w+(-4)=37
what is the w

The average rate of change of the given function is 10π.

Given function

a = πx^2

Where a is the area of a circle with radius x

The radius changes from x = 4 to x = 6.

Calculating the average rate of change of function:

The method of finding the average rate between the function value over a certain interval is called the average rate of change.

The formula is given by :

Average = \(\frac{f(b)-f(a)}{b-a}\)

Where f(a) and f(b) are the function value over the limit a and b.

Average = \(\frac{f(6)-f(4)}{6-4}\)

= \(\frac{\pi (6)^{2} -\pi (4)^{2} }{6-4}\)

= \(\frac{\pi (36-16)}{2}\)

= \(\frac{20\pi }{2}\)

= 10π

The average rate of change of the given function is 10π.

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Bleeding Kansas was a result of the conflict between pro-slavery and anti-slavery forces, fueled by westward expansion and popular sovereignty, resulting in violence in and around the anti-slavery center, Lawrence, and involving militant abolitionist John Brown, highlighting the deep divisions and paving the way for the Civil War.

In the 1850s, Kansas became a battleground for pro-slavery and anti-slavery forces, with each side hoping to gain control of the territory in order to influence the balance of power in Congress.

This conflict was fueled by a number of factors, including westward expansion, manifest destiny, and the idea of popular sovereignty, which held that the people of a given territory should be allowed to decide for themselves whether to allow slavery.

As tensions rose, violence erupted in and around the town of Lawrence, Kansas, which was seen as a center of anti-slavery sentiment. Pro-slavery forces attacked the town, burning buildings and killing several people, leading to the name "Bleeding Kansas" being attached to the area. John Brown, a militant abolitionist, played a key role in these events, leading a group of supporters in a retaliatory raid on a pro-slavery settlement.

The situation in Kansas highlighted the deep divisions between pro-slavery and anti-slavery forces in the United States and helped to pave the way for the Civil War. While the conflict in Kansas was ultimately resolved in favor of the anti-slavery forces, it came at a high cost in terms of human life and suffering.

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The coordinates of the other two vertices are (-c/m, 0) and (-d/n, 0).

The coordinates of the two lines intersecting at (-3, 1) can be represented as (x, mx + c) and (x, nx + d), where m, c, n, and d are constants.

To form an equilateral triangle, the distance between the y-intercepts of the two lines should be equal to the distance between the y-intercept and the point of intersection.

Let's calculate the distance between the y-intercept and the point of intersection:

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Considering the y-intercept for the first line is (0, c), and for the second line is (0, d), the distance between the y-intercept and the point of intersection is:

sqrt((-3 - 0)^2 + (1 - c)^2) = sqrt((-3 - 0)^2 + (1 - d)^2)

Simplifying the equation, we get:
(-3)^2 + (1 - c)^2 = (-3)^2 + (1 - d)^2

Simplifying further, we find:
(1 - c)^2 = (1 - d)^2

Taking the square root of both sides, we have:
1 - c = 1 - d

Simplifying, we find:
c = d

Therefore, the y-intercepts of the two lines are equal.

Now, let's find the coordinates of the other two vertices:

The y-intercept of each line is equal to the y-coordinate of the point of intersection, which is 1.

For the first line, the y-intercept is (0, 1). The x-intercept can be calculated by substituting y = 0 into the equation mx + c = 0, which gives us:
mx + c = 0
mx = -c
x = -c/m

So, the coordinates of the first vertex are (-c/m, 0).

For the second line, the y-intercept is also (0, 1). Similarly, the x-intercept can be calculated by substituting y = 0 into the equation nx + d = 0, which gives us:
nx + d = 0
nx = -d
x = -d/n

So, the coordinates of the second vertex are (-d/n, 0).

Therefore, the coordinates of the other two vertices are (-c/m, 0) and (-d/n, 0).

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Amy will choose the second restaurant to purchase pizza. Because the second one is cheaper.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given,

the first restaurant charges a delivery fee of $6 for the entire purchase and $13 per pizza.

The second restaurant has no delivery fee and charges $16 per pizza.

And Amy will choose between two restaurants to purchase pizzas for her party.

The cost of one pizza of the first restaurant:

Cost = delivery fee + price of one pizza

        = $6 + $13

         = $19

The cost of one pizza of the second restaurant:

Cost = delivery fee + price of one pizza

          = $0 + $16

         = $16

And 16< 19

The second restaurant is cheaper.

Therefore, Amy will choose the second restaurant to purchase pizza.

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An engineer is designing a fuel tank in the shape of a cylinder, the approximate radius of the cylinder is 8.2 inches.

Volume:

V = πr²h

Height:

h = 2r

V = πr²h

V= πr²(2r)

V= 2πr³

And we know that the volume must be 3,500 in³, now we can replace that and solve for R, we will get:

V= πr²h

3500 = 3.14 x 2 x (r)³

r = 8.2 inch

The cylinder's approximate radius must be 8.2 inches.

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In several contemporary fields of geometry and topology, a cylinder can alternatively be characterised as an infinitely curved surface.

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Answer:

4

Step-by-step explanation:

The sum of first 10 terms is 72.

Concept: Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.

Arithmetic Progression Formula

= an - a. nth term of an AP: an = a + (n - 1)d. Sum of n terms of an AP: Sn = n/2(2a+(n-1)d) = n/2(a + l), where l is the last term of the arithmetic progression.

Given:

Eighth term is 8.2

Common difference is 0.4

a(8) = 8.2

a + 7d = 8.2

Since d = 0.4

a + 7(0.4) =8.2

a = 5.4

Sum of 10 terms = n/2 (2a+(n-1)d)

= 5(2*5.4 + 9*0.4)

=5(10.8 +3.6)

Sum=72

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Answer:

y - 1 = (-2/3)(x + 9)

Step-by-step explanation:

Here you are given a point on a line and the slope of the line.  You'll need to apply the "point-slope" formula

y - k = m(x - h) (Memorize this)

Then m = slope = -2/3, h = -9 and k = 1.

Making the appropriate substitutions, we get:

y - 1 = (-2/3)(x + 9)

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The number 2.5 represents the amount of money required to go on 1 ride.

therefore, the correct choice is :

Answer:

the second option

Step-by-step explanation:

because 2.5 approximately 1

The better buy is given by the following brand:

Brand A.

The better buy is obtained applying the proportions in the context of the problem.

A proportion is applied as the cost per ounce is given dividing the total cost by the number of ounces.

Then the better buy is given by the option with the lowest cost per ounce.

The cost per ounce for each brand is given as follows:

$8 per ounce is a lesser cost than $9.3 per ounce, hence the better buy is given by Brand A.

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Answer:

Step-by-step explanation:

The translated point of the given point P will be ( 4, - 2 ).

The process of changing the location of the image on the coordinate system will be known as the translation.

Given that the point has coordinates of ( -1, 5 ) is translated by 5 units to the right and 7 units down.

The translated point will be calculated as below:-

( -1, 5 ) ⇒ ( -1 + 5 , 5 - 7 )

( -1, 5 ) ⇒ ( 4, -2 )

The point is also plotted on the graph that is attached with the answer below.

Therefore, the translated point of the given point P will be ( 4, - 2 ).

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The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

The slope of the secant line PQ can be found by calculating the difference in y-coordinates divided by the difference in x-coordinates between the points P and Q. In this case, when x = 16.1, the slope of PQ can be determined.

To find the slope of the secant line PQ, we need to calculate the difference in y-coordinates and the difference in x-coordinates between the points P(16, 9) and Q(x, √(x) + 5). The slope of a line is given by the formula: slope = (change in y) / (change in x).

Given that P(16, 9) lies on the curve y = √(x) + 5, we can substitute x = 16 into the equation to find the y-coordinate of point P. We get y = √(16) + 5 = 9.

Now, for Q(x, √(x) + 5), we have x = 16.1. Substituting this value into the equation, we find y = √(16.1) + 5.

To find the slope of PQ, we calculate the difference in y-coordinates: (√(16.1) + 5) - 9, and the difference in x-coordinates: 16.1 - 16. Then, we divide the difference in y-coordinates by the difference in x-coordinates to obtain the slope of PQ when x = 16.1.

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Answer:

Idaho

Step-by-step explanation:

Answer:

2) 45

3) 25

4) 50%

5) 33.3%

6) 17.6

7) 500

8) 35%

9) 60

10) 87.5%

11) 2.64

12) 25%

13) 5.7

14) 85%

16) 75%

Step-by-step explanation:

2) 9 = 20% of x

9 * 5 = 45

3) 8% of x = 2

12.5 * 2 = 25

4) 39 = x(78)

39/78 = 1/2 = 50%

5) x(36) = 12

12/36 = 1/3 = 33.3...%

6) x = 0.8(22)

22/10 = 2.2

2.2* 8 = 16 + 1.6 = 17.6

7) 55 = 0.11(x)

55/11 = 5

5 * 100 = 500

8) 7/20 = 35/100 = 35%

9) 27 = 0.45(x)

27/45 = 3/5

3/5 * 100 = 300/5 = 60

10) . 49/56 = 7/8 = 0.875 = 87.5%

11) 6/100 = 0.06

0.06 * 44 = 2.64

12) 48/192 = 6/24 = 1/4 = 25%

13) 95/100 = 0.95

0.95 * 6 = 5.40 + 0.3 = 5.7

14) 68/80 = 34/40 = 17/20 = 85%

16) 108/144 = 9/12 = 0.75 = 75%

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

- 1

Step-by-step explanation:

Using the trigonometric identity

cos(- x) = cosx and exact value cos60° = \(\frac{1}{2}\)

Given

f(x) = - 2cosx , then

f(- 300° )

= - 2cos(- 300)°

= - 2cos(300)°

= - 2cos(360 - 300)°

= - 2cos60°

= - 2 × \(\frac{1}{2}\)

= - 1

Answer:

a) x=3

y=6*3+4

=22

b) x=4

y=6*4+4

=24

c) x=6

y=6*6+4

=40

d) x=7

y=6*7+4

=46

Answer:

y = 2

Step-by-step explanation:

Given

y = x² + 2x + 3 ← substitute x = - 1

y = (- 1)² + 2(- 1) + 3 = 1 - 2 + 3 = 2

Answer:

x < -17/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

-46 - 8x > 22

Step 2: Solve for x

Answer: x < −17/2

Step-by-step explanation:

Let's solve your inequality step-by-step.

−46 − 8x > 22

Step 1: Simplify both sides of the inequality.

−8x − 46 > 22

Step 2: Add 46 to both sides.

−8x − 46 + 46 > 22 + 46

−8x > 68

Step 3: Divide both sides by -8.

−8x/−8 > 68/−8

x < −17/2

The equation of the trajectory which can be described using the equations for projectile motion is; y(t) = x·tan(θ) - g·x²/(2·v₀²·cos²(θ)), which is a quadratic equation with a path of a parabola

Projectile motion is the motion of an object that is projected in the air under the influence of gravitational attraction.

Let θ represent the angle at which the path of the object makes with the horizontal, and let v₀ represent the velocity of the object. The path of the object can be described using the equations of the motion of a projectile, as follows;

Horizontal component of the velocity, v₀ₓ = v₀ × cos(θ)

Vertical component of the velocity, \(v_{0y}\) = v₀ × sin(θ)

The horizontal motion of the object is therefore;

x(t) = v₀ₓ × t = v₀ × cos(θ) × t

The vertical motion which is under the influence of gravity is; y(t) = \(v_{0y}\)  × t - (1/2) × g × t²

v₀ × sin(θ) × t - (1/2) × g × t²

The horizontal component indicates that we get;

t = x/(v₀ × cos(θ))

Plugging in the above expression for t into the equation for y(t), we get;

y(t) = \(v_{0y}\)  × t - (1/2) × g × t² = \(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

\(v_{0y}\)  × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = (v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))²

(v₀ × sin(θ)) × x/(v₀×cos(θ)) - (1/2) × g × (x/(v₀×cos(θ)))² = x·tan(θ) - g·x²/(2·v₀×cos(θ))²

The equation, y = x·tan(θ) - g·x²/(2·v₀×cos(θ))², is a quadratic equation, which is an equation of a parabola, therefore, the trajectory of an object thrown at an angle to the horizontal is a parabola.

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Answer: $300

Step-by-step explanation:

To calculate the total revenue from selling oranges, we need to multiply the amount of oranges sold by the price per pound.

In this case, we sold 100 pounds of oranges at $3 per pound. So, the total revenue for that day is:

Total revenue = Amount of oranges sold × Price per pound

Total revenue = 100 pounds × $3

Total revenue = $300

Answer:

20 units squared

Step-by-step explanation:

Using pythagorean theorum, we can find the hypotenuse(the long side). \(\sqrt{2^2 + 4^2} = \sqrt{20}\). Since the area of a square is one of the sides multiplied by itself, we get 20 units squared

SOLUTION

From the question, we are given

Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as

But writing the forces in vector form, we have

Applying the formula above, we have

Now, theta becomes

hence the answer is option B, 53 degrees

SOLUTION

From the question, we are given

Now, to find the angle between the ropes, we will take the dot product of two vectors. This is given as

But writing the forces in vector form, we have

Applying the formula above, we have

Now, theta becomes

hence the answer is option B, 53 degrees

The first option is correct. There is no significant difference in the purchasing patterns across career types

In order for a dataset to be a valid representation of the total population, it needs to be collected in a way that ensures that it is a fair and accurate sample of the population.

One way to ensure this is through random sampling, where individuals are selected to participate in the study without any bias or preconceived notions about their characteristics. This helps to reduce the potential for selection bias and ensures that the sample is representative of the larger population.

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Answer:

Length is approximately 7.073 m

Step-by-step explanation:

One of the formulas we can use for surface area of a triangular prism is:

SA = bh + L(s1 + s2 + s3), where

So far, we know that the surface area is 297 and the height is 8.7.

Step 1:  We see that the line indicating the height splits the larger triangle into two right triangles, Thus, we can find the base of one of the right triangles using the Pythagorean theorem and multiply this by 2 to find the measure of the entire base.

