The absolute value of the given modulus function are -1 and 7.
What is defined as the modulus function?A modulus function returns this same magnitude of a number regardless of its sign. It's also acknowledged as the absolute value function. This same modulus function, signified by |x| in mathematics, gives the modulus of such a real number x. It returns a non-negative value for x. The modulus but rather absolute value of a number too is known as the number's distance from the origin or zero.The given modulus function is;
|4x - 12| = 16
Removing modulus sign will provide two values;
4x - 12 = ±16
Solve for positive value of modulus function;
4x - 12 = 16
Add 12 on both side;
4x - 12 + 12 = 16 + 12
4x = 28
Dive both side by 4.
x = 7
Now, solve for negative value of modulus function.
4x - 12 = -16
Add 12 on both side;
4x - 12 + 12 = -16 + 12
4x = -4
Divide both side by 4;
x = -1
Thus, the two value of the given modulus function are -1 and 7.
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Manipulating Positive Rational Numbers LC) What is 6 over 8 written as a decimal? 0.6 0.75 1.3 4.8
Answer:
0.75
Step-by-step explanation:
[tex]\frac{6}{8}[/tex] = 6 ÷ 8 = 0.75
Raj wrote -(5^4) = (-5^4). Is Raj correct? Why or why not?
Raj is incorrect as the negative signs are put in different place.
What are integers?An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.
given:
-(5^4) = (-5^4).
Raj is incorrect because the in LHS part the negative sign is out of the exponent term and in RHS part the negative sign is within exponent.
-(5^4) gives - 625
and, (-5^4) gives 625
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Simplify each number. 4¹.⁵
The result of simplifying the number (4¹)⁵ using the exponent rules is 1024
To solve this exercise we have to resolve algebraic operations following the exponent rules.
Note the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
(4¹)⁵ =
4 ⁽¹*⁵⁾ =
4⁵ =
4*4*4*4*4 =
1024
What is an exponent?In mathematics an exponent is the number of time that a number, called (base) is multiplied by itself. It is also called, power or index.
Example: 3² = 3*3 = 9
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The greater of two numbers is 3 more than twice the smaller.Their sum is 24. Find the numbers.
Solve each equation. 3/2log₂4- 1/2log₂x=3
The value of x using the properties of logarithm is 1.
What are the various properties of the logarithm?
Out of several properties of logarithms, some of the main properties are given below:
Product Rule
log (ab) = log a + log b
Change of base
log ₇ x = log x / log 7
Power Rule
log a² = 2 log a
Quotient Rule
log (a / b) = log a - log b
Solving the given equation for x
We are given a logarithmic expression: 3/2 log₂4 - ½ log₂x = 3
Using properties of the logarithm, we have
3/2 log₂4 - ½ log₂x = 3
3/2 (2 log 2 / log 2) - ½ (log x / log 2) = 3
3 - ½ (log x / log 2) = 3
½ (log x / log 2) = 0
log x = 0
log x = log 1
On applying exponent both sides, we get,
x = 1
Hence, the value of x is 1.
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find the magnitude of the sum of these two vector
please vind the direcion too
OK PLEASE I NEED HELP NOW IM RUNNING OUT OF POINTS :(
The magnitude of the sum of these two vectors is approximately 11.791 units.
How to find the magnitude of the sum of two vectors
In this question we have the representations of two vectors on a Cartesian plane, of which we must find the magnitude of the two vectors. There are different methods to find it, we decide to use a vectorial method. First, sum the two vectors:
R(x, y) = A(x, y) + B(x, y)
R(x, y) = 7.70 · (cos 27.8°, sin 27.8°) + 16.3 · (- sin 20°, - cos 20°)
R(x, y) = (6.811, 3.591) + (- 5.574, - 15.317)
R(x, y) = (1.237, - 11.726)
Second, use the Pythagorean theorem:
R = √[1.237² + (- 11.726)²]
R ≈ 11.791
The magnitude of the sum of these two vectors is approximately 11.791 meters.
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Jackson has a points card for a movie theater. • He receives 35 rewards points just for signing up. • He earns 8.5 points for each visit to the movie theater. • He needs 154 points for a free movie ticket. Write and solve an equation which can be used to determine x, the number of visits Jackson must make to earn a free movie ticket.
The number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Jackson has a points card for a movie theater. He receives 35 reward points just for signing up. He earns 8.5 points for each visit to the movie theater.
Let x be the number of visits Jackson must make to earn a free movie ticket.
