1
A line passes through the point (-7, 5) and has a slope of 2. Which is another point that the line passes through?
O (-13, 9)
O (-9, 13)
O (9, 13)
O (13,9)

\(y = (1/5) x^5 + Ce^ {(-x^5)}\) is the general solution of the given differential equation.

The given differential equation is:

y' + 5x⁴ y = x⁴

To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is \(e^{(int 5x^4 dx)}\):

\(e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}\)

The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is \(e^{(x^5)}\):

\(e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)\)

Now we can recognize the left-hand side as the product of the derivative of the product of \(e^{(x^5)\)and y:

\((d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}\)

Integrating both sides with respect to x, we get:

\(e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C\)

where C is the constant of integration. Dividing both sides by \(e^{(x^5)}\), we get the general solution:

\(y = (1/5) x^5 + Ce^(-x^5)\)

where C is an arbitrary constant.

\(y = (1/5) x^5 + Ce^{(-x^5)}\) is the general solution of the given differential equation.

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Answer:

Hello! answer: 39

Step-by-step explanation:

Formula for triangles area: base × height ÷ 2

Formula for squares area: base × height

5 × 3 = 15 15 ÷ 2 = 7.5 since there are 4 triangles that are the exact same I will just multiply by 4 so I have all the triangles so 7.5 × 4 = 30 now the square is just 3 × 3 so... 3× 3 = 9 now we add these up 30 + 9 = 39 therefore the surface area is 39

Answer:

39

Step-by-step explanation:

5x3=15

15/2=7.5

7.5x4=30

3x3=9

30+9=39

We can obviously see the -2 point on the y - axis where the value of x is 0.

So the y-intercept is -2.

Now to simply find the slope.

Using the formula:

y2 - y1/x2 -  x1

Find two random points (preferably in the same quadrants):

(4, 1) and (8, 4)

Now we plug in:

8 - 4/ 4 - 1

4/1

4

Hence, the equation is y = 4x - 2.

Thanks.

The value of x , y and z in the parallel line is 50 degrees.

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

Therefore, let's use the angle relationships to find the angle, x, y and z as follows:

Therefore,

x = 360 - 310(sum of angles in a point)

x = 50 degrees

Therefore,

x = y(alternate interior angles)

Alternate interior angles are congruent.

Hence,

y = 50 degrees

Therefore,

x = z(alternate interior angles)

z = 50 degrees.

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Step-by-step explanation:

i dont know

A. pyramid has only one base, B. The base of a pyramid is a polygon, C. If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height, F. The slant height is used to calculate the lateral area.

Let’s verify all the options:

A) A pyramid has only one base.

By definition, a pyramid has only one base

So, A is TRUE

B) The base of a pyramid is a polygon.

By definition, a pyramid is a polyhedron formed by a polygonal base.

So, B is TRUE

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Given, the right pyramid and if the length of the base is known. Then, we can find the half distance of the base and it will form a right-angled triangle. Hence Pythagorean theorem can be used to find its slant height.

So, C is TRUE

D) The slant height is always the same length as the base of the pyramid.

No, the slant height is not always the same as the base of the pyramid.

So, D is FALSE

E) The lateral faces of a pyramid are rectangles.  

By definition, the shape of the lateral faces of the pyramids is triangular.

So E is FALSE

F) The slant height is used to calculate the lateral area.

The formula for the lateral surface area of the pyramid is given:

Lateral Surface Area = (P × L), where

P is the perimeter of the base

L is the slant height.

So F is TRUE

Hence the true options are A, B, C, and F.

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

Your question was incomplete. Please refer the content below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

The options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

Now, we will see all the options one by one:

option (A) A pyramid has only one base.

Yes, it is true as it can only have 1 base.

option (B) The base of a pyramid is a polygon.

Yes, it is true as the base will always be a polygon only.

option (C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Yes, it is true as Pythagoras theorem can be used in a right angles triangle which will be formed by the slant height.

option (D) The slant height is always the same length as the base of the pyramid.

No, it is false as it can be different according to the pyramids.

option (E) The lateral faces of a pyramid are rectangles.  

No, it can be triangular also.

option (F) The slant height is used to calculate the lateral area.

Yes, it is true as the formula for the lateral surface area of the pyramid is given as:

Lateral Surface Area = (P × L), where

L represents the slant height.

Therefore, the options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

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The steps that she could use to solve the quadratic equation is determined as 2(x² + 6x + 9) = 18 + 3.

We have Equation: 2x²+ 12x - 3= 0

Now, simplifying the equation as

2x² + 12x - 3 = 0

2x² + 12x = 3

divide both side by 2

x² + 6x = ³/₂

Now, take half of coefficient of x and add the square of it both sides of the equation

(x + 3)² = ³/₂ + 3²

x² + 6x + 9 = 9 + ³/₂

2(x² + 6x + 9) = 18 + 3

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Answer:

(0, 1 )

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

y - 4x = 1 ( add 4x to both sides )

y = 4x + 1 ← in slope- intercept form

with c = 1

the coordinates of the y- intercept are (0, 1 )

Answer:

Apartment 1 is his best option

Answer: Apartment 1

Step-by-step explanation:

Answer:

cot B = 48/55

Step-by-step explanation:

cot B = 48/55

Answer:I think you can say like the most bought music in class B is alternative and the lowest one is classical and so on

Step-by-step explanation:

Answer:

346.36

Step-by-step explanation:

C=piD

so the21 is theD

A=piR^2

R=D/2(1/2D)

A=22/7×21/2^2=346.36

1/13

Probability is the likelihood or chance that an event will occur. Mathematically;

Since there are 52 cards in a deck of cards, hence the total outcome will be 52.

Next is to get the expected outcome. Since we need the probability of being dealt a five and there 4 fives in a deck of cards. The expected outcome will be 4

The required probability is expressed as:

Hence the probability of being dealt a five is 1/13

If the resulting F-statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances are significantly different.

The F-test is a statistical test used to compare the variances of two groups.

In this problem, we will use it to compare the variance of the value added by the manufacturer and the variance of the cost of materials in manufacturing. The F-test is performed by dividing the larger variance by the smaller variance. The resulting F-statistic is then compared to the critical value of an F-distribution with degrees of freedom equal to the sample size minus one for each group.

Before we can perform the F-test, we need to determine which variable will be group 1. Typically, the variable with the smaller mean is designated as group 1. This is because we want to minimize the chance of making a type II error, which is failing to reject the null hypothesis when it is false. If we designated the variable with the larger mean as group 1, we might not detect a significant difference between the groups, even if one exists.

Once we have designated which variable will be group 1, we can perform the F-test. If the resulting F-statistic is greater than the critical value of the F-distribution, we reject the null hypothesis and conclude that the variances are significantly different.

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\(\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{1.45\% of 68052}}{\left( \cfrac{1.45}{100} \right)68052}\implies 986.754~\hfill \stackrel{about}{\approx 986.76}\)

The centroid of the thin plate bounded by the graphs of g(x) = x²(x-1)+2 and f(x) = x² + 2 with δ = 1 and M = area of the region covered by the plate is  = (3/2, 211/140).

To find the centroid  of the thin plate bounded by the graphs of g(x) = x²(x-1)+2 and f(x) = x² + 2 with δ = 1 and M = area of the region covered by the plate, we need to compute the following integrals:

M = ∫[0,1] (f(x) - g(x)) dx

= (1/M) ∫[0,1] x(f(x) - g(x)) dx

= (1/M) ∫[0,1] ((f(x))^2 - (g(x))^2) dx

First, let's compute M:

M = ∫[0,1] (f(x) - g(x)) dx

= ∫[0,1] [(x² + 2) - (x²(x-1) + 2)] dx

= ∫[0,1] (x³ - x²) dx

= [x⁴/4 - x³/3] from 0 to 1

= 1/12

Next, let's compute :

= (1/M) ∫[0,1] x(f(x) - g(x)) dx

= (1/(1/12)) ∫[0,1] x[(x² + 2) - (x²(x-1) + 2)] dx

= 12 ∫[0,1] x(1 - x²) dx

= 12 [x²/2 - x⁴/4] from 0 to 1

= 3/2

Finally, let's compute

= (1/M) ∫[0,1] ((f(x))^2 - (g(x))^2) dx

= (1/(1/12)) ∫[0,1] [(x² + 2)² - (x²(x-1) + 2)²] dx

= 12 ∫[0,1] [-x⁶ + 3x⁵ - 4x⁴ + 5x³ - 8x²] dx

= 12 [-x⁷/7 + 3x⁶/6 - 4x⁵/5 + 5x⁴/4 - 8x³/3] from 0 to 1

= 211/140

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Leonora made 12 number of 2-point baskets, solved using the system of equations

In the question, we are given that Leonora made 14 total baskets during her basketball game, in which she made x baskets worth 2 points each and y baskets worth 3 points each.

We are asked that if she scored 30 points total throughout the game, how many 2-points basket did she make.

Number of 2-points basket scored = x.

Number of 3-points basket scored = y.

Thus, total number of baskets scored = x + y.

But, the total number of baskets scored is given to be 14.

Thus, we get an equation x + y = 14 ... (i).

The total worth of 2-points basket scored = 2x.

The total worth of 3-points basket scored = 3y.

