Anna , Bob , Chris weigh 108 pounds , 118 pounds , 92 pounds respectively .
Solve a linear equation in three variables by completing the following steps: Take any two equations and solve them for one variable Again, take two more pairs of equations and solve for the same variables. We have two systems of equations with two unknown variables. solve two equations Again, substitute the calculated values of the variables into one of the original equations and solve for the unknown variables.Let the Anna weigh = x pounds
Let the Bob weigh = y pounds
Let the Chris weigh = z pounds
According to the question Anna and Bob together weigh 226 pounds which can be written as [tex]x+y=226[/tex] ..(1)
According to the question Bob and Christ together weigh 210 pounds. which can be written as [tex]y+z=210[/tex] ...(2)
According to the question Anna and Chris together weigh 200 pounds. which can be written as [tex]x+z=200[/tex] ..(3)
From equation (1) [tex]y=226-x[/tex] putting this value in equation (2) , we get
[tex]226-x+z=210\\16=x-z\\16+z=x[/tex] ..(4)
Putting above value in equation (3) , we get
[tex]16+z+z=200\\2z=184\\z=92[/tex]
Putting z = 92 in equation (4) , we get
[tex]x=16+92\\x=108[/tex]
Putting x = 108 in equation (1) , we get
[tex]y=226-108\\y=118[/tex]
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I need this answered please
What is the image of the point (3,2) after a rotation of 90 counterclockwise about the origin?
Answer:- 3,2
Step-by-step explanation:
its hard to explain without a whiteboard feature
A circular pillar candle is 2.8 inches wide and 6 inches tall. What are the lateral area and surface area of the candle? Round to the nearest tenth if necessary.
Lateral area and surface area of candle is 52.8 inches² and 65.1 inches².
We are given the height and width of pillar candle. So, firstly writing the formula of lateral area and surface area of cylinder followed by calculation.
Lateral area of cylinder = 2πrh, where r stands for radius and h represents height.
Surface area of cylinder = 2πrh + 2πr²
Radius = diameter÷2
Radius = 2.8÷2
Radius = 1.4 inches
Keep the values in formula for calculation -
Lateral area of cylinder = 2×3.14×1.4×6
Lateral area of cylinder = 52.78 inches²
Surface area of cylinder = 2×3.14×1.4×6 + 2×3.14×1.4²
Surface area of cylinder = 65.09 inches²
Rounding off to nearest tenth-
Lateral area of cylinder = 52.8 inches²
Surface area of cylinder = 65.1 inches²
Hence, the lateral area and surface area of cylinder is 52.8 inches² and 65.1 inches².
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How much volume (in cm3 ) is gained by a person who gains 11.0 lblb of pure fat?
The person who have gained 11 lb. of pure fat will gain 5,500 cm³ of volume.
It is given in the question that the person gains 11 lb. of pure fat.
We have to find the volume (in cm3 ) gained by the person.
We know that,
The density of fat is about 0.9 grams/ml
Converting this in pounds, we get :-
0.9 grams/ml * 1 lb. / 454 grams * 1 ml / 1 cm³= 0.002 lb./cm³
We know the formula of density:-
Density = mass / volume
Hence,
Volume = mass / density
Volume = 11 / 0.002
Volume = 5,500 cm³.
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Determine which line passing through the given points has a steeper slope.
Line 1:(0,-4) and (2,2)
Line 2:(0,-4) and (4,5)
The line which have a steeper slope is Line 1.
It is given in the question that the points on the line are given by:-
Line 1: (0,-4) and (2,2)
Line 2:(0,-4) and (4,5)
We have to find which line has a steeper slope.
First we will find the slope of each line.
We know that slope of a line with points (a,b) and (c,d) is given by:-
(d-b)/(c-a)
Slope of Line 1:
(2-(-4))/(2-0) = 6/2 = 3
Slope of Line 2:
(5-(-4))/(4-0) = 9/4 = 9/4 = 2.25
We know that greater the slope of the line means greater the steep of the line.
As,
3 > 2.25
Hence, Line 1 is steeper than Line 2.
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Nina added 15 more songs to her MP3 player, resulting in a total of more than 120 songs. How many songs were originally on the player?
Nina originally had more than 105 songs on her MP3 player
Information about the problem:
Initial songs = xsongs added = 15Total songs = 120To solve this problem, we have to state the equation using the information of the problem:
Initial song + songs added > Total songs
x + 15 > 120
x > 120 - 15
x > 105 song
What are algebraic operations?We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.
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у < 2x + 3
2x + 5y ≥ 10
Can you please help me!
Step-by-step explanation:
Do you understand if you don't understand the answer notify me
Evaluate the expression 21 divided by 7(6 divided by 3) cube +1
Answer:
48 I think
Step-by-step explanation:
(6 divided by 3)= 2
2 cubed= 16
21 divided by 7= 3
3 times 16= 48
Answer:
Step-by-step explanation:
21 / 7(6/3)^3 + 1
= 21/7 * 2^3 + 1
= 3*8 + 1
= 25.
Explain why the sum of the probabilities of two mutually exclusive events is not always 1 .
The probabilities of mutually exclusive events are always smaller than 1.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.The probability of events that are mutually exclusive cannot ever be added up to greater than one.
Unless the same set of occurrences is also exhaustive, in which case the total of their probabilities is exactly 1, the probabilities of mutually exclusive events are always smaller than 1.
The likelihood that none of these occurrences, which are mutually exclusive, will occur is (1 - the sum of their probabilities).
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The art teacher gave each student half a sheet of paper and told the students to color one fourth of their pieces of paper. What part of the original sheet did the students color?
Position and label each triangle on the coordinate plane.
isosceles ΔW X Y with height h and base W Y with length 2 a .
The position and label triangle on the coordinate plane is shown in figure.
And, The coordinates of ΔW X Y are W (-a, 0), Y (a, 0) and X (0, h).
Here,
Given that;
Isosceles ΔW X Y with height h and base WY with length 2a.
We have to draw position and label triangle on the coordinate plane.
What is Isosceles triangle?
A triangle that has at least two sides of equal length is called Isosceles triangle.
Now,
The position and label triangle on the coordinate plane is shown in figure
with isosceles triangle ΔW X Y with h and base WY with length 2a.
And, The coordinates of ΔW X Y are W (-a, 0), Y (a, 0) and X (0, h).
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A central angle of a polygon is formed by line segments drawn from the center to two __ vertices.
The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon.
The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon. If you were to draw a line from any two adjacent vertices to the center, they would make the central angle. Because the polygon is regular, all central angles are equal. It does not matter which side you choose.
All central angles would add up to 360° (a full circle), so the measure of the central angle is 360 divided by the number of sides. Or, as a formula:
[tex]central \ angle = \frac{360}{n}[/tex] degrees
where n is the number of sides
The measure of the central angle thus depends only on the number of sides. The angle depends only on the number of sides, not the size of the polygon. If you change the number of sides, you will see that as the number of sides gets larger, the cenral angle gets smaller.
Therefore, The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon.
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The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon.
The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon. If you were to draw a line from any two adjacent vertices to the center, they would make the central angle. Because the polygon is regular, all central angles are equal. It does not matter which side you choose.
All central angles would add up to 360° (a full circle), so the measure of the central angle is 360 divided by the number of sides. Or, as a formula:
midpoint = [tex]\frac{360}{9}[/tex]degrees
where n is the number of sides
The measure of the central angle thus depends only on the number of sides. The angle depends only on the number of sides, not the size of the polygon. If you change the number of sides, you will see that as the number of sides gets larger, the cenral angle gets smaller.
Therefore, The central angle is the angle made at the center of the polygon by any two adjacent vertices of the polygon.
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Izzie is trying to solve this inequality. After she solves it, she shows it to you, and she asks you if she did it correctly. This is the work she completed:
3(t+1)−4t≥−5
Step 1: 3t +3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−8
Step 4: t≥8
The solution when Izzie is trying to solve this inequality 3(t+1)−4t≥−5 is incorrect.
How to illustrate the information?From the information, Izzie is trying to solve this inequality. After she solves it, she shows it to you, and she asks you if she did it correctly.
3(t+1)−4t≥−5
3t + 3 - 4t ≥ -5
Collect like terms
3t - 4t ≥ −5 - 3
-t ≥ −8
Divide by -1
t <= 8
Therefore, the solution of Is lzzie is incorrect.
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Izzie is trying to solve this inequality. After she solves it, she shows it to you, and she asks you if she did it correctly. This is the work she completed:
3(t+1)−4t≥−5
Step 1: 3t +3−4t≥−5
Step 2: −t+3≥−5
Step 3: −t≥−8
Step 4: t≥8
Is Izzie correct?
Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x)=17 x+3 for x=4
f (4) = 71 is the output for the given input .
How can you tell whether a function is linear or not?
Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.f(x)= 17 x+3
Put x = 4 ⇒ 17 * 4 + 3
⇒ 68 + 3
⇒ 71
Therefore f (4) = 71
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Evaluate each infinite geometric series. 3+1+1/3 +1/9+ . . . .
A baseball diamond is a square with 90 -ft sides. What is the length from 3rd base to 1st base? Round to the nearest tenth.
F 155.9 ft
G 141.6 ft
H 127.3 ft
J 118.2 ft
The length from 3rd base to 1st base is 127.3 ft
The correct answer is an option (H)
In this question,
A baseball diamond is a square with 90 -ft sides.
A baseball "diamond" is a square, each side of length 90 ft, with home plate and the three bases on the four corners.
Let s be the side length of the square.
The length from the 3rd base to 1st base is the diagonal of the square.
Using Pythagoras theorem, we formulate
diagonal = √(s² + s²)
diagonal = √(2s²)
diagonal = s√2
diagonal = (90)√2
diagonal = 127.28 ft
Therefore, the length from 3rd base to 1st base is 127.3 ft
The correct answer is an option (H)
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Are parallel lines (parallelism) and collinear points (collinearity) preserved under all transformations? Explain.
Yes, all transformations such as translations, reflections, dilations, and rotations preserve parallel lines (parallelism) as well as collinear points (collinearity).
Parallel lines:
Parallel lines are coplanar straight lines that don't intersect at any point in geometry. Parallel planes are planes that never meet in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance.Collinear points:
The collinearity of a series of points in geometry is the property of their being on a single line.A set of points with this property is known as a collinear set. In a broader sense, the term has been applied to aligned objects, that is, things that are "in a line" or "in a row."So,
Translation, reflection, dilation, and rotation are all examples of transformation. In all of the preceding cases, parallel lines or collinear points will remain parallel or collinear.Therefore, yes, all transformations such as translations, reflections, dilations, and rotations preserve parallel lines (parallelism) as well as collinear points (collinearity).
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Lacey has two pieces of ribbon, one 30 inches long and the other 48 inches long. To decorate an album, she wants to cut them up to produce many pieces of ribbon that are all of the same length, with no ribbon left over. What is the greatest length, in inches, that she can make them?
The greatest length, in inches, that she can make from the two pieces of ribbon is 6 inches
Greatest common factorRibbon A = 30 inches longRibbon B = 48 inches longFind the factors of 30 and 48
30 = 1, 2, 3, 5, 6, 10, 15 and 30.48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.The greatest common factor of 30 and 48 is 6
Therefore,
Ribbon A can be cut into = 30 / 6
= 5 pieces
Ribbon B = 48/6
= 8 pieces
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Determine the slope of the line that contains the given points.
R(2,-6), S(-6,5)
The slope of the line that contains the points R(2,-6), S(-6,5) is [tex]\frac{-11}{8}[/tex] .
Slope of a line containing two points (a,b) and (c,d) is denoted by
slope =[tex]\frac{d-b}{c-a}[/tex].
In the given question
The points given are R(2,-6) and S(-6,5)
a=2, b= -6 and c= -6 and d=5
Substituting the values in formula of slope we get
[tex]Slope=\frac{d-b}{c-a}[/tex]
Slope=[tex]\frac{5-(-6)}{-6-2}[/tex]
[tex]=\frac{5+6}{-8} \\ \\ =\frac{-11}{8}[/tex]
Therefore , the slope of the line that contains the points R(2,-6), S(-6,5) is [tex]\frac{-11}{8}[/tex].
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3.06 + 7.162 + 6.58 = ___
16.28
16.748
16.802
17.342
Answer:
16.802
Step-by-step explanation:
I just used a calculator
State whether each sentence is true or false. If false, replace the underlined term to make a true sentence.
A right solid has an axis that is also an altitude.
The given statement "A right solid has an axis that is also an altitude" is False. The Correct statement is "A right Cone has an axis that is also an altitude".
The altitude of the cone is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is also the height of the cone. So we can say that A right Cone has an axis that is also an altitude.
A right solid have an axis that is also an altitude is the incorrect statement. So, the correct statement is that a right cone has an axis that is also an altitude.
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what does (0,0) represent
Answer:
0,0 represents the origin of the graph
How is finding a missing term of a geometric sequence using the geometric mean similar to finding a missing term of an arithmetic sequence using the arithmetic mean? How is it different?
The two are similar, because: in both AP and GP, we can find the mean value using first and last values.
The two are different because: in both AP and GP, different methods are used to find the mean value.
What is an arithmetic and a geometric progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.Now,
AP and GP are similar because the middle value, or mean value in both AP and GP, can be determined by using the initial and last values. They differ because there are various methods for calculating that number, and each phrase is distinguished by either a common ratio or a common difference.To learn more about arithmetic and geometric progressions, refer to the link: https://brainly.com/question/13899779
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Each graph shows a relation. The first and second numbers of each ordered pair in the
relation are members of the set of real numbers. In each case, find the domain and the
range of the relation and determine whether the relation is a function. a
x
The required domain of the function is x = -2, and the required range of is -2 ≤ y <1. And also it is not function.
Given that,
The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case. The domain and the range of the relation and determine whether the relation is a function is to be determined.
The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
Here, From the graph, the value is only defined at x = -2, Thus, its domain is x = -2 And also the at x = -2 the vertical line is from -2 to 0.99 Thus, its range is -2 ≤ y <1.
Since the curve has a number of pre-images more than one at a single value of x thus it is not a function.
Thus, the required domain of the function is x = -2, and the required range of is -2 ≤ y <1. And also it is not function.
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Please Help
Simplify (4⁴)−1.
Answer:
255
Step-by-step explanation:
[tex](4^4)-1 \\ \\ =256-1 \\ \\ =255[/tex]
Find the missing angle
URGENTTT PLEASE HELP !! :3
HELP PLEASE!!!!!
Chantel has a goal to complete a triathlon. The race consists of a 2.4-mile swim, a 112-mile bike ride, and a 26.2-mile run. In training, Chantel can swim at an average pace of 1.2mph. She rides her bike at an average of 18.8mph and runs at 6.2mph. Estimate how long it will take her to complete the triathlon.
Chantel will take approximately 12.19 hours to complete the triathlon with the given speed of his.
Total distance covered for the race is:
For swimming = 2.4 miles
Speed of Chantel in swimming = 1.2 miles per hour.
So, time taken for completing the swimming part = 2.4 / 1.2 = 2 hours.
For bike ride = 112 miles
Speed of Chantel in bike riding = 18.8 miles per hour
So, time taken for completing the bike riding part = 112 / 18.8 = 5.96 hours.
For running = 26.2 miles
Speed of Chantel in running = 6.2 miles per hour.
So, time taken for completing the running part = 26.2 / 6.2 = 4.23 hours.
Total time = 2 + 5.96 + 4.23 = 12.19 hours.
Therefore, Chantel will take approximately 12.19 hours to complete the triathlon with the given speed of his.
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A cake has 77 slices. Harry ate 48 slices; Jack ate 17 slices; Dave ate 3 & Mary ate 6 slices. What fraction of the cake is remaining?
Answer:3/77
because 77/77 minus 48/77 is 29/77-17/77 is 12/77 minus-9(because I just added 3 and 6 so don't hey confused I just added them up) is 3/77 and thats your answer (3/77)
Step-by-step explanation:
Mr McCormick's wife is building some IKEA furniture, and the table below from the instructions show the lengths of different parts. Which part letter is the longest?
LENGTH (IN.)
Part A
Part B
Part C
Part D
Answer: Part B
Step-by-step explanation:
A = 1.2857...
B = 1.3
C = 1.15
D = 1.05
Cause yes
