Answers
In mathematics, a variable is a symbol and placeholder for any mathematical object. In particular, a variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set
While multiplying two integer numbers, the rule is simple.
If both the integers have the same sign, then the result is positive.
If the integers have different signs, then the result is negative.
For example,
(+2) x (+3) = +6
(+3) x (-4) = – 12
The major Properties of Integers are:
Closure Property
Associative Property
Commutative Property
Distributive Property
Additive Inverse Property
Multiplicative Inverse Property
Identity Property
According to the distributive property of integers, if a, b and c are integers, then:
a x (b + c) = a x b + a x c
Example: Prove that: 3 x (5 + 1) = 3 x 5 + 3 x 1
LHS = 3 x (5 + 1) = 3 x 6 = 18
RHS = 3 x 5 + 3 x 1 = 15 + 3 = 18
Since, LHS = RHS
Hence, proved.
1) (a-b)+c
a= 0.5 , b= 2, c= -1
(0.5- 2)+-1
=-1.5-1
=-2.5
2) a= 3 . b=-4, c=-2
(3-(-4)+-2
= (3 +4)+2
= 9
3) a= -8, b= 5, c= 3
(-8+5)+3
=-3+3
= 0.
-(a-b)-c
1) a=0.5 , b= 2, c=-1
-(o.5-2)-(-1)
=-0.5+2+1
= 2.5
2) a= 3, b= -4, c=-2
-(3-(-4)-(-2)
-(3+4)+2
-3-4+2
= -5
3) a= -8, b=5 ,c=3
-(-8-5)-3
=(8+5)-3
= 13-3
= 10.
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Related Questions
Solve each equation. If necessary, round to the nearest ten-thousandth. log 4+2 log x=6
Answers
The solution of the given equation by rounding off it to the nearest ten-thousandth is 10.0427.
What is a round-off of the digit?
In mathematics, a round-off is defined as an approximation of the given number to a fewer number of significant digits by taking into consideration some rules.
For eg: 13.58 ~ 13.6
Solving the given equation: log 4 + 2 log x = 6
We are given a logarithmic expression: log 4 + 2 log x = 6
We know that e^(log b) = b
a log b = (log b)^a
log a + log b = log (ab)
Using exponential on both sides, we have
e^(log 4 + 2 log x) = e^6
e^(log 4 + log x² ) = 403.428
e^(log 4x² ) = 403.428
4x² = 403.428
x² = 403.428 / 4
x² = 100.857
x = 10.0427
Hence, the solution of the given equation rounded off to the nearest ten-thousandth is 10.0427.
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what is the slope-intercept equation of the line that includes the points in the table?
Answers
If we have two pairs (x₁, y₁) and (x₂, y₂) on the table, use the following formula to get the slope:
a = (y₂ - y₁)/(x₂ - x₁)
How to get the slope for any table?
A general linear equation in the slope-intercept form can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Now, if the linear equation has a table with some values:
X Y
x₁ y₁
x₂ y₂
x₃ y₃
etc...
Then you can select any two of the pairs on the table, for example (x₁, y₁) and (x₂, y₂), and use the following formula to get the slope:
a = (y₂ - y₁)/(x₂ - x₁)
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help pls explain this to meeeeee
(image included)
Answers
The equation of the line passing through the given coordinate with the given slope is; y = 2x + 11
What is the equation of the line in point slope form?
The formula for equation of line in point slope form is;
(y - y1) = m(x - x1)
We are given the slope is 2
Now, if the line passes through the coordinate (-4, 3), then the equation of the line is;
(y - 3) = 2(x - (-4))
y - 3 = 2x + 8
y = 2x + 11
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What is the solution of the equation (4x+3)^2=18
Answers
Answer:
x= 0.31066017 rounded to 0.31
Step-by-step explanation:
first you take out the exponent (2) by getting the square root of 18 so the equation will be 4x+3=18squared rooted. the primary factors of 18 are 2*3 squared. so instead of 18 put the factors is.so now you will get
4x+3=3^2*2 square rooted.
then you apply the radical rule so square root each of the digits.that will simplify to 4x=3square rooted by 2 divide by 4 on both sides minus 3/4 and if you simplify it should give you the answer
Solve for the value of a.
104°
(8a-4)°
Answers
Answer:
a = 10
Step-by-step explanation:
The image is showing a linear pair which equals 180°
104° is shown.
If you take 180° and subtract 104° you should get the answer to what (8a -4)° should equal to.
180° - 104° = 76°
Your equation should look like : 8a - 4 = 76°
-- Add 4 to both sides
8a - 4 = 76°
+4 +4
= 8a = 80
-- Divide 8 on both sides
8a/8 = 80/8
a = 10
Proof:
8(10) - 4 =
80 - 4 = 76°
104° + 76° = 180°
Hope this helps!
--Blu
The larger of two numbers is eight more than the smaller. If the sum of the two numbers is 32, what are the two numbers
Answers
The two numbers are 12 and 20
How to determine the numbers
Let the small number be x
Let the large number be y
We have that;
y = 8 + x (1)
But;
x + y = 32 (2)
Now, substitute the value of y as 8 + x in equation (2)
x + 8 + x = 32
collect like terms
2x + 8 = 32
2x = 32 - 8
2x = 24
Make 'x' the subject
x = 24/ 2
x = 12
But;
y = 8 + x
y = 8 + 12
y = 20
Thus, the two numbers are 12 and 20
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9 is added to the product of 9 and a number.
Answers
The algebraic expression for the given statement is: 9x + 9.
How to Translate a Phrase into Algebraic Expression?Given the statement above, the unknown number can be represented with variable "x".
The number = x
"Product" means multiplication.
"Product of 9 and x" = 9x
If 9 is added to the "product of 9 and x", the algebraic expression would be: 9x + 9.
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Highest Common Factors (HCF)
Find the HCF of these pairs of num
a. 6 and 9
Answers
Answer:
3
Step-by-step explanation:
6=2*3
9=3*3
The only common factor is 3
Identify the equation that represents the sentence “Find two consecutive odd integers whose sum is 116”.
Multiple choice question.
cross out
A)
n
(
n
+
2
)
=
116
cross out
B)
n
(
n
+
1
)
=
116
cross out
C)
2
n
+
2
=
116
cross out
D)
2
(
n
+
2
)
=
116
Answers
Answer:
Answer: 57 & 59
Step-by-step explanation:
Let us assume first odd integer is 'x'
Then, next consecutive integer should be 'x+2'. RIGHT?
Now, put in the form of equation:
x + (x+2) = 116
x + x + 2 = 116
2x + 2 = 116
2x = 116 - 2
2x = 114
x = 114 / 2 => 57
Now, put the value of 'x' in second step:
x + 2 => 57 + 2 = 59
Therefore, answer would be 57 & 59
The loudness in decibels dB of a sound is defined as 10 log I/I₀ , where I is the intensity of the sound in watts per square meter (W / m²) . I₀ , the intensity of a barely audible sound, is equal to 10⁻¹²W/m². Town regulations require the loudness of construction work not to exceed 100 dB . Suppose a construction team is blasting rock for a roadway. One explosion has an intensity of 1.65x10²W/m² . Is this explosion in violation of town regulations?
b. What values should you use for I and I₀?
Answers
a) The explosion does violate the town regulation
b) The values are , I = [tex]1.65 * 10^{2} W/m^{2}[/tex] and [tex]I_{0}[/tex] = [tex]10^{-12} W/m^{2}[/tex]
The values that we have been given are
L = loudness of the sound = 10log(I/[tex]I_{0}[/tex])
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
[tex]I_{0}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
Putting the required value in the equation of the loudness we get
a) L = [tex]10*log (\frac{1.65*10^{2} }{10^{-12} } )[/tex]
L = 10*14.217 dB = 1142.17 dB
And according to the town regulation the loudness of the construction work should not exceed 100dB.
Thus the explosion is in violation of the town regulation as it exceeds 100dB.
b) The respective values of I and [tex]I_{0}[/tex] are
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
= intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
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How am I supposed to find out how what angle EFG is so I can solve this problem?
Answers
let's recall that an angle bisector, bisects = cuts into two equal halves.
Check the picture below.
2. Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard. (3 points)
Answers
The time taken for Mel to finish mowing the yard if they have 80 minutes is 53 minutes.
What is a fraction?It should be noted that this represents the number of pieces removed from the whole. The denominator of a fraction is the numerical value that comes before the brings together various.
Given that,
Michael mows = 1/3 of the yards
Mel will cut: 1 - 1/3 = 2/3
Therefore, the time taken for Mel to mow the yard will be:
= 80 × 2/3
= 53 minutes
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After Michael mows ⅓ of the yard, Write a fraction division problem that you can use to find out how long it will take Mel to finish mowing the yard if they have 80 minutes.
Make the non testable questions be testable questions. (Only 2) PLEASE HELP!!
"Which planet is the most interesting to study?"
"What happens if you do not eat breakfast?"
Answers
When the given non testable questions are made into testable questions, they become:
What planetary conditions are considered subjects of interest for study?How is your body affected when you do not eat breakfast?How to write testable questions?A testable question is one that requires the answer to be acquired by means of experimentation.
Instead of asking, "Which planet is the most interesting to study?" you could ask about the conditions that a planet has which are considered subjects of interest.
Also, instead of asking, "What happens if you do not eat breakfast?" you could ask about how the body is affected when we skip breakfast. This can be tested in an experiment that checks the body's functions when breakfast isn't eaten.
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How do I solve this problem?
Answers
write the negation of the proposition. then state the truth value of the original proposition and its negation. antarctica is in the northern hemisphere.
Answers
The negation is "antarctica is not in the northern hemisphere" & the truth value of the original proposition is FALSE and its negation is TRUE.
The sentences that can be classified as true or false , but not both are called as propositions.
For Example , "Shirt is yellow" is a proposition whereas "a is less than 2" is not a proposition as the value of a is not fixed.
Negation of proposition means writing the opposite of the given proposition.
If the proposition is true then it's truth value is "True".
If the proposition is false then it's truth value is "False".
According to the given Question
The negation of the statement "antarctica is in the northern hemisphere" is "antarctica is not in the northern hemisphere"
The truth value of the original proposition is FALSE as Antarctica is in the Southern hemisphere.
The truth value of the negation is TRUE as Antarctica is not in the Northern hemisphere it is in southern Hemisphere.
Therefore , the negation is "antarctica is not in the northern hemisphere" & the truth value of the original proposition is FALSE and its negation is TRUE.
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Reginald wallace's gross weekly salary is $515. his weekly federal withholding is $55. the social securit
tax is 6.2 percent of the first $90,000. the medicare tax is 1.45 percent of gross pay. the state tax is 1.5
percent of gross pay. each week he pays $12.40 for medical insurance. how much is deducted from
wallace's weekly wages for state tax and medicare tax?
$17.67
$15.19
b. $12.22
d. $16.19
c.
a.
Answers
If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.
State tax and Medicare taxState tax=1.5 percent of gross pay
Medicare tax=1.45 percent of gross pay
State tax=$515 ×0.015
State tax= $7.725
Medicare tax=$515× 0.0145
Medicare tax = $7.4675
Hence:
State tax and Medicare tax=$7.725+$7.4675
State tax and Medicare tax=$15.1925
State tax and Medicare tax=$15.19 (Approximately)
Therefore If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.
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5) Three consecutive odd integers are such that the sum of the first and the third is 70.Find the integers
Answers
Solution : Three consecutive odd integers are 33,35,37
Three consecutive odd integers :
Odd numbers are whole numbers that when divided by 2 give the remainder as one. Odd numbers are written in the form 2x+1,x∈N where N is the natural numbers
the sum of the first and the third is 70.
1 st number is = a
2nd number = b
3rd number = c
Let the required one integer be x. We need three integers so one integer is x next odd integer can be written as x+2 and the third integer can be written as x+4
a+c = 70 ...1
a= x
b=x+2
c= x+4
for equation 1
x+x+4 = 70
2x+4 =70
2x= 70-4
2x= 66
x=66/2
x=33
a=33
b= x+2 =33+2 =35
c= x+4 = 33+4 = 37
Three consecutive odd integers are 33,35,37
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53.93 rounded to the nearest whole number
Answers
Answer:
54
Step-by-step explanation:
Solve for g: 3/4(4g + 5)=6
Answers
Decimal form: G=0.75
Given ƒ(x) = −4x − 5, find ƒ(5)
Answers
The output value of f(5) in the given function f(x) = -4x - 5 is -25
What is the output value of f(5) in the given function?A function is simply a set of ordered pairs where each first element is paired with one and only second element and also no element in either pair is without a partner.
Given the data in the question;
f(x) = -4x - 5f(5) = ?To determine the output value of f(5), replace the variable x with 5 and simplify.
f(x) = -4x - 5
f(5) = -4(5) - 5
Perform the multiplication operation to remove the parenthesis.
f(5) = -4(5) - 5
f(5) = -20 - 5
f(5) = -25
Therefore, the output value of f(5) in the given function f(x) = -4x - 5 is -25.
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Under her cell phone plan, Bao pays a flat cost of $40.50 per month and $5 per gigabyte. She wants to keep her bill under $60 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Bao can use while staying within her budget.
Answers
The number of gigabytes Bao can use while staying within her budget is 3.9 gigabytes.
How to illustrate the inequality?From the information, plan, Bao pays a flat cost of $40.50 per month and $5 per gigabyte and she wants to keep her bill under $60 per month.
The inequality will be:
40.50 + 5g < 60
where g = number of gigabytes
40.50 + 5g < 60
5g < 60 - 40.50
5g < 19.50
g < 19.50 / 5
g < 3.9
Therefore, the number of gigabytes will be less than 3.9 g.
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Find the area of the triangle.
Do not include units (square units) in your answer.
Answers
Answer:
Step-by-step explanation:
The area is 6
because the base is 4 units and the height it 3 units, and base times height will give you 6.
The function f is defined on the real numbers by f(x) = 2 + x − x2
Answers
The numeric values of the function are given as follows:
f(-3) = -2.75.f(2) = 4.f(5) = -0.75.What is the missing information?The function is missing, and is given as follows:
f(x) = 0.25x - 2, x ≠ 2.f(x) = 4, x = 2.It asks for the following numeric values:
f(-3), f(2), f(5).
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.
Hence, for this function, the numeric values are:
f(-3) = 0.25(-3) - 2 = -2.75.f(2) = 4.f(5) = 0.25(5) - 2 = 1.25 - 2 = -0.75.More can be learned about the numeric values of a function at brainly.com/question/28367050
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Write the negation of the hypothesis and the
negation of the conclusion for each conditional.
SEE EXAMPLES 3 and 4
24. If the sum of the interior angle measures of a
polygon is 180, then the polygon is a triangle.
Answers
the negations of the hypothesis and conclusion for the given conditional statement are:
not P = "The sum of the interior angle measures of a polygon is not 180°"
not Q = "The polygon is not a triangle"
How to write the negations of the hypothesis and conclusion?For two defined propositions P and Q, we define a conditional statement as a sentence of the form:
If P, then Q.
Particularly in this case, P is called the hypothesis and Q is called the conclusion of the conditional statement.
For the given one:
"If the sum of the interior angle measures of a polygon is 180, then the polygon is a triangle."
We will have that the hypothesis is:
The sum of the interior angle measures of a polygon is 180°
The conclusion will be:
The poñyogn is a triangle.
Now we want to negate these two, it is really simple, for the hypothesis we will have that the sum of the interior angles can be any number but 180°, then we can write the negation as:
"The sum of the interior angle measures of a polygon is not 180°
Similar for the conclusion, we just need to state that the polygon is not a triangle, we will get:
"The polygon is not a triangle"
Then the negations of the hypothesis and conclusion for the given conditional statement are:
not P = "The sum of the interior angle measures of a polygon is not 180°"
not Q = "The polygon is not a triangle"
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please help this is my question
find the value of x in each of the following here are the questions
2x=10
3x=27
Answers
Step-by-step explanation:
1)x=10/2=5
x=5
2)x=27/3=9
x=9
Write each expression as a single logarithm.
log₄2+log₄8
Answers
If the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.
Given that the expression is log₄2+log₄8.
We are required to express the given expression in single logarithm.
Product property of logarithm basically tells that says that the logarithm of a product is equal to a sum of logarithms and because logs are exponents, and we multiply like bases, we can add the exponents.
The expression is log₄2+log₄8.
log₄2+log₄8=[tex]log_{4}[/tex](8*2) (We are not required to write the base separately)
=[tex]log_{4}[/tex]16
Hence if the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.
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A stack of boxes is 6/5 meters tall. Each box is 3/10 meter tall. How many boxes are in the stack
Answers
The 4 number of boxes are in the stack.
What is arithmetic?
Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
A stack of boxes is 6/5 meters tall.
Each box is 3/10 meter tall.
According to given question we have
The number of boxes are in the stack
[tex]\frac{6/5}{3/10} \\\\=\frac{6*10}{3*5} \\\\=4[/tex]
Therefore, the 4 number of boxes are in the stack.
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What is the value of the expression below when w = 9 and x = 8?
Answer:
9w7x
Submit Answer
Answers
Answer:
Step-by-step explanation:
4,536
When solving an equation, Bianca's first step
is shown below. Which property justifies
Bianca's first step?
Original Equation:
2(x + − 2) =
=
-4
First Step:
2x + 4 = -4
division property of equality
distributive property of
multiplication over addition
multiplication property of equality
O addition property of equality
Answers
Answer: associative property of adding
1) 0, -2, 1
What is the largest integer
Answers
Answer:
it would be 1 (im not really sure what it would be, let me know if this helps)
Step-by-step explanation: