Answer:
5^20
Step-by-step explanation:
since you have brackets around (5^5) you can multiply the exponents. if you think about it what you're essentially doing is
(5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) * (5 * 5 * 5 * 5 * 5) *
(5 * 5 * 5 * 5 * 5)
which is why you can multiply the exponents to simplify
Need help (pic included)
The value of the coefficient of xy is 0.
What is an algebraic expression?It is an expression made of numbers and letters where the numbers are called coefficient.
Analysis:
(ax+by)(cx-dy)
ac[tex]x^{2}[/tex] -adxy +bcxy -bd[tex]y^{2}[/tex]
But, ac = 18, ad=bc, bd = 50
18[tex]x^{2}[/tex] -xy(bc -ad) - 50[tex]y^{2}[/tex]
since bc = ad, the coefficient of xy = 0
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Find the indicated side of the
right triangle.
30°
X
X
60
= [?]√]
7
Enter
Answer:
[tex]7\sqrt{3}[/tex]
Step-by-step explanation:
This is a special triangle with the angles being 30-60-90. The adjacent side to the angle of 30 degrees has a length of x * sqrt(3). The opposite side has a length of x. Since the opposite side has a length of 7 here you simply plug that into x * sqrt(3) to find the length of the adjacent side of the angle 30 degrees which gives you 7 * sqrt(3)
What is the effect on the graph of f(x) = x² when it is transformed to
h(x)=x²-16?
A. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units down.
B. The graph of f(x) is horizontally compressed by a factor of 7 and
shifted 16 units down.
C. The graph of f(x) is vertically compressed by a factor of 7 and
shifted 16 units to the right.
D. The graph of f(x) is horizontally stretched by a factor of 7 and
shifted 16 units to the right.
The correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
What is a graph?
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given functions are:-
f(x) = x²h(x)=x²-16When we plot the graph of the two functions given in the question we will see that the graph of the function F(x) = x²-16 is compressed by the factor 7 and the vertex of the graph shifted to the 16 points down.
Therefore the correct answer is option A which is the graph of f(x) is vertically compressed by a factor of 7 and shifted 16 units down.
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On Tuesday, a city’s parking meter income is up $311 from Monday’s income, m. So, Tuesday’s income is m + 311
If m is 894, what is m + 311
Chocolate cost $1.50 and was paid for with $5 which three coins were given as change
Answer: $3.5
Step-by-step explanation:
If a product cost $1.50 and you paid $5, the change will be equal to
$5 - $1.50 = $3.5 for change
please narrate every step you make and make a 2 column proof!
thank you!!
Hang on ,it is already proven through given .
So The proof is of one line only
ray FEH bisects <DFG (Given)Hence proved .
Find the Value of log10 (0.0001). Rescue me!
Let's see
[tex]\boxed{\sf log_aa=1}[/tex]
Now
[tex]\\ \rm\Rrightarrow log_{10}0.0001)[/tex]
[tex]\\ \rm\Rrightarrow log_{10}10^{-4}[/tex]
[tex]\\ \rm\Rrightarrow -4log_{10}10[/tex]
[tex]\\ \rm\Rrightarrow -4[/tex]
Answer:
This has already been answered correctly, but I'll add an additional perspective. The log of (0.0001 to the base 10 is -4.
Step-by-step explanation:
log(base 10) says give us an exponent, x, that would be required to make [tex]10^{x}[/tex] equal to a specified number, in this case 0.0001.
[tex]10^{0}[/tex] = 1
[tex]10^{1}[/tex] = 10
[tex]10^{-1}[/tex] = 0.1
[tex]10^{-2}[/tex] = 0.01
[tex]10^{-4}[/tex] = 0.0001
The log of (0.0001) to the base 10 is -4.
(Giving 80 points, Please do not answer if you don't know. The second and third answer are not 4 btw)
Point A is on the point −6 and Point B is on the point 0. Let's use the Ruler Postulate to find the length of AB¯¯¯.
AB=|a−b|
AB=|−6−0|
AB=|−6|
AB=6
The length of AB¯¯¯¯ is 6. We can also write this as AB=6 or mAB¯¯¯¯=6.
