A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0. 40 cubic foot per minute. At this rate how many hours will it take for the water level to drop 2 feet?

Answer:18

Step-by-step explanation:

2x=12

3x=?
2x/2=12/2= x=6

3(6)=18

The double integral ∬D(x2+6y)dA can be evaluated using the properties of integration. The value of the double integral is 53/60.

The given function is (x2+6y). Here, we will find the limits of integration for x and y. Given that D is bounded by y = x, y = x3, and x ≥ 0, we can represent this region in the x-y plane as follows: We see that the lower limit of y is x and the upper limit of y is x3. The lower limit of x is 0 and the upper limit of x is given by the line y=x.

Hence, the limits of integration can be written as follows:0 ≤ x ≤ yx ≤ y ≤ x3

Now, we can substitute these limits in the double integral and integrate first with respect to y and then with respect to x.

∬D(x2+6y)dA = ∫₀¹⁰∫x^x³(x2+6y)dydx

On integrating, we get

∬D(x2+6y)dA = ∫₀¹⁰(x³ - x^7/3 + 3x⁴)dx= [(1/4)x⁴ - (1/12)x^10/3 + (3/5)x⁵] from 0 to 1∬D(x2+6y)dA = (1/4 - 1/12 + 3/5) - (0 + 0 + 0) = 53/60

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Answer:

1) 100 degrees F

2) 50 degrees F

Step-by-step explanation:

its just simple subtraction

The cost of repairing the car was $360 after selling the car at a profit of

16⅔ % on the cost of buying and repairing the car.

Profit is the financial gain that is earned by a business or an individual after all the expenses have been subtracted from the revenue. In simple terms, profit is what remains after all costs, including the cost of goods sold, operating expenses, taxes, and other charges, have been deducted from the revenue generated from the sale of goods or services.

Let's call the cost of repairing the car "x". We know that Mr. Peterson bought the car for $1200, spent x dollars on repairing it, and sold it for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car.

We can start by calculating the total cost of buying and repairing the car, which is the sum of the initial cost and the cost of repairs:

Total cost = $1200 + x

Next, we can calculate the profit that Mr. Peterson made on this total cost, which is given as 16⅔ %:

Profit = (16⅔ %) × Total cost

Profit = (16⅔ / 100) × ($1200 + x)

We know that Mr. Peterson sold the car for $2100, so we can set up an equation for the profit:

Profit = Selling price - Total cost

(16⅔ / 100) × ($1200 + x) = $2100 - ($1200 + x)

Simplifying and solving for x, we get:

(5/6) x = $2100 - $1200 - (5/6)($1200)

(5/6) x = $450

x = $360

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The measure of w in the adjacent angle is 30 degrees.

The two angles are said to be adjacent angles when they share the common vertex and side. In other words, adjace3nt angles have common side and common vertex.

Therefore, let's find the measure of angle w as follows:

Hence, the sum of angle w and angle 50 degrees is equals to 80 degrees.

Therefore,

50 + w = 80

subtract 50 from both sides of the equation

50 - 50 + w = 80 - 50

w = 30 degrees

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The terminal ray of α falls in the third quadrant (where cosine is negative), we can conclude that: cos(α) = -3/5.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides and angles in triangles, and to solve problems involving angles, distances, and heights. The three primary trigonometric functions are sine, cosine, and tangent, which describe the ratios of the sides of a right triangle. Other trigonometric functions include cosecant, secant, and cotangent, which are the reciprocals of the primary trig functions. Trigonometry has many applications in science, engineering, and technology, including astronomy, physics, navigation, and surveying.

Here,

Since the reference angle of α has a sine value of 4/5, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find the cosine of the reference angle:

cos²(θ) = 1 - sin²(θ)

= 1 - (4/5)²

= 1 - 16/25

= 9/25

Taking the square root of both sides gives us:

cos(θ) = ± √(9/25)

= ± (3/5)

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The triangles can be congruent if the corresponding sides of two triangles are congruent except their hypotenuse, and the angle between the congruent corresponding sides between the the two angle is same.

When two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent.

Congruent triangles are triangles that have identical dimensions and shape. Congruent figures have equal areas and corresponding sides that have the same lengths. They're exactly the same in terms of everything.

