What is the equation of a line that passes through the point 2 3 and 4 7?

Resonance causes the amplitude of vibrations to increase.

This statement is correct because resonance is the phenomenon that occurs when an object is vibrating at its natural frequency and it is in phase with an external force, such as a sound wave. When this happens, the amplitude of the vibrations increases and the object can reach a large amplitude of oscillation. Resonance can be observed in many physical systems such as bridges, musical instruments, mechanical systems and electrical circuits.

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Answer:

The area of the book is 108 square inches.

Step-by-step explanation:

This is calculated by multiplying the base (9 inches) by the height (12 inches). The area of a right triangle is equal to one-half of the base multiplied by the height.

Answer:

108 inches

Step-by-step explanation:

Multiply 12 by 9

The numerical coefficient in the expression 5x is 5. 5x denotes a 5 times multiplier applied to the variable x.

A phrase or a number that is multiplied by a variable is referred to as a coefficient. In most cases, the constant word comes before the variable term.

In a polynomial series or an equation, a coefficient is often a multiplicative factor.

Mathematical statements known as expressions are made up of two words, at least one of which must contain either variables, integers, or both. These expressions can either be expressed as numbers, variables, or as a product of numbers and variables. The mathematical operators used to separate the integers in these expressions are a mixture of numbers.

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-11 number represents the yardage for play.

A series of plays that starts with the ball being positioned on the ground with its longest axis perpendicular to the goal line is known as scrimmage.

We know that

The quarterback backups to 5 yards (negative number).

He falls back another 6 yards more (negative number).

To know the total number of yards the quarterback felt back, we just need to sum these negative numbers.

-5-6=-11

-11 number represents the yardage for play.

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Taking into account the definition of a system of linear equations,  there are 550 and 500 calories are in one cheeseburger and one order of fries respectively.

A system of linear equations is a set of linear equations, in which two or more unknowns are related.

Solving the system consists of calculating the unknowns so that all the equations of the system are fulfilled simultaneously.

A system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

3c + 3f= 3150

7c + 4f= 5850

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "c" from the first equation:

3c= 3150 - 3f

c= (3150 - 3f)÷3

c= 1050 - f

Substituting the expression in the second equation:

7×(1050 -f) + 4f= 5850

Solving:

7×1050 - 7f + 4f= 5850

7350 - 7f + 4f= 5850

- 7f + 4f= 5850 -7350

-3f= -1500

f= (-1500)÷ (-3)

f= 500

Remembering that c=1050-f, you get:

c= 1050 -500

c= 550

Finally, there are 550 calories are in one cheeseburger and 500 calories are in one order of fries.

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The measures of KM, KQ, LK, LR, NK and PM are 2, 2, 4, 4, 6 and 2 respectively.

1) KM: Since N is the midpoint of QR, we know that QN = NR, so QN + NR = QN + QN = 2QN = 26 = 12. Therefore, KM = KR - QN = (PK+KQ) - QN = 4 - 6 = -2.

2) KQ: Since PK = 4 and KM = -2, we have KQ = PK + KM = 4 + (-2) = 2.

3) LK: The median of a triangle connects a vertex to the midpoint of the opposite side, and it's length is 2/3 the length of the hypotenuse of the right triangle formed by the median and the two segments from the vertex to the endpoints of the median.

In this case, LK = (2/3)(PQ) = (2/3)(4+2) = (2/3)*6 =4

4)LR: In this case, LR = LK = 4

5) NK: NK = QN = 6

6) PM: PM = PK - KQ = 4 - 2 = 2

Please note, that in order to be able to calculate all these lengths and measures, it is assumed that the triangle PQR is a valid triangle i.e, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.

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The construction manager will need 6 more workers  to complete the project

To determine how many more workers are needed to complete the project in 36 days, the construction manager would need to determine the rate of work per worker and then calculate how many more workers are needed to achieve the desired rate.

