A rectangle has a length that is 5 inches greater than its width, and its area is 104 square inches. The equation (x + 5)x = 104 represents the situation, where x represents the width of the rectangle.

The first step in solving by factoring is to write the equation in standard form, setting one side equal to zero. What is the equation for the situation, written in standard form?

a. x2 – 99 = 0
b. x2 – 99x = 0
c. x2 + 5x + 104 = 0
d. x2 + 5x – 104 = 0

The area of the polygon with 12 sides is 48 square units.

To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:

A = 12 * Area of 1 triangle

Where

Area of 1 triangle = 1/2 * radius * sin(360/n)

So, we have

Area of 1 triangle = 1/2 * 4^2 * sin(360/12)

Area of 1 triangle = 1/2 * 4^2 * sin(30)

Evaluate

Area of 1 triangle = 4

Substituting the given values, we get:

A = 12 * 4

Evaluate

Area = 48

So the area is 48 square units.

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Answer:

42

Step-by-step explanation:

evaluate each expressions when a=2and b=6. 7a-ab+b

If integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, the probability that ad-bc is even is 10/16.

To solve the problem, we need to consider the parity of the product ad and bc separately. If both ad and bc are even, then their difference (ad-bc) is even. If both ad and bc are odd, then their difference is even as well. However, if one of ad and bc is odd and the other is even, then their difference is odd.

For ad to be even, either a or d (or both) must be even. Similarly, for bc to be even, either b or c (or both) must be even. Therefore, the probability that ad and bc are both even is the product of the probabilities that a, b, c, and d are even:

P(ad even) = P(a even)P(d even) = (1004/2008)^2 = 1/4

P(bc even) = P(b even)P(c even) = (1004/2008)^2 = 1/4

The probability that ad-bc is even is the sum of the probabilities that both ad and bc are even and that both ad and bc are odd:

P(ad-bc even) = P(ad even and bc even) + P(ad odd and bc odd)

= P(ad even)P(bc even) + P(ad odd)P(bc odd)

= 1/4 * 1/4 + 3/4 * 3/4

= 1/16 + 9/16

= 10/16

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Answer:

Step-by-step explanation:

1000 / 5 = 200

So if their 5 people they would share the money 200 hundred per person.

Absolute Value Equation for a Horizontal Line Passing Through Two Points -1/2 and 3/2.

The solution set given as a straight horizontal line passing through the points -1/2 and 3/2 can be represented as:

| x - 1 | = 1/2

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Step-by-step explanation:

Approx  9.81 m/s^2

Answer:

1.83 yards

Step-by-step explanation:

the initial concentration of the solution in the tank is 0.04 kg/L.

Tank contains 80 kg of salt and 2000 L of water. A solution of a concentration 0.02 kg of salt per liter enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the same rate.

What is the concentration of our solution in the tank initially?

Initially, the tank contains 80 kg of salt and 2000 L of water. To determine the initial concentration of the solution in the tank, we need to use the following formula:

concentration = mass of solute / volume of solution

In this case, the mass of solute (salt) is 80 kg and the volume of solution is 2000 L. Therefore, the initial concentration of the solution in the tank is:concentration = 80 kg / 2000 L = 0.04 kg/L

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The Equation of the linear function is y = 2x + 1.

Here's a step-by-step explanation using the terms you've provided:

1. Identify the slope (m) and y-intercept (b): In a linear function, the equation is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

2. Find the slope: If you're given two points on the line (x1, y1) and (x2, y2), you can find the slope by using the formula: m = (y2 - y1) / (x2 - x1).

3. Determine the y-intercept: If you know the slope and one point on the line (x, y), you can find the y-intercept by rearranging the equation: b = y - mx.

4. Write the equation: Once you have the slope and y-intercept, you can write the equation in the form y = mx + b.

For example, suppose you are given two points on a line: (1, 3) and (3, 7). To write the equation of the linear function:

Step 1: Find the slope (m):
m = (7 - 3) / (3 - 1) = 4 / 2 = 2

Step 2: Determine the y-intercept (b) using one of the points, say (1, 3):
b = 3 - (2 * 1) = 1

Step 3: Write the equation:
y = 2x + 1

So, the equation of the linear function is y = 2x + 1.

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As Ron said he would spend $400 of his paycheck on these items, it is not reasonable because the total cost of the items is $450, which is $50 more than the amount he planned to spend. So, option A is correct.

As per given information,

Ron want to spend $400.

Ron wants to buy nine items that each cost $50.
To find the total cost of these items, we need to multiply the number of items by the cost of each item .
So,

Total cost of items = 9 x 50  

Total cost of items = 450
This results in a total cost of $450.

This is not reasonable because nine items at $50 each would cost $450

Therefore, option A is correct.

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Answer:

Your answer of 4¹⁸ is correct.

Step-by-step explanation:

In (4⁶)³ the exponents would be multiplied. 6 multiplied by 3 is 18 and therefore the correct answer would be 4¹⁸

Answer:

B. 4^18

Step-by-step explanation:

(4^6)= 4096

(4096)^3= 68,719,476,736

So, (4^6)^3= 68,719,476,736

AND

4^18= 68,719,476,736

Hope it helped! :)

Brainliest? Please.

The value of the logarithm of numbers is 1/4

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithm is 1 + log₇25

Simplifying this we have log₇25 = -1

Taking the logarithm of both sides we have

log₇25  = -100x

25 =7⁻¹⁰⁰ˣ

100x = 25

Dividing by 100

x = 25/100

X = 1/4

Therefore the value of the logarithm is 1/4

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Answer:

the price that generates maximum profit is $152.94, rounded to the nearest cent.

Step-by-step explanation:

Let's begin by finding the profit generated by the promotion at each price point.

At $17.99/person:

Profit = Revenue - Cost

Profit = $17.99 x 112 - (10 + 5 + 3) x 112

Profit = $2016.64

At $19.99/person:

Profit = Revenue - Cost

Profit = $19.99 x 96 - (10 + 5 + 3) x 96

Profit = $1497.12

To find the price that generates maximum profit, we need to use the formula:

Price = (Fixed Cost + Variable Cost) / Number of Customers + Profit per Customer

We can assume that the fixed cost for the restaurant is $10,000 per day, and the variable cost per person is $5 for ingredients and $3 for labor.

For $17.99/person:

Price = ($10,000 + (5 + 3) x 112) / 112 + ($2016.64 - $17.99)

Price = $152.94

For $19.99/person:

Price = ($10,000 + (5 + 3) x 96) / 96 + ($1497.12 - $19.99)

Price = $156.24

Therefore, the price that generates maximum profit is $152.94, rounded to the nearest cent.

Answer:

x = 23

Step-by-step explanation:

180 - 100 = 80

51 + 80 = 131

180- 131=49

49= 2x +3

49 - 3= 46

46=2x

46/ 2= 23

X= 23

Answer:

2 bus

Step-by-step explanation:

The expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student.

The expected value of a random variable represents the average value of that variable over multiple trials. In this case, x is a random variable representing the number of students on the bus carrying the randomly selected student, and y is a random variable representing the number of students on the randomly selected bus.

The expected value of x can be calculated as follows:

E[x] = (10/100)×10 + (20/100)×20 + (30/100)×30 + (40/100)×40

= 16 + 12 + 9 + 16

= 53/4

= 13.25

This means that, on average, the bus carrying the randomly selected student would have 13.25 students.

The expected value of y can be calculated as follows:

E[y] = (1/4)×10 + (1/4)×20 + (1/4)×30 + (1/4)×40

= 25

This means that, on average, the randomly selected bus would have 25 students.

As expected, the expected value of y is larger than the expected value of x. This is because y takes into account the number of students on all 4 buses, while x only takes into account the students on the bus with the randomly selected student. Since the number of students on the other 3 buses can vary widely, y has a higher expected value than x.

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The correct order of the polynomial [tex]7x^3y^3 - 3xy^5 + 2x^2y^4 - x^4y^2[/tex] in descending powers of x is:

[tex]-x^4y^2 + 7x^3y^3 + 2x^2y^4 - 3xy^5[/tex]

Therefore, the answer is option A.

What is polynomial function?

A polynomial function is a mathematical function that consists of a sum of terms, where each term is a constant multiplied by one or more variables raised to a non-negative integer power.

When we arrange a polynomial in descending order of powers of one of its variables, it means we are writing the terms with the highest power first, followed by terms with the next highest power, and so on until we reach the constant term (which has no variable).

In this case, the polynomial is [tex]7x^3y^3-3xy^5+2x^2y^4-x^4y^2[/tex]. To write this in descending order of powers of x, we need to start with the term that has the highest power of x, which is [tex]-x^4y^2[/tex].

Then we write the term with the next highest power of x, which is [tex]7x^3y^3[/tex]. After that, we write the term with the next highest power of x, which is [tex]2x^2y^4[/tex]. Finally, we write the term with the lowest power of x, which is [tex]-3xy^5[/tex].

So the correct order of the polynomial in descending powers of x is option A: [tex]-x^4y^2+7x^3y^3+2x^2y^4-3xy^5[/tex].

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Step-by-step explanation:

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

james sets off from home on a bike.The graph journey.

a)what is james' average speed on his outward journey

Joe will reach the dam on June 6, which is 5 days after he starts his journey on June 1.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other.

Let's first calculate the net distance Joe travels each day:

Net distance = Distance paddled upstream - Distance pushed downstream by the current

Net distance = 5 miles - 3 miles

Net distance = 2 miles

This means that Joe moves 2 miles closer to the dam each day.

To reach the dam, Joe needs to cover a distance of 10 miles upstream from his starting point. Since he covers 2 miles per day, he will take:

Days taken to reach the dam = Distance to cover ÷ Distance covered each day

Days taken to reach the dam = 10 miles ÷ 2 miles per day

Days taken to reach the dam = 5 days

Therefore, Joe will reach the dam on June 6, which is 5 days after he starts his journey on June 1.

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Answer:

Let B be the other endpoint of AB.

We know that the midpoint M of AB has coordinates (5, -9), which means that the average of the x-coordinates of A and B is 5, and the average of the y-coordinates of A and B is -9:

Substituting the coordinates of point A (-8, 4), we can solve for the x-coordinate of point B:

Simplifying the equation, we get:

Now, substituting the same coordinates of point A and the y-coordinate of midpoint M (-9), we can solve for the y-coordinate of point B:

Simplifying the equation, we get:

The area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

The size of a patch on a surface is determined by its area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

The area of a plane figure is the area that its perimeter encloses.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

Area of the cutout:

A = s²

A = 3²

A = 9mm²

Area of the coin:
A = πr²

A = π9.8²

A = π9.8²

A = π96.04

A = 301.5656

Then,

301.5656 - 9

292.5656

Rounding off: 293 mm²

Therefore, the area of the cutout and the coin is as follows:

(A) 9mm²

(B) 293 mm²

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Having factorized using identities, the result is [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]

One possible approach to factorizing the expression is to use the identity:

a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc)

If we let a = b/c, b = c/a, and c = a/b, then we can substitute these expressions into the identity and simplify:

(a/b)^3 + (b/c)^3 + (c/a)^3 - 3abc/a^3b^3c^3

= [(a/b) + (b/c) + (c/a)][(a/b)^2 + (b/c)^2 + (c/a)^2 - (a/b)(b/c) - (a/b)(c/a) - (b/c)(c/a)]

= [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2)/(a^2b^2c^2) - 1]

= [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]

Therefore, the factorization of the given expression is:

(a/b)^3 + (b/c)^3 + (c/a)^3 - 3 = [(a^2c + b^2a + c^2b)/(abc)][(a^2 + b^2 + c^2 - a^2b^2c^2)/(a^2b^2c^2)]

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Answer:

2

Step-by-step explanation:

14/2=7

34/2=17

To express the ans in scientific notation is 1.98 x [tex]10^{10}[/tex] text messages per month.

