Which equation represents the line shown on the graph?
A- y=-2x
B- y=x+2
C- y= -x+2
D- y=2x

Answer

• a) Range: (-∞, –1)

• b) Horizontal asymptote when x ≤ 2: y = –3. Vertical asymptote when x > 2: x= 2. Horizontal asymptote when x > 2: y = –1.

• c) When x decreases, it approaches –3, and when x increases, it approaches –1.

Explanation

• Part A: Graph the piecewise function f (x) and determine the range.

Using a graphing tool we can get the following graph:

As the range is all the y-values included in the function, we can see that in this case, the range is:

• Part B: Determine the asymptotes of f (x). Show all necessary calculations.

We have to get the asymptotes from the part where x ≤ 2 and x > 2.

In x ≤ 2 we do not have a vertical asymptote as it is not a rational function, but we do have a horizontal asymptote, which is y = k when we have the function:

Thus, in our case y = –3.

In x > 2, we do have a vertical and horizontal asymptote. We can get the vertical asymptote by setting the denominator of the function to 0:

If we solve the expression by factoring we get two solutions:

Based on our function we can see that the vertical asymptote is x = 2 when x > 2. Then, the horizontal asymptote can be calculated with the limit:

Thus, our horizontal asymptote is y = –1 when x > 2.

• Part C: Describe the end behavior of f (x).

The end behavior of a function is how the function acts when x increases or decreases. Based on our graph we can see that when x decreases, it approaches –3, and when x increases, it approaches –1.

If we have a y intercept of -8, that means that the point falls on the y-axis, therefore x = 0. So, we have a point (0, -8) and we have a slope m = 23.

y = mx + b

y = 23x + b

Now, we can plug in the point values x = 0, y = -8

-8 = 0 + b

b = -8

If we plug b back into our original formula, we get:

y = 23x - 8

Answer:

3\(x^{2}\)+9x-30

Step-by-step explanation:

Multiply the three into each number

3\(x^{2}\)+9x-30

Answer:

3x² + 9x - 30

Step-by-step explanation:

3 × x² = 3x²

3 × 3x = 9x

3 × -10 = -30

3x² + 9x - 30

The equation to represent the total cost of large cheese pizza the large one topping is: T = $5C + $6d .

A per the given question.

Large cheese pizza cost five dollars.

Let the number of large cheese pizzas be 'C'.

Thus,

The price of 'C' of large cheese pizza = C*Cost of 1 large cheese pizza = $5c

1 large one-topping pizza costs $6.

d = number of large one-topping pizzas

Thus,

Cost of 'd' number of topping pizza = d* cost of 1 large one topping pizza

= $6d

Cost of a large cheese pizza plus the cost of a large one-topping pizza

= $5C +$6d

T represents the total cost.

T = $5C + $6d

Thus, the equation to represent the total cost of large cheese pizza the large one topping is: T = $5C + $6d .

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Answer:

So let's say if we have a function f of x. Let's say it looks like this let's call this point a and point b. Now if the function f of x if it's continuous on the closed interval a b.

Step-by-step explanation:

The point c = 11/2 is the point in (-2, 2) such that f'(c) = (f(2) - f(-2))/(2 - (-2)).

The Mean Value Theorem states that if a function f is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in (a, b) such that f'(c) = (f(b) - f(a))/(b - a). The Mean Value Theorem is a useful tool for finding the maximum and minimum values of a function on an interval.

To solve a Mean Value Theorem problem, the first step is to identify the function f, its domain of definition, and the interval [a, b]. Then, use the theorem to find the point c in the interval (a, b) such that f'(c) = (f(b) - f(a))/(b - a).

For example, suppose we have the function f(x) = x2 + 3x + 4 defined on the interval [-2, 2]. To find the point c in the interval (-2, 2) such that f'(c) = (f(2) - f(2))/(2 - (-2)), we first calculate the derivatives of f(x). The derivative of f(x) is f'(x) = 2x + 3. Substituting x = 2 in the derivative gives f'(2) = 11. Now, we can use the Mean Value Theorem to find the point c:

f'(c) = (f(2) - f(-2))/(2 - (-2))

11 = (12 - (-2))/(2 - (-2))

11 = 14/4

c = 11/2

Therefore, the point c = 11/2 is the point in (-2, 2) such that f'(c) = (f(2) - f(-2))/(2 - (-2)).

