algebraic equation solving x, we concluded that In the year 1980 the approximate number of oil barrels imported from Country B per day will be 1.89 million.
What exactly is a mathematical linear equation?An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Given the equation is :y=0.051x+1.38
Let us put y = 1.89
1.89 = 0.051x + 1.38
⇒ x = 0.51/0.051
⇒ x = 10
After ten years, 1.89 million oil barrels per day will be roughly imported from Country B.
Around 1.89 million oil barrels per day would be imported from Country B in the year 1980.
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Consider the axiomatic system and theorem below:
• Axiom 1: If there is a pair of points, then they are on a line together.
• Axiom 2: If there is a line, then there must be at least two points on it.
• Axiom 3: There exist at least two distinct points.
• Axiom 4: If there is a line, then not all the points can be on it.
Theorem 1: Each point is on at least two distinct lines.
A. List all undefined terms involved in the given axiomatic system, including all elements and relations.
B. Explain how the axioms require that the system has three distinct points.
Note: The use of models may be helpful in developing this explanation.
C. Prove theorem 1 for three points, using only the provided axioms.
Note: You do not need to use all four axioms.
(A) Undefined terms are Point and Line.
(B) Each point has at least two separate lines.
(C) "P" does not lay on "m," hence the statement is contradictory.
A set of axioms from which one or more theorems may be logically deduced is known as an axiomatic system in mathematics and logic. A theory is a coherent, mostly self-contained body of knowledge that typically includes an axiomatic framework and all of the theorems that are deduced from it.
(A) Undefined terms are :
A location is a point. It is empty, meaning it has no width, length, or depth. A dot indicates a point.
A line is described as a collection of points that stretches in both directions indefinitely.
(B) Each point now has at least two separate lines.
A line 's' that is not incident on point 'P' must exist according to axiom 4 if we use point 'P' as our starting point.
Axiom 2 states that if a line exists, it must have the two points "R" and "S" on it.
(C) Since "P" does not lie on "m." P thus differs from 'e' and 's'
Points that stand out. They are different because they would be referred to as "m" if both lines "n" and I passed via "r" and "s."
However, "P" does not lay on "m," hence the statement is contradictory.
So it is proved
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90.97 ÷ 8.6 =
please help me!
I'm looking for a full positive integer for K as my answers.
The value of full positive integer k such that [tex]O(n^k)[/tex] is the most restrictive polynomial-time upper bound of f(n) are as follows : (A) 9 (B) no integer exists (C)5/3(not an integer) (D)no integer exists (E) [tex]3e^{99}[/tex]
Using the Lower and Upper Bound Theory, it is possible to identify the algorithm with the lowest level of complexity. Let's quickly review what Lower and Upper bounds are before we can understand the theory.
If there are two constants C and N such that U(n) = C*g(n) for n > N, then g(n) is the Upper Bound of A. Let U(n) be the running time of an algorithm A(say). An algorithm's upper bound is displayed using the asymptotic notation Big Oh(O).If there are two constants C and N such that L(n) >= C*g(n) for n > N, then g(n) is the Lower Bound of A. Let L(n) be the running time of an algorithm A(say). The asymptotic notation known as Big Omega displays an algorithm's lower bound.A)[tex]2^{lg(3n+4n+5)}+lg {\spaceh} n \inO(n^k)[/tex]
or, [tex]O(2^{lgn^9}+lgn)\inO(n^k)[/tex] since [tex]3n^9+4n+5=O(n^9)[/tex]
or, [tex]O(2^{lgn^9})\in O(n^k)[/tex] as [tex]2^m+lg m=O(2^m)[/tex]
Applying lg 2 on both sides we get:
[tex]lg_22^{lgn^9}=lg_2n^k[/tex]
solving we get:
k=9 × lg2 × lg n
At n=1/2
k=9
Hence the minimum integer for K is 9.
B) [tex]7lgn+13lg^5n\in O(n^k)[/tex]
Solving for k we get:
k=lgₙ(lg⁵n)
C) [tex]\sqrt[3]{7n^5+2n^3-4}\in O(n^k)[/tex]
Solving by exponent rule we get:
[tex]O(n^{5/3})\in O(n^k)[/tex]
k=5/3
D)[tex]13lg2^{3^n\inO(n^k)}[/tex]
or, [tex]k=lg_n(lg2^{3^n})[/tex]
E)[tex]7^{20!+1} \inO(n^k)[/tex]
As we don't have any term of n on the Left Hand Side, therefore no most restrictive polynomial-time upper bound exist for [tex]O(n^k)[/tex]
[tex]k=e^{99}[/tex]
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Solve F(x)=2x²+3x+5
Help please, very difficult.
Answer:
No Solution
Step-by-step explanation:
i need a equation for 4x + 12 = 64
thanks :)
Answer: x=13
Step-by-step explanation: i think
2 x 2 x 2 x 2 ( 5.2 - 3.2 ) divided by 4
Answer:
8
Step-by-step explanation:
you first do operation in the brackets and then multiply and then divide:
2*2*2*2*2 / 4 = 8
Pomoże ktoś z matematyki?
Przykład 5.
a) The plot cross the horizontal line [tex]y=2[/tex] when the time is [tex]t=5,5[/tex], so it took 5,5 s to cover the first 2 m.
b) If [tex]f(x)[/tex] denotes the distance from the starting position of the object, then its average speed over the entire 6-s period is
[tex]v_{\rm ave} = \dfrac{3\,\mathrm m - 0\,\mathrm m}{6\,\mathrm s - 0 \,\mathrm s} = \dfrac36 \dfrac{\rm m}{\rm s} = \boxed{0,5 \dfrac{\rm m}{\rm s}}[/tex]
c) In the last 3 seconds, the object covers a distance of
[tex]3\,\mathrm m - 1\,\mathrm m = \boxed{2\,\mathrm m}[/tex]
d) False. The average speed over the first 3-s period is
[tex]v_{\rm ave[0,3]} = \dfrac{1\,\mathrm m - 0\,\mathrm m}{3\,\mathrm s - 0\,\mathrm s} = \dfrac13 \dfrac{\rm m}{\rm s} \approx 0,33 \dfrac{\rm m}{\rm s}[/tex]
while over the second 3-s period, it is
[tex]v_{\rm ave[3,6]} = \dfrac{3\,\mathrm m - 1\,\mathrm m}{6\,\mathrm s - 3\,\mathrm s} = \dfrac23 \dfrac{\rm m}{\rm s} \approx 0,66\dfrac{\rm m}{\rm s} \neq 0,33\dfrac{\rm m}{\rm s}[/tex]
Przykład 2.
In total there are
8 + 24 + 28 + 16 + 4 = 80
graded assignments. Compute the percentages of students whose scores fall into the given categories:
• 0-8 : 8/80 = 1/10 = 10/100 = 10%
• 9-16 : 24/80 = 3/10 = 30/100 = 30%
• 17-24 : 28/80 = 7/20 = 35/100 = 35%
• 25-32 : 16/80 = 1/5 = 20/100 = 20%
• 33-40 : 4/80 = 1/20 = 5/100 = 5%
See the attached pie chart.
Zadanie 3.
From the plot, it appears that Mateusz
• took 6 min to reach the bus stop
• waited for 2 min
• took 5 min to return home
• took 1 min to grab his notebook
• took 5 min to return to the bus stop
• waited for 3 min
• and after the bus arrives, moves further away over the next 4 min
This means the total time Mateusz needed to (1) return home to get the notebook, (2) find the notebook, and (3) return to the bus stop is
5 min + 1 min + 5 min = 11 min
Zadanie 4.
True. Mateusz walks the distance between his house and the bus stop within the first 6 min, which is 2/5 of 1 km = 0,4 km = 400 m.
True. The bus arrives after 22 min, and its average speed is equal to Mateusz's average speed over the next 4 min. At 22 min, he is 0,4 km from home, and at 26 min, he is 4 km away from home, so the average speed is
[tex]v_{\rm ave} = \dfrac{4\,\mathrm{km} - 0,4\,\mathrm{km}}{26\,\mathrm{min} - 22\,\mathrm{min}} = \dfrac9{10} \dfrac{\rm km}{\rm min} = 0,9\dfrac{\rm km}{\rm min}[/tex]
Convert the speed to km/h.
[tex]\dfrac9{10} \dfrac{\rm km}{\rm min} \times \dfrac{60\,\rm min}{1\,\rm h} = 54 \dfrac{\rm km}{\rm h}[/tex]
how do i solve for 6+3+11/4=5
Answer:
6+3+11/4[tex]\neq[/tex]5
Step-by-step explanation:
Answer:
The answer to the question is 0
Write 5 x 10^-4 in standard notation
What is 31/50 as a percent
Answer:
62%
Step-by-step explanation:
31/50 can be multiplied by 2 to get 62/100. 62/100 is equal to 62%. to get percents, attempt to get the demoninator (bottom number in fraction) to be 100, then the top number is the percent (because its basically saying 62 out of 100 pieces, which is 62 percent)
7/39
in lowest terms.
Answer: 7/39
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator GCD of 7 and 39 is 1
Divide both the numerator and denominator by the GCD 7 ÷ 1 39 ÷ 1
Reduced fraction: 7 39 Therefore, 7/39 simplified to lowest terms is 7/39.
Write an equation in point-slope form of the line
(-7,2); m=2
Answer: y - 2 = 2(x + 7)
Step-by-step explanation:
Point-slope form is written as y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex]) where m is the slope and ( [tex]x_{1}[/tex], [tex]y_{1}[/tex]) are points on the line.
y - [tex]y_{1}[/tex] = m(x - [tex]x_{1}[/tex])
y - 2 = 2(x + 7)
Mr jacobs backyard mesures 150 ft. he wants to fence it to secure his garden, how many meters of fence would he need?
The number of meters of fence he would need is 45.72 meters
How to determine how many meters of fence would he need?The given parameters are
Length of backyard = 150 ft
As a general rule, we have the following conversion equation
1 foot = 0.3048 meters
So, we have
Length of backyard = 150 * 0.3048 meters
Evaluate the product
So, we have
Length of backyard = 45.72 meters
Hence, the number of meters of fence he would need is 45.72 meters
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please help!
maths geometry
Step-by-step explanation:
the diagonals in a square are intersecting each other at 90°.
that means that G1 + G2 = 90
and because of the symmetry of a kite, it also means that G1 = G2.
combined this tells us
G1 = G2 = 90/2 = 45°.
also due to its symmetry one of the rules of a kite is that its diagonals are also intersecting each other at 90°.
so,
E1 = E2 = 90°.
the sum of all angles in a triangle is always 180°.
so,
180 = F1 + G1 + (D2 + D3) = F1 + 45 + 110
F1 = 180 - 45 - 110 = 180 - 155 = 25°
again, due to the symmetry of the kite
F1 = F2 = 25°.
also
C2 + C3 = D2 + D3 = 110°
due to the properties of a square (e.g. the angle in every corner is 90°, the diagonals are splitting each corner angle in half) we know that
D1 = D2 = 45°.
and again, therefore
C1 = C2 = D1 = D2 = 45°
and so
(1)
due to the law of the angles of a line intersecting parallel lines are equal for every parallel line, we see that
the line BD intersects the lines AD and GEF equally at 45°. therefore, GEF || AD.
(2)
as we know that F1 = F2 = 25°,
F1 + F2 = 2×25 = 50°
(3)
the angles in the triangle GDE are
E1 = 90°
D2 = 45°
G1 = 45°
the angles of GE and DE with their baseline GD are equal, that means this is an isoceles triangle, meaning the legs have an identical length, and therefore
DE = GE.
(4)
as GDE is a right-angled triangle we can use Pythagoras :
GD² = GE² + DE² = 2×DE² = 2×GE²
GD = 3×sqrt(2)
GD² = 9×2 = 18
18 = 2×DE² = 2×GE²
DE² = GE² = 18/2 = 9
DE = GE = 3
The function f(x) = |x| is graphed over the interval [−6, 3].
Which translation of the graph has the domain [−3, 6]?
A. g(x) = |x| + 3
B. g(x) = |x + 3|
C. g(x) = |x| − 3
D. g(x) = |x − 3|
The translation of the graph that has the domain [−3, 6] is:
B. g(x) = |x + 3|.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
In this problem, the parent function is given by:
f(x) = |x|.
The domain changed by [−6, 3] to [-3,6], meaning that 3 units was added to each bound of the domain, hence x -> x + 3 and:
g(x) = |x + 3|.
Which means that option B is correct.
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Which is a correct way of writing the equation of the line that passes through the points shown in the
table?
XY
-2-2
02
26
The correct way of writing the equation of the line that passes through the points are y = -3x - 5.
What are equation ?Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
The slope-intercept form, point-slope form, and standard form are the three primary types of equations. These equations provide sufficient details about the line to make graphing them simple.
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Determine the number of 1/2 inch cubes that can pack the prism shown
The total number of Cubes that can be packed in the Rectangular Prism will be 84 Cubes
In the picture mentioned below, We have a Rectangular prism with the dimensions Length = [tex]3\frac{1}{2}[/tex] in, Breadth = 2 in, Height = [tex]1\frac{1}{2}[/tex] in
Also, It is given that cubes of Dimension [tex]\frac{1}{2}[/tex] inches are to be packed in the Rectangular Prism.
Firstly, We need to find the volume of Both the Prism & the Cube.
Since, The it is a Rectangular Prism, Volume of cuboid = ( l*b*h )
Volume of Prism, V1 = l*b*h => l =[tex]3\frac{1}{2}[/tex], b = 2, h = [tex]1\frac{1}{2}[/tex]
=> V1 = [tex]3\frac{1}{2} * 2 * 1\frac{1}{2}[/tex] => V1 = 10.5 [tex]in^{3}[/tex]
Volume of Cube, V2 = l * l * l => l = [tex]\frac{1}{2}[/tex]
=> V2 = [tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex] => V2 = 0.125 [tex]in^{3}[/tex]
To find out the number of cubes that can fit inside the prism we need to divide the volume of the prism by the volume of cube => V1/V2
=> N = [tex]\frac{V1}{V2}[/tex] => [tex]\frac{10.5}{0.125}[/tex]
=> N = 84 Cubes.
Hence, the Total number of cubes that can fit inside the Prism will be 84.
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Lines a & m are parallel. Using the diagram below, what is the degree measure of angle 2?
Enter the numerical answer only. Example, if the answer is 12 degrees, only enter 12.
Answer:
27
Step-by-step explanation:
just subtract 153 from 180
Given the points A (-4,-2) and B (4, 10), find the
coordinates of point P on directed line segment AB that is 3/4 is of the way from A to B.
Answer:
P = (2, 7)
Step-by-step explanation:
You want to find coordinates of P on segment AB such that P is 3/4 is of the way from A to B.
Equation for PFor some fraction q of the distance from A to B, the point P that lies at that fraction of the distance is given by ...
P = A +q(B -A) = (1 -q)A +qB
ApplicationFor q = 3/4, the location of P is ...
P = (1 -3/4)A + 3/4B = (A +3B)/4
Using the given point coordinates, we have ...
P = ((-4, -2) +3(4, 10))/4 = (-4 +12, -2 +30)/4 = (8, 28)/4
P = (2, 7)
sin 496.4 degrees
Please don’t give just the answer! I would like to fully understand how you got to your answer, thank you!
The value of Sin 496.4° is 0.6896.
Trigonometry functions:
Trigonometry is a type of mathematics that deals with the specific function of angles and their application.
There are six functions of an angle used in trigonometry sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec) and cosecant(cosec). All these functions are based on the measurement of the triangle.
Given,
Sin 496.4°
Here we need to find the value of it.
While using the sine table,
The value of 496.4° = 0.6896
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Out of 350 racers who started the marathon, 310 completed the race, 30 gave up, and 10 were disqualified. What percentage did not complete the marathon?
Answer:
The answer is %11.42 I think
Step-by-step explanation:
30+10=40
40/350= 0.1142
0.1142x100= %11.42
First divide the total of people who didn't complete the race by the total of racers which is 350 total racers.
Then u multiply ur answer by 100 to get ur percentage which is 11.42.
Question 8 of 10
What
transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = -1/(x+5)+7?
A. Shifted up 7 units
B. Shifted right 5 units
C. Vertically compressed by a factor of 2
D. Reflected over the x-axis
The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.
If the function f(x) reflected across the x-axis, then the newfunction g(x) = - f(x)
If the function f(x) reflected across the y-axis, then the newfunction g(x) = f(-x)
If the function f(x) translated horizontally to the rightby h units, then the new function g(x) = f(x - h)
If the function f(x) translated horizontally to the leftby h units, then the new function g(x) = f(x + h)
If the function f(x) translated vertically upby k units, then the new function g(x) = f(x) + k
If the function f(x) translated vertically downby k units, then the new function g(x) = f(x) – k
A vertical stretching is the stretching of the graph away from
the x-axis
A vertical compression is the squeezing of the graph towardthe x-axis.
If k > 1, the graph of y = k*f(x) is the graph of f(x) verticallystretched by multiplying each of its y-coordinates by k.
If 0 < k < 1 (a fraction), the graph is f(x) vertically compressedby multiplying each of its y-coordinates by k.
If k should be negative, the vertical stretch or compress isfollowed by a reflection across the x-axis.
So, we can write,
f(x) = x
g(x) = -1/(x+5)+7
-1 means the graph is vertically compressed by a factor of 1and reflected over the x-axis
x + 5 means the graph shifted to the left 5 units + 7 means the graph shifted up 7 unitsReflected over the x-axisTherefore,
The transformation was not done is Shifted right 5 units and vertically compressed by a factor of 2.
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how to construct a population data set for which N=6 u=5
A population with 6 elements and mean 5 is given by:
4, 4, 5, 5, 6, 6
What is the mean?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
Hence, for this problem, we need 6 observations which add to 30, hence one possible population is:
4, 4, 5, 5, 6, 6
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geometry NEED HELP ASAP THX
By consideration of congruence and collinearity, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.
What is the value of the variable behind a geometric system formed by two collinear line segments?
Two line segments are congruent when the line segments have the same length, then the following condition has to be fulfilled:
AB = BC (1)
Where AB and BC are the lengths of the line segments AB and BC.
If we know that AB = 4 · x + 1 and BC = 20 · x - 5, then we solve the equation for x is:
4 · x + 1 = 20 · x - 5
6 = 16 · x
16 · x = 6
x = 6 / 16
x = 3 / 8
Then, the value of x behind the geometric system formed by two collinear linear segments is equal to 3 / 8.
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Find two numbers that have a sum of -10 and a product of -56.
find last years salary if after a 2% pay raise this years salary is $40,290
Answer:
2/100*40290
=805.8
40290 - 805.8
=$39484. 2
Find the circumference.
Use 3.14 for T.
r = 4 cm
C = ? cm
C =
Answer:
25.12 cm
Step-by-step explanation:
The circumference of a circle can also be understood as the perimeter of the circle.
Circumference of circle= 2πr= πd
r refers to radius while d refers to diameter
Given that r= 4,
circumference of circle
= 2(π)(4)
= 8π
≈ 8(3.14)
= 25.12 cm
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Determine the cardinality of the given set.
Answer:
1.) 9
2.) 15
3.) 7
Step-by-step explanation:
1.) There are no repeat letters, so the cardinality is the number of letters, here 9
2.) There's half the numbers from 1 to 30 in the set, so 30/2 = 15
3.) There are 7 distinct days of the week, so the answer is 7
3x divided by -8 = -21 divided by 4. The answer is 14. I'm trying =g to figure out why it was not a negative 14
Answer:
See explanation
Step-by-step explanation:
3x/(-8)=-21/4
-3x/8=-21*8/4
-3x*8/8=-21*8/4 ==> multiply 8 on both sides to get rid of denominator
-3x=-21*2
-3x=-42
3x=42 ==> Multiply by -1 on both sides to get positive values on both sides
x=14
Ty was making a map of his neighborhood and decided to use the scale of 1 inch : 2 miles. He measured that the distance from his garage to the entrance of the skatepark was 3,520 feet. How far should he make this distance on his map? (note 1 mile = 5,280 feet). Write your answer as a fraction.
The distance on the map is 3/4 inch
Given data
scale of the map = 1 inch : 2 miles
measurement from garage to the entrance of the skatepark = 3,520 feet
1 mile = 5,280 feet
How to solve for the distance on his mapThe required measurement to convert to map measurement = 3520 feet
we solve for number of miles in 3520 feet knowing that 1 mile = 5,280 feet. we solve this by:
5280 / 3520= 3 / 2 miles
so if scale of the map is 1 inch : 2 miles
x : 3 / 2 miles
we cross multiply to find x as
x = 3/2 / 2
x = 3/4
The distance on the map is 3/4 inch
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