Use the function f(x) to answer the questions:
F(x)=2x²-x-10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or a minimum? What are the coordinates of the vertex? Justify your answers and show
work. (3 points)
Part C: What are the steps you would use to graph fx)? Justify that you can use the answers obtained in Part A and Part B to draw the graph (5 point

Answer:

:)

Step-by-step explanation:

This is a calculus problem that involves using differentials to estimate the maximum error in the area of a circle given the error in its radius. According to 1, the errors are related by ΔA=drdAΔr=2πrΔr

Therefore, Δr=2πrΔA

If the radius is 21 cm correct to the nearest cm, then the possible error in the radius is ±0.5 cm. Using this value in the formula above, we get ΔA=2π(21)(0.5)≈65.97 cm2

This is the possible maximum error when calculating the area of a circle with radius 21 cm correct to the nearest cm.

The solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].

To solve the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] , we need to consider two cases: when the expression inside the absolute value is positive and when it is negative. Here's a step-by-step explanation:

Case 1: |[tex]2x+1[/tex]| ≥ [tex]3[/tex]

Subtract 1 from both sides of the inequality:

[tex]2x + 1 - 1[/tex] ≥ [tex]3 - 1[/tex]

2x ≥ 2

Divide both sides of the inequality by 2:

[tex]$\frac{2x}{2} ≥ \frac{2}{2}$[/tex]

x ≥ 1

Case 2: -([tex]2x+1[/tex]) ≥ [tex]3[/tex]

Multiply both sides of the inequality by -1 (to reverse the inequality):

-[tex]1(2x + 1)[/tex] ≤ [tex]-1(3)[/tex]

-2x - 1 ≤ -3

Add 1 to both sides of the inequality:

[tex]-2x - 1 + 1[/tex] ≤ [tex]-3 + 1[/tex]

-2x ≤ -2

Divide both sides of the inequality by -2 (note that we need to reverse the inequality sign when dividing by a negative number):

[tex]$\frac{-2x}{-2} ≥ \frac{-2}{-2}$[/tex]

x ≥ 1

Combining the solutions from both cases, we have x ≥ 1.

Therefore, the solution to the inequality |[tex]2x+1[/tex]| ≥ [tex]3[/tex] is [tex]x[/tex] ≥ [tex]1[/tex].

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Note tha the   surface area of the toy box is 390cm².

To find the surface area of the toy box, we need to calculate the areas of all the faces and then sum them up.

The toy box is in the shape of a rectangular prism with dimensions:

Length = 15 cm

Width = 5 cm

Height = 6 cm

The surface area of a rectangular prism can be found using the formula  

Surface Area = 2(LW + LH + WH)

Substituting the values we have  -

Surface Area = 2(15 * 5 + 15 * 6 + 5 * 6)

= 2(75 + 90 + 30)

= 2(195)

= 390 cm²

Hence, the surface area of the toy box is 390 square centimeters.

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Answer:

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

To factor this quadratic equation, we look for two numbers that multiply to give -20 and add up to -1 (the coefficient of the x-term). The numbers -5 and 4 satisfy these conditions:

2x² - 5x + 4x - 10 = 0

x(2x - 5) + 2(2x - 5) = 0

(x + 2)(2x - 5) = 0

Setting each factor equal to zero gives us:

x + 2 = 0 or 2x - 5 = 0

Solving these equations, we find:

x = -2 or x = 5/2

Therefore, the x-intercepts of the graph of f(x) are -2 and 5/2.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we can look at the coefficient of the x² term. Since the coefficient is positive (2), the parabola opens upwards, and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the x² and x terms, respectively.

In this case, a = 2 and b = -1:

x = -(-1) / (2 * 2) = 1/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation:

f(1/4) = 2(1/4)² - 1/4 - 10

f(1/4) = 1/8 - 1/4 - 10

f(1/4) = -81/8

Therefore, the vertex of the graph of f(x) is a minimum and has coordinates (1/4, -81/8).

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

1. Plot the x-intercepts: Mark -2 and 5/2 on the x-axis.

2. Plot the vertex: Mark (1/4, -81/8) as the lowest point on the graph.

3. Determine additional points: Choose a few more x-values, calculate the corresponding y-values using the equation f(x) = 2x² - x - 10, and plot these points.

4. Draw a smooth curve: Connect the plotted points with a smooth curve, keeping in mind that the parabola opens upward.

Using these steps, you can graph f(x) and accurately represent the x-intercepts, vertex, and overall shape of the parabolic curve.

Hello!

