There are 27 open spots to compete in the fishing tournament. If each boat can hold 5 people, how many boats are needed to hold all 27 competitors during the tournament?

Answer:

y=-35

Step-by-step explanation:

Steps

$\frac{y}{5}-=-7$

$\mathrm{Subtract\:}-\mathrm{\:from\:both\:sides}$

$\frac{y}{5}=-7$

$\mathrm{Simplify}$

$\frac{y}{5}=-7$

$\mathrm{Multiply\:both\:sides\:by\:}5$

$\frac{5y}{5}=5\left(-7\right)$

$\mathrm{Simplify}$

$y=-35$

Answer:

y = 35

Step-by-step explanation:

    multiply by -5 on both sides

    -5 and -5 cancel out

    -5 times -7 is 35

    y = 35

Answer:

(x + 3)² + (y - 1)² = 80

Step-by-step explanation:

Circle equation: (x - h)² + (y - k)² = r²

We are given h and k, so we just plug that in:

(x + 3)² + (y - 1)² = r²

To find r, we need to use distance formula: \(d = \sqrt{(x2-x1)^2+(y2-y1)^2}\) between the center of the circle and the point on the circle. We should get √80 as r. We plug that in to get our answer:

(x + 3)² + (y - 1)² = 80

Answer:

-8x² - 12x + 1

Step-by-step explanation:

just add or subtract values with the same terms. eg -7x + 4x ,, etc

Since there are a adults and c children

Since there are 187 tickets sold

Then the number of adults and children is 187

Add a and c, then equate the sum by 187

Since the price of each adult's ticket is $25

Since the price of each child ticket is $13

Since the total revenue is $3223

Then multiply a by 25, c by 13, then add the products and equate the sum by $3223

Now, we have a system of equations to solve it

Multiply equation (1) by -13 to make c equal in values and opposite in signs to eliminate it

Add equations (2) and (3)

Divide both sides by 12

Substitute a by 66 in equation (1) to find c

Subtract 66 from both sides

The answers are:

a) The system of equations is

b) There were 66 adult tickets sold

c) There were 121 children's tickets sold

Answer:

32

Step-by-step explanation:

its 32

Answer:

x^4

Step-by-step explanation:

For the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. Yet, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.

The distance formula for the coordinates is given as:

d(A, B) = |x1 - x2|

From the figure we observe that,

d(A, B) = |2 - 4|

d(A, B) = |-2|

d(A, B) = 2 units.

Hence, option A is correct.

Also, the length of A'B' is:

d(A', B') = |3 - 6| = |-3| = 3 units.

Hence, option B is correct.

The original shape is called the pre-image in a transformation (in this example, a dilation), and the transformed shape is called the image.

The third response is untrue since the picture is larger than the pre-image.

The scale factor of the images is:

2k = 3

k = 3/2.

Hence, option 4 is correct.

The last option is also false, as the scale factor is already determined.

Hence, for the given dilation of the polygons the correct answer are The length AB is 2. The length A'B' is 3. The scale factor is Three-halves.

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The complete question is:

Answer:

2,957,468

Step-by-step explanation:

Each digit to the left is worth 10 times more than the same digit one place to the right.

If 2,957,648 becomes 2,957,468, the 4 moves from the tens place to the hundreds place, and now its value is 400 instead of 40, so it's 10 times greater.

Expression 8x²-12xy-8y² is equivalent to 4(x+2y)(2x+y) is false.

A polynomial function is a mathematical function of one or more variables in which each term is a constant, a variable raised to a non-negative integer power, and a coefficient multiplying the variable term.

For example, the function f(x) = 3x⁴+ 2x³ - 5x² + x - 2 is a polynomial function of degree 4. Polynomial functions are used in various fields of mathematics, including algebra, calculus, and numerical analysis.

Given expression

8x²-12xy-8y²

Taking 4 common from each terms,

4(2x²-3xy-2y²)

We can write -3xy as -4xy and +xy

4(2x²-4xy+xy-2y²)

Simplifying the terms

4(2x(x-2y)+y(x-2y))

4(x-2y)(2x+y)

Hence, expression 8x²-12xy-8y² is equivalent to 4(x+2y)(2x+y) is false.

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Answer:

255 caps were sold

Step-by-step explanation:

25x+10y = 9000

25(258) + 10y = 9000

6450 + 10y = 9000

-6450 + 10y = -6450

10y = 2550

2550/10y

y = 255

By applying Fundamental counting principle, it can be concluded that there are 2560 different shoe combinations that can be created.

Fundamental counting principle states that if the first event can be done in k₁ different ways, the second event can be done in k₂ different ways, and so on until the \(n^{th}\) event, then the number of different ways of all these events is K, where:

K = k₁ x k₂x . . . x kₙ

The following table shows the design components and how many options Lamar has for each:

Design component      Number of options

   Primary color                        8

 Secondary color                     8

      Sole color                           8

      Lace color                          5

Then we can calculate the number of different combinations that can be created as follows:

Number of combinations = number of option₁ x number of option₂ x

                                             number of option₃ x number of option₄

                                          = 8 x 8 x 8 x 5

                                          = 2560

Thus there are 2560 different shoe combinations that can be created.

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A  quadratic equation in math is nothing but an equation of the form ax² + bx + c = 0

We know that a quadratic equation is nothing but a polynomial equation of the second degree.

The standard form of quadratic equation is ax² + bx + c = 0, where a and b are the real valued coefficients, x is the variable.

In the above equation, the value of 'a' can not be zero (a ≠ 0) in order to be a quadratic equation.

The coefficient 'a' is called as leading coefficient of quadrtic equation, c is called as constant term, and 'b' is the middle term.

In order to determine the type of roots a quadrtic equation may have, first we find the value of   b² - 4ac

If b² - 4ac > 0, then the equation has two distinct real roots.

If b² - 4ac = 0 then the equation has one real root.  

And if b² - 4ac < 0 then in this case, the equation does not have real roots.

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Answer:

minutes took to finish the race = 54 minutes

Step-by-step explanation:

It's known that:

\(speed = \frac{distance}{time}\)

then:

\(time = \frac{distance}{speed}\)

IN THE 1ST 10 MILES:

time = \(\frac{10}{25} = \frac{2}{5} = 0.4 hours\)

IN THE 2ST 10 MILES:

time = \(\frac{10}{20} = 0.5 hours\)

Hence, Overall time took to finish the race = 0.4 + 0.5 = 0.9 hours

time in minutes = 0.9 × 60 = 54 minutes


Another Solution:

Overall speed = \(\frac{S_1 + S_2}{2}\), Where: S1: 1st speed, S2: 2nd speed

then:

speed = \(\frac{25 + 20}{2}= 22.5 mph\)

Hence, time took = \(\frac{20}{22.5} = 0.9 hours = 54 minutes\)




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The gas mileage in miles per gallon = 44.690mi/gal.

A vehicle's mileage is the number of miles it can drive solely on a single gallon or liter of fuel. They are ready to pay up to $500 more for fuel-efficient vehicles. 3. a noncountable noun.

Subtract the original tachometer reading from either the new one to get the miles traveled first from the trip odometer. Divide the distance traveled by the number of gallons used to fill the tank. As a result, your car's overall kilometers per gallon yield for that driving period will be calculated.

1 km = 0.621371 mi

1 L = 0.264172 gal

calculating that the amount of gas mileage in miles per gallon by multiplying with distance and gas used per miles.

19 km/L = (19*0.621371)/0.264172 mi/gal

= 44.690 mi/gal

the gas mileage in miles per gallon = 44.690mi/gal.

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The factors of the given expression are 2av² and (2av³-9).

The given expression is 4a²v⁵-18av².

The factors are the polynomials which are multiplied to produce the original polynomial.

2av²(2av³-9)

Therefore, the factors of the given expression are 2av² and (2av³-9).

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(a) The distance of P from O when it is instantaneously at rest is 40 metres. (b) The values of t are 5 and 1 second. (c) The average velocity = 2/2 = 1 m/s. (d) The total distance travelled in the first 6 seconds is -234 meters.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

a) To find the distance of P from O when it is instantaneously at rest, we need to find the value of s when t = 0.

s = t³ - 9t² + 15t + 40

s = 0 - 9(0)² + 15(0) + 40

s = 40

So the distance of P from O when it is instantaneously at rest is 40 metres.

b) To find the values of t when the acceleration has a magnitude of 9 ms, we need to find the roots of equation 3t² - 18t + 15 = 0.

We can solve this equation by factoring or using the quadratic formula.