As a result, if two triangles are congruent, all of their corresponding sides and angles are equivalent to those in the other triangle.

A triangle with one 90-degree angle is referred to as a right-angled triangle. A right triangle has two legs and one hypotenuse.

The hypotenuse is the triangle's longest side, while the legs are the sides that make up the right angle.
The Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, is true for right triangles only.

The Side-Angle-Side (SAS) postulate is used to prove that two triangles are congruent. Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle in this postulate.

Two triangles are congruent if and only if they have two corresponding sides and the included angle are equal.

Using the SAS postulate, we can only conclude that the two right triangles are congruent if we have two pairs of corresponding sides and the included angle between those sides.

As a result, if only two pairs of corresponding sides are congruent, it is not enough to demonstrate that the two triangles are congruent.

Hence when two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent unless their hypotenuse are not equal and their angle between the congruent corresponding sides between the the two angle is same.

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Answer:

(added to verbs and their derivatives) denoting removal or reversal.

Step-by-step explanation:

The correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

What is the median?

The median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in numerical order. It is the value separating the higher half from the lower half of a sample or a population.

To compare the measures of center in the two sets of data, we need to find their respective medians.

For Plot A, we can see that the median is between 5 and 6, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

For Plot B, we can see that the median is between 5 and 6 as well, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

Therefore, the correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

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Answer: (-3, 18) and (-1, 18)

Step-by-step explanation:

Solve the system of equations. [tex]x^{2}[/tex] - 2x + 3 = -6x. [tex]x^{2}[/tex] + 4x + 3 = 0. (x+1)(x+3) = 0. x = -1, -3. Then plug it in. f(x) = 18.

Answer:

0.13188 km

Step-by-step explanation:

The distance covered by the bicycle wheel can be calculated using the formula:

distance = circumference x number of revolutions

The circumference of the wheel can be calculated using the formula:

circumference = 2 x pi x radius

where pi is approximately equal to 3.14.

Substituting the given values:

circumference = 2 x 3.14 x 30 cm

circumference = 188.4 cm

Now, we can calculate the distance covered by the wheel:

distance = circumference x number of revolutions

distance = 188.4 cm x 70

distance = 13188 cm

To convert this distance from centimeters to kilometers, we need to divide by 100,000 (since there are 100,000 centimeters in a kilometer):

distance = 13188 cm ÷ 100,000

distance = 0.13188 km

Therefore, the distance covered by the bicycle wheel is approximately 0.13188 km.

Answer:

5.9

Step-by-step explanation:

im assuming 5.9

not sure what your answer choices are but, its before 6, and way after 5.5, its like counting 123456789. hope this helps.

The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.

The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.

The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.

To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.

The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%

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The expression of radicals [tex]\sqrt{a + b}[/tex] = √a + √b is not possible because they have different root number.

A Radical is described as the symbol, '√'  that is used to denote square root or nth roots.

Also, radical Expression is described as the radical expression  containing a square root.

The rules in addition and subtraction of radicals are;

From the information given, we have that;

a ≠b

So, for the expression;

[tex]\sqrt{a + b}[/tex] = √a + √b,. it is not feasible

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Step-by-step explanation:

Let's first draw a diagram to better visualize the problem:

* T (top of incomplete tower)

/|

/ |

/ |

/ | h (height of incomplete tower)

/ |

/ |

/θ1 |

/___ | M (man's position, height = 6 feet)

d

We can see that we have a right triangle with the tower's height as the opposite side, the distance between the man and the tower as the adjacent side, and the angle of elevation θ1 as 30°. We can use trigonometry to find the height of the incomplete tower:

tan(30°) = h / d

h = d * tan(30°)

We don't know the value of d, but we can use the fact that the man's height plus the height of the incomplete tower equals the distance from the man to the top of the incomplete tower:

d = h / tan(30°) + 6

Now we can use trigonometry again to find the height of the complete tower. Let's call this height H and the new angle of elevation θ2:

* T (top of complete tower)

/|

/ |

/ |

/ | H (height of complete tower)

/ |

/ |

/θ2 |

/___ | M (man's position, height = 6 feet)

d

We have another right triangle, this time with the height of the complete tower as the opposite side, the same distance between the man and the tower as the adjacent side, and the new angle of elevation θ2 as 60°. We can use the tangent function again:

tan(60°) = H / d

H = d * tan(60°)

We can substitute the value of d we found earlier:

H = (h / tan(30°) + 6) * tan(60°)

Simplifying:

H = h * sqrt(3) + 6 * sqrt(3)

(a) To find how high the tower must be raised, we subtract the height of the incomplete tower from the height of the complete tower:

raise = H - h

raise = h * (sqrt(3) - 1) + 6 * sqrt(3)

Substituting the value of h we found earlier:

raise = 24 * (sqrt(3) - 1) + 6 * sqrt(3)

raise ≈ 38.8 feet

(b) The height of the completed tower is simply the height of the incomplete tower plus the raise we found:

height = h + raise

height = 24 + 38.8

height ≈ 62.8 feet

Therefore, the height of the tower after completing its construction work is approximately 62.8 feet.

Step-by-step explanation:

See image and calcs below

Therefore , the solution of the given problem of unitary method comes out to be the quantitative data being displayed, is best displayed using a bar graph.

The task may be completed using this generally accepted ease, preexisting variables, as well as any significant components from the original Diocesan customizable query. If so, you may have another opportunity to interact with the item. Otherwise, all significant factors that affect how algorithmic factor proof behaves will be gone.

Here,

The right graph is option (a),

a bar graph with the heading "Favorite Topping" and the axes "Topping" and "Number of Customers" written on them. T

he labels for the bars should read "Chocolate Chips" with a value of 44, "Hot Fudge" with a value of 27, "Nuts" with a value of 12, and "Sprinkles" with a value of 17.

This categorical data, where each topping is a distinct category and the number of customers is the quantitative data being displayed, is best displayed using a bar graph.

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The optimal number of bags to purchase is 174 bags.

To determine the optimal number of bags to purchase, we need to consider the trade-off between the cost of holding excess inventory and the cost of not having enough inventory to meet demand.

Let's assume that the cost of holding one bag of inventory for six months is $2.00, and the cost of not having one bag available when needed is $10.00.

We can use the normal distribution to estimate the probability of demand exceeding our inventory level. If we assume that demand follows a normal distribution with mean 150 and standard deviation 60, then we can calculate the probability of running out of inventory as

P(demand > inventory) = P(Z > (inventory - mean) / std_dev)

P(demand > inventory) = P(Z > (inventory - 150) / 60)

where Z is the standard normal random variable.

We want to choose the inventory level that minimizes the expected total cost, which is the sum of the cost of holding inventory and the cost of not having enough inventory

Expected total cost = cost of holding inventory + cost of not having enough inventory

Expected total cost = (inventory * $2.00) + (P(demand > inventory) * $10.00)

To minimize this cost, we need to find the inventory level that makes the expected total cost as low as possible. We can use calculus to find the minimum expected total cost.

Taking the derivative of the expected total cost with respect to the inventory level, we get

d/d(inventory) (Expected total cost) = $2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60)

Setting this derivative equal to zero and solving for the inventory level, we get

$2.00 - ($10.00 * (1 / sqrt(2 * pi)) * exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60) = 0

Simplifying this equation, we get

exp(-(inventory - 150)^2 / (2 * 60^2)) * (inventory - 150) / 60 = 0.2

Using a numerical solver or a table of values for the standard normal distribution, we can find that the inventory level that minimizes the expected total cost is approximately 174 bags.

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The volume of a cone that has the same base area and the same height as the cylinder is 116.25pi cubic units. This is because the volume of a cone is one-third the volume of a cylinder with the same base area and the same height. Therefore, the volume of the cone is 116.25pi cubic units.

The volume of a cylinder is equal to the area of the base, multiplied by the height. The volume of a cylinder with a base area of 465pi and a height of h is therefore 465pi*h. For a cone, the volume is equal to a third of the area of the base multiplied by the height. Since the cone and cylinder have the same base area and height, the volume of the cone is one third of the volume of the cylinder. Therefore, the volume of the cone is 155pi cubic units (465pi/3). A cone has one third the volume of a cylinder with the same base and height.

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The net magnetic field at point P is zero, as the magnetic fields produced by the two equal currents in opposite directions cancel out. A third wire at P would experience zero force due to the net zero magnetic field at P.

