Answer:
True
Step-by-step explanation:
A chord of a circle is a straight line segment whose endpoints both lie on the circle.
Vertical Angles are the angles opposite each other when two lines cross.
Any intersecting segments (chords or not) form a pair of congruent, vertical angles.
Attachment Below, please help, I'm not timed
Answer:
Step-by-step explanation:
x + 2x + 4x = 49
7x = 49
x = 7
2(7)= 14 hours he worked on Wednesday
PLEASE!!! HELP!!! Question: If you have points on a graph that plot (1,7), (2,8), (3,5) and (4,6) what would be the slope?
Answer:
1
Step-by-step explanation:
You only need two points to find the slope.
Let's use (1,7) and (2,8).
The formula for slope is (y2-y1)/(x2-x1)
Let's plug the values in:
(8-7)/(2-1) = 1.
So, the slope is 1.
Karl set out to Alaska on his truck.
The amount of fuel remaining in the truck's tank (in liters) as a function of distance driven (in kilometers) is
graphed.
How much fuel did the truck consume every 100 kilometers
Answer:
the amount of fuel consumed every 100 kilometers is 62.5 litres.
Step-by-step explanation:
To determine the amount of fuel consumed every 100 kilometers.
Note: since the graph is a straight line graph (linear graph) the amount of fuel consumed every 100 kilometers is constant (i.e the same for every 100 kilometers). So, we only need to derive the amount of fuel consumed any 100 kilometers on the graph.
From the graph, the amount of fuel consumed for the first 100 kilometers is;
[tex]F = F_0 - F_{100} .........................1[/tex]
[tex]F_0 = 500\\F_{100} \simeq 437.5\\[/tex]
substituting into equation 1.
[tex]F = F_0 - F_{100} \\F = 500 - 437.5\\ F = 62.5 litres\\[/tex]
Therefore, the amount of fuel consumed every 100 kilometers is 62.5 litres.
Answer:500
Step-by-step explanation:got it on Kahn
Find the missing side lengths. Leave your answers as radicals in simplest form.
ANSWER QUICK
Answer:
C
Step-by-step explanation:
It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.
Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.
3^2 is 9 so you get 18
the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18
Hope this helps!
There are blue, red and green pencils in the box—20 pencils total. There are 6 times more green pencils than blue pencils. There are fewer red pencils than green pencils. How many pencils do you need to take out of the box in order to get at least one red pencil among them?
Answer:
15
Step-by-step explanation:
Try 1, 2, 3, or 4 blue pencils. Then green is 6 times as many. Red must be the rest to make up 20 total.
No. of blue No. of green No. of red
1 6 13
2 12 6
3 18 -1
You can't have 3 blue pencils because 3 blue + 18 green = 21 pencils, and there are only 20.
If you have 1 blue and 6 green, then there must be 13 red, but red must be less than green, and 13 is not less than 6.
The only possibility is
2 blue, 12 green, 6 red
If you start taking out pencils, when you take out the first 14 they may be all blues or green, so only when you take out the 15th pencil do you know for sure there must be 1 green pencil.
Please Help!! I will give brainliest to correct answer
A carpool service has 2,000 daily riders. A one-way ticket costs $5.00. The service estimates that for each $1.00 increase to the one-way fare, 100 passengers will find other means of transportation. Let x represent the number of $1.00 increases in ticket price.
Choose the inequality to represent the values of x that would allow the carpool service to have revenue of at least $12,000. Then, use the inequality to select all the correct statements.
options:-
The price of a one-way ticket that will maximize revenue is $7.50.
The price of a one-way ticket that will maximize revenue is $12.50.
-100x^2 + 1,500x + 10,000 >/= 12,000
The maximum profit the company can make is $4,125.00.
The maximum profit the company can make is $15,625.00.
100x^2 - 1,500x - 10,000 >/= 12,000
100x^2 + 1,500x - 10,000 = 12,000
(There can be more than one correct answers)
Answer.
Step-by-step explanation:
A rectangle with an area of 192 square meters has a length and width in a ratio of 3:1. What are the length and width?
Answer:
Step-by-step explanation:
let width=x
length=3x
area=3x×x=3x²
3x²=192
x²=192/3=64
x=√64=8
width=8 m
length=3×8=24 m
Answer:
Length= 24 meterWidth= 8 meterSolution,
Let the length be 3x meter.
