solve by completing the square x^2-14x+49=16

Answer:

Step-by-step explanation:

eeee

The formula for the area of a rectangle is length times width, or in this case (x+6)(x+2) or x^2 + 8x + 12 in standard form.

To simplify this expression, we can use the distributive property to multiply the two binomials:

(x+6)(x+2) = x(x+2) + 6(x+2)

= x² + 2x + 6x + 12

= x² + 8x + 12

To express the area of the entire rectangle, we need to multiply the length (x + 6) by the width (x + 2). This will give us a polynomial in standard form.

Step 1: Write down the expression for the area of the rectangle.
Area = (x + 6)(x + 2)

Step 2: Use the distributive property (also known as the FOIL method) to expand the expression.
Area = x(x + 2) + 6(x + 2)

Step 3: Continue to expand and simplify the expression.
Area = (x² + 2x) + (6x + 12)

Step 4: Combine like terms.
Area = x² + 8x + 12

So the area of the entire rectangle is expressed as the polynomial x² + 8x + 12 in standard form.

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Ans. Correct option in (c) 12!/11!

we know that

the formula of nPr is n! / (n−r)!.

in this question

n = 12 and r = 1

so putting values we get ,

= 12! / (12-1)!

=  12!/11!

The value of x is approximately 61.7 degrees using the Law of Sines.

To find the value of x, we can use the Law of

Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides. Mathematically, we can write:

a/sin A = b/sin B = c/sin C

where a, b, and c are the side lengths of the triangle, and A, B, and C are the angles opposite those sides.

Using the given information, we can set up the

equation as follows:

12/sin 42° = 22/sin x

Multiplying both sides by sin x°, we get:

sin x = (22/12) x sin 42°

sin x = 1.6977

Taking the inverse sine of both sides, we get:

x* = sin" (1.6977)

x = 61.7°

Rounding to the nearest tenth, we get:

x = 61.7°

Therefore, the value of x is approximately 61.7

degrees.

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The complete question is:

In the given figure , find the X (round to the nearest tenth) , where the sides are marked as 12cm and 22 cm with the angle of 42°.

It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:

$8000 = $5400e^(0.07t)

Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:

ln(8000/5400) = 0.07t

Simplifying the left side of the equation, we get:

ln(4/3) = 0.07t

Solving for t, we get:

t = ln(4/3)/0.07 ≈ 7.62 years

Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

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The probability of getting a prime number on the spinner is 2/4 or 1/2.

There are four possible outcomes on the spinner: 6, 7, 8, and 9. To determine the probability of getting a prime number, we need to first identify which of these numbers are prime. Prime numbers are numbers greater than 1 that can only be divided by 1 and themselves without leaving a remainder.

Out of the four possible outcomes, only two of them are prime: 7 and 9. Therefore, the probability of getting a prime number is the number of favorable outcomes (2) divided by the total number of possible outcomes (4), which simplifies to 1/2.

To see why this is true, we can think of the probability as a fraction where the numerator is the number of ways to get a prime number and the denominator is the total number of possible outcomes. In this case, there are two ways to get a prime number (7 and 9), and four possible outcomes (6, 7, 8, and 9). Therefore, the probability r is 2/4 or 1/2.

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Answer:p(x)=3x+5

Step-by-step explanation:

f(x)=2x+3

g(x)=x+2

p(x)=(2x+2)+(x+2)= 3x+5

Answer:

p(x)=ax + b

Step-by-step explanation:

Answer: 20.054

Step-by-step explanation:

D = 2R

R = (C/2π)

The correct statement that compares the value of the 6 in 26.495 and 17.64 is the value of the 6 in 26.495 is 10 times the value of the 6 in 17.64. Therefore, the correct option is D.

This is because the value of a digit is determined by its place in the number. In 26.495, the 6 is in the tenths place, which means it represents 6/10 or 0.6. In 17.64, the 6 is in the hundredths place, which means it represents 6/100 or 0.06. Therefore, the value of the 6 in 26.495 is 0.6 and the value of the 6 in 17.64 is 0.06.

To compare these values, we can divide the value of the 6 in 26.495 by the value of the 6 in 17.64. This gives us 0.6/0.06 = 10. Therefore, the value of the 6 in 26.495 is 10 times greater than the value of the 6 in 17.64 which corresponds to option D.

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The rate of change is 10.

