express the following fractions as the sum or difference of two fractions (x^2+y^2)/x^4

The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer:

5h

Step-by-step explanation:

300÷60=5

km÷km/h=h

=5h

\(\text{Given that,}\\\\z = \sin(xy)\\\\\text{Now,}\\\\\textbf{L.H.S}\\\\=\dfrac 1y \cdot\dfrac{\partial z }{\partial x}\\\\\\=\dfrac{1}{y} \cdot \dfrac{\partial }{\partial x}(\sin(xy))\\\\\\=\dfrac 1y \cdot \cos(xy) \cdot y\dfrac{\partial }{\partial x}(x)\\\\\\=\cos(xy)\)

\(\textbf{R.H.S}\\\\=\dfrac 1x \cdot \dfrac{\partial z }{\partial y}\\\\\\=\dfrac 1x \cdot \dfrac{\partial }{\partial y}(\sin (xy))\\\\\\=\dfrac 1x \cdot x \cdot \cos(xy) \dfrac{\partial }{\partial y}(y)\\\\\\=\cos(xy)\\\\\)

\(\textbf{L.H.S} = \textbf{R.H.S}\\\\\text{Showed.}\)

Answer:

The required equation is \(\tan\theta=\dfrac{7}{5}\).

Step-by-step explanation:

Consider the provided information.

The required figure is shown below:

It is given that the radius of the base is 5 inches and the height of the cone is 7 inches.

We need to given the equation which gives the measure of \(\theta\).

Now consider the right angle triangle making an angle \(\theta\).

\(\tan\theta=\frac{\text{Opp}}{\text{Adj}}\)

\(\tan\theta=\dfrac{7}{5}\)

Hence, the required equation is \(\tan\theta=\dfrac{7}{5}\).

Answer:

2

Step-by-step explanation:

In this question, we will have to solve the expression with our given variable.

Plug in 4 to x and solve:

-0.4(3(4) - 2) + 2 + 4

-0.4(12 - 2) + 2 + 4

-0.4(10) + 2 + 4

Evaluate -0.4(10):

-4 + 2 + 4

-2 + 4

2

Your final answer would be 2.

A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.

To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.

First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4

So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)

Integrating this expression with respect to t over the interval [0,3], we get:

\(\int\limits^3_0\) M(t) dt = \(\int\limits^3_0\) (4 - 0.75sin(t) + 0.25sin(3t)) dt

= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]

= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))

= 11.544

Therefore, the answer is (C) 11.544.

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The tangential and normal components of the acceleration when s = 10 m is 40 m/s^2 and 8 m/s^2 respectively.

In the given question, a car is travelling along the road with a speed of 2s m/s, where s is in meters.

We have to determine the tangential and normal components of the acceleration when s = 10 m.

Speed (v) = 2s  

Motion is circular so, Radius of circle = 50m

Tangential acceleration = dv/dt

Tangential acceleration = d(2s) / dt

Tangential acceleration = 2(ds)/dt

Tangential acceleration = 2v

Tangential acceleration = 2(2s)

Tangential Acceleration = 4s

As given s = 10 m

Tangential acceleration = 4 x 10

Tangential acceleration  = 40 m/s^2

Normal acceleration = v^2/ r

Normal acceleration = 4s^2/r

Normal acceleration = {4 x 10^2}/50

Normal acceleration = {4 x 100}/50

Normal acceleration = 400/50

Normal acceleration = 8 m/s^2

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The complete question is:

A car is travelling along the road with a speed of 2s m/s, where s is in meters. Determine the tangential and normal components of the acceleration when s = 10 m. Treat the car as a particle

The values of h and k used to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.

The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex. To rewrite the given function in vertex form, we need to complete the square.
Starting with the function f(x) = x^2 + 12x + 6, we can rewrite it as f(x) = (x^2 + 12x + 36) - 36 + 6. Notice that we added and subtracted the square of half the coefficient of x, which is (12/2)^2 = 36.
Simplifying further, we have f(x) = (x + 6)^2 - 30. Comparing this form with the vertex form, we can see that h = -6 and k = -30.
Therefore, the correct values for h and k to write the function f(x) = x^2 + 12x + 6 in vertex form are h = -6 and k = -30.

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Answer: 4)90˚

Step-by-step explanation:

(90˚ is more towards the middle

A regular octagon is a shape with 8 congruent sides.