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Answer:B

Step-by-step explanation:

Adjacent side to the given angle = 7.072

Hypotenuse = opposite side to given angle ^2 + adjacent side to given angle ^2

Hypotenuse = 8.27666502886

Answer:

Vvvgfffff

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 9.4 \ units}\)

Step-by-step explanation:

Coordinates are (0,5) and (8,0)

\(\sf Distance\ Formula = \sqrt{(x2-x1)^2 + (y2-y1)^2} \\\\D = \sqrt{(8-0)^2 + (0-5)^2} \\\\D = \sqrt{8^2 + (-5)^2} \\\\D = \sqrt{64+25} \\\\D = \sqrt{89} \\\\D = 9.4\ units\)

The value of the expression is -295/36. None of the given options is correct.

As per the given information,

the expression is 1 1/4j - 5/8k.

And j= 8/9 and k= 14/1.

Now, to find the value of the expression, first, simplify the expression,

1 1/4j - 5/8k = 5/4j - 5/8k.

Substitute the provided values j= 8/9 and k= 14/1 to the above expression, we get,

5/4j - 5/8k = 5/4(8/9) - 5/8(14/1)

5/4j - 5/8k = 40/72 - 70/8

5/4j - 5/8k = (40 - 630)/72

5/4j - 5/8k = -590/72

5/4j - 5/8k = -295/36.

Therefore, the value of the expression is -295/36.

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Answer:

m /CBA = 82 degree

Step-by-step explanation:

if you want explanation tell me

The depth of the scientist below sea level after traveling downward for 102 seconds can be found by multiplying her speed by the time she traveled:

Distance = Speed x Time

Distance = 4.2 feet/second x 102 seconds

Distance = 428.4 feet

Since she traveled straight down, this distance is also her depth below sea level.

Next, we need to find how far she ascended. The distance she traveled upward can be found in the same way:

Distance = Speed x Time

Distance = 1.9 feet/second x 112 seconds

Distance = 212.8 feet

However, since she traveled upward, this distance is subtracted from her previous depth:

Final depth below sea level = Initial depth below sea level - Distance traveled upward

Final depth below sea level = 428.4 feet - 212.8 feet

Final depth below sea level = 215.6 feet

Therefore, the scientist is 215.6 feet below sea level at this point.

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The radius AO of the circle is approximately 1.414 units when rounded to one decimal place.

To find the radius AO of the circle, we can use the properties of a regular polygon inscribed in a circle.

In a regular polygon, all sides and angles are equal. Let's consider one of the isosceles triangles formed by the center of the circle O, one of the vertices A, and the midpoint of one of the sides.

The triangle OAM is a right triangle with OA as the hypotenuse and AM as the adjacent side. The measure of angle OAM is half the central angle of the regular polygon, which is 360 degrees divided by the number of sides.

In this case, since the polygon is not specified, we cannot determine the exact central angle. However, we are given that the length of the side of the polygon is 8 units.

Using trigonometry, we can express the adjacent side AM in terms of the central angle (θ) and the radius (OA) as AM = OA × cos(θ).

Since AM is half the length of the side, we have AM = 4 units.

Substituting these values into the equation, we get 4 = OA × cos(θ).

Now, we can solve for the radius AO. Rearranging the equation, we have OA = 4 / cos(θ).

Using a calculator, we can calculate the value of cos(θ) by dividing the length of the side by 2 times the radius, which gives us 4 / (2 × OA).

Simplifying this expression, we have 2OA = 4 / (2 × OA).

Multiplying both sides by 2OA, we get 2OA^2 = 4.

Dividing both sides by 2, we have OA^2 = 2.

Taking the square root of both sides, we find OA = √2.

Using a calculator, we can evaluate this to be approximately 1.414.

Therefore, the radius AO of the circle is approximately 1.414 units when rounded to one decimal place.

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Answer:

Step-by-step explanation:

Let x represent the number of pounds of the more expensive candy. Then the price of the mix is ...

  1.40x +0.40(100 -x) = 0.85(100)

  x +40 = 85 . . . . . . simplify

  x = 45 . . . . . . . . subtract 40

  100 -x = 55 . . . pounds of cheaper candy

The grocer must use 45 pounds of $1.40 candy and 55 pounds of $0.40 candy to make the mix.