So the 2 angles of the base are equal, so:

(180 - 74)/2 = 53° one of the 2 angles

          74°

          /\
        /    \
      /        \
    /            \

53°             53°

180 - 74*2 = 32°

          32°

          /\
        /    \
      /        \
    /            \

74°             74°

So the others angles can be:

- 74° and 53°

- 74° and 32°

Answer:

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

We have two similar triangles:

The ratio of corresponding sides of similar figures is same.

Set up equal ratios and find the missing side:

Answer:

To find the sum of x₁ and x₂, we need to solve the system of equations:

y = x² ...(1)

y = 1,002x - 2,000 ...(2)

Since both equations are equal to y, we can set them equal to each other:

x² = 1,002x - 2,000

To solve this quadratic equation, we can rearrange it into standard form:

x² - 1,002x + 2,000 = 0

Now, we can factorize the equation:

(x - 2)(x - 1,000) = 0

Setting each factor equal to zero, we get two solutions:

x - 2 = 0 => x = 2

x - 1,000 = 0 => x = 1,000

The sum of distinct solutions x₁ and x₂ to the system of equations y = x² and y = 1,002x - 2,000 is 1,002.

The problem here involves finding the solutions to the system of equations. Those equations are y = x² and y = 1,002x - 2,000. To solve this system of equations, we can set the two equations equal to each other, because they both equal y.

So, we have: x² = 1,002x - 2,000. Rearranging, we get x² - 1,002x + 2,000 = 0. This is a quadratic equation, and we can solve for x using the quadratic formula: x = [1,002 ± sqrt((1,002)² - 4*1*2,000)] / (2*1). This will yield 2 solutions for x, let's call them x₁ and x₂.

The question asks for the sum of x₁ and x₂. In a quadratic equation ax² + bx + c = 0, the sum of solutions is given by -b/a. Here, a = 1 and b = -1,002, so the sum of solutions x₁ and x₂ is -(-1,002)/1 = 1,002.

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The student in the video is trying to determine if the number of sides of a regular polygon has a relationship to the sum of its interior angles.

They are specifically interested in finding a formula that can be used to calculate the sum of the interior angles of any regular polygon, given the number of sides.

The student's conjecture is that the sum of the interior angles of a regular polygon is equal to (n-2)*180, where n is the number of sides.

In order to test their conjecture, the student drew a regular polygon with 3 sides, 4 sides, 5 sides, and so on, up to a regular polygon with 100 sides. They then calculated the sum of the interior angles of each polygon and compared their results to their conjecture.

The student's results showed that the sum of the interior angles of each regular polygon was equal to (n-2)*180, as they had conjectured. This suggests that their conjecture is correct.

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Using cosine Rule, the value of the requested angle is 33.12°

Since the three sides are given, we use the Cosine rule :

Hence,

CosA = (10²+4²-7²) / (2 × 10 × 4)

Cos A = 67/80

Cos A = 0.8375

A = [tex] {cos}^{ - 1} (0.8375)[/tex]

A = 33.12

Therefore, the value of the missing angle is 33.12

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Answer:

12 km (565m)

Step-by-step explanation:

Answer:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

The measure of angel BDC in this problem is given as follows:

m < BDC = 43º.

The angle measures for this problem are given as follows:

As the figure is a rectangle, these two angles are complementary, hence the value of x is given as follows:

7x + 1 + 9x - 7 = 90

16x = 96

x = 6.

Then the measure of angle BDC is given as follows:

m < BDC = 7(6) + 1

m < BDC = 43º.

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The actual bearing of the flight would be N 16.38° W.

North: 420 mph * cos(15) = 406.6 mph

West: 420 mph * sin(15) = 108.8 mph

The wind's velocity vector, when decomposed into north and west components, would be:

North: -15 mph * cos(25) = -13.6 mph (negative because it's in the south direction)

West: 15 mph * sin(25) = 6.3 mph

Now, add the corresponding components of the airplane and wind vectors:

North: 406.6 mph - 13.6 mph = 393 mph

West: 108.8 mph + 6.3 mph = 115.1 mph

Finally, to get the actual bearing, we can calculate the inverse tangent of the west component over the north component, but in this case, we need to consider the fact that we are dealing with bearings, which are usually measured from the North, moving in a clockwise direction.

Let's calculate the angle:

θ = atan(West/North) = atan(115.1/393) = 16.38°

So, the actual bearing of the flight would be N 16.38° W.

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The measure of angle D of the given Kite is: 127°

From the diagram, the figure represents a kite.

Properties of a kite are:

- Two pairs of adjacent sides are equal.

- Two diagonals intersect each other at right angles.

- The longer diagonal bisects the shorter diagonal.

- The angles opposite to the main diagonal are equal.

