What value of b will cause the system to have an infinite number of solutions?

To find the consecutive even positive integers, we set up an equation based on the given information and solve for the variables.

Let's assume the first even positive integer is x. Therefore, the next consecutive even positive integer will be x + 2. According to the problem, the product of these two integers is 782 more than their sum. We can set up the equation as x(x + 2) = x + x + 2 + 782.

Simplifying the equation, we get x^2 + 2x = 2x + 784.

By solving this quadratic equation, we find that the value of x is 26. Therefore, the consecutive even positive integers are 26 and 28.

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To find the x-intercepts of the parabola given its vertex and y-intercept, we can first determine the equation of the parabola. Then, we set y equal to zero and solve for x. In this case, the x-intercepts are 0 and -6.

The x-intercepts of a parabola can be found by setting the y-coordinate to zero and solving for x. The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (-3, -18), so the equation of the parabola is y = a(x + 3)^2 - 18. Since the y-intercept is at (0, 0), we can substitute these values into the equation to solve for a. Plugging in the values gives: 0 = a(0 + 3)^2 - 18. Solving for a, we get a = 2. Therefore, the equation of the parabola is y = 2(x + 3)^2 - 18. To find the x-intercepts, we set y equal to zero and solve for x: 0 = 2(x + 3)^2 - 18. Simplifying, we have 2(x + 3)^2 = 18. Dividing both sides by 2 gives (x + 3)^2 = 9. Taking the square root of both sides, we get x + 3 = ±3. Solving for x gives the x-intercepts as x = 0 and x = -6.

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Answer:

The length is [tex]8[/tex] feet.

Step-by-step explanation:

we know that

the area of the rectangle is equal to

[tex]A=xy[/tex]

where

x is the length side of rectangle

y is the width side of rectangle

In this problem we have

[tex]A=48\ ft^{2}[/tex]

so

[tex]48=xy[/tex] ----> equation A

[tex]y=x-2[/tex] ------> equation B

substitute equation B in equation A

[tex]48=x(x-2)[/tex]

[tex]x^{2}-2x-48=0[/tex]

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2}-2x-48=0[/tex]

so

[tex]a=1\\b=-2\\c=-48[/tex]

substitute in the formula

[tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-48)}} {2(1)}[/tex]

[tex]x=\frac{2(+/-)\sqrt{4+192}} {2}[/tex]

[tex]x=\frac{2(+/-)14} {2}[/tex]

[tex]x=\frac{2+14} {2}=8\ ft[/tex]  -----> the solution

[tex]x=\frac{2-14} {2}=-6[/tex]

The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is [tex]\( \frac{6}{97} \)[/tex], which is approximately 0.0619 or 6.19%.

To find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force, we need to divide the number of women in the Air Force by the total number of single parents in the military.

1. First, find the number of women in the Air Force from the table. This is given as 6 thousand.

2. Next, find the total number of single parents in the military. This is given as 97 thousand.

3. Finally, divide the number of women in the Air Force by the total number of single parents in the military and express the result as a fraction or decimal to represent the probability.

So, the probability P can be calculated as:

[tex]\[ P = \frac{{\text{Number of women in the Air Force}}}{{\text{Total number of single parents}}} \][/tex]

Substituting the values:

[tex]\[ P = \frac{6}{97} \][/tex]

[tex]\[ P ≈ 0.0619 \][/tex]

Therefore, the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is approximately 0.0619 or 6.19%.

Complete question:

This problem involves empirical probability. The table shows the breakdown of 97 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is a woman in the Air Force.

             Army    Navy   Marine Corps  Air Force  Total

Male        27         26            4                      14           71

Female    11            8             1                       6            26

Total        38          34           5                      20          97

The probability that a randomly selected single parent in the U.S. military is a woman in the Air Force is?

Since bank charges are deductions from the bank statement balance, the correct answer is:

B. a deduction from the balance per bank statement.

When reconciling a bank statement with the company's books, bank charges are typically deducted from the balance per bank statement.

Let's break down the process:

1. Balance per bank statement: This is the ending balance reported by the bank on the statement.

2. Additions to the bank statement balance: These are items such as deposits in transit (deposits made but not yet recorded by the bank), interest earned, or other credits.