Thus, the total points scored = 2x + 3y.

But, the total points scored is given to be 30.

Thus, we get an equation 2x + 3y = 30 ... (ii).

(i) and (ii) together gives us a system of equation.

To solve the system of equations, we multiply (i) by 3, and then subtract (ii) from it.

3x + 3y = 42

2x + 3y = 30.

(-) (-)     (-)

__________

x = 12.

Thus, Leonora made 12 number of 2-point baskets, solved using the system of equations.

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The given statement "A synonym for pyramidal plan is cubism, which also describes the artistic emphasis on geometric shape" is False

A Pyramidal Plan is a specific kind of floor plan with a triangular shape that has a broad base and converges to a point at the top, resembling the shape of a pyramid.

Pyramidal plans can be found in many different types of buildings and structures, including churches, temples, and other religious structures, as well as some secular structures.

Cubism is a style of art that emerged in the early twentieth century and was characterized by a focus on geometric shapes and forms.

The term "cubism" comes from the fact that many of the paintings and sculptures created in this style consisted of complex shapes that were organized into a grid-like pattern that resembled a series of cubes.

However, the given statement is false. Pyramidal Plan is not a synonym for cubism as pyramidal plan has nothing to do with art or geometry.

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Answer:

3/30

Step-by-step explanation:

Answer:

c is correct answer any doubt

Answer:

(A) is your answer

Step-by-step explanation:

Solve the equation once for y and once for x...

When you solve for y, set x = 0... in this scenario, y = 2 when x = 0

Then do the opposite for when you solve for x, set y = 0....x = -5

Find those points on the graph that has the line intersecting them.

(0, 2) and (-5, 0)

The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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The type of errors and number of errors depend on the experiment, that is how it is set up and the devices that one is using for measurement.

Assuming that we are using simple lab equipments and the experiment to be performed is - dropping a ball from a fixed height and measuring the time it takes for the ball to hit the ground. Let us also consider that the distance of the ball from the ground is already known. We can think of no such complex or non-measurable errors that can occur in this  experiment if performed with utmost care.

There can be two  possible errors that can occur in this simple experiment ( excluding errors from calculations)that are as follows :

1.If using a metre rule then there can occur systematic error.

2.Random errors can occur which are actually human errors, that is the stopwatch might not be started or stopped exactly when the ball is dropped or touched the ground respectively.

If we use a light gate, digital sensors and a computer software then the above errors are eliminated or at least gets significantly reduced.

Thus the measured value for g may not be the accepted value.

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Answer:

34

Step-by-step explanation:

Based on the triangle inequality theorem, the that is false about the relationship of the side of the triangle given is: D. x = 7.

The triangle inequality theorem holds that the length of any side of a triangle is less than the sum of the length of the sides of the other two sides.

Applying the triangle inequality theorem, it means the following should be true for any value of x given:

x + 2 + x + 3 > 3x - 2

2x + 5 > 3x - 2

Plug in x = 3 to find out:

2(3) + 5 > 3(3) - 2

11 > 4 (True)

Plug in x = 1 to find out:

2(1) + 5 > 3(1) - 2

8 > 2 (True)

Plug in x = 7 to find out:

2(7) + 5 > 3(7) - 2

19 > 19 (FALSE)

Therefore, the false statement is: D. x = 7.

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Answer:

46.80

Step-by-step explanation:

because 45/4%=1.80 and 45+1.80=46.80

Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

gusto Kita Alam muba

Step-by-step explanation:

gusto Kita ok lang ba I don't know what is the answer

The standard deviation of the data set 6.5, 11.2, 13, 6.3, 7, 8.8, and 7.4 is 2.98, rounded to the nearest hundredth.
To find the standard deviation of the given data set {6.5, 11.2, 13, 6.3, 7, 8.8, 7.4}, follow these steps:

1. Calculate the mean (average) of the data set:
  (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4) / 7 = 60.2 / 7 = 8.6

2. Find the difference between each data point and the mean, then square each difference:
  (6.5 - 8.6)^2 = 4.41
  (11.2 - 8.6)^2 = 6.76
  (13 - 8.6)^2 = 19.36
  (6.3 - 8.6)^2 = 5.29
  (7 - 8.6)^2 = 2.56
  (8.8 - 8.6)^2 = 0.04
  (7.4 - 8.6)^2 = 1.44

3. Find the average of these squared differences:
  (4.41 + 6.76 + 19.36 + 5.29 + 2.56 + 0.04 + 1.44) / 7 = 39.86 / 7 = 5.694

4. Take the square root of the average squared difference:
  √5.694 = 2.39 (rounded to the nearest hundredth)

The standard deviation of the data set is approximately 2.39.

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