Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. Please explain how you got the answer.
e^x=3.4

2^x+6=3

Answers

Answer 1

Answer: $e^x=3.4\n x=\ln 3.4\approx1.22\n\n 2^x+6=3\n 2^x=-3\n x\in\emptyset$

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Factor completely 2x2 − 18
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Factor completely 9r^3-72r^2

Answers

Answer:

9r²(r - 8)

Step-by-step explanation:

Step 1: Write expression

9r³ - 72r²

Step 2: Factor out 9

9(r³ - 8r²)

Step 3: Factor out r²

9r²(r - 8)

If Leah is 6 years older than her sister,Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?

Answers

Let us assume the age of Sue = x years
Then
Age of Leah = x + 6
Age of John = 5 + (x + 6)
= x + 11
Total of their ages = 41
So
x + x + 6 + x + 11 = 41
3x + 17 = 41
3x = 41 - 17
3x = 24
x = 24/3
= 8 years
So Sue is 8 years old.

She is 30 years old.

Substitution and elimination are two symbolic techniques used to solve linear equations. For example, if it is easy to set up an equation for substitution where 1 variable is on 1 side, then use that; For example, 4y=16+4x, you can easily divide by 4, get y=4+x (or y=x+4), and plug that into the other equation. In other cases where it may not be so easyFractions/decimals, etc., then you would probably rather use elimination.

1) The substitution method. This method is best utilized when one of the variables in one of the equations has a coefficient of 1 or -1, otherwise you will introduce fractions. Substitution can also be used for nonlinear systems of equations.
(2) Linear combinations also called the elimination method, multiplication and addition method, etc... My personal favorite as it can be done efficiently. It generalizes well to larger systems and is the underpinning of various other solution methods.
As the name implies it requires the equations to be linear.
You need to know both and be comfortable switching between them.

Can we get one for the elimination method too?
Also, can you solve the same problem using either of the two techniques?

Answers

A simple sample problem for Elimination:

x - y = 1
x + y = 5

You can solve the same problem using either technique, as far the equations are linear equations.

An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 foot shadow. What is the approximate height of the building to the nearest foot?A) 40 feet
B) 49 feet
Eliminate
C) 56 feet
D) 63 feet

Answers

I think it would be C) 56 feet. See, if we take the height of the woman(5) over the shadow she casts(8), and crossmultipy it with the height of the building(?) over the shadow of the building(90), it would be approximately 56 feet. 5/8 ?/90 90x5= 450 450/8= 56.25

Julie just doesn't get how fraction division works .None of it makes sense she whined to Scott one day why does 3 over 4 divide by 2 equals to 3 over 8?

Answers

Explanation:

Division by any number is the same as multiplication by its inverse (reciprocal). In this case, ...

$(\left((3)/(4)\right))/(2)=(3)/(4)\cdot(1)/(2)=(3\cdot 1)/(4\cdot 2)=(3)/(8)$

Multiplication of fractions is done in the usual way.

Your mother has left you in charge of the annual family yard sale. Before she leaves you to your entrepreneurial abilities, she explains that she has made the job easy for you: everything costs either $1.50 or $3.50. She asks you to keep track of how many of each type of item is sold, and you make a list, but it gets lost sometime throughout the day. Just before she’s supposed to get home, you realize that all you know is that there were 150 items to start with (your mom counted) and you have 41 items left. Also, you know that you made $227.50. Write a system of equations that you could solve to figure out how many of each type of item you sold.A) x + y = 109
(1.5)x + 227.50 = (3.5)y
B) x + y = 109
(3.5)x + 227.50 = (1.5)y
C) x + y = 41
(1.5)x + 227.50 = (3.5)y
D) x + y = 109
(1.5)x + (3.5)y = 227.50
E) x + y = 150
(1.5)x + (3.5)y = 227.50
F) x + y = $3.50
(1.5)x + (3.5)y = 227.50