Please answer correctly !!!!!!! Will mark brainliest !!!!!!!!!!!

The equation square root of (x + 3) + 6 = 9 has two potential solutions, x = 0 and x = 6. However, upon analysis, it is determined that x = 0 is an extraneous solution while x = 6 is not extraneous.

To find the result of the given equation, we'll break it step by step and also determine if any results are extraneous.

 The given equation is

 √( x + 3) 6 = 9

 Let's break it

Step 1 Subtract 6 from both sides of the equation

√( x +3) = 9- 6

√( x +3) = 3

 Step 2 Square both sides of the equation to exclude the square root

( x + 3) = \(3^{2}\)

( x + 3) = 9

 Step 3 Subtract 3 from both sides of the equation

x = 9- 3

x = 6

 The result to the equation is x = 6.

Now, let's determine if this result is extraneous or not.

 To check if the result is extraneous, we need to substitute it back into the original equation and see if it holds true.

Original equation √( x + 3) + 6 = 9

 Substituting x = 6

√( 6 +3) + 6 = 9

√ 9 +6 = 9

3 +6 = 9

9 = 9

Since the equation holds true when x = 6, the result x = 6 is NOT an extraneous result.

thus, the correct statements are

 x = 0; not extraneous

x = 6; not extraneous

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The expression 4^3/2 is equal to 32 in exponentiation operation and  4√2 in division operation.

If the exponentiation operation (4^3) is performed before the division operation (/2), then the expression can be written as:

4^3/2 = (4^3) / 2

= (4 × 4 × 4) / 2

= 64 / 2

= 32

If the division operation (/2) is performed before the exponentiation operation (4^3), then the expression can be written as:

4^3/2 = 4^(3/2)

= 4^(1.5)

= 2 × 2 × 2^(0.5)

= 2 × 2 × √2

= 4√2

It's important to note that when dealing with expressions involving exponents, the order of operations matters and can significantly affect the resulting value.

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Answer:

6000 pounds or lbs.

Step-by-step explanation:

A ton=2000 lbs.

Hope this helps! ;-)

The expression that can be used to represent the total price is 3(p - $0.75) + 5(p - $1).

The expression that can be used to determine the total amount spent in store A is:

5(p - $1)

The expression that can be used to determine the total amount spent in store B is:

3(p - $0.75)

Total price = 3(p - $0.75) + 5(p - $1)

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Answer:

The total bill was $98.

Step-by-step explanation:

Matt and 6 of his friends = 7 people

Each person paid $14

$14 x 7 = $98 in total

Differential equations are mathematical equations that involve derivatives. They describe the relationship between an unknown function and its derivatives, helping to model and understand dynamic systems in physics, engineering, and other scientific disciplines.

To find the general solution of the given system of differential equations by decoupling, we first need to rewrite the given equation in a more standard form. The equation provided is: x1' = x1 * x.

Step 1: Rewrite the equation
x1' = x1 * x can be rewritten as dx1/dt = x1 * x, where x1 is a function of time t.

Step 2: Separate variables
Now, we separate variables by dividing both sides of the equation by x1, and then multiplying both sides by dt:
(dx1/x1) = x * dt

Step 3: Integrate both sides
Now we can integrate both sides of the equation with respect to their respective variables:

∫(dx1/x1) = ∫(x * dt)

After integrating, we get:
ln|x1| = (1/2) * x^2 + C₁, where C₁ is the constant of integration.

Step 4: Solve for x1
To find the general solution for x1, we need to exponentiate both sides of the equation to eliminate the natural logarithm:

x1(t) = Ce^(1/2 * x^2), where C = e^(C₁) is a new constant.

So, the general solution of the given system of differential equations is x1(t) = Ce^(1/2 * x^2), where C is an arbitrary constant.

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Answer:

4m+7

Step-by-step explanation:

4(m+(-2))+15

4(m-2)+15

4m-8+15

4m+7

Answer:

1/ x +8

*The 1 over x + 8

Answer:

\(\frac{1}{x+8}\)

Step-by-step explanation:

Here is your original equation:

What we need to focus on is simplification, specifically simplifying the denominator. First, let's isolate the denominator (we'll get back to \(x-5\) later):

\(x^{2} +3x-40\)

Next, we take a look at -40. Our goal is to find what factors of 40 create a sum of 3 so we can separate the equation for polynomial division.

Let's begin building our expressions. We know that \(x^{2}\) has an exponent of 2. When variables are multiplied, the exponents are added, meaning that \(x*x=x^{2}\). (Or \(x^{1} + x^{1} =x^{2}\) , the 1s just don't show)

We can also see that -40 is a negative number. A negative multiplied by a positive makes a negative product, so we can also include one positive and one negative in each expression.

\(x^{2} +3x-40 = (x+)(x-)\)

Next, let's look at the factors of 40:

1 and 40   2 and 20   4 and 10   5 and 8

Which of these factors can make a sum of 3? Remember that one number has to be positive and the other has to be negative!

In this instance, our positive number is 8 and our negative number is 5. They create the sum of 3 that we're splitting in \(3x\). Therefore, \(8(-5)=-40\).

Now let's go back to our original equation and substitute our old expression with the new one:

Do you notice that the numerator and part of the denominator are equal? This means that they can cancel each other out! Think of it as a \(\frac{1}{1}\).

Therefore, your simplified answer is  \(\frac{1}{x+8}\) !

Here's the whole process:

\(\frac{x-5}{x^{2} +3x-40} \\\\(x+?)(x-?)\\\\40:\\1, 40\\2, 20\\4, 10\\5, 8\\\\8-5=3 \\(8x-5x=3x)\\\\(x+8)(x-5)\\\\\frac{x-5}{(x+8)(x-5)}=\frac{1}{x+8} \\\\\frac{1}{x+8}\)

To check your answer, confirm your expressions using the box method attached.

I hope this helps! If you have any more questions or concerns about the answer or the process, let me know!

1.The beginning balance should be $4,000

2.The amount to be adjusted is $2554

3.The ending balance of the account after the adjustment $2554

4. Office Supplies Account is $14846

"Information available from the question"

The Office Supplies account started the year with a $4,000 debit balance

The company purchased supplies for $13,400,

The inventory of supplies available at the end of the year totaled $2,554.

Now, According to the question:

1. The beginning balance should be $4,000

2.The adjusted amount is

Opening balance = 4000

Add: New purchases = 13400

Balance after Purchase = 17400

Less: Year end balance = 2554

3. The ending balance is $2,554

4. The adjusting journal entry is

Dr. Supplies Expense Account is 14846

Adjustment in the year = Cr. 14846 (subtracted from the balance)

Office Supplies Account is 14846

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The 8-puzzle problem can be categorized as a "Pathfinding problem."

The 8-puzzle is a classic problem in artificial intelligence and computer science. It involves a 3x3 grid with eight numbered tiles and one empty space. The objective is to rearrange the tiles from an initial configuration to a goal configuration by sliding them into the empty space.

The reason why the 8-puzzle problem is classified as a pathfinding problem is that it involves finding a sequence of moves or actions to reach a desired state or goal. In this case, the desired state is the goal configuration of the puzzle. The problem requires determining the optimal sequence of moves that lead to the goal state while considering the constraints and limitations of the puzzle.

Pathfinding problems involve finding the shortest or optimal path from a starting point to a goal or destination. In the 8-puzzle problem, the empty space serves as the movable "agent" that can slide adjacent tiles. The objective is to find the shortest sequence of moves or actions to transform the initial configuration into the goal configuration, effectively finding a path to the solution.

Therefore, due to its nature of finding an optimal sequence of moves to reach a goal state, the 8-puzzle problem can be categorized as a pathfinding problem.

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Yes each side and each angle has a congruent corresponding part

Answer:

it is nothing

Step-by-step explanation:

1-1=2

There are 7 months in the year that have thirty-one days.

These months are January, March, May, July, August, October, and December.

There are seven months in the Gregorian calendar that have thirty-one days: January, March, May, July, August, October, and December.

This pattern of months with 31 days followed by months with fewer days repeats throughout the year.

This pattern was established by the Roman calendar, which had ten months totaling 304 days in a year.

The months of January and February were later added by King Numa Pompilius to align the calendar with the lunar year.

The months of January and February initially had 29 and 28 days respectively, but in 45 BC, Julius Caesar added one day to January and one day to August, which was originally a 30-day month, to make them both 31-day months.

In the Gregorian calendar, which is the most widely used calendar in the world, January, March, May, July, August, October, and December all have 31 days.

The remaining five months have fewer days, with February having 28 days most of the time, and 29 days in a leap year.

Knowing the number of days in each month is important for various reasons, such as planning events, scheduling appointments, and calculating pay periods.

There are several mnemonics used to remember the number of days in each month, such as "30 days hath September, April, June, and November, all the rest have 31, except February, with 28 days clear, and 29 in each leap year."

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Only (B) 4.72% of the couples polled have 5 or more children.

To find what number of children occurred the least frequently:

The percentage is as follows:

Therefore, only (B) 4.72% of the couples polled have 5 or more children.

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The complete question is given below;
A random sample of 1,250 couples was asked the question, "How many children presently reside in your household?"

Number of Children—Frequency

0——250

1——-112

2——560

3 ——201

5 or more ——59

What number of children occurred the least frequently? Calculate this percent

A) 2, 55.2%

B)5 or more, 4.72%

C)5 or more, 11.91%

D)4.21.67%

Answer:

14.88 km

Step-by-step explanation:

add both base 1 and base 2 together divide them by 2 then multiply by the height.

y = .08x+175000

175000 is the y intercept and because its increasing by .08 thats x you can always check these in desmos graphing calculator

Answer:

vertex is (2 , -21)

x = -2 +√10

y = (x-3)²+1

Step-by-step explanation:

x² - 4x - 17

(x² - 4x + 4) - 4 - 17

(x-2)² - 21

vertex is (2 , -21)

2x² +8x = 12

x² + 4x = 6

(x² +4x + 4) - 6 - 4

(x+2)²  - 10

x+2 = √10

x = -2 +√10

y = (x-3)²+1

Answer:

The first option will be your answer

Step-by-step explanation:

The final speed v2 is √6 times the initial speed v1, when the net force is 2f1 and the object moves the same distance d while the force is being applied.

We can use the work-energy theorem to solve this problem, which states that the work done on an object by a net force is equal to the change in its kinetic energy.

When the force has magnitude f1 and the object moves a distance d, the work done is:

W = f1 * d

This work changes the kinetic energy of the object from zero to (1/2) * m * v1^2, where m is the mass of the object. Therefore, we have:

f1 * d = (1/2) * m * v1^2

Solving for v1, we get:

v1 = sqrt((2 * f1 * d) / m)

Now, when the net force has magnitude f2 = 2f1 and the object moves the same distance d, the work done is:

W = f2 * d = 2f1 * d

This work changes the kinetic energy of the object from (1/2) * m * v1^2 to (1/2) * m * v2^2, where v2 is the final speed of the object. Therefore, we have:

2f1 * d = (1/2) * m * (v2^2 - v1^2)

Solving for v2, we get:

v2 = sqrt(v1^2 + (4 * f1 * d) / m)

Substituting the expression for v1, we get:

v2 = sqrt((4 * f1 * d) / m + (2 * f1 * d) / m)

Simplifying, we get:

v2 = sqrt(6) * v1

Therefore, the final speed v2 is sqrt(6) times the initial speed v1.

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The car's worth after 3 years will be $5,463.64 compounded annually.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/100)t

Here P = $5000

R = 3%

T = 3 years.

A = 5000(1+3/100)³

A = $463.64

So the total amount is P+A = $5,463.64

Hence, The worth of the car after 3 years will be $5,463.64

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Answer:

Step-by-step explanation:

Answer:4

Step-by-step explanation:

it shows it on the table

Answer:

Step-by-step explanation:

going by the assumption tha the radius is 10inches.

area would be pi r^2

which would be pi(10)^2 = 100pi =314.16 (rounded)

Answer: 4 i think

Step-by-step explanation:

Answer:

0.69465837 is the answer

Answer: ∠1 = 90°

Step-by-step explanation:

      There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.

      First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).

89° = 51° + ∠3

∠3 = 38°

      Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.

90° = ∠3 + ∠2

90° = 38° + ∠2

∠2 = 52°

      Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.

180° = 38° + ∠1 + ∠2

180° = 38° + ∠1 + 52°

180° = 90° + ∠1

∠1 = 90°

Answer:

90

Step-by-step explanation:

I started by finding angle 5

180 - 89 = 91  Supplemental angles

Then I found angle 3

The sum of the interior angles of a triangle is 180

180-89-91 = 38

Angle2 and 3 are complementary angles

90- 38 =52

the sum of the interior angles of a triangle is 180

Angle 1

180 - 52 - 38 = 90

Answers:

=================================================

Explanation:

Let's say that the letter k replaces the green box

We have the equation y = kx

Plug in (x,y) = (7,35) to get the equation 35 = k*7

Dividing both sides by 7 leads to k = 5

Therefore, the direct variation equation is y = 5x

We can check this by plugging in x = 7

y = 5x

y = 5*7

y = 35

So x = 7 leads to y = 35 as expected.

-------------

Do the same for x = 4

y = 5x

y = 5*4

y = 20 when x = 4

Side note: direct variation equations always go through the origin.

Answer:

20

Step-by-step explanation:

if y varies directly with x, then it takes the form y=mx

to find m, substitute in the values of x and y to get 35=m*7 and simplify to get that m=5

then the equation becomes y=5x

substitute in the value they gave for x which is 4 to get y=5*4

to get that y=20