Part A: The vertex, domain, and range of the function are respectively; (5, 0), ( - ∞ , ∞ ), [0, ∞ ]\
Part B: The function f(x) = |x| is vertically shifted by 3 units to get the function h(x) = |x| + 3. The y-coordinate of the vertex is shifted by 3 units.
How to find the domain and range of a function?Part A: The given function is g(x) = | x - 5 |.
The x-coordinate of the vertex will be: x - 5 = 0
x = 5
Therefore, the y-coordinate of the vertex will be:
y = g(x) = |x - 5|
y = g(5) = |5 - 5|
y = 0
So, the absolute value vertex is (5, 0).
Now, all real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number. Thus;
Interval Notation: ( - ∞ , ∞ )
Set builder Notation: { x | x ∈ R }
The set of all legitimate y values is the range.
Interval Notation: [0, ∞ ]
Set builder Notation: { y | y ≥ 0}
Part B: h(x) = |x| + 3 is the transformed version of the parent function f(x) = |x|.
For the parent function f(x) = |x|, the vertex is ( 0, 0).
The range of an absolute function in the form c( | ax + b | ) + k is f(x) ≥ k.
Therefore, the range of the function f(x) = |x| is f(x) ≥ 0 and in interval notation is [ 0, ∞ ).
For the transformed function h(x) = |x| + 3.
The vertex of the function is ( 0, 3 ).
The range of function is h(x) ≥ 3 and in interval notation is [3, ∞ ).
Hence, the y coordinate of the vertex is transformed by 3.
Read more about Domain and Range at; https://brainly.com/question/2264373
#SPJ1
Can someone help me with this question?
Answer:
A
Step-by-step explanation:
Please help me!! I need help asap
The Expression Above Gives The Amount Of Money, In Dollars, Generated In A Year By A $1,000 Deposit In A Bank Account That Pays An Annual Interest Rate Of R %, Compounded Monthly. Which Of The Following Expressions Shows How Much Additional Money Is Generated At An Interest Rate Of 5% Than At An Interest Rate Of 3% ?
a. 1000 (1=5-3/1200)12
b. 1000 (1=5/3/1200)12
c. 1000 (1=5/1200)12
d. 1000 (1=5/1200)12-(1=3/1200)12
The expression which shows how much additional money generated at an interest rate of 5% than at an interest rate of 3% is: (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12). The correct answer is option D.
The amount of money generated at the interest rate of 5% is shown by A₅ :
1,000 (1 + 5 / 1,200) ^12
And similarly, the amount of money generated at the interest rate of 3% is shown by A₃ :
1,000 (1 + 3 / 1,200) ^12
Hence, the additional amount of money will be shown by A₅ – A₃ :
(1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)
Learn more about compound interest rate at: https://brainly.com/question/16044693
#SPJ4
Although part of your question is missing, you might be referring to this full question: 1,000 (1 + r/1,200) ^12. The expression above gives the amount of money, in dollars, generated in a year by a $1,000 deposit in a bank account that pays an annual interest rate of r%, compounded monthly. Which of the following expressions shows how much additional money is generated at an interest rate of 5% than at an interest rate of 3%?
A. 1,000 (1 + (5 – 3) / 1,200) ^12
B. 1,000 (1 + (5 / 3) / 1,200) ^12
C. (1,000 (1 + 5 / 1,200) ^12) / (1,000 (1 + 3 / 1,200) ^12)
D. (1,000 (1 + 5 / 1,200) ^12) – (1,000 (1 + 3 / 1,200) ^12)
(Guys i need an expert verified)
Solve y3 = −216.
A: y = −72
B: y = ±72
C: y = −6
D: y = ±6
Answer: y = -6.
Step-by-step explanation: -6^3 is -216. Sorry if this isn't a clear explanation, but it seems like the correct choice.
Have a great day! :)
Solve 2/3x+2=4/3x-6 please help‼️
Answer:12
Step-by-step explanation:4/3x-2/3x=2/3x
6+2=8
2/3x=8
x=12
Answer:
X = 12
Step-by-step explanation:
2x+2=34x−6
Multiply both sides of the equation by LCM
(32x+2)×3=(34x−6)×3
CalculateMore Steps
2x+6=(34x−6)×3
CalculateMore Steps
2x+6=4x−18
Move the variable to the left side
2x+6−4x=−18
Subtract the termsMore Steps
−2x+6=−18
Move the constant to the right side
−2x=−18−6
Subtract the terms
−2x=−24
Multiply both sides
−2x(−21)=−24×(−21)
SimplifyMore Steps
−2x(−21)=12
Solution
x=12
The
graph of a quadratic function with vertex (0, 3) is shown in the figure below.
Find the domain and the range.
Write the domain and range using interval notation.
The domain of the quadratic function is (-∞,∞). The range of the quadratic function is (-∞,3].
What is interval notation?
Interval Notation is a method of representing a subset of real numbers by the numbers that connect them.
The vertex of the quadratic function is (0,3).
The function extended downward direction in a vertical. The function extended on both sides of the x-axis horizontally.
The x-coordinate of the points on the quadratic function is the domain.
The y-coordinate of the points on the quadratic function is the range.
The x-coordinate of the points on the quadratic function is from -∞ to ∞.
The y-coordinate of the points on the quadratic function is from -∞ to 3.
The domain of the function is (-∞,∞).
The range of the function is (-∞,3].
To learn more about domain and range, click on the below link:
https://brainly.com/question/29201293
#SPJ1
The Quasi JX is a new car model. Under ideal driving conditions, the Quasi Jx’s fuel economy is E kilometers per liter (E*km/L) when its driving speed is constant at S kilometers per hour (S*km/h).
In terms of the variables S and E, select the expression that represents the number of liters of fuel used in 1 hour of driving under ideal driving conditions at a constant speed S, and select the expression that represents the number of liters of fuel used in a 60 km drive under ideal driving conditions at a constant speed S. Make only two selections, one in each column.
Liters of fuel in 1 hr is S/E and Liters of fuel in 60 km is 60/E
Liters of fuel in 1 hr: The Quasi JX travels E kilometers per liter of fuel (EkmL)(EkmL) at S kilometers per hour (Skmhr)(Skmhr). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Since the Quasi JX travels S kilometers per hour, it requires 1E1E LkmLkm × S km/hr, or SELhrSELhr
Thus, Liters of fuel in 1 hr is S/E.
Liters of fuel in 60 km: The Quasi JX travels E kilometers per liter of fuel (EkmL). Therefore the Quasi JX requires 1E1E liters of fuel to travel 1 km. Given this, the Quasi JX uses 1/E L/km × 60 km, or 60/E L of fuel to travel 60 km.
Thus, Liters of fuel in 60 km is 60/E.
To know more about litres visit: brainly.com/question/25546396
#SPJ4
The expression that represents the number of liters of fuel used in a 60 km drive under ideal driving conditions at a constant speed S is written as 60/E
Here we have given that RO1, Liters of fuel in 1 hour
Here we also know that the Quasi JX travels E kilometers per liter of fuel (E km/L) at S kilometers per hour (S km/hr)
Now, we have to know that the Quasi JX requires 1/E liters of fuel to travel 1 km.
Here the JX travels S kilometers per hour, and here it requires
=> (1/E x L/km) × (S km/hr)
Then it can be written as when we apply the value of Ro1 is 60, then we get
=> 60/E
To know more about Expression here.
https://brainly.com/question/14083225
#SPJ4
please help me so love this problem?
Answer:
12.7 ==> distance of RS
24.2 ==> distance of RT
Step-by-step explanation:
Distance is always positive. So if you get a negative value, take the absolute value of the negative number:
For example, between point R and S:
-17.2 - (-4.5) =
-17.2 + 4.5 = ==> subtracting a negative number is equivalent to adding a
positive number
-(17.2 - 4.5) = -12.7
-12.7 ==> |-12.7| = 12.7 ==> distance of RS
For RT:
-17.2 - 7 =
-(17.2 + 7) = -24.2
-24.2 ==> |-24.2| = 24.2 ==> distance of RT
Triangle DEF is shown below.
How many degrees GREATER is the sum of the measures of angle D and E than the measure of angle f?
The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The information is given below.
∠D = 3(x + 10)
∠E = (2x + 15)
∠F = 2(x + 10)
The sum of the measures of angle D and E than the measure of angle F is calculated as,
⇒ ∠D + ∠E - ∠F
⇒ 3(x + 10) + 2(x + 10) - (2x + 15)
Simplify the expression, then we have
⇒ 3(x + 10) + 2(x + 10) - (2x + 15)
⇒ 3x + 30 + 2x + 20 - 2x - 15
⇒ 3x + 30 + 5
⇒ 3x + 35
The sum of the measures of angles D and E and the measure of angle F will be 3x + 35. Then the correct option is C.
More about the triangle link is given below.
https://brainly.com/question/25813512
#SPJ1
What is the opposite of 19(4/3) ?
A. 19(4/3)
B. -19(4/3)
C. 91(4/3)
D. -91(4/3)
E. 19(3/4)
The opposite of the number 19(4/3) is
B. -19(4/3)What is additive inverse?Additive inverse is the opposite of a number in terms of addition, this is the number that gives zero when added to the original number.
To get a result equal to 0, add the original number and the additive inverse or by simply changing the sign of the integer. On the basis of negation of the original number.
In the problem, the opposite of 19(4/3) is solved as follows
let x be the opposite
19(4/3) + x = 0
x = -19(4/3)
Learn more about additive inverse here:
https://brainly.com/question/29600182
#SPJ1
The measures of the interior angles of a polygon are 133, 110, 140, 158°, 85°, and x. Find the value of x.
Events A and B are independent.
P(A)=0.85 and P(B)=0.05
Find P(A and B)
P(A and B)=
Which three side
lengths best describe the triangle in the diagram?
A. 3 cm, 4 cm, and 5 cm
cm, 8 cm, 8 and 10 cm
C. 6 cm, 8 cm, and 10 cm
D 6 cm, 8 cm, and 9 cm
Answer:can you please give brainliest will give answer
Step-by-step explanation:
11 + 15x = -7 + 13x simplify as much as possible
A bait and tackle shop has fishing lures in the following weights. Write the weights of the lures in order from least to greatest. 5 BOZ 몸으 1 2-07 3 g-oz
Based on the information, it can be inferred that the order from lightest to heaviest lure would be: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).
How to calculate the weights of the lures?To calculate the weights of the lures we must take into account that they are fractional, that is to say that to find an exact number of the weight of each one of the lures we can carry out the division of the fractional to have a decimal number that allows us to organize more easily the pesos.
According to the above information, the weights would be the following:
a. 5/8 = 0.625
b. 9/16 = 0.5625
c. 1/4 = 0.25
d, 3/8 = 0.372
Then, the weights organized from smallest to largest would look like this: 0.25 (c), 0.372 (d), 0.5625 (b), and 0.625 (a).
Note: This question is incomplete because there is some information missing. Here is the complete information:
Options:
a. 5/8OZ
b. 9/16 OZ
c. 1/4OZ
d. 3/8OZ
Learn more about lures in: https://brainly.com/question/12041670
#SPJ1
4 + 2(5 + (-3)
Circle the terms and calculate the value of this expression
The terms of the expression are 4, 2(5) and -3 and the value of the expression is 11
How to determine the terms of this expressionFrom the question, we have the following parameters that can be used in our computation:
4 + 2(5 + (-3)
Rewrite properly
So, we have
4 + 2(5) + (-3)
For an expression ax + by
The terms are ax and by
This means that the terms of 4 + 2(5) + (-3) are 4, 2(5) and -3
How to calculate the value of this expressionHere, we have
4 + 2(5) + (-3)
Remove the brackets
4 + 2(5) + (-3) = 4 + 10 - 3
Evaluate the like terms
4 + 2(5) + (-3) = 11
Hence, the value is 11
Read more about expressions at
https://brainly.com/question/15775046
#SPJ1
find the volume of the solid whose base is bounded by the graphs of y= x+1 and y=(x2)+1, with the indicated cross sections taken perpendicular to the x-axis.
a) squares
b) rectangles of height 1
The volume of the solid is a) 1/30 and b) 1/6.
When the solid’s base is located in the xy plane and the cross-section is taken perpendicular to the x-axis with known cross sectional area given by A(x) for all the x in the interval [a,b], then the volume of the solid is given as the definite integral of these cross-sectional areas.
V = ∫_a^b▒A(x)dx
By graphing the given equations, we see that the area is bounded by the line y= x+1 and parabola y=x^2+1 on the interval on x-axis as [0,1].
a) The base of each square has length
f(x) – g(x) = (x + 1) – (x^2 + 1) = x – x^2
and the solid is square.
The area of cross section is
A(x) = (x – x^2)^2 = x^2 – 2x^3 + x^4
Hence, the volume is
∫_0^1▒A(x)dx
∫_0^1▒〖(x^2-2x^3+x^4)dx〗
[1/3 x^3-1/2 x^4+1/5 x^5]1¦0
[1/3 -1/2 +1/5]
1/30
b) The base of each rectangle has length
f(x) – g(x) = x – x^2
and the height of each rectangle is 1.
The area of cross section is
A(x) = (x – x^2)(1) = x - x^2
Hence, the volume is
∫_0^1▒A(x)dx
∫_0^1▒〖(〖x-x〗^2)dx〗
[1/2 x-1/3 x^3]1¦0
[1/2 -1/3]
1/6
Learn more about Volume of the solid:
https://brainly.com/question/24259805
#SPJ4
Arnold is studying the prevalence of three health risk factors, denoted by A, B, and C, within a population of men. For each of the three factors, the probability that a randomly selected man in the population has only this risk factor (and none of the others) is 0.1. For any two of the three factors, the probability that a randomly selected man has exactly these two risk factors (but not the third) is 0.14. The probability that a randomly selected man has all three risk factors, given that he has A and B is 1/3. The probability that a man has none of the three risk factors given that he does not have risk factor A is p/q, where p and q are relatively prime positive integers. Find p+q.
The value of p + q is 17.
The probability that one of the three risk factors will be present in exactly the right amount for a randomly chosen individual can be calculated using the inclusion-exclusion principle. The probabilities that a man has risk factors A (but not B or C), B (but not A or C), and C (but not A or B) are, accordingly, denoted by the letters P(A), P(B), and P(C). Next, we have:
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B) - P(A and C) - P(B and C) + P(A and B and C)
P(A) = P(B) = P(C) = 0.1 and P(A and B) = P(A and C) = P(B and C) = 0.14 are both supplied to us.
Additionally, it is stated that if a guy possesses both A and B, there is a 1/3 chance that he possesses all three risk factors. Using this knowledge, we can calculate P. (A and B and C).
P(A, B, and C) = P(A, B | C) * P(C) = (1/3) * 0.1 = 1/30 is what we got.
These values are then reinserted into the equation above to produce the following result: P(A or B or C) = 0.1 + 0.1 + 0.1 - 0.14 - 0.14 - 0.14 + 1/30 = 0.44/30 = 11/75
None of the three risk factors are present in a guy in a likelihood of 1 - P(A or B or C) = 1 - 11/75 = 64/75. As a result of the reduction of the proportion 64/75 to 8/9, p = 8 and q = 9, and p + q = 8 + 9 = 17.
