The 2x2 linear system can be solved by the method of substitution .
In the question ,
it is given that ,
a 2x2 linear system is the system in which there are 2 equations with two unknown ,
Step (1) : we take the value of 1 variable from 1 equation ,
Step(2) : we substitute the value of that variable in equation(2) and solve to get the solutions .
let us understand the method of substitution with the help of example .
Let the 2x2 linear system be 2x + 3y = 14 and x + y = 12
From , x+y=12 , we get
x = 12 - y ,
Substituting the value of x in 2x + 3y = 14 ,
we get ,
2(12 - y) + 3y = 14
So , y = -10
putting in x = 12 - y ,
we get ,
x = 12-(-10) = 22 .
Therefore , the method to solve the 2x2 linear system is explained .
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You are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 78 7 8 inch and an inside diameter of 34 3 4 inch. How much refrigerant can 12 feet of the tubing hold?.
557,568 inch³ of refrigerant can be held by the tubing.
Here we have to find how much a refrigerant can hold.
Data given:
outer diameter (d) = 78inch
outer radius(r) = 39 inch
inner diameter (d') = 34 inch
inner radius (r') = 17inch
Height (h) = 12 feet
= 12 × 12
= 144 inch
the formula to find the volume of the cylinder:
volume= пr²h
So here we get
Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder
= πr²h - πr'²h
= πh(r² - r'²)
= π ×144 ( 39² - 17²)
= π × 144 ×56 × 22
= 22/7 × 144 × 56 × 22
= 557,568 inch³
Therefore the refrigerant can hold 557,568 inch³.
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Jake has a 10 inch stick which he cuts into 3 pieces. The first piece is twice as long as the second. If the three pieces can form a triangle, which of the following could NOT be the length if the third piece?Jake has a 10 inch stick which he cuts into 3 pieces. The first piece is twice as long as the second. If the three pieces can form a triangle, which of the following could NOT be the length if the third piece?
The measures that the third piece cannot assume are given as follows:
z < x - y if x is the greater measure.z > x + y if z is the greater measure.When a set of measurements can represent a triangle?A set of measurements can represent a triangle if the sum of the two smaller measurements is greater than the greater measures.
The sum of the measurements in this problem is given as follows:
x + y + z = 10.
The first piece is twice as long as the second,hence:
x = 2y.
Thus:
3y + z = 10.
The condition needed for a triangle to be formed is given as follows:
y + z > x if x is the greater measure.x + y > z if z is the greater measure.Missing InformationThe options are missing, hence the answer was given in general terms, with the concept used presented.
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Complete the inequality. 13/18___ 11/14 < > =
Answer:
Your answer is <, Hope it helps.
Please help meeeee……..
I honestly do not know???
Find the area of the surface. The part of the plane x + 2y + 3z = 1 that lies inside the cylinder x2 + y2 = 5.
The surface area of the plane is π√14 sq. units.
It is given in the question that the equation of the plane = x+2y+3z=1 and that of the cylinder
= x² + y² = 5 [1]
Let J be the projection on the plane x+2y+3z=1
We know that the surface area of an equation is
∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
We know that the plane is inside the cylinder.
By using the coordinates of the cylinder we can get
x = r cosθ and y = rsinθ
Squaring both sides gives us
x² = r²cos²θ
y² = r²sin²θ
Therefore we get,
x² + y² = r²cos²θ + r²sin²θ
= r²(cos²θ + sin²θ)
We know that cos²θ + sin²θ = 1. Hence,
= r² [2]
From equations [1] and equation [2] we get
r² = 5
or, r = √5
Hence,
J = {(r,θ)/ 0 ≤ r ≤ √5, 0 ≤ θ ≤ 2π}
Therefore,
x +2y + 3z =1
or, z = 1/3(1 - x - 2y)
Partially differentiating z with respect to x and with respect to y gives us
∂z/∂x = -1/3
and,
∂z/∂y = -2/3
Therefore,
We already know that Surface Area = ∫∫j √{1+(∂z/∂x)² + (∂z/∂y)²} dA
= ∫∫j √{1+ (-⅓) ² + (-⅔) ²} dA
= ∫∫j √(9+1+4)/√9 dA
= √14 /3∫∫j dA
=√14/2 [2π - 0]
= π√14 sq units
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How long does it take to travel 150 km?
It takes 3.33 hours of time to travel a distance of 150 km by bus
The problem is related to time, which basically depends on the speed at which the bus is moving, as we knew the formula for time is distance/speed, here we are provided with the distance which is 150km also equal to 150000m. For normal conditions where the speed of the bus is h 45km per hour, therefore
=>Distance = Speed × Time
=>150km = 45 Km/hr × Time
Time = 150/45 hr = 3.33 hr ,Which is almost 3.33 hours
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How do you solve 3 step equations with fractions?
To solve a linear equation with fractions, more than two procedures are required. To undo each action in reverse order, use inverse operations.
Any number of equal parts is represented by a fraction, which also represents a portion of a whole.
If a mathematical equation contains fractions, divide both sides by the LCD to eliminate the fractions.
Solving a Multi-Step Equation in Steps
Step 1, eliminate the fractional equation.
Step 2: Remove the parentheses from either side using the Distributive Property.
Combining similar phrases on each side in step three.
Step 4: Reverse any additions or subtractions.
Step 5: Reverse division or multiplication.
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why is it important to evaluate non-critical paths that possess large variances or path times that are close to critical in duration?
All the given options are correct.
what is random?
The lack of pattern or predictability in events, whether it be apparent or real, is referred to as randomness. Sometimes there is no order or discernible pattern or combination in a random series of events, symbols, or processes.
a)Random uncertainty present in the network may exhibit cumulative interactions reflecting the inherent randomness of independent activities within the network.
b)An activity having only a relative small amount of slack could potentially exceed the critical time calculated from the expected critical path.
c)As statistical variances rise in relation to expected duration, the range of uncertainty in near-critical paths will exhibit wider dispersion.
Hence all the given options are correct.
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Complete Question
Why is it important to evaluate non-critical paths that possess large variances or path times that are close to critical in duration?
A) Random uncertainty present in the network may exhibit cumulative interactions reflecting the inherent randomness of independent activities within the network.
B) An activity having only a relative small amount of slack could potentially exceed the critical time calculated from the expected critical path.
C) As statistical variances rise in relation to expected duration, the range of uncertainty in near critical paths will exhibit wider dispersion.
D) All of the above.
consider two hexadecimal numbers: x434f4d50 and x55544552. what values do they represent for each of the five data types shown?
The values they represent for each of the five data types shown are below.
What is hexadecimal numbers?
The base-16 numbering scheme is known as hexadecimal. Consequently, this system uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 15. That implies that the two-digit decimal numbers 10, 11, 12, 13, 14, and 15 cannot exist in this numbering system unless they are represented by a single numeral.
For x434F4D50
Unsigned binary - 0000 0100 0011 0100 1111 0100 1101 0101 0000
1's complement - 1111 1011 1100 1011 0000 1011 0010 1010 1111
2's complement 1111 1011 1100 1011 0000 1011 0010 1011 1111
IEEE 754 Floating point - 207.302001953125
ASCII string -COMP
For x55544552
Unsigned integer: 0000 0101 0101 0101 0100 0100 0101 0101 0010
1's complement 1111 1010 1010 1010 1011 1011 1010 1010 1101
2's complement1111 1010 1010 1010 1011 1011 1010 1010 1110
IEEE floating point 1.4587137097728E13
ASCII string: UTER
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I need help please, it’s asap
The interquartile range of the given data set is 2.16.
The given data is 2.35, 1.56, 1.77, 2.45, 6.02, 4.38, 2.77, 5.23, 2.22 and 3.26.
What is the interquartile range?The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.
Formula to find the interquartile range is Interquartile range = Upper Quartile - Lower Quartile =Q2=Q3-Q1
The order of the given data is 1.56, 1.77, 2.22, 2.35, 2.45, 2.77, 3.26, 4.38, 5.23, 6.02.
Here,
Q1= 1/4 (n+1) = 11/4= 2.75
= 2.22
Q3 = 3/4 (n+1) = 8.25
= 4.38
Q2 =4.38-2.22
= 2.16
Therefore, the interquartile range of the given data set is 2.16.
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What happens to the area of a figure when a scale factor is applied?
The area of figure will change quadratically in proportion to length squared when a scale factor is applied
A scale factor is simply a number that multiplies a shape's dimensions. This can enlarge a shape. The scale factor for larger shapes will be greater than one. So, if the scale factor is three, the new shape's dimensions will be three times larger than the original.
A scale factor can also reduce the size of a shape. Smaller shapes have a scale factor that is less than one.
When you dilate a figure, it becomes larger or smaller
With a certain factor, the length of its sides either increases or decreases.
As a result, a change in length will affect the total area of the figure with that scale factor.
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According to the pattern shown below, what is the number in the blank?
1, 1 ,2,3,7,23 ,164,…
The number pattern is 1, 1 ,2,3,7,23 ,164,3,776
What is the definition of a number pattern?
Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.
1 + 1 = 2 + 0 = 2
3 x 2 = 6 + 1 = 7
7 x 3 = 21 + 2 = 23
23 x 7 = 161 + 3 = 164
164 x 23 = 3772 + 4 = 3776
Therefore, The number pattern is 1, 1 ,2,3,7,23 ,164,3,776
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how many ways are there to deal a hand of 4 cards if i don't care about the order of cards in my hand?
There are 270725 different ways to select 4 from 52 cards if I don't care about the order of cards in my hand.
Permutation and combination: The process of ordering objects or numbers is known as permutation. Combinations are a method of choosing items or numbers from a collection or group of items so that the order of the items is irrelevant.
Combinations are used to group objects or to determine how many subgroups can be formed from the given collection of objects. Additionally, we use permutations to determine the number of potential combinations of unrelated objects.
For example, if we want to select 2 players from 6. This will be:
= 6! / 2! (6 - 2)!
= 15 ways
In the given question use the combination. We can write as:
[tex]52C_{4}[/tex] = 52!/4! (52-4)!
This expression could be written in the form
[tex]52C_{4}[/tex] = 52!/4! (52-4)!
[tex]52C_{4}[/tex] = 52!/(4! (48)!)
[tex]52C_{4}[/tex] = 52 x 51 x 50 x 49 x 48!/(4 x 3 x 2 x 48!)
As, 48! cancel out. We get,
[tex]52C_{4}[/tex] = 52 x 51 x 50 x 49/24
= 6497400/24 = 270725
Hence, there are 270725 ways.
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the letters of the word better appear on a child's blocks, one letter per block. the child arbitrarily selects two of the blocks. find the probability that the child selects an e followed by b. (enter your probability as a fraction.)
the probability as a fraction will be 3/12.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
the letters of the word better appear on a child's blocks, one letter per block. the child arbitrarily selects two of the blocks.
PE followed R When 2blocks selected) - 5 = Bois obtaining R from the remaining 3 people selected 12 men & 10
Hence the probability as a fraction will be 3/12.
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A middle school took all of its 6th-grade students on a field trip to see a ballet at a theater that has 1500 seats. The students filled 1320 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
The percentage of the seats in the theater that were filled by the 6th graders on the trip is 88%.
What percentage of the seats in the theater were filled by the 6th graders on the trip?Given that the middle school took all of its 6th-grade students on a field trip to see a ballet at a theater that has 1500 seats and the students filled 1320 of the seats in the theater.
The percentage of the seats in the theater were filled by the 6th graders on the trip will be:
= Number of 6th graders / Total students × 100
= 1320 / 1500 × 100
= 88%
The percentage is 88%.
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Latanya has $1.90 worth of nickels and dimes. She has a total of 24 nickels and dimes altogether. Determine the number of nickels and the number of dimes that Latanya has.
Answer:
10 nickels and 14 dimes
Step-by-step explanation:
Show me how to do Literal Equations
Solve for X
360=2x+y
Answer:
[tex]x = 180 - \frac{y}{2}[/tex]
Step-by-step explanation:
Our goal here is to isolate [tex]x[/tex] on one side of the equals sign
[tex]360 = 2x + y[/tex]
Here we have 2 terms on the right side of the equals sign, [tex]2x[/tex] and [tex]y[/tex]
in order isolate the [tex]x[/tex] term we must subtract [tex]y[/tex]
However, if we subtract [tex]y[/tex] from one side of the equation we must also do the same to the other side to a maintain balanced equation.
[tex]360 = 2x + y[/tex]
[tex]-y[/tex] [tex]-y[/tex]
[tex]360 - y = 2x[/tex]
Now to remove "2" from [tex]2x[/tex] we must do the opposite of multiplication, which is division.
[tex]\frac{360}{2} - \frac{y}{2} = \frac{2x}{2}[/tex]
simplify.
[tex]180 - \frac{y}{2} = x[/tex]
If np is greater than mp, which must be true?segment op is longer than segment mq. Segment mn has the same length as segment mp. The measure of angle q equals the measure of angle o. Angle o is larger than angle q.
The side opposite the larger angle is larger and you know that MN>NP, so the angle O's measure is more than the angle Q's measure.
Describe angle.
Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned. Angles are also produced when two planes intersect. These are what are known as dihedral angles.
Here,
Greater is the side that is on the other side of the greater angle.
MN>NP.
Consequently, the measure of angle O is greater than angle Q's measure.
Option D is correct since MN>NP is true and the side that opposes the bigger angle is larger. The measure of angle O is therefore greater than the measure of angle Q.
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Lance has saved $45. He earns $30 dollars every week walking dogs, which he
also saves.
Which function can be used to find t, the amount of money Lance will have
saved at the end of n weeks of walking dogs?
Answer: 30n+45=t
Step-by-step explanation:
If a voltage of 0.5 V (volts) is driving a current of 0.03 A (amps) through a resistor, what is the resistance to the resistor, measured in ohms? Round to the nearest hundredths.
Answer:
To find the resistance of a resistor, you can use the formula R = V / I, where R is the resistance in ohms, V is the voltage in volts, and I is the current in amperes. Using the values provided, we can calculate the resistance as follows:
R = 0.5 V / 0.03 A = 16.67 ohms
Rounded to the nearest hundredths, the resistance is 16.67 ohms.
what is slope of y=4x-5 and what do you do to find it?
Answer:
4
Step-by-step explanation:
Slope form is:
y=mx+b
4 represents m
m is the slope, or change in y over change in x
Answer:
Using the slope-intercept form, the slope is −4 .
Step-by-step explanation:
The slope-intercept form is y=mx+by=mx+b, where mm is the slope and bb is the y-intercept.y=mx+by=mx+b
Using the slope-intercept form, the slope is −4-4.m=−4
How do i solve for DG?
Answer:
25.9
Step-by-step explanation:
Tangents drawn from a common external point are equal.
[tex]10x-31=2x+17 \\ \\ 8x-31=17 \\ \\ 8x=48 \\ \\ x=6 \\ \\ \implies GE=29 \\ \\ DG=\sqrt{29^2-13^2} \approx 25.9[/tex]
In triangle ABC, m∠B = (12x − 26)° and the measure of the exterior angle to ∠B is (7x − 22)°. Find m∠B. 34° 12° 118° 62°
The angle B for the triangle ABC has a measure of 118° so the correct option is 118°.
How to solve for the angle BThe angle B and its exterior angle lie on a straight line, thus their sum is equal to 180°
From the question, we are given that;
m∠B = (12x − 26)° and the exterior angle = (7x − 22)°
so;
12x - 26 + 7x - 22 = 180° {collect like terms}
19x - 48 = 180°
19x = 180° + 48° {add 48° to both sides}
19x = 228°
x = 228°/19 {divide through by 19}
x = 12
Therefore, by putting the value 12 for x in m∠B = (12x − 26) we get the angle B as;
B = 12(12) - 26
B = 144 - 26
B = 118°
In conclusion, the triangle ABC, with m∠B = (12x − 26)° and the measure of the exterior angle to ∠B is (7x − 22) have the angle B equal to 118°.
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Solve this equation: 33 + 7s = -3 ( 2s + 9 )
Answer:
Exact form:
[tex]s = - \frac{60}{13} [/tex]
Decimal form:
[tex]s = - 4.615384[/tex]
Mixed Number Form:
[tex]s = - 4 \frac{8}{13} [/tex]
Question 1 Please Help Me!!
Answer:
Step-by-step explanation:
the answer is b the arrow BD make angels equal in both sides
How do I work out this question please help
factorise 3x + 12
Answer: 3(x+4)
Step-by-step explanation:
Let's start with what we know. To factor problems, we just find a common divisor. Here, the common divisor is 3 so:
3(x+4)
Write a fact family for each set of numbers.
1. 2, 5, 10
2. 5, 8, 40
3. 4, 9, 36
4. 6,9, 54
Answer: in every case, the first two number multiplied equal the third number, I don't quit understand if that's the answer you were looking for,
but that's the first thing that occurred to me
I need help please! I’m struggling
Answer:
24
Step-by-step explanation:
Clara builds 3 parts of the fence per hour--
if she works for 8 hours-- we know she built 3 fences each hour-- you would multiply,
8(hours) x 3 (fences) = 24
we know this is right because 3 parts are built for every hour
(3+3+3+3+3+3+3+3 = 24)
she worked for 8 hours and built 3 parts of the fence every hour
in total, she built 24 parts of the fence.
what is 30 times 36 i really dont understand it
Answer:
1080
Step-by-step explanation:
what is the best approximation for the area of this circle? use 3.14 to approximate pi.
The best approximation for the area of the circle is 201.0in³
What is an area?The size of a region on a planar or curved surface is expressed mathematically as area. The term "surface area" refers to the area of an open surface or the perimeter of a three-dimensional object, whereas "plane area" refers to the area of a shape or planar lamina. Area can be thought of as the amount of a certain thickness of material required to construct a model of the shape. For the areas of basic forms like circles, triangles, and rectangles, there are a number of well-known formulas. Any polygon can be divided into triangles to get its area using these formulas. Calculus is commonly needed to calculate the area of forms having curved boundaries. Calculus' historical growth was in large part driven by the issue of figuring out the area of plane figures.
It is possible to calculate a shape's area.
As we already know that,
The area of a circle=πr²
Here, r=8in
π=3.14
Then,
A=(3.14)(8²)
A=201.0in²
Therefore, Area=201.0in²
Hence, the best approximation for the area of the circle is 201.0in³
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The complete question is:
"What is the best approximation for the area of this circle? Use 3.14 to approximate pi. 25.1 in² 50.2 in² 201.0 in² 803.8 in² Circle with radius labeled 8 in."