Area of irregular shapes

The equation of the path of the parabola is y = a(x - 13)² + 27

Given data ,

To represent the path of Al's toss, we can assume that the path is a parabolic trajectory.

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

where (h, k) represents the vertex of the parabola

Now , the balloon was released from the 10-yard line and landed at the 16-yard line, we can determine the x-values for the vertex of the parabola.

The x-coordinate of the vertex is the average of the two x-values (10 and 16) where the balloon was released and landed:

h = (10 + 16) / 2 = 13

Since the height of the balloon reached 27 yards, we have the vertex point (13, 27)

Now, let's substitute the vertex coordinates (h, k) into the general equation:

y = a(x - 13)² + k

Substituting the vertex coordinates (13, 27)

y = a(x - 13)² + 27

To determine the value of 'a', we need another point on the parabolic path. Let's assume that the highest point reached by the balloon is the vertex (13, 27).

This means that the highest point (13, 27) lies on the parabola

Substituting the vertex coordinates (13, 27) into the equation

27 = a(13 - 13)² + 27

27 = a(0) + 27

27 = 27

Hence , the equation representing the path of Al's toss is y = a(x - 13)² + 27, where 'a' can be any real number

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Answer:

The rate of change is - 1/4

The number of men living in the village is 260.

A collection of many linear equations that include the same variables is referred to as a system of linear equations. A linear equation system is often composed of two or more linear equations with two or more variables.A linear equation with two variables, x and y, has the following general form:

                                           \(ax + by = c\)

Given:

Total inhabitants in the village: 817

Number of children: 241

There are 56 more women than men in the village

Total adults = Total inhabitants - Number of children

Total adults = 817 - 241

Total adults = 576

Let number of men in the village be 'x' and number of women in the village be 'y',

∴ y=x+56 (given) ..................(1)

Also, x+y=576 .................(2)

From equation (1) and (2),

x + (x + 56) = 576

2x + 56 = 576

2x = 576 - 56

2x = 520

x = 520 / 2

x = 260

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The inequality is 0.2x + 0.3y ≤ 24 and the x intercept is 120 cinnamon rolls.

Inequality is an expression that is used to show the non equal comparison of numbers and variables.

Let x represent the ice cones and y represent the cinnamon rolls.

Given that Sam has $24 to use in purchasing supplies, hence:

The x intercept is at y = 0, hence:

0.2x + 0.3(0) ≤ 24

x ≤ 120

The inequality is 0.2x + 0.3y ≤ 24 and the x intercept is 120 cinnamon rolls.

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16 percentage of the unknown number is 73.6

To solve the problem, we can use the relationship between percentages and multiply/divide by factors of 100.

Let's start by finding the whole number that corresponds to 1% of the unknown number

1% of the number = 4.6

100 times 1% of the number = 100 x 4.6

Whole number corresponding to the unknown number = 460

We can now use this value to find 5% of the unknown number:

5% of the number = 5/100 x the number = (5/100) × 460 = 23

So we have confirmed that the number we found is correct.

Finally, to find 16% of the number, we can use the same approach

16% of the number = 16/100 x the number = (16/100) × 460 = 73.6

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Answer:

false

Step-by-step explanation:

This is because the ones that most likely have a computer are going to play and the ones that dont arent going to play.

Answer:

def random(dkh):

varb= []

for dkh in dkh:

varb.sum()

print(dkh)

Answer:

1 hour

Because 3 - 2  = 1.

Therefore, 1 hour only.

Answer:

40°

Step-by-step explanation:

Given l \\ m,

m∠13 = m∠7 (alternate interior angles)

m∠13+m∠15 = 180° (Sum of angles in a straight line)

\(6x+4+(14x-4)=180\\6x+4+14x-4=180\\20x=180\\x=\frac{180}{20} \\=9\\\\\)

Substitute x to find m∠13

m∠13= 6x+4 = 6(9)+4 = 36 + 4 = 40°

Answer:

-8r-4

Step-by-step explanation:

2(-2-4r)=?

2(-2)= -4

2(-4r)= -8r

2(-2-4r)=-8r-4

Answer:

brainliest plssssssss

Step-by-step explanation:

2(−2−4r)

=(2)(−2+−4r)

=(2)(−2)+(2)(−4r)

=−4−8r

=−8r−4

its letter b. 120 degrees

To  calculate unit vector online we have to divide the original value of the vector by its magnitude.

A vector with a length of one is known as a unit vector. A direction vector is a unit vector that represents a spatial direction.

