Statistics can be used to evaluate data sets, tables, charts, and graphs by using methods such as correlation, regression, and analysis of variance, as well as descriptive statistics such as the mean, median, and standard deviation. Statistical tests such as the chi-square test can also be used to test hypotheses and draw conclusions about the data.
Statistics can be used to evaluate the information in data sets, tables, charts, and graphs. Statistical methods such as correlation, regression, and analysis of variance can be used to determine relationships between different variables. Additionally, descriptive statistics such as the mean, median, and standard deviation can be used to summarize the data and gain insights into the data set. Finally, statistical tests such as the chi-square test can be used to test hypotheses and draw conclusions about the data.
Statistics can be used to evaluate data sets, tables, charts, and graphs by using methods such as correlation, regression, and analysis of variance, as well as descriptive statistics such as the mean, median, and standard deviation. Statistical tests such as the chi-square test can also be used to test hypotheses and draw conclusions about the data.
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Evaluating information in data sets, tables, charts, and graphs using statistics involves several steps:
Examine the data to ensure that it is accurate, complete, and in the appropriate format.
Determine the type of data (e.g., numerical or categorical) and select appropriate statistical techniques for analysis.
Identify any outliers or unusual observations in the data and decide how to handle them.
Use descriptive statistics, such as measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation) to summarize the data.
Use inferential statistics, such as hypothesis testing or regression analysis, to make inferences about the population from the sample data.
Create appropriate charts, graphs, and tables to visually display the data and the results of the statistical analysis.
Interpret the results of the statistical analysis and present them in a clear and meaningful way.
Check assumptions of the statistical method you used.
Describe any limitation of your analysis and how that limitation might affect the conclusion
It's important to note that this is a general process and that depending on the specific data set, the question you are trying to answer, the type of data and the statistical methods used, the process can vary.
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265+(65-152)+9845 = ?
Please help me answer this question. Thank you!
Answer:
10023
Step-by-step explanation:
265 + ( - 87 ) + 9845
= 178 + 9845
= 10023
The finite region bounded by y=12-2x^2 and y=x^2-8. (This is for area between curves, Calculus)
Answer:
≈ 68.8530
Step-by-step explanation:
You want the area between the curves y = 12 -2x² and y = x² -8.
AreaThe area will be the integral of the difference between the curves, between the points where the curves intersect.
h(x) = (12 -2x²) -(x² -8) = 20 -3x² . . . . . height of a differential of area
The point where the curves intersect has an x-value that makes h(x) = 0. We choose to call the positive value 'a'. The curves also intersect at x=-a.
h(a) = 0
20 -3a² = 0
a² = 20/3
a = √(20/3) = (2/3)√15
So, the integral is ...
[tex]\displaystyle A=\int_{-a}^a{(20-3x^2)}\,dx=\left(20x-\dfrac{3x^3}{3}\right)_{-a}^a\\\\A=2a(20-a^2) = \dfrac{4}{3}\sqrt{15}\cdot\left(20-\dfrac{20}{3}\right)\\\\A=\boxed{\dfrac{160\sqrt{15}}{9}\approx68.8530}[/tex]
The area between the curves is about 68.8530 square units.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
The matched statements are:
1↔a, 2↔c, 3↔b, 4↔d
What is mensuration ?Mensuration is the branch of mathematics that studies the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc.
Given radius (r) of the cylinder, cone and sphere = r
Height (h) of the cone and cylinder = 2r
Volume of cylinder = πr²h
⇒π(r²)(2r)
⇒2πr³
Volume of cone = 1/3 πr²h
⇒1/3π(r²)2r
⇒2/3 πr³
Volume of sphere = 4/3 πr³
⇒4/3 πr³
From the above calculation we can match the given question:
1. The volume of 3 cones = 3×2/3πr³ = 2πr³ ↔ a) The volume of 1 cylinder
2.The volume of 2 cones = 2×2/3πr³=4/3πr³ ↔ c)
The volume of 1 sphere
3. The volume of 1 sphere ↔ b) 2/3 volume of 1 cylinder = 2/3×2πr³=4/3πr³
4. The volume of 1 cone ↔ d) 1/3 volume of 1 cylinder = 1/3×2πr³=2/3πr³
Hence, by the above calculation the matched statements are as follows:
1↔a, 2↔c, 3↔b, 4↔d.
