Answers
(a) BC = 40
(b) GF = 15
(c) CD = 45
(d) KM = 37.5
=========================================================
Explanations:
Part (a)
GF is a midsegment of triangle ABC, so GF is half that of the parallel base AC
AC = 30 so GF = (1/2)*AC = 0.5*30 = 15
--------------------------
Part (b)
For similar reasons as part (a), FB if half that of BC. This leads to FB = FC
FB = FC
FC = 20
since FB = 20
Now use the segment addition postulate
BC = BF + FC
BC = 20 + 20
BC = 40
Note: FB is the same as BF. The order of the letters does not matter.
--------------------------
Part (c)
GF = AD are the same length because of the single tickmark
GF = 15 so AD = 15
use the segment addition postulate
CD = CA + AD
CD = 30 + 15
CD = 45
--------------------------
Part (d)
EG = 15 since GF = 15 (and EG = GF by the single tickmark)
use the segment addition postulate
EF = EG + GF
EF = 15 + 15
EF = 30
The length of KM is the average of the base lengths EF and DC, since KM is a midsegment of the trapezoid
KM = (EF+DC)/2
KM = (30+45)/2
KM = (75)/2
KM = 37.5
The measures are:
(a) BC = 20 mm
(b) GF = 10 mm
(c) CD = 10 mm
(d) KM = 10 mm
To find the measures you're looking for in the given diagram, we'll use properties of midsegments in triangles and trapezoids.
First, let's establish some properties:
In triangle ABC, FG is the midsegment, so FG is parallel to BC and half the length of BC.
In trapezoid CDEF, KM is the midsegment, so KM is parallel to EF and half the length of EF.
EF is parallel to KM and also parallel to DC.
Now, let's find the measures:
(a) BC:
Since FG is the midsegment of triangle ABC, FG is parallel to BC, and FG is half the length of BC. Therefore, BC = 2 * FG.
(b) GF:
GF is the midsegment of triangle ABC, so it's half the length of BC. Thus, GF = BC / 2.
(c) CD:
Since EF is parallel to DC and KM is the midsegment of trapezoid CDEF, CD is also half the length of EF. Therefore, CD = EF / 2.
(d) KM:
KM is the midsegment of trapezoid CDEF, so it's half the length of EF. Thus, KM = EF / 2.
Now, let's find the specific values using the information given:
Given values:
BC = 20 mm (from the diagram).
EF = 20 mm (since BC is parallel to EF in the same trapezoid).
(a) BC:
BC = 2 * FG
BC = 2 * GF (since GF is half the length of BC)
BC = 2 * (BC / 2) (substituting the given value for BC)
BC = BC
(b) GF:
GF = BC / 2
GF = 20 mm / 2
GF = 10 mm
(c) CD:
CD = EF / 2
CD = 20 mm / 2
CD = 10 mm
(d) KM:
KM = EF / 2
KM = 20 mm / 2
KM = 10 mm
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Related Questions
Solve for x in the equation x^2+10x+12=36.
A. x = –12 or x = 2
B. x = –11 or x = 1
C. x = –2 or x = 12
D. x = –1 or x = 11
Answers
x^2 + 10 x + 12 = 36
36 = 36:
x^2 + 10 x + 12 = 36
Subtract 12 from both sides:
x^2 + 10 x = 24
Add 25 to both sides:
x^2 + 10 x + 25 = 49
Write the left hand side as a square:
(x + 5)^2 = 49
Take the square root of both sides:
x + 5 = 7 or x + 5 = -7
Subtract 5 from both sides:
x = 2 or x + 5 = -7
Subtract 5 from both sides:
Answer: x = 2 or x = -12 Thus the Answer is A.
To solve the equation x^2+10x+12=36, subtract 36 from both sides and factor or use the quadratic formula to find the solutions. The solutions are x = -12 or x = 2.
Explanation:To solve the equation x^2+10x+12=36, we need to bring all terms to one side of the equation and then factor or use the quadratic formula. Subtracting 36 from both sides gives us the equation x^2+10x-24=0. We can then factor this equation as (x+12)(x-2)=0. Setting each factor equal to zero, we find that x = -12 or x = 2.
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What is the value of x?
x=23
x=35
x=58
x=93
Answers
what triangle congruence theorem is needed?
Answers
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4. An airplane at T(80,20) needs to fly to both U(20,60) and V(110,85). What is the shortest possible distance for the trip?
165units
170units
97units
169 units
is the answer A?
Answers
D=sqrt( (x1-x2)^2 + (y1-y2)^2 )
From T to U
D= sqrt((80-20)^2 + (20-60)^2) = 72.11
Then flying from U to V
D= sqrt((20-110)^2 + (60-85)^2) = 93.4
So T to U to V = 72.11+93.4 = 165.5
BUT checking also T to V to U
From T to V
D= sqrt((80-110)^2 + (20-85)^2) = 71.6
Then from V to U
D= sqrt((110-20)^2 + (85-60)^2) = 93.4
So from T to V to U = 165
Pretty much the same both directions
So yes the answer is A
Which polynomial is a perfect square trinomial?
A. x^2 +5y + 25
B. x^2 +10y+25
C.x^2+5y+100
D. x^2+10y-25
Answers
When a square of a number (3*3=9) can also add up to another number in the trinomial (3+3=6)
In my example here the equation, in order to be a perfect square trinomial, would be: X^2+6y+9
Now to look at the problem. We can instantly single out C because 10*10 is 100 but 10+10 is not five.
If we look at A we can find the root of 25 (5) but 5+5 is 10 not five. So A is incorrect
Using our previous calculation we know that 5 is our magic number. Leaving us with B and D. If we look at D we can conclude that -5*5 would be -25 but -5+5 is zero. So, it is not D
Using power of elimination we can easily conclude that B is the correct answer. If you wish to check: (5+5=10) (5*5=25)
Answer: B
Hope this helped!
A vacant lot is in the shape of an isosceles triangle. It is between two streets that intersect at an 85.9degree angle. Each of the sides of the lot that face these streets is 150 ft. Long. Find the perimeter of the lot to the nearest foot.
Answers
Sin(α)=Opposite/Hypotenuse
α=89.5°/2=42.95°
Opposite=x
Hypotenuse=105
Sin(42.95°)=x/105
x=(105)(Sin(42.95°))
x=71.54 feet
2. Then the other side of the isosceles triangle (b), is:
b=2x
b=2x71.54 feet
b=143.08 feet
3. The perimeter of the isosceles triangle, is:
P=2a+b
P=2(105 feet)+143.08 feet
P=210 feet+143.08 feet
P=353 feet
If you worked for 6 days for a total of 67.8 hours. If I worked the same number of hours each day, how many hours did I work in a day?
Answers
To solve this problem, we need to divide 67.8 by 6 to find the amount of hours each day.
67.8 / 6 = 11.3
You worked 11.3 hours each day.
Hope this helps!
A particular computer takes 13 minutes to download a 39-minute TV show. How long will it take the computer to download a 2-hour movie?
Answers
It will take the computer 40 minutes to download a 2-hour movie based on its current download speed, which is 3 minutes of video per minute of download time.
Explanation:To answer this question, we first need to establish the download speed of the computer. This can be done by dividing the length of the TV show by the time it takes to download it. In this case, the computer can download 39 minutes of video in 13 minutes, so its download speed is 39/13 = 3 minutes of video per minute of download time.
To find out how long it will take to download a 2-hour movie, we first need to convert the length of the movie to minutes, because our speed is in minutes of video per minute of download time. Two hours is equal to 2*60 = 120 minutes. Therefore to download a 120-minute video, it will take 120/3 = 40 minutes.
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. Classify the triangle according to side length and angle measurement.
(1 point)
isosceles; right
equilateral; obtuse
scalene; acute
scalene; right
Answers
Final answer:
The question requests the classification of a triangle by both its side length and angle measurement. An isosceles triangle has two equal sides, and if it also includes a right angle, it is classified as isosceles; right. This understanding combines the concepts of triangle classification by sides and angles.
Explanation:
The question asks to classify a triangle according to side length and angle measurement. When classifying triangles by side lengths, we have three categories: isosceles, scalene, and equilateral. An isosceles triangle has two sides of equal length, a scalene triangle has all sides of different lengths, and an equilateral triangle has all sides of equal length. In terms of angle measurements, triangles can be classified as right (one 90-degree angle), acute (all angles less than 90 degrees), or obtuse (one angle greater than 90 degrees).
According to the information provided and referencing the 4th Theorem, in an isosceles triangle, the angles opposite to the equal sides are equal. This property helps in classifying a triangle when given its angles or side lengths. Furthermore, for a triangle to be a right triangle, it must include a 90-degree angle. This is crucial when identifying a triangle as isosceles; right, which means it is an isosceles triangle with a right angle, typically resulting in the two equal sides being adjacent to the right angle.
On a circular playground, the distance from its center to the edge of the playground is 35 feet. What is the approximate circumference of the playground?
Answers
Hope this hels!
a poll shows that 76% of voters in a city favor an initiative to increase spending on public schools. if 10 voters are selected at random, wht is the probability that exactly five of them will vote in favor of the initiative?,
Answers
Lesson 8: Binomial Distributions
1. a. 91%
2. a. 5.1%
3. c. s^5-25s^4v+250s^3v^2-1250s^2v^3+3125sv^4-3125v^5
4. d. 55.8%
Help me please.....
3.you have a mortgage payment of $1,248.90/month. Using proportions, what is the minimum amount you must have in realized income per month to keep your housing expense in the acceptable range?,
Answers
To determine the minimum amount of realized income per month to keep your housing expense in the acceptable range, set up a proportion using 30% of the mortgage payment and solve for x.
Explanation:To determine the minimum amount of realized income per month to keep your housing expense in the acceptable range, we can use a proportion. Let's assume that the acceptable range for housing expense is 30% of your income.
First, we need to find the total monthly income that corresponds to 30% of the mortgage payment. We can set up a proportion:
x/1248.90 = 30/100
Cross-multiplying, we get:
100x = 30 * 1248.90
Simplifying, we find:
x = (30 * 1248.90)/100 = $374.67
Therefore, the minimum amount you must have in realized income per month to keep your housing expense in the acceptable range is $374.67.
PLEASE HELP ASAP! BRAINLIEST TO BEST/RIGHT ANSWER
Answers
A recipe calls for 1 1 2 cups of flour. how many cups will you need if you are preparing 5 batches of the recipe?
Answers
A brand new filled jar of salsa is 11 cm tall and a has a radius of 6 cm. Kelly eats some of the salsa and the salsa in the jar is now 6 cm high. Approximately how much salsa did Kelly eat? Round your final answer to the nearest whole number.
188 cm³
565 cm³
679 cm³
1244 cm³
Answers
A 565 cm
Answer:
Ok the answer is 565 but I'm going to break it down for those who wanna know how
Step-by-step explanation:
So first let's just assume the jar is a cylinder which means to use the formula
[tex]V=\pi r^{2} h[/tex]
They saved you time of having to finf the Radius and such
firstly, we're gonna solve before she eats all that salsa lol
r = 6
h = 11
we're gonna substitute 3.14 for pi
of course you'll solve for it which you'll get
v = 1243.44
now you need to find the volume after she eats the salsa which the only difference is that the height will be 6 instead of 11
substitute
solve and you'll get
678.24
now that you have the volume of before and after she eats the salsa all you need to do is subtract to find the difference
1243.44 - 678.24
which you'll get
565!
Hope this helps!
CHECK MY ANSWER??
Which statement describes the first step to solve the equation by completing the square? 3x^2 + 18x= 21
A. Multiply both sides of the equation by 19.
B. Add 81 to each side of the equation.
C. Add 9 to each side of the equation.(MY ANSWER)
D. Multiply both sides of the equation by 13 .
Answers
3 x^2 + 18 x = 21
Subtract 21 from both sides:
3 x^2 + 18 x - 21 = 0
3 x^2 + 18 x - 21 = 3 (x^2 + 6 x - 7):
3 (x^2 + 6 x - 7) = 0
Divide both sides by 3:
x^2 + 6 x - 7 = 0
x = (-6 ± sqrt(6^2 - 4 (-7)))/2 = (-6 ± sqrt(36 + 28))/2 = (-6 ± sqrt(64))/2:
x = (-6 + sqrt(64))/2 or x = (-6 - sqrt(64))/2
sqrt(64) = sqrt(2^6) = 8 = 8:
x = (-6 + 8)/2 or x = (-6 - 8)/2
(-6 + 8)/2 = 2/2 = 1:
x = 1 or x = (-6 - 8)/2
(-6 - 8)/2 = -14/2 = -7:
Answer: x = 1 or x = -7
a cupcake recipe calls for 1/6 cups of milk and you have 5/8 cups of milk in the refrigerator how many cups of milk will you have remaining after baking the cupcakes
Answers
15 - 4 = 11 11/24 cups of milk left
Hope this helps
Answer: 1/8
Step-by-step explanation:
What is the area of this figure?
Answers
5 x 5 = 25
4 x 2.5 = 10
25 + 10 = 35.
Hope this helps!:)
Your friend has prepared his monthly budget and asks you if he has overlooked anything in this planning. Which of the following questions points out his most serious omission?
a. What if your income from stocks is lost? b. What if you need to go to the doctor? c. What if the electric bill increases? d. What if you need to replace the furnace?
Answers
The population of trout in a certain pond doubles every year. The current population of the pond is 275 trout.
Answers
I really need help on all of these please
Answers
the adjacent is the part of the angle that connects with the hypotenuse to form the angle. So in the 1st triangle the hypotenuse along with segment XZ forms angle Z. That means that XZ is the adjacent.
To identify the opposite, you find the segment that connects the adjacent to the hypotenuse.
SO in the 1st triangle, segment XY connects the adjacent XZ with the hypotenuse. So that means that XY is the opposite of angle Z.
Solve the inequality.
1
_ c < B
4
C < 32
C < -4
C > 12
C > 32
Solve the equation. Y + 13 = 10
Y = -23
Y = 3
Y= -3
Y = 23
Multiply. 7(x -2)
7x - 2
7x - 14
7x - 9
X - 14
Mary and her brother John collect foreign coins. Mary has three times the number of coins that John has. Together they have 160 foreign coins. Find out how many Mary has.
112
120
24
40
Answers
Y=-3 -3+13= 10
7x-14 Multiply
112
How do u do question 25. How do u find the measure of X?
Answers
now, arc's get their angle measure from the central angle they're in, in this case, "x" is the central angle, and therefore, it has the same measure of 360° - 250°.
If the product of two positive integers is 180 and the larger number is 5 times the smaller number, what are the numbers
Answers
The bigger number is 5x
5x(x) = 180
5x² = 180
x² = 180÷5
x²=36
x=√36
x = 6
x=6
5x = 6 x 5
5x = 30
So the two numbers are 6 and 30
which expression is equivalent to 4√24x∧6y÷ 128x∧4y∧5
Answers
Answer:
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Step-by-step explanation:
[tex]\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}}[/tex]
[tex]\sqrt[4]{(\frac{24}{128})\times (\frac{x^{6}}{x^{4}})\times (\frac{y}{y^{5}})}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times {(x)^{6-4}}\times{(y)^{1-5}}}[/tex]
= [tex]\sqrt[4]{(\frac{3}{16})\times x^{2}y^{-4}}[/tex]
= [tex]\sqrt[4]{\frac{3}{(2)^{4}}\times x\times y^{-4}}[/tex]
= [tex]\sqrt[4]{(3\times x^{2)\times (\frac{y^{-1}}{2})^{4}}}[/tex]
= [tex]\frac{y^{-1}}{2}\sqrt[4]{3x^{2}}[/tex]
= [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex]
Option D. [tex]\sqrt[4]{\frac{3x^{2}}{2y}}[/tex] is the correct answer.
Assume that there are 2 trials.
X = 2 where X represents the number of successes.
Which probability matches the probability histogram?
Round the answer to one decimal place.
P(success)=0.3
P(success)=0.4
P(success)=0.6
P(success)=0.7
Answers
Your question is a little unclear, but I believe you are asking about the probability that at least one of the trials in the experiment were successful.
If that is the case, you simply have to add the probability of 1 success with the probability of 2 successes.
That is 0.48 + 0.16 = 0.64
Rounding our answer to one decimal place gives us 0.6.
The correct answer on the test was
P(success)=0.4
Situation: A 15 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1405. N Noe No initial mass (at time 0) N mass at time t k a positive constant that depends on the substance itself and on the units used to measure time t time, in days
Answers
Your welcome
Answer: 4.9
Step-by-step explanation:
Hope this helps
Johns father is 2 meters tall how many meters tall how many centimeters tall is johns father
Answers
Answer: He is 6'5
Step-by-step explanation: He is 6'5 because 2 meters it equal to 6'5
A research firm conducts a sample survey and discovers that, of all the new watchers of three-dimensional tv, 77% have not reported any side effects such as vertigo, headache, or undue eyestrain compared with watching regular television. if this sample questionnaire had 2,100 respondents, what is the margin of error (me), rounded to the nearest thousandth? hint: me equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over n end fraction end square root comma where p hat is the yes proportion in the sample and n is the sample size. me = ±0.009 me = ±0.017 me = ±0.018 me = ±1.837
Answers
All you have to do is plug the known values into the equation and evaluate it.
First, do the work under the square root sign. 0.77(1-0.77) / 2100 gives you a very small number. If you take the square root of that, you will have 0.0091.
The last step is to just multiply that by 2 and you will have 0.018
Which of the economic goals correlates with the explanation "the ability of people to make choices"?
A. equity
B. innovation
C. efficiency
D. freedom
I got D as my answer, is that correct?,