It is possible to determine the unit vector along the same direction if you are given an arbitrary vector. To accomplish it, use the following formula:

û = u / |u|,

Our distance calculator can be used to determine a vector's magnitude, or you can use the straightforward equation:

|u| = √(x² + y² + z²)

Finding the midpoint of a segment can be done with the help of the vector magnitude calculation.

When defining linear transformations, the unit vector is a helpful concept to understand. The matrix norm, for instance, represents the amount by which a unit vector is stretched when multiplied by a matrix.

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Answer:

(15×7)×29/€549×898×68

Answer: Equation: 4/3x + 4

Step-by-step explanation: Use Webmath for questions like these but if you want it graphed use desmos.

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

Volume is a measure of the amount of space that a three-dimensional object occupies or contains. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet.

In the given question,

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where r is the radius of the base, h is the height, and π is approximately 3.14.

Substituting the given values, we get:

V = (1/3) × 3.14 × 3² × 3.8

V ≈ 35.63

Rounding to the nearest whole number, the approximate volume of the mountain is 36 cubic kilometers.

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Answer:

Its A

Step-by-step explanation:

To determine whether x and y have a proportional relationship, see if the line through these points passes through the origin (0, 0). The points are on a line that passes through the origin. So, x and y have a proportional relationship.

 Hope this helps, and please mark brainliest.

Answer:

she can feed 2,220 people with 555555 pancakes.

Step-by-step explanation:

Answer:20 people

Step-by-step explanation:

we can solve the problem by setting a simple proportion.

We know that 22 pancakes can feed 8 people, so we have to find the number x which corresponds to the number of people that can be feeded with 55 pancakes:

Solving the proportion, we find

So, 55 pancakes can feed 20 people.

The value of z is equal to 50.28.

System of linear equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point at which the lines intersect.

These numbers are represented by a ratio between two integers numbers (\(\frac{a}{b}\)), where b\(\neq\)0.  Besides, this ratio can be simplified in decimal form.

For solving this equation, firstly, rewrite the information given:

                                          \(y=512x \;(1)\\ \\ z=50.25+x \;(2)\\ \\ y=15.5 \;(3)\)

As the question gives the values for y, you can find x.

                                        \(y=512x\\ \\ 15.5=512x\\ \\ x=\frac{15.5}{512} =0.03\)

Applying x=0.03 in the equation (3), you can find z.

                              \(z=50.25+x \\ \\ z=50.25+0.03\\ \\ z=50.28\)

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Answer:

123

Step-by-step explanation:

thats answrr gimme that brainliest

answer is 123

Step-by-step explanation:

-135-(-258)

as we then - x - = +

then -135+258

and we got answer 123

The cost to fill the 8-meter tank is $5,200.

To find the cost to fill a tank with an 8-meter diameter, we can use the concept of similarity between the two tanks.

The ratio of the volumes of two similar tanks is equal to the cube of the ratio of their corresponding dimensions. In this case, we want to find the cost to fill the larger tank, so we need to calculate the ratio of their diameters:

Ratio of diameters = 8 m / 4 m = 2

Since the ratio of diameters is 2, the ratio of volumes will be 2^3 = 8.

Therefore, the larger tank has 8 times the volume of the smaller tank.

If the cost to fill the 4-meter tank is $650, then the cost to fill the 8-meter tank would be:

Cost to fill 8-meter tank = Cost to fill 4-meter tank * Ratio of volumes
                          = $650 * 8
                          = $5,200

Therefore, the cost to fill the 8-meter tank is $5,200.

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Answer:

65 = <JKL

Step-by-step explanation:

There are two expressions that represent the same thing.

The diagram shows that <JKL = 45 + x

The question states that JKL = 3x + 5

The two expressions must be equal since they represent the same thing.

3x + 5 = x + 45

Subtract 5 from both sides

3x + 5 -  5 = x + 45 - 5

3x = x + 40                     Subtract x from both sides

3x - x = x - x + 40

2x = 40                          Divide by 2

2x/2 = 40/2

x = 20

So x + 45 = 20 + 45 = 65

or

3x + 5 = 3*20 + 5 = 60 + 5 = 65

6 or more terms should be used to estimate the sum of the entire series with an error of less than 0.0001.

To determine the number of terms needed to estimate the sum of the series within an error of less than 0.0001, we can apply the Alternating Series Estimation Theorem. The given series is (-1)^n * 1 / (n + 15)^4. Let's break down the steps to find the required number of terms:

The Alternating Series Estimation Theorem states that if a series is alternating, meaning its terms alternate in sign, and the absolute value of each term is decreasing, then the error made by approximating the sum of the series with a partial sum can be bounded by the absolute value of the first omitted term.

