What are the missing numbers ( ),9.8,9.1,( ),7.o,6.3,5.6
Answers
Answer: 8.4 , 7.7
Step-by-step explanation:
Related Questions
A triangle is both isosceles and acute. If one angle of the triangle measures 30°, what are the measures of the largest and smallest angles of the triangle? a) largest angle = 87"; smallest angle = 30° b) largest angle = 150°; smallest angle = 75° c) largest angle = 75°; smallest angle = 30° d) largest angle = 165°; smallest angle = 75 e) largest angle = 86°; smallest angle = 30° f) largest angle = 120°; smallest angle = 30°
Answers
The only valid solution for a triangle to be both isosceles and acute. is c) largest angle = 75°; smallest angle = 30°.
Since the triangle is isosceles, two of its angles must have the same measure. Let's call this measure "x". Therefore, the other angle of the triangle (the one that measures 30°) must be different from "x".
Since the triangle is also acute, all three of its angles must be less than 90°.
Let's consider two cases:
Case 1: The angle that is different from "x" is smaller than "x". In this case, the smallest angle of the triangle is 30°, and it is equal to the angle that is different from "x". The other two angles are both "x". We know that the sum of the angles of a triangle is 180°, so we can write:
30 + x + x = 180
Simplifying the equation, we get:
2x + 30 = 180
2x = 150
x = 75
Therefore, the largest angle of the triangle is also "x", which is 75°.
Answer: c) largest angle = 75°; smallest angle = 30°
Case 2: The angle that is different from "x" is larger than "x". In this case, the largest angle of the triangle is 90° (because the triangle is acute), and it is equal to the angle that is different from "x". The other two angles are both "x". We know that the sum of the angles of a triangle is 180°, so we can write:
x + x + 90 = 180
Simplifying the equation, we get:
2x = 90
x = 45
However, this solution is not valid because it implies that one angle of the triangle is 90°, which contradicts the fact that the triangle is acute.
Therefore, the only solution is c) largest angle = 75°; smallest angle = 30°.
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Given the following sequence of numbers find the recursive formula, and the appropriate sequence formula,(arithmetic or geometric) and find the next three numbers in the sequence.8. 3, 9, 15, 21, 27,9. 5, 9, 13, 17, 21,10. -243, 81, -27, 9,11. Using the sequence find the n for the following terms 6, 1, 4,-9...... -254
Answers
see explanation below
Explanation:8) 3, 9, 15, 21, 27
The common difference = 15-9 = 9-3
The common difference = d = 6
Hence, it is an arithmetric sequence
The recursive formula:
\(\begin{gathered} a_{n+1}=a_n+\text{ 6} \\ \text{OR} \\ a_n=a_{n-1}+\text{ d} \\ a_n=a_{n-1}+6 \end{gathered}\)The appropriate formula:
\(\begin{gathered} a_n=a_1+\text{ (n-1)d} \\ \text{where a}_1\text{ = }3\text{ } \\ a_n=3_{}+\text{ (n-1)d} \end{gathered}\)The next three numbers in the sequence:
\(\begin{gathered} \text{The last term in the sequence given was 6th term. } \\ \text{The next }3\text{ terms will be: 7th, 8th and 9th term} \end{gathered}\)\(\begin{gathered} a_7\text{ = 3 + (7-1)}\times6 \\ =\text{ 3+ (6)(6) = 3 + 36} \\ 7th\text{ term = }a_7=39 \end{gathered}\)\(\begin{gathered} a_8\text{ = 3 + (8-1)}\times6 \\ =\text{ 3+ (7)(6) = 3 + 4}2 \\ 8th\text{ term = }a_8\text{ =}45 \end{gathered}\)\(\begin{gathered} a_9\text{ = 3 + (9-1)}\times6 \\ a_9\text{ = }3\text{ + 8(6) = 3 + 48} \\ 9th\text{ term = }51 \\ \end{gathered}\)Sara went shopping and bought a pair of shoes for $33.00. The shoes cost $35.31 after tax. What was the tax rate?