The minimum angle of rotation is 45 degrees

The number of sides of a regular octagon is:

\(\mathbf{n = 8}\)

The total angle at the center of the regular octagon is:

\(\mathbf{\theta = 360}\)

So, the minimum angle of rotation is calculated as follows:

\(\mathbf{\alpha = \frac{\theta}{n}}\)

This gives

\(\mathbf{\alpha = \frac{360}{8}}\)

\(\mathbf{\alpha = 45}\)

Hence, the minimum angle of rotation is 45 degrees

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When three circles of radius 1 are externally tangent to each other and internally tangent to a larger circle.  Then the radius of the large circle will be 2.83

The radius of the larger circle can be calculated using the Pythagorean theorem. The three small circles are externally tangent, meaning the distance between their centers is 2.

Therefore, the distance between the center of the large circle and the centers of the small circles must also be 2. The hypotenuse of the triangle is formed by the centers of the small circles and the center of the large circle is the radius of the large circle. This is equal to the square root of 8

√8=2.83.

Therefore, the radius of the large circle is 2.83.

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Answer:

there is no table so we are therefore unable to answer this question

Step-by-step explanation:

sorry

Answer:

(0.5,0) , (-3,0) ,and (0,-1.5)

Step-by-step explanation:

Just look where the points touch the x- and y-axis.

It touches twice on the x- and once on the y-axis.

Hope that helps!

no, 5 is in the thousandths place

Answer:

Step-by-step explanation:

No there is only .3 hundreds

The Linnaean class system provides a framework for understanding the diversity of life on Earth by grouping similar organisms together based on shared characteristics.

By comparing and contrasting the definitions of each class, we can see how different groups of animals are related to each other and how they differ in terms of their biological traits.

The Linnaean class system is a way of organizing living things based on shared characteristics. Let's compare and contrast the definitions of the Linnaean classes using a Venn diagram.

First, we have the class Mammalia, which includes all animals that have hair or fur, produce milk to feed their young, and have specialized teeth. This class overlaps with the class Aves, which includes all birds, because some birds have specialized beaks and feathers that are similar to mammalian hair and teeth. However, birds do not produce milk.

Next, we have the class Reptilia, which includes animals that are cold-blooded, lay eggs, and have scales or plates on their skin. This class overlaps with both Mammalia and Aves in terms of species that lay eggs, such as monotremes (platypus and echidnas) and some birds (ostriches and emus). However, reptiles lack specialized teeth and do not produce milk.

Finally, we have the class Amphibia, which includes animals that are cold-blooded, breathe through their skin, and undergo metamorphosis from a water-dwelling larval stage to a land-dwelling adult stage. This class overlaps with Reptilia in terms of some shared characteristics, but Amphibia also lacks specialized teeth and does not lay eggs with hard shells like reptiles.

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Answer:

1

Step-by-step explanation:

14 x + 3 = 12x + 5

or, 14 x - 12x = 5 - 3

or, 2x = 2

or, x = 2÷2

therefore , x = 1

hope this answer will help u.

The probability was broken by Bob is, 0.003 or 3%.

What is probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Alonzo, Bob, and Casper are each assigned three chances to bus tables and to fix any broken dishes, respectively.

P(Alonzo bussing tables) = 50% = 0.5

P(Bob bussing tables) = 15% = 0.15

P(Casper bussing tables) = 35% = 0.35

P(Alonzo breaking a dish) = 6% = 0.06

P(Bob breaking a dish)  = 2% = 0.02

P(Casper breaking a dish)  = 4% = 0.04

As the likelihood of dish breakage does not change with the busing of the tables, this is all about independent events.

Consequently, P(A and B) = P(A) + P (B)

So, if a dish is broken, the likelihood that Bob broke it is;

P(Bob breaking dishes and busing tables) = P(Bob busing tables) x P (Bob breaking a dish)

                                                                       = 0.15 x 0.02

                                                                       = 0.003

P(Bob breaking dishes and busing tables)  = 0.003 0r 0.3%

Hence, the probability was broken by Bob is, 0.003 or 3%.

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The equation of the graph shown can be written in factored form as follows:

y = a(x - h)(x - k)(x - m)

To find the equation, we need to identify the x-intercepts and the minimum point of the graph.

From the description, we know that the graph starts at the top left and continues down through the x-axis at x = -4. This means that one of the factors is (x + 4).

Next, the graph reaches a minimum around y = -2.8. This indicates that the graph touches the x-axis at this point, so another factor is (x + 2).

Moving forward, the graph goes back down to another minimum around y = -0.4. Again, this means the graph touches the x-axis at this point. So we have another factor, (x + 1).

Now we have all the necessary factors: (x + 4), (x + 2), and (x + 1). To determine the coefficient "a," we can use the fact that the graph goes up after crossing the x-axis at x = -2. This suggests that "a" must be positive.

Therefore, the equation of the graph in factored form is:

y = a(x + 4)(x + 2)(x + 1)

Please note that without specific points, it is not possible to determine the exact value of "a" or the precise shape of the graph. The equation provided represents a general equation that satisfies the given conditions.

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No, it doesn't show that single individuals under the age of 25 have more insurance claims than the nationwide percent reported by the big insurance firm.

Hypothesis

Null hypothesis : H0: p = 0.68

Alternative hypothesis : Ha: p > 0.68

A random sample of 53 claims showed that 41 were made by single people under the age of 25.

Thus; p^ = 41/53 = 0.7736

The test statistic is

z = (p^ - p_o)/√(p_o(1 - p_o)/n)

z = (0.7736 - 0.68)/√(0.68(1 - 0.68)/41)

z = 0.0936/0.07285

z = 1.28

The p-value from z-score calculator, using z = 1.28, one tail hypothesis and significance level of 0.05,we have;

P(z > 1.28) = 0.100273

The p-value gotten is greater than the significance value and so we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

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Answer:

x = 6.

Step-by-step explanation:

JK = JG + GK = 6 + 4 = 10

Scalar factor(k) = JK/JG

k = 10/4 = 5/2

Scalar factor (k) = JL/GH

5/2 = x/15

5 × x = 2× 15

5x = 30

hence x = 6

Answer:

Step-by-step explanation:

12

Answer:

a) 12

b) 11

c) 8

Step-by-step explanation:

Using the Pythagorean Theorem: \(a^2 + b^2 = c^2\)

a is the shorter side,

b is the longer side,

c is the hypotenuse.

a) \(a^2 + b^2 = c^2\\5^2+b^2=13^2\\25+b^2=169^2\\b^2=169-25\\b^2=144\\b=\sqrt{144}=12\\ b=12\)

b)\(a^2 + b^2 = c^2\\a^2+60^2=61^2\\a^2+3600=3721\\a^2=3721-3600\\a^2=121\\a=\sqrt{121}=11\\ a=11\)

c)\(a^2 + b^2 = c^2\\a^2+15^2=17^2\\a^2+225=289\\a^2=289-225\\a^2=64\\a=\sqrt{64}=11\\ a=8\)

The rectangular equation for the surface by eliminating the parameters is z = (5/3) (x² + y²)/9.

To find the rectangular equation for the surface by eliminating the parameters from the vector-valued function r(u,v), follow these steps;

Step 1: Write the parametric equations in terms of x, y, and z.  

Given: r(u, v) = 3 cos(v) cos(u)i + 3 cos(v) sin(u)j + 5 sin(v)k

Let x = 3 cos(v) cos(u), y = 3 cos(v) sin(u), and z = 5 sin(v)

So, the parametric equations become; x = 3 cos(v) cos(u) y = 3 cos(v) sin(u) z = 5 sin(v)

Step 2: Eliminate the parameter u from the x and y equations.  

Squaring both sides of the x equation and adding it to the y equation squared gives; x² + y² = 9 cos²(v) ...(1)

Step 3: Express cos²(v) in terms of x and y.  Dividing both sides of equation (1) by 9 gives;

cos²(v) = (x² + y²)/9

Substituting this value of cos²(v) into the z equation gives; z = (5/3) (x² + y²)/9

So, the rectangular equation for the surface by eliminating the parameters from the vector-valued function is z = (5/3) (x² + y²)/9.

The rectangular equation for the surface by eliminating the parameters from the vector-valued function is found.

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The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The equation of the functions is given below.

Equation  1: f(x) = 2x³ + 24x + 2

Equation 2: f(x) = 4ˣ

The graph of the functions is given below.

From the graph, the intersection of the graph is at (-0.044, 0.9407).

The first x-value when the y-value of equation 2 is higher than the y-value of equation 1 will be less than - 0.044.

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The simplest form of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Both given expressions are not equivalent.

What is an expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the expression 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given expression is 3x + 14 – x + \(1\frac{1}{2}\)

Now combine like terms:

= (3x - x) + (14 + \(1\frac{1}{2}\))

= 2x +  (14 + \(1\frac{1}{2}\))

Convert mixed fraction to improper fraction:

= 2x +  (14 + 3/2)

= 2x + 31/2

= 2x + \(15\frac{1}{2}\)

The equivalent expression of 3x + 14 – x + \(1\frac{1}{2}\) is  2x + \(15\frac{1}{2}\). Therefore, 3x + 14 – x + \(1\frac{1}{2}\) is not equivalent to 4x + \(1\frac{3}{4}\).

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Answer:

4

Step-by-step explanation:

substitute 4 and 0 into the equation so it becomes ax4 + 5x0 = 16

5x0 = 0

16/4 = a = 4

Answer:

Johnson rode her bike 5 miles

Step-by-step explanation:

The area of the square of sides when it is increased by a scale factor

of 5 is 400cm² & 100 cm² respectively.