We want to estimate the sum of the series with an error of less than 0.0001. This means that we need to find the number of terms such that the absolute value of the first omitted term is less than 0.0001.

The given series is an alternating series as it alternates in sign with (-1)^n. To ensure the series satisfies the conditions of the Alternating Series Estimation Theorem, we need to verify that the absolute value of each term is decreasing.

Let's examine the absolute value of each term: |(-1)^n * 1 / (n + 15)^4|. Since the numerator is always 1 and the denominator is (n + 15)^4, we can see that the absolute value of each term is indeed decreasing as n increases.

Now, we need to find the number of terms such that the absolute value of the first omitted term is less than 0.0001. Let's denote this number of terms as N.

We can set up an inequality based on the first omitted term: |(-1)^(N+1) * 1 / (N + 15)^4| < 0.0001.

To simplify the inequality, we can remove the absolute value signs and solve for N:

(-1)^(N+1) * 1 / (N + 15)^4 < 0.0001.

Considering the (-1)^(N+1) term, we know that its value alternates between -1 and 1 as N increases. Therefore, we can ignore it for now and focus on the other part of the inequality:

1 / (N + 15)^4 < 0.0001.

To eliminate the fraction, we can take the reciprocal of both sides:

(N + 15)^4 > 10000.

Taking the fourth root of both sides, we have:

N + 15 > 10.

Solving for N, we get:

N > 10 - 15,

N > -5.

Since the number of terms must be a positive integer, we can round up to the nearest whole number:

N ≥ 6.

Therefore, 6 or more terms should be used to estimate the sum of the entire series with an error of less than 0.0001.

In summary, according to the Alternating Series Estimation Theorem, 6 or more terms should be used to estimate the sum of the series (-1)^n * 1 / (n + 15)^4 with an error of less than 0.0001.

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Answer:

4 (c - 6)

Step-by-step explanation:

Simplify the following:

6 c - 2 c - 16 - 8

Hint: | Group like terms in 6 c - 2 c - 16 - 8.

Grouping like terms, 6 c - 2 c - 16 - 8 = (6 c - 2 c) + (-8 - 16):

(6 c - 2 c) + (-8 - 16)

Hint: | Combine like terms in 6 c - 2 c.

6 c - 2 c = 4 c:

4 c + (-8 - 16)

Hint: | Evaluate -8 - 16.

-8 - 16 = -24:

4 c + -24

Hint: | Factor out the greatest common divisor of the coefficients of 4 c - 24.

Factor 4 out of 4 c - 24:

Answer: 4 (c - 6)

The length of the missing side (hypothenuse) is equal to 5

"Information available from the question"

Opposite side of the triangle(y) = 3

Adjacent side of the triangle (z)= 4

Hypothenuse side of the triangle = x

Pythagorean Theorem

This formula is used to find the missing side of a right angle triangle if two sides are given.

\(x^{2} =y^2+z^2\)

Let's substitute the values into the formula and solve for the hypothenuse

\(x^{2} =3^2+4^2\)

\(x^{2}\) = 9 + 16

\(x^{2}\) = 25

\(x=\sqrt{25}\)

x = 5

The length of the missing side (hypothenuse) is equal to 5.

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The root of the equation sinx = 2x-3 is 0.8401 (approx).

Given equation is sinx = 2x-3

We need to solve this equation using false position method.

False position method is also known as the regula falsi method.

It is an iterative method used to solve nonlinear equations.

The method is based on the intermediate value theorem.

False position method is a modified version of the bisection method.

The following steps are followed to solve the given equation using the false position method:

1. We will take the end points of the interval a and b in such a way that f(a) and f(b) have opposite signs.

Here, f(x) = sinx - 2x + 3.

2. Calculate the value of c using the following formula: c = [(a*f(b)) - (b*f(a))] / (f(b) - f(a))

3. Evaluate the function at point c and find the sign of f(c).

4. If f(c) is positive, then the root lies between a and c. So, we replace b with c. If f(c) is negative, then the root lies between c and b. So, we replace a with c.

5. Repeat the steps 2 to 4 until we obtain the required accuracy.

Let's solve the given equation using the false position method.

We will take a = 0 and b = 1 because f(0) = 3 and f(1) = -0.1585 have opposite signs.

So, the root lies between 0 and 1.

The calculation is shown in the attached image below.

Therefore, the root of the equation sinx = 2x-3 is 0.8401 (approx).

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