Answers
Step-by-step explanation:
so if 33.00$ were 100% then you have to fund how many % is 35.31$
to do that you can just multiply 35.31$ to 100 and then divide it too 33.00$
\((35.31 \times 100) \div 33 \)
that is 107 % and so
35.31 = 107%
33.00=100%
substract 107 from 100 and you get the tax rate
107-100=7 % tax
hope you understood :)
Answer:
7%
Step-by-step explanation:
Tax price = 35.31 - 33
=>Tax price = 2.31
Tax rate = Tax Price/Original Price x 100
= 2.31/33 x 100
= 0.07 x 100
= 7%
¿ cuál será el volumen de una pirámide hexagonal si las aristas de la base miden 8cm, la apotema vale9.93cm y su altura es de 28cm?
Answers
Answer:
2224.32 cm³
Step-by-step explanation:
La fórmula para el volumen de una pirámide hexagonal = 1/3 (1/2 × P × a) × h
Donde a = Apotema = 9,93 cm
P = Perímetro =
Pirámide hexagonal = 6 × Bordes de la base = 6 × 8 cm = 48 cm
h = Altura = 28 cm
Por eso,
Volumen de la pirámide hexagonal = 1/3 (1/2 (48 × 9.93) × 28 cm
= 1/3 × 238.32 × 28 cm
= 2224.32 cm³
Volumen de la pirámide hexagonal = 2224.32 cm³
student researchers wanted to see whether a short delay between seeing a list of words and when people were asked to recall them would hinder memorization. the subjects were shown a list of words to memorize for 1 minute and were then given 1 minute to recall as many words as they could. each subject did this once with no delay between memorizing and recall and another time with a 30-second wait between memorizing and recall. they were randomly assigned the order of the two conditions. the number of words memorized under each condition can be found in the statcrunch data set memorizingwords. questions: use the appropriate simulation applet to calculate an approximate p-value. is there strong evidence that a short delay hinders the memorization process? explain.
Answers
The appropriate simulation applet to calculate an approximate p-value is 0.0077.
The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.
Delay or no delay, answer: the number of words remembered
The mean distance between words remembered with and without delay over time is null, or zero.
Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.
Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.
The mean distance in words remembered is 1.85.
1)0.0077 as the p-value
2)Strong data suggests that a brief delay impairs memorization.
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Catherine has $460 to spend at a bicycle store for some new gear and Viking outfits assume all prices list include tax when she buys the bicycle for $362.68 she buys three bicycle reflectors for $10.20 each and a pair of bike gloves for $12.54 she plans to spend some more or all of the money she has left to buy new biking office for $27.09 each
Answers
Answer:
Catherine buys 3 bicycle reflectors at $10.20 each, for a total cost of 3 * $10.20 = $30.60
She buys a pair of bike gloves for $12.54
She buys a bicycle for $362.68
The total cost of these items is $362.68 + $30.60 + $12.54 = $405.82
Catherine has $460 - $405.82 = $54.18 left to spend on new biking clothes.
She can buy 2 biking clothes for $27.09 each, with her remaining money.
Step-by-step explanation:
Two customers spent the same total amount of money at a restaurant.
• The first customer bought 8 hot wings and left a $4 tip.
• The second customer bought 10 hot wings and left a $2.80 tip.
• Both customers paid the same amount per hot wing.
How much does one hot wing cost at this restaurant in dollars and cents?
Record your answer in the boxes below. Be sure to use the correct place value.
+/-
Answers
Explanation:
We’ll solve this with a set of equations since the price per wing is fixed and they paid the sam amount at the restaurant. Let x represent the cost of 1 wing.
8x + 4.00 = 10x + 2.80
4.00 = 2x + 2.80
1.20 = 2x
0.60 = x
So, we have found that one wing cost $0.60.
Cheers.
Greg started to run on a treadmill after setting it’s timer for 98 minutes the display says that he has finished 57% of his run how many minutes have gone by
Answers
A total of 55.86 minutes have gone by since Greg started his run on the treadmill.
How many minutes have gone byIf Greg has completed 57% of his run, it means he has 43% of his run remaining.
To find out how many minutes have gone by, we can use proportions.
Let's say x is the total number of minutes Greg needs to complete his run:
x = 57% * 98 minutes
Evaluate
x = minutes
Therefore, approximately 55.86 minutes have gone by since Greg started his run on the treadmill.
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there are 12 bars of soap for 10.00 or 5 bars of soap for 4.00
Answers
Answer:
13
Step-by-step explanation:
a nintendo is very hard to get ahold of and if you do it right then you can get ur hands on one but yeah thats all that matters
HI hope you are well can you please please please help me with this question thank you alot
Answers
Answer:
£231,525
Step-by-step explanation:
We are told that the value of Lucy's house
In 2014 = £200,000
And the house increased by 5% every year
In 2015 , 5% of £200,000
= 5/100 × £200,000
=£10,000
Start of 2015 = £200,000 + £10,000
= £210,000
In 2016 , 5% of £210,000
= 5/100 × £210,000
=£10500
Start of 2016 = £210,000 + £10,500
= £220,500
In 2017 , 5% of £220,500
= 5/100 × £220,500
=£11,025
Start of 2017 = £220,500 + £11,025
= £231,525
Therefore the value of Lucy's house at the start of 2017 = £231,525.
Need help with this geometry assignment due soon
Answers
Answer:
1. x = 20
2. x = 60
3. x = 30
Step-by-step explanation:
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
I agree with the person who answered before me it's 100% correct.
SHOULD GIVE THEM THE BRAINLIEST!!!
Use the below information for questions 2a - 2b:
State Probability Return on A Return on B Return on C
Boom 0.30 0.35 0.25 0.10
Average 0.50 0.20 0.15 0.25
Bust 0.20 0.05 0.10 0.35
2a. Find the Mean and Variance of Asset A
2b. Find the Correlation coefficient of A and C
Answers
Answer to 2a: The mean of Asset A is 0.235 and the variance is 0.0123
Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).
2a. Mean of Asset A (Expected Value):
The mean of Asset A (E(A)) can be calculated as:
\(\[E(A) = \sum_{i} (x_i \cdot P_i)\]\)
where \(\(x_i\)\) represents the return on Asset A in each state and\(v \(P_i\)\) represents the probability of that state.
Using the given information, we have:
Boom:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Average:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Bust:
\(\(E(A) = (0.35 \cdot 0.30) + (0.20 \cdot 0.50) + (0.05 \cdot 0.20) = 0.235\)\)
Therefore, the mean of Asset A is\(\(E(A) = 0.235\).\)
2b. Correlation Coefficient of A and C:
The correlation coefficient\((\(\rho\))\)between Asset A and C can be calculated using the formula:
\(\[\rho = \frac{{\text{{Cov}}(A, C)}}{{\sigma_A \cdot \sigma_C}}\]\)
where\(\(\text{{Cov}}(A, C)\)\) represents the covariance between Asset A and C, and \((\sigma_A\)\) and\(\(\sigma_C\)\)represent the standard deviations of Asset A and C, respectively.
Using the given information, we have:
Boom:
\(\(\text{{Cov}}(A, C) = (0.35 - 0.235) \cdot (0.10 - 0.25) = -0.017\)\)
Average:
\(\(\text{{Cov}}(A, C) = (0.20 - 0.235) \cdot (0.15 - 0.25) = -0.005\)\)
Bust:
\(\(\text{{Cov}}(A, C) = (0.05 - 0.235) \cdot (0.35 - 0.25) = -0.017\)\)
Now, we calculate the standard deviations of Assets A and C:
\(\(\sigma_A = \sqrt{{\text{{Var}}(A)}} = \sqrt{0.0123} \approx 0.1108\)\)
\(\(\sigma_C = \sqrt{{\text{{Var}}(C)}} = \sqrt{0.0517} \approx 0.2274\)\)
Finally, we can calculate the correlation coefficient:
Boom:
\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)
Average:
\(\(\rho = \frac{{-0.005}}{{0.1108 \cdot 0.2274}} \approx -0.187\)\)
Bust:
\(\(\rho = \frac{{-0.017}}{{0.1108 \cdot 0.2274}} \approx -0.670\)\)
Therefore, the correlation coefficient between Asset A and C is approximately\(\(\rho \approx -0.670\) (Boom), \(\rho \approx -0.187\) (Average), and \(\rho \approx -0.670\) (Bust).\)
Answer to 2a: \(The mean of Asset A is \(0.235\) and the variance is \(0.0123\.\)
Answer to 2b: The correlation coefficient between Asset A and C is approximately\(\(-0.670\) (Boom), \(-0.187\) (Average), \(-0.670\)\)(Bust).
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Joseph Bettino purchased an 11.5-ounce box of cereal for $3.99. What is the unit price of the cereal?
Answers
Answer:
$0.35 per ounce. (rounded.)
Step-by-step explanation:
you just divide.
The cost of one pound of cereal Joseph Bettino purchased is $2.88.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Joseph Bettino purchased an 11.5-ounce box of cereal for $3.99.
Now, To obtain the cost of per pound of cereal we have to divide the total pounds of cereal by the total amount of money which is,
= $(11.5/3.99)
= $2.88.
So, The cost of one pound of cereal is $2.88 it can also be referred as the unit price of the cereal.
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a30 arithmetic sequence of 1,-4,-9,-14
Answers
The 30th term a30 of the sequence is -1445
How to determine the value of a30?The definition of the function is given as
arithmetic sequence of 1,-4,-9,-14
The above definitions imply that we simply subtract 5 from the previous term to get the current term
Using the above as a guide,
so, we have the following representation
First term, a = 1
Common difference, d = 5
An arithmetic sequence is represented as
a(n) = a + (n - 1)d
For the 30th term, we have
a(30) = a + 29d
So, we have
a(30) = 1 + 29 * -5
Evaluate
a(30) = -144
Hence, the value of a30 is -144
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Two-ninths of h
algebraic expression translate
Answers
The algebraic expression "two-ninths of h" can be written as (2/9)h, where h is the variable being multiplied by the fraction 2/9.
"Two-ninths of h" is an algebraic expression that represents a quantity that is equal to two-ninths of the value of h. It can be written as 2h/9 or (2/9)h. In this expression, h represents an unknown value or variable, and 2/9 is a constant that specifies the fraction of h that is being considered. This expression can be used in mathematical equations to represent a specific portion or amount of h, depending on the context of the problem.
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State whether the following statements are True or
False. If False correct it
1)0.002 × 100 = 20.
Answers
Answer:
False
Step-by-step explanation:
The statement is false because 0.002×100=0.2
One correction is 0.002×10000=20
Choose the correct graph that illustrates the equation by clicking on the image{(x, y): -1 ≤ x ≤ 3
Answers
See attachment for the graph of the inequality -1 ≤ x ≤ 3
What is a linear inequality?A linear inequality is an inequality that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the correct graph?In this question, the expression of the inequality is given as:
-1 ≤ x ≤ 3
The above means that the set of values of x is between -1 and 3 (-1 and 3 are inclusive of the values of x)
So, the possible values of x are -1, 0, 1, 2 and 3
When the graph of the inequality is plotted, the graph would have the following properties:
x values = -1, 0, 1, 2 and 3Double closed circles or thick linesNext, we plot the graph of the inequality -1 ≤ x ≤ 3
See attachment for the graph of the inequality -1 ≤ x ≤ 3
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hat dose 2+7x=5x+14 equal
Answers
Answer:
x = 6
Step-by-step explanation:
2 + 7x = 5x + 14
7x - 5x = 14 - 2
2x = 12
x = 12 : 2
x = 6
Good luck !
sorry if it’s too blurry but i need help with this
Answers
You multiply the bases, then add the exponents.
7x7 = 49
-8 + (-3) = -11
49 ^-11
Find the slope of the line that passes through the given points.
