Write an equation for a polynomial function whose graph intercepts the
horizontal axis at -7, 8, and 15.

Answer:

12 arrangments, 2 blue carnations in each arrangement, 3 red carnations in each arrangment.

Step-by-step explanation:

We can find the gcd of 24 and 36, getting 12.

Therefore, there should be 12 total arrangements.

There are 24 blue carnations:

24 / 12 = 2 blue carnations in each arrangement.

There are 36 red carnations:

36 / 12 = 3 red carnations in each arrangment.

Answer:Yes the answer would be 700 since that is the starting amount.

Step-by-step explanation:

The  |120-x| simplifies to 120-x when x is less than 120.

S If x is less than 120, then the expression |120-x| simplifies to 120-x. This is because the absolute value bars mean that the result must be positive,

so if x is already less than 120, then subtracting x from 120 will give a positive result.

For example, if x is 115, then |120-x| would equal |120-115|, which simplifies to |5|, which equals 5.  

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

y = 2x+4

Step-by-step explanation:

First find the slope

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

    = ( 12-6)/(4-1)

   = 6/3

    = 2

The slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 2x+b

Using a point from the table

10 = 2(3)+b

10 = 6+b

10-6 = b

4=b

y = 2x+4

The number of flu virus particles in a person's body after 1 day is 28.46 billion, based on the given polynomial function.

The polynomial given to us is, y = −0.74x⁴ + 2.8x³ + 26.4 which describes the billions of flu virus particles in a person’s body. To find the number of virus particles in a person's body after 1 day, we need to substitute x = 1 into the given polynomial and evaluate it.

So, we have,

y = -0.74(1)⁴ + 2.8(1)³ + 26.4

= -0.74 + 2.8 + 26.4

= 28.46

Therefore, the number of virus particles in a person's body after 1 day is 28.46 billion.

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Complete question - The polynomial y=−0.74x⁴ + 2.8x³ + 26.4 describes the billions of flu virus particles in a person’s body x days after being infected. find the number of virus particles, in billions, after 1 day.

The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Given stress function is 50x² - 60xy - 70y²

To determine whether the stress function satisfies the conditions of compatibility for a two-dimensional problem, it is required to find the strains and then check for compatibility equations.

Strain components are given as,

εx = ∂υ/∂x + (du/dx)

εy = ∂υ/∂y + (du/dy)

γxy = ∂υ/∂y + (du/dx)

Here,

υ = 50x² - 60xy - 70y²

du/dx = 100x - 60

ydu/dy = -60x - 140y

∂υ/∂x = 100x - 60y

∂υ/∂y = -60x - 140y

∂²υ/∂y² = -140

∂²υ/∂x² = 100

Now,εx = 100x - 60

yεy = -140y - 60

xγxy = -60y - 60x

Taking derivative of εy w.r.t x,

∂(εy)/∂x = -60

Similarly, taking derivative of εx w.r.t y,

∂(εx)/∂y = -60

∴ The stress function satisfies the conditions of compatibility for a two-dimensional problem.

Stress components are given as,

σx = (C11εx + C12εy)

σy = (C21εx + C22εy)

τxy = (C44γxy)

Here,C11 = C22 = 100, C12 = C21 = -60 and C44 = 0

Therefore,

σx = 100(100x - 60y) - 60(-140y - 60x)

= 19600x - 8800

yσy = -60(100x - 60y) + 100(-140y - 60x)

= -19600y + 8800x

τxy = 0

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The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).

In mathematics, an inequality is a connection that does not have an equal sign between two expressions or values. Inequality follows imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Use the not equal symbol, which is most often used, when two values are not equal (). No matter how little or huge the values, various inequalities are employed to contrast them. The two sides can be changed until the variables are all that is left in order to solve several basic inequalities. Unevenness is caused by a number of factors, including: The sum or division of negative values on both sides. The left and right are exchanged.

given

inequality for y

5x – 2y ≤ 10

– 2y ≤ – 5x + 10

y ≥ 5/2x - 5

When dividing by a negative number, remember to switch the inequality sign.

In a linear inequality, you will shade below the boundary line if the sign is (less than) or (less than or equal to).  The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).

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The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.

So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.

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As a result, the equation ((2w + 9) + ((4 - 3w) = 0) has no answer.

The term "radical" is used to represent the square root or nth elements. Expression with a square base is referred to as a radical expression. Radicand: A value or phrase contained within the radical sign. Equation with radical formulas and factors as radicands is referred to as a radical equation.

√(2w + 9) + √(4 - 3w) = 0

We need to isolate the variable w.

First, we can move the second term to the other side of the equation by subtracting it from both sides:

√(2w + 9) = -√(4 - 3w)

Next, we can square both sides of the equation to eliminate the square roots:

(√(2w + 9))^2 = (-√(4 - 3w))^2

2w + 9 = 4 - 3w

Now, we can simplify and solve for w:

5w = -5

w = -1

In this case, when w = -1, both square roots are defined, and we can substitute this value back into the original equation to verify:

√(2(-1) + 9) + √(4 - 3(-1)) = √7 + √7 = 2√7

Since 2√7 is not equal to 0, our solution is not valid.

Therefore, there is no solution to the equation √(2w + 9) + √(4 - 3w) = 0.

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Answer:

(x+12, y-24)

Step-by-step explanation:

The rule is (x, y) -> (x+12, y-24)

Answer:

The force of friction is 19.1 N

Step-by-step explanation:

According to Newton's second law, the net force acting on the bag is equal to the product between its mass and its acceleration:

where

is the net force

m is the mass

a is the acceleration

The bag is moving at constant speed, so its acceleration is zero:

Therefore the net force is zero as well:

Here we are interested only in the forces acting along the horizontal direction, therefore the net force is given by:

where

is the horizontal component of the applied force, with

F = 22.5 N

is the force of friction

And solving for , we find

Answer:

26.40+257.60=

284

284÷18

15.7

Answer:

2(3x+2)

Step-by-step explanation:

Answer:

Which property can be used to show that if 16=9+7 then 9+7=16 ?

Commutative property of addition

xXxAnimexXx

ANSWER

commutative property

Step-by-step explanation:

A+B=C

C=A+B

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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a) r>0 is the domain of A. b) r = (4/2π + 16)^1/2 - 4

A(r) is a function representing the surface area of a cylinder of height = 8inches and radius = r.

A(r) = 2п\(r^{2}\) + 16пr

r must be a positive number, as we can't have a radius of negative length, so the domain of A(r)  is r>0.

Solving for r in terms of A is an odd question, and a little challenging but possible using completing the square:

A/2п = \(r^{2}\) + 8r

A/ 2п + 16 = \(r^{2}\) + 8r + 16

A/2п + 16 = \((r + 4)^{2}\)

r =( A/2п + 16) ^1/2 - 4

Therefore we get to know the range of r i.e., r>0 and radius = (A/2п + 16 )^1/2 - 4

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The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)

The equation can be split as follows:

y = 1 - cos(x)

y = 2 - 2sin²(x)

Next, we plot the graph of the above equations (see graph 1)

Under the domain interval (-π, π), the curves of the equations intersect at:

(-π/3, 0.5) and (π/3, 0.5)

Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)

Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)

The equation can be split as follows:

y = 4cos⁴(x) - 5cos²(x) + 1

y = o

Next, we plot the graph of the above equations (see graph 2)

Under the domain interval [0, 2π), the curves of the equations intersect at:

(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)

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The speed of the tip of the blade is approximately 1.05 meters per second.

