unit 1 equations & inequalities homework 3

Equations and Inequalities (Algebra 2 Curriculum Unit 1) | All Things Algebra®

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This Equations and Inequalities Unit Bundle includes guided notes, homework assignments, two quizzes, a study guide and a unit test that cover the following topics:

• Simplifying Radicals

• Classifying Numbers (the Real Number System)

• Order of Operations (Includes absolute value and square roots)

• Evaluating Expressions (Includes absolute value and square roots)

• Solving Multi-Step Equations

• Literal Equations

• Word Problems

• Multi-Step Inequalities

• Compound Inequalities • Special Case Compound Inequalities

• Absolute Value Inequalities

ADDITIONAL COMPONENTS INCLUDED:

(1) Links to Instructional Videos: Links to videos of each lesson in the unit are included. Videos were created by fellow teachers for their students using the guided notes and shared in March 2020 when schools closed with no notice.  Please watch through first before sharing with your students. Many teachers still use these in emergency substitute situations. (2) Editable Assessments: Editable versions of each quiz and the unit test are included. PowerPoint is required to edit these files. Individual problems can be changed to create multiple versions of the assessment. The layout of the assessment itself is not editable. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own.

(3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. Each page is set to the background in Google Slides. There are no text boxes;  this is the PDF in Google Slides.  I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead! 

This resource is included in the following bundle(s):

Algebra 2 Curriculum

More Algebra 2 Units:

Unit 2 – Linear Functions and Systems

Unit 3 – Parent Functions and Transformations

Unit 4 – Quadratic Equations and Complex Numbers

Unit 5 – Polynomial Functions

Unit 6 – Radical Functions

Unit 7 – Exponential and Logarithmic Functions

Unit 8 – Rational Functions

Unit 9 – Conic Sections

Unit 10 – Sequences and Series

Unit 11 – Probability and Statistics

Unit 12 – Trigonometry

LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable , meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at [email protected].

COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

© All Things Algebra (Gina Wilson), 2012-present

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Math With Mrs. Molina

There are two things we must give children: the first one is roots and the other wings., unit 3: equations and inequalities, click here to go to the ixl website for all kinds of 8th grade topics and review problems..

What is an equation?

Examples: 4 + 3  = 7        or        3x + 5 = 10

An equation is a number sentence. We call it an equation because it has an equal sign.

The 5 Steps to Writing an Equation or Inequality

Step 1. read and  underline   the question, step 2. find your   χ  (your variable/unknown) and box it, step 3. circle the math words  (product, quotient, each,                per, together, sum, difference, squared ), step 4 . replace the operation words with their symbols (              • , + , – ,  ÷ , / , = , < , > , ≤ , ≥ ,√ , ≠ , ² , ³ ), step 5. write the equations.

  Don’t forget our cool ‘dance’ we did to remember this!

WRITING EQUATIONS PRACTICE PROBLEMS:

Click here  to practice Writing Equations online and get automatic feedback (it grades it)! 🙂

With Equations, Inequalities and Expressions we always want to combine like terms 1st!

Here is an example on how to do that:

Once all like terms have been combined then we can solve.

Solving Equations with Models

To create your own equations using models click here !

MODELING EQUATIONS PRACTICE PROBLEMS:

Click here  to practice Modeling Equations online and get automatic feedback (it grades it)! 🙂

Solving Equations Algebraically

Here is another example solving algebraically, solve √(x/2) = 3.

And the more “tricks” and techniques you learn the better you will get.

Here is an example of how we solved equations in class:

SOLVING EQUATIONS (with variables on both sides PRACTICE PROBLEMS:

Click here  or here  to practice Solving Equations online and get automatic feedback (it grades it)! 🙂

Systems of Equations

For information on systems of equations click here ., simple vs. compound  interest, introduction to interest :.

http://www.mathsisfun.com/money/interest.html

SIMPLE INTEREST

  I = Prt  

• I = interest owed  [$] (this is ONLY the interest borrowed)
• P = amount borrowed (called “Principal”)  [$]
• r = interest rate   [%] (you have to divide the percent by 100)  For information On Percents click here !
• t = time    [years]

Simple interest is money you can earn by investing some money (the principal). The interest (percent) is the rate that makes the money grow!