(-5, 2) and (-2,8)
A 1/2
B 2
C -2
D) 6/7
E -6/7
Answers
Answer:
I do not know
Step-by-step explanation:
A stack of boards is 24 inches high. Each board is 38 of an inch thick. How many boards are in the stack? 10 points pls help this is a math test
Answers
There are 64 boards in the stack.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
A stack of boards is 24 inches high.
Each board is 3/8 of an inch thick.
As, When dividing fraction, multiply the first fraction by the reciprocal of the second fraction. (A reciprocal is an upside down fraction)
Then, number of boards
= 24 x 8/3
= 8 x 8
= 64
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A parabola can be drawn given a focus of
(-7, 6) and a directrix of y = 2. Write
the equation of the parabola in any form.
Answers
The equation of a parabola with a focus of (-7, 6) and a directrix of y = 2 is (x + 7)² = 8(y - 4).
What is the standard equation of a parabola?The standard equation of a parabola whose axis is parallel to the y-axis, vertex at (h, k), focus at (h, k + a) and the equation of the directrix is y - k + a = 0 is
(x - h)² = 4a(y - k)
Calculation:The required parabola has focus at (-7, 6) and a directrix is of y - 2 = 0.
On comparing with the standard values, we get
h = -7; k + a = 6; and k - a = 2
On simplifying, we get k = 4 and a = 2.
So, the vertex of the parabola is at (-7, 4) and a = 2 (upside open).
Then the equation of the parabola is
(x - h)² = 4a(y - k) ⇒ (x + 7)² = 4(2)(y - 4)
⇒ (x + 7)² = 8(y - 4)
Therefore, the equation of the given parabola is (x + 7)² = 8(y - 4).
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2(4x+3)=10x-2
So like how in hell do you do this I’m soooo confused
Answers
Answer:
4Solution,
2(4x+3)=10x-2
or,8x+6=10x-2
or,8x-10x=-2-6
or,-2x=-8
or,X=-8/-2
X=4
Hope it helps
Good luck on your assignment
Answer:
x = 4
Step-by-step explanation:
First you want to distribute the terms:
2(4x+3) = 10x-2
8x+6 = 10x-2
then combine like terms:
8x+6 = 10x-2
-8x -8x
6 = 2x-2
+2 +2
8 = 2x
x = 4
in the market for milk portrayed in this figure, which price yields an efficient outcome?
Answers
The efficient outcome in the market for milk portrayed in the figure would be where the marginal cost (MC) curve intersects with the demand (D) curve, which is at a price of $3 per gallon.
To determine which price yields an efficient outcome in the market for milk, we need to find the equilibrium price. The equilibrium price is where the supply and demand curves intersect, which represents the point at which the quantity demanded equals the quantity supplied.
At this price, the quantity of milk produced and consumed will be at the socially optimal level where the marginal benefit (MB) equals the MC, resulting in a Pareto efficient outcome. It is important to note that this assumes no externalities or market failures are present in the market for milk.
1. Identify the supply and demand curves in the figure. The demand curve typically slopes downward, while the supply curve slopes upward.
2. Locate the point where the supply and demand curves intersect.
3. Find the price corresponding to this point on the vertical axis (price axis).
The equilibrium price found in step 3 is the price that yields an efficient outcome in the market for milk.
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a polygon has 50 sides
all but one of its angle is 170 degrees
what is the size of the other angle?
Answers
Answer:
.2 degrees
Step-by-step explanation:
180-170 is 10
10/50 is .2
The size of the other angle will be 0.2 degrees.
What are polynomials?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
It is given that a polygon has 50 sides but one of its angles is 170 degrees.
The remaining angle will be calculated as:-
180-170 = 10
The size of the other angle is calculated below:-
Angle = 10/50
Divide the value 10 by 50 to get the angle.
Angle = 0.2
Therefore, the size of the other angle will be 0.2 degrees.
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What is the surface area of this square base pyramid? 3 cm 2 cm 2 cm
Answers
Answer: I have no idea my friend but it's real hard Iwish you luck!
Answer:
16.
Step-by-step explanation:
The formula for a triangle is \(\frac{1}{2} * b * h\)
So, we take the triangle we see and but in in the formula.
