When solving the quadratic equation x^2-10x+9=0
by completing the square, which of the following equations is a step in the process ?

a) The vertical component of the velocity v upwards will be v0sinθ, where the angle is formed with respect to the y axis.

b)  The final velocity of the rock approaches the free-fall velocity √(2gh) and Vav-y approaches this same value.

Here, the initial velocity is given V0. It is the product of acceleration g and time t. thus, u = gt.

The height travelled within the time t and acceleration g, is written as:

h = 1/2 gt²

The two components of velocity in the two axis are,

vertical component = v sinθ

Horizontal component = v cosθ.

Here, the vertical component along the y -axis with an angle θ being,

⇒ V0 sinθ.

b) . If the height of the building H is zero, then the rock is not thrown up in the first place, and instead, it is simply dropped from the roof.

In this case, the initial velocity V0 is zero, and the rock falls straight down to the ground.

Since the rock is only moving in the downward direction, the vertical component of the average velocity Vav-y is simply the final velocity of the rock just before it hits the ground.

The final velocity is given by,

⇒ v= √(2gh),

where g is the acceleration due to gravity and h is the height of the building.

Therefore, as H approaches zero, the final velocity of the rock approaches the free-fall velocity √(2gh) and Vav-y approaches this same value.

c) Equation (2.10) states that the displacement y of an object in free fall near the surface of the Earth is given by:

y = v0t + 1/2gt²

where v0 is the initial velocity, g is the acceleration due to gravity, t is the time, and y is measured in the vertical direction.

Apply this equation to the motion of the rock from the roof to the ground, we can set the initial velocity v0 to the upward velocity with which the rock is thrown from the roof.

Since the direction of motion changes from up to down, the final displacement y should be negative, representing the distance traveled in the downward direction.

Therefore, we have:

y = -H

v0 = V0

g = -9.8 m/s²

t = the time it takes for the rock to fall from the roof to the ground

Using this information, we can rearrange the equation to solve for the time t:

t = √(2H/g)

Now, we can use this expression to calculate the vertical component Vav-y of the average velocity of the rock:

Vav-y = (y - v0t) / t

Plugging in the values for y, v0, and t, we get:

Vav-y = (-H - V0 * sqrt(2H/g)) / √(2H/g)

Simplifying this expression, we get:

Vav-y = -√(2gH)

This result agrees with the value of the average velocity of the object in free fall near the surface of the Earth, which is given by Eq. (2.10), since the vertical component of the velocity is simply the derivative of the displacement with respect to time:

Vav-y = dy/dt = v0 + gt

For an object in free fall near the surface of the Earth with an initial velocity of V0 = 0, this reduces to:

Vav-y = gt

Using the acceleration due to gravity g = -9.8 m/s² and the time t = √(2H/g), we get:

Vav-y = -√(2gH)

which is the same as our previous result.

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The greatest power of "p" in this situation is 4, which is the coefficient of p4. Consequently, the polynomial has a degree of 4.

Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates.

This equation is provided:

1) \($2p^{4}+p^{3}$\)

The greatest power of the polynomial's variable "p" must be identified to categorize this polynomial by degree.

Therefore, the polynomial \($2p^{4}+p^{3}$\) is a polynomial of the fourth degree.

2) \($2x^{2}$\)

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 2, which is the coefficient of . Consequently, the polynomial has a degree of 2.

Therefore, the polynomial \(2x^2\) is a polynomial of the second degree.

3) \($-5n^{4}+10n-10$\)

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 4, which is the coefficient of . Consequently, the polynomial has a degree of 4.

Therefore, the polynomial \(n^4\) is a polynomial of the fourth degree.

4) 6n

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 1, which is the coefficient of \(n^1\). Consequently, the polynomial has a degree of 1.

Therefore, the polynomial \(n^1\) is a polynomial of one degree.

5) -6

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The polynomial in this instance doesn't have a component. It has a value of 6 and is a constant word. A constant word is thought to have a degree of zero.

Therefore, equation 6 is a zero-degree polynomial.

6) \($x^{3}-3$\)

The greatest power of the polynomial's variable "x" must be identified to categorize this polynomial by degree.

The greatest power of "x" in this situation is 3, which is the coefficient of . Consequently, the polynomial has a degree of 3.

Therefore, the polynomial \(x^3\) is a polynomial of the third degree.

7) \($2n^{5}$\)

The greatest power of the polynomial's variable "n" must be identified to categorize this polynomial by degree.

The greatest power of "n" in this situation is 5, which is the coefficient of . Consequently, the polynomial has a degree of 5.

Therefore, the polynomial \(n^5\) is a polynomial of the fifth degree.

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The goal of a confidence interval is to provide a range of values that are reasonable for the parameter of interest. So the correct option is (A).

The goal of a confidence interval is to provide a range of values that is reasonable for the parameter of interest. The confidence interval is based on the sample data and the level of confidence. The level of confidence is the probability that the confidence interval contains the true value of the parameter.

The confidence interval is calculated using the sample mean, the sample standard deviation, and the level of confidence. The confidence interval is calculated by adding and subtracting the margin of error from the sample mean. The margin of error is the product of the critical value and the standard error. The critical value is based on the level of confidence. The standard error is the standard deviation of the sampling distribution.

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Answer:

8, 9

Step-by-step explanation:

The answer is 8, and 9

72 = x*(x+1)

Lets factor out 72

1 x 72

2 x 36

3 x 24

4 x 18

....

8 x 9

8 and 9 are consecutive

Answer: 380 ft

Step-by-step explanation: To find the length in between, you simply subtract the numbers.

1,515 - 1,135 = 380

Therefore, the ladder needs to be extended 380 ft.

Answer:

The temperature of the chemical solution after t hours is \(-14.96-2.9t\;^{\circ}C\)

Step-by-step explanation:

Given that the initial temperature of the chemical solution, \(T_0= -14.96^{\circ}C\).

The rate of decreasing temperature, \(R = 2.9^{\circ}C/ hour\)

So, after t hours, the temperature of the chemical solution will decrease by \(Rt=2.9t^{\circ}C\).

So, the temperature of the chemical solution after t hours,

\(T=T_0-Rt \\\\\Rightarrow T = -14.96-2.9t\;^{\circ}C\)

Hence, the temperature of the chemical solution after t hours is \(-14.96-2.9t^{\circ}C\).

Answer:

Graph C

Step-by-step explanation:

Khan Academy

The correct graph that represents the given data effectively would be:

Graph C

Thus, 'graph C' in the scatter plot format is the correct answer.

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First, convert 23% into a fraction.

23% =

\(23 \div 100 = \frac{23}{100} \)

Now the expression to determine 23% of 122 is

\( \frac{23}{100} \times 122 \\ = ( \frac{23}{100} )(122)\)

Answer:

23/100*112this is the answer

The total Cost of a bench is 1.008x.

According to the statement,

We have to find that the cost of the bench.

So, For this purpose, we know that the

The cost function may be accustomed find the typical cost, which is that the average amount of cash it costs to provide a unit.

From the given information:

The owner of the outdoor furniture center decides to use the 120% markup. at the tip of the season, he wants to sell all the benches that are available. he sells the benches for 20% off.

Then

Since we've provided that

Let the price price be 'x'.Mark up % = 120%

So, price value would be 120x/100

Then

Discount % = 20%

Amount of discount is given by

20* 1.2x/1000.

24x

So, it becomes,

Amount after discount is given by

1.2x - 0.24x = 0.96x

Amount of sales tax would be

100+5/100*0.96x

105/100*0.96x

1.008x.

So, The total Cost of a bench is 1.008x.

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according to defination of collinear points :Three or more points are said to be collinear if they all lie on the same straight line.

therefore, A,B,C points are collinear.

Answer:

$45.15

Step-by-step explanation:

$42*107.5%

=$45.15

PLS GIVE BRAINLIEST

Answer:

45.15

Step-by-step explanation:

Take 100% (Original Price) and add the 7.5, Aka 107.5.

Multiply the price (42) and the percent that you just got, 107.5%.

Use the percent sign!!!

The answer then should be 45.15

The jars are nor enough because the applesauce is more than 35 cups which is what 20 glass jars can contain. Since each of the cup will hold 1 3/4 cups of applesauce.

Given data

number of cups of apple sauce = 40

number of glass jars = 20

number of cups each glass jar can hold = 1 3/4

solution

if one glass jar hold 1 3/4 cups then 20 glass jars will hold

= 20 * 1 3/4

= 35 cups

Since there are 40 available cups of apple sauce and the 20 glass jars is equivalent to 35 cups, hence the glass jars will contain 35 cups and there will be 5 cups left.

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1. The monthly payment of the 5-year loan is approximately $2,225.77.

2. The equivalent uniform annual cost for the tractor is approximately $5,572.50.

1. To calculate the monthly payment of a loan, we can use the formula for an amortizing loan. The formula is:

PMT = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

PMT = Monthly payment

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate divided by 12)

n = Total number of payments (number of years multiplied by 12)

In this case, the principal amount (P) is $100,000, the annual interest rate is 12%, and the loan duration is 5 years.

r = 12% / 12 = 1% per month

n = 5 years * 12 months/year = 60 months

PMT = 100,000 * (0.01 * (1 + 0.01)^60) / ((1 + 0.01)^60 - 1)

PMT ≈ $2,225.77

Therefore, the monthly payment of the 5-year loan is approximately $2,225.77.

2. To calculate the equivalent uniform annual cost, we need to consider the initial cost of the tractor, salvage value, maintenance costs, and the interest rate.

The equivalent uniform annual cost (EUAC) can be calculated using the formula:

EUAC = (Initial cost - Salvage value) + (Annual maintenance cost * Present worth factor)

The present worth factor can be calculated using the formula:

Present worth factor = (1 - (1 + r)^-n) / r

Where:

r = Interest rate (10%)

n = Number of years (10 years)

EUAC = ($7,500 - $5,000) + ($500 * ((1 - (1 + 0.10)^-10) / 0.10))

EUAC = $2,500 + ($500 * ((1 - 0.3855) / 0.10))

EUAC ≈ $2,500 + ($500 * 6.145)

EUAC ≈ $2,500 + $3,072.50

EUAC ≈ $5,572.50

Therefore, the equivalent uniform annual cost for the tractor is approximately $5,572.50.

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Step-by-step explanation:

1. f(x) = 6x - 14

Slope is the coefficient of x

Slope = 6

2. f (x) =6x+ 9 +x

f(x) = 7x +9

Slope = 7

3. The last option because it is not a line.

4. The third option. x and y do not get multiplied in linear equations.

5. The last option.

the first one is y=x

the second one is y =-x

the third one is y=0x - 2

the last one is wrong because if x is - 1 or - 2 twice, it should still give the same vue for y.

I hope this helps.

Please gimme brainliest. Thank you

By using the inverse function definition and the fact that: f⁻¹(y) = x, we will see that the point that must be on the inverse function is (5, -7)

For an invertible function f(x), we define its inverse f⁻¹(x) such that:

if f(x) = y

then:

f⁻¹(y) = x

And because of that, we have the properties:

f(f⁻¹(x) ) = x

f⁻¹( f(x)) = x

Then if the point (-7, 5) is on the function f(x), this means that:

f(-7) = 5

And using the inverse property, we know that:f⁻¹(5) = -7

Then the point that lies on the inverse function is (5, 7), the correct option is the first one.

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Answer:

about 10 dollers

Step-by-step explanation:

The image doesn't load for me.

Answer:

Step-by-step explanation:

The expression 3√x5y is equivalent to option (a) xy³√x2.

To simplify 3√x5y, we can break it down into individual factors within the cube root and simplify each term separately.

3√x5y = 3√(x³ * x² * y) = 3√(x³) * 3√(x²) * 3√y = x * x^(1/3) * y^(1/3) = xy^(1/3)x^(1/3) = xy³√x²

Answer:

It's all of them

Step-by-step explanation:

All the options given above are true.

the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles.

According to our study,

All the options given above are true.

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In the case of the electronic chess game, with a useful life that follows an exponential distribution with a mean of 30 months, we need to determine the length of service time after which the percentage of failed units will approximately equal 50 percent. The options provided are 9 months, 16 months, 21 months, and 25 months.

For the major television manufacturer, the service life of its 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. We are asked to calculate the probability of service lives of at least five years.

1. Electronic Chess Game:

The exponential distribution is characterized by a constant hazard rate, which implies that the percentage of failed units follows an exponential decay. The mean of 30 months indicates that after 30 months, approximately 63.2% of the units will have failed. To find the length of service time when the percentage of failed units reaches 50%, we can use the formula P(X > x) = e^(-λx), where λ is the failure rate. Setting this probability to 50%, we solve for x: e^(-λx) = 0.5. Since the mean (30 months) is equal to 1/λ, we can substitute it into the equation: e^(-x/30) = 0.5. Solving for x, we find x ≈ 21 months. Therefore, the length of service time after which the percentage of failed units will approximately equal 50 percent is 21 months.

2. LED Televisions:

The service life of 50-inch LED televisions follows a normal distribution with a mean of six years and a standard deviation of half a year. To find the probability of service lives of at least five years, we need to calculate the area under the normal curve to the right of five years (60 months). We can standardize the value using the formula z = (x - μ) / σ, where x is the desired value, μ is the mean, and σ is the standard deviation. Substituting the values, we have z = (60 - 72) / 0.5 = -24. Plugging this value into a standard normal distribution table or using a calculator, we find that the probability of a service life of at least five years is approximately 1.0000 (or 100% with four digits after the decimal point).

Therefore, the probability of service lives of at least five years for 50-inch LED televisions is 1.0000 (or 100%).

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Answer:

14xx2(square) + 7x - 6 + 6x - 9x + 16

14x2x(square) + 7x - 6 - 3x + 16

114x2(square) + 7x - 3x - 6 + 16

14x2(square) + 4x - 10

The other rotation that can be used to achieve the transformation is; C: 270° counterclockwise

What is the rotation used?

From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;

(x, y) -----> (-y, x)

Now, this pattern of transformation occurs when;

There is a 90° clockwise rotation. However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation

Answer: Triangle XYZ can be rotated 90° counterclockwise using the origin as the center of rotation to create triangle X’Y’Z’. To obtain the original triangle XYZ, we need to rotate the triangle X'Y'Z' by 90° clockwise using the origin as the center of rotation. This means that rotating the triangle X'Y'Z' by 90° clockwise is the same as rotating triangle XYZ by 90° counterclockwise, so the answer is 90° clockwise.

The government needs to raise spending by $3300 to bring the economy to full employment.

The formula for the GDP of a closed economy is given by the following:

Y = C + I

whereY = Aggregate Income

C = Aggregate Consumption

I = Investment

Therefore,Y = C + I250 + 0.75

Y = 100 + Y

Where Y is the full-employment GDP, we have to solve for Y in order to find out the output level that corresponds to full employment.

To do so, let's subtract 0.75Y from both sides of the equation: 250 + 0.25Y = 100

Adding -250 to both sides of the equation: 0.25Y = -150

Dividing both sides of the equation by 0.25Y = -600

Thus, at full employment, Y = 4000 and at the initial equilibrium, Y = 600.

Therefore, the desired increase in government spending (G) can be calculated as follows:

4000 = 250 + 0.75Y + G

Substituting Y = 600, we get:

4000 = 250 + 0.75(600) + G4000 = 250 + 450 + G3300 = G

Therefore, the government needs to raise spending by $3300 to bring the economy to full employment. Rounded to the nearest whole value, this is $3300.

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Answer:

The length of the hypotenuse is \(2\sqrt{10}\) ≅ 6.325

Step-by-step explanation:

∵ A right angle is formed by the x-axis, y-axis and the line y = -3x + 6

∴ The line intersected the x-axis at point (x, 0)

→ To find x substitute y in the equation by 0

∵ 0 = -3x + 6

→ Add 3x to both sides

∴ 0 + 3x = -3x + 3x + 6

∴ 3x = 6

→ Divide both sides by 3

∵ \(\frac{3x}{3}=\frac{6}{3}\)

∴ x = 2

∴ The line intersected the x-axis at point (2, 0)

∵ The line intersected the y-axis at point (0, y)

→ Substitute x in the equation by 0 to find y

∴ y = -3(0) + 6

∵ y = 0 + 6

∴ y = 6

∴ The line intersected the xyaxis at point (0, 6)

∵ The endpoints of the hypotenuse are (2, 0) and (0, 6)

→ Use the rule of the distance d = \(\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}\) to find it

∵ x1 = 2 and y1 = 0

∵ x2 = 0 and y2 = 6

∴ h = \(\sqrt{(0-2)^{2}+(6-0)^{2}}=\sqrt{4+36}=\sqrt{40}=2\sqrt{10}\)

∴ The length of the hypotenuse is \(2\sqrt{10}\) ≅ 6.325

The attached figure for more understanding

Answer:

The period of the function is 12π

Answer:

\(x^7\sqrt{x}\)

Explanation:

\(\sqrt{x^{15}}\)

apply exponent rule:

\(\sqrt{x^{14}x}\)    

apply radical rule:

\(\sqrt{x^{14}}\sqrt{x}\)

simplify more:

\(\sqrt{x^{7*2}}\sqrt{x}\)

final answer:

\(x^7\sqrt{x}\)

Answer:

\(x^7\sqrt{x}\)

Step-by-step explanation:

\(\sqrt{x^{15}} =\sqrt{x^{(14+1)}}\)

Apply the exponent rule \(a^{b+c}=a^b \cdot a^c\)

\(\implies \sqrt{x^{(14+1)}}=\sqrt{x^{14}x^1}=\sqrt{x^{14}x}\)

Apply the radical rule \(\sqrt{ab} =\sqrt{a}\sqrt{b}\):

\(\implies \sqrt{x^{14}x}=\sqrt{x^{14}} \sqrt{x}\)

Apply the radical rule \(\sqrt[a]{x^b} =x^{\frac{b}{a}}\):

\(\implies \sqrt{x^{14}} \sqrt{x}=x^{\frac{14}{2}}\sqrt{x}=x^7\sqrt{x}\)

If James and Apple have AGI of $417,100, file jointly, and claim three dependent children, the total child and other dependent credit for James and Apple is $0.

To calculate the total child and other dependent credit for James and Apple, we need to use the information provided and the IRS guidelines.

The child and dependent care credit allows eligible taxpayers to reduce their tax liability based on qualifying expenses paid for the care of a qualifying individual. For three dependent children, the maximum credit allowed is $6,000.

However, the credit amount is reduced based on the taxpayer's AGI. The credit is reduced by 1% for each $2,000 (or fraction thereof) by which the taxpayer's AGI exceeds $125,000. The credit is reduced to a minimum of 20% of the qualifying expenses.

In this case, James and Apple's AGI of $417,100 exceeds $125,000 by $292,100, which is 146 times $2,000. Therefore, the credit is reduced by 146%, and the maximum credit of $6,000 is reduced to $0.

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Complete question is:

James and apple have a AGI of $417,100,file jointly and claim three dependent children ages 7, 10, and 19

calculate the total child and other dependent credit.

The values from the graph are P(x) = (-6x + 6)(2x - 4)

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

The zeros are x = 1 and x = 2

Using the above as a guide, we have the following:

P(x) = a(x - 1)(x - 2)

From the graph, we have (0, -24)

This gives

a(0 - 1)(0 - 2) = -24

Evaluate the products

2a = -24

Divide by 2

a = -12

So, we have

P(x) = -12(x - 1)(x - 2)

This can be expressed as

P(x) = -6(x - 1)(2x - 4)

Another expression is

P(x) = (-6x + 6)(2x - 4)

Hence, the expression is P(x) = (-6x + 6)(2x - 4)

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Answer:

B

x is the price of the sweater so 3x  and add $15 for the skirt which would add up to $90

Answer:

3x + 15 = 90

Step-by-step explanation:

hope this helps!