Thus:

The angle B = the angle D

The sum of all angles of a quadrilateral = 360

Given: ∠A = 36 and ∠C = 70

Thus:

2∠D = 360 - (36 + 70)

2∠D = 254

∠D = 127°

So, the measure of angle D = 127°

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The steps that should be followed in order to solve the inequality statement -3t + 7 ≥ 9 include the following: B. subtract 7, divide by -3, and flip the inequality symbol.

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Based on the information provided above, we have the following equation (inequality);

-3t + 7 ≥ 9

By subtracting 7 from both sides of the equation (inequality), we have;

-3t + 7 - 7 ≥ 9 - 7

-3t ≥ 2

By dividing both sides of the equation (inequality) by -3, we have;

t ≥ 2/-3

t ≤ 2/3 (flip the inequality symbol).

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Answer:

C

Step-by-step explanation:

x + [tex]\frac{3}{4}[/tex] y = 5 ( multiply through by 4 to clear the fraction )

4x + 3y = 20 → (1)

x - [tex]\frac{1}{2}[/tex] y = 0 ( multiply through by 2 to clear the fraction )

2x - y = 0 → (2)

multiplying (2) by 3 and adding to (1) will eliminate y

6x - 3y = 0 → (3)

add (1) and (3) term by term to eliminate y

(4x + 6x) + (3y - 3y) = 20 + 0

10x + 0 = 20

10x = 20 ( divide both sides by 10 )

x = 2

Analyzing the graph, we can see that initially, as the quantity of bagels increases, the cost decreases due to spreading the fixed cost over more units.

To complete the table and plot the data in one graph, we will calculate the average fixed cost, average variable cost, average total cost, and marginal cost based on the given fixed cost and variable cost information.

Quantity of Bagels represents the number of units produced, while Total Cost represents the sum of Fixed Cost and Variable Cost.

Now, let's plot the data on a graph:

The x-axis represents the Quantity of Bagels, and the y-axis represents the costs.

   |

$14 |                                                     Marginal Cost

   |                                                     -

   |                                                    |

$12 |                                                ----

   |                                              /

   |                                           ---

$10 |                                         /

   |                                      ---

   |                                  ----

$8  |                                /

   |                              --

   |                          ---

$6  |                        /

   |                      --

   |                   ---

$4  |                 /

   |               --

   |           ---

$2  |         /

   |       --

   |  ---

$0  |-----------------------

    0   5   10   15   20

             Quantity of Bagels

The graph shows the different cost curves:

Average Fixed Cost (AFC) curve starts high but decreases as the quantity of bagels increases, as the fixed cost is spread over more units.

Average Variable Cost (AVC) curve starts low but increases as the quantity of bagels increases, indicating diminishing returns.

Average Total Cost (ATC) curve is the sum of AFC and AVC and exhibits a U-shaped curve.

Marginal Cost (MC) curve intersects the AVC and ATC curves at their minimum points, indicating the change in cost for producing one additional unit.

Analyzing the graph, we can see that initially, as the quantity of bagels increases, the cost decreases due to spreading the fixed cost over more units. However, after a certain point, the diminishing returns of variable cost start to outweigh the benefit of spreading fixed costs, causing the average cost to increase.

Understanding cost behavior is essential for decision-making in business, such as pricing, production planning, and profit analysis. The graph provides insights into the relationship between the quantity produced and the associated costs, allowing businesses to optimize their production levels and pricing strategies to maximize profitability.

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Answer:

Assuming that a movie has strong marketing and positive reviews, it is reasonable to expect that it could earn $16 million in its opening weekend.

Step-by-step explanation:

The question of when a movie will earn $16 million is a complex one that depends on a variety of factors. The success of a film is influenced by its marketing, critical reception, and competition from other movies in the marketplace. However, there are some general trends that can be observed when it comes to box office performance.

Typically, the first week of a movie's release is the most important for earning revenue. This is because theaters often give priority to new releases and allocate more screens to them.

Answer: 1/ 3 ^9

Step-by-step explanation:

Answer:

1/39

Step-by-step explanation:

3-9=1/39

The answer is 0ne over three exponent nine

Answer:

-6

Step-by-step explanation:

Simply substitute x = 2 & y = -1 into the function:

[tex]f(2,-1) =[/tex] [tex]\\\sf{3x + 4y - 8[/tex]

               [tex]3(2) + 4(-1) - 8[/tex]

                [tex]6 - 4 - 8[/tex] = -6

Therefore, the value of f(2, -1) for the function f(x, y) = 3x + 4y - 8 is -6.

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The expression (-9x)^4 can be represented as -6561x^3 without using exponents.