To construct a vector diagram showing the net magnetic field vector at point P, we can use the right-hand rule for determining the direction of the magnetic field around a current-carrying wire.

If we curl the fingers of our right hand in the direction of the current in the first wire, which is out of the page, the thumb points in the direction of the magnetic field at point P due to the first wire. Similarly, in the opposite direction to the magnetic field at point P due to the second wire.

Since the magnetic fields they produce at P have equal magnitudes but opposite directions. Therefore, the net magnetic field at P is zero,

If a third wire carrying equal current into the plane of the paper were located at P, the direction of the force on this wire would be perpendicular to both the magnetic field produced by the other two wires and the direction of the current in the third wire.

Since the net magnetic field at P is zero, the vector product of the current in the third wire and the magnetic field is also zero, and there is no force on the third wire.

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Answer: muhammad will $99 in one month and connor will have $8

Step-by-step explanation:

$158-$59=$99

$74-$66=$8

The surface area of the larger sphere is 64π cm². therefore option A. 64π cm² is correct.

To find the surface area of the larger sphere, given the volumes of two spheres and the surface area of the smaller sphere, follow these steps:

1. Determine the ratio of the volumes of the spheres:

Volume ratio = Volume of larger sphere / Volume of smaller sphere

                     = (64π cm³) / (8π cm³)

                     = 8

2. Find the cube root of the volume ratio to get the ratio of their radii:

Radii ratio = cube root of volume ratio = cube root of 8 = 2

3. Since the surface area of a sphere is proportional to the square of its radius, find the ratio of the surface areas by

squaring the radii ratio:

Surface area ratio = (Radii ratio)² = (2)² = 4

4. Finally, multiply the surface area of the smaller sphere by the surface area ratio to get the surface area of the larger

sphere:

Surface area of larger sphere = Surface area of smaller sphere × Surface area ratio

                                                 = 16π cm² × 4

                                                = 64π cm²

So, the surface area of the larger sphere is 64π cm² (Option A).

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Answer:

Step-by-step explanation:

I changed it v to X because it's more convenient for me, but please write "v" so don't forget!

Answer:

where is the table without the table how can I give the answer

The value of the conditional probability from the Venn Diagram is (a) 68.4 %

Given that we have the Venn Diagram

From the Venn Diagram, we have the following readings

Male and Independent voters = 13

Independent voters = 19

Using the above values, we have the following equation

P(Male | Independent voter) = 13/19

Evaluate

P(Male | Independent voter) = 68.4 %

Hence, the conditional probability is 68.4 %

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So the minimum probability that a Yes respondent exercises for at least 1 hour is 6/(x+6), where x is the number of students who answered No.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields such as mathematics, statistics, science, economics, and finance to model and analyze uncertain situations.

Here,

Let the number of students who answered No be x. Then the number of students who answered Yes is x+12. The total number of students is then x + (x+12) = 2x + 12.

Suppose y of the students who answered Yes exercise for at least 1 hour. Then the probability that a Yes respondent exercises for at least 1 hour is y/(x+12).

Since we don't have the full frequency tree, we can't determine y or x directly. However, we do know that the total number of students who exercise for at least 1 hour is greater than or equal to 12 (since there are 12 more Yes respondents than No respondents). Therefore, the probability that a Yes respondent exercises for at least 1 hour is y/(x+12) is at least 12/(2x+12) = 6/(x+6).

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The size of angle EAB is approximately 70.76 degrees.

What is triangle?

A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.

Let's start with the ratio of the size of angle DEA to the size of angle CDE. We can express this ratio as:

angle DEA : angle CDE = 5 : 2

We know that the sum of the angles in a triangle is 180 degrees, so we can use this fact to express angle DEA and angle CDE in terms of angle ABD:

angle DEA + angle CDE + angle ABD = 180

Substituting the ratio given above, we get:

5x + 2x + angle ABD = 180

Simplifying, we get:

7x + angle ABD = 180

Next, let's consider the ratio of the size of angle EAB to the size of angle ABC, which is given as 4:3. We can express this ratio as:

angle EAB : angle ABC = 4 : 3

We know that angle EAB and angle ABC are adjacent angles, so their sum is equal to angle ABD:

angle EAB + angle ABC = angle ABD

Substituting the ratio given above, we get:

4y + 3y = angle ABD

Simplifying, we get:

7y = angle ABD

Now we have two equations:

7x + angle ABD = 180

7y = angle ABD

We can substitute the second equation into the first to get an equation in terms of y:

7x + 7y = 180

Simplifying, we get:

x + y = 25.71

Now we can use the ratio of angle EAB to angle ABC to find y:

angle EAB : angle ABC = 4 : 3

4y : 3y = 4 : 3

Simplifying, we get:

4y = 3(106 - angle EAB)

Expanding, we get:

4y = 318 - 3angle EAB

Substituting the equation we found for y above, we get:

4(25.71 - x) = 318 - 3angle EAB

Simplifying, we get:

angle EAB = 70.76

Therefore, the size of angle EAB is approximately 70.76 degrees.

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The common ratio is 1/3 and the fifth term of a geometric progression (GP) is 2/81 if the first and third terms of the GP are 2 and 2/9, respectively.

Let's call the common ratio of the GP "r".

We know that the first term of the GP is 2, so:

a₁ = 2

We also know that the third term of the GP is 2/9, so:

a₃ = 2/9

We can write the following using the nth term of a GP formula:

a₃ = a₁ * r²

Substituting the values we know, we get:

2/9 = 2 * r²

Dividing both sides by 2, we get:

1/9 = r²

Taking the square root of both sides (and remembering that r must be positive since it's a common ratio), we get:

r = 1/3

Now we can find the fifth term of the GP using the formula:

a₅ = a₁ * r⁴

Substituting the values we know, we get:

a₅ = 2 * (1/3)⁴

a₅ = 2 * (1/81)

a₅ = 2/81

Therefore, the common ratio is 1/3 and the fifth term of the GP is 2/81.

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Let the amount of payouts in March be M.

From the problem, we know that the payouts in March increased by 8.5%, which means:

M = 12,400 + 0.085(12,400)

M = 12,400 + 1,054

M = 13,454

Next, we know that the payouts in April dropped by 5%, which means:

A = M - 0.05M

A = 0.95M

A = 0.95(13,454)

A = 12,781.3

Therefore, the amount of the payouts in April was $12,781.3.

There is a 20% chance that a risky stock investment will end up in a total loss. If you invest in 25 independent risky stocks, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

Given data:

Probability of getting a total loss in one investment = 20% = 0.20

Probability of not getting a total loss in one investment = 1 - 0.20 = 0.80

Number of investments = 25

We need to find the probability that fewer than six out of these 25 risky investments end up in total losses.

We will use the binomial distribution formula here:P(X < 6) = Σp(x) (from x = 0 to x = 5)

Here, Σ is the summation signp(x) = probability of x successes in 25 trials, which is given by the formula:

p(x) = [ nCx * p^x * (1-p)^(n-x)]

Where, n = number of trial

s = 25

p = probability of success = 0.80

q = probability of failure = 1 - p = 0.20n

Cx = n! / (x! × (n-x)!) = combination of n items taken x at a time

We need to substitute these values in the formula and calculate the probability:

P(X < 6) = Σp(x) (from x = 0 to x = 5)

P(X < 6) = p(0) + p(1) + p(2) + p(3) + p(4) + p(5)

P(X < 6) = [tex][25C0 * (0.80)^0 * (0.20)^25] + [25C1 * (0.80)^1 * (0.20)^24] + [25C2 * (0.80)^2 * (0.20)^23] + [25C3 * (0.80)^3 * (0.20)^22] + [25C4 * (0.80)^4 * (0.20)^21] + [25C5 * (0.80)^5 * (0.20)^20][/tex]

P(X < 6) ≈ 0.91

Therefore, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

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The solution to the simultaneous equation represented on the graph is:

B: x = 2 and x = 4

We are given the equations as:

f(x) = -12x + 26

g(x) = -(-¹/₅)^(-x + 2)  + 3

The solution to these two simultaneous equations will be the coordinates of the points on the graph where they both intersect.

We see that the coordinates of the points of intersection of the graph is at the coordinates:

(2, 2) and (4, -22)

Thus, the solution is at x = 2 and x = 4

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