With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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a. The equation representing the cost of buying and operating the Super Cool X1400 is: C = 800 + 60m. b. The equation representing the cost of buying and operating the Efficient Energy X2000 is: C = 1200 + 40m. c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase. d. Figuring your family will only use the air conditioner for four months each year, you would have to wait 5 years to start saving money overall.

a. The cost of buying the Super Cool X1400 is a one-time expense of $800. Additionally, the cost of operating it is $60 per month. Therefore, the equation representing the cost C as a function of months m is C = 800 + 60m.

b. The cost of buying the Efficient Energy X2000 is a one-time expense of $1200. The operating cost is $40 per month. Hence, the equation representing the cost C as a function of months m is C = 1200 + 40m.

c. To compensate for the additional cost of the original purchase (which is $400), we equate the two cost equations and solve for m:

800 + 60m = 1200 + 40m

20m = 400

m = 20

Therefore, your family would have to use the Efficient Energy model for 20 months (or 10 months more than the Super Cool X1400) to compensate for the additional cost.

d. Considering your family only uses the air conditioner for four months each year, we divide the total number of months (20) by four to find the number of years needed to start saving money overall:

20 months / 4 months/year = 5 years

Hence, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

a. The cost of buying and operating the Super Cool X1400 is represented by the equation C = 800 + 60m.

b. The cost of buying and operating the Efficient Energy X2000 is represented by the equation C = 1200 + 40m.

c. Your family would have to use the Efficient Energy model for 10 months to compensate for the additional cost of the original purchase.

d. Assuming your family uses the air conditioner for four months each year, you would have to wait 5 years to start saving money overall by choosing the Efficient Energy X2000.

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complete question- Your family plans to buy a new air conditioner. They can buy the Super Cool X1400 for $800, or they can buy the Efficient Energy X2000 for $1200. Both models will cool your home equally well, but the Efficient Energy model is less expensive to operate. The Super Cool X1400 will cost $60 per month to operate, while the Efficient Energy X2000 costs only $40 per month to operate. a. Write an equation to represent the cost of buying and operating the Super Cool X1400 where C= cost and m= months. b. Write an equation to represent the cost of buying and operating the Efficient Energy X2000. c. How many months would your family have to use the Efficient Energy model to compensate for the additional cost of the original purchase? d. Figuring your family will only use the air conditioner for four months each year, how many years ill you have to wait to start saving money overall?

The hight above the first floor to second floor is 15 ft , for this we have Trigonometry angles.

Angles determined by the ratios of the trigonometric functions are known as trigonometric angles.

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths.

Given h = 60 ft, we have to find p

Sin 15° = p/h

0.25 = p/60

p = 15 ft

So, the hight above the first floor to second floor is 15 ft.

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a. The problems with the layout and display of the current line chart are:

1. The y-axis label "Testar" is cut off and unclear.
2. The x-axis labels are not evenly spaced, making it difficult to compare revenue values between months.
3. There is no title or legend to provide context for the data.
4. The colors used for the line chart are not visually appealing and can be confusing to interpret.

b. To create a new line chart for the monthly revenue data at Tedstar, Inc., we can follow these steps:

1. Open a new Excel sheet and enter the monthly revenue data for Tedstar, Inc.
2. Select the entire range of data (including the month column).
3. Click on the "Insert" tab and choose the "Line" chart type.
4. Choose the first line chart option, which shows markers and lines.
5. Excel will generate a line chart based on the data. Add a title to the chart and label the x-axis and y-axis appropriately.
6. Format the chart by selecting the chart area and using the formatting options to adjust the colors and design to make it visually appealing and easy to read.
7. Add a legend to the chart to help identify the data series.
8. Finalize the chart by adding any additional details or labels that may be helpful.

By creating a new line chart in this way, we can improve the layout and display of the data to make it easier to interpret and understand.
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Answer:

a= 12

Step-by-step explanation:

Use pythagorean theorem

a^2 + b^2 = c^2 where c is the hypotenuse

so 9^2 + a^2 = 15^2

81 + a^2 = 225

a^2 = 144

square root both sides to get a = 12

The characteristics of the channel or transmission medium, and other factors related to the specific system being considered.

If we assume that the probability of error (the probability that the decoder will make a mistake) is greater than 0, then the probability that the decoder will know with certainty what the source bit was is 1 minus the probability of error.

Let's denote the probability of error as p_error. The probability that the decoder will know the source bit with certainty (probability of correct decoding) can be expressed as:

P_correct = 1 - p_error

Since we assume that p_error is greater than 0, the probability of correct decoding will be less than 1 but greater than 0.

It's important to note that this is a general concept and the specific value of p_error would depend on the decoding algorithm, the characteristics of the channel or transmission medium, and other factors related to the specific system being considered.

