Answer:
True
Step-by-step explanation:
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.
Figure 2
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
,
1
0
0
]
(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.
The table below gives a summary of interval notation.
Summary of interval notation. Row 1, Inequality: x is greater than a. Interval notation: open parenthesis, a, infinity, close parenthesis. Row 2, Inequality: x is less than a. Interval notation: open parenthesis, negative infinity, a, close parenthesis. Row 3, Inequality x is greater than or equal to a. Interval notation: open bracket, a, infinity, close parenthesis. Row 4, Inequality: x less than or equal to a. Interval notation: open parenthesis, negative infinity, a, close bracket. Row 5, Inequality: a is less than x is less than b. Interval notation: open parenthesis, a, b, close parenthesis. Row 6, Inequality: a is less than or equal to x is less than b. Interval notation: Open bracket, a, b, close parenthesis. Row 7, Inequality: a is less than x is less than or equal to b. Interval notation: Open parenthesis, a, b, close bracket. Row 8, Inequality: a, less than or equal to x is less than or equal to b. Interval notation: open bracket, a, b, close bracket.
Which of the following illustrates the truth value of the given conditional statement?
If 6 • 3 = 18, then 4 + 8 = 20.
Answer:
6x3
Step-by-step explanation:
sorry if wrong
which choice is equivalent to the quotient below?
Answer:
B (9)
Step-by-step explanation:
Find the values of x and y if 5 ˣ⁻³ x 3²ʸ⁻⁸ =225
Answer:
x = 5, y = 5
Step-by-step explanation:
[tex] {5}^{x - 3} \times {3}^{2y - 8} = 225 \\ {5}^{x - 3} \times {3}^{2y - 8} = 25 \times 9 \\ {5}^{x - 3} \times {3}^{2y - 8} = {5}^{2} \times {3}^{2} \\ equating \: like \: power \: terms \: from \: both \:\\ sides \\ {5}^{x - 3} = {5}^{2} \\ x - 3 = 2 (Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ x = 3 + 2
\\ \huge \red{ \boxed{ x = 5}} \\ \\
{3}^{2y - 8} = {3}^{2} \\ 2y - 8 = 2(Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ 2y = 2 + 8 \\ 2y = 10 \\ y = \frac{10}{2} \\ \huge \purple{ \boxed{y = 5}}[/tex]
in the following triangle theta=60.Find the values of the angles of the angles B and B'
Answer:
180-60 = 120 if triangle is not equilateral it cannot be isosceles then depending where the angles are they will show 60,60,60 if equilateral
For isosceles it would need to be 58 61 61 as 60, 60,60 cannot be isosceles.
Vectors 60 if right angled triangle = 90-60 = 30
So angles = 30 and 90 degree or just 120 if angle theta is a vector as explained below.
Step-by-step explanation:
Statement: If two vectors are represented by the sides of a triangle both in magnitude and direction taken in order, the resultant sum of the vectors is given by the closing third side of the triangle taken in the reverse order both in the magnitude and direction
In the diagram below, AB is parallel to CD. What is the value of x?
À
*
45°
O A. 45
OB. 30
O C. 60
OD. 135
SUBMIT
Answer:
x = 45 ⁰ ( corresponding angle )
Answer:
[tex]x = 45 \: \: degrees[/tex]
Answer A is correct
Step-by-step explanation:
[tex] x= 45[/tex]
(Corresponding angles)
Below are two parallel lines with a third line intersecting them.
56°
Answer:
x=56
if the line is parallel bothe the angles will be equal to each other
Find the equation of the line below. If necessary, use a slash (/) to indicate a
division bar.
Answer: y=[tex]\frac{1}{5}x[/tex]
Step-by-step explanation: Let me know if you need an explanation.
Answer:
As shown in picture, the line passes (0, 0) then it has form of y = ax
This line also passes (5, 1) => 1 = 5a => a = 1/5
=> The equation of this line: y = (1/5)a
Hope this helps!
:)
Find the surface area
Answer: 952.46
Step-by-step explanation:
Answer:
1,305
Step-by-step explanation:
15 x 15 = 225 divided by 2 = 112.5
5 x 15 = 225 divided by 2 = 112.5
15 x 24 = 360
15 x 24 = 360
15 x 24 = 360
ADD THEM ALL UP
You get 1305
What is the value of hin the figure below? In this diagram, ABAD ~ ACBD.
A. 5
B. 80
c. 16/5
D. 80
E. 16
F. 8
Answer:
F. 8
Step-by-step explanation:
The ratio of the long side to the short side is the same in similar triangles. The long side of triangle BAD is AD, which has length 20-4 = 16.
