Equations may be true or false, just as word sentences may be true or false. The equation:
3 + x = 7
will be false if any number except 4 is substituted for the variable. The value of the variable for which the equation is true (4 in this example) is called the solution of the equation. We can determine whether or not a given number is a solution of a given equation by substituting the number in place of the variable and determining the truth or falsity of the result.
Example 1 Determine if the value 3 is a solution of the equation
4x - 2 = 3x + 1
Solution We substitute the value 3 for x in the equation and see if the left-hand member equals the right-hand member.
4(3) - 2 = 3(3) + 1
12 - 2 = 9 + 1
10 = 10
Ans. 3 is a solution.
The first-degree equations that we consider in this chapter have at most one solution. The solutions to many such equations can be determined by inspection.
Example 2 Find the solution of each equation by inspection.
a. x + 5 = 12
b. 4 · x = -20
Solutions a. 7 is the solution since 7 + 5 = 12.
b. -5 is the solution since 4(-5) = -20.
Solve: $|2x - 1| = |3x + 5|$. write your answers as a list of numbers, separated by commas,
e.g. "23, 19" (but without the quotes).
Solution 1:
If |a| = |b|, then either a = b or a = -b. Hence, if |2x - 1| = |3x + 5|, then either 2x - 1 = 3x + 5 or 2x - 1 = -(3x + 5).
If 2x - 1 = 3x + 5, then x = -6. If 2x - 1 = -(3x + 5), then x = -4/5. Therefore, the solutions are x = \boxed{-6, -4/5}.
Solution 2:
Another approach is to square both sides. Squaring both sides, we get 4x^2 - 4x + 1 = 9x^2 + 30x + 25 (because |a|^2 = a^2 for all a). This simplifies to 5x^2 + 34x + 24 = 0, which factors as (x + 6)(5x + 4) = 0, so the solutions are x = -6 and x = -4/5, as before. You must be careful when using this approach because squaring both sides of an equation can introduce false solutions. Thus, we need to check that both of these "solutions" work in the original expression before declaring them correct.
Joey has 5.75 made up of all dimes and quarters. If joey has 38 coins. How many of each each coin does he have?
Find the markup $111.00 percent of markup 50%
Answer:
$166.50
Step-by-step explanation:
Which expressions have a value of 1/2?
Choose all answers that are correct.
A) 2^3/2^4
B) 2^-1
C) 2^0
D) 2^1
what is 1/8(−8c+16)−1/3(6+3c)?
Thank you!!
Answer: The required simplified expression is -2c.
Step-by-step explanation: We are given to simplify the following expression :
[tex]E=\dfrac{1}{8}(-8c+16)-\dfrac{1}{3}(6+3c)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following distributive property :
[tex]a(b+c)=ab+ac.[/tex]
From expression (i), we get
[tex]E\\\\\\=\dfrac{1}{8}(-8c+16)-\dfrac{1}{3}(6+3c)\\\\\\=\dfrac{1}{8}\times(-8c)+\dfrac{1}{8}\times16-\dfrac{1}{3}\times6-\dfrac{1}{3}\times3c\\\\=-c+2-2-c\\\\=-2c.[/tex]
Thus, the required simplified expression is -2c.
Use inductive reasoning to describe each pattern and find the next two terms of each sequence.
1, 4, 9, 16, 25, …
Answer:
B. Multiply by 2; 64, 128.
An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be represented using the sequence shown.
110, 130, 150, 170, ...
Which recursive formula can be used to determine the total amount of money earned for each successive hour worked based on the amount of money currently earned?
The recursive formula that could be used for measuring the total amount of money is f(n+1)=f(n)+20.
Given that,
The electrician earns $110.And, the sequence should be 110, 130, 150, 170, and so on. Here we assume that f(x) represent pay. And, x be the number of hours worked.Based on the above information, we can see that there are 20 increments in every next number.
So, the equation should be f(n+1)=f(n)+20
Learn more: brainly.com/question/11679190
The table shows a function. Is the function linear or nonlinear? x y 8 14 9 8 10 0
"cary is 8 8 years older than dan. in 5 5 years the sum of their ages will be 96 96. find the age of each man now."
"Cary is 8
years older than Dan. In 5 years the sum of their ages wil equal 96. Find both
their ages now. Solve using equations."
x = Dan's age now
x + 8 = Cary's age now {Cary is 8 yrs older than Dan}
x + 5 = Dan's age in 5 years
x + 13 = Cary's age in 5 years
x + 5 + x + 13 = 96 {in five years the sum of their ages will be 96}
2x + 18 = 96 {combined like terms}
2x = 78 {subtracted 18 from both sides}
x = 39 {divided both sides by 39}
x + 8 = 47 {substituted 39, in for x, into x + 8}
Dan is 39 years old
Cary is 47 years old
A triangle has a perimeter of 10x+2. Two sides have lengths of 5x and 2x+9. What is the length of the 3rd side
f(x) = 2x + 6, g(x) = 4x2 Find (f + g)(x).
Answers are: 8x^3 + 24x
2x+6/4x^2
4x^2 + 2x + 6
-4x^2 + 2x + 6
Answer: The correct option is
(C) [tex]4x^2+2x+6.[/tex]
Step-by-step explanation: We are given the functions f(x) and g(x) as follows :
[tex]f(x)=2x+6,\\\\g(x)=4x^2.[/tex]
We are to find the value of (f+g)(x).
We know that
for any two functions p(x) and q(x), we have
[tex](p+q)(x)=p(x)+q(x).[/tex]
So, we get
[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=2x+6+4x^2\\\\=4x^2+2x+6.[/tex]
Thus, the required value is [tex](4x^2+2x+6).[/tex]
Option (C) is CORRECT.
Graph y=3x and make a table of values too
1. Congruent triangles are ______ similar
A. Never
B. Always
C. Sometimes
2. Similar triangles are ____ similar
A. Sometimes
B. Always
C. Never
Simplify the expression.
12 x [(9 + 6) / 3}
A.
38
B.
54
C.
60
D.
110
Find two consecutive even numbers such that the sum of the number and twice the greater number is 100
Write the equation of the linear function for which f(0)=3 and f^-1(0)=-2
3. Start with the following statement: Vertical angles are congruent. a. State the conditional and three other forms of the statement. b. Write all 4 forms of the statement using symbols. c. If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? BONUS: Use at least one truth table AND at least one property to support your reasoning.
a bunch of has 10 3/4 lb of ground beef that will be priced at 3:40 per pound he divides the me into 8 equal packages to the nearest cent what will be the price of each package
What is the exact value of the expression the square root of 294. - the square root of 24. + the square root 54.? simplify if possible. 8the square root of 2. 8the square root of 6. 12the square root of 2. 12the square root of 6?
NEED ANSWERS ASAP 80 POINT QUESTIONS
a) The value of homes in one area went up by an average of 2.3% in the past year. Estimate the value today of a home that was valued at $265,000 last year.
b) This year, the annual sales through one Century 21 office with 12 sales agents were $42 million. Estimate the revenue for the office if it received an average of 20% of the 6% commission on sales.
c) a) From the revenue in part (b) above, the office manager must pay all costs of operating the sales office, including advertising, utilities, phones, insurance, and salaries for all noncommission employees. For the current year, these costs amount to $468,000. Find the profit as a percent of total revenue to the real estate office and round to the nearest tenth of a percent.
A) 265,000* 1.023 = $271,095
B) 42,000,000*0.06 = 2,520,000*0.20 = $504,000
C) 504000 - 468000 = 36000/504000 = 0.0714 = 7.1%
Now suppose that the 5 (identical) prizes will be distributed among the 8 people. a winner can receive more than one prize. in how many ways could the 5 prizes be distributed?
which is larger 42mm or 10cm, 15mm or 0.15, 10mm or 2 cm
1. 10 cm
2. 15 mm
3. 2 cm
Hope this helps even though it's pretty late!
A bit-map terminal has a 1024x768 display. the display is redrawn 75 times a second. how long is the pulse corresponding to one pixel
The pulse corresponding to one pixel is approximately 1.27 microseconds.
Explanation:In this case, we can calculate the duration of the pulse corresponding to one pixel by dividing the time required to redraw the display by the total number of pixels.
Given that the display is redrawn 75 times a second, and the display has a resolution of 1024x768 pixels, the total number of pixels is 1024 * 768 = 786,432 pixels.
To find the duration of the pulse corresponding to one pixel, we can divide the time required to redraw the display (1/75 seconds) by the total number of pixels (786,432 pixels).
Therefore, the pulse corresponding to one pixel is approximately 1.27 microseconds.
Can someone please simplify 6c^2 + 2.5d - d + 2c^2 - 3d for me?
The sides of a triangle are in the ratio 3:4:5. What is the length of each side if the perimeter of the triangle is 30 cm?
A. 2.5 cm, 5. cm, 7.5 cm
B. 9 cm, 10 cm, 11 cm
C. 7.5 cm, 10 cm, 12.5 cm
D. 2.5 cm, 7.5 cm, 12.5 cm
what makes this graph misleading?
The penny size d is given by the literal equation d = 4n - 2, solve for n
Answer:
The value of the equation for n is [tex]n=\frac{d +2}{4}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]d = 4n - 2[/tex]
We need to solve the equation for n.
Add 2 from both the sides.
[tex]d +2= 4n - 2+2[/tex]
[tex]d +2= 4n [/tex]
Divide both side of the equation with 4.
[tex]\frac{d +2}{4}= \frac{4n}{4} [/tex]
[tex]\frac{d +2}{4}= n [/tex]
Hence, the value of the equation for n is [tex]n=\frac{d +2}{4}[/tex].
The difference of three times a number and 4 is -19?
A number minus two-thirds of that number is 24
What is 3/10 divided by 4/5