Consider the function f(x)=15x^2+60x-19
Name the vertex for the function

The curl and the divergence of the vector field is illustrated below.

The term vector in math contains both position and magnitude.

Here we need to find the curl and the divergence of the vector field.

While we looking into the given question, we have the function

=> F(x, y, z) = <ex, exy, exyz>

AS per the concept of convergence, here we have consider that F=⟨P,Q,R⟩  is a vector field in  R3  and  Px, Qy,  and  Rz  all exist here then the divergence of F is defined by as,

=> div F = Px + Qy + Rz

=> div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z.

The term curl in vector field is defined as a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space

And the curl of the vector field is calculated as,

=> curl F = (Ry−Qz)i + (Pz−Rx)j + (Qx−Py)k

=> curl F = (∂R/∂y−∂Q/∂z)i + (∂P/∂z−∂R/∂x)j + (∂Q/∂x−∂P/∂y)k.

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Answer:

The graph f(x)=2×+3 will have y-intercepts of (0,3) and a slope of 2.

In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.

There are 3 main rules:

Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below.

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According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

According to the SSS rule, two triangles are considered to be congruent if the corresponding three sides of each triangle are equal to each other.

The triangles are congruent if all three sets of comparable sides are present.

The side-side-side shortcut is a congruence technique (SSS).

Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.

Therefore, according to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle.

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(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

What is a direct variation?

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation.

In the given question, M is directly proportional to r²

M ∝ r²

M = kr²

Now When r = 2, M = 14,

k = 14/(2)²

k = 7/2

(a) When r = 12,

   M = (7/2)(12)² = (7/2)*144 = 72 * 7

  M = 504

(b)When M = 224,

  224 = (7/2)r² = (224*2)/7 = 32 * 2

  M = 64

Hence,

(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

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The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:

What is the partial quotient method?

when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.

The final quotient of 84÷4 as follows:

84÷4 =21

hence the sum of quotients is 21.

The possible combinations are only two.

The other combinations are incorrect.

7 is a constant value and it is a polynomial of degree 0.

7 is a polynomial.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

7

This can be assumed as 0x³ + 0x² + 0x + 7.

This is a polynomial.

Thus,

7 is a polynomial.

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The correct sentence is C, "-3 > -8."

Here's how you can determine which sentence is correct:

In sentence A, -3 is not greater than 2, so sentence A is incorrect.

In sentence B, -3 is not less than -6, so sentence B is incorrect.

In sentence C, -3 is indeed greater than -8, so sentence C is correct.

In sentence D, -3 is not greater than -2, so sentence D is incorrect.

Remember that when comparing two negative numbers, the one with the smaller absolute value is the larger negative number. For example, -8 is a larger negative number than -3 because -8 is closer to 0 (which is the smallest possible number). Similarly, -2 is a larger negative number than -3 because -2 is closer to 0.

Hence, The correct sentence is C, "-3 > -8."

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Answer:

[tex]b=\dfrac{2V}{ah}-c[/tex]

Step-by-step explanation:

Given equation:

[tex]V=\dfrac{1}{2}a(b+c)h[/tex]

Multiply both sides of the equation by 2:

[tex]\implies 2 \cdot V=2 \cdot \dfrac{1}{2}a(b+c)h[/tex]

[tex]\implies 2V=a(b+c)h[/tex]

Divide both sides by ah:

[tex]\implies \dfrac{2V}{ah}=\dfrac{a(b+c)h}{ah}[/tex]

[tex]\implies \dfrac{2V}{ah}=b+c[/tex]

Subtract c from both sides:

[tex]\implies \dfrac{2V}{ah}-c=b+c-c[/tex]

[tex]\implies \dfrac{2V}{ah}-c=b[/tex]

Therefore:

[tex]\implies b=\dfrac{2V}{ah}-c[/tex]

The unit conversion from celsius to fahrenheit is given by the formula

F = (9/5)C + 32.

The same attribute is expressed using a unit conversion but in a different unit of measurement. For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other measurement unit instead of miles.

We know we can convert temperatures from celsius to fahrenheite or from fahrenheite to celsius.

The conversion of celsius to fahrenheit is given by the formula,

C = (5/9)(F - 32).

Now, we have to solve for F.

C = (5/9)F - (160/9).

Now to get rid of the fraction we'll multiply 9 to each term.

9C = 5F - 160.

5F = 9C + 160.

Solving for F we have,

F = (9/5)C + 32.

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The figure is attached.

The axis of symmetry is a straight line that makes the shape of the object symmetrical. The axis of symmetry creates the exact reflections on each of its sides.

Given that, draw line segment AB and find its axis of symmetry​

Let's first draw a line segment of length 7.3 cm.

1) Draw a line l, mark point A on it.

2) Since length is 7.3 cm, we measure 7.3 cm using ruler and compass.

3) Now, keeping compass opened the same length, we keep pointed end at point A and draw an arc on line l.

So, the required line segment is AB = 7.3 cm.

Now, we need to find its axis of symmetry.

1) Given a line segment AB.

2) Now with A as centre, and radius more than half AB, draw an arc on top and bottom of AB.

3) Now with B as centre, and same radius, draw an arc on top and bottom of AB.

4) Where the two arcs intersect above AB is point C and where the two arcs intersect below AB is point D.

Join CD.

CD is the line of symmetry of line segment AB.

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The equation for adding "n" numbers in a row is [a + (a + 1) + (a + 2) +.... a + (n-1)]. As a result, (n/2) (first number + last number) is the sum of "n" consecutive numbers or "n" terms of AP (Arithmetic Progression). The formula for even consecutive numbers is 2n, 2n+2, 2n+4, 2n+6, and so on.

The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11. Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.

Any collection of consecutive odd numbers starting with 1 has a sum that is always equal to the square of the total number of digits. If the numbers 1, 3, 5, 7, 9, 11,..., and (2n-1) are odd, then the sum of the first odd number is 1. First two odd numbers added together equal 1 + 3 = 4 (4 = 2 x 2). Two successive odd numbers added together are always divisible by 4.

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Answer:

x=4.6 answer is at most 4 people can go

Step-by-step explanation:

32.50x+10.50=160.00

- 10.50 -10.50

149.50

32.50x = 149.50

Divide 32.50 and 149.50 to find x.

x = 4.6 round down because you cant have a fraction of a person. so 4 people can go.

Answer:

the answer it's-7a^5+10m

Answer:

10$

Step-by-step explanation:

Because if you divide you get 10$ per hour so if you divide 50 by 5 = 10 so your answer is 10$.

Hope this helps :D

Answer:

A.  50

Step-by-step explanation:

a + b = 90

b = 90-50 = 40

b + c = 90

c = 90-40 = 50

The volume of a pyramid that has the same base and height if a prism has a volume of 45 m cube is 15 cu. m.

In this question we have been given the volume of a prism which is of 45 m cube.

we need to find the volume of a pyramid that has the same base and height.

We know that the formula of the volume of prism is:

V = base area * height of prism  

From given, V = 45 m^3

But as we know prism and pyramid have same base area and height.

We know that the formula for the volume of pyramid.

volume of pyramid = 1/3 * base area * height

volume of pyramid = 1/3 * V

volume of pyramid = 1/3 * 45

volume of pyramid = 15 cubic meter

Therefore, the volume of pyramid is 15 m^3

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C. The amount he gained each month in order from least to greatest is One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.

Sam recorded how many pounds he gained each month for four months and recorded. First, we need to convert the fractions into decimals. One-eighth is equal to 0.125, two-fifth is equal to 0.4, and the tart fraction 5 over 6 end fraction is equal to 0.833.

Therefore, the amounts gained each month in order from least to greatest are 0.125, 0.75, 0.4, and 0.833.4. The correct answer is C. One-eighth, 0. 75, two-fifth, tart fraction 5 over 6 end fraction.

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Answer:

x = 3 and JL = 18

Step-by-step explanation:

JN and NL are equal to each other so set both equations equal to each other
15 - 2x = 4x - 3

solve for x by moving terms to other side

x = 3

plug in 3 for x in JN's equation

JN = 15 - 2(3)

JN = 9

Since JN and NL are equal to each other, JL is just the sum of those two lengths combined

so all you have to do is double JN

9 x 2

is 18

so JL is 18

Answer:

The circumference of a circle is given by the formula $C = 2\pi r$, where $r$ is the radius of the circle. In this case, the circumference of the circle is $13\pi$ cm, so we can set up the equation $13\pi = 2\pi r$ to solve for the radius. Dividing both sides by $2\pi$, we get $r = \frac{13\pi}{2\pi} = \frac{13}{2}$ cm. The area of a circle is given by the formula $A = \pi r^2$, so the area of this circle is $A = \pi \left(\frac{13}{2}\right)^2 = \frac{169}{4}\pi$ square cm. Therefore, the area of the circle is $\frac{169}{4}\pi$ square cm.

Step-by-step explanation:

Answer:

so to mu calculation I prideict your answer is 10

Answer:

Step-by-step explanation:

Given 64 feet of fencing that can be used for three sides of a rectangular enclosure next to a barn wall, you want a function for area in terms of enclosure width, the width that maximizes area, and the maximum area.

If we define the width (x) as the dimension parallel to the barn wall, then the fence available for the "height" (out from the barn wall) is (64-x) in length. Half that is used on either end of the enclosure, so the area is ...

  A = WH

  A(x) = x(64 -x)/2

We notice this function describes a parabola that opens downward, with zeros at x=0 and x=64. The vertex (maximum) is on the line of symmetry, halfway between the zeros:

  x = (0 +64)/2 = 32

The width that maximizes area is x = 32 ft.

Using x=32 in the area formula, we find the maximum area to be ...

  A(32) = 32(64 -32)/2 = 1024/2 = 512 . . . . square feet

The maximum area is 512 square feet.

__

Additional comment

Perhaps you can see that the best width is half the length of the available fence. The other half of the fence is used for the ends of the enclosure. This is the generic solution to this kind of problem.

The first 20 multiples of 27 are as follows:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

A multiple in mathematics is created by multiplying any number by an integer.

In other words, if b = na for some integer n, known as the multiplier, it can be said that b is a multiple of a given two numbers, a and b.

This is equivalent to stating that b/a is an integer if an is not zero.

A is known as a divisor of b when a and b are both integers and b is a multiple of a.

First 20 multiples of 27:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

Therefore, the first 20 multiples of 27 are as follows:

27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, and 540.

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Correct question:

What are the first 20 multiples of 27?

It is formed by simply drawing lines connecting the data points. Also called linear chart.

A line chart is a graphical representation of changes that occur over a period of time. A line chart has a horizontal axis called the x-axis and a vertical axis called the y-axis. The x-axis usually has a period of time over which we want to measure the quantity of a particular thing or item on the y-axis. Line charts are useful for analyzing trends, whether the quantity on the y-axis is increasing or decreasing over time. A line chart clearly shows an uptrend or a downtrend.

The line chart above represents bike sales by bike company from January to June, with the x-axis representing the time interval and the y-axis representing the number of bikes sold per month. Black dots in the graph indicate data points. A data point in a line chart represents the magnitude or number corresponding to a specific time on the x-axis. In this example, 50 bikes were sold in January. 30 bikes were also sold in February. This data can be interpreted by month using data points. Line segments connecting these individual data points show whether bike sales are trending upwards or downwards.

The key points of line charts are:

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The given data is 24,26,23,26,22,25,26,28

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 24-1 the number 24 appears only 1 time.

2. 26-3 the number 26 appears three times.

3. 23-1 the number 23 appears only one time.

4. 22-1 the number 22 appears only one time.

5. 25-1 the number 25 appears only one time.

6. 28-1 the number 28 appears only one time.

So, the mode of the given data is 26 as it appears the most number of times.

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The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

A score that is 3 standard deviations above the mean is consider as a very high score relative to the rest of the scores in the population.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The sum of all values divided by the total number of values determines the mean  of a dataset.

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A. From the Limit Comparison Test, the series converges conditionally.

The Limit Comparison Test can be used to determine whether a given series converges or diverges. In this case, the given series is sigma^infinity_k = 0 9(-1)^k/k^4 + 2.

To use the Limit Comparison Test, we need to compare the given series to a known series. For example, we can compare it to the series sigma^infinity_k = 1/k^4.

We can then calculate the ratio of the two series:

sigma^infinity_k = 0 9(-1)^k/k^4 + 2

sigma^infinity_k = 1/k^4

Ratio: sigma^infinity_k = 0 9(-1)^k / (1/k^4)

Since the limit of the ratio of two series is a finite number, the given series converges. However, since the ratio is not 1, it converges conditionally, not absolutely.

Therefore, the answer is A - From the Limit Comparison Test, the series converges conditionally.

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Answer:

d = 18

Step-by-step explanation:

d = square root (x2 -  x1)^2 + (y2 - y1)^2

Point A ( -1,2) Point B (1,-2)

Now let's put the number in

d = square root ( 1 -(-1)^2 + (-2 - 2)^2

Now let's get rid of the square root, and we have

(1-(-1) + (-2 -2)^2

2 + (-4)^2

2 + 16

18

So, the distance AB = 18

Answer:

[tex]AB = 4.5[/tex]

Step-by-step explanation:

⭐To find the distance between two points, you can use the distance formula: [tex]d = \sqrt{(x_2-x_1)^2 +(y_2 - y_1)^2}[/tex], where:

First, identify the coordinates you need to find the distance between, and label one coordinate as [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

Next, substitute [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] into the distance formula.

[tex]d = \sqrt{(1-(-1))^2+(-2-2)^2}[/tex]

[tex]d = \sqrt{(1+1)^2+(-4)^2}[/tex]

[tex]d = \sqrt{2^2+(-4)^2}[/tex]

[tex]d = \sqrt{4+16}[/tex]

[tex]d = \sqrt{20}[/tex]

∴ d ≈ 4.5

Answer:

     [-9,0]

Step-by-step explanation:

Look along the y inercept and find where the lines end

plus they are solid circles so it'd be closed

Answer: see below

Step-by-step explanation:

The range is the set of possible output values shown on the y-axis.

This graph's maximum y value, or the highest y value, is 0. The lowest y value is -9

R:yE[-9,0]