ABC is a right triangle at B such that
AB = 8 cm and AC = 10 cm.
1° Calculate BC
2º Consider a point M of the segment [AB]
The line passing through M and parallel to the
line (AC) cuts the line (BC) in N.
Supposing that AM = x, calculate MB and BN in
5
terms of x. then verify that MN (8 - x).
4
3° Let D be the fourth vertex of rectangle
ABCD.
The parallel to (BD) passing through M.cuts the
line (AD) at P
Calculate AP and MP in terms of x
4° Prove that the perimeter of the polygon
MNCDP is independent from x
Answers
Answer:
Question 1
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, or a right triangle)
Given:
a = BCb = AB = 8cmc = AC = 10 cm⇒ BC² + 8² = 10²
⇒ BC² = 36
⇒ BC = 6 cm
Question 2
Given:
AB = 8 cmAM = x⇒ MB = AB - AM = 8 - x
As ΔABC ~ ΔMBN
⇒ AB : AC = MB : MN
⇒ 8 : 10 = (8 - x) : MN
[tex]\sf \implies \dfrac{8}{10}=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies \dfrac45=\dfrac{(8-x)}{MN}[/tex]
[tex]\sf \implies MN=\dfrac54(8-x)[/tex]
Question 3
D = (6, 8)
As ΔBAD ~ ΔMAP
⇒ AB : AD : BD = AM : AP : MP
⇒ 8 : 6 : 10 = x : AP : MP
[tex]\sf \implies \dfrac{8}{6}=\dfrac{x}{AP}[/tex]
[tex]\sf \implies AP=\dfrac34x[/tex]
[tex]\sf \implies \dfrac{8}{10}=\dfrac{x}{MP}[/tex]
[tex]\sf \implies MP=\dfrac54x[/tex]
Question 4
Perimeter of MNCDP = MN + NC + CD + PD + MP
As ΔABC ~ ΔMBN
⇒ AB : BC : AC = MB : BN : MN
⇒ 8 : 6 = (8 - x) : BN
[tex]\sf \implies \dfrac86=\dfrac{(8-x)}{BN}[/tex]
[tex]\sf \implies BN=\dfrac34(8-x)[/tex]
NC = BC - BN
[tex]\sf \implies NC=6-\dfrac34(8-x)[/tex]
PD = 6 - AP
[tex]\sf \implies PD=6-\dfrac34x[/tex]
Perimeter of MNCDP = MN + NC + CD + PD + MP
[tex]\sf \implies perimeter=\dfrac54(8-x)+6-\dfrac34(8-x)+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10-\dfrac54x+6-6+\dfrac34x+8+6-\dfrac34x+\dfrac54x[/tex]
[tex]\sf \implies perimeter=10+8+6=24[/tex]
Related Questions
Please help me with this please and thank you
Answers
Answer:
A
Step-by-step explanation:
it's a geometric sequence since it is continuously being multiplied by the same number which in this case is 2.
Answer:
A. 3, 6, 12, 24
Step-by-step explanation:
In A, you're multiplying by 2 each time.
What is the distance between (4, 6) and (4, -1)?
O 7 units
O 5 units
O 4 units
O I don't know.
Answers
Answer:
7 units
Step-by-step explanation:
[tex]d=\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
[tex]d=\sqrt{(4-4)^2+(-1-6)^2}[/tex]
[tex]d=\sqrt{(0)^2+(-7)^2}[/tex]
[tex]d=\sqrt{49}=7[/tex]
Distance = 7 units
I hope this helps!
Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A?
Enter your answer in the box. C is labeled 74
Answers
Answer:
Step-by-step explanation:
URGENT!!! HELP!!!
You spend a $20 per turn on a fair game to win $50 for each win. You lose the first round but win the next two rounds.
What was the net payoff?
$100
-$60
-$30
$40
Answers
The net payoff obtained during the game is $40. Option D is the correct answer.
What is net payoff?The term "net payoff" describes the profit or loss realised from a transaction or operation after deducting all costs, charges, and taxes. It is determined by deducting the total cost of the activity or investment from the total income received. A gain is shown by a positive net reward, whereas a loss is indicated by a negative net payoff.
Given that, each round cost $20, and each win gives $50.
Now, for 3 rounds the total cost is:
$20 x 3 = $60
After winning the two round the win amount is:
$50 x 2 = $100
Now, the net payoff is:
$100 - $60 = $40.
Hence, the net payoff obtained during the game is $40. Option D is the correct answer.
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What is the numerator for the following
Answers
Answer:
Can you please check the photo I sent you it has the answer and step-by-step explanation
Step-by-step explanation:
Problem 2
Write each expression as a multiple of a power of 10.
Expression
As a Multiple of a Power of 10
42300
2000
9200000
Four thousand
80 million
32 billion
Whoever does this quicker gets Brainly and stuff
Answers
Answer:
4.23 x 10 to the 4, 2 x 10 to the 3, 9.2 x 10 to the 6, 4 x 10 to the 3, 8 x 10 to the 7, and 3.2 x 10 to the 10.
Step-by-step explanation:
I will explain in the comments to this response
The Scientific notation of the number 42300 is 4.23×10⁴.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.
Here, 42300 in Scientific notation as 4.23×10⁴.
2000 in Scientific notation as 2×10³.
9200000 in Scientific notation as 9.2×10⁶.
42300 in Scientific notation as 4.23×10⁴.
4000 in Scientific notation as 4×10³.
80 million=80000000 in Scientific notation as 8×10⁷.
32 billion=32,000,000,000 in Scientific notation as 3.2×10¹⁰.
Therefore, the Scientific notation of the number 42300 is 4.23×10⁴.
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What is the mean and MAD of this data set? (image below)
Answers
Answer:
Mean = 8 gerbils
MAD = 4.29 gerbils
Step-by-step explanation:
Find the mean:
Mean= 0+3+6+9+11+13+14 ÷ 7
Mean = 56 ÷ 7
Mean = 8 gerbils
you have to find the distance of each value of gerbil from the mean
8,5,2,1,3,5,6
MAD = 9+6+3+0+2+4+5 ÷ 7
MAD = 30 ÷ 7
MAD = 4.29 gerbils
A bowl contains 7 white pebbles and 11 black pebbles. A pebble is chosen and not replaced, then another pebble is picked. What is the
probability that the first one is a white pebble and the second one a black pebble?
O a
7
18
Ob
11
18
Ос
11
17
Od
77
306
Answers
Answer:
17 because 2 is taken from 18 and 18-2=16 but 17 and 17 is close to 16
Where is the first error made in the proof?
Answers
Answer: Step 4
Step-by-step explanation:
There is no equation to substitute into, the reason should be 'Pythagorean theorem'.
answer this and i will never forget about you. ever.
Answers
Answer:
(B) 70.5
Step-by-step explanation:
During the first second the acceleration is 2, and the distance is 2
During the second second the acceleration is 5, and the distance is 4.5
During the third second the acceleration is 4, and the distance is 9
During the last 5 seconds the acceleration is 0, velocity is 11 and the distance is 55 m
2 + 4.5 + 9 + 55 = 70.5 (B)
select the correct answer from each drop-down menu.
A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use. What is the area of the tarp?
To find the height, first find that is
. This means the height of the trapezoid is approximately
feet. So, the area of the tarp is approximately
square
Answers
The height of the trapezoidal is 4.33 feet. Then the area of the tarp to cover the pool is 51.96 square feet.
What is a trapezoidal?It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoidal, one pair of opposite sides are parallel.
A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use.
Then the area of the trapezoidal will be
Area = 0.5(sum of parallel sides) height
Then the height of the trapezoidal will be
[tex]\rm h = 5 \times \sin 60 \\\\h = 4.33 \ ft[/tex]
Then the area of the trapezoidal will be
Area = 0.5 × (10 + 12) × 4.33
Area = 51.96 ft²
The area of the tarp to cover the pool is 51.96 square feet.
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Answer:
1. 120 degrees
2. 4.3
3. 47.3
Step-by-step explanation:
PLATO/EDMENTUM
what is the value of 25.761-17.49
Answers
Answer - 25.761-17.49=?
Then,
the answer is 8.271
Alondra wrote the following incomplete statement
4.3 < 4 ___
Which of the following strategies could Alondra use to help her complete the statement? Answer all that apply
Answers
Answer:
4.3< 4.1
Step-by-step explanation:
its 4.1 because 4 is the same and three is greater than one
What is the exact value of tan 150
Answers
Answer:
-0.5774
Step-by-step explanation:
Tan 150 degrees is the value of tangent trigonometric function for an angle equal to 150 degrees. The value of tan 150° is -1/√3 or -0.5774 (approx).
the quotient of 254 and k is 94
Answers
Answer:
k is 23876
Step-by-step explanation:
you have to multiply 254 and 94 by eachothe then that's your answer!
I have 39 test to do and it takes me approximately 5 minutes to do one. How long will it take me to do all of them?
Answers
Answer:
3 hrs and 15 minutes :)
Step-by-step explanation:
We can solve this by multiplying :)
39 x 5 = 195 minutes
195/60 = 3 hrs and 15 minutes :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer: 195 minutes or 3 hours and 15 mintues
Step-by-step explanation:
We will multiply the number of tests by the amount of time it takes to do each test.
39 total tests * 5 minutes = 195 minutes
195 minutes or 3 hours and 15 mintues
For any value of x, the sum
3
∑ k(2x-1)
k=0
is equivalent to
Answers
The equivalent value of the sum for any value of "x" is 12x - 6
How to find the sum of functions?Given the sum of the expression as:
3
∑ k(2x-1)
k=0
We need to take the sum of the function at the point where k = 0 to 3
3
∑ k(2x-1) = 0(2x-1) + 1(2x - 1) + 2(2x-1) + 3(2x - 1)
k=0
3
∑ k(2x-1) = 2x-1+4x-2+6x-3
k=0
3
∑ k(2x-1) = 12x - 6
k=0
Hence the equivalent value of the sum for any value of "x" is 12x - 6
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A picture 8 3/4 feet long is to be centered on a wall that is 12 1/2 feet long. How much space is there from the edge of the wall to the picture?
Answers
Answer:
15/4
Step-by-step explanation:
Find a common denominator in this case 4.
Turn both mixed numbers to an improper fraction
12 1/2 = 25/2
8 3/4 = 35/4
multiply 2 to 25/2 = 50/4
50/4 - 35/4 = 15/4
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Key: 2|5 means 25
Answers
Answer:
42
Step-by-step explanation:
If you add all the number in the stem and leaf plot it equals 336 and you divide by how many numbers there are and there are 8 numbers so 336/8=42
Please mark as Brainliest
what type of line is this
Answers
~Denki Kaminari here~
Answer:
its a best fit line
Step-by-step explanation:
because it is in-between the blue and yellow points, that is what i assume the answer is.
hope this helps :D
Answer:
oblique line.
Step-by-step explanation:
hops this helps
A cube is also a right rectangular prism. What is the surface area of this cube?
6 units
6 units
6 units
Answers
Answer:
I think it is 216 sorry if it is wrong
Step-by-step explanation:
The distance between City A and City B is 250 miles. A length of 1.7 feet represents this distance on a certain wall map. City C and City D are 3.06 feet apart on this map. What is the actual distance between City C and City D?
Answers
Divide 250 by 1.7 to get how many miles are equal to just 1 foot.
250/1.7 = 147.058824 miles per 1 foot
Multiply that times 3.06 feet (the distance between C and D on the map)
147.058824m/1ft x 3.06ft = 450m
The actual distance between City C and City D should be 450 miles.
Identifying Characteristics of Circles from Equations
The equation for a circle is (x + 2)2 + (y – 5)2 = 9.
What is the radius of the circle?
✔ 3
What is the x-coordinate of the circle’s center?
✔ -2
What is the y-coordinate of the circle’s center?
✔ 5
The answers are correct!
Answers
Answer:
Step-by-step explanation:
WHOEVER HELPS ME WILL GET MARKED BRAINLIEST PLSSSSS HELP
Answers
Answer:
D please mark brainliest
Step-by-step explanation:
Answer:
The answer to your question is D(-6, -3)
Step-by-step explanation:
So I need help trying to answer these triangle problems. I don't know how to find the measure of an angle
Answers
Answer:
try using a protractor
Step-by-step explanation:
when you use a protractor it can be easier and collect all like terms together
PLEASE HELP find value of X
x^2 = 9, x = ?
Answers
Answer:
3
Step-by-step explanation:
x^2 means squared
to get x you need to get the square root of 9
which is
3
PLEASE HELP ILL GIVE BRAINLIEST
james bought a movie ticket for $4.05. he paid the movie ticket with quarters and dimes. if james used 18 coins in all, how many quarters (q) and dimes (d) did he use?
Answers
Answer:
15q + 3d
Step-by-step explanation:
15 quarters = 3.75
4.05 - 3.75 = 0.30
3 dimes = 0.30
sooo.
3.75 (15q) + 0.30 (3d) = 4.05
Doctor Jones starts an appointment every 20 minutes.
Doctor Warholm starts an appointment every 35 minutes.
The first appointment for both doctors starts at 8.30 am.
What is the next time that they have an appointment start at the same time?
Answers
The first appointment for both doctors starts at 8:30am.
To find:Next appointment that they start at same time.
Solution:For the same time same time take LCM of 20 and 35.
20= 2x2x5
35= 5×7
hcm (20,35) = 2X2X5X7 = 140
They will take appointment after 140 minutes. 1.e. 2 hours 20 minute.
so, next appoitment will be 10:50a.m.
The next time that they have an appointment start at the same time is at 10:50 a.m.
How do we calculate the appointment time start?We are given that the first appointment for both doctors starts at 8:30am while the Next appointment also started at same time but Doctor Jones starts his every 20 minutes while Doctor Warholm starts his every 35 minutes.
First stepFor the same time, take LCM of 20 and 35.
20 = 2 * 2 * 5
35 = 5 * 7
Second stepHCM (20, 35) = 2 * 2 * 5 * 7
HCM (20, 35) = 140
Hence, it will take the appointment after 140 minutes which equals to 2 hours 20 minute.
Now, from 8.30 am, the addition of the 2 hours 20 minute gives us 10:50 a.m which is the next time that they have an appointment start at the same time.
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x^2-6x+1=0 solve by completing square
Answers
Answer:
x = 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
x² - 6x + 1 = 0 ( subtract 1 from both sides )
x² - 6x = - 1
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 3)x + 9 = - 1 + 9
(x - 3)² = 8 ( take square root of both sides )
x - 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( add 3 to both sides )
x = 3 ± 2[tex]\sqrt{2}[/tex]
An equation is shown below: 3(2x − 7) = 9
Part A: How many solutions does this equation have?
Part B: What are the solutions to this equation? Show your work.
Answers
Answer:
1 solution
Step-by-step explanation:
3(2x-7)=9
dustribute: (3)(2)+(3)(-7x)=9
6+-21x=9
subtract 6 from both sides: -21x=3
Divide both sides by -21: x=-1/7
so your 1 solution is x = - 1/7
