Midsegment- Find x (x+10)(x+2)

By using completing the square method, the solution to this quadratic equation is x = √13 ± 2.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Next, we would solve the given quadratic equation by using the completing the square method;

x² - 4x - 9 = 0

x² - 4x = 9

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² - 4x + (4/2)² = 9 + (4/2)²

x² - 4x + 4 = 9 + 4

x² - 4x + 4 = 13

By simplifying, we have;

(x - 2)² = 13

x = √13 ± 2

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By answering the presented question, we may conclude that Therefore, equation the distance between the student and the mirror is approximately 8.82 feet.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

Based on the given information

\((4.5 + 0) / d = 30 / (50 + d)\\(4.5 + 0)(50 + d) = 30d\\225 + 4.5d = 30d\\225 = 25.5d\\d = 8.82 feet\)

Therefore, the distance between the student and the mirror is approximately 8.82 feet.

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Answer:

585

Step-by-step explanation:

just use a calculator‍♀️

Answer:

554 N

Step-by-step explanation:

We're looking for the magnitude of the force - angles don't matter.

We need to resolve the two forces.

As you can see in the attached drawing, this basically just becomes Pythagoras.

\( {f}^{2} = {355}^{2} + {425}^{2}\)

\(f = \sqrt{ {355}^{2} + {425}^{2} } \)

\(f = 553.76\)

Answer:

x = 25

Step-by-step explanation:

Given:

Amount invest p = Tk.x

Number of year t = 4

Rate r = x%

Profit = Tk.x

Find:

Value of x

Computation:

Profit = prt / 100

Tk.x = [(Tk.x)(x)(4)] / 100

x = 100 / 4

x = 25

The volume of the solid formed by rotating the region inside the first quadrant enclosed by the curves y = x and y = 5x about the x-axis is (250π/7) cubic units. When finding the volume of a solid of revolution, we use the method of cylindrical shells.

To calculate the volume, we integrate the area of each cylindrical shell formed by rotating an infinitesimally small strip about the x-axis. The height of each shell is the difference between the y-values of the two curves, which is (5x - x²). The circumference of each shell is given by 2πx, and the thickness is dx. Therefore, the volume of each shell is 2πx(5x - x²)dx.

To find the total volume, we integrate this expression over the interval where the two curves intersect. Setting\(y = x^2\)and y = 5x equal to each other, we get x² = 5x. Solving this equation, we find two intersection points: x = 0 and x = 5. Thus, the limits of integration are from 0 to 5.

Integrating the expression \(2\pi x(5x - x^2)dx\) from 0 to 5 gives us the volume of the solid formed by rotating the region inside the first quadrant. Evaluating this integral, we find the volume to be (250π/7) cubic units.

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The archway is a combination of a semi-circle and two rectangles. Then the area of the archway is 13.5π + 24 square units.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The archway with a semicircle top arch and two rectangular pillars. The lower supports are and the area of the two supports is square meters.

The upper arch can be decomposed as one semicircle with radius meters minus a semicircle with a radius of 3 meters.

The archway is a combination of a semi-circle and two rectangles.

Area of archway = 2 × Area of rectangle + Area of a semicircle

Area of semicircle will be

\(\rm Area\ of\ semicircle = \dfrac{1}{2} \pi (r_2^2-r_1^2)\\\\Area\ of\ semicircle = \dfrac{1}{2} \pi (6^2 - 3^2)\\\\Area\ of\ semicircle = \dfrac{1}{2} \pi (36-9)\\\\Area\ of\ semicircle =\dfrac{1}{2}* 27 \ \pi \\\\Area\ of\ semicircle = 13.5 \ \pi\)

The area of the rectangle will be

\(\rm Area\ of\ rectangle = Length * Width \\\\Area\ of\ rectangle = 3*4\\\\Area\ of\ rectangle = 12\)

Then the area of the archway will be

Area of archway = 2 × 12 + 13.5π

Area of archway = 13.5π + 24

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Answer:

congruent rectangles, 24, 6, & 13.5

Step-by-step explanation:

i did it

Answer:

how many

Step-by-step explanation:

Answer:

the answe

Step-by-step explanation:

Answer:

You didn't provide any choices or options to pick from but here are the possible answers is:

- Encourage the use of the incentive spirometer every 2 hours

-Instruct to splint incision when coughing and deep breathing.

-Reposition the client every 2 hours

-Assist with early ambulation.

Step-by-step explanation:

Hope I could help!

In the plan of care to prevent postoperative atelectasis, interventions should not include the use of tobacco products or exposure to secondhand smoke.

The nurse should include several interventions in the plan of care to prevent postoperative atelectasis, but there are specific interventions that should not be included. Atelectasis is the partial or complete collapse of the lung, and preventing it is crucial after surgery. Here are some interventions that should be included:

Incentive Spirometry: The nurse should encourage the client to use an incentive spirometer to promote deep breathing and lung expansion.

Early Ambulation: Encouraging the client to get out of bed and walk as soon as possible after surgery helps improve lung function.

Pain Management: Adequate pain control measures should be in place to ensure the client can take deep breaths without discomfort.

Coughing and Deep Breathing Exercises: The nurse should teach and encourage the client to perform regular coughing and deep breathing exercises to clear the airways and prevent mucus buildup.

Positioning: Proper positioning, such as elevating the head of the bed, can aid lung expansion.

What should not be included in the plan of care is the use of tobacco products or exposure to secondhand smoke, as smoking and smoke exposure are detrimental to lung health and can worsen atelectasis. These should be strictly avoided to prevent postoperative complications.

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Answer:

5/9

Step-by-step explanation:

brainliest when possible.

Tom will need to bring to the closing $54,341.27 He would need 12 and it would cost 50k.

The meaning down payment is a part of the full price paid at the time of purchase or delivery with the balance to be paid later.

We have given that,

Tom buys a condominium for $42,600.

Inspection, $110; mortgage fee, $852; legal fees, $450; title insurance, $286

He makes a down payment of 15% and pays these closing costs to survey $225.

9% payments: $563.24

7% payments: $494.75.

Monthly savings: $69.49

9% total repaid: $2022,764.90  

7% total repaid: $148,423.63

Savings: $54,341.27

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Answer:

The height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.

Step-by-step explanation:

The polynomial expression representing the charge for Claire's paintings is:

C = 50x² + 250

The polynomial expression representing the charge for Richard's paintings is:

R = 49x² + 350

Here x represents the height of the paintings feet.

Now compute the value of x such that both Claire and Richard charge the same amount as follows:

C = R

50x² + 250 = 49x² + 350

50x² - 49x² = 350 - 250

x² = 100

x = 100

Thus, the height of the painting has to be 10 feet for both Claire and Richard to charge the same amount.

Answer:

$30

Step-by-step explanation:

6 • 1/3 = 18

18 • 1/2 = 36

36 - 6 = 30

Connie spends 30 dollars at Allen's Grocery Store.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

Operators which let do a basic mathematical calculation

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

Given that after shopping Connie had 6 dollars left.

Connie spent one-third of her money at Cafe

So, 6 (1/3) ⇒ 18

Connie spent one-half of her money at Grocery Store

So, 18 (1/2) ⇒ 36

So, Connie spends total money at Allen's Grocery Store

⇒ 36 - 6

⇒ 30 dollars

Hence, Connie spends 30 dollars at Allen's Grocery Store.

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Answer: False. Maximum parsimony is a method used in phylogenetic analysis that aims to find the tree that requires the fewest number of evolutionary events (such as mutations or character state changes) to explain the observed data. It is not directly based on the probability of these events. However, the choice of the most parsimonious tree can be influenced by probability-based models of evolution, such as the assumption that evolutionary events occur randomly and at a constant rate over time.

Step-by-step explanation:

Given :

☄ Radius of circular pond = 6 m

☄ The path has a width = 1 m

To Find :

☄ Area of the path = ?

Formula we have to use here :

☄ Area of path = Length of path × width

☄ Length of path = Circumference of pond

Solution :

☄ Area of the path is 37.72 m²

Required Explaination :

☃ Length of path = Circumference of pond ☃

Now, subsitute the given values in above formula we get :

→ Length of path = Circumference of pond

→ Length of path = 2πr

→ Length of path = 2 × 22/7 × 6

→ Length of path = 264/7 m

Now,let's find the area of the path :

→ Area of path = Length of path × width

→ Area of path = 264/7 × 1

→ Area of path = 37.72 m²

The function has a minimum of -4.35125

From the question, the equation of tis given as

f(x)=2x^2-9.1x+6

Rewrite the function as follows

f(x) = 2x² -9.1x + 6

Next, we differentiate the function

This is represented as

f'(x) = 2 * 2x - 1 * 9.1 + 0 * 6

Evaluate

f'(x) = 4x - 9.1

Set the differentiated function to 0

This is represented as

f'(x) = 0

So, we have

4x - 9.1 = 0

This gives

4x = 9.1

Divide by 4

x = 2.275

Substitute x = 2.275  in f(x) = 2x² -9.1x + 6

f(2.275) = 2(2.275)² - 9.1(2.275) + 6

Evaluate

f(2.275) = -4.35125

Hence, the minimum is -4.35125

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Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

The proportion of a circle's circumference to its diameter is denoted by the mathematical constant pi (). It cannot be written as a simple fraction since it is an irrational number. Pi is approximately equal to 3.141592, or 3.15.

We must first determine the circle's radius in order to determine the length of Mr. Chang's string.

C = 2πr, where C is the circle's circumference and r is its radius, is the formula for a circle's circumference.

Given that the circle's circumference is 31.4 meters, we can solve for r using the following method:

C = 2r 31.4

=2x3.14xr

= 31.4/(2x3.14)r

= 3.14/6.28r

r = 5

Thus, the circle's radius is roughly 5 meters.

The diameter of the circle, which is twice as long as its radius, will be equal to Mr. Chang's stake because it is in the center of the circle.

Mr. Chang's string will therefore be about 10 meter long rounded to nearest meter

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Answer:

Step-by-step explanation:

Slope of the line.

Answer:

The Oort Cloud

Step-by-step explanation:

The Oort Cloud is a predicted collection of icy objects farther away than everything else in the solar system.

Hope this helped!!!

The image is formed behind the mirror, and the image is upright.

Given data: Object height, h = 3.0 cm Image distance, v = ? Object distance, u = -20.0 cmFocal length, f = -60.0 cmUsing the lens formula, the image distance is given by;1/f = 1/v - 1/u

Putting the values in the above equation, we get;1/-60 = 1/v - 1/-20

Simplifying the above equation, we get;v = -40 cm

This negative sign indicates that the image is formed behind the mirror, as the object is placed in front of the mirror.

Hence, the image is virtual and erect. Using magnification formula;M = -v/uWe get;M = -(-40) / -20M = 2Hence, the height of the image is twice the height of the object.

The height of the image is given by;h' = M × hh' = 2 × 3h' = 6 cm Now, let's draw the ray diagram:

Thus, the position of the image is -40.0 cm and the height of the image is 6 cm.

The image is formed behind the mirror, and the image is upright.

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The term that is not affected the standard error of an estimator is population size, from the provide data in options. So, option (c) is right one.

The standard error is a statistical term that used to measured the accuracy that a sample distribution represents a population by using standard deviation. The standard error(SE) is very similar to standard deviation of a distribution. Both are used to measure the spread of distribution. Higher the value SE, the more spread out your data is. In statistical way, standard error is also called standard error of mean, SEM, it represents the deviation of sample mean deviates from the actual mean of a population.

It is calculated simply by dividing the standard deviation by the square root of the sample size. That is \(SE = \frac{σ }{\sqrt{n}}\)

where , n --> sample size

σ --> population standard deviations

Now, from the above formula it is clearly seen that standard error term or an estimator affected by sample size (n) and population standard deviations ( σ). So, right choice for answer is population size.

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Complete question:

standard error of an estimator is not affected by the multiple choice question.

a) population standard deviation

b) sample size

c) population size

The number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totaling $1.40.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jill has 20 coins, consisting of nickels and dimes totaling $1.40.

Let the number of nickels be n, and the number of dimes is 20 - n.

$1 = 10 dimes

$1 = 20 nickels

(1/20)n + (1/10)(20 - n) = 1.40

After solving:

n = 12

The number nickel = 12

The number dimes = 20 - 12 = 8

Thus, the number nickel is 12, and the number dimes are 8 if Jill has 20 coins, consisting of nickels and dimes totalling $1.40.

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The system is consistent and independent.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have the system of equations:

y = 4x - 4

y = -4x + 4.

Let's take the quotient between both the equations as;

(y/y) = (4x - 4)/(-4x + 4)

1 = (4x - 4)/(-4x + 4)

Solve for x;

1*(-4x + 4) = 4x - 4

-4*x + 4 = 4x - 4

-4x - 4x = -4 - 4

-8*x = -8

x = -8/-8 = 1.

To find the value of y, we can input this value of x in one of the equations:

y = 4 x1 - 4 = 0.

Then we have only one solution, (1, 0).

Therefore, the system is consistent and independent.

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Answer:

\( - 13 - \frac{2}{x - 2} \)

Step-by-step explanation:

\( - 13 - \frac{2}{x - 2} \)

Answer:

.165. Round up to 17 cents.

Step-by-step explanation:

The same person also took a midterm in their marketing course and the class mean for this exam was 77 with a standard deviation of 4.7. The z-score for the score on this exam is 1.9. Calculate the actual score this person received for the marketing exam (to 2 decimal places).

Here is how we can calculate the actual score this person received for the marketing exam. First, we know that the Z score is given by the formula:

Z = (X - μ)/ σ

where X = actual score, μ = Mean, σ = Standard Deviation

Given that the Z score is 1.9, i.e., Z = 1.9

Hence,X = μ + Zσ

On substituting the given values, we get: X = 77 + 1.9 * 4.7X = 86.13 (approx.)

Therefore, the actual score that this person received for the marketing exam is 86.13 (to 2 decimal places).Note that the score is rounded to 2 decimal places as required by the question.

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Answer: A. 42

7/8 = ?/48

8 * 6 = 48

7 * 6 = 42

? = 42

The roots are

The polynomial can be modellled as ;

Let us use f(2) to obtain a value for a

The polynomal f(x) is given as