Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P.

[tex]P = 4xr^{2} .[/tex]

Which equation correctly rewrites the formula to solve for I?

A. [tex]I = \frac{P}{4xr^{2} }[/tex]
B. [tex]I = \frac{Pxr^{2} }{4}[/tex]
C. [tex]I = 4Pxr^{2}[/tex]
D. [tex]I = \frac{4P}{xr^{2} }[/tex]

The initial polynomial result will include several terms, but after simplification, there may only be one or two terms left.

Each polynomial must be considered to be in standard form. The initial multiplication will result in a total of m and n terms since each of the m terms of the first polynomial will be multiplied by each of the n terms of the second.

When the sum is simplified, some of those elements may be combined, resulting in a final product with only one or two terms.

1. 2 × b = 2b . . . . . each has 1 term; the result has 1 term.

2. (x -a)(x +a)  = x² -ax + ax -a² (2×2=4 terms) = x² -a² . . . . the results has 2 terms.

3.  (x -a)(x³ +x) =  x⁴ -ax³ + x² -ax . . . the results has 2×2 = 4 terms

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The equation of the line that passes through the points (- 6, - 3) and (4, 5) is y = (4 / 5) · x.

In this question we have the knowledge of two points, of which we must derive the equation of a line, whose definition is shown below:

y = m · x + b

Where:

The slope of the line can be determined by secant line formula:

m = Δy / Δx

Where:

First, determine the slope of the line:

m = [5 - (- 3)] / [4 - (- 6)]

m = 8 / 10

m = 4 / 5

Second, determine the intercept of the line:

b = y - m · x

b = 5 - (4 / 5) · 4

b = 5 - 5

b = 0

Third, write the equation of the line:

y = (4 / 5) · x

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Answer:7 7/8. pounds.

Step-by-step explanation:

[tex]4r + 14 - r - 6[/tex]

Combine Like Terms:

[tex](4r-r)+(14-6)[/tex]

[tex]=\fbox{3r + 8}[/tex]

Answer:

9

Step-by-step explanation:

18/5 ÷ 2/5 = 18/5 x 5/2 = 9

Answer:-4x^2-2x+46.

Step-by-step explanation:

To simplify this expression, you can start by distributing the negative sign to the first set of parentheses:

(-3)(x+4)(x-6)-(x^2+8x-10)

Then, you can distribute the -3 to the terms inside the first set of parentheses:

(-3x-12)(x-6)-(x^2+8x-10)

Then, you can combine like terms:

-3x^2+6x+36-x^2-8x+10

This simplifies to:

-4x^2-2x+46

Therefore, the expression that is equivalent to -3(x+4)(x-6)-(x^2+8x-10) is -4x^2-2x+46.

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Answer:

10:12:8

Step-by-step explanation:

so, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. so it would look like this     10:12:8

Answer:

≈ 2.76%

Step-by-step explanation:

Price increase

297.9 - 289.7 = 8

% increase

8/289.7 * 100 = 2.7614773904%

≈ 2.76%

(1). ΔIJH ≅ ΔKHJ, by SSS criterion,

and (2) we need,  ΔTNS and ΔUHS are right-triangles and S is the mid-point to prove  ΔTNS ≅ ΔUHS, by HL criterion.

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.

We have the triangle:

ΔIJH ≅ ΔKHJ.

To prove the congruent by SSS:

We have to show that three sides of the triangle are congruent to three sides of  the other triangle.

Here,

IJ ≅ KH.

IH ≅ JH, Given.

And both triangles share the same side JH.

So,

JH ≅ JH

So, ΔIJH ≅ ΔKHJ, by SSS criterion.

ΔTNS ≅ ΔUHS.

To prove the congruent by HL:

We have to show that the triangles are right-triangle and one leg and hypotenuse of the triangle is congruent to one leg and hypotenuse of the other triangle.

So, we need;

ΔTNS and ΔUHS are right-triangles.

S is the mid-point.

So,

SN ≅ SH.

ST ≅ US

So, ΔTNS ≅ ΔUHS, by HL criterion.

Therefore, ΔIJH ≅ ΔKHJ, by SSS criterion and we need;

ΔTNS and ΔUHS are right-triangles and S is the mid-point.

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Answer:

[tex]x^2+14x-51=0[/tex]

Step-by-step explanation:

Since the entire cabinet door is a rectangle, its area is given by:

[tex]A=w\ell[/tex]

The center of the cabinet door measures 12 inches by 16 inches.

And the border of the cabinet door has a width of x inches.

Therefore, the total width of the cabinet door will be (12 + 2x).

Likewise, the total length of the cabinet door will be (16 + 2x).

Thus, the area of the entire cabinet door will be:

[tex]A=(2x+12)(2x+16)[/tex]

We are given that this entire area is 396 square inches. Thus:

[tex]396=(2x+12)(2x+16)[/tex]

Simplify. We can factor out a two from both of the factors on the right-hand side:

[tex]396=2(x+6)(2)(x+8)[/tex]

So:

[tex]396=4(x+6)(x+8)[/tex]

Dividing both sides by four yields:

[tex]99=(x+6)(x+8)[/tex]

Distribute the right-hand side:

[tex]x^2+14x+48=99[/tex]

Therefore, our equation in standard form is:

[tex]x^2+14x-51=0[/tex]

Edit:

We want to find the width of the board. So, we simply have to solve for x. We previously obtained:

[tex]x^2+14x-51=0[/tex]

We can factor:

[tex](x+17)(x-3)=0[/tex]

By the Zero Product Property:

[tex]x+17=0\text{ or } x-3=0[/tex]

Solve for both cases:

[tex]x=-17\text{ or } x=3[/tex]

Length/width cannot be negative. So, we can reject the first solution.

Thus, our only solution is:

[tex]x=3[/tex]

The width of the border of the cabinet door is 3 inches.

This means that the total length of the cabinet is 16 + 2(3) = 22 inches, and the total width of the cabinet is 12 + 2(3) = 18 inches.

Answer:

$60,000 as down payment and remaining difference for loan is 300,000 - 60,000 = $240,000.

The money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000

A percentage is a number or ratio that can be expressed as a fraction of 100.

A loan is money, property, or other material goods given to another party in exchange for future repayment of the loan value amount with interest.

Given value of the house is $300,000.

The bank recommends that you have a 20% down payment before it approves a loan i.e. is $300,000× 20% = $60,000

The remaining difference that you will need to borrow is $300,000 - $60,000= $2,40,000

Thus the money you need to save before you will be approved for a loan is $60,000 and the remaining difference that you will need to borrow is $2,40,000

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The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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The product of f(x) and g(x) is always a polynomial. By the definition of

polynomials the product of polynomials is always a polynomial because

the coefficient are real numbers and the exponents are whole

numbers. Real numbers and whole numbers are closed under addition

and subtraction.

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) with coefficients, that is either a constant or the indeterminates (also called variables or x's). The most common examples are the quadratic equation, cubic equation, and so on. The degree of a polynomial is the highest power of the indeterminate in the polynomial. For example, a polynomial with three indeterminates to the power of 2 is said to have a degree of 2.

Here f(x) and g(x) are two given polynomial,

let f(x) = x+1 ang g(x) = x-1

f(x).g(x) = (x+1)(x-1).

f(x).g(x) = x²-1.

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Answer:u cheating like a mfka lol

Step-by-step explanation:dwd

Answer:

200 is your answer

Step-by-step explanation:

First, multiply:

8 × 5 × 4 = 160

Then, multiply:

4 × 5 × 2 = 40

Next, add them up.

160 + 40 = 200

Lastly, have a great day!

Answer:

y = -3/4x -1.5

Step-by-step explanation:

-6+3 = -3

3+1 = 4

-3/4

y = -3/4x +b

3 = -3/4(-6) +b

3 = 4.5 +b

b = -1.5

y = -3/4x -1.5

Answer:

y=-4 /3x– -5

Step-by-step explanation:

mrk me brainliest

Answer:

C

Step-by-step explanation:

1 pound sand for 1 2/3 pounds gravel.

1 pound gravel for 2/5 pound cement.

3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =

= 5 pounds gravel.

5 pounds gravel = 5 × 2/5 = 2 pounds of cement

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given  :

=> -x-y=-2

=>  5x + 7y= 28

So ,

=>x = 2-y

thus,

=> 5(2-y) + 7y =28

=> 10 -5y + 7y =28

=> 10 -2y = 28

=> -2y = 18

=> y =-9

and

=> x  = 2 - (-9)

=> x  = 11

Therefore , the solution of the given problem of equation comes out to be x = 11 and y =-9.

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Answer:

B

Step-by-step explanation:

1) transform mm in cm

12 : 10 = 1,2 cm

2) find the base area

base area = (leg 1 x leg 2)/2 = (1,2 x 4,5)/2 = 2,7 cm^2

did not mean to press answer sorry

Answer: x = 4

Step-by-step explanation:

Based on the given distances and angle measures, DE is congruent to XY, DF is congruent to ZX, and EF and ZY are congruent.

This means that:

[tex](4x-1)=15[/tex]

Simplify and solve for x.

[tex]4x-1=15\\4x=16\\x=4[/tex]

So, x = 4

9514 1404 393

Answer:

  y = 3x -7

Step-by-step explanation:

The given point is the y-intercept, so we can write the equation in slope-intercept form.

  y = mx + b . . . . . line with slope m through point (0, b)

For your slope and point, the equation is ...

  y = 3x -7

10.625 pounds of peanuts mixed with almonds priced $5.35 perpound

Weight is measured in pounds. 16 ounces or 0.453592 kilos make up one pound.

Let's name the weight in pounds of almonds and peanuts that we need x.

We are aware that our ultimate goal is to produce 20 pounds of the mixture, which will sell for $4.50 each pound. The mixture will therefore cost 20 * $4.50, or $90, in total.

Additionally, we are aware that peanuts cost $3.75 per pound and almonds cost $5.35 per pound.

As a result, the price of the almonds we use is 5.35x, while the price of the peanuts we use is 3.75(20 - x) = 75 - 3.75x.

We may create an equation since our goal is to produce a mixture that costs $90 in total:

5.35x + (75 - 3.75x) = 90

When we simplify this equation, we get:

1.6x + 75 = 90

75 is subtracted from both sides to produced

1.6x = 15

By multiplying both sides by 1.6, we get:

x = 9.375

To create a mixture that will sell for $4.50 per pound, we must combine around 9.375 pounds of almonds with (20 - 9.375) = 10.625 pounds of peanuts

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4.8

Divide 250 by 2 which is 125 then do 600 divided by 125. Then your answer should be 4.8.