Let the width be X meter
Area of rectangle= 192 square metres
Now,
Area of rectangles= length * breath
[tex]192 = 3x \times x \\ 192 = 3 {x}^{2} \\ {x}^{2} = \frac{192}{3} \\ x^{2} = 64 \\ x = \sqrt{64} \\ x = 8 \: meter[/tex]
Width = 8 meterReplacing value,
Length= 3x[tex] \: \: \: 3 \times x \\ \: \: = 3 \times 8 \\ \: \: \: \: = 24[/tex]
Length= 24 meter.Hope this helps...
Good luck on your assignment...
8. Evelyn flips three coins simultaneously. The theoretical probability that only two of the coins will turn up heads is. If Evelyn flips the three coins simultaneously 200 times, how many times can
she expect only two heads to turn up?
Answer:
134 will be heads.
Step-by-step explanation:
200÷3 = 66.66
Round that of to the nearest whole number = 67
67 x 2 = 134
Answer:
75
Step-by-step explanation:
i took the semester exam
Construct perpendiculars image below
Answer: draw a straight line trough point B, same thing with the second one,for the third you must draw a straight line from the angle across to the segment. (make sure all of the intersections are 90 degrees
Differentiate... How to solve this type of problem? y = cos^2(x^2 + x^3)
Answer:
[tex]\frac{d y}{d x} = - (2 x + 3 x^{2} )sin2(x^{2} +x^{3})[/tex]
Step-by-step explanation:
Step(i):-
Given y = cos² (x² + x³) ....(i)
By using differentiation formulas
a) [tex]\frac{d}{dx} (cosx) = -sinx[/tex]
b) [tex]\frac{d}{dx} (x^{n} ) = n x ^{n-1}[/tex]
Step(ii):-
Differentiating equation (i) with respective to 'x'
First apply formula [tex]\frac{d}{dx} (x^{n} ) = n x ^{n-1}[/tex]
[tex]\frac{d y}{d x} = 2 cos (x^{2} +x^{3} )^{2-1} \frac{d}{d x} (cos(x^{2} +x^{3})[/tex]
Now we will apply formula
[tex]\frac{d}{dx} (cosx) = -sinx[/tex]
[tex]\frac{d y}{d x} = 2 cos (x^{2} +x^{3} ) (-sin(x^{2} +x^{3})\frac{d}{dx} (x^{2} +x^{3} )[/tex]
Again apply formula [tex]\frac{d}{dx} (x^{n} ) = n x ^{n-1}[/tex]
[tex]\frac{d y}{d x} = 2 cos (x^{2} +x^{3} ) (-sin(x^{2} +x^{3}) (2 x + 3 x^{2} )[/tex]
[tex]\frac{d y}{d x} = -2 sin (x^{2} +x^{3} ) cos(x^{2} +x^{3}) (2 x + 3 x^{2} )[/tex]
we know that trigonometric formulas
Sin 2θ = 2 sinθ cosθ
[tex]\frac{d y}{d x} = -sin2(x^{2} +x^{3}) (2 x + 3 x^{2} )[/tex]
Final answer:-
[tex]\frac{d y}{d x} = - (2 x + 3 x^{2} )sin2(x^{2} +x^{3})[/tex]
What's the standard equation of the circle with the general equation x2 + y2 + 4x – 2y – 20 = 0? answers: 1) (x + 2)2 + (y – 1)2 = 5 2) (x – 2)2 + (y + 1)2 = 25 3) (x + 1)2 + (y – 2)2 = 5 4) (x + 2)2 + (y – 1)2 = 25
Answer:
4). (x + 2)^2 + (y - 1)^2 = 25.
Step-by-step explanation:
x^2 + y^2 + 4x - 2y - 20 = 0
x^2 + 4x + y^2 - 2y = 20
Completing the square on the x and y terms:
(x + 2)^2 - 4 + (y - 1)^2 - 1 = 20
(x + 2)^2 + (y - 1)^2 = 20 + 4 + 1
(x + 2)^2 + (y - 1)^2 = 25.
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x₁, y₁) and radius r is (x-x₁)²+(y-y₁)²=r²
The given circle equation is x²+ y²+4x-2y-20=0.
Here, x²+ y²+4x-2y=20
By completing the square on the x and y terms:
Now, add 4 on both the sides of an equation, we get
x²+ y²+4x-2y+4=20+4
x²+4x+4+y²-2y=24
Add 1 on both the sides of an equation, we get
(x+2)²+y²-2y+1=24+1
(x+2)²+(y-1)²=25
The standard equation of the circle with the given equation is (x+2)²+(y-1)²=25. Therefore, option 4 is the correct answer.
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Find the volume of a right circular cone that has a height of 18.8 in and a base with a
diameter of 14.3 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
The volume of the cone is 1006.9in³
Step-by-step explanation:
Given
[tex]Height = 18.8\ in[/tex]
[tex]Diameter = 14.3\ in[/tex]
Required
Calculate the volume;
The volume of a cone is calculated as thus;
[tex]V = \frac{1}{3} \pi r^2h[/tex]
Where V represents volume; r represents radius; and h represents height
The radius is calculated as thus;
[tex]r = \frac{1}{2}Diameter[/tex]
[tex]r = \frac{1}{2} * 14.3[/tex]
[tex]r = 7.15[/tex]
Substitute [tex]r = 7.15[/tex]; [tex]h = 18.8[/tex] and [tex]\pi = \frac{22}{7}[/tex]
[tex]V = \frac{1}{3} \pi r^2h[/tex] becomes
[tex]V = \frac{1}{3} * \frac{22}{7} * 7.15^2 * 18.8[/tex]
[tex]V = \frac{1}{3} * \frac{22}{7} * 51.1225 * 18.8[/tex]
[tex]V = \frac{22* 51.1225 * 18.8}{3 * 7}[/tex]
[tex]V = \frac{21144.266}{21}[/tex]
[tex]V = 1006.86980952[/tex]
[tex]V = 1006.9\ in^3[/tex] (Approximated)
Hence, the approximated volume of the cone is 1006.9in³
Answer:1006.5
Step-by-step explanation:
Helpppppppppppppp !!!
Answer:
a) 8
b) 2 1/4 hours
c) 4 7/8 hours
d) 4 1/8 hours
Step-by-step explanation:
a) LCD to be used to solve this problem is calculated as the Lowest common denominator of the above mixed fractions.
We have 1 1/2 hours and 1 1/8 hours
The lowest common denominator is the denominator calculated by
Multiplying the two denominators together and dividing by the common factor of the two denominators
Hence , we have
2 × 8 = 16
The common factor of 2 and 8 = 2
LCD = 16/2 = 8
b) How long did Matt drive?
We are told that Matt drove twice as long as John
John drove for 1 1/8 hours
Hence, the number of hours that Matt drove for =2 × 1 1/8
= 2 × 9/8 = 9/4 hours = 2 1/4 hours
c) How long the Sam, John and Matt drive ?
We are told in the question that
Sam drove for 1 1/2 hours
John drove for 1 1/8 hours
Matt drove for 2 1/4 hours
We would sum up the number of hours that each of them drove.
1 1/2 + 1 1/8 + 2 1/4
The Lowest common multiple of denominators is 8
= (1 + 1 + 2)( 4 + 1 +2/8)
= 4(7/8)
= 4 7/8 hours
d) How many hours is left for Bob to drive
We are told that the entire journey = 9 hours
The number of hours Sam, John and Matt drove for has been calculated in question c as 4 7/8 hours
The number of hours Bob will drive for is calculated as
9 hours - 4 7/8 hours
= 4 1/8 hours
Find the missing segment in the attached image
Answer:
The length of the missing segment is 36
Step-by-step explanation:
Given
The figure above
Required
Determine the missing segment
Let the missing segment be represented with x
Given that, there exist parallel lines between the two triangles;
The relationship between the sides of the triangles is as follows;
[tex]\frac{20}{24} = \frac{30+20}{24+x}[/tex]
[tex]\frac{20}{24} = \frac{50}{24+x}[/tex]
Cross Multiply
[tex]20 * (24 + x) = 24 * 50[/tex]
[tex]20 * (24 + x) = 1200[/tex]
Divide both sides by 20
[tex]\frac{20 * (24 + x)}{20} = \frac{1200}{20}[/tex]
[tex](24 + x)= \frac{1200}{20}[/tex]
[tex]24 + x= 60[/tex]
Subtract 24 from both sides
[tex]24 - 24 + x = 60 - 24[/tex]
[tex]x = 60 - 24[/tex]
[tex]x = 36[/tex]
Hence, the length of the missing segment is 36
PLEASE HELP! WILL MARK BRAINLIEST! 30 POINTS! ONLY DUE TOMORROW!
1. How many palindromes of length 5 can you form using letters with the following properties: they start with a consonant, and the consonants and vowels alternate; no letter appears more than twice. (Note: assume letters "a", "e", "i", "o", and "u" are the vowels of the English alphabet).
2. How many different words can be formed with the letters AAAABBCCD (not necessarily meaningful words)?
3. How many six-digit numbers have all their digits of equal parity (all odd or all even)?
4. You want to distribute 7 candies to 4 kids. If every kid must receive at least one candy, in how many ways can you do this?
5. In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.
THANK YOU SO MUCH!
Answer:
Step-by-step explanation:
5. cut the five fruits into 3 equal parts....
5x3=15 pieces
15/3(bowls)=5 pieces in each bowl
cut the fruits in multiples of 5 divisible by 3....that many ways possible
(similarly 4th qstion can be done)!!
Find the missing length indicated.
Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓64*36=✓8^2*6^2
x=8*6
x=48
simplify this please 41 =12d-741=12d−7
Answer:
Simplifying
41 = 12d + -7
Reorder the terms:
41 = -7 + 12d
Solving
41 = -7 + 12d
Solving for variable 'd'.
Move all terms containing d to the left, all other terms to the right.
Add '-12d' to each side of the equation.
41 + -12d = -7 + 12d + -12d
Combine like terms: 12d + -12d = 0
41 + -12d = -7 + 0
41 + -12d = -7
Add '-41' to each side of the equation.
41 + -41 + -12d = -7 + -41
Combine like terms: 41 + -41 = 0
0 + -12d = -7 + -41
-12d = -7 + -41
Combine like terms: -7 + -41 = -48
-12d = -48
Divide each side by '-12'.
d = 4
Simplifying
d = 4
NEED HELP ASAPPP!!! Drag each scenario to show whether the final result will be greater than the original
value, less than the original value, or the same as the original value.
1. A $30 increase followed by a $30 decrease
2. A 20% decrease followed by a 40% increase
3. A 100% increase followed by a 50% decrease
4. A 75% increase followed by a 33% decrease
5. 55% decrease followed by a 25% increase
Answer:
Greater than the original = 2, 4
Less than the original = 5
Same as the original = 1, 3
Step-by-step explanation:
Let the original value be x.
1. A $30 increase followed by a $30 decrease.
New value [tex]=x+30-30=x[/tex], it is same as original value.
2. A 20% decrease followed by a 40% increase.
Afer 20% decrease.
New value [tex]=x-\dfrac{20}{100}x=x-0.2x=0.8x[/tex]
Afer 40% increase.
New value [tex]=0.8x+\dfrac{40}{100}(0.8x)=0.8x+0.32x=1.12x[/tex], it is greater than original value.
Similarly check the other values.
3. A 100% increase followed by a 50% decrease.
New value [tex]=x+\dfrac{100}{100}x-\dfrac{50}{100}(x+x)=x[/tex], it is same as original value.
4. A 75% increase followed by a 33% decrease
New value [tex]=x+\dfrac{75}{100}x-\dfrac{33}{100}(x+0.75x)=1.1725x[/tex], it is greater than the original value.
5. 55% decrease followed by a 25% increase
New value [tex]=x-\dfrac{55}{100}x+\dfrac{25}{100}(x-0.55x)=0.5625x[/tex], it is less than the original value.
Therefore, Greater than the original = 2, 4, Less than the original = 5, Same as the original = 1, 3 .
A 100% increase followed by a 50% decrease
A $30 increase followed by a $30 decrease
Less Than The Original:55% decrease followed by a 25% increase
Greater Than The Original:A 20% decrease followed by a 40% increase
A 75% increase followed by a 33 1/3% decrease
60%
12. Your math teacher allows you to choose the most favorable measure of central tendency of your test scores to determine your grade for the term. On
six tests you earn scores of 89, 81, 85, 82, 89, and 89. What is your grade to the nearest whole number, and which measure of central tendency
should you choose?
95
Answers:
89; the mean
91; the mode
89; the mode
87; the median
Answer:
To answer the question above,
If you entered your test scores correctly, then your choices are off the wall.
The median is 87
The mode is 89
The mean is 85.833...
There is not a mode of 91 !
I hope this helps
Step-by-step explanation:
Points E, F, and D are on circle C, and angle G
measures 60°. The measure of arc EF equals the
measure of arc FD.
Which statements about the arcs and angles are
true? Select three options,
O ZEFD - ZEGD
E
O ZEGD ZECD
ED FD
С
G60°
mEF = 60
OmFD = 120
Mark this and return
Save and Exit
Next
Submit
Answer:
The correct statements are:
1: mEFD = mEGD
3: mED = mFD
5: mFD = 120°
Step-by-step explanation:
Let's analyse each statement:
1: mEFD = mEGD
Let's find the value of the angle ECD, using the sum of the internal angles of a quadrilateral:
[tex]60 + 90 + 90 + mECD = 360[/tex]
[tex]mECD = 120\°[/tex]
The angle ECD is a central angle, related to the arc ED, so the arc ED also has 120°.
The angle EFD inscribes the arc ED, so we have:
[tex]mEFD = mED/2[/tex]
[tex]mEFD = 120/2 = 60\°[/tex]
So the angles mEFD and mEGD are equal. The statement is TRUE.
2. mEGD = mECD
This statement is FALSE, because mEGD = 60° and mECD = 120°
3. mED = mFD
If mED is 120° and mEF = mFD, we have:
[tex]mED + mEF + mFD = 360[/tex]
[tex]2*mFD = 360 - 120[/tex]
[tex]mFD = 120\°[/tex]
So the statement is TRUE, both arcs have 120°.
4. mEF = 60°
This statement is FALSE, because we calculated before that mEF = mFD = 120°
5. mFD = 120°
This statemente is TRUE, because we calculated before that mFD = 120°.
So the correct statements are 1, 3 and 5
The true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]
Start by calculating the measure of angle ECD.
We have:
[tex]\angle ECD = 2 * \angle EGD[/tex]
So, we have:
[tex]\angle ECD = 2 * 60[/tex]
[tex]\angle ECD = 120[/tex]
The above means that:
[tex]\overset{\huge\frown}{ED} = 120[/tex]
So, the measure of angle EFD is:
[tex]\angle EFD = 0.5 * \overset{\huge\frown}{ED}[/tex]
[tex]\angle EFD = 0.5 * 120[/tex]
[tex]\angle EFD = 60[/tex]
From the question, we have:
[tex]\angle EGD = 60[/tex]
So, it is true that:
[tex]\angle EFD =\angle EGD[/tex]
To calculate the measure of arc FD, we have:
[tex]\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} + \overset{\huge\frown}{EF} =360[/tex]
Lengths EF and DE are congruent.
So, we have:
[tex]2\overset{\huge\frown}{FD} + \overset{\huge\frown}{DE} =360[/tex]
[tex]\overset{\huge\frown}{DE} = \overset{\huge\frown}{ED} = 120[/tex]
So, we have:
[tex]2\overset{\huge\frown}{FD} + 120 =360[/tex]
Divide through by 2
[tex]\overset{\huge\frown}{FD} + 60 =180[/tex]
Subtract 60 from both sides
[tex]\overset{\huge\frown}{FD} =120[/tex]
This means that:
[tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex] are true
Hence, the true statements are: [tex]\angle EFD =\angle EGD[/tex], [tex]\overset{\huge\frown}{FD} = \overset{\huge\frown}{ED}[/tex] and [tex]\overset{\huge\frown}{FD} =120[/tex]
Read more about cyclic theorems at:
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how would a bank represent a withdrawal of 19.43 dollars?
Answer:
-19.43
Step-by-step explanation:
Withdrawals are negative
Please could I have some help :)
Answer:
a) x = 128 degrees
b) Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
Step-by-step explanation:
Given:
attached diagram
ABC is a straight line
Solution:
a) Find x
ABC is a straight line
angle ABD = supplement of CBD = 180-CBD = 180-116 = 64 degrees.
x is the central angle of the arc APD
so angle ABD is the inscribed angle which equals half of the arc angle =>
angle ABD = x/2 = 64 degrees
Solve for x
x/2 = 64
x = 2*64
x = 128 degrees
b.
Angle APD is the arc angle, which is equal to the central angle x subtended by the arc. Therefore angle APD = 128 degrees (and not 116 degrees)
MATH— Please help me answer this question. Hopefully you can see the picture
*LAST QUESTION , PLEASE ANSWER TY* (: Quadrilateral ABCD is inscribed in a circle. If angle A measures (3x – 10)° and angle C measures (2x)°, find x.
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Quadrilaterals.
Basically we know that, the sum of opposite angles of a quadrilateral inscribed in a circle is always 180°.
so applying this law here, we get as,
2X + (3X-10) = 180°
=> 5X - 10° = 180°
=> 5X = 190°
=> X = 190°/5
=> X = 38°
thus the angle X= 38°.
You are taking 1500 US dollars on a trip. After checking the exchange rate, you figure out the exchange rate is 1 US dollar to 0.74 euros. Task: write an equation to convert US dollars to euros. Will mark most brainiest if you answer!
Answer:
1500*0.74 = (1,110 euros)
Step-by-step explanation:
1. Use the equation, 1500*0.74.
2. Multiply 1500 and 0.74 to find out how many euros can be converted with 1500 US dollars.
3. Once you multiply them together, the final answer is 1,110 euros.
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
Substitution
Step-by-step explanation:
The subtraction property of equality is when you subtract from both sides, they will still be equal. The multiplication property is the same thing but with multiplication.
Answer:
Substitution
Step-by-step explanation:
Substitution: If a = b, then either a or b may be substitued for the other in any equation (or inequality).
Multiplication: If a =b, then ca = cb.
Subtraction: If a=b and c=d, then a-c=b-d
Substitution is the closest.
Alex, Toby and Samuel are playing a game together.
At the end of the game, they will make a classification with one of them in First
place, one of them in Second place and one of them in Third place.
Work out how many possible outcomes there could be at the end of their game.
The number of possible outcomes there could be at the end of their game is 6 outcomes
This is a permutation problem since it required arrangement
If Alex, Toby, and Samuel are playing a game together and at the end, they will make a classification with one of them in first place, one of them in Second place and one of them in Third place, this can be done in 3! ways
Since n! = n(n-1)(n-2)!
Hence 3! = 3(3-1)(3-2)
3! = 3 * 2 * 1
3! = 6 ways
Hence the number of possible outcomes there could be at the end of their game is 6 outcomes
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Keiko estimated the height of her office building to be 45 ft. The actual height of her office building is 42 ft
Find the absolute error and the percent error of Keiko's estimate. If necessary, round your answers to the nearest tenth.
% error formula: | true value minus "your" (as in Keiko's) value | over true value, times 100.
so: 42 - 45 = 3 (it would be negative but we used absolute value, which is how it is supposed to be done. 3 is your absolute error).
3/42 = 0.07143
0.07142 * 100 = 7.142%. she was only 7.142% off from the right answer.
Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized
Answer:
[tex]m = 5 \sqrt{3}[/tex]
[tex]n = 5[/tex]
Step-by-step explanation:
Given
The triangle above
Required
Find the missing lengths
The missing lengths can be calculated by applying trigonometry ratios
From the triangle above,
the Hypotenuse is 10
Angle = 60
Calculating m
The relationship between m, the Hypotenuse and angle 60 is defined as follows;
[tex]sin \theta = \frac{Opp}{Hyp}[/tex]
Where [tex]\theta = 60[/tex]
[tex]Opp = m[/tex]
[tex]Hyp = 10[/tex]
The above formula becomes
[tex]sin60= \frac{m}{10}[/tex]
Multiply both sides by 10
[tex]10 * sin60= \frac{m}{10} * 10[/tex]
[tex]10 * sin60= m[/tex]
In radical from, [tex]sin60 = \frac{\sqrt{3}}{2}[/tex]
[tex]10 * sin60= m[/tex] becomes
[tex]10 * \frac{\sqrt{3}}{2}= m[/tex]
[tex]\frac{10* \sqrt{3}}{2}= m[/tex]
[tex]5 \sqrt{3}= m[/tex]
[tex]m = 5 \sqrt{3}[/tex]
Calculating n
The relationship between n, the Hypotenuse and angle 60 is defined as follows;
[tex]cos\theta = \frac{Adj}{Hyp}[/tex]
Where [tex]\theta = 60[/tex]
[tex]Adj = n[/tex]
[tex]Hyp = 10[/tex]
The above formula becomes
[tex]cos60= \frac{n}{10}[/tex]
Multiply both sides by 10
[tex]10 * cos60= \frac{n}{10} * 10[/tex]
[tex]10 * cos60= n[/tex]
In radical from, [tex]cos60= \frac{1}{2}[/tex]
[tex]10 * cos60= n[/tex] becomes
[tex]10 * \frac{1}{2}= n[/tex]
[tex]\frac{10*1}{2}= n[/tex]
[tex]5 = n[/tex]
[tex]n = 5[/tex]