calculate the absolute value
| 4 - 3x | = 5x + 4
Recall the definition of absolute value:
• |x| = x if x ≥ 0
• |x| = -x if x < 0
So we have 2 cases to consider:
• If 4 - 3x ≥ 0, then |4 - 3x| = 4 - 3x, and we have
4 - 3x = 5x + 4
8x = 0
x = 0
• If 4 - 3x < 0, then |4 - 3x| = -(4 - 3x) = 3x - 4, which gives
3x - 4 = 5x + 4
2x = -8
x = -4
However, keep in mind that |x| is always non-negative. If x = -4, then the right side of the equation becomes
5(-4) + 4 = -20 + 4 = -16 < 0
so the solution in this case is extraneous.
Which of the following collections of subsets of the plane, R2
, are partitions?
(a) {{(x; y) | x + y = c}| c R}
(b) The set of all circles in R2
(c) The set of all circles in R2
centered at the origin together with the set {(0; 0)}
(d) {{(x; y)} | (x; y) R
[tex]\{(x,y) | \ \ x+y = c, \ c \in \mathbb{R}\}[/tex]
Explanation:
The notation for choice A basically says "we have a line of the form x+y = c where c is a real number". Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house. There are no gaps or overlaps (ignore the regions in the walls).
Take note that if a point is on a line like x+y = 5, then it cannot be on any other line of the form x+y = c, where c is not equal to 5. Something like (x,y) = (2,3) is on x+y = 5 and not on any other line. If c is allowed to be any real number, then x+y = c will be able to partition the real numbers.
Put another way, we can pick any real number we want (aka the number c) and break it down into a sum of x and y values. Such a sum cannot yield any other c value. So going back to the house/room analogy, any particular (x,y) ordered pair will belong to one and only one room.
Let's look at an example of a non-answer. Choice B is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions. This idea also means choice C is false as well.
Choice D can be ruled out because the notation should be (x,y) in R2 and not simply R.
The collections of subsets of the plane, R2 is (a) {{x,y) : x + y = c} : c ∈ R}
What is a subset ?If X is a subset of Y then all the elements of A also contained in B.
According to the given statement we have o determine which of the following collections of subsets of the plane R2.
R2 defines a two dimension plane.
x+y = c where c is a real number.
Then points on the line in the form (x,y) will form a particular partition. A partition is where we break a set up into non-overlapping subsets and there are no gaps. Think of it like breaking up a house into multiple rooms. Each room is a subset of the house.
Take note that if a point is on a line like x+y = 7, then it cannot be on any other line of the form x+y = c, where c is not equal to 7. Something like (x,y) = (3,4) is on x+y = 7 and not on any other line.
B. Is not correct because it is perfectly possible to have circles intersect. Intersecting circles share at least one common point. Those common points are what break the idea of partitions.
C. is false as well
D. Is ruled out because the notation should be (x,y) in R2 and not simply R.
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(c) 5 points possible (graded) The problem you encountered in part (b) is called separation . It occurs when the can be perfectly recovered by a linear classifier, i.e., when there is a such that In order to avoid this behavior, one option is to use a prior on . Let us investigate what happens if we assume that is drawn from a distribution, i.e., What is the joint log likelihood of this Bayesian model
We have that these are the key points given below
The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event.
Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.
Bayesian Theorem
The Bayesian Theorem is a theorem that centers or basis its claim on the facts that the probability of an event occurring is based on Prior Knowledge that of situation or Prior factors of the Event
i'll explain further with an example
Given that when two unfair dice are thrown a 100 times the probability of getting the higher figure in the range of 6-8 , Therefore the Bayesian Theorem simply assumes that this range of 6-8 to be the highest for all 100 throws of two dice.
The Bayesian model is given as
[tex]B=Prior * Likelihood=Posterior * Marginal[/tex]
Bayesian model is a statistical model.
This leads us to the definition of the Likelihood function
Likelihood function is a function that take into account all statistical model and determine there best application given the statistical data given.
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A square has a a side lenght of 5 feet what is its area?
Answer:
25 sq feet
Step-by-step explanation:
Length = 5 feet
Area = (Length)²
= 5²
= 25 sq feet
Does this picture indicate that < JAC =
Answer:
No
Step-by-step explanation:
<JAC = 93
< DBE = 90
The two angles are not equal
What is the Answer to 50 + 10 x 0 + 7 + 2
Arithmetic involves carrying out addition, subtraction, division and multiplication on numbers and expressions. The result of [tex]50 + 10 \times 0 + 7 + 2[/tex] is [tex]59[/tex]
Given that:
[tex]50 + 10 \times 0 + 7 + 2[/tex]
To do this, we apply BODMAS.
First, we evaluate all multiplication operations
[tex]50 + 10 \times 0 + 7 + 2 = 50 + 0 + 7 + 2[/tex]
Then evaluate all addition operations
[tex]50 + 10 \times 0 + 7 + 2 = 59[/tex]
Hence, the result of [tex]50 + 10 \times 0 + 7 + 2[/tex] is [tex]59[/tex]
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Solve the equation.
