Se desea construir una letra "ene" mayúscula de tal manera que sus segmentos paralelos midan 25 cm y el
segmento oblicuo que une ambos mida 65 cm. ¿Qué distancia en línea recta separará los segmentos paralelos?
Answers
Answer:
La distancia en línea recta que separa los segmentos paralelos es 60cm.
Step-by-step explanation:
Esta pregunta se puede resolver usando el teorema de Pitágoras:
[tex] \\ c^2 = a^2 + b^2[/tex] [1]
Es decir, en triángulos rectágulos, el cuadrado de la hipotenusa es igual a la suma de los cuadrados de los catetos de dicho triángulo. Un triángulo es rectángulo cuando el ángulo que forman sus dos catetos es recto o de 90 grados sexagesimales.
Es importante notar que la letra N tiene dos lados paralelos y el lado oblicuo (o inclinado) une ambos lados paralelos. Pues bien, la letra N puede formar dos triángulos iguales. Escojamos uno de ellos para obtener la respuesta, es decir, la distancia en línea recta que separa los segmentos paralelos (segmentos verticales de la N)
El lado oblicuo (inclinado) es la hipotenusa de ese triángulo (es decir, c). De los catetos, uno está representado por uno de los segmentos paralelos (verticales) de la N (digamos que es b), y, el otro cateto, es la distancia horizontal que une ambos segmentos verticales (digamos que es a).
Si unimos el segmento inferior del cateto b con el extremo inferior de la hipotenusa, se forma el cateto a. Este cateto a forma un ángulo recto con el cateto b y, por lo tanto, forma un triángulo recto. Los lados de un triángulo recto pueden resolverse usando el teorema de Pitágoras, descrito en [1].
Usando [1] y despejando a, tenemos:
[tex] \\ c^2 = a^2 + b^2[/tex]
Restamos [tex] \\ b^2[/tex] de ambos lados de la igualdad:
[tex] \\ c^2 - b^2 = a^2 + b^2 - b^2[/tex]
[tex] \\ c^2 - b^2 = a^2 + 0[/tex]
[tex] \\ c^2 - b^2 = a^2[/tex]
Luego
[tex] \\ a^2 = c^2 - b^2[/tex]
Extrayendo la raíz cuadrada en cada lado de la igualdad:
[tex] \\ \sqrt{a^2} = \sqrt{c^2 - b^2}[/tex]
Entonces
[tex] \\ a = \sqrt{c^2 - b^2}[/tex]
Asimismo, tenemos que [tex] \\ c = 65[/tex]cm y [tex] \\ b = 25[/tex]cm
Entonces,
[tex] \\ a = \sqrt{65^2 - 25^2}[/tex]
[tex] \\ a = \sqrt{4225 - 625}[/tex]
[tex] \\ a = \sqrt{3600}[/tex]
[tex] \\ a = 60[/tex]cm
De esta manera, el valor de a, o la distancia en línea recta que separa los segmentos paralelos, es 60cm.
Podemos comprobar el resultado anterior haciendo uso del mismo teorema de Pitágoras:
[tex] \\ 65^2 = 60^2 + 25^2[/tex]
[tex] \\ 4225 = 3600 + 625[/tex]
[tex] \\ 4225 = 4225[/tex]
En la figura anexa se aprecia gráficamente lo anteriormente explicado.
Related Questions
Which of the following is always true of the vertical angles formed by
perpendicular lines? Check all that apply.
A. They are congruent.
B. They are right angles.
C. They are acute.
D. They are obtuse.
Answers
Answer:
A
Step-by-step explanation:
This is because vertical angles are always congruent, they cross diagonally which makes them equal to each other.
When two perpendiculars line intersect the angles formed must be a right angle. Hence option b is correct.
What is angle?The angle can be defined as the one line inclined over other line.
Here, When perpendicular lines intersect each other the angle formed between them is 90 degree. So the angles are right angles.
Thus, when two perpendiculars line intersect the angles formed must be a right angle.
Learn more about angles here:
https://brainly.com/question/13954458
#SPJ2
When Mr. Shelton preheated his oven, the oven's temperature rose 3 degrees in 1/6
of a minute. At that rate, how much will the oven heat up in 1 minute?
Answers
Answer:
Step-by-step explanation:
18 degrees
Express 27 1/3 in simplest radical form
Answers
Answer:
this answer is attached to the picture
Radical function or values are values inside the square root. This shows that the cube root of the given value is 3
Radical functionRadical function or values are values inside the square root. For instance;
√a is a radical function.
According to the law of indices
a^1/3 = ∛a
Given the expression
27^1/3 = ∛27
∛27 = 3
This shows that the cube root of the given value is 3
Learn more on radical function here:https://brainly.com/question/13430746
a)Work out an estimate for the mean time it took the students.Round your answer to 2 significant figures.
b)What fraction of the students finished in less than 20 minutes?
Answers
5. An airplane 30,000 feet above the ground begins to descend at a
rate of 2,000 feet per minute. Choose an equation to model this
situation.
A y = 30,000 – 2,000x
B
y = 30,000x - 2,000
Cy= 30,000 + 2,000x
D y = 30,000x + 2,000
Answers
Answer:
A
Step-by-step explanation:
If the airplane is 30,000 feet above the air and descends 2,000 feet it's going down 2,000 feet per minute and cause we don't know how many minutes he was going down we put that as x. and multiply 2,000 for what ever x is.
I just started learning about rate and I am stuck on a question.(A watch keeps perfect time but only has an hour hand. If the hour hand is three fifths of the distance between 1and2, determine the actual time in hours and minutes)
Answers
Answer:
36 minutes past 1, or 1:36
Step-by-step explanation:
A watch normally has an hour hand that does one revolution in 12 hours.
It takes 1 hour to go from the 1 o'clock position to the 2 o'clock position.
Since 1 hour equals 60 minutes, it takes 60 minutes to go from the 1 o'clock position to the 2 o'clock position.
The hour hand is 3/5 of the way from 1 to 2, so the number of minutes past 1 o'clock is 3/5 of 60 minutes.
3/5 of 60 minutes =
= 3/5 * 60 minutes
= 3/5 * 60/1 minutes
= 180/5 minutes
= 36 minutes
The time is 36 minutes past 1, or 1:36
4. Find the length of side EG.
Answers
Answer:
42 cm
Step-by-step explanation:
the first triangle is 7 times bigger than the second triangle. ( 4 x 7 = 28)
so to find out line EG, you times 6 cm by 7. which is 42
a section in a stadium has 24 seats in the first row, 29seats in the second row. increasing by 5 seats each row for a total of 34 rows. how many seats are in this section of the stadium
Answers
Answer:
The answer is 2,142.
Step-by-step explanation:
Mark me brialianist of its right
What is the value of a?
6/2
9
8V
36v2
Answers
Step-by-step explanation:
a= the height of the triangle=h
[tex]h^{2} = ef[/tex]
by ef, e= 18 & f=4
so...
[tex]h^{2} = 18 \times 4 = 72[/tex]
so you put both of them in a square root
[tex] \sqrt{h} = \sqrt{72}[/tex]
so the answer will be
[tex]h = \sqrt{72} = 6 \sqrt{2} [/tex]
Answer:
The answer is A
Step-by-step explanation:
Edg2020
Find 3 rational numbers between ¼ and ½
Answers
Answer:
5/16 and 3/8 are two
Step-by-step explanation:
idk a third
What is the answer to angle A? And do you mind to explain how
Answers
Answer:
45 degrees
Step-by-step explanation:
The sum of the angles of a triangle always adds up to 180.
10x + 8x + 5 + 85 = 180
Simplify by combining like terms.
18x + 90 = 180
Subtract 90 from both sides.
18x = 90
Divide both sides by 18.
x = 5 degrees
But the question didn't ask for x, it asked for angle A. So plug back in.
A = 8x + 5
A = 8(5) + 5
A = 40 + 5 = 45 degrees
Answer:
[tex]45 \: \: degrees[/tex]
Step-by-step explanation:
[tex]10x + 8x + 5 + 85 = 180 \\ 18x + 90 = 180 \\ 18x = 180 - 90 \\ 18x = 90 \\ \frac{18x}{18} = \frac{90}{18} \\ x = 5[/tex]
[tex]angle \: \: \: a = 8x + 5 \\ = 8 \times 5 + 5 \\ = 40 + 5 \\ = 45 \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Please help! Correct answer only!
I've been on this question for more than an hour...
You pick a card at random. Without putting the first card back, you pick a second card at random.
What is the probability of picking a 3 and then picking a 3?
Simplify your answer and write it as a fraction or whole number.
Answers
Answer:
You have three card : 3, 4, 5 and 6.
You first pick one card randomly, the probability of picking a 3 is:
P = 1/4
You then pick a second card without putting the first card back, the probability of picking a 3 is:
P = 1/3
=> The probability of picking a 3 and then picking a 3:
P = (1/4) x (1/3) = 1/12
Hope this helps!
:)
Pleaseee helpp i will let you brainlest
Answers
Answer:
13
Step-by-step explanation:
use Pythagorean
it is usually, 5, 12, 13
Explanation:-
2 2
Hypotenuse (x) = 12 + 5
= 144 + 25
= 169 route is
= 13
Jeffery surveyed 50 randomly selected workers at a factory. He collected data about the individual output of a worker on an average day. The results are shown using the box-and-whisker plot. What percent of workers have output more than 70 units?
Answers
Answer:
the answer is 30% of the workers have output more than 70 units.
Step-by-step explanation:
Answer: I believe the answer is 25%.
Correct answers only please! I keep loosing points...
Quincy has $6,000 in a savings account that earns 4% interest, compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answers
Answer:
$ 7,299.92
Step-by-step explanation:
A = $ 7,299.92
A = P + I where
P (principal) = $ 6,000.00
I (interest) = $ 1,299.92
Your Monthly Net Pay
If your gross monthly income will be $3,750, you need
to determine the net pay for your monthly budget.
Your monthly net pay is
Monthly gross pay
$3,750
Federal withholding
$238.00
Social Security
$232.50
Medicare
$54.38
State tax
$236.00
Net pay
$?
Answers
Answer:
2989.12
Step-by-step explanation:
238.00+232.50+54.88+236.00= 760.88
3750-760.88=2989.12
In how many ways can a
recorder, facilitator, and
questioner be chosen in a club
containing 14 members?
Answers
Answer:
The answer is 364. There are 364 ways of choosing a recorder, a facilitator and a questioner froma club containing 14 members.
This is a Combination problem.
Combination is a branch of mathematics that deals with the problem relating to the number of iterations which allows one to select a sample of elements which we can term "r" from a collection or a group of distinct objects which we can name "n". The rules here are that replacements are not allowed and sample elements may be chosen in any order.
Step-by-step explanation:
Step I
The formula is given as
[tex]C (n,r) = \frac{n}{r} = \frac{n!}{(r!(n-r)!)}[/tex]
n (objects) = 14
r (sample) = 3
Step 2 - Insert Figures
C (14, 3) = [tex](\frac{14}{3})[/tex] = [tex]\frac{14!}{(3!(14-3)!)}[/tex]
= [tex]\frac{87178291200}{(6 X 39916800)}[/tex]
= [tex]\frac{87178291200}{239500800}[/tex]
= 364
Step 3
The total number of ways a recorder, a facilitator and a questioner can be chosen in a club containing 14 members therefore is 364.
Cheers!
A stock has a price of $72.31. This is $6.28 less than the price of the stock yesterday. Write and solve an equation to find the price p (in dollars) of the stock yesterday. An equation is =72.31. The price of the stock yesterday was $ .
Answers
Answer: The price of the stock yesterday was $78.59
Step-by-step explanation:
p - 6.28=72.31
+6.28 + 6.28
p= 78.59
Answer:
78.59$
Step-by-step explanation:
p-6.28=72.31
p=72.31+6.28
p=78.59$
It’s a proof... but I don’t think it’s that hard! *sorry I’m just dumb so please do this proof for me...*
Answers
Answer:
1. given
2. bisected angles create two congruent angles
3. same side length
4. ASA: angle, side, angle congruency
5. the two triangles are congruent, meaning all of their side lengths correspond, meaning that YZ and WZ are equivalent.
3 1/2 divided by 2 3/5
Answers
Step-by-step explanation:
31/2×5/23 (use reciprocal)
31×5=155
155÷46=3.369565217
155/46
3 and 17/46
Please find attached.
Answers
Answer:
5.83
Step-by-step explanation:
[tex]c=\sqrt{a^2+b^2\\} =\sqrt{3^2+5^2}\\=5.83[/tex]
Answer:
5.83
Step-by-step explanation:
rs²=3²+5²
rs²=9+25
rs²=34
rs=5.83
help i will give brainliest
Answers
Answer:
1/9
Step-by-step explanation:
The area of a polygon is the old area multiplied by the scale factor squared
New area = old area ( SF) ^2
The scale factor is 1/3
(1/3) ^2 = 1/9
The fraction is 1/9
Find the volume of each cylinder. Which cylinder has the greater volume? Use 3.14 for . For cylinder A , h=5 m &c=3 m, cylinder B, h=3 m & c=5 m.
Answers
Answer:
Cylinder B has a greater volume
Step-by-step explanation:
Volume of a cylinder[tex]=\pi r^2h[/tex]
Cylinder A
h=5m, r=3m
Volume
[tex]=3.14 *3^2*5\\=141.3m^3[/tex]
Cylinder B
h=3m, r=5m
Volume
[tex]=3.14 *5^2*3\\=235.5m^3[/tex]
Cylinder B has a greater volume.
Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if
there are at least 100 people on the plane. Write a compound inequality to show the possible number of
people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight.
Answers
Answer:
562
Step-by-step explanation:
if 240 equals 100
Divide X^4 + 2x^2+1 by x+1
Answers
=x^5+2x^3+1+x÷×
Step-by-step explanation:
x^4+2x^2+(1÷x)+1
make 1÷x a fraction
x^4+2x^2+1/x+1
=x5+2x^3+1+x/x
Tammy bought two rolls of tape. The first roll had 4.8 feet of tape and the second roll had 9.87 feet of tape. How many feet of tape did Tammy buy in all? *
Answers
Answer:
14.67ft of tape
Step-by-step explanation:
4.8+9.87=14.67
Some help please? I’m lost
Answers
Answer:
1/2
Step-by-step explanation:
When you find the sine of an angle, it is the opposite side / hypotenuse. This means that the hypotenuse of this triangle is 2 and the side opposite to 60° is √3. This means that the side adjacent to 60° is 1 (Pythagorean Theorem). When you find the cosine of an angle, it is the adjacent side / hypotenuse, which in this case will be 1 / 2. Hope this helps!
Answer:
1/2.
Step-by-step explanation:
Sine = opposite side / hypotenuse.
The side opposite 60 degrees has length√3 and the hypotenuse = 2.
By Pythagoras the side adjacent to the angle 60 = √( 2^2 - 3)
= 1 unit.
So cos 60 = adjacent / hypotenuse = 1/2.
In the problem 8^3 - 10 × 5 - 4
Answers
Answer: 458
Simplify
8³=8×8×8
Multiply
8×8×8=512
10×5=50
Subtract
512-50=462
462-4=458
Answer:
458
Step-by-step explanation:
8×8×8=512
10×5=50
512- 50 = 462
462-4= 458
Fill in the missing portions of the function to rewrite g(x) = 3a^2 − 42a + 135 to reveal the zeros of the function. What are the zeros of g(x)? (show your work!)
Enter your answers in the blanks:
g(x) = 3(_____)(_____)
Zeros: ______ and ______
Answers
Answer:
g(x) = 3(x-9)(x-5)
Zeros: x = 9 and x = 5.
Step-by-step explanation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]g(x) = 3x^{2} - 42a + 135[/tex]
So
[tex]a = 3, b = -42, c = 135[/tex]
[tex]\bigtriangleup = (-42)^{2} - 4*3*135 = 144[/tex]
[tex]x_{1} = \frac{-(-42) + \sqrt{144}}{2*3} = 9[/tex]
[tex]x_{2} = \frac{-(42) - \sqrt{144}}{2*3} = 5[/tex]
So
g(x) = 3(x-9)(x-5)
Zeros: x = 9 and x = 5.
What is the solution to the linear equation? 2/4x - 1/2 = 1/3 + 5/6x
Answers
Answer:
x=-60/24 or -5/2
Step-by-step explanation:
u have to find X
2/4x - 1/2 = 1/3 + 5/6x
subtract 2/4x from both sides
to do that u need to have common denominator
2/4= 6/12
5/6=10/12
-1/2=1/3+4/12x
subtract 1/3 on both sides and u need common denominator
-1/2=-3/6
1/3=2/6
-5/6=4/12x
multiply 12/4 on both sides
x=-60/24
Answer:
x=-5/2
Step-by-step explanation:
2/4x-1/2=1/3+5/6x
-5/6x -5/6x
2/4x-5/6x-1/2 =1/3
+1/2 +1/2
6/12x-10/12x=2/6+3/6
-4/12x=5/6
x=5/6:(-4/12)=5/6*(-12/4)=-5/2
x=-5/2