To find the speed of the tip of a blade, we need to use the formula:

Speed = (2 * π * radius * revolutions) / time

a) For a blade that does 45 revolutions per minute and has a length (radius) of 4 feet:

1. Convert the length from feet to inches: 4 feet = 4 * 12 inches = 48 inches.
2. Convert the time from minutes to seconds: 45 revolutions per minute = 45 / 60 revolutions per second = 0.75 revolutions per second.
3. Substitute the values into the formula:

  Speed = (2 * π * 48 inches * 0.75 revolutions) / 60 seconds
 
  Simplifying, we get:
 
  Speed ≈ 3.14 * 48 inches * 0.75 revolutions / 60 seconds
        ≈ 3.14 * 48 inches * 0.0125 revolutions / 1 second
        ≈ 1.88 inches/second

Therefore, the speed of the tip of the blade is approximately 1.88 inches per second.

b) For a blade that does one revolution every 4.3 seconds and has a length (radius) of 2 inches:

1. Convert the length from inches to feet: 2 inches = 2 / 12 feet = 1/6 feet.
2. Substitute the values into the formula:

  Speed = (2 * π * 1/6 feet * 1 revolution) / 4.3 seconds
 
  Simplifying, we get:
 
  Speed = (2 * π * 1/6 feet) / 4.3 seconds
        ≈ 0.1 * π feet / 4.3 seconds
        ≈ 0.0233 feet/second

Therefore, the speed of the tip of the blade is approximately 0.0233 feet per second.

c) For a blade that rotates 65° in one second and has a length (radius) of 31 cm:

1. Convert the length from centimeters to meters: 31 cm = 31 / 100 meters = 0.31 meters.
2. Substitute the values into the formula:

  Speed = (2 * π * 0.31 meters * 65°) / 1 second
 
  Simplifying, we get:
 
  Speed = (2 * π * 0.31 meters * 65°) / 1 second
        ≈ 0.62 * π * 65° meters / 1 second
        ≈ 0.333 * π meters/second
        ≈ 1.05 meters/second

Therefore, the speed of the tip of the blade is approximately 1.05 meters per second.

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Answer:

36%

Step-by-step explanation:

1 = 100%

so 1.36 is increasing by 36%

Answer: D

Explanation:

Use the vertex formula, -b/2a. Because the quadratic formula is ax^2+bx+c, -b would be 5 in this case and a would be 2 in this case. Plug the numbers in and you get 5/4. The AOS or vertex would be 5/4 or 1.25. Because the a-value is a positive in this equation, the parabola would have a minimum.  

Answer:

The  area of triangle B is \(2.72cm ^{2}\)

Step-by-step explanation:

We will use the principle of similar triangles to solve the problem.

Since triangle A is just a scale version of triangle B, we can say that the two triangles are similar.

The area scale factor is the square of the length scale factor.

Given the length scale factor as 3,

The area scale factor will be 3 X 3 = 9 sq. cm

(Area of triangle A / Area of triangle B) =  (length of side A / Length of side B) square

\(\frac{24.5}{ area of B}= 3^{2}\)

\(\frac{24.5}{Area of B}= 9\\Area of B = \frac{24.5}{9}= 2.72 cm ^{2}\)

The  area of triangle B is \(2.72cm ^{2}\)

Answer:

14 hours

Step-by-step explanation:

If you need to take 1 pill every 3.5 hours then this suggest that the effects of 1 pill lasts for 3.5 hours.

Therefore, if you take 4 pills then they will last: 4 x 3.5 = 14 hours

Answer: y = 17x + 114

Step-by-step explanation:

The equation for the slope-intercept form is y = mx + b.

Arrange the equation so that it resembles y = mx + b.

You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.

y + 5 = 17(x + 7)

y + 5 = 17x + 119

y + 5 - 5 = 17x + 119 - 5

y = 17x + 114

Answer:

Y = 17x + 114

Step-by-step explanation:

1. Y + 5 = 17 (x+7)

2. Y + 5 = 17x + 119   [Multiply the numbers in parenthesis by 17.]

3. Y = 17x + 114.     [To keep the balance and move the 5 over, subtract it from 119.]

Answer:

x=16/3

Step-by-step explanation:

4=3/4x+0

4=3x/4

4=3x/2square

4times4=16

3x/3=16/3

x=16/3