In Functions and Function Notation, we were introduced to the concepts of domain and range. In this section we will practice determining domains and ranges for specific functions. Keep in mind that, in determining domains and ranges, we need to consider what is physically possible or meaningful in real-world examples, such as tickets sales and year in the horror movie example above. We also need to consider what is mathematically permitted. For example, we cannot include any input value that leads us to take an even root of a negative number if the domain and range consist of real numbers. Or in a function expressed as a formula, we cannot include any input value in the domain that would lead us to divide by 0.
Diagram of how a function relates two relations.
We can visualize the domain as a “holding area” that contains “raw materials” for a “function machine” and the range as another “holding area” for the machine’s products.
We can write the domain and range in interval notation, which uses values within brackets to describe a set of numbers. In interval notation, we use a square bracket [ when the set includes the endpoint and a parenthesis ( to indicate that the endpoint is either not included or the interval is unbounded. For example, if a person has $100 to spend, he or she would need to express the interval that is more than 0 and less than or equal to 100 and write
(
0
,
100
]
. We will discuss interval notation in greater detail later.
Let’s turn our attention to finding the domain of a function whose equation is provided. Oftentimes, finding the domain of such functions involves remembering three different forms. First, if the function has no denominator or an even root, consider whether the domain could be all real numbers. Second, if there is a denominator in the function’s equation, exclude values in the domain that force the denominator to be zero. Third, if there is an even root, consider excluding values that would make the radicand negative.
Before we begin, let us review the conventions of interval notation:
The smallest term from the interval is written first.
The largest term in the interval is written second, following a comma.
Parentheses, ( or ), are used to signify that an endpoint is not included, called exclusive.
Brackets, [ or ], are used to indicate that an endpoint is included, called inclusive.
thank you in advance
Answer:
the answer is option (b)
Answer:
First option: y= -4/3x + 7
Step-by-step explanation:
It's perpendicular
It takes 213 yards of denim to make one pair of jeans. How many yards would it take to make 5 pairs of jeans?
Answer:
1,065
Step-by-step explanation:
Multiply 213 by 5 to get your final answer.
Darby bought a rare baseball card for $2,000. Three years later, the value of the card had increased 35% of its original value. By how much did the value of Darby’s baseball card increase?
$___
WILL GIVE BRAINLIEST!!
In this lesson, you will learn more about the properties and characteristics of triangles and.
rectangles
cylinders
rhombii
circles
Answer:
rectangles
Step-by-step explanation:
Answer:
rhombii
Step-by-step explanation:
If a cylinder with height 9 inches and radius rr is filled with water, it can fill a certain pitcher. How many of these pitchers can a cylinder with height 9 inches and radius 3r3r fill?
Answer:
9 pitchers
Step-by-step explanation:
Given
Cylinder 1:
[tex]Radius = r[/tex]
[tex]Height = 9[/tex]
Cylinder 2:
[tex]Radius = 3r[/tex]
[tex]Height = 9[/tex]
Required
How many pitchers' cylinder 2 can fill
First, we calculate the volume of both cylinders
Volume is calculated as:
[tex]Volume = \pi r^2h[/tex]
For A:
[tex]V_A = \pi r^2*9[/tex]
[tex]V_A = 9\pi r^2[/tex]
For B:
[tex]V_B = \pi (3r)^2 * 9[/tex]
[tex]V_B = \pi *9r^2 * 9[/tex]
[tex]V_B = 9* 9\pi r^2[/tex]
In (a): [tex]V_A = 9\pi r^2[/tex]
So, we have ve:
[tex]V_B = 9*V_A[/tex]
[tex]V_B = 9V_A[/tex]
If the first cylinder can fill 1, then the second can fill 9 pitchers
Please help me with this question I really need help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
The angles of a triangle add up to 180°.
∠4 = 180°-35°-90° = 55°
Question 5 (4 points)
(06.01)
Evaluate the expression 43 ÷ (7 − 3) × 2. (4 points)
Answer:
21.5
Step-by-step explanation:
(solve in parentheses first)
43/(7-3)x2
(43/4)x2
86/4
21.5
Answer:
[tex]21.5[/tex]
Step-by-step explanation:
First you have to simplify 7 - 4 to 3.
[tex]43 \div 4\times 2[/tex]
Then Simplify 43 ÷ 4 to 10.75.
[tex]10.75 \times 2[/tex]
And lastly, Simplify.
[tex]21.5[/tex]
Therefor, the answer is, 21.5.
Given that 7x – 4y = 6
Find x when y=9
Answer:
6
Step-by-step explanation:
Substitute y for 9: 7x - 36 = 6
Add 36 to both sides: 7x = 42
Divide both sides by 7: x = 6
It's 6, do you need something more simplified?
Help pleeeeaase!! Marking most Brainly
Please please give answer
Answer:
A
Step-by-step explanation:
iTS JUST a
Answer:
Step-by-step explanation:
i cant see it
simply combining like teams 3a-2b-ab-(a-b+ab)-4ab+2b-a STEP explanation plss
Answer:
-6 a b + b + a
Step-by-step explanation:
Simplify the following:
-(a - b + a b) - a b - 4 a b + 2 b - 2 b + 3 a - a
Hint: | Group like terms in 3 a - 2 b - a b - (a b - b + a) - 4 a b + 2 b - a.
Grouping like terms, 3 a - 2 b - a b - (a b - b + a) - 4 a b + 2 b - a = -(a b - b + a) + (-a b - 4 a b) + (3 a - a) + (2 b - 2 b):
-(a b - b + a) + (-a b - 4 a b) + (3 a - a) + (2 b - 2 b)
Hint: | Combine like terms in -a b - 4 a b.
a b (-1) + a b (-4) = -5 a b:
-(a b - b + a) + -5 a b + (3 a - a) + (2 b - 2 b)
Hint: | Combine like terms in 3 a - a.
3 a - a = 2 a:
-(a b - b + a) - 5 a b + 2 a + (2 b - 2 b)
Hint: | Look for the difference of two identical terms.
2 b - 2 b = 0:
-(a b - b + a) - 5 a b + 2 a
Hint: | Distribute -1 over a b - b + a.
-(a b - b + a) = -a b + b - a:
-a b + b - a - 5 a b + 2 a
Hint: | Group like terms in -a b - 5 a b + b + 2 a - a.
Grouping like terms, -a b - 5 a b + b + 2 a - a = (-a b - 5 a b) + b + (-a + 2 a):
(-a b - 5 a b) + b + (-a + 2 a)
Hint: | Combine like terms in -a b - 5 a b.
a b (-1) + a b (-5) = -6 a b:
-6 a b + b + (2 a - a)
Hint: | Combine like terms in 2 a - a.
2 a - a = a:
Answer: -6 a b + b + a
A percentage is another way to write a _________________.
Answer: fraction
Step-by-step explanation:
Answer:
Decimal
Step-by-step explanation:
For example, 10% can also be .10.
You just move the decimal two places to the right or left depending on which one you want.
User will enter three grades averages (exam, project, and lab). Determine which of the three grades (consider any ties) is the highest grade and display the results. Determine which of the three grades (consider any ties) is the lowest grade and display the results. Check for any grades failing below 70% and display each individual grade. Calculate the average grade using the three grades and display the average grade. If they are all 70 and above then display the fact that they are all 70% or above.
Answer:
In Python:
exam = int(input("Exam: "))
project = int(input("Project: "))
lab = int(input("Lab: "))
if exam >= project and exam >= lab:
print("Highest Grade: "+str(exam))
elif project >= exam and project >= lab:
print("Highest Grade: "+str(project))
else:
print("Highest Grade: "+str(lab))
if exam <= project and exam <= lab:
print("Lowest Grade: "+str(exam))
elif project <= exam and project <= lab:
print("Lowest Grade: "+str(project))
else:
print("Lowest Grade: "+str(lab))
print("\nGrades below 70")
if exam < 70:
print("Exam: "+str(exam))
if project < 70:
print("Project: "+str(project))
if lab < 70:
print("Lab: "+str(lab))
print("\nAverage: "+str((exam+project+lab)/3))
if exam > 70 and project >70 and lab > 70:
print("All grades are above 70")
Step-by-step explanation:
The next three lines get input for exam, project and lab
exam = int(input("Exam: "))
project = int(input("Project: "))
lab = int(input("Lab: "))
This condition checks if exam is the highest grade
if exam >= project and exam >= lab:
If true, exam is printed as the highest grade
print("Highest Grade: "+str(exam))
This condition checks if project is the highest grade
elif project >= exam and project >= lab:
If true, project is printed as the highest grade
print("Highest Grade: "+str(project))
If otherwise
else:
lab is printed as the highest grade
print("Highest Grade: "+str(lab))
This condition checks if exam is the lowest grade
if exam <= project and exam <= lab:
If true, exam is printed as the lowest grade
print("Lowest Grade: "+str(exam))
This condition checks if project is the lowest grade
elif project <= exam and project <= lab:
If true, project is printed as the lowest grade
print("Lowest Grade: "+str(project))
If otherwise
else:
lab is printed as the lowest grade
print("Lowest Grade: "+str(lab))
This prints the header "Grades below 70"
print("\nGrades below 70")
This checks if exam is below 70.
if exam < 70:
If true, exam score is printed
print("Exam: "+str(exam))
This checks if project is below 70
if project < 70:
If true, project score is printed
print("Project: "+str(project))
This checks if lab is below 70
if lab < 70:
If true, lab score is printed
print("Lab: "+str(lab))
This calculates and prints the average
print("\nAverage: "+str((exam+project+lab)/3))
This checks if all three scores are above 70
if exam > 70 and project >70 and lab > 70:
If true, the the message that all are above 70, is printed
print("All grades are above 70")
Tammy only has $550 of debt left. If Tammy were to pay off her debt completely today, how could you represent Tammy's situation as an equation? Who ever actually helps get brainliest.
Answer:
Step-by-step explanation:
If Tammy has $550 in debt, and she pays it off in one day, then the equation to represent her situation would look like this.
$550 - $550 = $0
Hope this helps!
Answer:If I let +t+=+0+ ( no months have passed )
+D%280%29+=+550+
-----------------
+t+=+1+
+D%281%29+=+550+-+.19%2A550+
+D%281%29+=+550%2A%28+1+-+.19+%29+
-------------------------
+t+=+2+
+D%282%29+=+550%2A%28+1+-+.19+%29+-+.19%2A%28+550%2A%28+1+-+.19+%29+%29+
+D%282%29+=+550%2A%28+1+-+.19+%29%2A%28+1+-+.19+%29+
+D%282%29+=+550%2A%28+1+-+.19+%29%5E2+
--------------------------
This pattern continues, so the general formula is:
+D%28t%29+=+550%2A%28+1+-+.19+%29%5Et+
+D%28t%29+=+550%2A.81%5Et+
I hope you see this. Each month 19% of the
PREVIOUS months balance gets subtracted.
Step-by-step explanation:
A penguin walks 10 feet in 6 seconds. At this speed:
1. How far does the penguin walk in 45 seconds?
2. How long does it take the penguin to walk 45 feet?
Explain or show your reasoning.
Answer:
1. 75 feet
2. 27 seconds
Step-by-step explanation:
1. If six seconds is equal to 10 feet that means that 42 seconds is equal to 70 feet (6 X 7 = 42) It also means that 3 seconds is equal to 5 feet. (42 + 3 = 45)
2. If 6 seconds is 10 feet, then 6 X 4 is 40 feet (24) And since 5 feet is equal to 3 seconds then we get 24 + 3 = 27
C gives the cost, in dollars, of a cafeteria meal plan as a function of the number of meals purchased, n. The function is represented by the equation C(n) = 4 + 3n. Find C(10) and explain what your answer means in context to the situation
Answer:
Ill help if u still need
Step-by-step explanation:
please help me asap!
Answer:
ST=18
Step-by-step explanation:
Drag each tile to the correct box.
Match each equation with its solution.
x = -0.4
x = 10
x = 2
x = -10
Equation
Solution
x − 6 = -4
arrowRight
x + 3 = -7
arrowRight
5x = -2
arrowRight
0.5x = 5
arrowRight
x - 6 = - 4
Answer: x = 2
x + 3 = -7
Answer: x = -10
5x = -2
Answer: x = -0.4
0.5x = 5
Answer: x = 10
The solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively
Solving equationsGiven the following equations
x − 6 = -4
Add 6 to both sides
x - 6 + 6 = -4 + 6
x = -4 + 6
x = 2
For the equation x + 3 = -7
Subtract 3 from both sides
x + 3 -3 = -7 - 3
x = -10
For the equation 5x = -2
x = -2/5
x = -0.4
For the equation
0.5x = 5
x = 5/0.5
x =10
Hence the solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively
Learn more on equation here: https://brainly.com/question/2972832
#SPJ2
What is the y value of y=2x-3 and y=3x-7
Step-by-step explanation:
hope the above solution will help you
WHAT IS THE LEGENTH OF ML. PLEASE HELP NOW
Answer:
gdfgdf
Step-by-step explanation:
17. Which is M=9pn solved for p? (1 point)
p = M/n p= M-9n. p= 9n/M. p=M/9n
B 56
Step-by-step explanation:
On a United States map, 1 inch represents
240 miles. Using this scale, find the distance
represented by 3.5 inches.
AND
On a California map, 1 inch represents 150 miles. Using this scale, find the distance represented by 2.5 inches.
3) A sample of 42 grams of an unknown substance has a half-life of 1,300 years.
(a) Write an equation to determine the amount of substance, S, left after t years.
(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?
Answer:
a) [tex]S(t) = 42(0.9995)^t[/tex]
b) It will take 10,692 years.
Step-by-step explanation:
Exponential function to determine the amount of substance:
An exponential function to determine the amout of substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
(a) Write an equation to determine the amount of substance, S, left after t years.
Half-life of 1300 years means that [tex]A(1300) = 0.5A(0)[/tex].
We use this to find r. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]0.5A(0) = A(0)(1-r)^{1300}[/tex]
[tex](1-r)^{1300} = 0.5[/tex]
[tex]\sqrt[1300]{(1-r)^{1300}} = \sqrt[1300]{0.5}[/tex]
[tex]1 - r = 0.9995[/tex]
[tex]r = 0.0005[/tex]
Sample of 42 grams means that [tex]A(0) = 42[/tex]. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
Replacing A by S, just for notation purposes
[tex]S(t) = 42(0.9995)^t[/tex]
(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?
This is t when [tex]S(t) = 0.2[/tex]. So
[tex]S(t) = 42(0.9995)^t[/tex]
[tex]0.2 = 42(0.9995)^t[/tex]
[tex](0.9995)^t = \frac{0.2}{42}[/tex]
[tex]\log{(0.9995)^t} = \log{\frac{0.2}{42}}[/tex]
[tex]t\log{0.9995} = \log{\frac{0.2}{42}}[/tex]
[tex]t = \frac{\log{\frac{0.2}{42}}}{\log{0.9995}}[/tex]
[tex]t = 10692[/tex]
It will take 10,692 years.
It cost a bicycle company $8750 to make 50 bikes in its first month of operation and $14925 to make 115 bikes during its second month. Find a linear equation to express the company’s monthly production cost, y, in terms of the number, x of bikes it makes. y=?
Answer:
Step-by-step explanation:
[tex]y=mx+b\\ \\ m=\frac{14925-8750}{115-50}=95\\ \\ y=95x+b,\ (50,8750)\\ \\ 8750=95(50)+b\\ \\ 8750=4750+b,\ b=4000\\ \\ y=95x+4000[/tex]
Monu
Exploring Decimals
What is this number in standard form?
(7 x 100) + (4 x 100 ) + (8 x
1,000)
Enter your answer in the box.
Answer:
Step-by-step explanation:
700+400+8000
9100
Answer: 9,100
Step-by-step explanation:
[tex](8*1,000)+(4*100)+(7*100)=\\8,000+400+700=\\8,400+700=\\9,100[/tex]
? QUESTION
Learning Page
The ratio of men to women working for a company is 5 to 4. If there are 243 employees total, how many women work for the company?
OO EXPLANATION
Answer:
108 women
Step-by-step explanation:
add the parts of the ratio together
5 + 4 = 9
divide the total number of employees by 9
243/9 = 27
now multiply the parts of the ratio by 27.
5 X 27 = 135
4 X 27 = 108
129-7+6
va dau coroana
Answer:
The correct answer is 128
5m - 4z + 8m + 3 – 2z
Answer:
13m-6z+3
Step-by-step explanation:
5m-4z+8m+3-2z
5m+8m-4z-2z+3
13m-6z+3
6 family members share 1/4 of a of chocolate fudge what fraction of a pound does each family member get if they share equally .
A.24
B.1/10
C.1/24
D.10
Answer:
The answer is 1/10
Step-by-step explanation:
X^4 - 3x^2 + 2y - 1 is a polynomial of degree
Answer:
thankyou uwhdjaossbehsa