Each shape below has an area of 60 square inches. Find the value of x.

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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Given statement solution is :- To find the area of the shaded region, we first need to determine the shapes involved and their respective areas.  A general process that you can apply to various scenarios, Identify the shapes , Break down the region, Calculate individual areas.

To find the area of the shaded region, we first need to determine the shapes involved and their respective areas. Without a specific diagram or description, I'll provide a general process that you can apply to various scenarios.

Identify the shapes: Examine the diagram and determine the shapes that make up the shaded region. These shapes can include rectangles, triangles, circles, or combinations of them.

Break down the region: If the shaded region consists of multiple shapes, break it down into simpler, recognizable shapes. This step is crucial for accurately calculating the total area.

Calculate individual areas: Determine the area of each shape by using the appropriate formulas. Here are some common formulas:

Rectangle: Area = length × width

Triangle: Area = (base × height) / 2

Circle: Area = π × radius²

Sum the individual areas: Add up the areas of all the individual shapes to find the total area of the shaded region.

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

For question 3.) The three ratios for the marked angle would be =9.45:sin90°, 5:sinB, 8:sinA

For question 3.)

To determine the three ratios, the sine rule needs to be obeyed and the formula is written below as follows;

Sine rule:

a/sinA = b/sinB = c/sinC

where;

a = 8

A = sinA

b = 5

B = SinB

c = 9.45

C = Sin 90°

The three ratios;

= 9.45:sin90°; 5:sinB; 8:sinA

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a.

The estimated total cost of the grocery items is $36.

b.

The actual total cost of the grocery items is $35.82.

for part a.

We will round each price to the nearest dollar:

$5.12 =  $5

$3.07 = $3

$7.11 = $7

$1.67 = $2

$13.18=  $13

$5.67 = $6

Summing them up, we have:

$5 + $3 + $7 + $2 + $13 + $6 = $36

the estimated total cost of the grocery items is $36.

for part b.

We will calculate the actual total cost of the grocery items by using a calculator:

$5.12 + $3.07 + $7.11 + $1.67 + $13.18 + $5.67 = $35.82

In conclusion, we will find the  actual total cost of the grocery items as $35.82.

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Answer:

12 km (565m)

Step-by-step explanation:

Answer:

24m

Step-by-step explanation:

If we imagine this situation as a right angled triangle, 25m is the hypotenuse, 7m is the height and we need the base length

so by Pythagoras thorium we can say that [tex]\sqrt[2]{25^2 -7^2}[/tex]= base length

which is= 24

The graph has: A. order 2 rotational symmetry about the origin.

In Mathematics and Geometry, the order of rotational symmetry of any geometrical shape can be defined as the number of times in which the geometrical shape can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a geometrical shape with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Based on this rule, we can reasonably infer and logically deduce that the order of rotational symmetry for this graph is equal to 2.

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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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Answer:

To find the values of the other three angles in a pentagon given that the sum of all angles is 450 degrees and one angle is 150 degrees, we can use the fact that the sum of the angles in any polygon with n sides is (n-2) * 180 degrees.

Let's denote the other three angles as A, B, and C.

The sum of the angles in a pentagon is given as 450 degrees, so we have:

150 + A + B + C = 450

We know that the sum of the angles in a pentagon is (5-2) * 180 = 540 degrees, so we have another equation:

A + B + C = 540

Now we have a system of two equations with two variables. We can solve this system to find the values of A, B, and C.

The correct subtraction should be:

(150 + A + B + C) - (A + B + C) = 540 - 450

Simplifying the equation, we have:

This equation is not valid, which means that the values given for the sum of angles and one angle are inconsistent with a pentagon. The sum of the angles in a pentagon should be 540 degrees. Please ensure the accuracy of the provided values.

You should buy approximately 1.067 kilograms of apples at $10.20 per kilogram in order to have the kilogram of fruit cost $8.15.

Let's assume that Sally bought x kilograms of apples at $10.20 per kilogram.

The total cost of bananas is given as AED 7.35 per kilogram, and Sally bought 1.4 kilograms of bananas. So, the cost of the bananas is:

Cost of bananas = AED 7.35 * 1.4 = AED 10.29

The total cost of apples is given by the equation:

Cost of apples = $10.20 * x

The total cost of the fruits combined should be AED 8.15 per kilogram. So, the equation becomes:

Total cost of fruits = (Cost of bananas + Cost of apples) / (1.4 + x) = AED 8.15

Substituting the known values, we have:

(10.29 + 10.20 * x) / (1.4 + x) = 8.15

Cross-multiplying and simplifying, we get:

10.29 + 10.20 * x = 8.15 * (1.4 + x)

Expanding the equation, we have:

10.29 + 10.20 * x = 11.41 + 8.15 * x

Rearranging the equation, we get:

10.20 * x - 8.15 * x = 11.41 - 10.29

1.05 * x = 1.12

Dividing both sides by 1.05, we find:

x = 1.12 / 1.05

x ≈ 1.067

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Answer:

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Step-by-step explanation:

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Answer:

6 Hrs 33 mins 49 sec

Step-by-step explanation:

For first we need to do it from second.

35-47

since 35 is less than 45 taking 1 min or 60 seconds from 9 min

new equation will be

(36+60)-47

=49 seconds

Secondly subtracting Mins

since we gave 60 sec or 1 min so

we have 9 min

equation will be

8-35

since 8 is less than 8 borrowing 60 min from hour

new equation will be

(8+60)-35

33 mins

Thirdly

subtracting hours

since we gave 60 min or 1 hour so

we have 13 hrs

equation will be

13-7

6 hours

Therefore Answer is 6 Hrs 33 mins 49 sec

The choice that shows a set of data that could be represented by the box plot below is (B)1,3,6,8,10,12,13,13,16,18,19

In the box plot, a left whisker extends from 1 to 6, therefore, the least value is 1.

The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. Therefore:

The lower quartile is 6

The median is 12

The upper quartile is 16

The right whisker extends from 16 to 19, therefore the highest value is 19.

The set of data that satisfies these conditions where the numbers in bold are the 5- number summary is

1,3,6,8,10,12,13,13,16,18,19The correct option is B.

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Which data set could be represented by the box plot shown below? A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated. Choose 1 answer: Choose 1 answer: (Choice A) A 1,3,6,8,10,12,13,13,16,18,201,3,6,8,10,12,13,13,16,18,201, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 20 (Choice B) B 1,3,6,8,10,12,13,13,16,18,191,3,6,8,10,12,13,13,16,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 12, comma, 13, comma, 13, comma, 16, comma, 18, comma, 19 (Choice C) C 1,3,6,8,10,11,13,13,18,18,191,3,6,8,10,11,13,13,18,18,191, comma, 3, comma, 6, comma, 8, comma, 10, comma, 11, comma, 13, comma, 13, comma, 18, comma, 18, comma, 19 (Choice D) D 1,3,6,8,10,11,13,13,16,18,191,3,6,8,10,11,13,13,16,18,19

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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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.

Answer: it stand for 3 million or 3,000,000

Step-by-step explanation:

Answer:

million

Step-by-step explanation:

millions always have six 0's behind it

The length of the segment AC is 15 units and the coordinate of point B is (-6, 7)

The length of the segment DF is √68  units and the coordinate of point E is (-6, -5)

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

A = (-10, 10) and (2, 1)

The length AC is then calculated as

AC = √[Δx² + Δy²]

So, we have

AC = √[(-10 - 2)² + (10 - 1)²]

Evaluate

AC = 15

The point B is calculated using

B = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where

m : n = 1 : 2 & x, y are the coordinates of A and B

Substitute the known values in the above equation, so, we have the following representation

B = 1/3 * (1 * 2 + 2 * -10, 1 * 1 + 2 * 10)

Evaluate

B = (-6, 7)

Hence, the coordinate of point B is (-6, 7)

Here, we have

(-10, -6) and (-2, -4)

The length DF is then calculated as

DF = √[Δx² + Δy²]

So, we have

DF = √[(-10 + 2)² + (-6 + 4)²]

Evaluate

DF = √68

The point E is calculated using

E = 1/(m + n) * (mx₂ + nx₁, my₂ + ny₁)

Where

m : n = 1 : 1 & x, y are the coordinates of E and F

So, we have

E = 1/2 * (1 * -2 + 1 * -10, 1 * -4 + 1 * -6)

Evaluate

E = (-6, -5)

Hence, the coordinate of point E is (-6, -5)

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The functions f(x) = -x² + 9 and g(x) = 6 - 2x can be plotted on the same system of axes with their intercepts labeled.

To draw the functions f(x) = -x² + 9 and g(x) = 6 - 2x on the same system of axes, we need to determine their intercepts with the x and y-axes.

Intercepts with the x-axis:

To find the x-intercepts, we set y = 0 for each function and solve for x.

For f(x):

0 = -x² + 9

x² = 9

x = ±√9

x = ±3

So, the x-intercepts of f(x) are x = -3 and x = 3.

For g(x):

0 = 6 - 2x

2x = 6

x = 6/2

x = 3

Therefore, the x-intercept of g(x) is x = 3.

Intercepts with the y-axis:

To find the y-intercepts, we set x = 0 for each function and solve for y.

For f(x):

y = -0² + 9

y = 9

So, the y-intercept of f(x) is y = 9.

For g(x):

y = 6 - 2(0)

y = 6

Therefore, the y-intercept of g(x) is y = 6.

Now, we can plot the points (-3, 0), (3, 0), (0, 9), and (0, 6) on the graph. Connect the points with a smooth curve to represent the function f(x) = -x² + 9.

The line representing g(x) = 6 - 2x will be a straight line with a slope of -2 and a y-intercept of 6.

The graph should show the curve of f(x) passing through the points (-3, 0), (3, 0), and (0, 9), and a straight line for g(x) passing through the points (3, 0) and (0, 6).

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The improper form of [tex]1 \frac{1}{2}[/tex] is 3/2 ([tex]\frac{3}{2}[/tex])

I hope this helps!

Answer: 3/2

Step-by-step explanation:

To create a graph, label the horizontal axis from 0 to 8 cm (1 cm = 0.5 m) and the vertical axis from 0 to 2 cm (1 cm = 500). Plot the points (2m, 400) as (4 cm, 1.6 cm) and (4m, 200) as (8 cm, 0.8 cm), then connect them with a line.

To create a graph with the provided scale, follow these steps:

1. Establish the horizontal axis: Label the axis from 0 to 8 cm, where each mark represents 1 meter. This means that 2 cm on the graph corresponds to 1 meter.

2. Set up the vertical axis: Label the axis from 0 to 2 cm, where each mark represents 500. This implies that 2 cm on the graph corresponds to 500.

3. Convert the given data points to fit the graph's scale:

For the point (2m, 400):

On the horizontal axis, 2 meters will be represented by 4 cm.

On the vertical axis, 400 will be represented by (400/500) * 2 cm = 1.6 cm.

For the point (4m, 200):

On the horizontal axis, 4 meters will be represented by 8 cm.

On the vertical axis, 200 will be represented by (200/500) * 2 cm = 0.8 cm.

4. Plot the converted points on the graph:

Place a point at (4 cm, 1.6 cm) to represent the point (2m, 400).

Place a point at (8 cm, 0.8 cm) to represent the point (4m, 200).

5. Connect the points with a line:

Draw a straight line to connect the two plotted points.

By following these steps, you will create a graph that visually displays the relationship between the given data points, adhering to the specified scale. Remember to provide appropriate titles and labels for the graph axes.

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a) The ratio of the number of large items in the store relative to the total number of items is given as follows: 2/5.

b) The percentage is given as follows: 40%.

The ratio and the percentage are obtained applying the proportions in the context of the problem.

40 out of 100 items are large items, hence the ratio is given as follows:

40/100 = 2/5.

The percentage is then given as follows:

2/5 x 100% = 40%.

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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:

Brainliest Plss

Based on the information, the minimum value is 15, and the maximum value is 30.

To find Q1: Calculate the position of Q1 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (25).

Position = (22 + 1) * (25 / 100) = 5.75 (rounded to 6)

Take the average of the values at positions 6 and 7 to find Q1.

Q1 = (18 + 19) / 2 = 18.5

To find Q2 (the median): Calculate the position of Q2 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (50).

Position = (22 + 1) * (50 / 100)

= 11.5 (rounded to 12)

The value at position 12 is the median.

Q2 = 21

To find Q3: Calculate the position of Q3 using the formula: Position = (n + 1) * (Q / 100), where n is the total number of values and Q is the desired percentile (75).

Position = (22 + 1) * (75 / 100) = 16.5 (rounded to 17)

Take the average of the values at positions 17 and 18 to find Q3.

Q3 = (28 + 29) / 2 = 28.5

The minimum value is 15, and the maximum value is 30.

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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 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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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:

446.95m²

Step-by-step explanation:

10+9+13.45=32.5

32.5x11=356.95

9x10=90

356.95+90=446.95

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

This equation can be factored as:

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

Setting each factor equal to zero, we get:

2x + 5 = 0 => 2x = -5 => x = -5/2

x - 2 = 0 => x = 2

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

Part B: The vertex of the graph of f(x) can be determined using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form (ax² + bx + c = 0).

In this case, a = 2 and b = -1. Plugging these values into the formula, we have:

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

To determine if the vertex is a maximum or a minimum, we can examine the coefficient of the x² term. Since the coefficient a is positive (a = 2), the parabola opens upwards, and the vertex represents a minimum point

Therefore, the vertex of the graph of f(x) is (1/4, f(1/4)), where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Part C: To graph f(x), we can follow these steps:

Plot the x-intercepts: Plot the points (-5/2, 0) and (2, 0) on the x-axis.

Plot the vertex: Plot the point (1/4, f(1/4)) as the vertex, where f(1/4) can be obtained by substituting x = 1/4 into the equation f(x).

Determine the direction of the graph: Since the coefficient of the x² term is positive, the graph opens upwards from the vertex.

Determine additional points: Choose a few x-values on either side of the vertex and calculate their corresponding y-values by substituting them into the equation f(x). Plot these points on the graph.

Draw the graph: Connect the plotted points smoothly, following the shape of the parabola. Ensure the graph is symmetrical with respect to the vertex.

The answers obtained in Part A (x-intercepts) and Part B (vertex) provide crucial points to plot on the graph, helping us determine the shape and position of the parabola.

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The x-intercepts from the graph attached are

The vertex  from the graph attached is

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

x = (-b ± √(b² - 4ac)) / (2a)

a = 2, b = -1, c = -10

Plugging these values into the quadratic formula:

x = (-(-1) ± √((-1)² - 4 * 2 * (-10))) / (2 * 2)

x = (1 ± √(1 + 80)) / 4

x = (1 ± √81) / 4

x = (1 ± 9) / 4

x₁ = (1 + 9) / 4 = 10 / 4 = 2.5

x₂ = (1 - 9) / 4 = -8 / 4 = -2

Therefore, the x-intercepts of the graph of f(x) are 2.5 and -2.

Part B

To find the coordinates of the vertex, we can use the formula:

x = -b / (2a)

x = -(-1) / (2 * 2) = 1 / 4 = 0.25

we substitute this value back into the original function:

f(0.25) = 2(0.25)² - 0.25 - 10

f(0.25) = 0.125 - 0.25 - 10

f(0.25) = -10.125

Therefore, the vertex of the graph of f(x) is located at (0.25, -9.125).

Part C: The steps to graph f(x) include:

Plotting the x-intercepts: Based on the results from Part A, we know that the x-intercepts are 2.5 and -2. We mark these points on the x-axis.

Plotting the vertex: Using the coordinates from Part B, we plot the vertex at (0.25, -9.125). This represents the minimum point of the graph.

Drawing the shape of the graph: Since the coefficient of the x² term is positive, the graph opens upward. From the vertex, the graph will curve upward on both sides.

Additional points and smooth curve: To further sketch the graph, we can choose additional x-values and calculate their corresponding y-values using the equation f(x) = 2x² - x - 10. Plotting these points and connecting them smoothly will give us the shape of the graph.

By using the x-intercepts and vertex obtained in Part A and Part B, we have the necessary information to draw the graph accurately and show the key features of the quadratic function f(x)

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