COMPOUND INTEREST

  A = P(1+r)^t  

• A = All of it / Actual / total amount owed (this amount includes the interest and the principal)   [$]
• P = amount borrowed (called “Principal”)    [$]
• r = interest rate     [%]

Compound interest is very similar to simple interest. The difference is that compound interest grows much faster ! The reason it grows faster is because the interest (percent) has an exponent .

********** MAKE SURE TO READ THE QUESTION AND SEE EXACTLY WHAT IT IS ASKING DOES IT JUST WANT THE INTEREST OR THE TOTAL (All of it) ???????? *************************

For information on compound interest click  here.

SIMPLE INTEREST PRACTICE PROBLEMS:

Click here  or here  to practice Simple Interest online and get automatic feedback (it grades it)! 🙂

COMPOUND INTEREST PRACTICE PROBLEMS:

Click here  or here  to practice Compound Interest online and get automatic feedback (it grades it)! 🙂

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Which values from the set (-6. -4, -3, -1, 0, 2) satisfy this inequality? -1/2x+3≥50 -4 -3. -1, 0, and 2 only O-1, 0 and 2 only 0-6, -4, -3, and -1 only 0 -6 and -4 only

D, -6 and -4 only​

Explanation:

Given the inequality:

First, subtract 3 from both sides:

Next, multiply both sides by -2.

Note that when inequality is multiplied by a negative number, the inequality sign is reversed.

Therefore, the values from the set (-6. -4, -3, -1, 0, 2) that satisfy this inequality are: -6 and -4 only​

Related Questions

Suppose the population of a certain clty is 3775 thousand it is expected to decrease to 2911 thousand in 50 years. Find the percent decreaseThe percent decrease is approximately %(Round to the nearest tenth )

The current population of the city is 3775000. Since it is expected to decrease to 2911000, the percent decrease would be

21. Higher Order Thinking Ms. Webster works 4 days a week at her office and 1 day a week at home. The route to Ms. Webster's office is 23.7 miles. The route home is 21.8 miles. About how many miles does she drive for work each week? Explain how you found your answer.

When she works at her office, she travels 23.7 miles from her home to her office and then 21.8 miles to return from the office to her home.

This adds 23.7+21.8 = 45.5 miles per day of work at the office.

The days she works at home, she does not travel.

Then, we can multiply the number of days seh work at the office by the distance she travels and we can find the miles she travels per week:

Answer: she drives 182 miles per week.

Graph the image of the given triangle, reflected across the y-axis.

The coordinates of the pre-image is A(-5, 3), B(3, -2), C(-2, -8). When reflected across the y-axis, the coordinates become A(5,3), B(-3, -2), C(2, -8). The reflected image is attached accordingly.

When a point is reflected across the y-axis, the y-coordinate stays unchanged, but the x-coordinate is assumed to be the additive inverse . That is, when the coordinate (x, y) is reflected over the y-axis, the resulting coordinate is (-x, y).

The coordinates of the pre-image is A(-5, 3), B(3, -2), C(-2, -8). After it is reflected across the y-axis, the coordinates change to A(5,3), B(-3, -2), C(2, -8). The new coordinates are the additive inverse of the original coordinates.

Learn more about reflection : https://brainly.com/question/26642069 #SPJ1

The ratio of Aspens to Ponderosa Pines in a part of a forest is 12 to 16. If there are 12 ponderosa Pines, how many Aspens are there?

If  there are 12 ponderosa Pines then there  will be 9 Aspens .

In the question ,

it is given that

the ratio of Aspens to Ponderosa Pines is 12 to 16 .

which is Aspens : Ponderosa = 12 : 16

it can be written as number of  Aspens = 12x

and number of Ponderosa Pines = 16x

given in the question , that number of Ponderosa pines = 12

So , number of  Aspens = 12x = 12(3/4) = 3*3 = 9

number of Aspens = 9

Therefore , If  there are 12 ponderosa Pines then there , will be 9 Aspens .

Learn more about Ratio here

https://brainly.com/question/69704

What is "a" in this equation?

Step-by-step explanation:

12a - 16a = -8

Collect like terms...

Divide both sides of the equation by -4 to isolate the unknown variable...

Hope this helps! :)

1. Factor out an [tex]a[/tex] from [tex]12a-16a[/tex] to get [tex]a(12-16)=-8[/tex]

2. Simplify  [tex]a(12-16)[/tex] to get [tex]-4a=-8[/tex]

3. Finally, we divide -4 from each side to get [tex]a=2[/tex]

(9+64x16) divided by (2+6)

We are required to solve:

We would be evaluating the numerator and denominator expressions and then we would take the division as shown below:

Don't forget the rule of BODMAS applies to this problem. So multiplicaton before adding

Answer: 129.125

9+64x16        =    1033

------------             --------

  2+6            =       8

1033 / 8.  = 129.125  

I need help with this question please. Ignore the wording below. Fyi this is a part of a homework practice

Given that the zeros of our polynomial function are:

We know that there are 2 real zeros, and 2 complex zeros. (3i and -3i).

So, what we're going to do to find the equation of this polynomial, is to multiply all zeros together, such that we obtain an expression that we can simplify. Like this:

Now, we're going to multiply and distribute:

Remember that:

So, we can rewrite:

Multiplying these terms, we got that:

QUICK ANSWERS ONLY! 47. Find the value of x. The diagram is not to scale.4242402323A. 80B. 84C. 40D. 46

The first Option is the correct option

Find the volume of a square pyramid with a perimeter of 56 inches and a slant height of 25 inches.

The volume of a square pyramid is

Where a is the length of each base side.

First, we have to find a using the perimeter.

Then, we find h using Pythagorean's Theorem,

Where c = 25in, b = 7in, and a represents the height h

Now, we find the volume

∠1 and ∠2 are vertical angles. m∠1 = 40° and m∠2 = (7x + 5)°.

The value of x is 5°.

∠1 and ∠2 are vertical angles , m∠1 = 40° and m∠2 = (7x + 5)°.

Vertical angles are angles that are opposite to each other and by definition these angles are congruent or equal.

That is m∠1 and m∠2 are equal.

40 = (7x + 5)

7x = 40 - 5

divide by 7 on both sides we get

7x/7 = 35/7

Therefore the value of x is 5°.

Learn more about the value and vertical angles here:

https://brainly.com/question/23087234

Remote Assignment 1-5 Score: 37/100 3/8 answered Progress saved Done Question 4 < > B0/13 pts 10 A BX bisects ZABC. If m ZABC = 9 x + 18 and mZCBX = 5 x + 7, find the value of mZABX. Submit Question

When a ray bisects an angle, it divides said angle in half. This means that the two new created angles will have the same measurement and when added they should be equal to the larger one. With this in mind we can find mABX as shown below:

We were given the values for mABC and mCBX, so we use those in the expression above and solve for the value of mABX. We have:

The value of mABX is "4x + 11".

Which system of linear inequalities is graphed? Responses {y≤2x+1x+y≥−2 {y≥2x+1x+y≤−2 {y>2x+1x+y<−2 {y<2x+1x+y>−2

The option 3  is correct y>2x+1 x+y<-2   system of linear inequalities is graphed.

Let's check the slope of y-intercepts of the given lines in the graph .

The y-intercept of first line or above line is 1 and slope m = 2/1  = 2.

Hence the equation should be y =2x+1

y-intercept of second line is -2 and slope m = -1/1

Hence the equation is y = -x-2.

Now check the shaded portion for inequality sign.

Both lines are dotted.

so the inequality sign would be less than or greater than(< or >)

For equation y = 2x+1: shading on the left side.

on the left side of the equation or line y = 2x+1, the y values are greater than on right side.

Hence, we obtain inequality y>2x+1

on the down of the line y = -x-2 the y values are less than topside of the line.

hence second line inequality should be y<-x-2 or y+x<-2.

Hence the option 3  is correct y>2x+1 x+y<-2 system of linear inequalities is graphed.

Learn more about the linear inequalities here:

https://brainly.com/question/11897796

609 4 What is the length of u and vin this 30-60-90 A triangle? U = 16 v = 8 U = 8v = 473 U = 473 V = 8 U = 42 y = 8

For a 30-60-90 triangle, we have a fixed ratio for the length of the sides of the triangle

These lengths are in the ratio;

Since u faces the right angle, it has the longest length, followed by v which faces the angle 60

The lengths are thus;

another ratio that is equivalent to the ratio 4:6. Your answer

The given ratio is 4:6

We can determine another ratio that is equivalent bymultiplying or dividing both numbers by a common factor.

If we divide by a common factor, we would be reducing the ratio to its lowest term. If we divide by 2, the equivalent ratio woyld be

Another equivalent ratio is 2:3

22/-2 how i do this am dum

Answer: -11

Step-by-step explanation: 22/2 is 11 because 11+11 is 22 and then because one of the numbers is negative it makes the final answer negative so that's -11

400 ft 175 ft 550 ft What is the area of this trapezoid? square feet

Let's begin by listing out the information given to us:

The area of this trapezoid

For the following population of N = 9 scores: 4, 2, 0, 5, 3, 2, 1, 7, 3a. Sketch a histogram showing the populationdistribution.

The population of N = 9 scores is 4, 2, 0, 5, 3, 2, 1, 7, 3

Sketch a histogram showing the population distribution.

Make a frequency table for the given data as:M

The surface area of a rectangular prism is 174 square inches. The rectangular base has one side length 3 times the other. The height of the prism is 5 inches. What are the maximum lengths of the sides of the base?A. 6 inches and 18 inchesB. 8.7 inches and 26.1 inchesC. 4.35 inches and 13.05 inchesD. 3 inches and 9 inches

EXPLANATION:

We are given the following details for a triangular prism;

Note that for the rectangular base, one side is 3 times the other. Hence, if the width is w, then the length would be 3 times w.

The surface area of a rectangular prism is;

With the side lengths given we can now substitute and we'll have;

Divide both sides by 2;

We shall now move all terms to one side of the equation;

We can now solve this quadratic equationwith the quadratic equation formula;

Where the variables are;

We now have two solutions. We shall take the positive one since our side lengths cannot be a negative value.

Therefore having the width as 3, the length which is 3 times the width is 3 times 3 and that gives 9.

...............need help

pls mark brainiest I solved it.

I don't know what to explain or how

PLS ANSWER I NEED IT NOW WILL GIVE FIRST ANSWER BRAINLIESTAlec paid the bill for dinner with his clients which totaled $140 before tax and tip. If an 8 percent sales tax was addedto the cost of the meal, and an automatic tip was added in the amount of $25.00, what was the total cost of the dinner?$151.20 $152.00$165.00$176.20

The total cost of the dinner is $176.20

Here, we want to calculate the total cost of the dinner

To calculate this total cost, we need to identify the parts necessary

These parts of the bill are;

a) Main cost of dinner

b) sales tax

By calculating and adding all of these, we get the total dinner cost

a) This is $140 from the question

b) This is 8% of the dinner cost which is 8% of 140

Mathematically, we have that as;

c) The tip cost which is $25

The total cost of the dinner is thus;

A hemisphere igloo has the volume of 9,202.8 meters cubed. What is the area of the floor of the igloo.

2527.43 square meters

The formula for calculate the volume of hemisphere is given as:

where "r" is the radius of the hemisphere

Given the following parameters:

• V = 9,202.8 meters cubed.

Substitute the given parameters into the formula to get the radius:

Determine the area of the floo r given the radius a bove:

Hence the area of the floor of the igloo is 2527.43 square meters

the value of a certain stock increased by 1 and (1/4)%. Explain how to write 1 1/4 percent as a fraction in simplest form

1.25% expressed in fractions is (1/80).

Explanation

We need to express

1 (1/4)% = 1.25%

1.25% = (1.25/100)

Hence, 1.25% expressed in fractions is (1/80).

Hope this Helps!!!

A rose garden is formed by joining a rectangle and a semicircle, as shown below. The rectangle is 23 ft long and 15 ft wide. If the gardener wants to build a fence around the garden, how many feet of fence are required? (Use the value 3.14 for 1, and do not round your answer. Be sure to include the correct unit inyour answer.)15 ft23ft

We were given the following information:

A rose garden is formed by joining a rectangle and a semicircle, as shown below:

Rectangle: Length = 23 feet, Width = 15 feet

Semicircle: Diameter = 15 feet; radius = Diameter/2 = 15/2 = 7.5 feet

We will calculate the perimeter of the garden as shown below:

Therefore, the gardener will need to build a fence of length 99.55 feet

IN ONE REGION 40% OF ALL RESIDENTIAL TELEPHONE NUMBERS ARE UNLISTED. IF 5 RESIDENTIAL HOUSING UNITS ARE RANDOMLY SELECTED FIND THE PROBABILITY THAT ALL OF THEM HAVE UNLISTED NUMBERS

Percentage of numbers unlisted = 40% = 0.40

Sample size, n = 5

Let's find the probability that all 5 of the selected houses have unlisted numbers.

To find the probability, we have:

p(numbers unlisted) = 0.40

Hence, we have:

q = 1 - p = 1 - 0.40 = 0.60

For the probability, apply the binomial probability:

Solving further:

Therefore, the probability that all 5 numbers have unlisted numbers is 0.01024

A plane leaves the ground with an elevation angle of 6 degrees. The plane travels 10 miles horizontally.How high is the plane at the time?What's the distance of the plane's path?

The height of the plane at that time is 1.1 miles

The distance of the plane's path is 10.1 miles

The situation models a right angle triangle as shown below

Using trigonometric ratio,

tan 6° = opposite / adjacent

The opposite side of the triangle is the height of the plane. The distance traveled horizontally is the adjacent side. Therefore,

The height of the plane at that time ≈ 1.1 miles

The hypotenuse of the triangle formed is the distance of the plane path.

Therefore, this distance can be calculated using Pythagoras rule as follows:

The distance of the plane's path = 10.1 miles

A ⊆ B S (B\A)=28, S(B)=5.S(A). S(A)=?

A ⊆B  means A is a proper subset of B. That means all elements of set A are also elements of set B

S(B\A) means the set of all elements of B that are not in set A . This is given as 28

We are also given S(B)  = 5.S(A)

Since A is a subset of B, S(B) = set of all elements in A and set of all elements in B but not in A

In other words S(B) = S(A) + S(B\A)

Since S(B) = 5S(A) we get

5S(A) = S(A) + S(B\A)

5S(A) = S(A) + 28

5S(A) - S(A) = 28

If an investment of $8000 accumulates to $8400 in seven and a half years, the annual simple interest rate is:

the annual interest rate is 0.67%

Amount invested = $8000

Future value = $8400

time = 7 1/2 yeras

To answer the question, we will apply the simple interset formula:

substitute the values into the simple interest formula to get r:

In percentage, the annual interest rate is 0.67%

After a dilation, triangle A(0,0), B(0,4), C(6,0) becomes triangle A'(0,0), B'(0,10), C'(15,0). Choose the scale factor for this dilation.

The scale factor is 2.5

for B = 10/4 = 2.5

for C = 15/6 = 2.5

1/10 Lance is buying new things for his room. He wants some posters and a new rug. He spent $44.50 total. If the rug costs $27 and the posters cost $2.50 each, how many did he buy? 2.5x + 27 = 44.5 44.5 2.5 27x - 2 27x + 2.5 44.5 3206 0755 = 44.5 = 2.5x27

The total cost is $44.50 Since the rug costs $27, the posters altogether cost : 44.50 - 27 = $17.50 We're given that the posters cost $2.50 each, and since they cost $17.50, the number of posters he bought was : 17.50 : 2.50 = 7 (posters)

Find the first term and the difference in an arithmetic sequence if the 100th term is 32 and the 200th term is 116.

Arithmetic sequence

100th term is 32 and the 200th term is 116.

a) Difference ,d

b) First term , a

as we know that the nth term of an arithmrtic sequence is given by

according to the question ,

solve these two equation by elimination method .

subtract both equation to eliminate a ,

now put value of d in one of the equation,

Final Answer

therfore , the difference = -0.84 and first term = 115.16