Algebra 1 is all about equations and functions. First, you learned about Linear Functions then Quadratic Functions. Next, you learned about Rational Functions (indirect variation), then Exponential and then Radical Functions. Before Algebra 1 comes to a close, it is good to review these functions and compare them side by side.


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Linear Quadratic Rational Exponential Radical

Parent Function:

Notation

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

Parent Function:

Graph

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

Translation:

Graph a function which extends

through quadrant 1, 2, and 4.

If it is not possible to graph

through these quadrants,

chose one or two quadrants and explain the choice.

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

Write the function notation

for the above function

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

Domain and Range of

translated function


Reflection: Write a paragraph summarizing what you learned from this activity.

A Line graph

Sure hope this helps you

Answer:

The answer is x = 10.

Step-by-step explanation:

Two options:

1. Looking at the image it looks like a parallelogram. So, most side lengths are equal to each other or are the same.

2. We can use the Pythagorean Theorem to solve for x.

Answer: Cyclic quadrilateral

Step-by-step explanation:

Since angles OMB and ONC are right angles, it follows that AMO and ANO are also right angles. Thus, there is a pair of opposite angles that are supplementary, and thus AMON is a cyclic quadrilateral.

Answer:

244.92 or A

Step-by-step explanation:

r=39, so we can then find the diameter.

39*2= 78 (the diameter)

c=(pi)(d)

c=3.14*78

c= 244.92

Answer:

B.

Step-by-step explanation:

[tex]x^2 - 16x - 64 = 0[/tex]

[tex](x-8)^2 = 128[/tex]

[tex]x = 8 + \sqrt{128}[/tex]

or

[tex]x=8-\sqrt{128}[/tex]

so x = 19.3

or x = 3.3

Answer:

  slope 4/5

Step-by-step explanation:

The attachment shows the rise in green (4 grid squares), and the run in red (5 grid squares). The slope is the ratio rise/run.

__

The slope is rise/run = 4/5.

Answer:

milk because ur dad left the milk

Step-by-step explanation:

ur mum bc she is a pro statue

Answer: D. Using another person's ideas or writing without citing them.

Step-by-step explanation: Plagiarism is the use of someones work and claiming it as their own without giving them credit

The function f(x) is the linear and the function g(x) is the exponential. Then the equations are f(x) = 6x and g(x) = 3(2)ˣ.

A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.

The functions f(x) and g(x).

The table is shown below.

Let the function f(x) be the linear function and the function g(x) be the exponential. Then we have

Then the function f(x) will be

f(x) = mx + c

Then we have

12 = 2m + c

6 = m + c

Then we have

m = 6 and c = 0

Then the equation will be

f(x) = 6x

Then the function g(x) will be

g(x) = abˣ

Then we have

48 = ab⁴

24 = ab³

We have

a = 3 and b = 2

Then the function g(x) will be

g(x) = 3(2)ˣ

More about the function link is given below.

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Answer:

$1,129.27

Step-by-step explanation:

Compounded interest formula is

[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]

Where [tex]A[/tex] is the final amount, [tex]P[/tex] is the principal, [tex]r[/tex] is the anual interest in decimal, [tex]n[/tex] is the numer of compounded periods in one year and [tex]t[/tex] is the time in years.

[tex]P= 800\\r= 0.09\\n= 1\\t= 4[/tex]

So then we plug our numbers...

[tex]A=800(1+\frac{0.09}{1})^{1(4)}=800(1.09)^{4}[/tex]

[tex]A=$1,129.27[/tex]

After 4 years the amount would be $1,129.27

Answer:

D.72

Step-by-step explanation:

first you have to divide 96 and 4 than it will equal 24 than you multiple by 3 and so 24×3=72

Answer:

#3

A

#2

D

#1

B

Hope this helps

Answer:

1.) 10/16 = 5/8  

2.) 14/16 = 2 7/8

3.) 6/16 = 1 3/8

Step-by-step explanation:

Just count the lines.

Answer:

Area = 50.125 cm^2

Perimeter = 26 + 15 = 41 cm

Step-by-step explanation:

Area Rectangle = 6 * 7 = 42 cm^2

Area Triangle = 1/2 * (9.5 - 7) * 6.5

Area Triangle = 1/2 * (2.5) * 6.5 = 8.125 cm^2

Total Area = 42 + 8.125 = 50.125 cm^2

Perimeter Rectangle = 6 + 7 + 6 + 7 = 26 cm

Perimeter or Triangle = 2.5 + 6.5 + 6 = 15 cm

Total Perimeter = 26 + 15 = 41 cm

Answer:

2

Step-by-step explanation:

first, add terms

8 + 5 + 12 + 4 + 5 + 8 + 7 = 49

seven terms, therefore we divide by 7

49/7 = 7

find distance

8-7= 1

7-5= 2

12-7=5

7-4=3

7-5=2

8-7=1

7-7=0

added together you get 14,

14/7 = 2

your answer is 2

hope this helps:)

Answer:

See below

Step-by-step explanation:

Not sure what they are looking for here....unless there is more info

[tex]\sqrt[14]{y}[/tex]  =  [tex]y^{1/14}[/tex]     perhaps?

Answer:

3.5 centimeters

Step-by-step explanation:

75% of 2 cm = .75 x 2 = 1.5 cm

2 cm + 1.5 cm = 3.5 cm

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Given equation -

[tex]\bold{(x + 2) {}^{2} + 4(x + 2) - 5 = 0} \\ [/tex]

solve the parenthesis so as to obtain simpler terms

[tex]\bold{\implies \: ( x {}^{2} + 4x + 4 ) + 4x + 8 - 5 = 0}\\ [/tex]

solve the like terms and you'll obtain the required equation !

[tex]\bold{\implies \: x {}^{2} + 8x - 7 = 0}[/tex]

hope helpful ~

[tex]{\large{\red{\mapsto{\maltese{\underline{\green{\boxed{\blue{\underbrace{\overbrace{\pink{\pmb{\bf{Answer:}}}}}}}}}}}}}}[/tex]

x = -7, -1

Step-by-step explanation:

[tex] \sf {(x + 2)}^{2} + 4(x + 2) - 5 = 0[/tex]

let (x + 2) = y

So equation will be

[tex] \sf {y}^{2} + 4y - 5 = 0[/tex]

Further it becomes quadratic equation

we will solve it by breaking middle term method

[tex] \sf \implies {y}^{2} + 5y - y - 5 = 0 \\ \\ \sf \implies y(y + 5) - 1(y + 5) = 0 \\ \\ \sf \implies (y + 5)(y - 1) = 0[/tex]

Now put the value of y

[tex] \sf \implies (x + 2 + 5)(x + 2 - 1) = 0 \\ \\ \sf \implies (x + 7)(x + 1) = 0[/tex]

(x + 7) =0⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀(x + 1) = 0

x = -7⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ x = -1

Answer:

the measure of the fourth angle is 104 degrees

Step-by-step explanation:

Answer:

Fourth angle = 104º

Step-by-step explanation:

Angles in a quadrilateral add to 360º so:

90 + 46 + 120 + fourth angle = 360º

90 + 166 + fourth angle = 360º

256 + fourth angle = 360

fourth angle = 104º

The sum of the expression (x - 2) and (x+6) is 2x + 8

The sum of numbers simply means to add up the numbers.

Therefore,

(x  -2) + (x + 6)

Hence,

(x - 2) + (x + 6)

open the brackets

Therefore,

x - 2 + x + 6

combine like terms

x + x + 2 + 6

add or subtract the like terms

2x + 8

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Answer:

a) x=loge3 ( log e base 3)

b)4=e^y

Answer:

A.) loge(x)=3

B.)  e^y =4

Step-by-step explanation:

A.) loge(x)=3

B.)  e^y =4

Answer:

2:3

Step-by-step explanation:

Simplica Los dos numeros

6 ÷ 3 = 2

9 ÷ 3 = 3

Answer:

Option C is the correct answer

Step-by-step explanation:

The Cost of Carl's first item is 3.95. The Cost of his second item is 4.95. To find the total amount we need to add these two numbers together.

3 plus 4 is 7

95 cents plus 95 cents is 1.90

7+1.90 is 8.90

The total cost is $8.90

Hope this helps!

Considering the equation of the circle graphed on this problem, the value of y is given by:

[tex]y = -\frac{1}{4}[/tex]

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In this problem, the circle is centered at the origin, with radius 1, hence the equation is given by:

[tex]x^2 + y^2 = 1[/tex]

Hence, when [tex]x = -\frac{\sqrt{15}}{4}[/tex], the values of y are given by:

[tex]y^2 = 1 - x^2[/tex]

[tex]y^2 = 1 - \frac{15}{16}[/tex]

[tex]y^2 = \frac{1}{16}[/tex]

Looking at the graph, we want the negative value of y, hence:

[tex]y = -\sqrt{\frac{1}{16}}[/tex]

[tex]y = -\frac{1}{4}[/tex]

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Answer: its positive 1/4

Step-by-step explanation: got the question right

A mean is an arithmetic average of a set of observations. The height of the 9th-grade students will be 66.7±4 inches.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given the height of the 10 selected students is {66, 61, 67, 61, 75, 71, 70, 61, 61, and 74}, also, the standard deviation of the 9th-grade students is 4 inches. Therefore, The mean height in inches of the selected students is,

Mean = (66+61+67+61+75+71+70+61+64)/10 = 66.7inches

Therefore, the height of the 9th-grade students will be 66.7±4 inches.

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Answer:

[tex]\displaystyle \boxed{ \frac{dz}{du} = \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }[/tex]

[tex]\displaystyle \boxed{ \frac{dz}{dv} = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Property [Addition/Subtraction]:
[tex]\displaystyle (u + v)' = u' + v'[/tex]

Derivative Rule [Basic Power Rule]:

Multivariable Calculus

Partial Derivatives

Partial Derivative Rule [Chain Rule]:
[tex]\displaystyle \frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{\partial x}{\partial t} + \frac{\partial w}{\partial y} \frac{\partial y}{\partial t} + \frac{\partial w}{\partial z} \frac{\partial z}{\partial t}[/tex]

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle x = 2u + v[/tex]

[tex]\displaystyle y = \frac{u}{v}[/tex]

[tex]\displaystyle z = e^{xy}[/tex]

Step 2: Find Derivatives

[tex]\displaystyle \frac{dz}{du}[/tex]:

We can find the partial derivatives by differentiating using basic differentiation rules found under "Calculus":

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial u} & = 2 \\\frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial y}{\partial u} & = \frac{1}{v} \\\end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{du} & = 2ye^{xy} + \frac{xe^{xy}}{v} \\& = \frac{2ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v} \\& = \boxed{ \frac{e^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 4u + v \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to u.

[tex]\displaystyle \frac{dz}{dv}[/tex]:

We can find the partial derivatives by using the same method(s):

[tex]\displaystyle\begin{aligned}\frac{\partial z}{\partial x} & = ye^{xy} \\\frac{\partial x}{\partial v} & = 1 \\ \frac{\partial z}{\partial y} & = xe^{xy} \\\frac{\partial x}{\partial v} & = \frac{-u}{v^2} \\ \end{aligned}[/tex]

Substituting in our partial derivatives and our variables x and y, we can obtain a final derivative:

[tex]\displaystyle\begin{aligned}\frac{dz}{dv} & = ye^{xy} + \frac{-uxe^{xy}}{v^2} \\& = \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} + \frac{-u(2u + v)e^\big{\frac{u(2u + v)}{v}}}{v^2} \\& = \boxed{ \frac{ue^\big{\frac{u(2u + v)}{v}}}{v} \Bigg[ 1 - \frac{2u + v}{v} \Bigg] }\end{aligned}[/tex]

∴ we have found the derivative of z with respect to v.

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Topic: Multivariable Calculus

Unit: Partial Derivatives and Applications

Answer:

BC = 6 units

Given following:

Solve for BC:

Formula:

[tex]\rightarrow \sf tan(A) =\dfrac{opposite}{adjacent}[/tex]

insert values and make them proportional

[tex]\rightarrow \sf tan(A) =\dfrac{BC}{AC} = \dfrac{3}{2} = \dfrac{6}{4}[/tex]

So, BC is 6 units.

Answer:

1)  BC = 6

2)  B = 33.7°  (nearest tenth)

3)  [tex]\sf AB=2\sqrt{13}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}[/tex]

where:

Given:

Substituting the values into the tan ratio:

[tex]\implies \sf \tan A=\dfrac{BC}{AC}=\dfrac{BC}{4}[/tex]

Given:

[tex]\sf \tan A=\dfrac{3}{2}[/tex]

Therefore:

[tex]\implies \tan \sf A = \tan \sf A[/tex]

[tex]\implies \sf \dfrac{BC}{4}=\dfrac{3}{2}[/tex]

[tex]\implies \sf BC=\dfrac{4 \cdot 3}{2}=6[/tex]

Given:

Substituting the values into the tan ratio and solving for B:

[tex]\implies \sf \tan B=\dfrac{AC}{BC}[/tex]

[tex]\implies \sf \tan B=\dfrac{4}{6}[/tex]

[tex]\implies \sf B=\tan ^{-1}\left(\dfrac{4}{6}\right)[/tex]

[tex]\implies \sf B=33.69006753...^{\circ}[/tex]

[tex]\implies \sf B=33.7^{\circ}\:(nearest\:tenth)[/tex]

Pythagoras’ Theorem

[tex]a^2+b^2=c^2[/tex]

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting the values into the formula and solving for AB:

[tex]\implies \sf AC^2+BC^2=AB^2[/tex]

[tex]\implies \sf 4^2+6^2=AB^2[/tex]

[tex]\implies \sf 16+36=AB^2[/tex]

[tex]\implies \sf AB^2=52[/tex]

[tex]\implies \sf AB=\sqrt{52}[/tex]

[tex]\implies \sf AB=2\sqrt{13}[/tex]

Answer:

y = -3x - 1

hope this helps!