The initial value of the equation is 45

The independent variable is the number of classes.

The dependent variable is the total cost.

The art class cost $45 for material and $10 per class. Therefore, let's represent the situation with a linear equation.

Linear equation can be represented in slope intercept form as follows:

y = mx + b

where

Therefore,

y = 45 + 10x

where

Therefore,

A. The rate of change is 10.

B. The initial value is 45

C. The independent variable is x(number of classes)

D. The dependent variable is total cost.

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Judith's account has less money than Alan's account after 9 months.

We can start by setting up an equation to represent the amount of money in each account after n months, where n is the number of months that have passed:

For Alan's account:

Amount of money after n months = $10,350 - $1,096n

For Judith's account:

Amount of money after n months = $8,400 - $822n

We want to find the value of n for which Judith's account has more money than Alan's account. In other words, we want to find the value of n that satisfies the following inequality:

8,400 - 822n > 10,350 - 1,096n

To solve for n, we can simplify the inequality by combining like terms:

1,096n - 822n > 10,350 - 8,400

274n > 1,950

n > 7.11

Since n represents the number of months, we can round up to the next whole number and conclude that at the end of the 8th month, Judith's account will have more money than Alan's account.

To check this result, we can substitute n=8 into the equations for the amount of money in each account:

For Alan's account: $10,350 - $1,096(8) = $2,942

For Judith's account: $8,400 - $822(8) = $2,256

We can see that Judith's account has less money after 8 months than Alan's account, so the result is not correct.

Let's try again with n=9:

For Alan's account: $10,350 - $1,096(9) = $1,846

For Judith's account: $8,400 - $822(9) = $1,518

We can see that Judith's account has less money than Alan's account after 9 months, so the correct answer is actually that Judith's account never has more money than Alan's account.

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In a binomial experiment with n = 10 and p = 0.40 there is a 57.0% chance of getting 5 or more successes in the 10 trials.

A binomial experiment is a statistical experiment that consists of a fixed number of independent trials, where each trial can have only two outcomes, typically called "success" or "failure." The probability of success for each trial is denoted by p, and the number of trials is denoted by n.

In this case, we are given n = 10 and p = 0.40. This means that we are conducting an experiment with 10 independent trials, where the probability of success for each trial is 0.40.

Using this information, we can answer questions about the probability of various outcomes. For example, we can calculate the probability of getting exactly 5 successes in the 10 trials:

P(X = 5) = (10 choose 5) * 0.40^5 * (1 - 0.40)⁽¹⁰⁻⁵⁾

P(X = 5) = 0.246

This means that there is a 24.6% chance of getting exactly 5 successes in the 10 trials.

We can also calculate the probability of getting 5 or more successes:

P(X >= 5) = P(X = 5) + P(X = 6) + ... + P(X = 10)

P(X >= 5) = 0.246 + 0.204 + 0.088 + 0.026 + 0.005 + 0.001

P(X >= 5) = 0.570

This means that there is a 57.0% chance of getting 5 or more successes in the 10 trials.

Overall, the binomial distribution is a useful tool for modeling situations where there are a fixed number of trials with a binary outcome, and the probability of success is known for each trial.

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The statements is true of this categorical proposition is: It is a standard-form categorical proposition because it is a substitution instance of this form: some s are not p option A.

A proposition or statement that is categorically affirmed or denied of all or part of the topic is known as a categorical proposition in syllogistic or classical logic. Hence, there are four fundamental types of categorical propositions: "Every S is P," "No S is P," "Some S is P," and "Some S is not P."

Every man is mortal, for instance, is an A-proposition since these forms are denoted by the letters A, E, I, and O, respectively. In particular, being declarations of reality rather than logical connections, they contrast significantly with hypothetical propositions, such as "If every man is mortal, then Socrates is mortal," which categorical propositions are to be differentiated from and enter into as integral words.

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Answer:

  g(x) = h(x -7) +5

Step-by-step explanation:

Given h(x) defines a parabola that opens upward with a vertex at (-2, -7) and g(x) defines the same parabola with its vertex at (5, -2), you want to express g(x) in terms of h(x).

The graph of f(x) is translated right h units and up k units by ...

  f(x -h) +k

We see that g(x) is a translation of h(x) right by 7 units and up by 5 units. This means (h, k) is (7, 5), and the translated function is ...

  g(x) = h(x -7) +5

__

Additional comment

This is confirmed by the plots in the second attachment.

Answer:  g(x)=h(x-7) +5

Step-by-step explanation:

The graph g(x) has been shifted up 5   (+5)   and right 7

When shift a function, the y change, up/down, goes at end of function

When shift in x direction happens, you take opposite sign so we will do -7

g(x)=h(x-7) +5

Using the completing the square method, the quadratic equation x²-5x=9 can be simplified to (x-2.5)²=15.25, and the solutions are x=2.5+√15.25 and x=2.5-√15.25.

To solve this quadratic equation using the completing the square method. Here are the steps

Move the constant term (in this case, 9) to the right-hand side of the equation

x² - 5x = 9 becomes x² - 5x - 9 = 0

To complete the square, we need to add and subtract a constant term inside the parentheses. The constant term we add is half of the coefficient of the x-term, squared. In this case, the coefficient of the x-term is -5, so we need to add and subtract (5/2)² = 6.25.

x² - 5x - 9 + 6.25 - 6.25 = 0

Rearrange the terms inside the parentheses to group the perfect square with the x-term

(x² - 5x + 6.25) - 15.25 = 0

Factor the perfect square trinomial inside the parentheses

(x - 2.5)² - 15.25 = 0

Add 15.25 to both sides of the equation

(x - 2.5)² = 15.25

Take the square root of both sides

x - 2.5 = ±√15.25

Add 2.5 to both sides

x = 2.5 ±√15.25

So the solutions to the equation x² - 5x = 9, using the completing the square method, are x = 2.5 + √15.25 and x = 2.5 - √15.25.

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--The given question is incomplete, the complete question is given

"Can anyone help? i need to solve these using the completing the square method

x²-5x = 9"--

In a case whereby Zelda has 8 rabbits with which to start an animal farm. If the rabbit population doubles each month, the number of  months that the rabbit population will be 5,800 is 9.5 months.

In order to calculatre the month then we can use the expression y = abⁿ

a = starting number ( 8 rabbits)

b = rate of change = (2)

n = number of months that we need to calculate

y = rabbit population = 5800

The we can substitute to have

5800 = 8 × 2ⁿ

5800 / 8 = 2ⁿ

725 = 2ⁿ

n = 9.5 months.

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The correct equation that represents Finley's annual salary, f(n), during the nth year is: [tex]f(n) = 56,000(1.06)^(n-1)[/tex] Thus, option D is correct.

What is an equation?

Finley's annual salary increases by 6% each year. This means that the salary for the second year is 6% more than the salary for the first year, the salary for the third year is 6% more than the salary for the second year, and so on.

To find an equation for Finley's annual salary during the nth year, we can use the initial salary of $[tex]56,000[/tex] and the fact that the salary increases by 6% each year. One way to write this equation is:

[tex]f(n) = 56,000(1.06)^(n-1)[/tex]

Here, the expression (1.06)^(n-1) represents the 6% increase in salary each year, starting from the second year (hence the (n-1) exponent). Multiplying this by the initial salary of $56,000 gives the salary for the nth year.

Therefore, the correct equation that represents Finley's annual salary, f(n), during the nth year is:[tex]f(n) = 56,000(1.06)^(n-1)[/tex]

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The amount the temperature during the day changed between 9 a.m. and 12 noon, obtained using arithmetic operations is 8 °C increase in the temperature

Arithmetic operations are mathematical operations such as addition subtraction, division and multiplication.

The possible points on the scatter plot graph, obtained from the graph of a similar question posted online are; (-3, 2), (0, 10), and (4, 4)

The coordinate point on the graph corresponding to 9 a.m. is (-3, 2)

Therefore, the temperature at 9 a.m. is 2°C

The coordinate point on the graph corresponding to 12 noon is (0, 10)

Therefore, the temperature at 12 noon. is 10°C

The change in temperature between the temperature at 9 a.m. and the temperature at 12 noon = 10°C - 2°C = 8 °C (Increase in temperature)

Please find attached the possible scatter plot in the question

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The intensity of the Galesburg earthquake was approximately 63.1 times larger than the intensity of the Stony Point earthquake.

To compare the intensities of the Galesburg and Stony Point earthquakes, we can use the Richter scale formula M = log(I/I₀), where M is the magnitude of the earthquake, I is the intensity of the earthquake, and I₀ is a reference intensity.

Given:

Magnitude of the Galesburg earthquake (M₁) = 4.2

Magnitude of the Stony Point earthquake (M₂) = 2.5

To find the intensity ratio between the two earthquakes, we can use the formula:

I₁/I₂ = 10^(M₁ - M₂)

Substituting the given magnitudes into the formula:

I₁/I₂ = 10^(4.2 - 2.5)

Calculating the exponent:

I₁/I₂ = 10^1.7

Using a calculator, we find that 10^1.7 is approximately 50.12.

Therefore, the intensity of the Galesburg earthquake (I₁) was approximately 50.12 times larger than the intensity of the Stony Point earthquake (I₂).

Alternatively, we can also express this as the intensity of the Galesburg earthquake being approximately 63.1 times larger than the intensity of the Stony Point earthquake (since 50.12 is approximately equal to 63.1).

Hence, the intensity of the Galesburg earthquake was approximately 63.1 times larger than the intensity of the Stony Point earthquake.

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The only possible value of W is:

W ≈ 71.6° to the nearest 10th of a degree.

We can use the Law of Cosines to find the angle W opposite to the side w:

cos(W) = (v^2 + w^2 - u^2) / (2vw)

cos(W) = (3.6^2 + 5.3^2 - u^2) / (2 * 3.6 * 5.3)

We can solve for u by using the Law of Cosines for the angle V:

cos(V) = (u^2 + v^2 - w^2) / (2uv)

cos(32°) = (u^2 + 3.6^2 - 5.3^2) / (2 * u * 3.6)

Simplifying the equation and solving for u, we get:

u = sqrt(3.6^2 + 5.3^2 - 2 * 3.6 * 5.3 * cos(32°)) ≈ 3.8 inches

Now we can substitute this value of u into the equation for cos(W) and solve for cos(W):

cos(W) = (3.6^2 + 5.3^2 - 3.8^2) / (2 * 3.6 * 5.3) ≈ 0.315

Taking the inverse cosine, we get:

W ≈ 71.6° or W ≈ 288.4°

Note that since the angle W is in a triangle, it must be between 0° and 180°. Therefore, the only possible value of W is:

W ≈ 71.6° to the nearest 10th of a degree.

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Brandon rode his bike 8.35 miles further than Randy.

To find out how much further Brandon rode his bike last month than Randy, you'll need to subtract Randy's miles from Brandon's miles using the given values.

Step 1: Identify the miles ridden by both Brandon and Randy.
- Brandon rode 56.28 miles.
- Randy rode 47.93 miles.

Step 2: Subtract Randy's miles from Brandon's miles.
- 56.28 miles (Brandon's miles) - 47.93 miles (Randy's miles) = 8.35 miles.

So, last month, Brandon rode his bike more than Randy.

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The equation that can be used to determine the number of minutes t, from now and height, ℎ (in feet), at which they will pass each other is 75t = h.

The time taken for them to pass each other is calculated as follows;

Apply the rules of relative velocity;

(V₂ - V₁)t = h

where;

(30 ft/min - ( -45 ft/min )t = h

75t = h

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a. The equation is Total Cost = 0.75x + $600

b. Total cost is $60,600 and net profit is $19,400.

c. The breakeven level of sales volume is $2,400.

a. The equation relating total cost and sales volume can be expressed as:

Total Cost = Cost of Goods Sold + Selling Expenses + Fixed Expenses

where Cost of Goods Sold = 60% (100% - 40%) of the sales volume

           Selling Expenses = 15% of the sales volume

           Fixed Expenses = $600.

Therefore, the equation can be written as:

Total Cost = 0.6x + 0.15x + $600
                 = 0.75x + $600

b. For sales of $80,000, we can substitute x = $80,000 into the equation:

Total Cost = 0.75x + $600
                 = 0.75($80,000) + $600
                 = $60,000 + $600
                 = $60,600

To calculate net profit before taxes, we need to subtract the total cost from the sales volume:

Net Profit before Taxes = Sales - Total Cost
                                       = $80,000 - $60,600
                                       = $19,400

c. To find the breakeven level of sales volume, we need to set the net profit before taxes to zero and solve for x:

Net Profit before Taxes = Sales - Total Cost
               0                      = x - (0.6x + 0.15x + $600)
               0                      = 0.25x - $600
            0.25x                  = $600
               x                       = $2,400

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The scale factor from A to B is 5 / 4.

The value of t in the diagram is 5.6 cm.

Scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Therefore, let's find the scale factor from the shape A to the shape B as follows:

5 / 4 = 15 / 12

Therefore, the scale factor is 5 / 4.

Hence, let's find the value of t in the diagram as follows:

Therefore, using the proportionality,

7 / t = 5 / 4

cross multiply

28 = 5t

divide both sides by 5

t = 28 / 5

t = 5.6 cm

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The equivalent ratio is 10:107.78

To solve this problem, we need to find a ratio that is equivalent to 10:9 but has a denominator of 97.

First, we can set up a proportion:

10/9 = x/97

To solve for x, we can cross-multiply:

10 * 97 = 9 * x

970 = 9x

To find the value of x, you divided both sides of the equation by 9, resulting in:

x = 107.78 (rounded to two decimal places)

So the equivalent ratio is 10:107.78, but since we can't have a fractional hat, we can round up to 108. Therefore, the answer is 10:108.

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Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

a. The total cost of the socks and shorts can be represented by the expression:

Total cost = Cost of shorts + Cost of 5 pairs of socks

= $19.95 + 5x

where x is the price of one pair of socks.

b. To write an equation that says Lamar spent exactly $35 on the socks and shorts, we can equate the total cost expression to $35:

$19.95 + 5x = $35

To solve for x, we can first subtract $19.95 from both sides:

5x = $15.05

Then, divide both sides by 5:

x = $3.01

So, Lamar spent $19.95 + 5($3.01) = $35 on the socks and shorts.

c. Other possible prices for the socks that would still allow Lamar to stay within his budget of $35 can be found by plugging in values of x that satisfy the inequality:

Cost of 5 pairs of socks = 5x ≤ $15.05

For example, if the socks cost $2.99 per pair, then the total cost would be:

$19.95 + 5($2.99) = $34.90

which is within Lamar's budget.

d. We can write an inequality to represent the amount Lamar can spend on a single pair of socks as:

x ≤ (35 - 19.95)/5

This simplifies to:

x ≤ $3.01

So, Lamar can spend at most $3.01 on a single pair of socks to stay within his budget.

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In ΔKLM, m = 17 inches, l = 44 inches, and ∠L = 153°. The possible value of ∠M is approximately 12.3°.

In any triangle, the sum of the interior angles is always 180°. First, we can find the third angle ∠K by subtracting ∠L from 180°: 180° - 153° = 27°. Next, we use the Law of Sines to find the possible values of ∠M. The formula is:

(sin ∠M) / m = (sin ∠K) / l

Plug in the given values:

(sin ∠M) / 17 = (sin 27°) / 44

To find sin ∠M, we multiply both sides by 17:

sin ∠M = (sin 27°) * (17 / 44)

Now, find the inverse sine (arcsin) of the result:

∠M = arcsin((sin 27°) * (17 / 44))

∠M ≈ 12.3°

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If a cube is sliced perpendicular to its base, the resulting two dimensional cross-section will be a square. This is because each face of a cube is a square, and a perpendicular slice across the base will result in a square shape. A trapezoid or a circle would not result from a perpendicular slice of a cube.

When a cube is sliced perpendicular to its base, the shape of the resulting two-dimensional cross-section is a square.

Step-by-step explanation:
1. A cube has six faces, all of which are squares.
2. When you slice the cube perpendicular to its base, you are cutting it in a direction that is at a 90-degree angle to the base.
3. Since all the faces of a cube are squares, the resulting cross-section from a perpendicular slice will also be a square.

So, the correct answer is option 2, a square.

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The required answers are  2.5 liters and  1.5 liters per minute.

Part A:

If we know that the pot has a capacity of 10 liters, we can use the equation y = 1.5x + 2.5 to determine how much soup was in the pot to start with, since at x = 0 minutes, no soup has been added yet.

Substituting x = 0 in the equation, we get:

y = 1.5(0) + 2.5

y = 2.5

Therefore, the pot had 2.5 liters of soup to start with.

Part B:

The equation y = 1.5x + 2.5 tells us how much soup is added to the pot in x minutes, so the rate at which the cook fills the pot can be found by taking the derivative of y with respect to x:

dy/dx = 1.5

Therefore, the rate at which the cook fills the pot is 1.5 liters per minute.

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