What is a scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object that is its representation but of a different size.

Scale factors are used in geometrical drawings and problems to solve problems involving large quantities.

We know that,

A = s²

Here A is the area of the square and s is the side square.

Let's take the side length is increased by a scale factor of 5,

This means the new side is 5s

A = (5s)²

= 25s²

= 25(4)²

= 25 × 16

A = 400

A = 25(2)²

= 25 × 4

A = 100

Therefore the area of the square of sides when it is increased by a scale factor of 5 is 400cm² & 100 cm² respectively.

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The area of the shaded region will be 8 square unit as per the given figure.

The rectangle has dimensions 2 x 4, so its area is:

Area of rectangle = length x width = 2 x 4 = 8 square units

The triangle has dimensions 4 x 8, so its area is:

Area of triangle = (1/2) x base x height = (1/2) x 4 x 8 = 16 square units

To find the area of the shaded region, we need to subtract the area of the triangle from the area of the rectangle.

Area of shaded region = Area of the triangle - Area of rectangle

Area of shaded region = 16-8

Area of shaded region = 8

The area of the shaded region will be 8 square units.

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Complete question:

Answer:

ASA

Step-by-step explanation:

I think

Answer:

c

Step-by-step explanation:

both use the same middle side

(a) In the equilibrium bidding strategy, bidders bid below their cost. The difference between a contractor's quote and their cost represents their strategic behavior in the auction.

By bidding below their cost, contractors try to increase their chances of winning the auction and securing the project.

This strategy allows them to potentially earn a higher profit if they win the auction and their cost turns out to be lower than their bid.

(b) The probability of contractor A winning when she submits a quote equal to b and contractor B submits a quote according to the equilibrium bidding function β(⋅) can be calculated as follows:

P(A wins) = P(A's bid ≤ B's bid)

Since the contractors' costs are independently drawn from a Uniform [0,1] distribution, the probability can be expressed as:

P(A wins) = P(A's cost + A's bid ≤ B's cost + B's bid)

Given that A's bid is b and B's bid is β∗(B's cost), the probability becomes:

P(A wins) = P(A's cost + b ≤ B's cost + β∗(B's cost))

(c) Contractor A's expected payoff when she has a cost of completing the project equal to c and submits a quote equal to b, while her rival bids according to the equilibrium strategy βx(⋅), can be calculated as follows:

Payoff(A) = P(A wins) × (b - c)

Using the probability expression from part (b), the expected payoff can be written as:

Payoff(A) = P(A's cost + b ≤ B's cost + βx(B's cost) × (b - c)

(d) To show that the bidding strategy βx(c) = 2/(1+c) is a (symmetric) Bayesian Nash Equilibrium, we need to verify two conditions:

(i) the strategy is optimal for a contractor given the strategies of other bidders, and

(ii) no bidder has an incentive to deviate from the equilibrium strategy.

(i) Optimality: Given the bidding strategy βx(c) = 2/(1+c), a bidder's expected payoff is maximized when they follow this strategy. This can be shown by calculating the expected payoff for a bidder who anticipates a cost of completing the project as c and submits a quote equal to βx(c). The expected payoff is maximized when the bidder follows the equilibrium strategy.

(ii) No incentive to deviate: Suppose a bidder deviates from the equilibrium strategy and chooses a different bidding strategy. In this case, the bidder's expected payoff would be lower than or equal to the expected payoff obtained by following the equilibrium strategy. Therefore, no bidder has an incentive to deviate from the equilibrium strategy, indicating that βx(c) = 2/(1+c) is a Bayesian Nash Equilibrium.

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Slope of the flights from point A to point B on the curve The slope of flights from point A to point B on the curve is obtained as shown Slope = Change in vertical distance / Change in horizontal distance.

We can determine that the vertical change from point A to point B is 900 km while the horizontal change is 1200 km. In this case, the slope of flights from point A to point B on the curve is 0.75. This implies that for every 1 unit of horizontal change, there is a vertical change of 0.75 units. This may mean charging more for flights that move on a curved path than those that move on a straight path. Therefore, the slope of flights from point A to point B on the curve is:

Slope = Change in vertical distance / Change in horizontal distance

Slope = 900 / 1200

= 0.75.

This will ensure that the airline operators are able to cover their costs and make a profit. From the graph, we can determine that the vertical change from point A to point B is 900 km while the horizontal change is 1200 km. This has an economic implication for airlines that operate flights on this route. It means that there is a higher cost for flights that move from point A to point B on the curve compared to those that move on a straight line. This may mean charging more for flights that move on a curved path than those that move on a straight path. This will ensure that the airline operators are able to cover their costs and make a profit.

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