3t² - 18t + 15 = 0

(t-5)(t-1) = 0

t = 5, 1

So the values of t are 5 and 1 seconds.

c) To find the average velocity of P during the first 2 seconds, we can use the formula for average velocity:

average velocity = (distance travelled)/(time taken)

We can find the distance travelled by finding the value of s at t = 2 and t = 0 and subtracting them.

s = t³ - 9t² + 15t + 40

s(2) = 8 - 36 + 30 + 40 = 42

s(0) = 0 - 9(0)² + 15(0) + 40 = 40

distance = 42 - 40 = 2 metres

time = 2 - 0 = 2 seconds

average velocity = 2/2 = 1 m/s

d) To find the total distance travelled in the first 6 seconds, we can find the value of s at t = 6 and t = 0 and subtract them.

s = t³ - 9t² + 15t + 40

s(6) = 216 - 540 + 90 + 40 = -194

s(0) = 0 - 9(0)^2 + 15(0) + 40 = 40

distance = -194 - 40 = -234 metres

So the total distance travelled in the first 6 seconds is -234 meters.

Note that distance travelled is negative, which means that the particle is moving in the opposite direction of O.

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Answer:

X es igual a 3

Step-by-step explanation:

x2 - 6 = 0

(3)2 - 6 = 0

Answer: $50

Step-by-step explanation:

Answer:

1,044

Step-by-step explanation:

14 x 46 = 644

16 x 25 = 400

644 + 400 = 1,044

Answer:

9

Step-by-step explanation:

the expression is 2ac, so multiply everything together

2 * 1/2 = 1

1 * 9 = 9

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(a) True.

Scalar multiplication is defined between any real number and any matrix. In scalar multiplication, each element of the matrix is multiplied by the scalar.

This operation is valid for any real number and any matrix, regardless of their dimensions. For example, if you have a matrix A = [1 2 3 4] and a scalar r = 2, you can multiply the scalar by the matrix as follows: rA = 2  [1 2 3 4] = [2 4 6 8].

(b) True.

Matrix addition is defined between any two matrices. In matrix addition, corresponding elements of the matrices are added together. For this operation to be valid, the matrices must have the same dimensions.

If matrix A and matrix B have the same dimensions, you can add them element-wise. For example, if you have matrix A = [1 2 3 4] and matrix B = [5 6 7 8], you can add them as follows: A + B = [1 + 5 2 + 6 3 + 7 4 + 8] = [6 8 10 12].

(c) True.

The statement is true. For scalars r and s, and a matrix A, the associative property of scalar multiplication allows us to rearrange the expression r(sA) as (rs)A. Scalar multiplication is associative, which means that the order of scalar multiplication does not matter.

Therefore, r(sA) = (rs)A holds true. For example, if you have scalar r = 2, scalar s = 3, and matrix A = [1 2 3 4], you can compute the expression as follows: 2(3A) = 2  (3  [1 2 3 4]) = (2  3) [1 2 3 4] = 6  [1 2; 3 4] = [6 12 18 24]. Similarly, (2  3)A = 6  [1 2 3 4] = [6 12 18 24]. The resulting matrices are the same, confirming the truth of the statement.

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Answer:

3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(11-8)/(7-6)

m=3/1

m=3

Circumference of the circle with the given diameter is 69.08 inches.

Circumference of a circle is defined as the total length of the boundary of the circle.

The concept is same as the perimeter for straight sided figures.

Given,

Diameter of the circle = 22 inches

Radius of the circle = Diameter / 2 = 22 / 2 = 11 inches

Circumference of a circle = 2πr, where r is the radius of the circle and the value of π is 3.14.

Circumference = 2 × 3.14 × 11 = 69.08 inches

Hence 69.08 inches is the circumference of the circle.

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To maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129.

If Talisa hits rock at 30 feet, then the depth of the pond will be limited to 30 feet. Therefore, she needs to modify the radius of the pond to maintain the original volume.

To do this, Talisa can use the formula for the volume of a circular cylinder, which is:

V = πr^2h

where V is the volume of the cylinder, r is the radius, and h is the height (or depth) of the cylinder.

Since Talisa wants to maintain the original volume of the pond, she can set the equation for the new cylinder equal to the equation for the original cylinder, and solve for the new radius, r2:

πr1^2h1 = πr2^2h2

where r1 is the original radius (unknown), h1 is the original height (36 ft), r2 is the new radius (unknown), and h2 is the new height (30 ft).

Simplifying this equation, we can cancel out the π and h1 terms:

r1^2 = r2^2(30/36)

Taking the square root of both sides, we get:

r1 = r2(√(30/36))

Thus, to maintain the original volume of the pond, Talisa needs to increase the radius by a factor of √(30/36), which is approximately 0.9129. In other words, she needs to multiply the original radius by 0.9129 to get the new radius.

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The median length of time required to review an application is 105 minutes.

To find the median, the data needs to be arranged in order from least to greatest: 19, 48, 140, 220.

Since there is an even number of data points, the median is the average of the two middle values, which in this case are 48 and 140. Adding them together and dividing by 2 gives 94, which is less than the next highest value of 220.

Therefore, the median length of time required to review an application is 105 minutes.

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Using the simplex method, the maximum value of Z=5A+4B is found to be 19.2 when A=3.6 and B=1.2. The calculations can be confirmed by using any software that solves linear programming problems.

To solve the given linear programming problem using the simplex method, we start by converting the problem into standard form. We introduce slack variables to convert the inequalities into equations.The initial tableau is as follows:

      | A | B | S1 | S2 | S3 | S4 |   RHS

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

 Z    | -5 | -4 | 0  | 0  | 0  | 0  |    0

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

 S1   |  6 |  4 | 1  | 0  | 0  | 0  |   24

 S2   |  1 |  2 | 0  | 1  | 0  | 0  |    6

 S3   | -1 |  1 | 0  | 0  | 1  | 0  |    1

 S4   |  0 |  1 | 0  | 0  | 0  | 1  |    2

We perform the simplex iterations until the optimal solution is reached. After applying the simplex method, the final tableau is obtained as follows:

      |  A  |  B  |  S1  |  S2  |  S3  |  S4  |   RHS

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

 Z    |  0  | 1.8 | 0.2  | -1   | -0.4 |  0.4 | 19.2

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

 S1   |  0  |  0  |  0   | 1.5  | -1   |  1   |  3

 S2   |  1  |  0  | -0.5 |  0.5 |  0.5 | -0.5 | 1.5

 A    |  1  |  0  | 0.5  | -0.5 | -0.5 |  0.5 |  0.5

 S4   |  0  |  0  |  1   | -1   | -1   |  1   |  1

From the final tableau, we can see that the maximum value of Z is 19.2 when A=3.6 and B=1.2. This solution satisfies all the constraints of the problem. The calculations can be verified using any software that solves linear programming problems, which should yield the same optimal solution.

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So from figure it is clear that Angle 1 = angle 3 =145 degree(vertically opposite angle) and angle 4=35 than angle 4=angle 2(vertically opposite angle).

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.

given= angle 1 is 145 degree

angle 1 = angle 3 =145 degree(vertically opposite angle)

and angle 1+ angle 4= 180 (linear pairs)

145+ angle 4=180

angle 4= 180-145

angle 4=35

than angle 4=angle 2(vertically opposite angle)

Therefore from figure it is clear that Angle 1 = angle 3 =145 degree(vertically opposite angle) and angle 4=35 than angle 4=angle 2(vertically opposite angle).

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Answer:

-2/8

Step-by-step explanation:

Answer:

1.5 ???

Step-by-step explanation:

Maybe??? ,:3

if u wanted the value its 1.5

John can buy any amount of chocolate between 0 and 2.2 pounds (rounded to one decimal place) and still have enough money to buy the jelly beans.

John brings $15 to the candy store and buys a bag of jelly beans for $4. He plans to buy some chocolate that costs $5 per pound. Let x be the number of pounds of chocolate John could buy.

The cost of the chocolate John plans to buy is $5 per pound, so the total cost of x pounds of chocolate is 5x. John's total budget is $15, so he must have enough money to buy the jelly beans and the chocolate. Therefore, the inequality that represents this situation is:

4 + 5x ≤ 15

To solve for x, we can begin by isolating the variable on one side of the inequality. We can do this by subtracting 4 from both sides of the inequality:

5x ≤ 11

Next, we can isolate x by dividing both sides of the inequality by 5:

x ≤ 11/5

Therefore, the possible values of x, the number of pounds of chocolate John could buy, are all real numbers less than or equal to 11/5. However, since John cannot buy a negative amount of chocolate, we must also restrict x to be greater than or equal to 0. Therefore, the solution to the inequality is:

0 ≤ x ≤ 11/5

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