\(\frac{1}{2} * 2 * 3 = 3.\)
Multiply that by 4, because there are four triangles that size.
\(3 * 4 = 12.\)
Now, we multiply 2 times 2 because that's the surface area for the bottom.
\(2 * 2 = 4.\)
Now, we add the two.
\(12 + 4 = 16.\)
The points (n,7) and ( – 1, – 9) fall on a line with a slope of 8. What is the value of n?
Answers
The value of n if the slope of the line that passes through points (n,7) and ( – 1, – 9) is 8, is calculated as: n = 1.
What is the Slope of a Line?The slope of a line is calculated as, m = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).
Given the following points that lies on a line that has a slope of 8 as (n, 7) and (-1, -9), therefore let:
(n, 7) = \((x_1, y_1)\)
(-1, -9) = \((x_2, y_2)\).
m = 8
Substitute the values into the slope formula:
8 = (-9 - 7) / (-1 - n)
8 = -16 / (-1 - n)
8(-1 - n) = -16
-1 - n = -16/8
-1 - n = -2
-n = -2 + 1
-n = -1
n = 1
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PLS HELP
What similarity property can be used to show that triangles ABC and DEF are similar?
Given
Answers
The similarity property that can be used for the triangles is SAS.
How to determine the similarity property?The congruence of any two figures is generally understood as two figures which can perfectly overlap each other. Congruent triangles are triangles that are perfect copies of one another. Various congruence rules are used to prove the congruency in two triangles
One of the conditions that make triangles congruent is:
if the two sides and the included angle of one triangle are respectively equal to the two sides and the included angle of the other( SAS).
Considering the given image:
If two triangles ABC and DEF are drawn in which AB/DE = AC/DF and the included angles <A and <D are equivalent i.e. <A ≅ <D
Since the two sides and the included angle of ΔABC are respectively equal to the two sides and the included angle of the ΔDEF
Therefore, the similarity property that can be used is SAS. The 3rd option is the answer
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If you are adding two fractions that are both less then 1/2 what must be true about the sum? Give three examples to support your thinking
Answers
Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.
What is fractions?A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.
Given data
The fractions can be represented as follows;
x < ½ and y < ½
The sum of both of the inequalities is;
x + y < (\(\frac{1}{4}\)) + (\(\frac{1}{4}\))
x + y < ½
Examples are-
\(\frac{1}{5}\)+ \(\frac{2}{3}\) =\(\frac{13}{15}\)
¼ + ½ = ¾
\(\frac{1}{2}\) +\(\frac{1}{3}\) = \(\frac{5}{6}\)
Therefore, Addition of two fractions which are both less than (1/2) must result in a fraction which is always less than 1.
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(L5) Theorem 5.5B states that if the measure of one angle of a triangle is greater than the measure of another angle, then the side __________ he angle with the greater measure will be longer than the side opposite the angle with the __________ measure.
Answers
Theorem 5.5B is a helpful theorem that relates the measures of angles in a triangle to the lengths of the sides opposite those angles. Specifically, it states that if one angle in a triangle has a greater measure than another angle, then the side opposite the angle with the greater measure will be longer than the side opposite the angle with the smaller measure.
This theorem can be useful in a variety of situations, such as when solving for unknown side lengths or angles in a triangle.
To understand why this theorem works, it can be helpful to think about the relationship between the measures of angles and the lengths of sides in a triangle. For example, we know that in any triangle, the sum of the measures of the three angles is always 180 degrees. We also know that the length of one side of a triangle is related to the measures of the angles opposite that side, according to the Law of Sines or the Law of Cosines.
Using these relationships, we can see why Theorem 5.5B makes sense. If one angle in a triangle is larger than another angle, then the remaining angle must be smaller to ensure that the sum of the angles adds up to 180 degrees. This means that the side opposite the larger angle must be longer than the side opposite the smaller angle, since the length of a side is related to the measure of the angle opposite that side.
In summary, Theorem 5.5B provides a helpful way to relate the measures of angles and the lengths of sides in a triangle. By understanding this theorem, we can solve problems involving unknown side lengths or angles with greater ease and accuracy.
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