} (a + 2) = {(2-a)
WWW.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Type an integer or a simplified fraction.)
B. The solution is all real numbers.
O C. There is no solution.
(Answer quickly)
evaluate the expression
Step-by-step explanation:
13
[tex]3 + (20 \div 5) - ( {2}^{2}) [/tex]
[tex]3 + 4 - 4 = 3[/tex]
15
[tex] \frac{10 - {3}^{2} }{20 - (3 \times 4)} [/tex]
[tex] \frac{10 - 9}{20 - 12} [/tex]
[tex] \frac{1}{8} [/tex]
Need help with solving please
Answer:
x=8
Step-by-step explanation:
4 ^(1/2x) = 256
Rewriting 256 as a power of 4
4 ^(1/2x) = 4^4
Since the bases are the same, the exponents are the same
1/2x = 4
Multiply each side by 2
1/2x *2 = 4*2
x=8
f(x)=19x+11 find f(4)
Answer:
87
Step-by-step explanation:
f(x)=19x+11
Let x = 4
f(4) = 19*4 +11
=76 +11
= 87
Answer:
[tex]f(x) = 19x + 11 \\ f(4) = 19 \times 4 + 11 \\ = 76 + 11 \\ = 87 \\ thank \: you[/tex]
Refer to the figure to answer the question.
Name the line of intersection of planes GABH and FEHG
HG
GA
FE
FD
Answer:
It's HG
Step-by-step explanation:
The line of intersection is where they cross, and this line is the line HG
Rose's rectangular backyard has an area of 672 square meters. Find the length of the backyard if the backyard is 7 meters wide.
[tex]\\ \rm\longmapsto Length(Breadth)=Area[/tex]
[tex]\\ \rm\longmapsto Length(7)=672[/tex]
[tex]\\ \rm\longmapsto Length=\dfrac{672}{7}[/tex]
[tex]\\ \rm\longmapsto Length=96m[/tex]
Is square root of 11+10 a rational or irrational number
Answer:
Irrational Number is the answer
Answer:
[tex] \sqrt{11 + 10} = \sqrt{22} = 4.69041576 [/tex]
THIS IS IRRATIONAL
Step-by-step explanation:
The correct answer is irrational and the reason for that is the decimals for sqrt of 22 are non-recurring, are non-terminating and lastly it cannot be expressed in a form of a fraction.
I hope this makes sense
:)
I’ll give you 50 points if it’s answer correctly
Answer:
. The line passes through the quadrants I, II and III. ii. The line intersects the Y-axis at (0, 1).
A car has been purchased for £5200 and is estimated to have an expected life driving 200,000
miles. At the end of that time its value is estimated to be £200. If the units-of-production
method is used to depreciate the car,
a) What is depreciation cost per mile?
b) What will be book value of the car after it has driven 55000 miles?
Answer:
a) 0.025£ b)3825£
Step-by-step explanation:
a) 5200-200=5000 - of the value will be lost after reaching the milleage of 200000 miles
200000-5000
1-x
200000=5000/x
x=5000/200000= 5/200=1/40=0.025£- the depreciation cost per mile
b)0.025*55000= 1375- the decreasing of the price
5200-1375=3825£- the book value of the car after it has driven 55000 miles
simplify y + 5 - y - 6
Answer:
-1
Step-by-step explanation:
Subtract the numbers: y+5-y-6
Combine like terms: y-1-y
= -1
what is the range of this function ??? please explain
Answer:
B. (2, 3, 4)
Step-by-step explanation:
The range of a function is the list of y values. In this instance, the y values present in this function are 2, 3, and 4. Therefore, the answer is B. (2, 3, 4).
can you help me to solve this
Answer:
<B = <C(angles in a isoceles traingle)
Answer:
angle B is equal to angle C because it's a isosceles triangle with two equal sides and two equal angles
Find the quotient.
154 divided by 14
Answer:
11
Step-by-step explanation:
[tex]\frac{154}{14} =11\\\\check: 11*14=154[/tex]
154 divided by 14 equals 11.
To find the quotient of 154 divided by 14, we perform long division as follows:
11
14 | 154
First, we consider how many times 14 can be divided into 15, which is 1. We write the quotient, 1, above the line.
Next, we multiply 14 by 1, which equals 14. We subtract 14 from 15, resulting in 1. We bring down the next digit, which is 4.
We now consider how many times 14 can be divided into 14, which is 1. We write the quotient, 1, next to the 1 above the line.
Multiplying 14 by 1 gives us 14. Subtracting 14 from 14 gives us 0.
Since there are no more digits to bring down, we can conclude that the quotient is 11.
Therefore, 154 divided by 14 equals 11.
Long division is a method used to find the quotient and remainder when dividing two numbers. It involves dividing, multiplying, subtracting, and bringing down digits until there are no more digits to bring down. In this case, the quotient is 11, indicating that 154 can be divided by 14 precisely 11 times without any remainder.