3. Deductions from the bank statement balance: These are items such as outstanding checks (checks issued by the company but not yet cleared by the bank), bank fees or charges, and NSF (non-sufficient funds) fees.

To determine the original price of Janelle's sneakers, we calculate the inverse of the 15% discount that left her with a final price of $75.65, revealing the original price to be $89.00.

To find the original price of the sneakers that Janelle bought with a 15% discount, we need to understand that the final price after the discount represents 85% of the original price. This is because a 15% discount reduces the original price by 15%, leaving us with 100% - 15% = 85% of the original price. Janelle's sneakers cost her $75.65 after the discount.

Let's denote the original price by x. Therefore, 85% of x is equal to $75.65. We can set up an equation to represent this relationship:
0.85x = $75.65

To find x, we divide both sides of the equation by 0.85:
X = $75.65 / 0.85
x = $89.00

Thus, the original price of the sneakers was $89.00 before the 15% discount.

To determine the number of rows in the theater, we use the given information to create the equation x * (x - 7) = 144 where x is the number of seats per row. Factoring out, we find 16 and 9 as a suitable pair, leading to the conclusion that there are 9 rows of seats in the theater.

The student's question involves finding the number of rows of seats in a theater given certain constraints. To solve this problem, let's designate x as the number of seats in each row. According to the question, the number of rows of seats is 7 less than the number of seats in a row, which can be written as x - 7. Since we know the theater can seat 144 people in total, we can create the following equation to represent the total number of seats:

x  imes (x - 7) = 144

Solving this quadratic equation by factoring will give us the value of x, which will then allow us to calculate x - 7 for the number of rows. By factoring 144, we find that 16 and 9 are factors that satisfy the equation (16  imes 9 = 144) and also meet the condition that one factor is 7 less than the other (16 - 7 = 9). Therefore, the number of seats in each row is 16, and the number of rows is 16 - 7 which gives us 9 rows in the theater.

The length of the rectangle will be 34 yards.

The space occupied by any two-dimensional figure in a plane is called the area. The two-dimensional space occupied by the rectangle is called the area of the rectangle.

Given that A rectangle has a length of 32 yards less than 3 times its width. If the area of the rectangle is 748 square yards. The length and the width will be calculated by forming an expression.

Area = L x W

Area = W ( 3W - 32 )

748 = 3W² - 32W

3W² -32W -748 = 0

W = 22 and W = -11

The width will be 22 yards put W in the expression of L to get L.

L= ( 3W - 32 )

L = ( 3 x 22 - 32 ) = 34 yards

Therefore, the length of the rectangle will be 34 yards.

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Rick's age cannot be determined based on his statement at his grandfather's funeral.

Rick's age cannot be determined based solely on his statement at his grandfather's funeral. Crying and expressing grief at a funeral is a normal response regardless of age. It is important to remember that people of all ages experience loss and express their emotions in different ways. Age is a complex and multifaceted characteristic influenced by a variety of factors. Therefore, it is not possible to accurately determine Rick's age based on the given information.

Answer:

The length of the wire in millimeters is 9 × 10² mm.

Step-by-step explanation:

1 meter is equal to 1000 millimeters. This is the ratio that we use to convert a length in meters to one in millimeters. A scientist is working with 0.9 m of gold wire. We will use a conversion fraction to express this number in millimeters.

0.9 m × (1000 mm/ 1 m) = 900 mm = 9 × 10² mm (we round off to 1 significant figure)

The length of the wire in millimeters is 9 × 10² mm.

Answer: 47.5 miles per hour

Step-by-step explanation:

We know that ,

[tex]\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

Given : The distance to the friend’s house is 276.45 miles. It takes the family 5.82 hours to complete the trip.

i.e. Distance = 276.45 miles

Time = 5.82 hours

Then, the rate(speed) for the family’s trip in miles per hour will be :-

[tex]\text{Speed}=\dfrac{276.45}{5.82}=47.5\text{ miles per hour}[/tex]

Hence, the rate for the family’s trip = 47.5 miles per hour

[tex]84[/tex]

[tex] \sqrt{84} [/tex]