Answer:
The GCF is 12
list the factors of 84 and 36
1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
1, 2, 3, 4, 6, 9, 12, 18, 36
both numbers have 1,2,3,4,6,9 and 12 as a common factor but 12 is the biggest so it is the gcf
GCF means both numbers have 12 as their biggest factor they have in common.
Hope this helps
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
The task is to find the greatest common factor of 84 and 36
First we find the prime factors of each number:
84= 2 × 2 × 3 × 736= 2 × 2 × 3 × 3Greatest common factor is the product of common factors of the given numbers
As per above, 84 and 36 have common factors of 2×2×3=12
So answer is 12
Chicken is normally $2.15/ib.but if you purchase 26 pounds for $41.34,how much do you save per pound
Answer:
$0.56/lb
Step-by-step explanation:
Given
Cost of a chicken = $2.15 per pound
26 pound of a chicken = $41.34
Required
Calculate how much saved.
The first step is to calculate the unit price of a chicken when 26 pound of chicken was bought.
Unit Price = Price ÷ Weight
Unit Price = $41.34 ÷ 26lb
Unit Price = $1.59/lb
The next step is to calculate the difference between these two prices
Difference = |$1.59/lb - $2.15/lb|
Difference = |-$0.56/lb|
Difference = $0.56/lb
The calculated difference is the amount saved per pound of chicken when I bought 26 pound of chicken.
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.
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...
Complete the following statements to prove that ∠IKL and ∠JLD are supplementary angles. It is given that ∠EIJ ≅ ∠GJI. Also, ∠EIJ ≅ ∠IKL and ∠GJI ≅ ∠JLK, as they are corresponding angles for parallel lines cut by a transversal. By the definition of congruent angles, m∠EIJ = m∠GJI, m∠EIJ = m∠IKL, and m∠GJI = m∠JLK. So, m∠IKL = m∠JLK by the ___________ (substitution property of equality, subtraction property of equality , or symmetry property of equality.) . Angle JLK and ∠JLD are supplementary angles by the _____________________ (vertical angles theorem, congruent supplements theroem, or linear pair theroem.) so m∠JLK + m∠JLD = 180°. By the (substitution property of equality reflexive property of equality, or division property of equality) , m∠IKL + m∠JLD = 180°. Therefore, ∠IKL and ∠JLD are supplementary angles by definition.
Answer:
1st blank: substitution property of equality
2nd blank: linear pair theorem
3rd blank: substitution property of equality
Step-by-step explanation:
1st blank
∠EIJ ≅ ∠GJI (eq. 1)
∠EIJ ≅ ∠IKL (eq. 2)
∠GJI ≅ ∠JLK (eq. 3)
Substituting eq. 3 into eq. 1:
∠EIJ ≅ ∠JLK
and then, substituting eq. 2:
∠IKL ≅ ∠JLK
which means that m∠IKL = m∠JLK
2nd blank
The Linear Pair Theorem states that two angles that form a linear pair are supplementary
3rd blank
m∠JLK + m∠JLD = 180°
Substituting with the previous result:
m∠IKL + m∠JLD = 180°
Answer:
1st blank: substitution property of equality
2nd blank: linear pair theorem
3rd blank: substitution property of equality
Step-by-step explanation:
there u go
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
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:
ABCD is a parallelogram.
Given that,
DC = CE
prove that,
area of the ADE triangle is equal to the area of the parallelogram.
need explanation
plzz help!!
will give the brainliest!!
Drop a perpendicular from [tex]\overline{AK}[/tex] to $\overline {DE}$.
Let $l(AK)=h$ and $l(AB)=l(DC)=L$
$h$ is the height of the parallelogram and the triangle.
$L$ is the length of the base of the triangle and one of the sides of parallelogram.
We have area of parallelogram $=A_{para}=hL$
And the area of triangle is:
$A_{tria}=\frac{1}{2} h\times (L+L)=hL$
Thus we can see that they are equal.
Answer:
See below
Step-by-step explanation:
Given:
ABCD is a parallelogram
DC = CE
To Prove:
area of the ADE triangle is equal to the area of the parallelogram.
Proof:
Let The Point between B and C be F
To prove that area of the ADE triangle is equal to the area of the parallelogram, we'll first prove that ΔADF ≅ ΔECF
Statements | Reason
DC ≅ CE | Given
But, CD ≅ AB | Opposite sides of a ║gm
So, CE ≅ AB | Transitive Property of Equality
∵ ΔABF ↔ ΔECF |
CE ≅ AB | Already Proved
∠CFE ≅ ∠ BFE | Vertical Angles
∠ECF ≅ ∠ABF | Alternate Angles
So, ΔABF ≅ ΔECF | S.A.A. Postulate
Now, |
Area of ║gm = Area of |
quad ADCF + ΔABF |
But, ΔABF ≅ ΔECF | Already Proved
So, |
Area of ║gm = Area of |
quad ABCF + ΔECF |
But Area of ΔADE = Area of |
quad ABCF + ΔECF |
So, |
Area of ║gm = Area of ΔADE | Hence Proved
The total surface area of a window is 2630in2. Use the fact that 1 in = 2.54 cm to convert this area to cm2.
2630 * 2.54 * 2.54 = 16967.71 cm2
The total surface area of the window in square centimeters is 17011 cm².
To convert the total surface area of a window from square inches to square centimeters, we can use the conversion factor of 1 in = 2.54 cm.
Here are the steps to follow:
Multiply the surface area in square inches by the conversion factor to get the surface area in square centimeters.
Round the answer to the nearest whole number.
Using the given surface area of 2630 in², we can convert it to square centimeters as follows:
2630 in² × (2.54 cm/in)² = 17010.76 cm²
Rounding to the nearest whole number, we get:
17011 cm²
Therefore, the total surface area of the window in square centimeters is 17011 cm².
Learn more about total surface area here: brainly.com/question/8419462
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What is the standard form of 7 + 3i / 2 - 5i
A. -29/21 + 4/21i
B. -29/21 - 4/21i
C. 1/29 - 41/29i
D. -1/29 + 41/29i
Answer:
Step-by-step explanation:
7 + 3i / 2 - 5i would be clearer if written as (7 + 3i) / (2 - 5i). We must remove the symbol i from the denominator, and that can be accomplished by multiplying both 7 + 3i and 2 - 5i by the conjugate 2 + 5i:
(2 + 5i)(7 + 3i)
--------------------
4 + 29
which simplifies to 14 + 6i + 35i - 15 over 33, or
-1 + 41i
------------
33
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.
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]
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:
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.
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:
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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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
how would a bank represent a withdrawal of 19.43 dollars?
Answer:
-19.43
Step-by-step explanation:
Withdrawals are negative
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
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.
To learn more about an equation of a circle visit:
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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
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)!!
The weights of a certain brand of candies are normally distributed with a mean weight of 0.8552 g and a standard deviation of 0.0519 g. A sample of these candies came from a package containing 442 candies, and the package label stated that the net weight is 377.3 g. (If every package has 442 candies, the mean weight of the candies must exceed StartFraction 377.3 Over 442 EndFraction equals0.8537 g for the net contents to weigh at least 377.3 g.) a. If 1 candy is randomly selected, find the probability that it weighs more than 0.8537 g. The probability is nothing. (Round to four decimal places as needed.)
Answer:
The probability that the weight of a candy randomly selected is more than 0.8537 is 0.7486
Step-by-step explanation:
The given parameters are;
The mean candle weight = 0.8552 g
The standard deviation = 0.0519 g
The number in the sample, n = 442 candles
By central limit theorem, the sample standard deviation, [tex]\sigma _{\bar x}[/tex] is given by the relationship;
[tex]\sigma _{\bar x} = \dfrac{\sigma}{\sqrt{n} } = \dfrac{0.0519}{\sqrt{442} } = 0.002469[/tex]
The probability is given by the relation;
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-\mu }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-\mu }{\dfrac{\sigma }{\sqrt{n}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (\dfrac{\bar{X}-0.8552 }{\dfrac{\sigma }{\sqrt{n}}} >\dfrac{0.8537-0.8552 }{\dfrac{0.0519 }{\sqrt{442}}} \right )[/tex]
[tex]P\left (\bar{X}>0.8537 \right )= P\left (z>-0.6076\right )[/tex]
The from the z-score table we have = 0.2514
The probability of P (z > -6076) = 1 - 0.2514 = 0.7486
The probability that the weight of a candy randomly selected is more than 0.8537 = 0.7486.
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
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
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
*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°.
Find the missing length indicated.
Answer:
Step-by-step explanation:
x=✓64*36=✓8^2*6^2
x=8*6
x=48
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
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
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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:
https://brainly.com/question/26168678