BD/DE = AD/BD
h/4 = 16/h
h^2 = 64 . . . . . . . multiply by 4h
h = 8 . . . . . . . . . . take the square root (matches selection F)
_____
Comment on this geometry
BD = √(AD·DC) is called the "geometric mean" of the segments AD and DC. This geometry has some other geometric mean relationships as well:
BC = √(AC·DC)
BA = √(AC·AD)
The length of a rectangular park is four timesfour times its width. The park is surrounded by a 33-foot-wide path. Let x denote the width of the park. Write a quadratic function to represent the total area of the park and the path.
The quadratic function that represents the total area of the park and the path is _____.
(Simplify your answer. Do not factor.)
Answer:
A(x) = 4x^2 + 330x + 4356
Step-by-step explanation:
width of park: x
length of park: 4x
width + path width = x + 66
length + path width = 4x + 66
area = (x + 66)(4x + 66)
area = 4x^2 + 66x + 264x + 4356
area = 4x^2 + 330x + 4356
A(x) = 4x^2 + 330x + 4356
John is paid $35 plus 15% of his groups
tips for each night her works. If y represent
his pay each night and x represents the
groups tips, which equation models this
relationship?
Answer:
y= 35+0.15x
Step-by-step explanation:
y= $35+ 15% of x
y= 35+0.15x is the correct one
option 3
An oil company fills 1 over 12 of a tank in 1 over 3 hour. At this rate, which expression can be used to determine how long will it take for the tank to fill completely?
1 over 12 ⋅ 3 hours
1 over 3 ⋅ 12 hours
1 over 3 ⋅ 1 over 12 hours
3 ⋅ 12 hours
Answer:
(1/3)x12 hrs
Step-by-step explanation:
Answer:1/12(3)
Step-by-step explanation:
It show that every hour 4 is added to the tank.
I took the test
The only case in which a conditional statement is false is when the hypothesis is true and the conclusion is Question 8 options: A) nonexistent. B) unknown. C) true. D) false.
Answer:
I believe is A is the right answer
Answer:
It's False
Step-by-step explanation:
FAST PLEASE
Which student’s answer most accurately describes the solution to the inequality x less-than negative 3? Andie’s Solution -contains only negative rational numbers -has a lower limit of –3 and no maximum value Bobby’s Solution -contains positive and negative rational numbers -has an upper limit of –3 and no minimum value Carrie’s Solution -contains positive and negative rational numbers -has a lower limit of –3 and no maximum value Deshawn’s Solution -contains only negative rational numbers -has an upper limit of –3 and no minimum value Andie’s Bobby’s Carrie’s Deshawn’s
Answer:
carries solution is the correct answer
Answer:
Carrie is correct
Step-by-step explanation:
Three points, Q, R, and S, lie on the same line such that R lies between Q and S. Find QS if RS = 19 and QR = 32
Answer:
QS=51
Step-by-step explanation:
It was given that RS = 19 and QR =32
QS=x
Q-R was measured and found to be 32
R-S was measured and found to be 19
Q-S will be the sum of Q-R and R-S which is 32+19= 51
QS=51
Answer:
51
Step-by-step explanation:
I just took the exam :)
Factor Out -1
1. 7-x
2. y-2d
3. -3h+2f
4. -4g-5t
Find the median of 6 8 10 12 14 15 15 20
Answer:
12.5
Step-by-step explanation:
mean is where u add them then divide it by how many there are
6+8+10+12+14+15+15+20=100
100 divided by 8
Answer:
The median is 13
Step-by-step explanation:
Hope this helps
Suppose that G(X) = F(x) - 3. Which statement best compares the graph of
G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) shifted 3 units to the right.
B. The graph of G(X) is the graph of F(x) shifted 3 units down.
C. The graph of G(x) is the graph of F(x) shifted 3 units to the left.
D. The graph of G(X) is the graph of F(x) shifted 3 units up.
Answer:
its B on edge!
Step-by-step explanation:
You deposit $4200 in a savings account that has a rate of 4%. The interest is compounded
quarterly
a) How much money will you have after ten years? Round to the nearest cent.
b) Find the interest after ten years.
Answer:
a) 6253.23
b) 2053.23
Step-by-step explanation:
A = P (1+r/n)^nt
Sullivan and Carter both went trick or treating in the neighborhood, and now they're
comparing their candy haul. If Sullivan got s number of pieces and Carter got 2s,
what does that tell you about the relationship between the amount of candy they
each had?
Answer:
Step-by-step explanation:
Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.
What is amount?" Amount is defined as the representation of total quantity of given object."
According to the question,
Number of candies Sullivan got = s
Number of candies Carter got = 2s
Compare the given amount of data we get,
Number of candies Carter got = 2(Number of candies Sullivan got )
This shows Carter got twice number of candies comparison to Sullivan.
or
Number of candies Sullivan got = [tex]\frac{1}{2}[/tex] (Number of candies Carter got)
Sullivan got half number of candies compare to Carter.
Hence, we conclude Carter got twice number of candies in comparison to Sullivan or Sullivan got half number of candies compare to Carter.
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Simplify the Problem?
The answer is in the pictures.
Point A is located at -11.25 on the number line. Point B is 7.5 less than point A. Where on the number line is point B?
Someone please help me on this and pls give brief and direct steps for this 7x-15=55. Thanks!
Step-by-step explanation:
7x - 15 =55
7x= 55 +15
7x =70
X=70/7
X=10
Hope this helps..
SUPER URGENT!! WILL VOTE MOST BRAINLY!!!
Use the graph to estimate x when y = 0.
You can use this table too. (y = 4x - 5)
｡☆✼★ ━━━━━━━━━━━━━━ ☾
You could just use the equation to get an answer
Substitute y in as 0
0 = 4x - 5
+ 5 to both sides
4x = 5
Divide both sides by 4:
x = 5/4 or 1.25
HOWEVER, you were supposed to use the graph.
If you look at where the line meets the x axis, you can see it is around 1.2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Help Please Fast, simple
Answer:
D
Step-by-step explanation:
[tex]KQ = PN[/tex]
We can't state that because we don't know if ∠NPK is 90º
Triangle KPN is similar to triangle KQN
It is the same case as the alternative a, we can't say the triangles are similar because we don't the angles for KPN. We know that LN is perpendicular to NP, but we don't if NP is perpendicular to PK, ∠NPK might be 89,9º, that is almost 90º.
KP = 0.5 LN
Once the four sides of the square are equal, LQ = QN. But from the picture we can only state that KP length is approximately the length of NQ (or 0.5 LN)
PN || KM
That's the correct answer! Once ∠QNP is 90º, PN is perpendicular to KM.
According to the order of operations, which of the following operations should be completed first in the following expression?
2(5 - 3)^2 + 6^2
a. multiply (5 - 3) by 2
b. square (5 - 3)
c. simplify (5 - 3)
d. add (5 - 3) to 6^2
Answer:
c. simplify (5 - 3)
Step-by-step explanation:
PEMDAS
P for parenthesis
Find the surface area of the sphere. Use 3.14 for pi. Round to the nearest
tenth. (Given diameter is 17)
Answer:
908, it's rounded to the nearest tenths
Step-by-step explanation:
Answer:
Step-by-step explanation:
Diameter = 17 units
Radius r = 17/2 = 8.5 units
Surface area of sphere = 4πr²
= 4 * 3.14 * 8.5 * 8.5
=907.46 square units
Jonathan must determine the solutions of the quadratic equation
0 = 2x^2 + x +4.
Which of the following is a solution to the equation?
Answer:
The answer to this question is C. I just took the test and i would guarantee it's correct. Hope for brainliest?
Step-by-step explanation:
The correct answer is Option (C) [tex]\frac{-1-i\sqrt{31} }4}[/tex]
What is discriminant?The discriminant is the part of the quadratic formula underneath the square root.The formula of Discriminant is [tex]b^{2} -4ac[/tex]How to solve the problem?The problem can be solved by following steps
The given equation is 2x^2 + x +4.Compare this equation with general equation ax^2+bx+c=0The value of a= 2 , b = 1 , c= 4.x =[tex]\frac{ -b ± \sqrt{b^2-4ac} }{2a}[/tex]
x = [tex]\frac{ -1 ± \sqrt{1^2-4(2)(4)} }{2(2)} \\\frac{ -1 ± \sqrt{1-32} }{4} \\= \frac{ -1 ± \sqrt{-31}}{4} \\\\= \frac{ -1 ± \sqrt{-31i^2}}{4} \\\\\\= \frac{ -1 ± i\sqrt{-31}}{4}\\[/tex]
Hence Option (C) is Correct
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3.) Alex makes $31,992 per year and pays about 15% of his gross monthly income in federal
taxes. He wants to find an apartment to rent. Estimate how much he can afford to pay for
rent each month. Then determine how much money he will have after taxes and rent are
paid.
Answer: 1699.5 dollars
Step-by-step explanation:
If Alex makes $31,992 per year, then his monthly income will be
31992/12 = 2666 dollars
and he pays about 15% of his gross monthly income. That is
15/100 × 2666 = 399.9
The remaining money will be
2666 - 399.9 = 2266.1
He should able to afford 25% of his monthly income for rent
25/100 × 2266.1 = 567 dollars
The money left after tax and payment for rent will be
2266.1 - 567 = 1699.5 dollars
Which of the following shows how the expression below can be factored using the
greatest common factor?
6p3 -12 p2 + 9p
A. 3(2p) - 4p? + 3p)
B. 3p(2p2 - 4p + 3)
C. 3p? (2p? - 4p +3)
D. 6p(p²-2p +9)
Answer:
B
Step-by-step explanation:
Given
6p³ - 12p² + 9p ← factor out 3p from each term
= 3p(2p² - 4p + 3) → B