The domain of h(z) would be (-8,3).
The range of h(z) would be (2,9).
Point (4,8) would be moved to (0,8)
What are the domain and range of a function?
The domain is the set of all x-values that can be used to make the function "work" and produce actual y-values.
A function's range is the variety of conceivable y-values (minimum y-value to maximum y-value)
For the function f(x):
Domain: (-4,7)
Range: (2,9)
The function f(x+4) is equal to 1 (f(x+4)).
This shows, inputs: -4, outputs: 1
Domain of f(x+4):
add -4 to the Domain values of f(x)
Domain:(-4-4,7-4)=(-8,3)
Range of f(x+4):
Multiply the range values of f(x) by 1
Range: (1*2,1*9)= (2,9)
Find, where the point (4,8) would be moved:
add -4 to 4, and multiply 8 by 1
(4-4,8*1)
=(0,8)
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Evaluate f(x) = log₂ (x) for f(8).
The value of f(8) is 3.
What is logarithm?
The opposite of exponentiation in mathematics is the logarithm. The exponent to which b must be raised in order to obtain a number x is hence the logarithm of a number x to the base b. For instance, since 1000 = 103, log10 of 1000 is 3, or [tex]log_1_0=3[/tex].
Let, [tex]f(x) = log_2(x)[/tex]
We have to find the value of f(8).
Plug x = 8 in the above equation.
[tex]f(8) =log_2(8)[/tex]
Here 8 = 2 x 2 x 2 = 2^3
So, replace 8 with 2^3 in the above equation.
[tex]f(8) = log_2(2^3)[/tex]
Using the log rule: [tex]log_a(a^b) = b[/tex]
Here a = 2, b = 3
So, [tex]log_2(2^3) = 3[/tex]
Hence, f(8) = 3.
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The area, Acm², of a patch of mould is measured daily. The area, n days after the measurements started, is given by the formula A = Asub0b^n". When n = 2, A = 1.8 and when n = 3, A = 2.4. Find the value of b.
Answer:
b = (4/3), with rounding
Step-by-step explanation:
Area = A, in cm^2
n = days
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
------------------
Data:
n = 2, A = 1.8
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
n = 3, A = 2.4
2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]
Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex]. Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]
1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex]
b(1.8 = [tex]A_{0}[/tex][tex]b^{2}[/tex])
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] . We can eliminate this term in the above relationship by substituting 2.4:
1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]
1.8b = 2.4
b = 1.3333
or (4/3)
Check:
Does the value of (4/3) for b work for both data points? To check this, we do need to assume an initial starting area. Lets assume the starting area, [tex]A_{0}[/tex] = 1.
n = 2, A = 1.8, b = (4/3)
A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]
1.8 = 1*[tex](4/3)^{n}[/tex]
1.8 = 1.78 Close enough?
n = 3, A = 2.4, b = (4/3)
2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]
2.4 = 1*[tex](4/3)^{3}[/tex]
2.4 = 2.37 Close enough?
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
The formula of nth term is = 10 - 3n
What is AP?
A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms. Take the numbers 5, 7, 9, 11, 13, and 15 as an example. . . is a sequence of numbers having a common difference of two.The n-th term of the sequence is given by:, if the beginning term of an arithmetic progression is and the common difference between succeeding members is, thenIf the AP contains m phrases, then denotes the final term, which is given by:The term "finite arithmetic progression" or "arithmetic progression" refers to a finite segment of an arithmetic progression. An arithmetic series is the total of a finite arithmetic progression.Acc to our question-
For the nth term in an algebraic seriesU(n) = a + (n - 1)dthe number of terms is n.The first term is a.d is the typical differenceFrom the preceding sequencea = 7d = 4 - 7 = - 3The nth term's formula isU(n) = 7 + (n - 1)-3= 7 - 3n + 3The ultimate solution is= 10 - 3nHence,The formula of nth term is = 10 - 3n
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Gwen opens a savings account with $50.00. Over the next year, she plans to deposit
$10.00 each month into the account. Write a linear function for the amount A, in
dollars, in Gwen's account after x months.
paing
force
area
A block exerts a force of 9 N on the ground.
Calculate the pressure the block exerts on the ground, in N/m², when
it is
a) flat on the ground, so that the area of its base is 0.04 m².
b) standing up on its side, so that the area of its base is 0.015 m².
pressure =
A block exerts a force of 9 N on the ground.
Calculate the pressure the block exerts on the ground, in N/m², when it is
a) 225N/m^2
b) 600N/m^2
Define pressure.
Force applied per unit area is the definition of pressure. P=FA, where F is the force acting perpendicular to the surface area A, is the formula used to calculate pressure mathematically. Having only magnitude and no directional vector properties, pressure is a scalar quantity. The pascal (Pa), or one newton per square meter (N/m 2), is the industry standard for measuring pressure.
Solution Explained:
Given, Force = 9N
For each part of the question we will use the formula
Pressure = Force / Area (Since, Force = Pressure X Area)
a) Here, Area = 0.04m^2
So using the formula, we have
P = 9/0.04 = 225N/m^2
b) Here, Area = 0.015m^2
So using the formula, we have
P = 9/0.015 = 600N/m^2
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A garden designer designed a square decorative pool. The pool is surrounded by a walkway. On two opposite sides of the pool, the walkway is 8 feet. On the other two opposite sides, the walkway is 10 feet. The final design for the pool and walkway covers a total area of 1,440 square feet. ---------- a. The side length of the square pool is x. Write an expression that represents: 1. The total length of the rectangle (including the pool and walkway) 2. The total width of the rectangle (including the pool and walkway) 3. The total area of the pool and walkway b. Write an equation of the form: your expression = 1,440. What does a solution to the equation mean in this situation?
Part 1: The total length of the rectangle; 20 + x (Expression).
Part 2: The total width of the rectangle; 16 + x (Expression).
Part 3: The total area of the pool along with walkway; (20 + x)(16 + x).
Define the term area of the rectangle?The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.The data for the question is given as-
The boardwalk around the pool is 8 feet long and on two different sides. The walkway is 10 feet wide on either two opposite sides. The pool and walkway's final design takes up a total of 1,440 square feet.The side length of the square pool is x.The expressions for the given cases are-
Part 1: The total length of the rectangle;
The total length of the rectangle = 10 + 10 + x
The total length of the rectangle = 20 + x (Expression)
Considering; 10 + 10 > 8 + 8
Part 2: The total width of the rectangle;
The total width of the rectangle = 8 + 8 + x
The total width of the rectangle = 16 + x (Expression)
Part 3: The total area of the pool along with walkway.
Area = length x breadth
Area = (20 + x)(16 + x).
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You are painting a room that is 18 ft long, 14 ft wide and
8 ft high. Find the area of the four walls that you are going to paint.
Answer:
do the answer is 532 ft.
u should be careful not to count the area of the ceiling and the floor of the room!
Answer:
512 ft²-------------------------
Perimeter of the room:
P = 2(18 + 14) = 2(32) = 64 ftArea of the four walls:
A = Ph = 64*8 = 512 ft²The line graphed below has a slope equal to -2. The point (3, 28) lies on
this line as shown. Determine the y-value on this line when the x-value is
equal to 11.
Answer:
y = 12
Step-by-step explanation:
We'll use the form of an equation of a straight line of y=mx+b, where m is the slope and b the y-intercept (the value of y when x=0).
We are told the slope, m, is -2.
That leads to: y = -2x + b
y = -2x + b
B, the y-intercept, can be found by using the given point (3,28) in the equation (it falls on the line, so must be a valid solution to the equation. Use the given x and y in the equation and solve for b:
y = -2x + b
28 = -2*(3) + b
28 = -6 + b
b = 34
The equation is y = -2x + 34
Use this to find y when x = 11:
y = -2(11) + 34
y = -22 + 34
y = 12
y is 12 when x is 11
See the attached graph.
x^2-36=0
solve by graphing
The solutions for the given equation is (6, -6). The graph for the given equation is plotted below.
The given equation is x²-36=0.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
We need to graph the given equation
x²-36=0
⇒ x²=36
⇒ x=±√36
⇒ x=±6
So, solution is (6, -6)
The graph for equation x²-36=0 is given below
The solutions for the given equation is (6, -6). The graph for the given equation is plotted below.
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Explain how it is possible to determine whether the graphs of 5x−3y=2 and 5x-3y=8 are parallel without doing any calculations
The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The slope of the parallel lines will be equal.
The equations are given below.
5x − 3y = 2 ...1
5x − 3y = 8 ...2
The slope of line 1 is given as,
5x − 3y = 2
y = (5/3)x − 2/3
The slope of line 1 is 5/3.
The slope of line 2 is given as,
5x − 3y = 8
y = (5/3)x − 8/3
The slope of line 2 is 5/3.
The slope of line 1 and line 2 are equal. Then the lines are parallel to each other.
The graph is given below.
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PLEASE I REALLY NEED HELP I DON'T UNDERSTAND PLEASE THANK YOU GUYS FOR THE HELP!! I APPRECIATE IT!!!
The value of KM in triangle ΔKLM is 110.
What is similarity?Similarity of a triangle is the ratio of their corresponding sides or angles which are equal .
In the given triangle ΔHIJ,
HI=13, HJ=25,
And in triangle ΔKLM,
KL=57, KM=?
triangle ΔHIJ is similar to ΔKLM,
By the property of similarity, HI/HJ=KL/KM
Substitute the values here,
13/25=57/KM
KM=25×57/13
KM=109.6
The value of KM=110.
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A goat is tied by a rope 2.5 m to a peg
in some grass. The goat eats 1 m² of
grass in
28 min. How long does it take to eat all that
it can reach?
Time taken to eat all = 549.5 minutes.
What is unitary method?
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The goat can rototate in a circule the radius of the curcle is 2.5 mSo the area of circle is;A=(pi) (r^2)A=(3.14)(2.5)^2A=19.625 m^2As 28 minutes for 1 m^2 so;Time taken to eat all = (28)(19.625)=549.5 minutesHence,Time taken to eat all = 549.5 minutes.
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Use the diagram shown.
Ж
If mz1 equals (4x + 2)° and mz2 equals 110°, what is the value of x?
О А. 14
O B. 15
О С. 16
O D. 17
By using the concept of straight angle, the value of x obtained is 17°
What is straight angle?
At first it is important to know about angle
When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle
Straight angle is the angle whose measure is 180°
Here,
[tex]m\angle 1 =(4x +2)\\m\angle 2 = 110\\[/tex]
[tex]\angle 1 \ and \ \angle 2[/tex] forms a straight angle
[tex]m\angle 1 + m\angle 2 = 180[/tex] [Angle on a straight line]
[tex]4x + 2 + 110 = 180\\4x +112 = 180\\4x =180-112\\4x = 68\\x = \frac{68}{4}\\x = 17[/tex]
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Which of the following sets of numbers can be the lengths of the sides of a triangle?
2.6, 8.1, 10.2
6, 7, 13
1.2, 10.5, 2.1
6, 6, 12
Answer:6, 6, 12
Step-by-step explanation
2 sides must be equal which means 6 and 6 points are moving towards each other and 12 is the length
19)
By which rule are these triangles congruent?
A)aas
B)asa
C)sas
D) SSS
Step-by-step explanation:
Angel side angle rule (ASA)
. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
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Enrique predicts that he can make additional money from sales of accessories and service for computer products sold by his store. The table at the right shows predicted percent returns for such sales. For example, if the store makes x dollars selling computer products, Enrique predicts the store with make 0.05x dollars from selling accessories. Part A In January and February of this year, the store made $2,500 from sales of accesories and services. Let x represent the amount the store with make from sales of computer products from March through December. Write an equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year. If Enrique predicts sales from accessories and services for the entire year will be $5,000, about how much money must be made from computer product sales from March through December? Explain.
The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
Given that:
Enrique predicts that he can make additional money from sales of accessories and services for computer products sold by his store.
The store makes x dollars selling computer products, Enrique predicts the store will make 0.05x dollars ($0.05) from selling accessories.
The following steps can be used in order to determine the equation that represents the predicted amount y:
Step 1 - According to the given data, the store makes x dollars selling computer products.
Step 2 - It is also given that, in January and February of this year, the store made $2,500 from sales of accessories and services.