You must add up all of the numbers in a set and divide the result by the total amount of numbers in order to determine the average of the set of numbers. The mean is another name for this.

The steps to calculating the average are as follows:

Sum up each of the set's numbers.

Count how many numbers there are in all.

subtract the total number of numbers from the sum of the numbers.

The average (mean) is calculated using the following formula:

Average equals ((Sum of Numbers)/ (Total Number of Numbers)

To calculate the total number of text messages sent by all teenagers in the United States in a month, we can multiply the number of teenagers by the average number of text messages sent by each teenager:

Total text messages = (number of teenagers) x (average number of text messages per teenager)

Total text messages = 22,000,000 x 900

Multiplying these numbers gives us:

Total text messages = √19,800,000,000

Total text messages = 140712.473 text messages per month.

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The derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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

y = 6x^3

To find the derivative of y with respect to x, we can use the power rule of differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1).

Using this rule, we can differentiate y = 6x^3 as follows:

dy/dx = d/dx (6x^3)

= 6 * d/dx (x^3)

= 6 * 3x^2 (applying the power rule with n=2)

= 18x^2

Therefore, the derivative of y = 6x^3 with respect to x is dy/dx = 18x^2.

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Answer:

Part 1: x = -2

Part 2: x = 56

Step-by-step explanation:

Part 1:

12x + 9 = -15

Given that-

12x + 9 = -15

12x + 9 - 9 = -15 -9                >> Subtract 9 to both sides

12x = -24

12x/12 = -24/12                    >> Divide both sides by 12

x = -2

Check Answer:

12(-2) + 9 = -15                 >> 12 × -2 = -24

-24 + 9 = -15                   >> -24 + 9 = -15

-15 = -15                        >> Correct

Part 2:

x/7 - 4 = 4

Given that-

x/7 - 4 = 4

x/7 - 4 + 4 = 4 + 4                 >> Add 4 to both sides

x/7 = 8                

7x/7 = 8 × 7                             >> Multiply both sides by 7

x = 56

Check Answer-

Substitute x in the equation the check.

56/7 - 4 = 4              >> 56/7 = 8

8 - 4 = 4                  >> 8 - 4 = 4

4 = 4                        >> Correct

RevyBreeze

Explanation:

We want a dice sum larger than 8. Meaning we want the sum to be either: 9, 10, 11, or 12

Here are the four ways to add to 9

3 + 6 = 9

4 + 5 = 9

5 + 4 = 9

6 + 3 = 9

Here are the three ways to add to 10

4 + 6 = 10

5 + 5 = 10

6 + 4 = 10

and here are the two ways to add to 11

5 + 6 = 11

6 + 5 = 11

and finally there's only one way to get a sum of 12

6 + 6 = 12

There are 4+3+2+1 = 10 different sums we want out of 6*6 = 36 dice rolls possible.

That's how we get to 10/36 as the final answer.

10/36 reduces to 5/18, but it appears your teacher decided not to reduce.

The correct option is D.

The probability of rolling a value higher than eight with a pair of fair dice is 4/36 or 1/9.What is the probability of rolling a value higher than eight with a pair of fair dice?To find the probability of rolling a value higher than eight with a pair of fair dice, you have to find the number of ways to get a sum greater than 8 and divide it by the total number of possible outcomes when rolling two dice.The maximum sum that can be obtained by rolling two dice is 12 (6 + 6). So, we need to find the number of ways that we can obtain 9, 10, 11, or 12. The possible combinations are:(3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), (6,5), and (6,6).Therefore, there are 10 possible outcomes in which the sum of the two dice is greater than 8. The total number of possible outcomes when rolling two dice is 6 × 6 = 36.So, the probability of rolling a value higher than eight with a pair of fair dice is:10/36 = 5/18 or approximately 0.277 or 27.7%.

Therefore the correct answer is option D ) 8/36.

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The calculatd value of the length of side WX is 1.25 cm.

Let's call the length of side WX "x".

The mid-segment of a trapezoid is the line segment connecting the midpoints of the non-parallel sides.

The length of the mid-segment is equal to the average of the lengths of the two parallel sides. In this case, the mid-segment is 2.75 cm long and connects the midpoints of sides WZ and XY.

We can use the formula for the length of the mid-segment of a trapezoid:

mid-segment length = (length of side WZ + length of side XY) / 2

Plugging in the values we know, we get:

2.75 = (x + 4.25) / 2

Multiplying both sides by 2, we get:

5.5 = x + 4.25

Subtracting 4.25 from both sides, we get:

x = 1.25

Therefore, the length of side WX is 1.25 cm.

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According to the question the measure of angle 3, or m∠3, is also 19 degrees since angle 2 and angle 3 are vertical angles. So: m∠3 = m∠23 = 19°

We know that vertical angles are congruent, so if angle 21 and angle 22 are vertical angles, then:

m∠21 = m∠22

We also know that angle 22 and angle 23 are complementary angles, which means:

m∠22 + m∠23 = 90°

Substituting m∠22 with m∠21, we get:

m∠21 + m∠23 = 90°

We are given that m∠21 = 71 degrees, so we can substitute that in the equation:

71° + m∠23 = 90°

Subtracting 71° from both sides, we get:

m∠23 = 19°

Therefore, the measure of angle 3, or m∠3, is also 19 degrees since angle 2 and angle 3 are vertical angles. So:

m∠3 = m∠23 = 19°

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The best measure of center for this data would be the median, as it is less affected by outliers and works well for skewed data. To find the median, we arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5. There are 16 data points, so the median would be the average of the 8th and 9th values, which is 3.5. Therefore, the best measure of center for this data is the median, and its value is 3.5.

So the correct answer is: The median is the best measure of center, and it equals 3.5.

Let's use "w" to represent the width of the rectangle and "l" to represent the length.

According to the problem statement, the area of the rectangle is numerically equal to its perimeter, so we can write:

2(l + w) = lw

Simplifying this equation, we get:

2l + 2w = lw

Dividing both sides by 2, we get:

l + w = 0.5lw

Multiplying both sides by 2, we get:

2l + 2w = lw

Since the length of the rectangle is 5 times its width, we can write:

l = 5w

Substituting this into the previous equation, we get:

2(5w) + 2w = 5w^2

Simplifying this equation, we get:

10w + 2w = 5w^2

12w = 5w^2

Dividing both sides by w, we get:

12 = 5w

So the width of the rectangle is:

w = 12/5 = 2.4 cm

And the length of the rectangle is:

l = 5w = 12 cm

Therefore, the width of the rectangle is 2.4 cm and the length of the rectangle is 12 cm.

Answer:

Width: 2.4 cm

Length: 12 cm

Step-by-step explanation:

Let the width of the rectangle be w cm, and the length be 5w cm. The area A and perimeter P of the rectangle can be expressed as follows:

Area (A) = length × width

A = 5w × w = 5w^2 cm^2

Perimeter (P) = 2 × (length + width)

P = 2 × (5w + w) = 2 × 6w = 12w cm

According to the problem, the area is numerically equal to the perimeter:

A = P

5w^2 = 12w

To solve for w, we can rearrange the equation:

5w^2 - 12w = 0

w(5w - 12) = 0

This equation has two possible solutions:

w = 0

In this case, the width would be 0 cm, which doesn't form a valid rectangle.

5w - 12 = 0

5w = 12

w = 12/5 = 2.4 cm

For the second solution, the width is 2.4 cm. Now, we can calculate the length:

length = 5w

length = 5 × 2.4 = 12 cm

So, the width of the rectangle is 2.4 cm, and the length is 12 cm.