To express the expression (-9x)^4 without using exponents, we can expand it by multiplying the base (-9x) four times using the multiplication property.

(-9x)^4 = (-9x) * (-9x) * (-9x) * (-9x)

To simplify this expression, we can multiply the terms together, taking care to apply the rules of multiplication:

(-9x) * (-9x) = (-9 * -9) * (x * x) = 81 * x^2 = 81x^2

So, by substituting this result back into the original expression, we get:

(-9x)^4 = 81x^2 * (-9x) = -6561 x^3

Therefore, the expression (-9x)^4 can be represented as -6561x^3 without using exponents.

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The distance between Basti and Cian is approximately 138.2 ft. Option D

To find the distance between Basti and Cian, we can use the Law of Sines, which relates the lengths of sides to the sines of their opposite angles in a triangle.

Let's label the points: A, B, and C. Ali is at point A, Basti is at point B, and Cian is at point C.

Given:

Angle ABC = 50 degrees (angle opposite side AC)

Angle BAC = 60 degrees (angle opposite side BC)

Ali is 150 ft away from Basti (side AB)

We want to find the distance between Basti and Cian, which is side BC.

Using the Law of Sines, we have:

BC/sin(50) = AB/sin(60)

Substituting the known values:

BC/sin(50) = 150/sin(60)

To find BC, we can rearrange the equation:

BC = (150/sin(60)) * sin(50)

Using a calculator to evaluate the expression:

BC ≈ 138.2 ft

Option D is correct.

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The measure of the angle B is 32. 0 degrees

To solve the given triangle, we need to know the different trigonometric identities and their ratios.

We have that these identities are;

From the information given, we have that;

Opposite side of angle B = 5

Hypotenuse side = 9.43

Using the sine identity, we get that;

sin B = 5/9.43

Divide the values, we have;

sin B= 0.5302

Find the inverse value of the sine identity and then substitute

B = 32. 0 degrees

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The simplified expression is m^1 or simply m.

To simplify the expression −m^(-8) * m^9 without using negative exponents, we can utilize the properties of exponents.

First, let's deal with the negative exponent. A negative exponent indicates that the term should be moved to the denominator. So, we can rewrite −m^(-8) as 1/m^8.

Now, we can simplify the expression further: 1/m^8 * m^9.

When multiplying terms with the same base, we add the exponents. In this case, we have m^(-8) * m^9, which becomes m^(-8 + 9) = m^1 = m.

Finally, multiplying 1/m^8 by m gives us (1/m^8) * m = 1/m^(8-1) = 1/m^7.

Therefore, the simplified expression is 1/m^7, where m is the variable restricted to those numbers for which the expression is defined. By eliminating the negative exponent and combining like terms, we've simplified the expression without using negative exponents.

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Assuming that you want this to be expanded, simply multiply each term in the first set of parentheses with each term in the second parentheses:

(-2x + 10) (-9x + 5)

18x^2 - 10x - 90x + 15

18x^2 - 100x + 15

If the question, instead, is asking you to find the x-intercepts, set the expression to zero and solve:

0 = (-2x + 10) (-9x + 5)

0 = -9x + 5 <- divide -2x+10 on all sides

5/9 = x

OR

0 = -2x + 10

5 = x

Answer:

(-2x + 10) (-9x + 5) is a polynomial expression that represents the product of two binomials. To solve this expression, you can use the FOIL method, which stands for First, Outer, Inner, Last.

FOIL method:

First: multiply the first terms of each binomial (-2x and -9x) to get 18x^2

Outer: multiply the outer terms of each binomial (-2x and 5) to get -10x

Inner: multiply the inner terms of each binomial (10 and -9x) to get -90x

Last: multiply the last terms of each binomial (10 and 5) to get 50

Then, combine like terms to get the final expression:

(-2x + 10) (-9x + 5) = 18x^2 - 100x - 90x + 50 = 18x^2 - 190x + 50

Step-by-step explanation:

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Hello!

[tex]\sf 89x - 135 = 24\\\\89x = 24 + 135\\\\89x = 159\\\\\boxed{\sf x = \dfrac{159}{89}} \\\\[/tex]

The temperature drops by [tex]31\°C[/tex] from day to night in this city.

To calculate the temperature drop from day to night in [tex]\°C[/tex], we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: [tex]-40\°C[/tex]

Average daily high temperature: [tex]-9\°C[/tex]

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = [tex]-9\°C - (-40\°C)[/tex]

Simplifying the equation:

Temperature drop = [tex]-9\°C + 40\°C[/tex]

Temperature drop = [tex]31\°C[/tex]

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by [tex]31\°C[/tex] from day to night in this city.

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Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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