The two essential characteristics of functions are domain and range. Function has a domain of (-1, ∞) and a range of (-∞, ∞), f(x) = log₂x - 1.
What is domain and range?Mathematical procedures are comparable to those of a soda vending machine. You can choose from a variety of sodas after you deposit a particular sum of money. Similar to how we enter different numbers into functions, we also receive new numbers as the outcome. The two essential characteristics of functions are domain and range.
A soda can be purchased using quarters and one dollar bills. If pennies are put into the machine, no soda flavor will be provided. As a result, domain depicts the possible inputs, which are quarters and one-dollar bills. No matter how much you pay, a Coke machine won't give you a cheeseburger. As a result, range refers to potential outputs, or in this case, soda tastes in machine. Let's discover how to graph and determine domain and range of a given function.
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Evaluate the expression: 9² × 2 - 4²2 × (10-2) ÷ 2²30 - (3³ - 8)
We have to evaluate the expressions.
We have to solve each operation in the correct order: first the operations within the parenthesis, and within them, first the powers, then the multiplication/quotients and lastly the adds/subtractions. Then, we apply the same sequence for the terms outside the parenthesis.
a)
[tex]\begin{gathered} 9^2\cdot2-4^2 \\ 81\cdot2-16 \\ 162-16 \\ 146 \end{gathered}[/tex]b)
[tex]\begin{gathered} \frac{2\cdot(10-2)}{2^2} \\ \frac{2\cdot8}{2^2} \\ \frac{2\cdot8}{4} \\ \frac{16}{4} \\ \\ 4 \end{gathered}[/tex]c)
[tex]\begin{gathered} 30-(3^2-8) \\ 30-(9-8) \\ 30-1 \\ 29 \end{gathered}[/tex]Answer: a) 146, b) 4 c) 29
what is 1 5/8 and 5/6 as a decimal? and more importantly, do i have to turn it into a bar notation?
Is 9 a factor of 76r+46s?
Answer:
No, 9 is not a factor of 76 and 46.
Step-by-step explanation:
No, 9 is not a factor of 76 and 46. 9 is a factor of 72 and 45.
I hope this helps!
Cooper is working two summer jobs, making $15 per hour of lifeguarding and $10 per hour washing cars. Cooper must earn a minimum of $110 this week. Write an inequality that would represent the possible values for the number of hours lifeguarding, ll, and the number of hours washing cars, WW, that Cooper can work in a given week.
Can you please help me answer this question, Thank you.
The inequality equation is = 15x +10y>=110. This equation represents the possible values for the number of hours lifeguarding and the number of hours washing cars = 15x +10y >= 110
Hourly wage of Cooper working as a lifeguard = $15
Hourly wage of Cooper washing cars = $10
Minimum income required this week = $110
Let x be the number of hours Cooper works as a lifeguard and y be the number of hours Cooper works washing cars
Income from working as a lifeguard based on the number of hours = 15x
Income from working washing cars based on the number of hours = 10y
Formulating the inequality equation we get the following:
15x + 10y >=110
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Nine months ago Alexa deposited 5,000 in a three year CD. She has received $124.16 in interest. She withdraws $500. This is before the CD matures, so she pays a $250 penalty. What is her balance after the withdrawal and fee(s)?
Step-by-step explanation:
my name is my name is mikiyas
determine the average rate of change, in mph, from 2 to 4 hours on the graph shown below
Answer:
maybe, probably 20mph
Step-by-step explanation:
The average rate of change is equal to 10 miles per hour.
What is the average rate of change?It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given that the function is changing from point (30,2) to (20,1). The average rate of the change will be calculated as,
The average rate of change = ( 30 - 20) / ( 2 - 1)
Average rate of change = 10 miles per hour
Therefore, the average rate of change is equal to 10 miles per hour.
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The area of a rectangular yard is 5,063 square feet and its length is 61 feet. What is its width? Explain or show your reasoning.
(EASY POINTS)
What is the measure of an exterior angle of a regular octagon?
(Read carefully)
The measure of an exterior angle of a regular octagon is 45 degrees
What are angles?Angles are formed when two or more lines intersect.
This in other words means that angles is the measure of space between the intersection of rays or lines
How to determine the measure of the exterior angle?The given parameters are:
Shape: regular octagon
A regular octagon has 8 sides, and the total sum of angles is 360
So, we have
Exterior angle = Total sum of angles/Number of sidee
This gives
Exterior angle = 360/8
Evaluate the quotient
Exterior angle = 45
Hence, the measure of the angle is 45 degrees
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An item costs $490 before tax, and the sales tax is 39.20. Find the sales tax rate
Answer:8%
Step-by-step explanation:
1. The graph shows the height of a plant after a certain amount of time measured in days. Do you think that there may be a proportional relationship between the number of days and the height of the plant? Explain your reasoning. The graph shows how much snow fell after a certain amount of time measured in hours. 2. Do you think that there may be a proportional relationship between the number of hours and the amount of snow that fell? Explain your reasoning.
Neither graph in this problem represents a proportional relationship, as they have different rates of change. Examples are as follows:
1. Different rates between days 0-10 and 30-40.
2. Different rates between hours 0 - 1 and 2 - 3.
What is a direct proportional relationship?A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality k, as the rule below shows.
y = kx
Hence, a function will only be proportional if the rate of change is constant for all intervals.
For item 1, we have that:
Between days 0 and 10, the rate of change is of approximately 0.4 cm a day, as the height grows from 0 cm to 4 cm in 10 days.Between days 30 and 40, the rate of change is of approximately 0.8 cm a day, as the height grows 8 cm in 10 days.Hence it is not a proportional relationship, due to the different rates.
For item 2, we have that:
During the interval from hour 0 to hour 1, the function is not constant, meaning that snow fell.During the interval from hour 2 to hour 3, the function is not constant, meaning that snow did not fell and the rate of change is of 0.For the same reason as item 1, of the different rates, it does not represent a proportional relationship.
What is the missing information?The graphs are missing and are given by the image at the end of the answer.
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what are the coordinates of the roots of the equation 3+2x-x^2=0?
The coordinates of the roots of the equation 3+2x-x^2=0 is (- 1, 0 ) and (3, 0 ).
What is a quadratic equation?A quadratic equation can be described as the algebraic equation that posses the second degree of x which can be seen in the form of ax2 + bx + c = 0 and this can be followed in solving the equation.
We were given:
3+2x-x^2=0
This equation can be re arranges as :
-x^2 + 3+2x=0
This can be factorized as :
(x + 1)(x - 3)
Hence the coordinates of the roots can then be written as (- 1, 0 ) and (3, 0 ).
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A brave leaves home and travels four blocks east then two blocks south and three blocks west how many blocks has he travel
Answer:
he has travelled nine blocks
Step-by-step explanation:
four blocks + two blocks + three blocks
=nine blocks
Which of the following is the BEST possible first step to solve for n:
Answer:
Subtract 8 from both sides
Step-by-step explanation:
You want to isolate the term with the variable you want to solve for.
Answer:
Subtract 8 from both sides.
P+4<10
The solution of the inequality is
[tex]p < 10-4\\p < 6[/tex]
P<6 is the solution
Be reminded <> change direction when you divide or multiply by a negative number.
how is the Associative Property of Multiplication similar or different from addition?
A company installs triangular pools at hotels. All of the pools are congruent and triangle JKL is congruent to triangle MNP in the figure. What is the perimeter of each pool?
The perimeter of each pool is 92 ft.
What is perimeter?
A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter.
Given, the triangles are congruent so,
20x-15 = 15x+15
=> 20x-15x = 15+15
=> 5x = 30
=> x = 30/5 = 6
Therefore, perimeter = (4x-4) + (5x+1) + 41
= (4x6 - 4) + (5x6 + 1) + 41
= 20 + 31 + 41
= 92
Hence, the perimeter of each pool is 92 ft.
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help with this question
The surface area of the given pyramid is equivalent to 760 square inches.
Surface area of a pyramidThe surface area of a figure is the sum of the area of the surfaces of such figure.
The given pyramid is made up of 5 big rectangles and 2 small rectangles
Surface area = Area of 4 large rectangles + 2(area of small rectangles)
Surface area = 2(22 * 10) + 2(22 * 5) + 2(10 * 5)
Surface area = 440 + 220 + 100
Surface area = 760 square inches
Surface area = 760 square inches
Hence the surface area of the rectangular based pyramid is 760 square inches
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what is the circumference if the diameter is 10/pi
Answer:
31.42cm
Step-by-step explanation:
We know that C = πd. Since the diameter is 10cm, we know that C = π x 10cm = 31.42cm (to 2 decimal places).
Answer:
31.42 centimeters.
Step-by-step explanation:
Are we in the same class? I had this same question and its due.
EARNINGS The graph shows the amount of money Ryan
earns. Use the graph to estimate the x- and y-intercepts of
the function, where the function is positive and negative,
and interpret the meanings in the context of the situation.
The most appropriate choice for equation of line in slope intercept form will be given by-
x intercept = 0 and y intercept = 0
This means that if Ryan do not work at all, he will not be paid.
