Determine the following for each sinsusoidal functions

The equivalent function of f(x) = 16x^2 - 1 is f(x) = (4x  + 1)(4x -1)

The function is given as:

f(x) = 16x^2 - 1

Express 16 as 4^2 and 1 as 1^2

f(x) = (4x)^2 - 1^2

Apply the difference of two squares

f(x) = (4x  + 1)(4x -1)

Hence, the equivalent function of f(x) = 16x^2 - 1 is f(x) = (4x  + 1)(4x -1)

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If the volume of the cube is 1/27 cubic inches. Then the volume of the prism will be 10 cubic inches.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

A prism is completely filled with 270 cubes that have an edge length of 1/3in.

Then the volume of the prism will be given as

Volume of prism = 270 (volume of the cube)

Then the volume of the cube will be

Volume of cube = (edge)³

Volume of cube = (1/3)³

Volume of cube = 1/27 cubic inches

Then the volume of the prism will be

Volume of prism = 270 × (1/27)

Volume of prism = 10 cubic inches

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Answer:

3(6g - 5)

Step-by-step explanation:

1. First, find the GCF of 15 and 18.

Factors of 15:

1, 3, 5, 15

Factors of 18:

1, 2, 3, 6, 9, 18

The GCF of 15 and 18 is 3.

2. Factorize

3(6g - 5)

3. Check you answer:

3(6g) + 3(-5)

18g - 15

Hope this helps!

Answer:

  53,157

Step-by-step explanation:

The population growth of a bacterial colony can be modeled by an exponential function of the form ...

  p(t) = a·b^t

where a is the initial population and b is the growth factor. The growth factor is ...

  b = 1 +r

where r is the growth rate.

__

In this problem we have ...

  a = 29,600

  b = 1 +5% = 1.05

  t = 12

So, the population after 12 hours is

  p(12) = 29600×1.05^12 ≈ 53,157

The colony will contain 53,157 bacteria in 12 hours.

Answer:

There is 57 snails after 14 weeks

Step-by-step explanation:

tripling every week means 3x

NOTE: x is defined as the number of weeks

started with 15 snails means at day 0 (x = 0 also known as y intercept)

y = mx + b       m is the slope, b is the y intercept

our equation: y = 3x + 15

y = 3(14) + 15

y = 42 + 15

y = 57

Answer:

let's find the value of x:

4)

5)

6)

Answer:

Goodluck and look at the pic

Addition:

Increased by, greater than, more than, sum

Subtraction:

Decreased by, decrease, less than, difference

Multiplication:

Times, equal groups, __ times as many, product

Division:

Quotient, divided by, goes into, split equally

There are 20 possible different combination of meals

The given parameters are:

Drinks = 4

Main dishes = 5

The number of different meals is calculated as:

Meals = Drinks * Main dishes

So, we have:

Meals = 4 * 5

Evaluate

Meals = 20

Hence, there are 20 possible different combination of meals

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Answer:

98°

142°

83°

97°

Step-by-step explanation:

m(arc)JL = 2 × 49° = 98°

m(arc)MJ = 360° - 120° - 98° = 142°

m<KJM = (120° + 46°)/2 = 83°

m<KLM = (360° - 120° - 46°)/2 = 97°

Answer:

The value of k to the nearest thousandth is -0.133

The of the turkey to the nearest degree after 4.5 hours is 186F

Step-by-step explanation:

Answer: [tex]4x^2-10x-6[/tex]

Step-by-step explanation:

[tex](x-3)(4x+2)[/tex]

[tex]Expand[/tex] [tex]the[/tex] [tex]polynomial[/tex] [tex]using[/tex] [tex]the[/tex] [tex]FOIL[/tex] [tex]method[/tex].

Therefore your answer is [tex]4x^2-10x-6[/tex]

Answer:

4x^2 -10x + 6

Step-by-step explanation:

multiply (x-3)(4x+2) using the foil method

(x*4x)+(x*2)+(-3*4x)+(3*2)= 4x^2+2x-12x+6 = 4x^2 -10x + 6

Answer:

22<x

Step-by-step explanation:

52-3x<-14

66<3x

(we divide both sides to 3)

22<x

Answer:

$288

Step-by-step explanation:

468 ÷ 26 = 18

so $18 per hour times 16 hours would give you $288, your right

Answer:

Area = 22.3 m^2

Perimeter 27.4 m^2

Step-by-step explanation:

Perimeter = __ m

Area __ m^2

The area of the triangle is about 4.2,

The area of the square is 4,

The area of the semicircle is 14.1,

14.1 + 4.2 + 4 = 22.3

Area = 22.3 m^2

9.4 + 6 + 4 + 4 + 4 = 27.4

Perimeter = 27.4 m^2

Therefore the area of the shape is about 22.3 m^2 and the perimeter is about 27.4 m^2.

There is no answer? So how am I supposed to answer it?

Answer:

Yeah How am I supposed to answer it?

Step-by-step explanation:

The linear equations for the system: y = x + 70 and y = 4x + 10

She'll attend 20 classes/month

The graph for the solution (20, 95) is in the image attached below

A linear equation can expressed in slope-intercept form, as, y = mx + b.

Linear equation for the first membership plan:

b = 70

m = 1

x = number of classes

y = total amount

Equation for the first membership plan: y = x + 70

Linear equation for the second membership plan:

b = 10

m = 4

x = number of classes

y = total amount

Equation for the second membership plan: y = 4x + 10

The system of equations are:

y = x + 70

y = 4x + 10

The solution is the point at which the line for both equations intersect on the graph as shown in the image attached below, which is: (20, 95).

This means Mary must attend 20 classes for each membership plan, she must attend 20 classes to pay the same total amount of $95 per month.

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The image of the triangle RST when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)

The coordinates of RST are given as:

R = (5,15)

S = (15,15)

T = (10,5)

The rule of 90° counterclockwise around the origin is:

(x,y) -> (-y,x)

So, we have:

R' = (-15,5)

S' = (-15,15)

T' = (-5,10)

Hence, the image of the triangle when rotated 90° counterclockwise around the origin is (-15,5), (-15,15) and (-5,10)

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Answer:

Step-by-step explanation:

Refer the attachment

Answer:

752.5 in³

Step-by-step explanation:

  Rectangular prism:

            l = 10 in ; w = 7 in ; h = 8 in

   [tex]\boxed{\text{Volume of rectangular prism=l*w*h}}[/tex]

                                                = 10 * 7 * 8

                                                = 560 in³

Half cylinder:

Diameter of the cylinder will be equal to the width of the rectangular prism.

       r = 7/2 = 3.5 inches ; h = 10 in

[tex]\boxed{\text{Volume of half cylinder =$\dfrac{1}{2}\pi r^2h$}}[/tex]

                                       [tex]\sf =\dfrac{1}{2}*3.14*3.5*3.510\\\\ = 192.5 \ in^3[/tex]

Volume of composite figure = 560 - 192.5

                                               = 752.5 in³

The probability of the sample having a mean gas mileage between 27 and 29 miles per gallon will be 0.0116.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

In 2014, new cars had an average fuel efficiency of 27.9 miles per gallon with a standard deviation of 6.8 miles per gallon. a sample of 30 new cars is taken.

Then the probability the sample has a mean gas mileage between 27 and 29 miles per gallon will be

The value of the z-score at x = 27, we have

[tex]z = \dfrac{27 - 27.9}{6.8}\\\\z = -0.13[/tex]

The value of the z-score at x = 29, we have

[tex]z = \dfrac{29 - 27.9}{6.8}\\\\z = 0.16[/tex]

Then the probability will be

[tex]\begin{aligned} P(-0.13 < z < 0.16 ) &= P (z < 0.16) - P(z > -0.13) \\\\&= P (z < 0.16) - [ 1 - P(z < -0.13) ]\\\\&= 0.56425 - (1 -0.44735)\\\\&= 0.0116 \end[/tex]

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Answer:

108

Step-by-step explanation:

x and 2/3 x are linear pair angles.

Sum of linear pair angles is 180.

x + 2/3 x = 180

3x/3 + 2x/3 = 180

( 3x + 2x )/3 = 180

5x/3 = 180

Cross multiply,

5x = 180 * 3

Divide 5 on both sides,

x = ( 180 * 3 )/5

  = 36 * 3

x = 108

Answer:

3x² - 3x + 16 = 0

Step-by-step explanation:

Standard form :

Solving :

Standard form ax²+bx+c=0

Done

Answer:

8 in is the answer

Step-by-step explanation:

The percentage of the seats in the theater were filled by the 6th graders on the trip is 78%.

Percentage is a measure of frequency that is expressed as the fraction of a number out of 100.

The percentage of the seats in the theater were filled by the 6th graders = (number of filled seats / total number of seats) x 100

(2496/3200) x 100 = 78%

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In a quadrilateral ABCD, the measure of the length of the quadrilateral CD will be 25.98 cm.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The length of AD will be

tan θ = AB/AD

AD = 12/ tan 35

AD = 17.14 cm

Then the value of the BD will be given by the Pythagoras.

BD² = AB² + AD²

BD² = 12² + 17.14²

BD² = 144 + 239.78

BD² = 437.78

BD = 20.92 cm

Then operate the sine rule in triangle BCD, we have

[tex]\dfrac{BD}{\sin C} = \dfrac{CD }{\sin B}\\\\\\\dfrac{20.92}{\sin 52} = \dfrac{CD }{\sin 102}\\\\\\CD = \dfrac{20.92 \times \sin 102}{\sin 52}[/tex]

On further solving, the value of CD will be

CD = 25.98

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Answer:

i think its 8z-9 if im not wrong :)

Step-by-step explanation: