Not all rational numbers a and b satisfy the equation |a+b|=|a|+|b|.
As a result, |a+b|=|a|+|b|.
If |a+b|=|a|+|b| for all rational numbers a and b, we must verify this.
A rational number is what?P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals).
Now,
a=-3 and b=5
|-3+5|=|-3|+|5|
⇒2≠8
A = 2 and B = 4
|2+4|=|2|+|4|
⇒6=6
As a result, we realized from the examples above that |a+b|=|a|+|b| isn't always true.
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The diameter of a circle is 8 m. Find its area in terms of pi
Answer:
50.28 m²
Step-by-step explanation:
Area of a circle = pi r²
= 22/7 × 4 × 4
= 50.28 m²
Assume you have applied for two jobs a and b. The probability that you get an offer for job a is 0. 25. The probability of being offered job b is 0. 20. The probability of getting at least one of the jobs is 0. 40. What is the probability that you will be offered both jobs? enter your answer as a decimal rounded to two places.
If you have applied for two jobs a and b and the probability that you get an offer for the job a is 0.25 and the probability of being offered job b is 0.20, then the probability that you will be offered both jobs is 0.05.
Probability is a term used in mathematics that is concerned with the numerical illustration of the possibility of an event to take place. Its value is between 0 and 1 where 0 illustrates the impossibility of the event to take place while 1 illustrates the certainty of an event to take place.
As the probability of both the jobs are not dependent on each other, the probability that both jobs will be offered can be calculated by the formula;
P(A∩B) = P(A) × P(B)
Here, P(A∩B) represents the probability of both the events to take place together
As P(A) is equal to 0.25
P(B) is equal to 0.20
P(A∩B) = (0.25)(0.20)
P(A∩B) = 0.05
Therefore, 0.05 is the probability that both jobs will be offered.
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PLEASE HELP ME NOW!!! I OBLY HAVE 1 HR TO SOLVE THIS!!!
If A=1, B=2, C=3, …, and Z=26, find a word whose letter will sum to 75.
Answer:
Arrow
Because I used a word calc that took me like 5 mins to find lol
Solve for x and graph the solution on the number line. If possible, resolve your answer to a single inequality. In case of no solution leave the number line blank.
22>=-3x+7 and -3x + 7 >-17
The solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x < 8
What is a number line?A number line is a vertical or horizontal line that has endpoints and it is used to represent numbers at a constant interval
How to plot the number line?The expression is given as
22 >= -3x + 7 and -3x + 7 >-17
The above expression is an inequality expression
As a general rule:
Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal
So, we have
22 >= -3x + 7 and -3x + 7 >-17
Evaluate the like terms
15 >= -3x and -3x >-24
Divide through by -3
So, we have
-5 <= x and x < 8
Combine the expressions
-5 <= x < 8
Hence, the solution to the inequality expression 22 >= -3x + 7 and -3x + 7 >-17 is -5 <= x < 8
See attachment for the number line
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Find the value of x.
3x = 2 + 31
Answer:
x=11
Step-by-step explanation:
3x=2+31
3x=33
divide both sides by the coefficient of x
x=11
A jar contains 0.25 liter of apple juice and 0.30 liter of grape juice. Melissa poured 0.75 liter of pineapple juice into the jar. She then drank 0.20 liter of the mixture.
Part A: Write an expression to represent the total amount of juice left in the jar.
Part B: Simplify the expression and identify which property is used in each step.
Part A: Expression to represent the total amount of juice left in the jar : (0.25 +0.30 + 0.75) - 0.20
Part B: Simplifying above expression using properties of addition and subtraction gives that total amount of juice left is 1.1 liter.
What is an expression?An expression is a group of terms consisting of numbers and mathematical operators ( +, -,*,/) and "=" is not there.
Given that a jar contains 0.25 liter of apple juice, 0.30 liter of grape juice, 0.75 liter of pineapple. Melissa then drank 0.20 liter of the mixture.
Therefore, total juice in the jar before Melissa drank it = quantity of (apple juice + grape juice + pineapple juice ) = (0.25+ 0.30+0.75) liters
After Melissa drank 0.20 liter juice left = total juice before - 0.20
Thus, Expression to represent the total amount of juice left in the jar is: (0.25 +0.30 + 0.75) - 0.20
And it can be solved as (0.25 +0.30 + 0.75) - 0.20 = (0.55+0.75)-0.20
= 1.30-0.20 = 1.1 liter
Thus, after simplifying expression we get that the left juice in the jar is 1.1 liter.
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Write each expression as a single logarithm. Identify any properties used. log 8+log 3
log (24) is each expression as a single logarithm.
A logarithm is defined simply.
The power to which a number must be increased in order to obtain another number is known as a logarithm (see Section 3 of this Math Review for more about exponents). For instance, since ten raised to the power of two equals 100, the base ten logarithm of 100 is 2: log 100 = 2.Each of the properties of exponential functions has an analog for
logarithmic functions.
logb(x)+logb(y)= logb(xy)
Use this properties
log 8+log 3 = log ( 8 * 3 )
log 8+log 3 = log (24)
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Simplify each number. 1000⁴/₃ / 100³/₂
The result of simplifying each number 1000⁴/₃ / 100³/₂ using the exponent rules is: 10
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(1000⁴/₃) / (100³/₂)
Base: 1000 = 10³
Base: 100 = 10²
As 1000 is the same as 10³ and 100 is the same as 10², we get:
(10³)⁴/₃ / (10²)³/₂
Using the power of a power rule that indicates that: the exponent result will be the multiplication of these exponents, we have:
10³*⁴/₃ / 10²*³/₂
10¹²/₃ / 10⁶/₂
10⁴ / 10³
Using the quotient rule that indicates that: the exponent result will be the subtraction of these exponents, we have:
10⁽⁴⁻³⁾
10
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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2\3 the long divided way
Using long division 2/3 is found to be 0.6667, the value is discontinued by approximating a 6 to 7
How to solve 2/3 in long division3 | 2 =
3 | 2 = 0.
3 | 20 = 0.
3 | 20 = 0.6 20 - 3 * 6 = 20 - 18 = 2
3 | 2 = 0.6
3 | 20 = 0.6
3 | 20 = 0.66 20 - 3 * 6 = 20 - 18 = 2
3 | 2 = 0.66
3 | 20 = 0.66
3 | 20 = 0.666 20 - 3 * 6 = 20 - 18 = 2
The procedure continues unending to get 0.666666666.........
Hence we say that 2/3 = 0.6666...≅ 0.6667
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How is the answer to 68-5-(13-27)= 77?
The answer of the given expression is 77 .
PEMDAS is word form accustomed mention the order of operations to be followed whereas determination expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.PEMDAS or order of operations may be a set of rules to perform operations in arithmetic expression. There ar completely different situations wherever everything goes through numerous steps during a mounted sequence.We have given an expression 68-5-(13-27)=77
First simplify LHS = 68-5-(13-27) ...(1)
According to BODMAS first solve the bracket term .
On solving the bracket term , we get
13 - 27 = - 14
Now put this value in equation (1) , we get
[tex]LHS = 68-5-(-14) \\LHS=68-5+14\\[/tex]
Now , apply addition and subtraction operation
[tex]LHS = 63+14\\LHS=77[/tex]
as RHS = 77 = LHS
Hence , the evalution is correct.
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Identify the algebraic expression for the given word phrase.
6 times the sum of r and 9
r (6 + 9)
6 (r + 9)
6r + 9
6 + r + 9
helpp!
Answer:
6 (r + 9)
Step-by-step explanation:
6 times the sum of r and 9 means 6 (r + 9)
A garden is in the shape of a square with a perimeter of 60 feet. The garden is surrounded by two fences. One fence is around the perimeter of the garden, whereas the second fence is
2 feet from the first fence on the outside. If the material used to build the two fences is $1.21 per foot, what was the total cost of the fences?
The total length between the two fences is 136 ft, and the total cost is 164.56 dollars.
What was the total cost of the fences?We have a square garden with a perimeter of 60ft. Then if the sidelength of the square is S, we have that:
60ft = 4*S
S = 60ft/4 = 15ft
We know that the first fence is around the perimeter of the garden, so the length of the first fence is exactly 60ft.
Now, the other fence is 2ft away from the first fence, so it forms a square of sidelength of:
15ft + 2*2ft = 19ft
Then the perimeter of this square is:
P = 4*19ft = 76ft
This means that the length of the second fence is 76 ft.
So the total length of fence is 76ft + 60ft = 136ft
And the cost is $1.21 per ft, then the total cost for the fence is:
C = 136*$1.21 = $164.56
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( 8, 2 ), ( 4, -4 ) find the distance between each pair
Answer:
52 is the answer to that question
Rearrange bn - w = f to make n the
subject.
Answer:
n = (f + w)/b
Step-by-step explanation:
bn - w = f
Rearrange the equation so that the subject is on its own, in the format Ax = B
bn - w + w = f + w
bn = f + w
Isolate the subject, so that it's in the format x = C
bn = f + w
bn/b = (f + w)/b
n = (f + w)/b
An object is 3 dimensional if and only if it has length, width, and depth.
True or false?
help me please !!!!!!!
The rate of change in gas usage is 34.70 miles per gallon.
What is the rate of change?The rate of change is the total gallons used for every one mile travelled. To determine the rate of change, divide the miles driven by the gallons used.
Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number. The sign used to represent division is ÷.
Rate of change = miles driven / gallons used
1041 / 30 = 34.70 miles per gallon
1596. 2 / 46 = 34.70 miles per gallon
1665.6 / 48 = 34.70 miles per gallon
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For A-D, select each fraction that is equal to 4 5
The fractions 16/20, 12/15, and 8/10 are equivalent fractions to 4/5.
When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.
Let us understand the two ways in which we can make equivalent fractions:
Now, Divide the denominator or numerator by the same number or multiply the denominator and the numerator by the same number.
So, the equivalent fractions for 4/5 are:
(4/5) × (2/2) = (4 × 2) / (5 × 2) = 8/10
(4/5) × (3/3) = (4 × 3) / (5 × 3) = 12/15
(4/5) × (4/4) = (4 × 4) / (5 × 4) = 16/20
After simplifying, 16/20, 12/15, and 8/10 equal 4/5, indicating that they are identical in nature.
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HOW DO I SOLVE THIS PLEASE HELP ITS DUE IN 30 MIN
The numeric values for the function are given as follows:
A. f(a) = 9a - 9.
B. f(a + h) = 9a + 9h - 9.
C. f(a + h) - f(a) = 9h.
D. (f(a + h) - f(a))/h = 9.
How to find the numeric value of a function/expression?To find the numeric value of a function, we replace each instance of the variable by the desired value.
For this problem, the function is given by:
f(x) = 9x - 9.
At x = a, the numeric value is given by:
f(a) = 9(a) - 9 = 9a - 9.
Hence:
f(a) = 9a - 9.
At x = a + h, the numeric value is given by:
f(a + h) = 9(a + h) - 9 = 9a + 9h - 9.
Hence:
f(a + h) = 9a + 9h - 9.
Subtracting these values, we have that:
f(a + h) - f(a) = 9a + 9h - 9 - 9a + 9 = 9h.
Hence:
f(a + h) - f(a) = 9h.
Dividing by h, we have that:
(f(a + h) - f(a))/h = 9h/h = 9.
Hence:
(f(a + h) - f(a))/h = 9.
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Amelia took a taxi from her house to the airport. The taxi company charged a pick-up fee of $4.60 plus $0.50 per mile. The total fare was $13.60, not including the tip. Write and solve an equation which can be used to determine
m
m, the number of miles in the taxi ride.
Solution: the number of miles in the taxi ride.= 180 miles
Miles : A unit of length equal to exactly 1.609344 kilometers.
Also equal to 1,760 yards or 5,280 feet.
The average walking speed is 3 miles per hour (so it takes about 20 minutes to walk 1 mile).
The taxi company charged a pick-up fee of $4.60
The taxi company charged $0.50 per mile.
The total fare was $13.60
The total fare = pick-up charged + traveling charged
the number of miles in the taxi ride = m
$13.60= $4.60 + m x $.50
$13.60-$4.60 = $.50m
9 =.50 m
9 /.50 = m
900/5 = m
180 = m
the number of miles in the taxi ride.= 180 miles
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One of the worlds largest crocodiles weighed 38,400 ounces how many tons did the crocodile weigh
Answer: 1.2 tons
Step-by-step explanation:
Answer: 1,777
Step-by-step explanation:
Leena consumes 400 calories at breakfast and 350 calories at lunch. She consumes StartFraction 2 Over 3 EndFraction. of her daily calories at dinner. If x represents the calories consumed at dinner, which statements describe the situation? Check all that apply.
Leena consumed 1,500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.
Leena consumed 500 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction left-parenthesis x right-parenthesis equals x left-parenthesis 400 plus 300 right-parenthesis.(x) = x(400 + 300) can be used to model the situation.
Leena consumed 1,000 calories at dinner.
The equation StartFraction 2 Over 3 EndFraction x left-parenthesis x plus 400 plus 350 right-parenthesis equals x.x(400 + 300) = x can be used to model the situation
The correct statement regarding the algebra will be:
A. Leena consumed 1,500 calories at dinner.
B. The equation StartFraction 2 Over 3 EndFraction left-parenthesis x plus 400 plus 350 right-parenthesis equals x.(x + 400 + 350) = x can be used to model the situation.
How to illustrate the information?Calories consumed at dinner = x
x = 2/3 of daily calorie
Hence, the fraction of calories consumed during breakfast and lunch can be calculated thus :
1 - 2/3 = 1/3
Let the total amount of calories consumed per day = c
1/3 × c = 750
c/3 = 750
c = 750 × 2 = 2250 calories
Calories consumed at dinner = (2250 - (750)) = 1500 calories
Therefore, the correct options are A and B.
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50 pts to whoever can solve these correctly
The quadratic equation is an equation of the form ax^2 + bx + c =0. Note that the quadratic equation is a polynomial of degree two. This implies that the highest power of x in the quadratic function is power two.
The quadratic formula is given by x = -b ± √b^2- 4ac/2a. The discriminant can be used to obtain the nature of the roots of a quadratic equation. If the roots are real and positive we would have a positive discriminant. If the value of the discriminant is negative then it implies that the roots of the equation are imaginary.
The discriminant can be given as √b^2 - 4ac. The statements that are true about the quadratic formula are;
x = -b/2a gives the line of symmetry
√b^2- 4ac/2a gives the maximum and the minimum points of the quadratic equation
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An ad for Speedy Delivery Service says When it has to be there fast, it has to be Speedy. Catalina needs to send a package fast. Does it follow that she should use Speedy? Explain
Yes. The Law of Detachment dictates that Catalina employ Speedy. The conclusion should come naturally if the hypothesis is correct.
According to the Law of Detachment, in order for our desires to manifest in the physical reality, we must dissociate ourselves from the outcome or result. For things to happen after we have done our part, we must learn to let go of the result. And when we do let go, things start to happen. They might not arrive in the manner we anticipated, but they do. Why is letting go so difficult? The most potent and difficult law is the Law of Detachment. The ability to accept things as they come, when they arrive, and in whatever form they take and to learn to be happy no matter what is closely tied to the law of detachment.
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V = pie r squared h solve for h
The isolated value of h is found to be V/πr²
The three-dimensional solid shape of a cylinder is made up of two parallel bases connected by a curved surface. These bases have the shape of a spherical disc. The axis of the cylinder is a line drawn through the centre or connecting the centres of two circular bases. The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the component.
According to given formulae:
V=πr²h
On dividing both side with πr² we get
⇒V/πr²=πr²h/πr²
(Solving R.H.S)
⇒h=V/πr²
Therefore, the value of h in the given question is V/πr²
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→
What single decimal multiplier would you
use to increase by 9% followed by a 6%
decrease?
There will be a 6% rise using the 0.9646 multiplier, then a 9% reduction.
What is a multiplier?Simply said, a multiplier is a factor that increases the basic value of another object. For example, a 2x multiplier would double the initial value. On the other hand, a multiplier of 0.5x would actually cut the basic amount in half. In finance and economics, multipliers come in a wide variety.
Say that Number is 100N.
growth of 6%
= (6/100)100N
= 6N
Number following reduction: 100N + 6N = 106N
9% lessening
= (9/100)106N
=954N/100
= 9.54N
Final result after reduction = 106N - 9.54N
=96.46N
=9646N/100
= 9646 * 100N/100 * 100
= 9646 * 100N/10000
= 0.9646 * 100N
There will be a 6% rise using the 0.9646 multiplier, then a 9% reduction.
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if you answered my other question please get ur points here
Answer:
Step-by-step explanation: Hope my explanation made sense
Answer:
Thank you, if you need more clarification on the system of parallelograms, let me know.
Write an equivalent expression by distributing the "—" sign outside the parentheses:
3v - (7.9w - 9.3)
By applying the distributive property, the equivalent expression to 3v - (7.9w - 9.3) is: 3v - 7.9w + 9.3.
What is an Equivalent Expression?Two expressions are equivalent if they both have equal values when simplified or evaluated.
How to Apply the Distributive Property?To apply the distributive property, the term or operation sign outside the parentheses is used to multiply each of the terms that are within the parentheses.
Given the expression, 3v - (7.9w - 9.3)
Apply the distributive property to find an equivalent expression
3v - (7.9w - 9.3) = 3v -(7.9w) - (-9.3)
3v - (7.9w - 9.3) = 3v - 7.9w + 9.3
Therefore, by applying the distributive property, the sign "-" is distributed to get the equivalent expression to 3v - (7.9w - 9.3, which is: 3v - 7.9w + 9.3.
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The measure of variability easiest to compute, but seldom used as the only measure, is the _____
The measure of variability easiest to compute, but seldom used as the only measure, is the range.
What is the range of values?The range is the term that is used to refer to the difference that lies between the highest value and the lowest value in a data set while computing a statistical data.
The measures of variability are 4 in number. These are
The rangeThe interquartile rangethe standard deviationThe variance.Hence we can conclude that The measure of variability easiest to compute, but seldom used as the only measure, is the range.
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Determine whether this statement is true or false. If false, identify the correct explanation.
If an angle is acute, then its supplement is a right angle.
true
false; the complement is a right angle
false; supplement is less than a right angle
false; supplement is an obtuse angle
If an angle is acute, then its supplement is an obtuse angle (true).
What is an Acute Angle?An acute angle is an angle that has a measurement that is below 90 degrees (right angle).
What is an Obtuse Angle?The measurement of an obtuse angle is less than 180 degrees but more than angle 90 degrees (right angle).
What is the Supplement of an Angle?The supplement of an angle is the measure of that angle subtracted from 180 degrees.
For example, if an acute angle measures 30°, therefore:
The complement of 30° = 90 - 30 = 60°. 60° is also an acute angle.
The supplement of 30° = 180 - 30 = 150°. 150° is an obtuse angle.
Therefore, we can conclude that: if an angle is acute, then its supplement is an obtuse angle (true).
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Simplify each number. (32)⁻⁴/₅
The result of simplifying each number (32)⁻⁴/₅ using the exponent rules is 1/16
To solve this exercise we have to resolve algebraic operations following the exponent rules.
(32)⁻⁴/₅
Base= 32
Exponent= -4/5
As we have a negative exponent, you have to pass the exponent to the denominator:
1/(32)⁴/₅
As we have a fractional exponent, you must convert the exponent to root:
1/[tex]\sqrt[5]{}[/tex](32)⁴
1/[tex]\sqrt[5]{}[/tex]1048576
1/16
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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