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The university of Michigan football stadium can hold 107,601 people. Michigan states football stadium can hold 75,001 people. 51,000 people can fit in the football stadium at the university of North Carolina and 40,004 people can fit in duke universities stadium which is also in North Carolina. How many more people can fit in the stadiums in Michigan combined than in the stadiums in North Carolina combined
Answer:
56,601
Step-by-step explanation:
Show Work! There are 380 students, teachers, and chaperones going on school buses for a field trip. Each school bus can hold 68 passengers. Everyone will ride on a school bus. How many school buses does this group need?
Answer:
6 buses
Step-by-step explanation:
i believe you just have to divide 380/68
then it'll give you 5.5 and then have to round to the nearest integer
You are wrapping a gift box that is 16 inches long,
7 inches wide, and 9 inches tall. Find the amount of
wrapping paper you need to wrap the gift box to the
nearest square inch.
Answer:
1008 inches
Step-by-step explanation:
Help please! Describe how figure 20 will look like
9514 1404 393
Answer:
Each colored block in Figure 20 will be a 20×20 square of smaller squares of the same color. The red-green pattern will be identical.
Step-by-step explanation:
Each colored block in Figure N is an N×N array of small blocks the same color. The pattern of red and green N×N blocks is the same from one figure to the next. We expect Figure 20 to fit this description.
Madura is 25 years younger than her father. Nadira's mother is two years younger than her father. Together Nadira, her mother and father have a combined age of 78. Work out their ages.
just solve by yourself
eg jammu jdndhdbshsbsbs
Answer:
A: [tex]3\frac{1}{3}[/tex]
B: [tex]3\frac{2}{3}[/tex]
I hope this helps!
pls ❤ and mark brainliest pls!
are these two line parallel to each other??
Answer:
No
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 1 ← is in slope- intercept form
with slope m = 3
Calculate the slope using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2,4) and (x₂, y₂ ) = (4, 12) ← 2 ordered pairs from the table
m = [tex]\frac{12-4}{4-2}[/tex] = [tex]\frac{8}{2}[/tex] = 4
Parallel lines have equal slopes
The slope of these 2 lines are not equal , thus not parallel
Okay imma ask a question and The first person to answer and get it correct wins and I will give you a Brillantest
196x84-23+56-109+54x345-56+34x856=
Answer:
yoooo it equals 1
Step-by-step explanation:
Any mathematician am giving brainliest for this question
9514 1404 393
Answer:
(x, y) = (1/2, 1)
Step-by-step explanation:
Subtract twice the second equation from the first to eliminate the x-variable.
(2/x +3/y) -2(1/x -4/y) = (7) -2(-2)
11/y = 11 . . . . . . . simplify
y = 1 . . . . . . . . multiply by y/11
__
Substituting into the second equation gives ...
1/x -4/1 = -2
1/x = 2 . . . . . . add 4
1/2 = x . . . . . . multiply by x/2
The solution is (x, y) = (1/2, 1).
_____
Additional comment
The attached graph seems to show that the graphs of the two equations also intersect at (x, y) = (0, 0). However, careful consideration of these equations leads to the conclusion that x=0 and y=0 are not in the domain of either equation. (Division by 0 is undefined.) So, the only solution is (x, y) = (1/2, 1).
If you were to multiply both equations by xy to eliminate fractions, you would, indeed, arrive at the conclusion that (x, y) = (0, 0) is a solution. As we noted, that "solution" is extraneous. Whenever you multiply an equation by an expression that can have the value 0, you need to be careful to exclude any "solution" that makes that expression 0.
find the defference between 5 2/7 and 2 2/4
Answer: 39/14
Step-by-step explanation:
Given
5 2/7 - 2 2/4
Convert mixed fraction to improper fraction
5 2/7 = (5 × 7 + 2) / 7 = (35 + 2) / 7 = 37/7
2 2/4 = (2 × 4 + 2) / 4 = (8 + 2) / 4 = 10 / 4 = 5/2
Find the common denominator for 37/7 and 5/2
First 10 multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
First 5 multiples of 7 = 7, 14, 21, 28, 35
Since 14 is the first common multiple in the lists, 14 would be the common denominator of 37/7 and 5/2
Convert to the common denominator
(37 × 2) / (7 × 2) = 74 / 14
(5 × 7) / (2 × 7) = 35 / 14
Simplify by subtraction of numerator
=74/14 - 35/14
=(74 - 35) / 14
=[tex]\boxed{\frac{39}{14} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Aim: I can solve two-step word problems involving per
1. A supermarket stocks 300kg of potatoes. 25% of the potatoes are
are sold in 1.5kg bags. What mass of potatoes are sold in 1.5kg b
Answer:
75 kg
Step-by-step explanation:
300*25/100
3*25
75 Kg
Answer:
75kg
Step-by-step explanation:
potatoes are stocked =300kg
25% of potatoes in kg= 25% * 300kg
=75kg
75kg potatoes are sold in 1.5kg bags.