Step 3 - So, the linear equation that represents the given situation is:
y = 0.05x + 2500
Hence the answer is The equation that represents the predicted amount y that the store will make from sales of accessories and services for the entire year is (y = 0.05x + 2500).
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The gradient of a curve C is given by
dy = x² + 6 + 9x-².
dx
The point (3, 20) lies on C. Find an equation for the curve C in the form y = f(x).
Answer:
[tex]y = \frac{1}{3} {x}^{3} + 6x - \frac{9}{x} - 4[/tex]
Step-by-step explanation:
explanation shown in picture ^^
Factor the expression
27 + 33 how do work it out
The factor of the expression 27 + 33 is 3.
What is meaning of factor?
A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.
Factors can be found using either division or multiplication. Rules of divisibility can also be applied.
What meaning of expression?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Given expression is 27 + 33
The factors of 27 are 1, 3, 9, 27.
The factors of 33 are 1, 3, 11, 33.
The common factor of 27 and 33 is 3.
Taking common 3 from the given expression:
27 + 33 = 3 (9 + 11)
The factor of the given expression is 3.
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The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season. x= 0 1 2 3 4 5, P(x)= 0.1666 0.3275 0.2875 0.1489 0.0382 0.0313. The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated? Compute the theoretical mean of the random variable X for the given probability distribution. (Round to three decimal places as needed.)
For a single game, the mean and the standard deviation of the number of hits is given as follows:
Mean: 1.659 hits.Standard deviation: 1.209 hits.For 25 games, the mean and the standard deviation are:
Mean: 1.659 hits.Standard deviation: 0.242 hits.For 50 games, the mean and the standard deviation are:
Mean: 1.659 hits.Standard deviation: 0.171 hits.This shows that as the number of trials increase, the standard error reduces.
How to obtain the mean and the standard deviation of a discrete distribution?The mean is given by the sum of each outcome multiplied by it's respective probability, hence:
E(X) = 0 x 0.1666 + 1 x 0.3275 + 2 x 0.2875 + 3 x 0.1489 + 4 x 0.0382 + 5 x 0.0313 = 1.659 hits.
The standard deviation is given by the square root of the sum of the differences squared between each observation and the mean, divided by the number of values, hence:
S(X) = sqrt((0-1.659)² x 0.1666 + (1-1.659)² x 0.3275 + (2-1.659)² x 0.2875 + (3-1.659)² x 0.1489 + (4-1.659)² x 0.0382 + (5-1.659)² x 0.0313) = 1.209.
Central Limit TheoremFor the repetition of n experiments, we have that the mean remains constant, while the standard deviation is given as follows:
s = S(X)/sqrt(n).
Meaning that it is divided by the square root of the sample size.
Hence, for 25 games, the standard deviation is:
S(X) = 1.209/sqrt(25) = 0.242.
For 50 games, the standard deviation is:
S(X) = 1.209/sqrt(50) = 0.171.
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37=18q+1 show work pls
Answer:
37=18q+1
subtract 1 on both sides
then divide both sides by 18
q=2
Step-by-step explanation:
Answer:
q = 2Step-by-step explanation:
[tex]\sf 37=18q+1[/tex]
[tex]\sf 18q+1=37[/tex]
Subtract 1 from both sides:-
[tex]\sf 18q+1-1=37-1[/tex]
Simplify:-
[tex]\sf 18q=36[/tex]
Divide both sides by 18:-
[tex]\sf \cfrac{18q}{18}=\cfrac{36}{18}[/tex]
[tex]\sf q=2[/tex]
_____________________
Hope this helps!
Have a great day!
What is the domain of the function y=2 x-6?
O -∞
O 0≤x<∞
O 3
O 6≤x<∞
The domain of the given function y = 2√(x - 6)
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values or numbers (x-values) to a function and the domain of a graph comprises all the input numerical values which are located on the x-coordinate.
In order to determine the domain of this function, we would equate the x-value to zero and then evaluate as follows:
x - 6 ≥ 0
x ≥ 6
Therefore, the domain of this function in interval notation is [6, ∞] as shown in the graph attached below.
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Complete Question:
What is the domain of the function y = 2√(x - 6)?
0 ≤ x < ∞
6 ≤ x < ∞
how does the symmetry of a parabolas hep you graph a quadratic function?
Answer:
It line splits the graph of a quadratic equation into two mirror image, or basically means every point on the parabola on one side of the axis will be a mirror image of the other side of the parabola.
np :d
What is the perimeter of pentagon ABCDE with the given vertices?
A (4,2)
B(4, 10)
C (7, 10)
D (15, 4)
E (7, - 2)
Answer:
36
Step-by-step explanation:
The perimeter of ABCDE is equal to AB + BC + CD + DE + AE.
AB = 10 - 2 = 8 (The x values of A and B are the same, therefore the distance between them is the difference between their y values.)
BC = 7 - 4 = 3 (The y values of B and C are the same, therefore the distance between them is the difference between their x values.)
CD = [tex]\sqrt{(X_D - X_C)^2 + (Y_D - Y_c)^2} = \sqrt{(15 - 7)^2 + (4 - 10)^2} = \sqrt{8^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]
DE = [tex]\sqrt{(X_E - X_D)^2 + (Y_E - Y_D)^2} = \sqrt{(7 - 15)^2 + (-2 - 4)^2} = \sqrt{(-8)^2 + (-6)^2} = \sqrt{64 + 36} = \sqrt{100} = 10[/tex]
AE =
[tex]\sqrt{(X_E - X_A)^2 + (Y_E - Y_A)^2} = \sqrt{(7 - 4)^2 + (-2 - 2)^2} = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5[/tex]
[tex]\Delta \text{ABCDE} = \text{AB} + \text{BC} + \text{CD} + \text{DE} + \text{AE} = 8 + 3 + 10 + 10 + 5 = 36[/tex]
n a recent survey in a statistics class, it was determined that only 60% of the students attend class on fridays. from past data it was noted that 98% of those who went to class on fridays pass the course, while only 20% of those who did not go to class on fridays passed the course. a. what percentage of students is expected to pass the course?
The percentage of students expected to pass the course is 66.8%
The given data represents;
In a recent survey in a statistics class, it was determined that only 60% of the students attend class on Fridays. from past data, it was noted that 98% of those who went to class on Fridays passed the course, while only 20% of those who did not go to class on Fridays passed the course.
We need to find the percentage of students who are expected to pass the course.
Let 'A' be the event of passing,
'B' be the event of attending on Fridays.
P (A I B) = 0.98 * P (A I B') = 0.2
P (B) = 0.6
Then, P (B') = 1 - 0.6
= 0.4
→ P (A ∩ B) = P (A I B) * P (B)
= 0.98 * 0.6
= 0.588
→ P (A ∩ B') = P (A I B') * P (B)
= 0.2 * 0.4
= 0.08
∴ P(A) = P (A ∩ B) + P (A ∩ B')
= 0.588 + 0.08
= 0.668
Hence, the percentage of students expected to pass the course is 66.8%
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3 is divided by the difference of 4 and a number
Answer:
[tex] \frac{3}{4 - x} [/tex]
help me please please please
Answer:
SA = 148 cm²
Step-by-step explanation:
the opposite faces of the cuboid are congruent , then
SA = 2(6 × 5) + 2(4 × 5) + 2(6 × 4)
= 2(30) + 2(20) + 2(24)
= 60 + 40 + 48
= 148 cm²
105 grams as percentage of 2kg
What is an equation of the line that passes through the points (-2, -7) and
(-1, -3)?
m= (6- 3)/ (-5 -1)
2x - y + 11= 0
Solve the equation 750 +0.05x = 1,100+ 0.025x for x.
O x = 140
O x = 350
O x = 1,850
O x = 14,000
Answer:
a
Step-by-step explanation:
The value of x will be; x = 14,000
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that the equation 750 +0.05x = 1,100+ 0.025x
Here, we need to solve for x;
750 +0.05x = 1,100+ 0.025x
combine the like terms;
750 - 1,100= -0.05x + 0.025x
-350 = - 0.025x
x = 14,000
Therefore, the solution will be as;
x = 14,000
The value of x will be; x = 14,000
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