Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7

The transformation f(x) ↦ f(x) - 8 shifts the graph of f(x) downward by 8 units.

More specifically, for any value of x, the output of the function f(x) is subtracted by 8. This means that the y-coordinate of each point on the graph of f(x) is decreased by 8 units.

For example, suppose that point (a, b) lies on the graph of f(x). After applying the transformation f(x) ↦ f(x) - 8, the point (a, b - 8) lies on the transformed graph.

So, if the original graph of f(x) was above the x-axis, the transformed graph will be shifted downward and intersect the x-axis 8 units below where the original graph intersected it. If the original graph of f(x) was below the x-axis, the transformed graph will be shifted downward and move further away from the x-axis.

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The average temperature in the five major cities was colder than in both Kansas City and New York.

We have,

We are not given the temperature in Kansas City and New York, but we know that Kansas City was warmer than Chicago and colder than New York.

Therefore, we can say that the temperature in Chicago was between the temperature in Kansas City and the temperature in New York.

Let's find the average temperatures in the five major cities:

average temperature

= (-12.5 - 11.7 - 12.4 - 12.6 - 12.3)/5

= -12.5

This means that the average temperature in the five major cities was -12.5 degrees Celsius.

Since we don't know the specific temperatures in Kansas City and New York, we cannot say for sure whether the temperature in Kansas City was warmer than in New York.

However, we can say that the average temperature in the five major cities was colder than in both Kansas City and New York.

Thus,

The average temperature in the five major cities was colder than in both Kansas City and New York.

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Answer: 1/2 of pizza and 2/3 of chips are left.

Step-by-step explanation:

Pizza- 1 minus 1/2 is a 1/2

Chips- 1 minus 1/3 is 2/3

The formula for continuous compounding is:

A = Pe^(rt)

where:

A = the amount of money at the end of the investment period

P = the principal amount (initial investment)

e = the mathematical constant approximately equal to 2.71828

r = the annual interest rate

t = the time in years

We are given that P = $5000, r = 3.5%, and we want to find t when A = $12,000. Substituting these values into the formula, we get:

$12,000 = $5000e^(0.035t)

Dividing both sides by $5000, we get:

2.4 = e^(0.035t)

Taking the natural logarithm of both sides, we get:

ln(2.4) = ln(e^(0.035t))

Using the rule of logarithms that ln(e^x) = x, we can simplify the right side to:

ln(2.4) = 0.035t

Dividing both sides by 0.035, we get:

t = ln(2.4) / 0.035 ≈ 26.7 years

Therefore, it will take approximately 26.7 years for the initial investment of $5000 to grow to $12,000 with continuous compounding at a rate of 3.5% per year.

As a result, the ladder ascends the structure 13.18 feet. The answer is 13 feet, rounded to the nearest foot.

The dimensions of a triangle's vertices can also be used to classify it. Right triangles only have one angle that is 90 degrees, whereas acute triangles only have angles that are less than 90 ° and obtuse triangles only have angles that are larger than 90 degrees. Trigonometry, arithmetic, physics, and geometry are just a few of the mathematical and scientific disciplines that make use of triangles. They are also utilised in daily life, such as in the construction of buildings and bridges, as well as in the production of artwork and beautiful patterns.

given

Let's call the ladder on the building's height "h" To find "h," we can utilise trigonometry.

A right triangle is created by the ladder, the structure, and the ground. The angle between the ground and the ladder (also known as the angle of elevation) is 70°, and the ladder is the hypotenuse of the triangle.

The height of the ladder on the structure, which is the other side, can be related to the hypotenuse using the sine function (the length of the ladder). The sine of 70 degrees is around 0.9397:

sin(70°) = h/14

When we multiply both sides by 14, we obtain:

h = 14 x sin(70°)

h ≈ 13.18

As a result, the ladder ascends the structure 13.18 feet. The answer is 13 feet, rounded to the nearest foot.

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Answer:

The slope of this line is 4.

Step-by-step explanation:

Using two points;

I'm picking (-2,-5) and (0,3) because they're easy to see right away...

Insert them into the equation for the slope of a line;

[tex]slope = \frac{y2-y1}{x2-x1} = \frac{3-(-5)}{0-(-2)} = 4[/tex]

The zero where the graph of f(x) touches but does not cross the x-axis is [tex]x = -2.[/tex]

To find the zeros of the function f(x)=(x+3)(x+2)(x-1) where the graph touches but does not cross the x-axis, we need to look for the point. where the function changes sign from positive to zero, without actually crossing the x-axis.

The function f(x) will touch but not cross the x-axis at the zeros where the multiplicity is even, which means that the factor (x-a) occurs in the factorization with an even exponent. Therefore, we need to find the roots of the function and determine their multiplicities.

To find the roots of the function, we set f(x) equal to zero:

[tex]f(x) = (x+3)(x+2)(x-1) = 0[/tex]

This equation has three roots, which are -3, -2, and 1. We can see that all three roots have multiplicity 1, because each factor appears only once in the factorization.

Now we need to check the multiplicity of each root by looking at the sign of the function near each root. We will use the first derivative test to determine the sign of the function.

[tex]f'(x) = 3x^2 + 8x - 6[/tex]

The critical points are the roots of the derivative, which are approximately -2.12 and 0.94. We can see that f'(x) is negative for x < -2.12, positive for -2.12 < x < 0.94, and negative again for x > 0.94.

Therefore, we can conclude that:

At x = -3, f(x) changes sign from negative to positive, so the graph of f(x) crosses the x-axis at x = -3.

At x = -2, f(x) changes sign from positive to zero, so the graph of f(x) touches but does not cross the x-axis at x = -2.

At x = 1, f(x) changes sign from negative to positive, so the graph of f(x) crosses the x-axis at x = 1.

Therefore, the zero where the graph of f(x) touches but does not cross the x-axis is  [tex]x = -2[/tex] .

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The total length of the metallic rod used for the diagonal is

The wooden frame is a parallelogram and the diagonals of a parallelogram bisects each other.

Using this property we set the equation

(2y - 1) ft = 9 ft

2y - 1 = 9

2y = 10

diving through by 2

y = 5

hence the first diagonal is 18 feet and the second diagonal is solved below

(y + 3) ft

= 5 + 3

= 8 ft

length of the diagonal

= 18 + 16

= 34 feet

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The approximation 0.5078125 is accurate to within about 0.0156.

To apply the bisection method, we need to find two values, a and b, such that f(a) and f(b) have opposite signs. Since e^(-x) is a decreasing function in the interval [0, 1], we know that f(0) = e^(-0) = 1 and f(1) = e^(-1) < 1. Therefore, we can choose a = 0 and b = 1.

Now, we can apply the bisection method to find the root of the equation f(x) = e^(-x) in the interval [0, 1]. Let c be the midpoint of the interval [a, b]. Then, we have:

c = (a + b) / 2 = (0 + 1) / 2 = 0.5

f(c) = e^(-c) = e^(-0.5) ≈ 0.6065

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 1]. Therefore, we set a = c and repeat the process:

c = (a + b) / 2 = (0.5 + 1) / 2 = 0.75

f(c) = e^(-c) ≈ 0.4724

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 0.75]. Therefore, we set b = c and repeat the process:

c = (a + b) / 2 = (0.5 + 0.75) / 2 = 0.625

f(c) = e^(-c) ≈ 0.5353

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 0.625]. Therefore, we set b = c and repeat the process:

c = (a + b) / 2 = (0.5 + 0.625) / 2 = 0.5625

f(c) = e^(-c) ≈ 0.5706

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 0.5625]. Therefore, we set b = c and repeat the process:

c = (a + b) / 2 = (0.5 + 0.5625) / 2 = 0.53125

f(c) = e^(-c) ≈ 0.5857

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 0.53125]. Therefore, we set b = c and repeat the process:

c = (a + b) / 2 = (0.5 + 0.53125) / 2 = 0.515625

f(c) = e^(-c) ≈ 0.5947

Since f(c) is positive, the root of the equation f(x) = 0 must be in the interval [0.5, 0.515625]. Therefore, we set b = c and repeat the process:

c = (a + b) / 2 = (0.5 + 0.515625) / 2 = 0.5078125

f(c) = e^(-c) ≈ 0.6002

Since f(c) is positive, the root of the equation f(x) = e^(-x) in the interval [0, 1] is approximately 0.5078125. This is the positive root between 0 and 1, since f(x) is a decreasing function in this interval and has only one root.

Note that the bisection method guarantees that the error in the approximation of the root is less than or equal to (b - a) / 2^n, where n is the number of iterations. In this case, the interval [0, 1] was bisected 6 times, so the error in the approximation is less than or equal to (1 - 0) / 2^6 = 1/64 ≈ 0.0156.

Therefore, the approximation 0.5078125 is accurate to within about 0.0156.

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The function reflected over the x-axis then translated 5 units left is given by the relation g ( x ) = -a ( x - ( h + 5 ) )² - k

Given data ,

Let the function be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = a(x - h)² + k

Now , on reflecting over the x-axis , we get

f' ( x ) = -a( x - h )² + k

On translating the function 5 units left , we get

g ( x ) = -a ( x - ( h + 5 ) )² - k

Hence , the transformed function is g ( x ) = -a ( x - ( h + 5 ) )² - k

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The translation that maps quadrilateral A B C D to A' B' C' D' is

Translation 2 units right

Translation 5 units down

Translation in geometry is the process of transposing a figure or an object in either a coordinate plane or 3D space without modifying its size, shape and alignment.

It involves "moving" or "sliding" the figure or entity along a straight line to a set distance while at the same time preserving its form and positioning.

For the quadrilateral, the translation involved are

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Step-by-step explanation:

6.75 That's The Answer I Hope You Enjoy

The initial velocity of the ball in terms of b and h is: v₀ₓ = b / √(2h / g).

Let's assume the following variables:

Since the angle of projection is given as 0 degrees, the ball is projected horizontally, and its initial velocity only has a horizontal component.

The horizontal distance b is equal to the horizontal component of velocity (v₀ₓ) multiplied by the time of flight (t), as the ball takes the same amount of time to reach the tree horizontally and vertically.

So we can write the equation for horizontal distance b as:

b = v₀ₓ * t

Now, the time of flight t can be calculated from the vertical motion of the ball. The ball is projected vertically upwards and hits the tree at a height h. The time of flight t can be calculated using the following kinematic equation:

h = v₀y * t + (1/2) * g * t²

where;

Since the ball is projected horizontally, v₀y is 0.

So the equation simplifies to:

h = (1/2) * g * t²

Solving for t, we get:

t = √(2h / g)

Now, substituting the value of t back into the equation for horizontal distance b, we get:

b = v₀ₓ * √(2h / g)

Solving for v0x, we get:

v₀ₓ  = b / √(2h / g)

Thus, the initial velocity of the ball in terms of b and h is:

v₀ₓ = b / √(2h / g)

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The volume of the cube is 2700 cm³ and the area of the cube is 360 cm³.

The side of the cube = a = 30 cm

Error in a = da = 1 cm

(1) Volume of the cube =a³

V=a³ (Taking derivation)

therefore (dV)/(da) = 3a²

dV = 3a² * da

At a = 30cm, da = 1cm ,

dV = 3 * (30)² * (1)

= 3(900)(1)

Volume of the cube = 2700 cm³

(ii) Area of the cube = 6a²

A = 6a²  (Taking derivatives)

d/dr (A) = 6(2a)

= 12a

dA = 12a * da

4 * da = 30cm, da = 1cm

dA = 12(30)(1) 

Area of the cube = 360 cm²

Therefore, the volume of the cube is 2700 cm³ and the area of the cube is 360 cm³.

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Answer: E: 71/100

Step-by-step explanation:

The survey results show that the most popular food choice among adults in the summer is ice cream, with 42% of adults who responded to the survey saying that it was their favorite summer food.
Hot dogs were the second most popular choice, with 37% of respondents saying that it was their favorite summer food.
Hamburgers and pizza were the least popular choices, with 29% and 12% of respondents respectively saying that they were their favorite summer food.

Amount is a word used to describe a quantity or measure of something. It is often used to refer to a sum of money, but can be used to describe any number or amount of something, such as time, materials, people, or objects. Amount is often used in financial contexts, such as when talking about the amount of money someone has saved, or the amount of money someone owes. It can also be used to refer to measurements, such as the amount of time it takes to finish a task, or the amount of ingredients needed for a recipe.

The best type of display to represent the percent of adults who most enjoy ice cream compared to other subjects is a pie chart. A pie chart is helpful in showing the relative proportions of different items. It can be quickly and easily interpreted, allowing viewers to quickly understand the data being presented.

In this case, the pie chart would show that 42% of adults who responded to the survey most enjoyed ice cream, 37% most enjoyed hot dogs, 29% most enjoyed hamburgers, and 12% most enjoyed pizza.

The calculation for this is as follows:

Ice cream: 42/120 * 100 = 35%
Hot dog: 37/120 * 100 = 30.833%
Hamburger: 29/120 * 100 = 24.167%
Pizza: 12/120 * 100 = 10%

Overall, a pie chart is the best type of display to represent the percent of adults who most enjoy ice cream compared to other subjects. It is a quick and easy way to compare data and can be easily interpreted by viewers.

In conclusion, the survey results show that the most popular food choice among adults in the summer is ice cream, with 42% of adults who responded to the survey saying that it was their favorite summer food. Hot dogs were the second most popular choice, with 37% of respondents saying that it was their favorite summer food. Hamburgers and pizza were the least popular choices, with 29% and 12% of respondents respectively saying that they were their favorite summer food.

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a)The additional cost in dollars incurred when output is increased from 4 to 20 units is $1,347.20.

b) The total cost function from components (a), C(20) equals $1,833.00.

To determine the additional cost incurred when production is increased from 4 to 20 units, we must compute the difference in total cost between manufacturing fifteen units and producing two units. This can be accomplished by calculating the definite integral of the marginal cost function from x = 4 to x = 20:

a. To compute the additional cost in dollars incurred when production is increased from 4 to 20 units, divide the total cost of manufacturing 20 units by the total cost of producing 4 units.

We may accomplish this by incorporating the marginal cost function:

C(x) = C'(x) dx = 0.03x3 - 2x2 + 60x + C(x)

where C is the integration constant. We can use the knowledge that C(4) = 203 to calculate C:

203 = 0.03(4)^3 - 2(4)^2 + 60(4) + C C = 67

As a result, the total cost function is:

C(x) = 0.03x^3 - 2x^2 + 60x + 67

We can now calculate the additional cost of making 16 units (the difference between 20 and 4 units):

C(20) - C(4) = (0.03(20)^3 - 2(20)^2 + 60(20) + 67) - (0.03(4)^3 - 2(4)^2 + 60(4) + 67) = $1,347.20

As a result, the additional cost in dollars incurred when output is increased from 4 to 20 units is $1,347.20.

b. Using the total cost function from component (a), we may find C(20):

C(20) = 0.03(20)^3 - 2(20)^2 + 60(20) + 67 = $1,833.00

As a result, C(20) equals $1,833.00.

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Answer:

  6

Step-by-step explanation:

You want to know the number of workers required to harvest a field in 8 hours if 4 workers can do the job in 12 hours.

Problems like this that involve effort usually measure the effort as a constant product of workers and time.

Here, that product is (4 workers)(12 hours) = 48 worker·hours.

If the same effort is accomplished in 8 hours, the number of workers required is ...

  (48 worker·hours)/(8 hours) = 6 workers

6 workers are needed to accomplish the task in 8 hours.

Using y-intercept we can see that Y intercept will be less and X intercept will be greater.

Option B is correct.

The y-intercept is the point at which the graph crosses the y-axis. The most important step in graphing any function with the formula y = f(x) is finding the intercepts. For a function, an intercept can take one of two forms. What they are is what the x-intercept and y-intercept are. The point on the axis where a function's graph intersects it is known as the intercept.

Let’s first establish a linear equation in the form y=mx+b. To do so, we must define the variables:

y=profit

x=miles travelled

m=$.25/mile

Recall that the profit is indicated on the y-axis (a positive value), but paying for a truck driver reduces the profit. As a result, the y-intercept, which represents the profit, will be reduced by the slope (starting point). This is so that the business can afford to pay a truck driver $.25 each mile to drive. As a result, the following equation emerges:

y=-.25x+b

This implies that the cost of hiring a driver will be reduced by the y-intercept, or "b" (profit).

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Answer: 53.84 rounded to the nearest percent is 54%.

Step-by-step explanation: Let's take a look at this value. To round 53.84 to the nearest percent, we must make it a whole number first. 53.84 rounded to the nearest whole number is 54. Therefore, that is also the percent.