The Pythagorean theorem is:

a^2 + b^2 = c^2, where

We have the measure of one leg (8.7 m) and the hypotenuse (10 m) and we must solve for leg:

a^2 + 8.7^2 = 10^2

a^2 + 75.69 = 100

a^2 = 24.31

a = √24.31 m

Multiplying this by 2 gives us that the measure of the entire base is 2√24.31 m.

Step 2:  Now we can plug in 297 for sa, 2√24.31 for b, 8.7 for h, and 10, 10, and 2√24.31 for s1, s2, and s3 respectively.  This will allow us to solve for L, the length of the triangular prism:

\(297 = (2\sqrt{24.31})(8.7)+L(10+10+2\sqrt{24.31})\\ 297=(17.4\sqrt{24.31})+L(20+2\sqrt{24.31} \\297-(17.4\sqrt{24.31})=L(20+2\sqrt{24.31})\\ (297-(17.4\sqrt{24.31}))/(20+2\sqrt{24.31})=L\\ 7.073063761=L\\ 7.073=L\)

Thus, the length of the missing side is approximately 7.073 m

Optional Step 3:  We can check that we've found the correct length of the missing side by plugging in 7.073 for L in the surface area formula and checking that we get 297 (or at least something very close to it):

297 = (2√24.31)(8.7) + 7.073(10 + 10 + 2√24.31)

297 = (17.4√24.31) + 7.073(20 + 2√24.31)

297 = (17.4√24.31) + 141.46 + 14.146√24.31

297 > 296.998096

You get approximately the same answer since we rounded the length to the nearest thousandth.  If you were to plug in a more exact answer like ((297 - (17.4√24.31)) / (20 + 2√24.31) for L, you'd get exactly 297 as I plugged this in for L on my TI-84 and got 297 exactly.

True. solving quadratic equations by completing the square is a legitimate and commonly used technique in algebra.

This method involves transforming a quadratic equation into a super square form, that could then be effortlessly solved for the variable. The procedure entails including or subtracting a constant term to both sides of the equation to create a perfect rectangular trinomial.

Which may be factored right into a binomial squared. the solution can then be acquired with the aid of taking the square root of both sides and solving for the variable. completing the rectangular is a beneficial method for fixing quadratic equations that can't be factored the usage of other strategies, which includes the quadratic formula.

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You can put 14 boxes of candy weighing 3/4 lb each in the bin.

To determine how many 3/4 lb boxes of candy can fit in a bin, we divide the total weight of the bin by the weight of each box.

First, let's convert the mixed number 10 1/2 lbs to an improper fraction.

10 1/2 lbs = (10 * 2 + 1) / 2 = 21/2 lbs

Next, we divide the total weight of the bin (21/2 lbs) by the weight of each box (3/4 lb):

(21/2 lbs) / (3/4 lb) = (21/2) * (4/3) = (21 * 4) / (2 * 3) = 84/6 = 14

As a result, you can fill the bin with 14 boxes of sweets that each weigh 3/4 lb.

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Answer:

The correct answer is c, Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

We want to study the possible solutions of a system of equations where one equation is a parabola and the other equation is a line.

We will see that the correct option is A:

"Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9."

-----------------------------------------

Here we have the system of equations:

Isabel claims that one of the solutions to the system must always be the vertex of the parabola.

Now, the solutions of the system are the points where both graphs intersect, so to find the solutions we can write:

(x + 3)^2 = y = m*x + 9

Then the solutions can be found by solving:

(x + 3)^2  = m*x + 9

Now, the vertex of the parabola is at x = 0, so to test Isabel claim, we can evaluate the above expression in x = 0 to get:

(0 + 3)^2  = m*0 + 9

3^2 = 9

9 = 9

This is true, so Isabel is correct, there will always be a solution and that solution is the vertex of the given parabola.

Then the correct option is:

A: Isabel is correct because the y-intercept of line B is (0, 9) and the value of y when x = 0 in parabola A is 9.

(Option B is incorrect because the y-intercept of line B is written incorrectly there).

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The volume of cylindrical tin is 1584 \(cm^3\). The depth of the oil in the tin is 9cm.

\(V_1 =\) VOLUME OF CYLINDRICAL TIN

   \(= \pi r^2 h\)

  \(=\frac{22}{7}\) x 6 x 6 x 14

  = 44 x 36

  = 1584 \(cm^3\)

\(V_2 =\) VOLUME OF RECTANGULAR TIN

    = lbh = 1584

    = (16)(11)(h) = 1584

    = 176h =1584

    = h = 1584 / 176

    = h = 9 cm

A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.

To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.

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Answer:

23+32−5+12 is the equaequation simplified

Step-by-step explanation: