A compound shape has a triangle and a rectangle and its total area is 52square cm. If the area of the triangle is 20square cm, then find the longest side of the rectangle.

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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The formula to solve Euler's Formula for e, which relates the number of vertices v, the number of edges e, and the number of faces f, of a polyhedron is e = v + f - 2.

Euler's Formula, v − e + f = 2, is a relationship between the number of edges e, the number of vertices v, and the number of faces f in a polyhedron. The formula can be rearranged to solve for e which is e = v + f - 2. This formula can be used to find the number of edges in a polyhedron when the number of vertices and faces are known. Therefore, this formula is used to calculate the number of edges in a polyhedron. The formula states that the number of vertices, minus the number of edges, plus the number of faces is always equal to 2.

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Answer:

Step-by-step explanation:

The question is incomplete. Here is the complete question;

A kid traveled a distance of 9 km by bike, and then walked a distance of x km.

a.Find the total distance traveled in terms of  x

b. If the total distance was less than 30 km, form an inequality in x, and

then solve it!

a) Total distance = distance travelled by bike + distance walked

Total distance = 9km + xkm

Total distance = (9+x)km

b)  If the total distance was less than 30 km, the inequality representing this is;

9+x < 30

Subtract 9 from both sides;

9+x-9 < 30-9

x < 21

hence the solution to the inequality is x< 21

Answer:

y=x-2+√3

Step-by-step explanation:

I'm not sure keep it up

Answer: f(x)=(x+3)^2-13 = (-3|-13)

Step-by-step explanation:

x^2+6x-4

x^2+6x+3^2-3^2-4

(x+3)^2-3^2-4

(x+3)^2-13

Answer:

Step by step solution

Step-by-step explanation:

\(a_1 = -1\\a_4 = 14\\a_4 = a_1 + 3d\\14 = -1 + 3d\\15 = 3d\\d = 5\\a_1 = -1\\a_2 = 4\\a_3 = 9\\a_4 = 14\)

Answer:

7

Step-by-step explanation: Trust me

Answer:

Calculate the average of the five original cards:

2+5+7+8+9=31

31/5 = 6.2

So, if a card was removed, the four remaining cards would have an average of 6, meaning that they would add up to 24.

31-x=24?

Subtract 31 from both sides: -x=-7

Divide by -1 on both sides: x=7

So, we know that 7 was removed.

Let me know if this helps!

A. The number of red balls he had was 8  at the beginning.

Duke's starting red ball total can be found by setting up a system of equations. First, let x represent the number of red balls and y represent the number of blue balls.

After 5 days, the equation is x-15=y+10. This equation states that after 5 days, the number of red balls (x) minus 15 will equal the number of blue balls (y) plus 10. After 9 days, the equation is x-27=2y+20.

This equation states that after 9 days, the number of red balls (x) minus 27 will equal twice the number of blue balls (y) plus 20. To solve for x, both equations can be set equal to each other and solved. This results in x=8. Therefore, Duke had 8 red balls at the beginning.

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Answer:

h=-18

Step-by-step explanation:

Here you go mate

Step 1

55 – -26h = -413  Question

Step 2

55 – -26h = -413

26h+55=-413

Step 3

26h+55=-413  Subtract 55

26h=-468

Step 4

26h=-468  Divide sides by 26

Answer

-18

The Element 22 from the scalar multiplication of the matrix is -30 and the right option is a. -30.

The term scalar multiplication refers to the product of a real number and a matrix.

To get the value of element 22 after scalar multiplication of matrix \(\left[\begin{array}{ccc}0&8\\6&-5\\\end{array}\right]\) by 6, we following the steps below.

Step 1:

Element 22 means element in the Second row and second column

performing the operetion, Multiplying 6 by the matrix

Hence, the right option is a. -30.

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Answer:

15+x=23

Step-by-step explanation:

Answer:

The second period from 1669 to 1687 was the highly productive period in which he was Lucasian professor at Cambridge. The third period (nearly as long as the other two combined) saw Newton as a highly paid government official in London with little further interest in mathematical research.

Step-by-step explanation:

Answer:

We conclude that it would take 4.5 minutes to fill the full barrel.

Step-by-step explanation:

It is stated that it took 3/4 of a minute to fill a barrel 1/6 full of water.

It is conditioned that the water continues at the same rate.

so

Total parts of a barrel = 6

It takes 0.75 minutes to fill the 1 part of a barrel

Thus, multiply 0.75 by 6 will determine the total time in minutes to fill all the 6 parts of a barrel (or a full barrel).

i.e.

0.75 × 6 = 4.5 minutes.

Therefore, we conclude that it would take 4.5 minutes to fill the full barrel.

The cost of a ticket to the basketball game is $7.50. Let's call the price of a ticket "x" and the price of a souvenir "y".

Then we can set up two equations based on the information given:

2x + y = 17.25   (equation 1)

5x + 2y = 42.00  (equation 2)

We can use these equations to solve for x, the cost of a ticket. One way to do this is to solve for y in equation 1 and substitute it into equation 2, then solve for x. Here are the steps:

Solve equation 1 for y: y = 17.25 - 2x.

Substitute this expression for y into equation 2: 5x + 2(17.25 - 2x) = 42.00.

Simplify the equation by distributing the 2: 5x + 34.50 - 4x = 42.00.

Combine like terms: x + 34.50 = 42.00.

Subtract 34.50 from both sides: x = 7.50.

So the cost of a ticket to the basketball game is $7.50.

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Answer:

  x = 6 m

Step-by-step explanation:

Given a diagram showing a semicircle atop a rectangle that is 8 m wide, you want to know the height of the rectangle when the overall height of the figure is 10 m.

All points on a circle are the same distance from its center. The center of a semicircle is the midpoint of its straight side. Here, the diameter of the semicircle is shown as 8 m, so the midpoint will be 4 m from either side.

The top point of the semicircle will be 4 m from the center on the top edge of the rectangle.

Since the overall height is 10 m, the rectangle must be 10 -4 = 6 meters high.

The value of x is 6 m.

Negative mass in the Dirac equation maintains the relativistic dispersion relation \(E^2 = p^2 + m^2\) for plane wave solutions, requiring a redefinition of the matrix β to change the sign of the mass parameter, m.

(a) To demonstrate that any plane wave solution of the Dirac equation obeys the relativistic dispersion relation \(E^2 = p^2 + m^2\), we substitute the plane wave solution ψ(x, t) = u(p)exp(-iEt + i→px) into the Dirac equation: iθ t​ψ=(α⋅ p^​+βm)ψ. Here, u(p) is the four-component spinor representing the particle's quantum state, E is the energy, p is the momentum, α and β are the Dirac matrices, and m is the mass parameter.

By substituting the plane wave solution into the Dirac equation and rearranging terms, we obtain the relation (α⋅p)^2u(p) = (\(E^2 - m^2\))u(p). Since the α matrices satisfy the anticommutation relations and (α⋅p)^2 = \(p^2\), we find that \(E^2 = p^2 + m^2\), which is the familiar relativistic dispersion relation.

(b) To change the sign of the mass parameter, m, in the Dirac equation, we need to redefine the matrix β. The Dirac matrices satisfy specific algebraic properties, and we can choose an appropriate representation for them. To change the sign of m, we can redefine β as β' = -β. This redefinition ensures that (α⋅p + β'm)ψ still satisfies the Dirac equation with a negative mass parameter. By making this substitution, we account for negative mass in the Dirac equation.

In conclusion, plane wave solutions in the Dirac equation with a negative mass still obey the usual relativistic dispersion relation, \(E^2 = p^2 + m^2\). To change the sign of the mass parameter, m, in the equation, we redefine the matrix β as β' = -β, ensuring that the modified equation still holds for negative masses.

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Answer: Infinitely many

Step-by-step explanation:

Let the value of \(\frac{x}{y}\) be \(k\), where \(k\) is an integer. Then, \(x=ky\).

\(\implies \frac{x+1}{y+1}=\frac{ky+1}{y+1}=\frac{k(y+1)}{y+1}+\frac{1-k}{y+1}=k+\frac{1-k}{y+1}\)

This means we need \(\frac{1-k}{y+1}\) to be an integer. If we let this fraction equal \(n\), then:

\(\frac{1-k}{y+1}=n \implies 1-k=ny+1 \implies y=\frac{-k}{n}\)

From this, we see that there are infinitely many pairs.

Answer:

14.5

Step-by-step explanation:

The radius is half the diameter.

29/2=14.5

The volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\) To find the volume when the area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we can use the method of cylindrical shells.

First, let's find the points of intersection between the two curves by setting them equal to each other:

\(\[x^2 = \frac{3}{x^3}\]\)

To simplify this equation, we can multiply both sides by \(\(x^3\)\):

\(\[x^5 = 3\]\)

Now, taking the fifth root of both sides:

\(\[x = \sqrt[5]{3}\]\)

So the two curves intersect at \(\(x = \sqrt[5]{3}\)\).

To calculate the volume area enclosed by the graphs of \(\(y = x^2\)\)and \(\(y = \frac{3}{x^3}\)\) is revolved about the x-axis, we need to integrate the circumference of each cylindrical shell multiplied by its height. The height of each shell is the difference in the y-values of the two curves, and the circumference is\(\(2\pi x\)\).

Let's integrate from \(\(x = 0\)\) to \(\(x = \sqrt[5]{3}\)\):

\(\[V = \int_0^{\sqrt[5]{3}} 2\pi x \left(\frac{3}{x^3} - x^2\right) \, dx\]\)

Simplifying this expression:

\(\[V = 2\pi \int_0^{\sqrt[5]{3}} \left(\frac{3}{x} - x^3\right) \, dx\]\)

Integrating each term separately:

\(\[V = 2\pi \left[3 \ln|x| - \frac{x^4}{4}\right]_0^{\sqrt[5]{3}}\]\)

Plugging in the limits of integration:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right] - 2\pi \left[3 \ln|0| - \frac{0^4}{4}\right]\]\)

Since \(\(\ln|0|\)\)is undefined, the second term on the right side is zero:

\(\[V = 2\pi \left[3 \ln|\sqrt[5]{3}| - \frac{\sqrt[5]{3}^4}{4}\right]\]\)

Simplifying further:

\(\[V = 2\pi \left[3 \ln 3^{\frac{1}{5}} - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

Using the properties of logarithms, we can simplify the first term:

\(\[V = 2\pi \left[3 \cdot \frac{1}{5} \ln 3 - \frac{3}{4} \cdot 3^{\frac{4}{5}}\right]\]\)

\(\[V = \frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\]\)

So the volume enclosed by the two curves when revolved about the x-axis is \(\(\frac{6\pi}{5} \ln 3 - \frac{3\pi}{2} \cdot 3^{\frac{4}{5}}\).\)

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Answer:

The y intercept of the scatterplot is 250 sweat shirts and the slope is 10/3

What is a linear function?

y = mx + b

where m is the rate of change and b is the y intercept.

Let y represent the number of sweat shirts sold and x represent the temperature.

The y intercept is at (0,250).

Using point (0,250) and (14,200):

Slope = (200-250) / (15-0) = 10/3

The y intercept of the scatter plot is 250 sweat shirts and the slope is (10/3)

Answer:

ubub

Step-by-step explanation:

f(x) = 7 is the output for only one input value, which is x = 3, because this is the only value that results in the maximum value of the function.

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

The function f(x) = −(x−3)²+7 is a quadratic function in vertex form. The vertex form of a quadratic function is given by f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (3, 7), which means that the parabola opens downwards and has a maximum value of 7. This also means that any value of f(x) less than 7 can be obtained from two different values of x, since the parabola is symmetric around its vertex.

However, f(x) = 7 is the maximum value of the function and can only be obtained for a single value of x, which is the x-coordinate of the vertex, namely x = 3. This is because the vertex is the highest point on the parabola, and any other value of x will result in a lower value of f(x).

Therefore, f(x) = 7 is the output for only one input value, which is x = 3, because this is the only value that results in the maximum value of the function.

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Answer:

18/12

Step-by-step explanation:

18- rise

12- run

Answer:

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

Step-by-step explanation:

Given

Shape: Cube

Dimension: (x+7y), (7x-y) and (xy-5).​

Required

Determine the volume

The volume is calculated by multiplying the dimensions:

\(Volume = (x+7y) * (7x-y) * (xy-5)\)

Evaluate the first 2 brackets

\(Volume = [x(7x-y)+7y(7x-y)] * (xy-5)\)

\(Volume = [(7x^2-xy)+(49xy-7y^2)] * (xy-5)\)

\(Volume = [7x^2-xy+49xy-7y^2] * (xy-5)\)

\(Volume = [7x^2+48xy-7y^2] * (xy-5)\)

Open brackets

\(Volume = xy[7x^2+48xy-7y^2] -5[7x^2+48xy-7y^2]\)

\(Volume = 7x^3y+48x^2y^2-7xy^3 -35x^2-240xy-35y^2\)

Answer:

A square.

Step-by-step explanation:

Answer:

C - 13

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

No need

Answer: 23 x 10,000

Step-by-step explanation:

23 multiplying with 10,000

you will get 230,000

Answer:

23 * 10000 or 23 * \(10^{4}\)

Step-by-step explanation:

23 * 10000 or 23 * \(10^{4}\)

The 4 angles inside EVERY 4-sided figure ALWAYS add up to 360 degrees.

Now you have been found !