdot x = 3[/tex]

(iii) [tex]y -5\cdot x = 3[/tex]

(iv) [tex]y +2\cdot x = 3[/tex]

(v) [tex]y -11\cdot x = 3[/tex]

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Final answer:

The expression to represent Jonas's total purchase is 3x - $20, where x is the price of one book.

Explanation:

To create an expression that represents the total purchase of Jonas's books, let's denote the price of each book as x. Jonas bought 3 books at the same price, so the cost of the books is 3x. However, with the coupon, Jonas gets $20 off the total cost. Therefore, the expression that represents the total purchase is:

3x - $20

This expression first calculates the total cost of the books (3 times the price of one book) and then subtracts the $20 discount from the coupon.

For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.

A quadrilateral is a closed shape in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral. The word "quadrilateral" is derived from the Latin "quadra" (four) and "latus" (sides).

For a quadrilateral to be a parallelogram, its opposite sides and angles must be congruent.

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The z-score corresponding to this value will be negative 0.6667.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

The z-score is given as

z = (x - μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

Test scores are typically conveyed with a mean of 100 and a standard deviation of 15. A singular's level of intelligence score is viewed as 90.

The z-value is given as,

z = (90 - 100) / 15

z = - 10 / 15

z = - 0.6667

The z-score relating to this worth will be negative 0.6667.

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Answer:

21km i beileve srry im late

Step-by-step explanation:

The length of each side of the wrestling mat is, 38 feet.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet.

Let the length of each side of the wrestling mat is, x

Hence, We get;

⇒ x² = 1444

⇒ x = √1444

⇒ x = 38 feet

Thus, The length of each side of the wrestling mat is, 38 feet.

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