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The area of the sector bounded by the 95° arc is approximately 379.94 square feet

To find the area of a sector bounded by a given arc, we need to know the radius and the central angle of the sector.

Given:

Radius (r) = 24 feet

Central angle (θ) = 95°

The formula to calculate the area of a sector is:

Area = (θ/360°) * π * r^2

Substituting the values into the formula:

Area = (95/360) * π * (24^2)

Area = (19/72) * π * 576

Area ≈ 379.94 square feet

Therefore, the area of the sector bounded by the 95° arc is approximately 379.94 square feet.

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Without the actual data, it is not possible to provide specific results or conclusions. We can gain insights into how the length of eruption influences the wait time until the next eruption at Old Faithful geyser.

To analyze the relationship between the length of eruption in minutes and the wait time until the next eruption at Old Faithful geyser in Yellowstone National Park, the data for 82 randomly selected eruptions was collected.

To understand this relationship, statistical measures such as correlation and regression analysis can be performed.

Correlation analysis helps determine the strength and direction of the relationship between two variables. The correlation coefficient, denoted by "r," ranges from -1 to +1. A positive value indicates a positive relationship, whereas a negative value indicates a negative relationship. A value of 0 suggests no relationship.

Regression analysis, on the other hand, helps to predict one variable based on the other. In this case, we can use the length of eruption in minutes to predict the wait time until the next eruption.

By performing these analyses on the data, we can gain insights into how the length of eruption influences the wait time until the next eruption at Old Faithful geyser. However, without the actual data, it is not possible to provide specific results or conclusions.

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Answer:

radio relationships?what do u mean?

Answer:

Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):

2.6

Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.

In short: 2.6 rounded to the nearest whole number is 3.

What we need

A function which has atleast the below parameters

The simplest function is

\(\sf y=\dfrac{\sqrt{-x^2-1}}{2}\)

How can we prove ?

So -x²-1<0

The dimensions of the rectangle are 10 feet (length) and 8 feet (width).

To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,

follow these steps:

1. Let the length of the rectangle be L feet and the width be W feet.

2. According to the given information, W = L - 2.

3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.

4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).

5. Solve the quadratic equation: 80 = L² - 2L.

6. Rearrange the equation: L² - 2L - 80 = 0.

7. Factor the equation: (L - 10)(L + 8) = 0.

8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).

9. Substitute L back into the equation for W: W = 10 - 2 = 8.

So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).

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The given information is as follows:A random sample of 150 teachers in an​ inner-city school district found that​ 72% of them had volunteered time to a local charitable cause within the past 12 months.

The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150

The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037

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Answer:

2

Step-by-step explanation:

Hey there!

Well the x intercept is the point the line touches the x-axis.

And to find it we need to graph the given equation.

7x - 2y = 14​

Look at the image below ↓

By looking at the given image we can tell that the x-intercept is 2.

Hope this helps :)

The statement which says that the measure of ∠ABD = ¹/₂ ∠ABC. So, the correct option is C.

An angle bisector is defined as a ray, segment, or line that bisects a given angle into two equal angles. The word bisection or half means dividing one object into two equal or identical parts. In geometry, we usually divide triangles and angles by lines or lines that are considered bisectors.

A geometric bisector is a ray, line, or segment that divides a given angle into two equal parts. For example, the bisector of a 60 degree angle divides it into two 30 degree angles. In other words, split the angle into two smaller congruent angles.

For the given case,

Ray BD bisects ∠ABC into two equal angles ∠ABD and ∠DBC; which can be written as ∠ABD = ¹/₂ ∠ABC.

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The complete question is as follows:

The volume of the pyramid is approximately 5.9 cm³.

To find the volume of a pyramid with a square base, you can use the formula:

Volume = (1/3) * base area * height

First, let's find the area of the square base. The perimeter of the base is given as 5.7 cm, which means each side of the square has a length of 5.7 cm / 4 = 1.425 cm.

The area of a square is given by the formula:

Area = side length * side length

Substituting the side length, we have:

Area = 1.425 cm * 1.425 cm = 2.030625 cm²

Now, we can calculate the volume of the pyramid:

Volume = (1/3) * base area * height

= (1/3) * 2.030625 cm² * 8.6 cm

= 5.91834375 cm³

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 5.9 cm³.

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Step-by-step explanation:

Perimeter of figure =

\(w + x + x + y + y + y + y \\ = 1 \times w + 2 \times x + 4 \times y \\ = w + 2x + 4y\)