Find the Length of CD¯¯¯¯
Now, let's find the length of CD¯¯¯¯. Point C is on the point 4 and Point D is on the point 8.
CD=|c−d|
CD=|4−8|
CD=|−4|
CD=4
The length of CD¯¯¯ is 4. We can also write this as CD=4 or mCD¯¯¯=4
Your Turn
1. What is the length of BC¯¯¯? 4
2. What is the length of AC¯¯¯¯?
3. What is the length of AD¯¯¯¯?
Answer:
1. 4
2. 10
3. 14
Step-by-step explanation:
A = -6
B = 0
C = 4
D = 8
1. BC = |0 - 4| = 4
2. AC = |-6 - 4| = |-10| = 10
3. AD = |-6 - 8| = |-14| = 14
Answer:
1. BC = 4
2. AC = 10
3. AD = 14
Step-by-step explanation:
Ruler Postulate
The distance between any two points on a number line is their difference.
Question 1
Given:
Point B = 0Point C = 4Therefore, using the Ruler Postulate:
⇒ BC = |b - c|
⇒ BC = |0 - 4|
⇒ BC = |-4|
⇒ BC = 4
Question 2
Given:
Point A = -6Point C = 4Therefore, using the Ruler Postulate:
⇒ AC = |a - c|
⇒ AC = |-6 - 4|
⇒ AC = |-10|
⇒ AC = 10
Question 3
Given:
Point A = -6Point D = 8Therefore, using the Ruler Postulate:
⇒ AD = |a - d|
⇒ AD = |-6 - 8|
⇒ AD = |-14|
⇒ AD = 14
answer?......................
Answer:
22
Step-by-step explanation:
6( n^2 +2)
-----------------
n
Let n = 3
6( 3^2 +2)
-----------------
3
Parentheses first
6( 9 +2)
-----------------
3
6( 11)
-----------------
3
Top of the fraction next
66
-----
3
Divide
22
The length of a spring varies directly with the mass of an object that is attached to it. When a 30-gram object is attached, the spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s? a s = StartFraction 3 Over 10 EndFraction m b s = StartFraction 10 Over 3 EndFraction m c m = StartFraction 3 Over 10 EndFraction s d m = StartFraction 1 Over 30 EndFraction s
The equation which relates the mass and length according to the task content is; l = (3/10)m.
What is the equation of proportionality?From the task content, it follows that the proportional relationship is direct. Hence, the constant of proportionality k can be evaluated as follows;
l = k × m
Hence, k = l/m = 9/30 = 3/10.
Therefore, the proportional relationship is given by the equation; l = (3/10)m
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Drag each tile to the correct location. The labels can be used more than once.
Match each polynomial expression with its degree.
0, 1, 2
The degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.
What is the degree of a polynomial?
The degree of the polynomial is defined as the highest power of the variable of the given polynomial or it is the maximum power of the polynomial.
The degree of the given expressions are shown as follows:-
(x-9) → degree 1,
(-4x²-6x+9) → degree 2,
(x²-2x+9) → degree 2,
(-3) → degree 0,
(3x-2) → degree 1,
(6x+2) → degree 1
(5) → degree 0.
Therefore the degrees of each expression will be (x-9) degree 1, -4x²-6x+9 degree 2, x²-2x+9 degree 2, -3 degree 0, 3x-2 degree 1, 6x+2 degree 1 and 5 degree 0.
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I'm gonna need so help
Answer:
-4 and -6 are the answers
Give me the hardest math equation you know and solve it
(Beware, if you joke and waste the points, I will not be very happy!)
1B + 26M - 26K
Answer That!! Hehehehe
Help i need it What is the product?
Answer:
[tex]12x^9+15x^8 -8x^6-10x^5[/tex]
Step-by-step explanation:
[tex]~~(x^4)(3x^3 -2)(4x^2 +5x)\\\\=(3x^7-2x^4)(4x^2 +5x)\\\\=12x^9+15x^8 -8x^6-10x^5[/tex]
Topic: Speed
Subject: Mathematics
Answer the Question
Q1: Express each of the following in km/h
a: 8.4 km/min b: 315 m/s
c: 242 m/min d: 125 cm/s
Hope this helps you
........
PLEASE ANSWER ASAP!!!!!!
The function f(x)=−6sin(7/3x+1/6)−5 models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit.
Over what range of temperatures does the average rate of change in temperature fall?
Enter a value in each box to correctly complete the statement.
The range in the average rate of change in temperature of the substance is from a low
temperature of ____ F to a high of ________ F
The range in the average rate of change in temperature of the substance is from a low temperature of 1 F to a high of -11 F.
What is a formula for Fahrenheit?The conversion formula for a temperature that is expressed on the Celsius (°C) scale to its Fahrenheit (°F) ;
°F = (9/5 × °C) + 32.
Given function:
f(x)= -6 sin(7/3 x+ 1/6) -5
The function will be maximum at the 7/3 x +1/6= 3π/2
So, the maximum temperature will be
= -6 sin (3π/2) -5
= 6 -5
= 1 F
The function will be minimum at the 7/3 x +1/6= π/2
Therefore, the maximum temperature will be
= -6 sin (π/2) - 5
= -6 -5
= -11 F
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the gomez family drove 476 miles in 7 hours. what was their average speed, in miles per hour?
The average speed is 68 miles per hour
How to determine the average speed?The given parameters are:
Distance = 476 miles
Time = 7 hours
The average speed is calculated as:
Speed = Distance/Time
So, we have:
Speed = 476 miles/7 hours
Evaluate
Speed = 68 miles per hour
Hence, the average speed is 68 miles per hour
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Pls help asap ily
one hour after junior space cadet had left his house, his sister gwen discovered that he had forgotten his head. if junior was driving at a speed of 50 mph, and gwen drove at a speed of 75 mph, how many hours did it take gwen to restore junior's head to his shoulders?
Answer:
2 hours
Step-by-step explanation:
you can write two linear equations and then set them equal to each other to see when they intersect. so for the first equation which will be representing the junior space cadets distance from his house. this can be written as
d = 50t + 50
where t represents time and d represents distance. there is 50 being added to the equation since he had already been traveling for an hour
the second equation which will represent his sister Gwen can be represented as
d = 75t
Now we set them equal to each other
50t + 50 = 75t
50 = 25t
2 = t
Calculate the AREA of the shape below. Give your answer in cm²
Answer:
[tex] \boxed{\bf 26\: cm^2} [/tex]Step-by-step explanation:
We got two shapes in the given figure,on the right we got a rectangle and on the left we have a square.
Area of rectangle:-
[tex]\bf 5 \times 2[/tex][tex]\bf 10 \:cm^{2} [/tex]Area of square :-
[tex]\bf 4 \times 4[/tex][tex]\bf 16 \: {cm}^{2} [/tex]Total area :-
[tex]\bf 10 + 16[/tex][tex]\boxed{\bf 26 \: {cm}^{2} }[/tex]_________________________Answer:
26 cm^2Step-by-step explanation:
you have two rectangles, the bigest has the base of 6cm and the height of 4cm, the area is 6 * 4 = 24cm ^ 2, the other rectangle has the base of 6 - 4 = 2 and the height of 5 - 4 = 1, 2*1=2.
we add the dimensions and we have the area of the complete figure 24 + 2 =
26 cm ^ 2
How many feet of fencing will George need for the dog run?
22 feet
68 feet
76 feet
82 feet
George will need to do 76 ft. of fencing , Option C is the correct answer.
What is a Rectangle ?A rectangle is a polygon with four sides , angles and vertices , the opposite sides are parallel and equal.
Area of the dog run = 240 sq.ft
Length of the run is 30 ft
Width is 30-x ft.
Area of a Rectangle = Length * Width
240 = 30 * (30-x)
8 = 30 -x
x = 22 ft.
Width is (30-220 = 8)
The perimeter of the rectangle is = 2(Length + Width )
Perimeter = 2( 30 +8)
Perimeter = 2 * 38 = 76 feet
Therefore George will need to do 76 ft. of fencing.