The graph is positive throughout
This means to get paid, Raid will have to spend some time doing .
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
x intercept = 0 and y intercept = 0
This means that if Ryan do not work at all, he will not be paid.
The graph is throughout positive.
This means to get paid, Raid will have to spend some time doing .
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Find all the integer solutions of each system of inequalities.
The integer solutions of the system of inequalities are x >= 1 and b <= 0
What are inequality expressions?Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
What are the integer solutions of the system of inequalities expressions?System of inequalities 1
Here, we have
3 - 18x < 0
0.2 - 0.1x > 0
Rewrite as
0 < 0.2 - 0.1x
The above means that
3 - 18x < 0.2 - 0.1x
Collect the like terms
So, we have
3 - 0.2 < 18x + 0.1x
Evaluate the like terms
So, we have
2.8 < 18.1x
Divide both sides by 18.1
So, we have
0.155 < x
Rewrite as
x > 0.155
The integer value greater than 0.155 is at least one
Hence, the integer solution of the system is x >= 1
System of inequalities 2
Here, we have
6 - 4b > 0
3b - 1 > 0
The above means that
6 - 4b > 0 < 3b - 1
Collect the like terms
So, we have
-4b > - 6 + 0 + 1< 3b
Evaluate the like terms
So, we have
-4b > -5 < 3b
Solve for b
b < -1.25 or -1.67 < b
The integer values in this case are 0
So, we have
b <= 0
Hence, the integer solution of the system is b <= 0
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at the grocery store you can get 2 bags of chips for $6 what would 10 bags cost
Answer:
10 bags would cost $30
Step-by-step explanation:
We have been given we can get 2 bags for $6
so we need to how many bags we would get for a dollar =
6/2 = 3
now we need the value for 10 bags =
10 times 3 =
$30
I have attached a image which makes the equation much more pleasing to look at, do check it out. :)
(Hi fyi this answer took a lot of time & effort to make sure it was accurate, precise and to the point to be produced, so if you could opt this answer as the brainliest it would mean the world to me,)
Stay positive and Take care,
A fellow mate,
Cheers !
Expand and simplify (x+3)(2x-1)(x+4)
The expansion and simplified form of the expression [(x+3)(2x-1)(x+4)] will be (2x³ + x² - 25x - 12).
As per the question statement, we are provided with the expression of [(x+3)(2x-1)(x+4)] where three separate factors of the variable "x" are multiplied with each other.
We are required to expand and simplify the above-mentioned expression to obtain our desired answer.
Given, [(x + 3)(2x - 1)(x + 4)]
= [{(x + 3)*(2x - 1)}(x + 4)]
= [{(x*2x) - (x*1) + (3*2x) - (3*1)}(x + 4)]
= [(2x² - x - 6x -3)(x + 4)]
= [(2x² - 7x -3)(x + 4)]
= [(2x²*x) + (2x²*4) - (7x*x) - (7x*4) - (3*x) - (3*4)]
= [2x³ + 8x² - 7x² - 28x - 3x - 12]
= [2x³ + (8x² - 7x²) - (28x + 3x) - 12]
= (2x³ + x² - 25x - 12)
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In trapezoid abcd with the legs ab and cd, point o is the intersection of the diagonals. Is the area of triangle abo =6in,find area if triangle cod
the area of triangle cod is 6 sq. inch
what is trapezoid ?A trapezoid is also as a trapezium, is a flat closed shape having 4 straight
sides, with one pair of parallel sides . a trapezium can also a parallel legs .
Point O (the point of intersection of diagonals )divides two diagonals AC and BD into parts that are proportional:
AO/CO = DO/BO
Then AO x BO = CO xDO
Consider triangle ABO. The area of this triangle is
Aabo = 1/2 x AO x BO x sin ∠AOB
Consider triangle COD. The area of this triangle is
Acod = 1/2 x CO x DO x sin ∠COD
Since AO x BO = CO x DO and angles AOB and COD are congruent as vertical angles
Acod = 1/2 x BO x AO x sin ∠ AOB = Aaob = 6. inc.sq.
hence ,
the area of traiangle cod is 6 sq. inc.
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The points X, Y, and Z are on the same directed line segment XYZ. The ratio of XY:XZ is 2:3. If point X is located at (6,10) and point Y is located at (-1,8), what are the coordinates of point Z?
The coordinates of Z are (-11.5, 5)
What is section formula?When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula. Let us say, we have a point P(x,y) that divides the line segment with marked points as A (x1,y1) and B(x2,y2). To find the coordinates, we use the section formula, which is mathematically expressed as:
P(x, y) = (m[tex]x_2[/tex] + n [tex]x_1[/tex] / m+ n, m [tex]y_2[/tex] +n[tex]y_1[/tex] /m+ n)
Given coordinates:
XY:XZ is 2:3
X is located at (6,10) and Y is located at (-1,8).
let the coordinates of Z(x, y)
using section formula
-1 = (2x + 18)/ 5
-5 = 2x +18
2x = -23
x= -11.5
and, 8 = 2y + 30 /5
40 = 2y + 30
2y= 10
y=5
Hence, the coordinates of Z are (-11.5, 5)
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Last week 3/5 of the students in mr.zankers class went on a field trip 7/10 of the students in mr haynes class went what is the average fraction of the students in the two classes who went on the field trip
Answer:
[tex]\dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]
where x = number of students in Zankers class and y = number of students in Haynes' class
If the number of students in these classes are equal then the average fraction is 13/20
Step-by-step explanation:
Let x = number of students in Zanker's class
Then number of students who went for the trip is [tex]\dfrac{3}{5}x[/tex]
Let y be the number of students in Haynes' clas
Number of students who went = [tex]\dfrac{7}{10}y[/tex]
Total number of students who went on the trip = [tex]\dfrac{3}{5}x + \dfrac{7}{10}y[/tex]
Total number of students in both classes = x + y
So average fraction
=
= [tex]\dfrac{\textsf {Total Number of Students On Trip}}{\textsf {Total Number of Students}}\\\\= \dfrac{\dfrac{3}{5}x + \dfrac{7}{10}y}{x + y}[/tex]
Without knowing how many students are in each class we can only come up with an equation
If we assume the same number of students in each class
Then we get total students who went on trip = [tex]\dfrac{3}{5} N + \dfrac{7}{10}N[/tex][tex]= \left( \dfrac{3}{5} + \dfrac{7}{10}\right)N= \left(\dfrac{13}{10}\right)N[/tex]
where N = total number of students
Since the total in 2 classes is 2N the average fraction
[tex]= \left(\dfrac{13}{10}\right)N \div 2N = \dfrac{13}{20}[/tex]
Wyatt, a chemist at a chemical supply company, has carefully measured out 100 gallons of a solution containing 14% acetone. He also has access to unlimited quantities of a 9% acetone solution. How many gallons of the 9% acetone solution must Wyatt add to the 14% acetone solution to create a solution that contains 10% acetone?
I got 165 but it says it wrong ?
A cell phone company charges a monthly fee plus $0.25 for each text message. The monthly fee is $30.00 and you owe $59.50. Write and solve an equation to find how many text messages x you had.
Answer:
x = 118 text messages
Step-by-step explanation:
Since the total cost of $59.50 is comprised of the flat fee of $30 plus $0.25 for each text message, we can write
$59.50 = $30 + $0.25x
$29.50 = $0.25x
x = 118 text messages
Refer to the figure. If m/2 = (a + 15); and m/3 = (a +35)*, find the value of a such that HLL
LHJ.
K
a=
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The value of a is 20.
What are Angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates.
Given that,
HL is perpendicular to HJ
m ∠2 = (a + 15)°
and
m ∠3 = (a + 35)°
If HL and HJ are perpendicular,
Then,
m ∠2 + m ∠3 = 90°
(a + 15)° + (a + 35)° = 90°
Now, solve for a
(a + 15)° + (a + 35)° = 90°
a + 15 + a + 35 = 90
a + a = 90 - 15 - 35
2a = 40
a = [tex]\frac{40}{2}[/tex]
a = 20.
Hence, the value of a is 20
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jklm and nopq are quadrilaterals given jklm nopq describe a sequence of rigid motions followed by a dilation with center (0,0) that maps jklm to nopq
The transformations that maps polygon jklm to polygon nopq are described as follows:
C. Reflection across the y-axis, translation 2 units left and 6 units up, dilation with center (0,0) and scale factor 1/2.
What are the transformations that map jklm to nopq?The first transformation was a reflection, changing the orientation of the polygon.
Due to the orientation assumed with the equivalent vertices, NL, KO, PJ and MQ, the reflection was over the y-axis, with vertex O assuming coordinates (2,-2).
Since vertex O is at the y-axis, the polygon was translated 2 units left and 6 units up, with O assuming coordinates (0, 4).
The final coordinates of O are (0,2), hence the polygon was dilated with a scale factor of 1/2, as 4 x 1/2 = 2, which is the final y-coordinate of O.
What is the missing information?The problem is incomplete, and the complete problem is given by the image at the end of the answer.
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