If 12 workers to complete a building project in 54 days. Then 1 work will complete work in:

12 × 54 days = 648 days /worker

If the building project needs to be completed in 36 days, you need:

648 / 36 = 18 workers

Number of workers left = 18 - 12 = 6 workers

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Answer: x=12

Step-by-step explanation:

The question: 1/4 of ___ = 3

Let's start solving it.

First, let's set ___ as x and rewrite the equation.

1/4 of x = 3

Now, when you say 1/4 of x, you mean that you multiply x by 1/4.

So the equation is:

1/4*x=3

Finally, multiply both sides by 4.

Answer: x = 12

Answer: 12x ft

Step-by-step explanation:

12 times x

           .    .

            ω

The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

θ = l/r where (θ is in radian)

A central angle is an angle whose legs (sides) are radii intersecting the circle at two different places, A and B, and whose apex (vertex) is the centre O of a circle. An arc between those two locations subtends central angles, and the central angle of a circle with radius one is the length of the arc (measured in radians).

Area of Sector = θ/360 x πr²

The piece of a disc (a closed region defined by a circle) enclosed by two radii and an arc is known as a circular sector, also known as a circle sector or a disc sector. The smaller area is known as the minor sector, and the larger area is known as the major sector.

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Answer: The tree is 500 centimeters high

Step-by-step explanation:

The area of the circle equation is shown below

From the question, we have the following parameters that can be used in our computation:

Area of radius 1 = π

The area of a circle is proportional to the square of its radius.

When the radius is multiplied by a scale factor of "r," the area is multiplied by the square of that factor: r^2.

So, the area of a circle of radius "r" is given by π * r^2 square units.

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The given equation y = -2x + 5 is a linear equation.

The given equation is:

y = -2x + 5

We observe the highest degree of x in a given equation to know whether it is a linear equation or not.

We know that if the highest degree of x in an equation is 1 then it is a linear equation else its a quadratic or non - linear equation.

In the given equation the highest degree of x is 1, hence it is a linear equation.

We can also check the same by graphing the equation.

If the graph of the given equation is a straight line then it is said to be a linear equation. The graph of this equation is also a straight line.

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So you can find out which is better by determining the cost per unit (load) or by cost for the five loads. In this case, you can simply multiply $2.50 by the five to get $12.50. From this you can determine that the loyalty has the better price at $11.50 ($2.30 per load).

3 different types of solutions for the quadratic formula are :

1. Factoring

2. Quadratic Formula

3. Completing the square

Quadratic formula/equation has a common formula

f(x) = a[tex]x^{2}[/tex] + bx + c

Where :

a is the coefficient of [tex]x^{2}[/tex]

b is the coefficient of x

c is the constant term

To solve that equation, we can use 3 solutions.

1. Factoring

This solution uses the factor of number and leaves 0 at the right side.

Common formula is ( x + a )( x + b ) = 0

Example :

[tex]x^{2}[/tex] + 6x + 8 = 0

(x + 4)(x + 2) = 0

x = -4 or x = -2

2. Quadratic Formula

The quadratic formula is

x = [tex]\frac{-b +- \sqrt[]{b^{2}-4ac } }{2a}[/tex]

Example :

[tex]x^{2}[/tex] + 6x + 8 = 0

x = [tex]\frac{-6 +- \sqrt{6^{2} -4(1)(8)} }{2(1)}[/tex]

x = [tex]\frac{-6 +- \sqrt{4} }{2}[/tex]

x = [tex]\frac{-6+2}{2}[/tex] or x = [tex]\frac{-6-2}{2}[/tex]

x = -2 or x = -4

3. Completing the square

Example :

[tex]x^{2}[/tex] - 6x + 5 = 0

[tex]x^{2}[/tex] - 6x = -5

because a = -1, add [tex](\frac{-6}{2}) ^{2}[/tex] or 9

[tex]x^{2}[/tex] - 6x + 9 = -5 + 9

[tex]x^{2}[/tex] - 6x + 9 = 4

[tex](x - 3 )^{2}[/tex] = 4

x-3 = ± 2

x -3 = 2 or x - 3 = -2

x = 5 or x = 1

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Answer:

(3,-5)

Step-by-step explanation:

Start by multiplying the bottom equation by 2

2(-2y+2x=16)=   -4y+4x=32

now when adding the y cancels out leaving you with:

5x=15

x=3

now plug the 3 into the first equation, and subtract it from both sides so

4y=-20

y=-5

The two real solutions to this quadratic equation are -2 and 3/2.

The Quadratic Formula is the most popular method for solving quadratic equations of the form ax²+bx+c=0. It is derived from the quadratic equation which states that if a, b, and c are real numbers, and a is not equal to zero, then the roots of the quadratic equation ax²+bx+c=0 can be determined by the following equation:

x = (-b ± √(b² - 4ac))/(2a)

The quadratic formula can be used to solve for the two real solutions of any quadratic equation. It works by determining the discriminant, which is the number under the square root in the equation. The discriminant is calculated by subtracting 4ac from b². The ± symbol indicates that there are two solutions, one with the plus sign and one with the minus sign.

For example, if we have a quadratic equation 2x²+5x-3=0, the discriminant can be calculated as follows:

b² - 4ac = (5)² - 4(2)(-3) = 25 + 24 = 49

The two solutions can then be found using the formula:

x = (-5 ± √49)/(2(2))

x = (-5 ± 7)/(4)

x = -2 or 3/2

Therefore, the two real solutions to this quadratic equation are -2 and 3/2.

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Complete question:

Which of the following methods can be used in solving quadratic equation of the form ax²+bx+c=0?​

A) Factoring

B) Completing the Square

C) Quadratic Formula

D) Graphing

The length of MA with the endpoints at M(7, -2) and A(2, -6) is √41 units.

MA has the endpoints at M(7, -2) and A(2, -6). The distance of MA can be found as follows:

Using distance formula, the formula follows Pythagorean principle.

d = √(y₂ - y₁)² + (x₂ - x₁)²

x₁ = 7

x₂ = 2

y₁ = -2

y₂ = -6

Applying the formula,

distance of MA = √(-6 + 2)² + (2 - 7)²

distance of MA = √(-4)² + (-5)²

distance of MA = √ 16 + 25

distance of MA = √41

Therefore, distance of MA is √41 units.

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The solution to this system of equations is (8,1).

An equation is an expression that uses mathematical symbols to represent a relationship between two or more things. Equations are often used to solve problems, describe patterns, and make predictions. Equations can involve numbers, variables, operations, and other mathematical elements.

The solution to this system of equations can be found by solving the two equations for x and y respectively. For the first equation, we can solve for y:

y = √9 - x

For the second equation, we can solve for x:

x = 6 - 2y

Substituting the value of y from the first equation into the second equation, we find that:

6 - 2√9 - x = 0

Solving for x yields the solution:

x = 8

Substituting the value of x into the first equation, we find that:

y = 1

Therefore, the solution to this system of equations is (8,1).

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The value of the unknown variable {t} is equal to 3/4.

        [tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]

Given is the equation as -

- 2 = (t/3) - 3t

The given equation is -

- 2 = (t/3) - 3t

Solving further , we get -

(t/3) - 3t = - 2

t/3 - 3t = - 2

t(1/3 - 3) = - 2

t(1 - 9)/3 = - 2

-8t/3 = -2

t = 2 x 3/8

t = 3/4

Therefore, the value of the unknown variable {t} is equal to 3/4.

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The estimated amount he paid at the other store is $5.5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, The amount(A₁) Gabe spent in dollars at one store is

A₁ = 13.09d + 28, where 'd' is the number of items he bought.

Then he spent 22 dollars at another store.

let, A₂ = 22 and he bought 4 items.

Therefore, The estimated amount he paid at the other store is,

= 22/4.

= $5.5

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a) The amplitude and period of the function that could model the height of the message in a bottle as a function of time, t are 2 feet and 24 seconds.

b) At t = 0, h(t) = 8 feet , the equation of the function that could represent the situation is h(t) = 2 Cos( π/12( t + 6) + 8.

We have, In a bottle a message is floating on top of the ocean in a periodic manner. The time between periods of maximum heights = 24 sec.

Average height of bottle = 8 feet

The distance from the highest and lowest point = 4 feet

The height at any movement of time can be modelled as a cosine function,

h( t) = A cos(B(t - C)) + D

Where A --> amplitude of wave function

2π/B--> periodicity

C --> phase shift ( right / left)

D --> vertical shift

a) Amplitude, A in feet is defined as the maximum height that bottle reaches from mean sea level. It is calculated by the difference between hightest and lowest point and divided by 2. In this case, the distance from the highest and lowest point is 4 feet. So, amplitude is

A = 4/2 = 2 feet .

Time period, T in seconds is the time taken by bottle to complete one cycle. In this case, it is equal to time taken to reach at maximum height. That is equals to 24 seconds.

b) Period = 2π/ B = 24 seconds , so

B = 2π/24 => B = π/12

Using the part A results, the equation of movement is, h( t) = 2 cos(π/12( t - C) + D

At t = 0 , the message in a bottle is at its average height, i.e., 8 feet and moves upwards after. This implies at t = 0 ,

h(t) = 8 feet

=> 8 = 2 cos(π/12( 0 - C)) + 8

=> 2 cos(π/12( 0 - C) )= 0

=> cos(π/12(-C) )= 0

=> cos( πC/ 12) = 0

=> πC/12 = cos⁻¹ ( 0)

=> πC/12 = π/2

=> C = 12/2 = 6

plugging all known values in cosine function equation to get required equation, h(t) = 2 Cos( π/12( t + 6) + 8

Hence, the required equation is h(t) = 2 Cos( πt/12 + π/2) + 8.

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Complete question :

A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 24 seconds, and the average height of the bottle is 8 feet. The bottle moves in a manner such that the distance from the highest and lowest point is 4 feet. A cosine function can model the movement of the message in a bottle in relation to the height.

Part A: Determine the amplitude and period of the function that could model the height of the message in a bottle as a function of time, t. (5 points)

Part B: Assuming that at t = 0 the message in a bottle is at its average height and moves upwards after, what is the equation of the function that could represent the situation? (5 points)

Answer:

a/3 = 6

Step-by-step explanation:

i don't see any equations to choose from

however, if 'a' represents the number of hours the cat sleeps then this equation would work:

1/3a = 6

or a/3 = 6

in this case, 'a' would equal 18

Answer:

Step-by-step explanation:

213

Answer:

x = -2, y = -5 and x = 5, y = 2

Step-by-step explanation:

The rate of interest be required in order for Deondra to end up with $201,000 is 14.88%

percentage, a relative value indicating hundredth parts of any quantity.

Given that Deondra is going to invest $90,000 and leave it in an account for 15 years.

We have o find the interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $201,000

A=PRT

201000=90000×R×15

201000=1350000R

Divide both sides by 1350000

R=0.1488×100

R=14.88

Hence, the rate of interest be required in order for Deondra to end up with $201,000 is 14.88%

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Answer: 9cm

Step-by-step explanation:

Answer:

The odometer shows that the car has traveled 41,000 miles by January 1, 2020, so we can use this as the starting point (x = 0) for our equation. We also know that the car travels 19,000 miles each year.

We can use this information to write an equation for the number of miles on the car's odometer x years after 2020.

The equation would be : y = 41,000 + (19,000 * x)

Where y represents the number of miles on the car's odometer and x represents the number of years after 2020.

The y is the number of miles at the odometer and x is the number of years passed from 2020.

This equation gives the number of miles on the car's odometer x years after 2020, whenever we have to know the number of miles on the odometer we just need to plug in the number of years passed in the equation.

The number of workdays that will allow Liliana to prepare enough paintings for the exhibit are 10 days, 5 days and 8 days (2nd - 4th option).

The first step is to determine the inequality sign that would be used in the inequality that represents the information in the question.

Here are inequality signs and what they mean:

The form of the equation is:

number of painting already made + (new paintings per day x number of days) > 26

10 + (4 x n) > 26

10 + 4n > 26

4n > 26 - 10

4n > 16

n > 16 / 4

n > 4

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