To know more about probability :
brainly.com/question/27223994
#SPJ4
Ricardo wants to know when he got the best price for gas. He paid $43.08 for 12 gallons two weeks ago. Last week he paid $31.14 for 9 gallons, and this week he paid $52.70 for 15} gallons of gas.
In which week did Ricardo get the best price per gallon? Explain how you know.
The best price can be obtained by taking the ratio and it is given for the case of two weeks ago.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
The price of gas per gallon for both the cases are calculated as below,
Two weeks ago it is given as,
Total price ÷ Number of gallons
⇒ 31.14 ÷ 9 = $3.46
And, for last week it is given as,
Total price ÷ Number of gallons
⇒ 52.70 ÷ 15 = 3.51
Thus, the price per gallon is cheaper two weeks ago.
Hence, the best price of gas is obtained for the case of two weeks ago.
To know more about ratio click on,
brainly.com/question/13419413
#SPJ6
Remote interior angles are formed on the outside of a triangle when a side is extended beyond the triangle.
true or false
Answer: True
Step-by-step explanation:
Remote interior angles are formed when a side of a triangle is extended beyond the triangle.
2 objects without replacement from 3 objects pencil, eraser, and desk how many ways can this be done taken and not taken into consideration
The total number of ways in which the selection can be done are 3.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is to take out 2 objects without replacement from 3 objects, pencil, eraser, and desk.
Combination is an arrangement of objects where the order in which the objects are selected does not matter.Mathematically : [tex]$_n C_r=\frac{n !}{r ! (n-r) !}[/tex]The total number of ways in which the selection can be done is -
C(3, 2) = (3!)/(2!)(1!) = 3
C(3, 2) = 3
Therefore, the total number of ways in which the selection can be done are 3.
To solve more questions on combinations, visit the link below -
brainly.com/question/1041084
#SPJ1
Sherry will reflect PQR over line m. What will be the
coordinates of the image of point R after PQR is reflected
over line m?
Answer:
(9,6)
Step-by-step explanation:
currently, point R is 4 units to the left of line m
after reflecting vertically over line m it must remain 4 units away
therefore R' would be at point (9,6)
Test this for x-axis symmetry y=-x^2-0.1
The axis of symmetry of the function is x = 0
How to determine the axis of symmetryFrom the question, we have the following parameters that can be used in our computation:
y = -x^2 - 0.1
Differentiate the function
So, we have the following representation
y' = -2x
Set the differentiated function to 0
This gives
-2x =0
Divide both sides by -2
x = 0
Hence, the axis of symmetry is x = 0
Read more about axis of symmetry at
https://brainly.com/question/15709421
#SPJ1
What expression is equivalent to 3 squared 256x10y^7
The expression that is equivalent to 3 squared 256x10y^7 is [tex]4x^3y^2\sqrt[3]{4xy}[/tex].
What is the expression?Each term of the expression can be wriiten so as to find their prime factorization which can be done as
256 = 2^3.2^3.2^2
x^10 = x^3.x^3.x
y^7 = y^3.y^3.y
We can perform some simplification by bringing triples out which will be outside the cube root : which are
2^3.2^3.x^3.x^3.y^3.y^3 = 2.2.3.3.y.y =[tex]4x^3y^2[/tex]
Then remaining terms will now be 2²(x)(y) will be in the cube root which = [tex]2^2xy[/tex]
Then we can write as [tex]4x^3y^2\sqrt[3]{4xy}[/tex]
Learn more about factorization at:
https://brainly.com/question/25829061
#SPJ1
Given the figure below, find the values of x and z .
Answer:
x = 19
z = 19
Step-by-step explanation:
8x - 88 + 5x + 21 = 180
13x - 67 = 180
13x = 247
x = 19
z = 19
24.
Events A and B
Events B and C
Events C and D
Events A and C
Events A and D
The pairs of events that are disjoint and cannot occur at the same time are; Option D: Events A and C
How to interpret disjoint events?In mathematical set problems, we usually say that two sets are said to be disjointed sets if they have no elements in common.
Since the spinner has 10 sections numbered 1 to 10, then the sample space is;
S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
We are told that Event A is the event of the Spin of an odd number. Thus;
Event A = { 1, 3, 5, 7, 9 }
Event B: Spin a number greater than 1 Thus;
Event B = { 2, 3, 4, 5, 6, 7, 8, 9, 10}
Event C: Spin a 2. Thus;
Event C = { 2 }
Event D: Spin a multiple of 2. Thus;
Event D = { 2, 4, 6, 8, 10}
Therefore;
A ∩ B = { 3, 5, 7, 9}
B ∩ C = {2}
C ∩ D = { 2 }
A ∩ C = { }
Thus, A ∩ C does not contains any element. So A and C is a disjoint event.
Read more about disjoint events at; https://brainly.com/question/14376050
#SPJ1
a belt is drawn tightly around three circles of radius 10 cm each, as shown. the length of the belt, in cm, can be written in the form a + b\pi for rational numbers a and b. what is the value of a + b?
Answer:
80 cm
Step-by-step explanation:
You want a function of the length of the perimeter belt around three packed circles of radius 10 cm.
PerimeterExamination of the attached figure shows the length of the belt is the sum of the lengths of the sides of an equilateral triangle with sides 20 cm, and the circumference of a circle with diameter 20 cm.
triangle perimeter = 3s = 3(20 cm) = 60 cm
circle circumference = πd = π(20 cm) = 20π cm
The length of the belt is the sum of these, or
60 cm +20π cm = (60 +20π) cm
FunctionCompared to (a +bπ) cm, we find a=60, and b=20. The desired sum is ...
a +b = 60 +20 = 80
__
Additional comment
You will notice that equilateral triangle PQR in the attached figure has side lengths that are twice the radius of the circle. The straight segments AB, A'B', A"B" are parallel to the triangle sides, and are the same length. (ABPR is a rectangle.)
Each circular arc, BA', for example, is 1/3 of the circumference of the circle, so the total length of all the arcs is the circumference of one 20 cm circle.
15. If the figures below are similar, give the scale
factor of Figure A to Figure B.
Answer:
The answer is 1.25.
Step-by-step explanation:
You can see what sides match up, and then you divide to find the scale factor.
17.5/14 = 1.25
20/16 = 1.25
y-12=c when you solve for y
is what?
Answer:
17
Step-by-step explanation:
If you are trying to solve the equation "y-12=c" for y, you would begin by adding 12 to both sides of the equation to obtain "y=c+12". This means that y is equal to the value of c plus 12.
For example, if you were given the equation "y-12=5", you would have "y=5+12" or "y=17".
Suppose that you want to design a set of four congruent square pyramids whose combined volume is the same as the volume of a single rectangular pyramid. What values of l and h for the four square pyramids and what values of l, w, and h for the rectangular pyramid will produce identical volumes? There is more than one correct answer.
The values of l and h, along with w for the rectangular pyramid, that will produce identical volumes, are given by the following relation:
w = 4l.
(the value of the height is free).
How to calculate the volume of a pyramid?The volume of a pyramid is calculated as the multiplication of the base area by the height, which is then divided by three.
Hence, the formula is given as follows:
V = Ab x h/3.
In which:
Ab is the base's area.h is the height.The base areas are calculated as follows:
Square pyramid: Ab = l².Rectangular pyramid: Ab = lw.Four congruent square pyramids whose combined volume is the same as the volume of a single rectangular pyramid, hence the relation is given as follows:
4l²h/3 = lwh/3.
w = 4l.
More can be learned about the volume of a pyramid at https://brainly.com/question/18994842
#SPJ1