The complete question is
George is building a fence around a rectangular dog run. He is using his house as one side of the run. The area of the dog run will be 240 square feet. The length of the run is 30 feet, and the width is (30 minus x) feet. The diagram below shows his plan. Recall the formulas for area and perimeter: A = lw and P = 2l + 2w. A rectangle labeled How many feet of fencing will George need for the dog run? 22 feet 68 feet 76 feet 82 feet
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Answer:
late a-s-f but 68 ft
Step-by-step explanation:
A 2-column table with 6 rows. The first column is labeled t with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries negative 12, m, 4, 0, negative 4, negative 2. If the table of the function contains exactly two potential turning points, one with an input value of –1, which statement best describes all possible values of m? m ≥ –12 –12 < m < 4 m ≤ 4 m ≥ 4 or m ≤ –12
Answer:
B
Step-by-step explanation:
right on edg3
can someone please help and explain its due in a littleee
[tex]f(x) = {x}^{2} - 3x + 2 [/tex]
••••••••••••••••••••••••••••••••••••••••put x = (-1)
[tex] f( - 1) = {( - 1)}^{2} - 3 \times ( - 1) + 2 \\ \\ 1 + 3 + 2 \\ \\ 6.[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (z)
[tex] f(z) = {z}^{2} - 3 \times z + 2 \\ \\ {z}^{2} - 3z + 2 \\ \\ {z}^{2} - 2z - z + 2 \\ \\ z(z - 2) - 1(z - 2) \\ \\ (z - 1)( z -2 ) \\ \\ (z - 1) = 0 \: \: , \: \: (z - 2) = 0\\ \\ z = 1 \:, \: 2[/tex]
••••••••••••••••••••••••••••••••••••••••put x = (x+1)
[tex]f(x + 1) = {x}^{2} - 3x + 2 \\ \\ {(x + 1)}^{2} - 3 (x + 1) + 2 \\ \\ {x}^{2} + 1 + 2x - 3x - 3 + 2 \\ \\ {x}^{2} - x \\ \\ x(x - 1) \\ \\ x(x - 1) = 0 \\ \\ x - 1 = \frac{0}{x} \\ \\ x - 1 = 0 \\ \\ x = 1.[/tex]
•••••••••••••••••••••••••••••••••put x = (√2 + 1 )
[tex]f( \sqrt{2} + 1) = {x}^{2} - 3x + 2 \\ \\ {( \sqrt{2} + 1) }^{2} - 3( \sqrt{2} + 1) + 2 \\ \\ 2 + 1 + 2\sqrt{2} - 3 \sqrt{2} - 3 + 2 \\ \\ 3 - 1 \sqrt{2} - 1 \\ \\ 2 - \sqrt{2} \\ \\ 2 - 1.4 (optional \: \: \: steps)\\ \\ 0.6 \: \: [/tex]
Help me with steps please!
Answer:
18, 36, 54
Step-by-step explanation:
Find the least common multiple of 6 and 9:
Multiples of 6: 6, 12, 18, ......
Multiples of 9: 9, 18, 27, ......
We see that 18 is the least common multiple of 6 and 9.
Additional multiples of 18 are 36 and 54.
If an integer is divisible by 6 and by 9 , then the integer must be divisible by 54.
How to estimate an integer which is divisible by 6 and by 9?Consider the statement as a contradiction.
The assertion exists that any natural number divisible by 6 and 9 exists also divisible by 54.
Let us consider divisible to mean that the outcome of the division of the number and 54 provides another natural number. We can take the prime factors of 6 and 9 which are {2,3} and {3,3}. We can consider that the product [tex]$2 \times 3 \times 3=18$[/tex] exists a number that exists divisible by 6 and 9 but exists not divisible by 54. Another instance exists the product of [tex]$2 \times 2 \times 3 \times 3=36$[/tex] which exists also not divisible by 54.
Therefore, the correct answer is option e) 54.
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A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?
A circle of radius 1 is inscribed within a square. What is the probability that a randomly-selected point with the square is also within the circle?
[tex] {p}^{2} > {p}^{2} \: \: and \: \: p {1}^{2} - \: p {2}^{2} \: < \frac{1}{3} [/tex]
Step-by-step explanation:
HOPE ITS HELP
Which statement is true about the ordered pair (3 , 4)? A. To plot the ordered pair (3 , 4), travel four units to the right on the y-axis and three units up on the x-axis, from the origin. B. To plot the ordered pair (3 , 4), travel four units to the right on the x-axis and three units up on the y-axis, from the origin. C. To plot the ordered pair (3 , 4), travel three units to the right on the x-axis and four units up on the y-axis, from the origin. D. To plot the ordered pair (3 , 4), travel three units to the right on the y-axis and four units up on the x-axis, from the origin.
