Answer: x=4
Step-by-step explanation:
8x-13=19
first, add 13 to both sides.
8x= 32
then, divide both sides by 8 to isolate x.
x= 32/8
x=4
For each relation, indicate whether it is reflexive or anti-reflexive, symmetric or anti-symmetric, transitive or not transitive.
a. The domain of the relation L is the set of all real numbers. For x, y ∈ R, xLy if x < y.
b. The domain for the relation D is the set of all integers. For any two integers, x and y, xDy if x evenly divides y. An integer x evenly divides y if there is another integer n such that y = xn. (Note that the domain is the set of all integers, not just positive integers.)
Answer:
(a)
L is not reflexive, L is anti-reflexive
L is not symmetric.
L is not anti-symmetric
L is transitive.
(b)
D is reflexive
D is not symmetric.
D is anti-symmetric
D is transitive.
Step-by-step explanation:
a)
Given that;
domain of the given relation L is the set of all real numbers
For x , y ∈ R , xLy if x less than y.
relation L, where xLy if x less than y, For x, y ∈ R
so For every x ∈ R, it is then false that x less than x.
That is (x, x) does not belongs to L.
∴ L is not reflexive, L is anti-reflexive.
For every x,y ∈ R, if (x,y) ∈ L (i.e. x < y), then (y, x) does not belongs to L, since it is false that y < x.
∴ L is not symmetric.
For every x ∈ R, we can say its false that x less than x. That is (x, x) does not belongs to L.
∴ L is not anti-symmetric.
For every x,y,z ∈ R, if (x, y) ∈ L(i.e. x < y) and (y, z) ∈ L(i.e. y < z), then (x, z) ∈ L, since it is true that x<z when x<y and y<z.
∴ L is transitive.
b)
Also lets consider a relation D, where xDy if there is an integer n such that y = xn, For x, y ∈ Z.
Now
For every x ∈ Z, it is true that x = x × 1. That is (x, x) belongs to D.
∴ D is reflexive,
For every x,y ∈ Z, if (x,y) ∈ P (i.e. y=x × n), then (y, x).
if (x,y) ∈ D, then there exist an integer n such that y=x × n.
Then x = y × (1/n).
Thus, (y,x) does not belongs to D, since 1/n is not an integer, but it is a real number.
∴ D is not symmetric.
For every x,y ∈ Z, if (x,y) ∈ D (i.e. y=x × n), then (y, x) also belongs to D only when x=y. where n=1.
∴ D is anti-symmetric.
For every x,y,z ∈ Z, if (x,y) ∈ D (i.e. x × n1= y), and (y,z) ∈ D (i.e. y × n2 = z), then (x,z)∈ D.
if (x,y) ∈ D, then there exist an integer n1 such that y=x × n1.
if (y,z) ∈ D, then there exist an integer n2 such that z=y × n2.
Thenz = (x × n1) × n2 ⇒ z=x × (n1 × n2).
where (n1 × n2) is an integer. Thus (x,z) ∈ Z
∴ D is transitive.
Solve for the indicated variable: ⅖(z + 1) = y for z.
Answer:
z = 5/2y -1
Step-by-step explanation:
We observe that z has ...
1 addedthe sum multiplied by 2/5To solve for z, we undo these operations in reverse order.
[tex]\dfrac{2}{5}(z+1)=y\qquad\text{given}\\\\z+1=\dfrac{5}{2}y\qquad\text{multiply by 5/2}\\\\\boxed{z=\dfrac{5}{2}y-1}\qquad\text{subtract 1}[/tex]
Step-by-step explanation:
Above is the solution....
Look at the factors of 18 and 30. What is the greatest common factor? factors of 18: 1, 2, 3, 6, 9, 18 factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Answer:
is number 6
Step-by-step explanation:
the greatest common factor is the largest common factor of those.
The greatest common factor of 18 and 30 is 6.
To find the greatest common factor (GCF) of 18 and 30, we can list their factors and identify the largest factor they have in common.
Factors of 18: 1, 2, 3, 6, 9, 18
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
The common factors between 18 and 30 are 1, 2, 3, and 6.
The largest common factor is 6.
Therefore, the greatest common factor of 18 and 30 is 6.
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Find the radius of a circle with the equation:
x2 + y2 – 18x – 14y + 124 = 0
Answer:
The radius of [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] is [tex]\sqrt{6}[/tex].
Step-by-step explanation:
The given expression must be converted into the standard form of a circle, which is described by:
[tex](x-h)^{2}+(y-k)^{2} = r^{2}[/tex]
Where:
[tex]h[/tex], [tex]k[/tex] - Location of center, dimensionless.
[tex]r[/tex] - Radius, dimensionless.
The expression is modified algebraically as follows:
1) [tex]x^{2}+y^{2}-18\cdot x - 14\cdot y +124 = 0[/tex] Given
2) [tex](x^{2}-18\cdot x)+(y^{2}-14\cdot y)+124 = 0[/tex] Commutative and associative properties.
3) [tex](x^{2}-18\cdot x+81)+(y^{2}-14\cdot y +49)+124 = 81+49[/tex] Commutative and associative properties/Compatibility with addition
4) [tex](x-9)^{2}+(y-7)^{2} + 124 = 130[/tex] Perfect square binomial/Definition of sum
5) [tex](x-9)^{2}+(y-7)^{2} = 6[/tex] Compatibility with addition/Existence of additive inverse/Modulative property/Result
Given that [tex]r^{2} = 6[/tex], the radius of the circle is [tex]\sqrt{6}[/tex].
Is this correct ? I think part of it is correct but I’m not sure
Answer: no
Step-by-step explanation:
Write the phrase as an algebraic expression. Use the variable x to represent the unknown number. Seven times a number.
Answer:
7x.
Step-by-step explanation:
Seven times a number = 7x.
An algebraic expression for the given statement is 7x.
The given statement is seven times a number.
We need to write an algebraic expression for the given statement.
What is an algebraic expression?An algebraic expression (or) a variable expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.
Given that, use the variable x to represent the unknown number.
Now, seven times a number=7x
Therefore, an algebraic expression for the given statement is 7x.
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Show all work to identify the asymptotes and zero of the function f(x)= 5x/x^2-25. Please answer ASAP!!!
Answers:
root: x = 0Vertical asymptotes: x = 5 and x = -5Horizontal asymptote: y = 0The term "root" is another way of saying "zero of a function"
============================================
Explanation:
To find the roots, we need to solve f(x) = 0 for x
f(x) = 0
5x/(x^2 - 25) = 0
5x = 0*(x^2-25)
5x = 0
x = 0/5
x = 0
Plugging x = 0 into f(x) leads to f(x) = 0.
The root is x = 0 meaning the x intercept is at 0 on the x axis number line. This is the origin (0,0).
---------------
To find the vertical asymptotes, set the denominator equal to 0 and solve for x
x^2 - 25 = 0
x^2 - 5^2 = 0
(x-5)(x+5) = 0 ... difference of squares rule
x-5 = 0 or x+5 = 0
x = 5 or x = -5
If either x = 5 or x = -5, then then the denominator x^2-25 is zero
We cannot divide by zero, so these values are excluded from the domain, and this produces the vertical asymptotes.
--------------
The horizontal asymptote is y = 0 because the degree of the numerator is 1, while the degree of the denominator is 2. The denominator's degree is larger, which leads to y = 0. The rules for finding the horizontal asymptote are
If m < n, then the horizontal asymptote is y = 0If m = n, then the horizontal asymptote is y = a/bIf m > n, then there is no horizontal asymptote (use polynomial long division to find the oblique asymptote)For those rules above, m and n are the degrees of the numerator and denominator respectively. The a,b refers to the leading coefficients of the numerator and denominator.
The asymptotes and zero of the function are ±5 and 0 respectively
Given the function below;
[tex]f(x)=\frac{5x}{x^2-25}[/tex]The vertical asymptotes occur at the point where the function goes large that is the denominator is zero.
If the denominator is zero, hence;
x^2 - 25 = 0
x^2 = 25
x = ±√25
x = ±5
Hence the asymptotes of the function is ±5
For the zero of the function;
[tex]\frac{5x}{x^2-25}=0\\5x = 0\\x = 0\\[/tex]
Hence the zero of the function is 0
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(5x10) plus (2x1/100)
Answer:
2501/50
Decimal:50.02
Step-by-step explanation:
5 × 10 + 2× 1/100
5 × 10 = 50
2 × 1/100 = 1/50
50 + 1/50
50×50. 1
_____ + ___
50. 50
50 × 50 + 1 = 2501 meaning 2501 over 50 is your answer
Answer:
100
Step-by-step explanation:
Hope this helped! ;)
how many times does 3/4 go into 4.5
Answer:
6 times
Step-by-step explanation:
Turn that fraction into a decimal. 3/4=0.75
Divide!