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What is the answer 3(x-4)=12x.
Distribute to create an equivalent expression with the fewest symbols possible.
1
— (3j + 6) =
3
The equivalent of the expression of the given expression (1/3) x (3j + 6) will be j + 2.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ (1/3) x (3j + 6)
Simplify the expression, then we have
⇒ (1/3) x (3j + 6)
⇒ j + 2
The equivalent of the expression of the given expression (1/3) x (3j + 6) will be j + 2.
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It costs $2.50 to rent bowling shoes. Each
game costs $2.25. You have $9.25. Write
and solve an equation to find out how
many games you can bowl.
Answer:
1.93
Step-by-step explanation:
Let G be the number of games you can bowl.
The cost to rent bowling shoes and play each game is 2.50 + 2.25 = $<<2.5+2.25=4.75>>4.75.
So the equation would be:
4.75G = 9.25
To solve the equation, we can divide both sides by 4.75:
G = 9.25 / 4.75
G = 1.93
You can bowl 1.93 games.
What does it mean for a number to be a solution to the inequality x < 24?
Answer:
Step-by-step explanation:
A solution to the inequality x < 24 is a value of x that makes the inequality true when it is substituted into the expression. In other words, when x is a solution to the inequality x < 24, it must be less than 24.
For example, some solutions to the inequality x < 24 include -5, 0, 23.5, and any other value that is less than 24. However, the numbers like 24 and greater than 24 are not solutions to the inequality x < 24.
Ujarak has 100 mL of a strong toothpaste with a 1.1% concentration of sodium fluoride. They have a weaker toothpaste with a 0.3% concentration of sodium fluoride. What volume, in milliliters, of the weaker toothpaste would Ujarak need to add to the strong toothpaste to create a blend with 0.8% components of sodium fluoride?
PLEASE HELP the question is in the picture
its due in 1 hour pls help
Looking at the triangle, the side CE is solved to be 45 m
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions
Examining the figure shows that pair of equivalent sides are
AB and BD, AC and CE,
The solution is worked out using sides AB and BD, AC and CE,
AB / BD = AC / CE
290 / 30 = (145 + 290) / CE
cross multiplying
290 * CE = 30 * (145 + 290)
CE = 13050 / 290
CE = 45
hence CE = 45
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Application
3. Compare the variety of vehicles detailed below. Each vehicle travels 15,000 km per year.
a. Complete the following table and graph the points on the given grid.
The completed table of values obtained by using the data and the values per 100 km is presented as follows;
3 a. [tex]\begin{array}{|c|c|c|c|}L \ per \, 100\, km & Litres \ used&L\, per \, 100\, km&Litres\ used \\23.5 &3525&3.9&585 \\11.7 & 1755 & 3.4&510\\7.8 & 1170&2.9&435 \\5.9 &885&2.6&390 \\ 4.7&705&2.3&345 \\\end{matrix}[/tex]
What is a data set?A dataset is a collection of information which are related but contains elements of different values, and can be analyzed or manipulated through the use of computation methods.
The table of values is completed using the following calculations;
The distance each vehicle travels in a year = 15,000 km
The amount of fuel each vehicle uses is calculated as follows;
First car;
1. L per 100 km = 23.5 L
Liter used per year = 15,000 km/(100 km) × 23.5 L = 3525 L
2. L per 100 km = 11.7 L
Liter used per year = 15,000 km/(100 km) × 11.7 L = 1755 L
3. L per 100 km = 7.8 L
Liter used per year = 15,000 km/(100 km) × 7.8 L = 1170 L
4. L per 100 km = 5.9 L
Liter used per year = 15,000 km/(100 km) × 5.9 L = 885 L
5. L per 100 km = 4.7 L
Liter used per year = 15,000 km/(100 km) × 4.7 L = 705 L
6. L per 100 km = 3.9 L
Liter used per year = 15,000 km/(100 km) × 3.9 L = 585 L
7. L per 100 km = 3.4 L
Liter used per year = 15,000 km/(100 km) × 3.4 L = 510 L
8. L per 100 km = 2.9 L
Liter used per year = 15,000 km/(100 km) × 2.9 L = 435 L
9. L per 100 km = 2.6 L
Liter used per year = 15,000 km/(100 km) × 2.6 L = 390 L
10. L per 100 km = 2.3 L
Liter used per year = 15,000 km/(100 km) × 2.3 L = 345 L
The above values are used to complete the table as shown in the main section of the page above;
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Write down the coordinates of the point of intersection of the two lines whose equations are 3x+2y=10 2x-6y=3 (1 mark)
Answer:
(3, [tex]\frac{1}{2}[/tex] )
Step-by-step explanation:
to find the point of intersection, solve the equations simultaneously.
3x + 2y = 10 → (1)
2x - 6y = 3 → (2)
multiplying (1) by 3 and adding to (2) will eliminate y
9x + 6y = 30 → (3)
add (2) and (3) term by term to eliminate y
11x + 0 = 33
11x = 33 ( divide both sides by 11 )
x = 3
substitute x = 3 into either of the 2 equations and solve for y
substituting into (1)
3(3) + 2y = 10
9 + 2y = 10 ( subtract 9 from both sides )
2y = 1 ( divide both sides by 2 )
y = [tex]\frac{1}{2}[/tex]
solution is (3, [tex]\frac{1}{2}[/tex] )
Which of the following statements must be true about this diagram? Check all that apply.
A. m<3 is greater than m<2
B. m<4 is greater than m<1
C. m<4 is greater than m<2
D. The degree measure of <3 equals the sum of the degree measures of <1 and <2.
E. The degree measure of <4 equals the sum of the degree measures of <1 and <2.
F. the degree measure of <4 equals the sum of the degree measures of <2 and <3.
The statements that must be true about this diagram will be ∠4 > ∠1, ∠4 > ∠2, and ∠4 = ∠1 + ∠2. Then the correct options are B, C, and E.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.
By the above theorem, the equation is given as,
∠4 = ∠1 + ∠2
The statements that must be true about this diagram will be ∠4 > ∠1, ∠4 > ∠2, and ∠4 = ∠1 + ∠2. Then the correct options are B, C, and E.
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The missing diagram is attached below.
Select the correct answer from the drop down menu
The equation of the function is f(x) =x³ - 2x² -5x + 6. Hence option B is the correct option.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Given graph cuts x at three points. Thus the degree of the given function is 3.
The x-intercepts of the function are the zeros of the function.
The x-intercepts of the graph are (-2,0), (1,0), and (3,0).
Thus the zeros of the function are -2, 1, and 3.
The equation of a function whose zeros are a,b, c is f(x) = (x-a)(x-b)(x-c).
Therefore the equation of the graph function is
f(x) = (x-(-2))(x-1)(x-3)
f(x) = (x + 2)(x-1)(x-3)
f(x) = (x² + 2x - x -2)(x-3)
f(x) = (x² + x -2)(x-3)
f(x) = (x³ + x² - 2x -3x² -3x +6)
f(x) =x³ - 2x² -5x + 6
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Simplify the expression x^-2/y^4
The value of the expression is 1 / (x² [tex]y^4[/tex]).
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]x^{-2}[/tex] / [tex]y^4[/tex]
[tex]x^{-2}[/tex] can be written as 1/x².
Now,
(1/x²)/[tex]y^4[/tex]
= 1 / (x² [tex]y^4[/tex])
Thus,
The value is 1 / (x² [tex]y^4[/tex]).
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What is the vertex of the graph y = |x + 2| + 3?
Answer:
(-2, 3)
Step-by-step explanation:
The vertex of an absolute value function is when the part of the equation that is inside absolute value signs is equal to 0:
In the equation: y = |x + 2| + 3,
x + 2 = 0 ==> x + 2 is the part that is inside the absolute value signs
x = -2 ==> subtract 2 on both sides
Now, plugin -2 into the equation y = |x + 2| + 3:
y = |(-2) + 2| + 3
y = |0| + 3
y = 0 + 3 ==> the absolute value of 0 is 0.
y = 3
Now with the x and y-coordinates, we can figure out the vertex point:
Answer: (-2, 3)
joe has 8/9 kilograms of clay. He uses 3/4 to make a vase. how much clay is left. How do I start helping my 10 year old solve this? thx!
Using the provided ratio of the clay and the proportions used to make a vase with the values given, The answer is 2/9.
What is a ratio?A ratio is a way of comparing two or more quantities by using division. It is a way of expressing a relationship between numbers, typically represented by a fraction. The numbers being compared are called the "terms" of the ratio. For example, a ratio of 3:5 compares the value of 3 to the value of 5. It can also be written as 3/5. Ratios can be used to compare many different types of quantities, such as lengths, weights, or time. Ratios are also used to express the relationship between different parts of a whole, for example, the ratio of girls to boys in a class, or the ratio of water to flour in a recipe.
Here,
A proportion is a statement that two ratios are equivalent. It is an equation that compares two ratios to see if they are equal. Proportions are written in the form of "a/b = c/d" where a, b, c, and d are numbers. For example, "3/5 = 6/10"
is a proportion because it states that the ratio of 3 to 5 is equal to the ratio of 6 to 10. A proportion can also be used to find a missing value when we have a proportion and the value of three of the terms. This method is called cross-multiplication.
Here,
clay used = 3/4 of 8/9
=2/3
remaining clay = 8/9 - 2/3 = 2/9
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Round 2484 to the nearest thousand
Answer: 2000
Step-by-step explanation: First, let's focus on the number 484. Let's always ask ourselves this: "Is this number (484 in our case) greater than 500?"
I say 500 because that's the number that we start to round up to the nearest thousandth. So, 484 is less than 500, telling us to round down.
So, therefore 2484 rounded to the nearest thousand is 2000. I hope this helped.
1/4 y + 3 =-5x what is it?
Answer:
y = -20x-12
Step-by-step explanation:
Subtract 4 from both sides.
1/4y = -5x-3
Multiply 4 by both sides to cancel the fraction.
y = -20x - 12
Brainliest if you found this helpful.
laster
10. To prepare for a downhill skiing competition,
Roman completed three training sessions. The
table shows his average time and distance for
each session. Did Roman's rate, in miles per
hour, increase from session to session? Write an
argument that can be used to defend your
solution.
per hr.
50
Session
1
2
3
Time (hr)
2
125
3
200
3
250
Distance (mi)
9
10
11
12
17
20
Yes, Roman's rate, in miles per hour, increase from session to session.
What is the speed?The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.
A) Given that, time =2/125 and distance =9/10
So, speed = Distance/Time
= 9/10 ÷ 2/125
= 9/10 × 125/2
= 56.25 miles per hour
B) Time =3/200 and Distance =11/12
Speed = 11/12 ÷ 3/200
= 12/11 × 200/3
= 72.73 miles per hour
C) Time =3/250 and Distance =17/20
Now, speed =17/20 ÷ 3/250
= 17/20 × 250/3
= 70.83 miles per hour
Yes, Roman's rate, in miles per hour, increase from session to session.
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16. Two numbers, n and p are plotted on the number line shown,
The numbers n-p.n.p. and p-n will be plotted on the number line.
Select an expression from each list to make this statement true.
The number with the least value is.
and the number with the greatest value is
Mathematics-Session 1
n-p
n+p
p-n
n-p
n+p
p-n
The number with the least value is n - p and the number with the greatest value is p - n.
How to determine the least value and the greatest value?Based on the number line (see attachment), we would assign a numerical value to the two numbers, n and p in order to determine their output (numerical value).
Assuming the variable n represents the numerical value -0.8 and the variable p represents the numerical value 0.4, we would evaluate each of the given mathematical expressions as follows;
n - p = -0.8 - 0.4
n - p = -1.2 (least value).
For the second mathematical expressions, we have the following numerical value:
n + p = -0.8 + 0.4
n + p = -0.4
For the third mathematical expressions, we have the following numerical value:
p - n = 0.4 - (-0.8)
p - n = 0.4 + 0.8
p - n = 1.2 (greatest value).
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Determine the number of triangles ABC possible with the given parts.
A = 42° a = 8.2 b = 10.4
How many possible solutions does this triangle have?a
The number of possible triangles for the given measurement are two.
What is a triangle?A polygon with three sides, vertex and angles refers as a triangle.
Given that, a triangle ABC, where, A = 42° a = 8.2 b = 10.4
We know that, we can determine, how many solutions there will be by using relation between a and bsinA
a > bsinA = two solutions
a < bsinA = no solution
a = bsinA = one solution
Finding relation between a and bsinA
a = 8.2 and b = 10.4 and A = 42°
bsinA = 10.4×sin42°
= 6.96
This gives, bsinA < a
Therefore, we get the case 1st,
Hence, The number of possible triangles is 2.
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The point (-6,4) is reflected over the point (1,-1) and it’s image is point B. What are the coordinates of point B?
The coordinates of point B are (8, -6).
What is midpoint?
The midpoint of a boundary is a point that is in the middle of, close to, or equally spaced from both ends of a line. the middle of something, as in the middle of a process, an event, or a situation: the middle of the negotiations. Geometry.
Given:
The point (-6,4) is reflected over the point (1,-1) and it’s image is point B.
We have to find the coordinates of point B.
Let the point (1, -1) be Midpoint M, and point B has coordinates of (x, y)
As the point A(-6, 4) reflects over the point M, it becomes the midpoint of segment AB
Using midpoint formula, finding the coordinates of the point B
[tex]1 = \frac{-6+x}{2} , -1 = \frac{4+y}{2} \\2 = -6 + x, -2 = 4 + y[/tex]
8 = x , -6 = y
x = 8, y = -6
Hence, the coordinates of point B are (8, -6).
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simplify √2+√5/√2−√5
The simplified value of the expression is -7/3 - 2√10/3.
What is simplification?To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.
Given (√2 + √5)/(√2 - √5)
simplifying the expression by rationalization
multiply and divide by (√2 + √5)
= (√2 + √5)/(√2 - √5) x (√2 + √5)/(√2 + √5)
= (√2 + √5)²/((√2)² - (√5)²)
using property (a + b)² = a² + b² + 2ab
= (2 + 5 + 2√10)/(2 - 5)
= -(7 + 2√10)/3 = -7/3 - 2√10/3
Hence the simplified form is -7/3 - 2√10/3.
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What is the value of jk
The value of JK is 30
What is quadrilateral?A quadrilateral in geometry is a four-sided polygon with four edges and four corners.
Given;
JKLM and PQRS are shown, where JKLM is similar to PQRS. Some measurements of the sides of JKLM and PQRS are given.
MJ = 21, JK = 4y-2, KL = 6x +3, LM = 36, PQ = 10, QR = 11, and RS = 12.
So,
JK is similar to PQ.
JK / PQ = LM / RS
4y-2 /10 = 36 / 12
4y -2 = 30
4y = 32
y = 8
So, the value of JK is 4(8) - 2
JK = 30.
Therefore, 30 is the value of JK.
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PLEASE HELP please..
The distance across the lake is as follows;
d = 45 m.
How to find the side of similar triangle?Similar triangle are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
Therefore, let's find the side d of the similar triangles DBA and ECA.
Hence, using proportion,
d / 30 = 145 + 290 / 290
d / 30 = 435 / 290
cross multiply
290d = 435 × 30
290d = 13050
divide both sides by 290
d = 13050 / 290
d = 45
Therefore,
d = 45 meters
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Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} be the universal set.
Let sets A and B be subsets of U, where:
A = {2, 3, 9}
B = {0, 1, 3, 5, 6, 8}
Write
¯¯¯
A
A
¯
:
¯¯¯
A
A
¯
=
Write
¯¯¯
B
B
¯
:
¯¯¯
B
B
¯
=
Write
A
∪
B
A
∪
B
:
A
∪
B
A
∪
B
=
Write
A
∩
B
A
∩
B
:
A
∩
B
A
∩
B
=
Write your answer using proper set notation. If the result is the empty set, enter { }
The elements of the sets are;
A¹ = { 0, 1, 4, 5, , 7 , 8 }
B¹ = { 2, 4, 7 , 9}
AUB = { 0, 1, 2 , 3, 5 , 6, 8, 9}
A∩B = { 3}
How to determine the value
From the information given, we have the parameters;
The universal setA, a subset of the universal setB, a subset of the universal setGiven that;
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {2, 3, 9}
B = {0, 1, 3, 5, 6, 8}
To determine primes of the subset represented as A¹
A¹ = elements uncommon between A and the universal set;
A¹ = { 0, 1, 4, 5, , 7 , 8 }
B¹ = elements uncommon between B and the universal set
B¹ = { 2, 4, 7 , 9}
AUB = all the elements in the set without repetition
AUB = { 0, 1, 2 , 3, 5 , 6, 8, 9}
A∩B = elements common in A and B
A∩B = { 3}
Hence, the elements in A∩B = {3}
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A boat travels 62 miles in 4 hours. What is the distance it travelled? 248mph
*Include the number and the unit
The distance the boat travelled is 248 miles.
What is distance?
Distance is defined as the amount of space between two objects or points. It can be measured in a variety of ways, such as kilometers, meters, miles, feet, and inches. Distance is not a static concept, as it can change over time, such as when two objects move closer or farther away from each other. Distance can also be used to measure the amount of time it takes for a person or object to travel from one point to another. In addition, distance can refer to the physical separation between two people or the emotional distance between two individuals.
This can be calculated by multiplying the speed of the boat by the amount of time it was travelling, i.e. 62 miles per hour (mph) multiplied by 4 hours. Therefore, the boat travelled a total of 248 miles.
It is important to note that the speed of the boat was 62 mph. This is the average speed of the boat over the 4-hour period. This can be calculated by dividing the total distance travelled by the amount of time it took to travel that distance, i.e. 248 miles divided by 4 hours. Therefore, the average speed of the boat was 62 mph.
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The distance the boat travelled is 248 miles.
What is distance?Distance is defined as the amount of space between two objects or points. It can be measured in a variety of ways, such as kilometers, meters, miles, feet, and inches. Distance is not a static concept, as it can change over time, such as when two objects move closer or farther away from each other. Distance can also be used to measure the amount of time it takes for a person or object to travel from one point to another. In addition, distance can refer to the physical separation between two people or the emotional distance between two individuals.
This can be calculated by multiplying the speed of the boat by the amount of time it was travelling, i.e. 62 miles per hour (mph) multiplied by 4 hours. Therefore, the boat travelled a total of 248 miles.
It is important to note that the speed of the boat was 62 mph. This is the average speed of the boat over the 4-hour period. This can be calculated by dividing the total distance travelled by the amount of time it took to travel that distance, i.e. 248 miles divided by 4 hours. Therefore, the average speed of the boat was 62 mph.
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If 780xa=1716xb find the least values of a and b.
By solving the equation and evaluating the values, we get, a = 11 and b = 5
what is equation?An equation is a mathematical statement that asserts the equality of two expressions. The expressions on either side of the equal sign are equivalent and can be substituted for one another. An equation typically contains one or more variables, which are placeholders for the unknown values that make the equation true.
Give the example of equation:For example, the equation 2x + 3 = 7 is a mathematical statement that asserts the equality of the expression 2x + 3 and the expression 7. The variable x in this equation represents an unknown value that when plugged in will make the equation true.
In the example I provided earlier, 780xa = 1716xb is a Diophantine equation where xa and xb are unknown values that when found, the left and right side of the equation will be equal.
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graph the function g(x)=2f(x+1)-2
The graph of the equation g(x) = 2(x + 1) - 2 on the coordinate plane is added as an attachment
How to graph the equation on the coordinate plane.From the question, we have the following parameters that can be used in our computation:
g(x) = 2f(x + 1) - 2
Also, we have
f(x) = 2x
Recall that, we have
g(x) = 2f(x + 1) - 2
Using the above as a guide, we have the following:
f(x) = 2x
Add 1 to x
So, we have
f(x + 1) = 2(x + 1)
Subtract 2 from the function
So, we have
f(x + 1) - 2 = 2(x + 1) - 2
Substitute f(x + 1) - 2 = 2(x + 1) - 2 in g(x) = 2f(x + 1) - 2
g(x) = 2(x + 1) - 2
Next, we plot the graph of the function
See attachment for the graph
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1. In ΔABC, m < C = 620, a = 18 and b = 17. Find the length of side c, to the nearest integer.
2. In a rhombus whose side measures 20 and the smaller angle is 54°, find the length of the larger diagonal, to the nearest tenth.
3. Three sides of a triangle measure 10m, 12m, and 20m. Find the largest angle of the triangle, to the nearest degree.
4. In ΔABC, m < C = 340, a = 30 and b = 19. Find the length of side c, to the nearest integer.
5. In a rhombus whose side measures 20 and the smaller angle is 38°. Find the length of the larger diagonal, to the nearest tenth.
6. Three sides of a triangle measure 12m, 16m, and 18m. Find the largest angle of the triangle, to the nearest degree.
7. In ΔABC, m < C = 580, a = 20 and b = 18. Find the length of side c, to the nearest integer.
8. In a rhombus whose side measures 18 and the smaller angle is 34°, find the length of the larger diagonal, to the nearest tenth.
All measures of sides and angles are listed below:
c ≈ 18 D ≈ 35.6 α ≈ 131° c ≈ 18 D ≈ 37.8 α ≈ 79° c ≈ 19 D ≈ 34.4How to resolve triangles by trigonometry
In this problem we should use trigonometry and theorems regarding triangles to determine missing sides and angles (i.e. Law of sine, law of cosine).
Case 1
Two sides and an angle opposite to unknown side are known and missing side length is found by law of cosine:
c = √(a² + b² - 2 · a · b · cos C)
Where:
a, b, c - Sides of the triangle.C - Missing angle of the triangle, in degrees.(C = 62°, a = 18, b = 17)
c = √(18² + 17² - 2 · 18 · 17 · cos 62°)
c ≈ 18.046
c ≈ 18
Case 2
The larger diagonal of a rhombus bisects the two smaller angles of quadrilateral. The length of the larger diagonal of a rhombus is found by the following formula:
D = 2 · a · cos 0.5α
Where:
D - Length of the larger diagonal.a - Side length.α - Measure of the smaller angle, in degrees.(a = 20, α = 54°)
D = 2 · 20 · cos 27°
D ≈ 35.640
D ≈ 35.6
Case 3
According to the law of cosine, the greater the side length, the greater the angle opposite to it:
20² = 10² + 12² - 2 · 10 · 12 · cos α
Where α is the angle opposite to the larger side, in degrees.
400 = 244 - 240 · cos α
156 = - 240 · cos α
cos α = - 13 / 20
α ≈ 130.541°
α ≈ 131°
Case 4
By using the approach used in case 1:
(C = 34°, a = 30, b = 19)
c = √(30² + 19² - 2 · 30 · 19 · cos 34°)
c ≈ 17.773
c ≈ 18
Case 5
By using the approach used in case 2:
(a = 20, α = 38°)
D = 2 · 20 · cos 19°
D ≈ 37.820
D ≈ 37.8
Case 6
By using the approach used in case 3:
18² = 12² + 16² - 2 · 12 · 16 · cos α
324 = 400 - 384 · cos α
- 76 = - 384 · cos α
cos α = 19 / 96
α ≈ 78.585°
α ≈ 79°
Case 7
By using the approach used in case 1:
(C = 58°, a = 20, b = 18)
c = √(20² + 18² - 2 · 20 · 18 · cos 58°)
c ≈ 18.506
c ≈ 19
Case 8
By using the approach used in case 2:
(a = 18, α = 34°)
D = 2 · 18 · cos 17°
D ≈ 34.427
D ≈ 34.4
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