Topic/Objective: Function Applications pp. 228-252
• Write the equation of a linear function and determine the rate of change of the function using a point on the line and the slope of the line.
Write the equation of a linear function and determine the rate of change of the function using two points on the line.
• Determine whether a function is linear or nonlinear using a graph.
• Determine whether a function is linear or nonlinear using a table.
• Determine whether a function is linear or nonlinear using an equation.
• Compare the properties of two linear functions that are represented differently.
Name
Class/Time
Date
Essential Question: How can we model relationships between quantities?
Questions/Voc. Terms/Properties

Define the vocabulary terms below:
Linear function
Nonlinear function
Increasing function
Decreasing function
Constant


How can linear models be interpreted?



How are independent and dependent variables represented on a coordinate plane?




What is the slope and y-intercept of the helicopter altitude from the graph?




What does 35 and 1.2 in the equation represent in the equation?


Describe the situation each equation represents for the water level in other tanks.
How can we represent the water level in a tank that’s empty at first but rises at a rate of 2.1 /s?


What is the process for solving problems involving constant rates?


What is the total cost for movie rental for 1 month? 5 months? 7 months? 1 year?

Is this a linear model? Explain.



What describes the relationship between the independent and dependent variables of the function?

What determines whether a function is linear or nonlinear?






How can we determine if a function is increasing or decreasing?

How can we determine whether a graph is increasing or decreasing?








How can functions be compared?


How can functions be represented?



How can we determine which line has a greater rate of change?




When interpreting a function graph, what key features can we look for?




How can we draw conclusions about an object’s speed?




Example Problems & Steps/Vocabulary Definitions/Property Descriptions

Write/type definitions beside each term below:








p. 228 Copy yellow box




p. 228 Copy purple box






pp. 228-229 Study graph and copy solutions below:
Example 1
A.

B.


pp. 229-230 Copy solution below:
Example 2

A.

p. 230 Copy solution below:
B.

p. 230 Copy solution below:
C.



pp. 231-231 Study table and graph and copy steps below:
Example 1



pp. 232-233 Study table and copy solution below:
Example 2
A.

Study rate of change between values and copy solution below:
B.


p. 234 See yellow box




pp. 234-235 Study tables & graph and copy solutions below:
Example 1
A. y = 2x - 1

B.



pp. 236 See pink box



pp. 236-237 Study graphs and write solutions below:
Example 2
A.

B.

C.

D.

p. 240 See yellow box


p. 240 See paragraph
Study functions pp. 240-244



p. 244 see graph and pink box





p. 246







p. 247 see pink box
Study pp. 247-252
Summary: Connections, Reflections, Analysis about what you learned (3 or more sentences, or you may use the following prompts - be specific):

Today my notes say…
I can use my notes to…
My notes mean…

Answer:

It will take the object 2 seconds to reach the maximum height.

Step-by-step explanation:

The original equation is [tex]h=-14t^2+56t+60[/tex].

The object reaches the maximum height when derivative of [tex]h[/tex] is zero

[tex]\frac{dh}{dt}=0[/tex]

So let us take evaluate the derivative of [tex]h[/tex]

[tex]\frac{dh}{dt} =\frac{d}{dt} (-14t^2+56t+60)=\frac{d}{dt} (-14t^2)+\frac{d}{dt}(56t)+\frac{d}{dt} (60)[/tex]

[tex]=-28t+56[/tex]

this must be equal to 0:

[tex]-28t+56=0[/tex]

[tex]t=\frac{-56}{-28}[/tex]

[tex]\boxed{ t=2}[/tex]

It will take the object 2 seconds to reach the maximum height.

Answer:

0.53

Step-by-step explanation:

5/10 + 3/100=0.53

Answer:

0.53

Step-by-step explanation:

5/10 + 3/100

by Elysium

(50 +3)/100

53/100

0.53

To solve the system of equations using substitution, Fina needs to isolate one variable and substitute it into the other equation. The solution to the system of equations is x = -3 and y = -9.

To solve this system of equations using substitution, Fina needs to isolate one variable in one of the equations and then substitute that expression into the other equation.

Here are the steps:

Choose one equation and isolate one variable. Let's isolate x in the first equation: 2x - y = 3. Add y to both sides: 2x = y + 3 and divide by 2: x = (y + 3)/2.

Substitute the expression for x in the other equation. Replace x in the second equation with (y + 3)/2: -1.5((y + 3)/2) + 3y = -18.

Solve the equation for y. Simplify the equation: -1.5y - 4.5 + 3y = -18. Combine like terms: 1.5y - 4.5 = -18. Add 4.5 to both sides: 1.5y = -13.5. Divide by 1.5: y = -9.

Substitute the value of y back into the expression for x to find its value. Replace y in x = (y + 3)/2 with -9: x = (-9 + 3)/2 = -6/2 = -3.

Therefore, the solution to the system of equations is x = -3 and y = -9.

Step-by-step explanation:

Given: slope of line m = 56 & line contain point is (−8,−4).

[tex] \therefore (x_1, \:\: y_1) = (-8, \:\: - 4)[/tex]

Equation of line in slope point form is given as:

[tex]y - y_1 =m(x - x_1) \\ \\ \therefore \: y - ( - 4) = 56 \{x - ( - 8) \} \\ \\ \blue{ \boxed{\therefore \: y + 4= 56 (x + 8) }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: point \: form)\\ \\ \therefore \: y + 4= 56x + 56 \times 8 \\ \\ \therefore \: y + 4= 56x + 448 \\ \\ \therefore \: y = 56x + 448 - 4 \\ \\ \huge \red{ \boxed{\therefore \: y = 56x + 444 }}\\ ..(this \: is \: the \: equation \: of \: line \: in \: \\ slope \: intercept \: form)[/tex]

Answer:

y+4 = 56(x+8)

Step-by-step explanation:

y-y1 = m(x-x1)

y-(-4) = 56(x-(-8))

y+4 = 56(x+8)

If needed, simply it further

y+4 = 56x+448

y = 56x+444

Answer:

[tex]m=-\frac{39}{80}[/tex]

Step-by-step explanation:

we have

[tex]\frac{2}{5}=2m+\frac{11}{8}[/tex]

Solve for m

That means ----> Isolate the variable m

Multiply both sides by 40 to remove the fractions

Note: 40=(8)(5)

[tex](40)\frac{2}{5}=(40)2m+(40)\frac{11}{8}[/tex]

[tex]16=80m+55[/tex]

subtract 55 both sides

[tex]16-55=80m\\-39=80m[/tex]

Divided by 80 both sides

[tex]m=-\frac{39}{80}[/tex]

Answer:

30+(5X12)+2x=90X2x

Step-by-step explanation:

5x12= 60

60+30=90

90x2x

We don't know how many times they use the facility so it stays 2x and you have to times that by 90 since that's the total cost minus the 2x.

Answer: 2 is the nearest whole number.

Step-by-step explanation:

Answer:

x=2, y=8. (2, 8).

Step-by-step explanation:

y-2x=4

2x+3y=28

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

y=2x+4

2x+3(2x+4)=28

2x+6x+12=28

8x+12=28

8x=28-12

8x=16

x=16/8

x=2

y-2(2)=4

y-4=4

y=4+4

y=8

Answer:

62.9mi/hr

Step-by-step explanation:

How far the car is moving is the speed.

We need to calculate the speed given that, the distance traveled is [tex]330\frac{1}{3} \:miles[/tex]

The time given is [tex]5\frac{1}{4}[/tex] hours.

Recall that: [tex]Speed=\frac{Distance}{Time}[/tex]

We plug in the values to get:

[tex]Speed =\frac{330\frac{1}{3} }{5\frac{1}{4} }[/tex]

We simplify to get:

[tex]Speed=\frac{3964}{63} =62.\overline{920634}[/tex]

Answer:

A(2,3), B(6,4), C(5,8), D(1,7)

Step-by-step explanation:

We were given the initial vertex at (2,3).

We want to create a square using the digits 0 to 9, at most one time each.

Keeping in mind the following properties of a square:

All sides are congruent

All angles are right angles

Hence the other three vertices are: B(6,4), C(5,8), D(1,7)

See attachment.

The question is about forming a square using unique digits from 0 to 9 to form coordinates with one vertex at (2,3). The coordinates of the square are (2,3), (4,3), (4,5) and (2,5) using digits 0,2,3,4 and 5.

This type of problem is a geometric shape puzzle that involves basic principles of coordinate geometry and the usage of digits 0 to 9. Let's consider the point (2,3) as the bottom-left vertex of the square.

We know that a square has all sides equal, so we can choose point (4,3) as the bottom-right vertex (2+2=4), then (4,5) as the top-right vertex (3+2=5), and finally (2,5) as the top-left vertex.

We used the numbers 0,2,3,4,5 from the set of digits from 0 to 9.

https://brainly.com/question/31981318

#SPJ3

b)

|2x−3y| if x=0.5; y=−0.7

Substitute: |2(0.5)-3(-0.7)|

Simplify: |1+2.1|

Simplify: |3.1|

Since it is an absolute value, it will always be positive: 3.1

d)

|−3 |x| +2x−1| if x=−5

Substitute: |-3(|-5|)+2(-5)-1|

Absolute value is positive: |-3(5)+5(-5)-1|

Simplify: |-15-25-1|

Simplify: |-41|

Absolute value always positive: 41

Answer for the first question:

[tex]a)3a+5b~,when~a=-2;b=-1[/tex]

[tex]=(3)(-2)+(5)(-1)[/tex]

[tex]=-11[/tex]

Answer for the second question:

[tex]b)2x-3y~,when~x=0.5;y=-0.7[/tex]

[tex]=(2)(0.5)-(3)(-0.7)[/tex]

[tex]=3.1[/tex]

Answer for the third question:

[tex]c)4a+8-a,~when~a=-2[/tex]

[tex]=(4)(-2)+8-(-2)[/tex]

[tex]=2[/tex]

Answer for the fourth question:

[tex]d)-3x+2x-1,~when~x=-5[/tex]

[tex]=(-3)(-5)+(2)(-5)-1[/tex]

[tex]=4[/tex]

Answer:

7x+5y

Step-by-step explanation:

Combine like terms:

5x+2x+(-y)+6y

7x+(6y-y)

7x+5y

Hope this helped!

Answer: 7x+5y

Step-by-step explanation:

(5x-y)+(2x+6y)

5x−y+2x+6y

(5x+2x)+(−y+6y)

7x+5y

Hope this helps, HAVE A BLESSED AND WONDERFUL DAY! I also hope you had a great Superbowl Weekend! :-)

- Cutiepatutie ☺❀❤

Answer:

-6-2x

Step-by-step explanation:

Expand:

(x+3)2 = 2x+6

-4(x+3) = -4x-12

2x+6-4x-12 = -6-2x

Answer:

b

Step-by-step explanation:

2 x 2 = 4/5

2 x -7 = -14 / 5

Answer:

B) 4/5x-14/5

Step-by-step explanation:

2/5(2x-7)

2/5*2x= 4/5x

2/5*7=14/5

Answer:

475

Step-by-step explanation:

To find the cost of the bench, subtract 99 from 1049, then divide by 2. Add 99 to the answer(475) to get the cost of the garden table(574).

Answer:

y=5m-3

Step-by-step explanation:

The cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

Solution:

Let "a" be the cost of each ribeye steak dinners

Let "b" be the cost of each grilled salmon dinners

A waitress sold 11 ribeye steak dinners and 12 grilled salmon​ dinners, totaling ​$560.63 on a particular day

Thus we frame a equation as:

11 x cost of each ribeye steak dinners + 12 x cost of each grilled salmon dinners = 560.63

[tex]11 \times a + 12 \times b = 560.63[/tex]

11a + 12b = 560.63 -------- eqn 1

Another day she sold 16 ribeye steak dinners and 6 grilled salmon​ dinners, totaling ​$584.46

Thus we frame a equation as:

16 x cost of each ribeye steak dinners + 6 x cost of each grilled salmon dinners = 584.46

[tex]16 \times a + 6 \times b = 584.46[/tex]

16a + 6b = 584.46 ------------ eqn 2

Let us solve eqn 1 and eqn 2

Multiply eqn 2 by 2

32a + 12b = 1168.92 ------- eqn 3

Subtract eqn 1 from eqn 3

32a + 12b = 1168.92

11a + 12b = 560.63

( - ) ----------------

21a = 1168.92 - 560.63

21a = 608.29

Divide both sides by 21

[tex]a = 28.96 \approx 29[/tex]

Substitute a = 29 in eqn 1

11(29) + 12b = 560.63

319 + 12b = 560.63

12b = 560.63 - 319

12b = 214.63

Divide both sides by 12

[tex]b = 20.13 \approx 20[/tex]

Thus cost of each ribeye steak dinner is $ 29 and cost of each grilled salmon dinner is $ 20

Answer:

[tex]f(w) = 15 - \frac{w}{8345}[/tex]

Step-by-step explanation:

Water begins draining from a tank when the tank has 15 gallons of water in it.

Now, if we define f(w) as a function that represents the number of gallons of water remains in the tank after w pounds of water that have drained from the tank since the tank started draining, then the function can be represented as

[tex]f(w) = 15 - \frac{w}{8345}[/tex]

Since, w pounds of water is equivalent to [tex]\frac{w}{8345}[/tex] gallons of water. (Answer)

(Recall that water weighs 8.345 pounds per gallon.)

The function f should be defined is [tex]f(w) = 15 - \frac{w}{8345}[/tex]

A tank has 15 gallons of water in it when water begins draining from the tank. (Recall that water weighs 8.345 pounds per gallon.)

Since we have to defined the function so it is f(w) that shows the number of gallons of water remains in the tank after w pounds of water.

So, the function should be [tex]f(w) = 15 - \frac{w}{8345}[/tex]

learn more about the function here: https://brainly.com/question/12394974

Answer:

Reflect the parent function over the x-axis, and translate it 8 units to the left.

Step-by-step explanation:

The given function is

[tex]y = - \sqrt{x + 8} [/tex]

The parent function is

[tex]y = \sqrt{x} [/tex]

Since there is a negative multiply the transformed function, there is a reflection in the x-axis.

Since 8 is adding, within the square root, there is a horizontal translation of 8 units to the left.

Therefore to graph the given function, reflect the parent function over the x-axis, and translate it 8 units to the left.

Take the reflection of the graph about the x-axis and then translate the graph of the function by 8 units in the left direction and this can be determined by using the rules of transformation.

Given :

Function  --  [tex]\rm y = - \sqrt{x+8}[/tex]

The following steps can be used in order to determine the correct statement:

Step 1 - The parent function is given below:

[tex]\rm y = \sqrt{x}[/tex]

Step 2 - Now, draw the graph of the parent function.

Step 3 - Take the reflection of the graph about the x-axis. So, the function becomes:

[tex]y =- \sqrt{x}[/tex]

Step 4 - Now, translate the graph of the function obtained in the above step by 8 units in the left direction. So, the function becomes:

[tex]y = -\sqrt{x+8}[/tex]

Therefore, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/14375099

The prime factorization of 356 is found by dividing it by the smallest prime numbers step by step, leading to the solution of 2×2×89.

The prime factorization of 356 involves breaking down the number into its prime factors, which are numbers that can only be divided by 1 and themselves. To start, we look for the smallest prime number that can divide 356. We find that 2 is the smallest prime factor of 356 (since 356 is an even number).

Dividing 356 by 2, we get 178. Continuing this process, 178 is also even, so we divide by 2 again to get 89. Upon reaching 89, we find that it is a prime number because it cannot be divided evenly by any number other than 1 and itself.

Therefore, the prime factorization of 356 is 2×2×89. This means that 356 can be expressed as a product of these prime numbers.

Answer:

In an isosceles right triangle, the equal sides make the right angle. They have the ratio of equality, 1 : 1. ... Therefore each of those acute angles is 45°.

Step-by-step explanation:

Yo sup??

Actually the lenght of the segment won't change cause rotation about origin doesn't affect the lenght of the triangle.

Therefore

ST=S'T'=8 units

Hope this helps.

Answer:

its 90cm^2

Step-by-step explanation:

hope d answer will help u

Answer:

the answer is x=6 or x=-16

The correct answer is x = 6 or x = -16.

To find the roots of the quadratic function f(x) = x2 + 10x - 96, we need to solve the equation x2 + 10x - 96 = 0 using the quadratic formula.

Using the quadratic formula, x = (-b ± √(b2 - 4ac)) / 2a, where a = 1, b = 10, and c = -96, we get x = 6 or x = -16 as the roots of the function f(x).

Therefore, the correct answer is x = 6 or x = -16.

Answer:

81

Step-by-step explanation:

3*3*3*3= 81

Answer: b is right

Step-by-step explanation:

Answer:

X Intercept: (-14/9,0) Y intercept: (0,-14)

Step-by-step explanation:

To find the X intercept, plug in y=0... so it would look like this, -9x-14=0, then solve. -9x=14...x=-14/9

To find the Y intercept, plug in x=0...so it would look like this, -9(0)-14=y, then solve. 0-14=y...-14=y

Answer:

The intersection with the x-axis is at B(-14/9,0), and with the y-axis at A(0,-14).

x=0, y=-9x-14, y=-9*0-14, y=-14 A(0,-14)

y=0, y=-9x-14, 0=-9x-14, 0+14=-9x

-9x=14, x=-14/9 B(-14/9,0)

Answer:

f(5) = 29

Step-by-step explanation:

Step 1:  Identify the function

f(x) = 4x + 9

Step 2:  Let x equal 5 in the function

f(5) = 4(5) + 9

Step 3:  Multiply

f(5) = 20 + 9

Step 4:  Add

f(5) = 29

Answer:  29

Answer:

[tex]F(x)=29[/tex]

Step-by-step explanation:

Given function:

                 [tex]F(x) = 4x+9[/tex]

                   Find F(x) at , [tex]x= 5[/tex]

The value of 'x' is given for which we have to find the value of F(x)

Putting the given 'x' in the function equation

                      [tex]F(x) = 4x+9\\\\ F(x) = 4(5)+9\\\\ F(x) = 20+9\\\\ F(x) = 29[/tex]

        So , [tex]F(x)=29[/tex] at  [tex]x=5[/tex]

Answer:

100=5x+15

x= # of days

Step-by-step explanation:

100 is the total. Then 5 tickets every day whivh would be 5x. And she already sold 15 so u add 5x and 15. (x wold be the amount of days)