4.5/0.75=6
A number 4.5 is 6 times of number 3/4.
We have to given that,
To find how many times does 3/4 go into 4.5.
Let us assume that,
x times does 3/4 go into 4.5.
Hence, It can be written as,
⇒ x × 3/4 = 4.5
Solve for x,
⇒ 3x /4 = 4.5
⇒ 3x = 4.5 × 4
⇒ 3x = 18
Divide by 3;
⇒ x = 18/3
⇒ x = 6
Therefore, 4.5 is 6 times of number 3/4.
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There are 45 children in a class. If
9 of them are absent, what
percentage of the class is absent?
Answer:
20%
Step-by-step explanation:
Total = 45
Absentees = 9
Percentage = (No. of absentees / total) × 100
= 9 / 45 × 100
= 0.2 × 100
= 20%
Answer:
20% of the children are absent
Step-by-step explanation:
Number of children absent = 9
Total children in the class = 45
Percent of absent children / total children is defined as the quotient 9/45 multiplied by 100. That is;
[tex]\frac{9}{45} \,*\,100 = 0.2 \,*\,100=20\,%[/tex]
SO the percentage is 20%
Hmm can you help me solve god bless you
Answer:
(3/2)x - 14
Step-by-step explanation:
If two lines are perpendicular, their slopes are mathematically negative reciprocals of one another.
Here the given line is y = (-2/3)x; the slope is -2/3, and the negative reciprocal of that is 3/2. The desired line will have this slope 3/2.
Using the slope-intercept form of the equation of a straight line, y = mx + b, we write out
-8 = (3/2)(4) + b, obtaining -8 = 6 + b, or b = -14.
The desired equation is (3/2)x - 14.
(-2,5) and (4,10) slope of the line containing points
Answer:
Step-by-step explanation:
(10-5)/(4+2) = 5/6
y - 5 = 5/6(x + 2)
y - 15/3 = 5/6x + 10/3
y = 5/6x + 25/3
My square orchid garden abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $4 per foot, and the fencing for the east and west sides costs $2 per foot. Find the total cost of the fencing as a function of the length of a side x.
Answer:
The total cost of the fencing as a function of side is [tex]C = 8\cdot x[/tex].
Step-by-step explanation:
Dimensionally speaking, the total cost is equal to the product of length and cost per length. Given that orchid garden has a square form, there is only an input: Side ([tex]x[/tex]), measured in feet. Therefore, the total cost of fencing is represented by the following formula:
[tex]C = (c_{west} + c_{south} + c_{east})\cdot x[/tex]
Given that [tex]c_{west} = c_{east} = 2\,\frac{\$}{ft}[/tex] and [tex]c_{south} = \$\,4\,\frac{\$}{ft}[/tex], the total cost of the fencing as a function of side is:
[tex]C = 8\cdot x[/tex]
An architect is redesigning a rectangular room on the blueprints of the house. He decides to double the width of the room, increase the length by 48 %, and increase the height by 18 %. By what factor has the volume of the room increased
Answer:
3.4928.Step-by-step explanation:
Initial volume of the rectangular room = Length * Width * Height
V = LWH .............1
If the width is doubled then new width W2 = 2W
If the length is increased by 48%, the new Length L2 = L + 0.48L = 1.48L
If the height is increased by 18%, the new height H2 = H + 0.18H = 1.18H
The new volume after increasing all the dimensions will be;
V2 = L2W2H2
V2 = (1.48L)(2W)(1.18H)
V2 = 3.4928LWH ................2
Now we will divide equation 2 by 1 to have;
V2/V = 3.4928LWH/LWH
V2/V = 3.4928
V2 = 3.4928V
This means that the volume of the room has increased by the factor of 3.4928.
31, -32, 33, -11, 5 least to greatest
Answer: -32, -11, 5, 31, 33
Answer:
-32, -11, 5, 31, 33
Step-by-step explanation:
The smallest one is -32. I know this because it's:
A negativeIs the farthest back on a number lineThe next one is -11. -11 is the next smallest because it's:
A negativeIs larger than -32 (it's closer to 0 and the positives on a number line)The third one is 5. It's the third greatest because it's:
A positiveIs the closest positive option to 0.The fourth one is 31. It's the fourth greatest because it's:
A positiveIt's larger than 5, but smaller than 33The last one is 33. It's the greatest because it's:
A positiveIt's larger than all the other numbersPlz help with this questio!
Thanks!♡︎
Answer:
Week 3.
Step-by-step explanation:
Add up the hours for each week.
Week 3 is the highest at 36 hours.
Answer:
week 3
Step-by-step explanation:
week 3. it totals for 36 hours in this week
Polygon A has one side that is 1.5 and two sides 2.5. How can I figure out how many times larger Polygon B is?
Look at the picture so you know what the problem is.
Excuse me, is this I ready because you know you can get reported right... just try your best, it's not a real grade! :)
& possibly delete this question because a bot can track and report this to your school. People at my school did that and got in 3 days detention...
Karen Sullivan delivers newspapers for the Tribune Dispatch. She
receives 18.2 cents per paper, 6 days a week (for the daily paper),
and 70 cents for the Sunday paper. She delivers 124 daily papers each
day and 151 Sunday papers each week. What is her total pay?
The correct answer is $241.1 each week and $964.4 each month
Explanation:
To calculate the amount Karen should receive, it is required to calculate the money she earned from Monday to Saturday and then the money she earned on Sunday as the amount paid per paper is different on Sunday.
Monday to Sunday:
Karen delivers 124 papers each day from Monday to Sunday. This means she delivers a total of 744 papers (124 papers each day x 6 days = 744 papers). Now, let's find the money she earned from Monday to Sunday:
744 papers x 18.2 cents = 13540 cents or 135.4 dollars (each dollar is equivalent to 100 cents, which means if you divide the cents into 100 you get the equivalent in dollars)
This means the total Karen earned from Monday to Saturday is $135.4
Sunday:
Karen delivers 151 Sunday papers and with each of these she earns 70 cents
151 papers x 70 cents = 10570 cents or 105.7 dollars
Total per week:
$135.4 + $105.7 = $241.1 each week, which is equivalent to $964.4 a month ($241.1 x 4 weeks = $964.4 )
Show how 10-6 helps solve 50-6
Answer:
The digit in the ones spot will come out to be 4.
Step-by-step explanation:
Since the are both an even number of ten, and you're subtracting 6, their both gonna come out to have a 4 in the ones spot in the number answer.
Well 50 is just 10 x 5 so...
if you solve 10 + 6 = 16 then you can do 50 + 6 = 56
A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. How many cupcakes will be sold on day n?
Answer: 4n-3
================================================
Explanation:
day 1 = 1 sold
day 2 = 5 sold
day 3 = 9 sold
day 4 = 13 sold
Each time we're going up by 4. This is effectively the slope of the line since it represents the rate of change. The starting amount sold (1) is the y intercept
So we go from y = mx+b to y = 4x+1
Afterward, replace x with n to get 4n+1
On day n = 0, we have 4n+1 = 4(0)+1 = 1 sold. While this is correct, it doesn't really help to start with day 0 and it's better to start with day 1 instead.
What we can do is replace n with (n-1) and then simplify
4(n-1)+1 = 4n-4+1 = 4n-3
Now plugging in n = 1 leads to 4n-3 = 4(1)-3 = 1
Plugging in n = 2 leads to 4n-3 = 4(2)-3 = 5
and so on.
Caleb bought stock in a company two years ago that was worth xx dollars. During the first year that he owned the stock, it increased by 38%. During the second year the value of the stock decreased by 12%. Write an expression in terms of xx that represents the value of the stock after the two years have passed.
Answer:
1.2144xx
Step-by-step explanation:
The multiplier of value for the first year was (1 +38%) = 1.38.
The multiplier of value for the second year was (1 -12%) = 0.88.
Then the multiplier of value for the two years was ...
1.38×0.88 = 1.2144
The value of the stock after 2 years was ...
1.2144xx
_____
Comment on the variable
We have used the variable given in the problem statement (xx). If you intend something different, replace xx with the variable you intend.
Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the
beach. He fell asleep halfway home. He didn't wake up until he still had half as far to go as he had already
gone while asleep. How much of the entire trip home was Samuel asleep?
Answer: One fourth of the entire trip.
Step-by-step explanation:
The initial distance is D.
" He fell asleep halfway home."
Then he fells asleep when the distance between his actual position and his house was half of D, or:
D/2.
"He didn't wake up until he still had half as far to go as he had already
gone while asleep."
So he wakes up when his actual position is a fourth of the initial distance:
(D/2)/2 = D/4.
Then if the entire trip has a distance D, and he was sleeping between:
D/2 - D/4 = 2D/4 - D/4 = D/4.
in a trip of a distance D, he was asleep a distance of D/4.
Then, returning to the question:
How much of the entire trip home was Samuel asleep?
This is equal to the quotient between the distance that he travels asleep and the total distance:
r = (D/4)/D = 1/4.
Then he was asleep in 1/4 of the entire trip.
the sum of a number and six is ten. find the number
The required number is 4.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The sum of a number and six is ten.
let the number be x.
So, x + 6 = 10
Now, solving for x
x = 10 - 6
x = 4
Hence, the value of x is 4.
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Define and give a visual example of the Commutative Property. 2. Explain the process ( Every Step ) that you would use to simplify the following expression. 7 ( c + 3 ) + -4 (3c -2 )
Answer:
The Commutative Property is a property that states the order of the numbers in addition and multiplication don't matter. 2+3+7 = 7+2+3
Step-by-step explanation:
7(c+3)+ -4(3c-2)
Distribute the 7 and the -4 to each of their parentheses.
7c+21-12c+8
You can use the Commutative Property to move the terms to places where they can be easily simplified.
7c-12c+21+8
Simplify.
-5c+29
Problem 1
Imagine a rectangle that is 2 by 3. You would have an area of 2*3 = 6 and it is the same as saying 3*2 = 6. The order of multiplication doesn't matter. Visually, we can rotate the rectangle to have the shorter side be horizontal and then make it vertical, and the area is still the same. All we're doing is shifting things around.
Another example is say you had a marching band with 10 rows and 2 columns. That gives 10*2 = 20 people total. Then we could easily form the same number of people into 2 rows and 10 columns. The order of rows and columns doesn't matter because we get the same total number as a result.
======================================================
Problem 2
7(c+3) + -4(3c-2) ..... is the original expression
7(c+3) - 4(3c - 2) .... adding a negative is the same as subtracting
7*c + 7*3 - 4*3c - 4*(-2) .... distributive property
7c + 21 - 12c + 8 .... multiply
(7c-12c) + (21+8) .... group like terms
-5c + 29 ... combine like terms
The original expression simplifies to -5c+29
Give the first two solutions of the n-Queens problem for n = 6 Write it in the form (1,2), (2,2), (3,2)
Answer:
(1,2), (2,4), (3,6), (4,1), ( 5,3), (6,5)
Step-by-step explanation:
Given the first two solutions of the n-Queens problem for n = 6
The solution requires that no two queens share the same row, column, or diagonal and each variable lies in the domain [1,6] (6 rows).while finding a solution we must ensure that no two queens are not placed on the same row and in the same diagonal
hence the first two solutions can be expressed as :
(1,2), (2,4), (3,6),(4,1),( 5,3), (6,5)
Rosanne makes 1 1 2 liters of strawberry lemonade. She pours 1 4 of a liter of lemonade into a thermos to take to the park. Her brother drinks 2 5 of the remaining lemonade. How much lemonade does Rosanne's brother drink?
Answer:
1/2 liter
Step-by-step explanation:
If she starts with 1 1/2 liters and removes 1/4 liter, the remaining amount is ...
(1 1/2) -(1/4) = 1 2/4 -1/4 = 1 1/4 . . . liters.
The brother drinks 2/5 of that, so drinks ...
(2/5)(1 1/4 L) = (2/5)(5/4 L) = 2/4 L = 1/2 L
Rosanne's brother drinks 1/2 L of the lemonade.
55 points! Need asap
Answer:
FG = 18
Step-by-step explanation:
to find the length FG
FG + 31 = 49
FG = 49 - 31
FG = 18
EFGH is a rhombus. Rhombus E F G H is shown. Diagonals are drawn from point E to point G and from point F to point H. All sides are congruent. Given EG = 16 and FH = 12, what is the length of one side of the rhombus? 6 units 8 units 10 units 14 units
Answer:
10 units
Step-by-step explanation:
The diagnonals of a rhombus meet at right angle to their selves and bisect each other.
So one quarter will form a right angle triangle of base 6 and height 8.
Let The length of one side of the rhombus be x
X²= 8²+6²
X²= 64+36
X²= 100
X= √100
X= 10 units
Answer:
answer is C. 10 units. Just took the test
Step-by-step explanation:
What is the sum of 637,391+372,088
Answer:
1009479
Step-by-step explanation:
637,391 + 372,088 = 1009479
Answer:
the answers 1009479
Step-by-step explanation: