4/23 lesson

4/23 lesson

Solving Equations, Exponents, & Scientific Notation

Question of the day: What is your favorite meal?

YOU ARE AMAZING!

I care so so much about all of you!

I believe in ALL of you, and know you all will do great on your EOGs!

I promise I will do everything I can to help you be prepared.

During review always give 110%!

Maximum Effort=Maximum Success!

Exponents

• An exponent tells us how many times to multiply the number by itself

• For example 7³ = 7 x 7 x 7

• If something is raised to the second power (8²), we would say "8 squared"

• If something is raised to the third power (8³), we would say "8 cubed"

Multiple Choice

 If the area of a square is $121\ in^2$ , what is the length of each side?

(hint: $\sqrt{121}=\ ?$ 

• 9

• 10

• 11

• 12

Multiple Choice

If the area of a square is $36\ in^2$ , what is the length of each side? 

• 5

• 6

• 72

• 3

Scientific Notation

• Scientific notation is how we write REALLY big or REALLY small numbers

• The first factor MUST be greater than or equal to 1, and the second factor is a power of 10

• Example $4.5\ \times10^5$  

More on scientific notation

• The exponent tells us how many times to move the decimal

• Positive exponents -> BIG NUMBERS

• Negative exponents -> SMALL NUMBERS

• Watch Ms. Horkan's example!

Multiple Choice

A good estimate of the age of the Earth is $4.54\times10^9$  . What is this number written in standard form? 

WRITE THIS OUT ON PAPER! 

• 45,400

• 4,540,000

• 454,000,000

• 4,540,000,000

Multiplying and Dividing #s in Scientific Notation

• When multiplying numbers in scientific notation, multiply the coefficients, and add the exponents.

• When dividing numbers in scientific notation, divide the coefficients, and subtract the exponents

Multiple Choice

The body of a 154-pound person contains approximately 2 × 10^-¹ milligrams of gold and 6 × 10¹ milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?

HINT: You are going to DIVIDE.

• 3 times more

• 30 times more

• 300 times more

• 3,000 times more

Solving Equations

• When solving equations, we use inverse operations (think opposites)

• The goal is to get the variable alone on one side

• We also use strategies like the distributive property, combining like terms, and cross-multiplication

Remember to always use inverse operations!

• Addition and subtraction are OPPOSITES

• Multiplication and division are OPPOSITES

• Finding a square of a number, and finding the square root are OPPOSITES

• Watch Ms. Horkan's example!

Multiple Choice

What value of x makes the equation 4(x – 6) = 2 + 2(4x + 1) true?

• 6

• 7

• -6

• -7

Slope

• To find the slope between two points, calculate using $\frac{change\ in\ y}{change\ in\ x}$  

• Always subtract in the same order

Slope-Intercept Form

• y = mx + b

• "m" is the slope

• "b" is the y-intercept

• x and y describe a specific point on the line

Multiple Choice

In the equation y = -1/2x - 10, what is the slope?

• -1/2

• 1/2

• 5

• -10

Multiple Choice

In the equation y = -1/2x - 10, what is the y-intercept?

• -1/2

• 5

• -10

• 10

Solutions to Equations

• A solution makes an equation TRUE

• When looking at 2 lines, it is the point where the lines INTERSECT

• Watch Ms. Horkan's example!

Multiple Choice

Calculate the slope using points (3, -6) and (12, 6)

• 3/4

• 4/3

• -3/4

• -4/3

Multiple Choice

Now that you know the slope is 4/3 when using points (3, -6) and (12, 6), calculate the y-intercept.

HINT: using y=mx+b, plug in your slope & one set of points. Solve for "b"

• b = -10

• b = 6

• b = 10

• b = -2