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
What is the product of (-a + 3)(a + 4)?
A. - a2 - a - 12
B. a2 - a + 12
C. - a2 - a + 12
D. a2 - a - 12
Answers
Answer:
-a^2-a+12
Step-by-step explanation:
Answer:
Option C.
[tex]-a^{2}-a+12[/tex]
Step-by-step explanation:
1. Distributive multiply
[tex]-a*(a+4)+3*(a+4)[/tex]
2. Distributive multiply
[tex]-a*a-a*4+3*(a+4)[/tex]
3. Multiply terms to exponential form
[tex](-1) *a^{2}-a*4+3*(a+4)[/tex]
4. Multiply constants
[tex]-a^{2}-4*a+3*(a+4)[/tex]
5. Distributive multiply
[tex]-a^{2}-4a+(3*a+3*4)[/tex]
6. Multiply constants
[tex]-a^{2}-4a+(3a+12)[/tex]
7. Reorder terms
[tex]-a^{2} -4a+(12+3a)[/tex]
8. Add terms
[tex]-a^{2}-a+12[/tex]
From a point, 50 feet from the base of a building, the angle of elevation from ground level to the top of the building is 66°. find the height of the building to the nearest hundredth of a foot
Answers
Answer:
112.30 ft
Step-by-step explanation:
The geometry can be modeled by a right triangle with a base of 50 ft, an angle adjacent to the base of 66°, and a side opposite the angle that is the height of the building. The relationship between these measures is given by the trig function ...
Tan = Opposite/Adjacent
tan(66°) = height/(50 ft)
Solving for the height gives ...
height = (50 ft)tan(66°) ≈ 112.30 ft
The height of the building is about 112.30 feet.
A repairman charges a flat fee of $50 to come to a customer's house, plus a charge per hour for any work completed. The repairman charged a customer $154 after 4 hours of work. Which function will calculate the cost of the repairman after x hours of work?
Answers
Answer:
50 - 4x = 154;
Step-by-step explanation:
50 - 4x = 154
154 - 50 = 104
104 / 4 = 26
x = 26
A rectangle has a length of 9 m and a width of 5 m. What is its perimeter?
14 m
40 m
28 m
26 m please help me
Answers
9 m length and 5m width.
to find:perimeter
solution:perimeter of rectangle= l+l+b+b
= 9+9+5+5
= 28m
You need to fill a cylindrical glass with water. the glass is 6 inches tall and 2
inches across at the widest point. how many cubic inches of water is needed to
fill the glass? enter the answer exactly as it appears on your calculator. no
rounding this time.
Answers
volume = pi x r^2 ×h
where r is radius and h is height.
h= 6 in
r= 1
V=(22/7)×1^2 ×6
V=18.857in^3
Step-by-step explanation: Since the glass cup is cylindrical in shape, we use the formula for find volume of a cylinder iff the glass cup is to be filled full.
The volume of water will be equal to the volume of the cup. Across the widest point means diameter, hence half diameter gives radius.
PLS HELPPPPPPP
A, B and C line up randomly to buy tickets. Find the probability that A is beside C in the queue
Answers
Answer:
Sample Space = {(ABC), (ACB), (BAC), (BCA), (CAB), (CBA)}
= 6
Instances when A is besides C {(ACB),( BAC),( BCA), ( CAB)}
=4
P( A is besides C)= 4/6
= 2/3MARK ME AS BRAINLISTFind the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are exactly that.
See picture for full problem. Please and thank you so very much.
Answers
Answer:
50 degrees
Step-by-step explanation:
the attached photo might help
There are 1,000 balls in a container. All of the balls are the same size and shape. In the container, there are 400 red balls; 250 orange balls; 100 green balls; and 250 yellow balls. A student will pick one ball at random from the container. What are the probabilities that the student will pick a ball that is either red, orange, or green? Select the three correct probabilities.
A) Red = 1/4
B) Red = 0. 4
C) Orange = 1/4
D) Orange = 0. 4
E) Green = 0. 1%
F) Green = 10%
Answers
Orange = 250/1000 = 1/4 [0.25]
Green = 100/1000 = 10%
What is the form of the Difference of Squares identity?
A. a^2 + b^2=(a - b)(a - b)
B. a^2- b^2 = (a+b)(a - b)
C. a^2 - b^2 = (a - b)(a - b)
D. a^2- b^2 = (a+b)(a + b)
Answers
The answer is B
seeing there are 3 way to put it
(a+b)(a-b)=a 2-b 2
(a+b)(a-b)=a^2-b^2
(a+b)(a-b)=a2-b2
and option B matches with the second way to put it i hope this helps
whats -2( 20x + 2) = -36
Answers
Answer:
[tex]x= \dfrac 45[/tex]
Step by step explanation:
[tex]-2(20x+2) = -36\\\\\implies 20x +2 = \dfrac{-36}{-2} = 18\\\\\implies 20x = 18 - 2=16\\\\\implies x = \dfrac{16}{20}=\dfrac{4}5[/tex]
-2x+4y=28
-3x +2y = 6
Solve for x
Answers
Answer:
x=4, y=9
Step-by-step explanation:
Solve with substitution.
HELP HELP I GIVE BRANLISEST
Answers
Area of triangle:-
1/2(6)(12)6(6)=36cm²Area of rectangle (Including semicircle)
12(21)252cm²Area of semicircle
πr²/2π(6)²/218πcm²56.52cm²TOTAL area:-
36+252-56.52288-56.52231.48cm²Answer:
231.48 cm²
Step-by-step explanation:
Formulae
Area of a rectangle = width × length
Area of a triangle = 1/2 × base × height
Area of a semicircle = 1/2 πr²
To find the shaded area:
Find the area of the rectangle. Subtract the area of the semicircle from the rectangle. Add this to the area of the triangle.
Area of the rectangle:
= 12 x 21
= 252 cm²
Area of the semicircle:
= 1/2 π(12 ÷ 2)²
= 1/2 · 3.14 · 6²
= 1/2 · 3.14 · 36
= 56.52 cm²
Area of the triangle:
= 1/2 x 6 x 12
= 36 cm²
Shaded area:
= area of rectangle - area of semicircle + area of triangle
= 252 - 56.52 + 36
= 194.48 + 36
= 231.48 cm²
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answers
To use the Pythagorean theorem:
⇒ define Pythagorean theorem
(look at the diagram attached for a better understanding)
Information Given:
length of the two legs: 5, 9Information Wanted:
length of hypotenuseSolve:
[tex]5^2+9^2=hypotenuse^2\\hypotenuse^2 = 5^2 +9^2 = 25 + 81 = 106\\hypotenuse = 10.29[/tex]
Rounded to nearest tenth:
Answer: Length of hypotenuse is 10.3
Hope that helps!
solve for x: 4x+1/2(2x+4) >12
Answers
Answer: x>2
Step-by-step explanation:
[tex]4x+\frac{1}{2} (2x+4) > 12[/tex]
Step 1: Simplify both sides of the inequality through the Distributive Property
[tex]4x+\frac{1}{2} (2x+4) > 12\\4x+(\frac{1}{2})(2x)+(\frac{1}{2})(4) > 12\\4x+x+2 > 12\\5x+2 > 12[/tex]
Step 2: Subtract 2 from both sides to isolate x
[tex]5x+2-2 > 12-2\\5x > 10[/tex]
Step 3: Divide both sides by 5 to full isolate x
[tex]\frac{5x}{5} > \frac{10}{5} \\x > 2[/tex]
Answer:
[tex]x > 2[/tex]
Step-by-step explanation:
[tex]4x+\frac{1}{2}(2x+4) > 12 < ==multiply\ the\ \#s\ in\ the\ parenthesis\ first\ using\ \frac{1}{2}\\\\4x+x+2 > 12 < ==combine\ any\ like\ terms\\\\5x+2 > 12 < ==subtract\ 2\ from\ both\ sides\\-2 \ \ \ \ \ -2\\\\5x > 10 < ==divide\ both\ sides\ by\ 5\\/5 \ \ \ \ /5\\\\x > 2[/tex]
This means that x can be any value that is greater than 2.
Hope this helps!
f(x)= -2x^2
what is the vertex of this and/or how do you find the vertex??
Answers
Answer:
(0,0)
Step-by-step explanation:
x value of vertex = -b/2a
ax^2+bx+c
-2x^2+0x+0 sinc you have no value of b & c in your quadratic function
-b = 0
2a = (2)(-2)
-b/2a = (0/-4) = 0
x value of the vertex = 0
plug 0 in for all values of x in the function to find y coordinate value
-2(0)^2 = 0
(x,y) = (0,0)
Fifteen is 3/8 of what number
Answers
Let's write the verbal phrase "fifteen is 3/8 of what number" as an algebraic equation ↓
15=3/8x (let x be the number)
Multiply by 8 on both sides to get rid of the fraction :
15*8=3x
120=3x
divide by 40 on both sides ↓
40=x
So 15 is 3/8 of 40.hope helpful ~
multiply (x-3)(x-6) with steps please
Answers
x
2
−
9
x
+
18
x
2
-
9
x
+
18
44 is the sum of 14 and Rick's savings.
Answers
HEL PLS ITS MY HOMEWORK AND I REALLY NEED HELP
Answers
Answer and explanation:
Take the area formula:
A = L * W
Then manipulate it to fit the context of which unknown you are finding:
Problem 1
[tex]\dfrac{36 = 4 * W}{4}[/tex]
[tex]9 = W[/tex]
So, the length of side c is 9 mm.
Problem 2
[tex]\dfrac{21 = W * 21}{21}[/tex]
[tex]1 = W[/tex]
So, the length of side a is 1 m.
Problem 3
[tex]\dfrac{49 = 7 * W}{7}[/tex]
[tex]7=W[/tex]
So, the length of side t is 7 cm.
Please help Will give BRAINLIEST !!! :)
Answers
Answer:
D no. is for sure another I also don't know. So sorry.......
I know it's not A. I need help please
Answers
Answer:
139 degrees
Step-by-step explanation:
The sum of the interior angles of a polygon :
sum = ( n-2) * 180 where n = number of sides
For this one there are 5 sides
so ( 5-2) * 180 = 540 degrees
angle U = 90 degrees
90 + 82 + Y + 121 + 108 = 540 Y=139 degrees
Answer:
It is C. 139
Step-by-step explanation:
Angles of TVXXYZ is 720 degrees. We know that angles Z, W and X are 82 degrees, 108 degrees and 121 degrees (311 degrees after adding them). T= 180-28=152 degrees
V=90+28=118 degrees
152+118=270 degrees
270+311=581
720-581=139 degrees
The answer is C. 139 degrees
Let A={1,2,3,4,5} and B={2,4} what is AnB
Answers
Answer:
AnB = { 2,4}
Step-by-step explanation:
A={1,2,3,4,5} and B={2,4}
AnB means A intersect B or what is common to both A and B
AnB = { 2,4}
help please find x and y, 10 points and brainliest to best answer
Answers
Answer:
y =8
x=80
Step-by-step explanation:
5y-10=3y+6
5y-3y=6+10
2y =16
y=8
x+30+x-10=180
2x+20=180
2x=160
x=80
Can someone help me please, its for plato algebra 2-1
Answers
Answer:
5
Step-by-step explanation:
Simplification:
[tex]\sqrt{2^3-7} + |-4|[/tex]
[tex]\sqrt{1} + 4[/tex]
1 + 4
5
You received an $40,000 bonus, which was 18% of your salary. What is the percentage of your salary is this bonus?
Answers
Answer:
2.3% is the percentage of the Salary
Step-by-step explanation:
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
PLEASEEEE HELLPPPP!!!!!!!!!!!!!!!!
Answers
180-165=x
X=15
If the two acute angles of a right triangle are congruent, then what is the measure of each acute angle?
Answers
I need this ASAP!!!!!
Answers
Answer:
7/5 y intercept 1
Step-by-step explanation
Answer:
B: slope 5/7 Y-intercept is 1
Step-by-step explanation:
To calculate the slope it is rise orver run
To calculate the Y intercept you look at the graph and where-ever x=0 and y=- is the number.
The slope is 5/7 because the rise is 10 and the run is 14. 10/14 is simplified to 5/7.
the Y intercept is 1 because on the vertical line the line passes through 0,1.
find the mean absolute deviation of the data below:
7,4,7,7,2,10,12,8,7,5
Answers
Answer:
1.9
Step by step answer
step1 finding the mean
(7+4+7+7+2+10+12+8+7+5)/10 = 6.9
step2 Difference between each data
Difference between 7 and 6.9 is 0.1
Difference between 4 and 6.9 is 2.9
Difference between 7 and 6.9 is 0.1
Difference between 7 and 6.9 is 0.1
Difference between 2 and 6.9 is 4.9
Difference between 10 and 6.9 is 3.1
Difference between 12 and 6.9 is 5.1
Difference between 8 and 6.9 is 1.1
Difference between 7 and 6.9 is 0.1
Difference between 5 and 6.9 is 1.9
step3 add all the Difference
0.1 + 2.9+0.1+0.1+4.9+3.1+5.1+1.1+1.9 = 19.4
step4 divde it by n
19.4/10 = 1.9
so the answer is 1.9