Answer:
C. To plot the ordered pair (3 , 4), travel three units to the right on the x-axis and four units up on the y-axis, from the origin.
Step-by-step explanation:
Which statement is true about the ordered pair (3, 4)?
A. To plot the ordered pair (3 , 4), travel four units to the right on the y-axis and three units up on the x-axis, from the origin.
The y-axis is the vertical line you can't go left or right, you go up or down
Hence this answer is NOT correct
B. To plot the ordered pair (3 , 4), travel four units to the right on the x-axis and three units up on the y-axis, from the origin.
The coordinates of a point is (x, y) where x = 3 and y = 4 so moving right 4 units is wrong as x = 3
Hence this answer is NOT correct
C. To plot the ordered pair (3 , 4), travel three units to the right on the x-axis and four units up on the y-axis, from the origin.
three units to the right on the x-axis
four units up on the y-axis
Hence this answer is the correct
D. To plot the ordered pair (3 , 4), travel three units to the right on the y-axis and four units up on the x-axis, from the origin.
y does not equal 3 and you cant move right or left on the y-axis
Hence this answer is NOT correct
what 1 - 2/9 - 1/3 - 1/6 =
Answer:
5/18
Step-by-step explanation:
The LCD of 9, 3, and 6 is 18.
1 - 2/9 - 1/3 - 1/6 =
= 18/18 - 4/18 - 6/18 - 3/18
= 5/18
Answer: 5/18
Step-by-step explanation:
1/1 - 2/9 - 1/3 - 1/6
18 - 4 - 6 - 3/18
5/18
Drag each tile to the correct box. The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below. A graph represents the water level to fill the tank on Y-axis per time on X-axis. Segments A, B, and C fill the tank from 10 to 60, 60 to 80, and 80 to 110 centimeters in the first 2, next 4, and last 3 minutes. Place the segments in the correct order from the least to the greatest rate of increase in the water level. B A C , ,
The least to greatest slope, the segments are B, C and A.
Given that,
Segments A, B, and C on the graph below represent the water level of the tank every minute since it started filling.
A graph shows the water level needed to fill the tank on the y axis per unit of time on the x axis.
The segment's slope indicates how quickly the water level is rising. The slope, which is determined by the segment's angle with the positive x axis, is the ratio of rise to run.
slope of segment A = 60₋10/2 = 25
slope of segment B = 80₋60/4 = 5
slope of segment C = 110₋80/3 = 10
We can see that section B has the least slope, followed by segment C, and then segment A, which has the greatest slope.
B, C, and A are the segments in descending order of least to greatest slope.
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(x+y)(x+6y) pls help me solve question pls and pls also give explanation if possible
Step-by-step explanation:
[tex] = (x + y)(x + 6y)[/tex]
[tex] = x \times x + x \times 6y + y \times x + y \times 6y[/tex]
[tex] = {x}^{2} + 6xy + xy + 6 {y}^{2} [/tex]
[tex] = {x}^{2} + 7xy + 6 {y}^{2} [/tex]
Shreya and Shanice are selling pies for a
school fundraiser. Customers can buy
blueberry pies and lemon meringue pies.
Shreya sold 4 blueberry pies and 2 lemon
meringue pies for a total of $76. Shanice
sold 4 blueberry pies and 13 lemon
meringue pies for a total of $230. What is
the cost each of one blueberry pie and
one lemon meringue pie?
Answer:
$26
Step-by-step explanation:
Let blueberry pies = x and lemon pies = y.
4x + 13y = 230
4x + 2y = 76
Using elimination, we see that 11y = 154. Therefore, y = 14.
4x + 2(14) = 76
4x + 28 = 76
4x = 48
x = 12
x + y = 12 + 14 = 26.
$26 is your answer.
Answer:
Step-by-step explanation:
Let B be the price of a blueberry pie. Let L be the price of a lemon meringue pie.
We are told that Shreya makes a total of $76 by selling 4 blueberry and 2 lemon meringue pies. This can be made into an equation:
Shreya: 4B + 2L = $76
We also learn that Shanice is doing particularly well:
Shanice: 4B + 13L = $320
We want to determine the prices for each type of pie, B and L. We have two equations and two unknowns. That means we should be able to find the answers by substitution.
Rearrange Shreya's equation to isolate B:
Shreya: 4B + 2L = $76
4B = $76 - 2L
B = ($76-2L)/4
Now use this definition of B in Shanice's equation:
Shanice: 4B + 13L = $320
4( ($76-2L)/4) + 13L = $320
($76-2L) + 13L = $320
11L = 244
L = $22.18
Use L = $22.18 in either equation and solve for B:
4B + 2L = $76
4B + 2*($22.18) = $76
4B = $31.64
B = $7.91
---
Blueberry pies are $7.91 each.
Lemon meringue pies are $22.18 each
=========
CHECK: Do these prices provide the correct sales for each person?
Price($/pie) Shreya Shanice
Blueberry 7.91 4 4
Lemon Mer. 22.18 2 13
Blueberry Sales ($) 31.64 31.64
Lemon Mer. Sales ($) 44.3 288.36
Total Sales $76 $320
YES - These prices account for each person's sales.
In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that apply.
m∠R > 90°
m∠S + m∠T < 90°
m∠S = m∠T
m∠R > m∠T
m∠R > m∠S
m∠S > m∠T
Answer:
1. m∠R > 90°
2. m∠S + m∠T < 90°
4. m∠R > m∠T
5. m∠R > m∠S
Step-by-step explanation:
General strategyprove the statement starting from known facts, ordisprove the statement by finding a counterexampleHelpful fact: Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.
Option 1. m∠R > 90°
Start with m∠R > m∠S + m∠T.
Adding m∠R to both sides of the inequality...
m∠R + m∠R > m∠R + m∠S + m∠T
There are two things to note here:
The left side of this inequality is 2*m∠RThe right side of the inequality is exactly equal to the Triangle Sum Theorem expression2* m∠R > 180°
Dividing both sides of the inequality by 2...
m∠R > 90°
So, the first option must be true.
Option 2. m∠S + m∠T < 90°
Start with m∠R > m∠S + m∠T.
Adding (m∠S + m∠T) to both sides of the inequality...
m∠R + (m∠S + m∠T) > m∠S + m∠T + (m∠S + m∠T)
There are two things to note here:
The left side of this inequality is exactly equal to the Triangle Sum Theorem expressionThe right side of the inequality is 2*(m∠S+m∠T)Substituting
180° > 2* (m∠S+m∠T)
Dividing both sides of the inequality by 2...
90° > m∠S+m∠T
So, the second option must be true.
Option 3. m∠S = m∠T
Not necessarily. While m∠S could equal m∠T, it doesn't have to.
Example 1: m∠S = m∠T = 10°; By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.
Example 2: m∠S = 15°, and m∠T = 10°; By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.
So, option 3 does NOT have to be true.
Option 4. m∠R > m∠T
Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.
Add m∠T to both sides.
(m∠S) + m∠T > (0) + m∠T
m∠S + m∠T > m∠T
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠T.
So, option 4 must be true.
Option 5. m∠R > m∠S
Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.
Add m∠S to both sides.
m∠S + (m∠T) > m∠S + (0)
m∠S + m∠T > m∠S
Recall that m∠R > m∠S + m∠T.
By the transitive property of inequalities, m∠R > m∠S.
So, option 5 must be true.
Option 6. m∠S > m∠T
Not necessarily. While m∠S could be greater than m∠T, it doesn't have to be. (See examples 1 and 2 from option 3.)
So, option 6 does NOT have to be true.
Answer: Option 1, 2, 4, & 5 or
A. m∠R > 90°; B. m∠S + m∠T < 90°; D. m∠R > m∠T; & E. m∠R > m∠S
Step-by-step explanation: Trust Me!
m∠R > 90°m∠S + m∠T < 90°m∠R > m∠Tm∠R > m∠S
If you are working on Edge the answer is correct. The proof is down below. I hope someone finds this helpful.
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