Measures of center describe the middle or typical value of a data set, while measures of variation describe how spread out the data is; the mean is a measure of center, the range is a measure of variation, and the median is also a measure of center.

What are measures of center and variation and how are they used to describe a data set?

The following statements are true:

The following statement is false:

The following statement is ambiguous or incorrect:

The question is incomplete; the full question is provided below -

Data sets can be described using measures of centre and variance.

Choose ALL truthful statements about these measurements.

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Answer:

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

Inverse variation equation:

Use the initial values to find the value of k:

Substitute the value of k to show the equation:

Find the value of x when y = 50:

Answer:

Step-by-step explanation:

Answer:

A) 17

B) 50

C) 9

Step-by-step explanation:

A)3 x 5 + 2

15 +2 =17

B) 2 x 5^2

2 x 25= 50

C) (5-2)^2

3^2= 9

the objective risk in Addis Ababa is higher than in Bahir Dar, because the standard deviation is greater. This means that there is more variability in the losses in Addis Ababa, which makes it riskier for the insurance company.

HOW TO SOLVE THE PROBLEM?

Objective risk refers to the expected losses that are based on historical data and statistical analysis. In this case, Nile Insurance Company (NIC) has 50,000 homes insured in Addis Ababa and 50,000 homes insured in Bahir Dar. The chance of loss in each city is 2%, which means that on average, 1000 homes should burn annually in each city.

However, the annual variation in losses is different in the two cities. In Addis Ababa, the annual variation ranges from 600 to 900, while in Bahir Dar, it ranges from 300 to 500. This means that the range of losses is much wider in Addis Ababa than in Bahir Dar.

To calculate the objective risk in the two cities, we can use the standard deviation formula, which is a measure of how spread out the data is from the mean. The formula for standard deviation is:

σ = √(Σ(xi - x)²/n)

where σ is the standard deviation, xi is the loss in each year, x is the mean loss, and n is the number of years.

Using this formula, we can calculate the standard deviation for losses in Addis Ababa and Bahir Dar. The standard deviation for losses in Addis Ababa is:

σ = √[((600-1000)² + (700-1000)² + (800-1000)² + (900-1000)²)/4]

σ = √(50000)

The standard deviation for losses in Bahir Dar is:

σ = √[((300-1000)² + (400-1000)² + (500-1000)²)/3]

σ = √(46667)

Therefore, the objective risk in Addis Ababa is higher than in Bahir Dar, because the standard deviation is greater. This means that there is more variability in the losses in Addis Ababa, which makes it riskier for the insurance company.

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Approximately 72.24% of men would have a body fat percentage within the normal range of 15-20%.

To solve this problem using the standard normal distribution and the process of standardization. We standardized the values of the range of 15-20% using the formula z = (x - μ) / σ.

Then use a normal distribution table or calculator to find the area under the curve between the standardized values.

Here we have

The average body fat percentage for men in the U.S. was 16.75 and the standard deviation was 2.1

To solve this problem, standardize the range of 15-20 using the formula:

=> z = (x - μ) / σ

Where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For the lower end of the range (15), the standardized value is:

z = (15 - 16.75) / 2.1 = -0.83

For the upper end of the range (20), the standardized value is:

z = (20 - 16.75) / 2.1 = 1.55

Now Find the area under the normal distribution curve between these two standardized values. For this use a standard normal distribution table or a calculator with a normal distribution function to find this area.

Using a calculator, we can use the normalcy function with the lower and upper bounds of -0.83 and 1.55, respectively, and a mean of 0 and a standard deviation of 1 (since we standardized the values):

=> normalcdf(-0.83, 1.55, 0, 1) ≈ 0.7224

This means that approximately 72.24% of men would have a body fat percentage within the normal range of 15-20%.

Therefore,

Approximately 72.24% of men would have a body fat percentage within the normal range of 15-20%.

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LM/PQ = MN/QR = LN/PR because triangle LMN and PQR are similar.

Similar triangles are triangles that have the same shape, but their sizes may vary. The conditions for two triangles to be similar are;

1. The corresponding angles of the similar triangles must be congruent i.e they must be equal.

2. The ratio of the corresponding sides are equal. The corresponding sides are :

LM and PQ, MN and QR , LN and PR

since LM/PQ = MN/QR = LN/PR , then we can say triangle LMN and PQR are similar.

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