8.5x + 35 = 154
8.5x = 154 - 35
8.5x = 119
x = 119/8.5
x = 14
Thus, the number of visits Jackson must make to earn a free movie ticket is 14 and the equation is 8.5x + 35 = 154.
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Tell which set or sets the 8 belongs to: natural numbers, whole, numbers, integers, rational numbers, irrational numbers, or real
numbers.
The number 8 is a natural number, whole number, integer, rational number, real number.
All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.
All natural numbers and 0 are included in the category of whole numbers. They are a subset of real numbers, which exclude negative numbers, decimals, and fractions. Whole numbers include counting numerals as well. In this post, let's study all there is to know about whole numbers.
The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion.
Irrational number, any real number that cannot be expressed as the quotient of two integers—that is, p/q, where p and q are both integers.
Real number is a value of a continuous quantity that can represent a distance along a line. Real numbers can be defined as the union of both rational and irrational numbers.
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ASAP need to turn in in 10 min
Answer:
24 gallons
Step-by-step explanation:
The total fuel capacity is 2/(1/24) = 24 gallons.
answer this and u will get 20 points
The rate of increase in the water pressure will be
0.000993 atmosphere per kilometers.
How to illustrate the information?From the information given,it should be noted that the water pressure on Mustafa was illustrated by 0.993 atmosphere per meter.
Therefore, it should be noted that the rate of increase per kilometers will be illustrated as:
1000 meters = 1 kilometer
This will be
= 0.993 / 1000
= 0.000993
This will be illustrated as 0.000993 atmosphere per kilometers.
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what relationship must hold for the point to be equidistant from the origin and the xz-plane? make sure that the relationship you state is valid for positive and negative values of a, b, and c
The relationship must hold for the point to be equidistant from the origin and the x z-plane is a^2+b^2+c^2 > b^2.
What is equidistant point:
A point is said to be equidistant from two other points when it is at an equal distance away from both of them. For example, the perpendicular bisector of a line segment is equidistant from both endpoints.
Now,
distance from P(a, b, c) and the Origin (0,0,0)
[tex]\sqrt{(a-0)^2+(b-0)^2+(c-0)^2} =\sqrt{a^2+b^2+c^2}[/tex]
distance from p(a ,b, c) and the x-z plane
[tex]\sqrt{(0-0)^2+(b-0)^2+(0-0)^2} = |b|[/tex]
Here,
P is equidistant from the Origin and the x - z plane
[tex]\sqrt{a^2+b^2+c^2} = |b|[/tex]
[tex]a^{2} +b^2+c^3 = b^2[/tex]
[tex]a^{2} +c^2 = 0[/tex]
Hence a=c=0 ,thus the point P must be of the form (0,b,0) for any b ∈R
Again,
point P far the from the origin than from the x z plane
[tex]\sqrt{a^2+b^2+c^2} > |b|[/tex]
[tex]a^{2} +b^2+c^2 > b^2[/tex]
[tex]a^{2} +c^2 > 0[/tex]
Hence a, c ∈R such that atleast one of the a ,b ,c is non-zero.
Therefore,
(a ,b ,c) for any b∈ R and for a, c ∈ R with atleast one of the a and c is non-zero.
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estimate 180 x 586 rounding
Answer:
12,000
Step-by-step explanation:
Since we're just estimating, we can just round the two numbers.
180 rounded to the nearest hundred is 200.
586 rounded to the nearest hundred is 600.
200 * 600 = 12,000
Therefore, 180 * 586 is roughly 12,000.
Which angle number represents the linear pair of \angle FHC∠FHC?
The angle number that represents the linear pair of angle FHC is: angle 5.
What is the Linear Pair?The linear pair consists of two adjacent angles that are on a straight line, whose sum will be equal to 180 degrees when added together.
Thus, the two adjacent angles share a common side and a common vertex, and they are supplements of each other. That is, they have a sum of 180 degrees.
Angle 4 represents angle FHC. Angle 5 is adjacent to angle 4, and both lie on a straight line.
Therefore, angle FHC + angle 5 = 180 degrees.
In conclusion, we can state that, the angle number that represents the linear pair of angle FHC is: angle 5.
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Which length of time is between 11.20 am and 2.05 pm ?
Answer:
2 hours 45 minutes.
Step-by-step explanation:
12.00 - 11.20 = 40 minutes
2. 05 = 14.05
14.05 - 12.00 = 2.05 = 2 hours 5 minutes
Answer = 2 hours 45 minutes.
Alan is driving on a highway. He uses one gallon of gas every 25 miles he drives. The distance, D (in
miles), he travels on g gallons of gas is given by the following function.
D(g)=25g
How far does Alan drive if he uses 4 gallons of gas?
Alan drive if he uses 4 gallons of gas is 75 miles distance
The following function calculates the distance (in miles) he travels on gallons of gas. D(g)=25g
Where D(g) is the distance traveled in gallons.
and g denoted the quantity of gasoline used
We are asked to calculate the distance traveled in three gallons of gasoline. To do this, we will set the value of g to 3 in our function.
D(3)=25 x 3 = 75
As a result, Chris's automobile traveled 75 miles on three gallons of petrol.
The length of the line segment connecting two places, for example, is the distance between them. a two-dimensional plane, which may also be in a three-dimensional plane. In coordinate geometry, there are several forms of distance formulae.
Distance between two locations in a two-dimensional plane
Distance between two locations in a three-dimensional plane
Distance in 2D from a point to a line
2D distance between two parallel lines
3D distance from a point to a line
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Assessment
Math
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Analytics
e County Public Schools Foundational Skills in Mathematics, Grade 9 Checkpoint: Solve linear equations and inequalities 2
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Recommendations
Some salespeople earn a commission that pays them a percentage of the price of the items
they sell. The equation I = hr + ps gives the income of a salesperson who receives an hourly
wage plus commission, where h is the number of hours worked, r is the hourly rate of pay, p
is the percent commission, and s is the dollar amount of the salesperson's sales.
Solve for s in terms of I, h, r, and p.
Submit
Skill plans
You have prizes to reveal!
Quest
answ
12
Tim
elap:
01
03
HR MI
Smarts
out of 1
in
Answer:
hope it helped!
Step-by-step explanation:
With the SmartScore, the learning process is rewarded and your students are constantly reassessed. When a student starts practicing a skill, the SmartScore ...
Missing: s h, r, p. Quest 12th Leap: MI
Greg is driving his motorhome. It uses 3 gallons of gas for every 21 miles he travels. Complete the table below showing the number of gallons used and the distance traveled
Answer:
I think the answer is 234 miles and 78 gallons.
Step-by-step explanation:
Hope this helped :)
Answer:
You didn't show the problem so ill just make it to where you can answer yourself
Step-by-step explanation:
so if he uses 3 gallons per 21 miles just divide 3 by 21(yes 3 by 21)
So 0.142 is used per mile
So because you don't show how many miles he traveled just take the number of miles he traveled and times it by 0.142
Example: 42 x 0.142 = 5.964 which when rounded is 6
PLS HELP WILL GIVE BRAINLIEST!!!!
Answer: 36 degrees
Step-by-step explanation: 180 degrees - 144 degrees = 36 degrees
Answer:
A = 54 d and x = 45 B = 45 so a = 54 and x= 45 and b= 45 and x = 45
a survey was conducted to study the relationship between the annual income of a family and the amount of money the family spends on entertainment. data were collected from a random sample of 280 families from a certain metropolitan area.
The scatterplot is the correct answer.
A scatter plot uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.
The dots in a scatter plot not only report the values of individual data points but also patterns when the data are taken as a whole.
Identification of correlational relationships is common with scatter plots. In these cases, we want to know, if we were given a particular horizontal value, what a good prediction would be for the vertical value.
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92x 4.6 divided by 2.3
Answer:
184
Step-by-step explanation:
92 x 4.6 is 423.2 then you divide it by 2.3 which gets you 184.
Answer:
184
92 times 4.6 = 423.2
423.2 divided by 2.3 = 184
Step-by-step explanation:
Hope it helps! =D
p(x)=x^3-4x^2-8x please help me solve
Answer: The value of p(x) = (-2,6) or p(x) = (-2,0)
Step-by-step explanation:
Given that,
p(x) = x^3-4x^2-8x
p(x) = [tex]x^{3}[/tex] - [tex]4x^{2}[/tex] - 8x
and replace with '0'.
x^3-4x^2-8x = 0
Now, factorizing equation is,
(x+2) ([tex]x^{2}[/tex] - 6x) = 0
(x+2) = 0
x= -2
Therefore, x = -2
and,
([tex]x^{2}[/tex] -6x) = 0
([tex]x^{2}[/tex] -6x+0) = 0
using quadratic formula = - [b ± √[tex]b^{2}[/tex]-4ac] / 2a
substitute the values,
a = 1, b = -6 , c = 0
p(x) = - [-6 ± √[tex]-6^{2}[/tex]-4.1.0] / 2.1
p(x) = - [-6 ± √36-4.1.0] / 2.1
p(x) = - [-6 ± √36-(0)] / 2.1
p(x) = - [-6 ± √36] / 2.1
p(x) = - [-6 ± 6] / 2
p(x) = [6 ± 6] / 2
p(x) = 3 ± 3
Therefore, p(x) = 3+3 = 6
p(x) = 3-3 = 0
So, that we can say the value of p(x) = (-2,6) or p(x) = (-2,0).
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Identify the type of fallacy being used in the statement.
Gone with the Wind is the top grossing movie of all time, so it must be the greatest movie of all time.
The type of fallacy which is being used in the statement is: Dicto Simpliciter.
What is a fallacy?A fallacy can be defined as a mistaken or false belief that are based on illogical arguments or reasoning.
The types of fallacy.In English literature, there are different types of fallacy and these include the following:
Appeal to authoritySlippery slopeFallacy of generalization.Ad HominemPost Hoc, Ergo Propter Hoc Non Sequitur Dicto Simpliciter Straw Man Appeal to Popularity (Ad populum)Fallacy of exclusionFalse Dilemma Petitio Principii What is Dicto Simpliciter?Dicto Simpliciter can be defined as a type of fallacy in which a general observation or rule is taken and assumed as generally (universally) true, regardless of the circumstances involved.
In this context, we can reasonably infer and logically deduce that the type of fallacy which is being used in the statement is Dicto Simpliciter.
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Complete Question:
Identify the type of fallacy being used in the statement. Gone with the Wind is the top grossing movie of all time, so it must be the greatest movie of all time.
Post Hoc, Ergo Propter Hoc
Non Sequitur
Dicto Simpliciter
Straw Man
Ad Hominem
False Dilemma
Petitio Principii
Argumentum ad populum
When finding the intersection of two lines from both Algebra I and Geometry, you first "set the linear equations equal to each other. Find the intersection Doint of the two lines whose equations are shown below. Be sure to find both the x and y coordinates. y=5x+1 and y=2x -11
The intersection point of two lines are (-4 , -19)
The intersection point are those point where two line met of cut each other are called intersection point.
the given line of equation are
y = 5x + 1
y = 2x - 11
On solving these two equation we get the values as follow,
value of x = -4
value of y = -19
hence by this we can say the the intersection point of the above lines are
( -4 , -19 )
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4xsquared-1 factories
Answer:
That is a quadratic equation and must be factorized using two brackets. It is just a little confusing to recognize it as a quadratic as the middle x value is not there so we treat it as 0 - which means the two numbers must cancel each other out:
(2x + 1) (2x - 1)
Step-by-step explanation:
help
Answer:
(2x - 1)(2x + 1)
Step-by-step explanation:
4x² - 1
is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
4x² - 1
= (2x)² - 1²
= (2x - 1)(2x + 1)
Solve. (x+1)³/₂-2=25
The values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
[tex] {(x + 1) }^{3/2} [/tex] - 2 = 25
Adding 2 on both the sides of the equation we get
[tex] {(x + 1) }^{3/2} [/tex] - 2 + 2 = 25 + 2
[tex] {(x + 1) }^{3/2} [/tex] = 27
On squaring both the sides of the equation we get
[tex] {x + 1}^{3/2 \times 2} [/tex] = 27²
(x + 1)³ = 729
Now, using the identity (a + b)³ = a³ + b³ + 3ab(a + b), we get
x³ + 1 + 3x² + 3x = 729
x³ + 3x² + 3x - 728 = 0 : Equation 1
By hit and trial method x = 8 is the solution of the equation 1.
Now, by remainder theorem we can write the equation 1 as
x³ + 3x² + 3x - 728 = (x - 8)(x² + 11x + 91) + 0
On solving quadratic equation x² + 11x + 91, we get
x = -b+✓(b² - 4ac)/2a and -b-✓(b² - 4ac)/2a
x = -11+✓(11² - 4×1×91)/2×1 and -11-✓(11² - 4×1×91)/2×1
x = -11+✓(121 - 364)/2 and -11-✓(121 - 364)/2
x = -11+✓(-243)/2 and -11-✓(-243)/2
x = -11/2 + ✓243i/2, -11/2 - ✓243i/2
Thus, the values of x are 8, -11/2 + ✓243i/2, -11/2 - ✓243i/2
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6. The Golden Gate Bridge was built at a height of 300 m over San Francisco
Bay. From the ends of the bridge, the angles of depression to a tugboat in
the middle of the river are 25° and 32° respectively.
Find the length of the bridge.
The length of the golden gate bridge is -163.250975.
What is trigonometry?
Trigonometry is the branch of mathematics that deals with particular functions of angles and how to apply them in calculations. There are six widely used angles-related trigonometric functions. Their respective names and acronyms are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).
What is length?
Length is a measure of distance. According to the International System of Quantities, length has the dimension of distance. Most measurement systems select a length base unit from which all other units are derived. The International System of Units' fundamental unit of length is the meter.
Given that,
The height of the bridge is 300m,
The angle of depression in the middle of the river are 25⁰ and 32⁰ respectively.
[tex]\frac{300}{tan(32)}[/tex] -[tex]\frac{300}{tan(25)}[/tex],
[tex]\frac{300}{0.624869}[/tex]-[tex]\frac{300}{0.466308}[/tex],
= -163.250975.
The length of the golden gate bridge is -163.250975.
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guys please help plsssssssss
Answer:
b = 15
Step-by-step explanation:
[tex]\frac{5\left(\frac{b-1}{2}-1\right)+2b}{3}\\5\left(\frac{b-1}{2}-1\right)+2b\\5\left(\frac{b-1}{2}-1\right)\\5\cdot \frac{b-1}{2}-5\cdot \:1\\5\cdot \frac{b-1}{2}\\\frac{\left(b-1\right)\cdot \:5}{2}\\\frac{5b-5}{2}\\\frac{5b-5}{2}-5\\\frac{5b-5}{2}-5+2b\\=\frac{5b-5}{2}+\frac{2b\cdot \:2}{2}\\=\frac{5b-5+2b\cdot \:2}{2}\\5b-5+4b\\5b+4b-5\\9b-5\\\frac{9b-5}{2}\\=\frac{9b-5}{2}-5\\=\frac{\frac{9b-5}{2}-5}{3}\\\frac{9b-5}{2}-5\\\frac{9b-5}{2}-\frac{5\cdot \:2}{2}\\[/tex]
[tex]=\frac{9b-5-5\cdot \:2}{2}\\9b-5-5\cdot \:2\\9b-5-10\\9b-15\\=\frac{9b-15}{2}\\=\frac{\frac{9b-15}{2}}{3}\\=\frac{9b-15}{2\cdot \:3}\\=\frac{9b-15}{6}\\\frac{3\left(3b-5\right)}{6}\\\frac{3b-5}{2}\\=\frac{3b}{2}-\frac{5}{2}\\\frac{3b}{2}-\frac{5}{2}=5+b\\=\frac{3b}{2}\cdot \:2-\frac{5}{2}\cdot \:2=5\cdot \:2+b\cdot \:2\\\frac{3b}{2}\cdot \:2\\\frac{3b\cdot \:2}{2}\\=3b\\-\frac{5}{2}\cdot \:2\\=\frac{5}{2}\cdot \frac{2}{1}\\=-\frac{5}{1}\\=-5\\5\cdot \:2\\=10\\=3b-5=10+b\cdot \:2[/tex]
[tex]\mathrm{Add\:5--both\:\:sides\:of\:the\:expression}\\3b-5+5=10+b\cdot \:2+5\\3b=2b+15\\\mathrm{Subtract}\\3b-2b=2b+15-2b\\\mathrm{Thus,}\\b=15[/tex]
Hope it helps. :-)
What is the value of ?
Answer:
25.49
Step-by-step explanation:
[tex]5^2 + 0.7^2 \\ \\ =25+0.49 \\ \\ =25.49[/tex]
Solve. Check for extraneous solutions. √3-x+ √x+2=3 Solve.
Find the amount in a continuously compounded account for the given conditions.principal: $ 1000 annual interest rate: 4.8% time: 2 years
A = $ 1100.76 the amount in a continuously compounded account for the given conditions.
What does compound interest entail?
Compound interest is when you receive interest on both your interest income and your savings. Let's imagine you invest $1,000 (your principal) and it earns 5% once a year in interest or profits (the compounding frequency).principal: $ 1000 annual
interest rate: 4.8%
time: 2 years
We know that continuously compound interest
A = [tex]P_{0} e^{rt}[/tex]
= [tex]1000 e_{(0.048)(2)}[/tex]
= [tex]1000 (e)^{0.096}[/tex]
= [tex]1000 ( 1.10075906 )[/tex]
= 1100 . 75906
A = $ 1100.76
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