Given:
Consider the sides of the triangle are 4x+10, 2x-5 and 18 (in feet).
Perimeter of this triangle is to be no more than 77 feet.
To find:
The inequality and solution of the inequality.
Solution:
Perimeter of a triangle is the sum of all side.
Perimeter of given triangle ![=(4x+10)+(2x-5)+18](https://tex.z-dn.net/?f=%3D%284x%2B10%29%2B%282x-5%29%2B18)
Perimeter of this triangle is to be no more than 77 feet. It means perimeter must be less than or equal to 77.
![(4x+10)+(2x-5)+18\leq 77](https://tex.z-dn.net/?f=%284x%2B10%29%2B%282x-5%29%2B18%5Cleq%2077)
![(4x+2x)+(10-5+18)\leq 77](https://tex.z-dn.net/?f=%284x%2B2x%29%2B%2810-5%2B18%29%5Cleq%2077)
![6x+23\leq 77](https://tex.z-dn.net/?f=6x%2B23%5Cleq%2077)
![6x\leq 77-23](https://tex.z-dn.net/?f=6x%5Cleq%2077-23)
![6x\leq 54](https://tex.z-dn.net/?f=6x%5Cleq%2054)
Divide both sides by 6.
![x\leq \dfrac{54}{6}](https://tex.z-dn.net/?f=x%5Cleq%20%5Cdfrac%7B54%7D%7B6%7D)
![x\leq 9](https://tex.z-dn.net/?f=x%5Cleq%209)
Therefore, the required inequality is
and the solution is
.
Se pueden concluir dos posibilidades para cada bolsa y toda la colección:
- 4 balones rojos y un balón azul, lo cual lleva a 16 balones rojos y 4 balones azules.
- 3 balones rojos y dos balones azules, lo cual lleva a 12 balones rojos y 8 balones azules.
<h3>¿Cuántos balones rojos tiene Roberto en las cuatro bolsas?</h3>
En este problema conocemos que Roberto tiene 20 balones entre azules y rojos y que existen más balones rojos que azules. Puesto que los balones son objetos que pueden contarse, los datos a buscar deben ser números enteros y positivos y que están distribuidos equitativamente en cuatro bolsas. Entonces las cantidades de balones por bolsa son:
x = 20 / 4
x = 5
Existen 5 balones por bolsa y bajo la consideración de que existen balones azules, que cada bolsa tienen la misma proporción de balones rojos a azules y que los balones rojos son más que los balones azules, se pueden concluir dos posibilidades para cada bolsa:
- 4 balones rojos y un balón azul, lo cual lleva a 16 balones rojos y 4 balones azules.
- 3 balones rojos y dos balones azules, lo cual lleva a 12 balones rojos y 8 balones azules.
Para aprender más sobre proporciones: brainly.com/question/27957192
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If we have a triangle with sides a and b and an included angle of C, then the area of the triangle would be:
A = (1/2) ab sin C
If angle C is bisected into two each angles each measuring x, then the area can be expressed as:
A = (1/2) ab sin 2x
Using the trigonometric identity for sin 2x = 2 sin x cos x, the area would now be:
A = ab sin x cos x
Since the line segment s divides the angle into two, it also divides the triangle into two. Another equation for the area is:
A = (1/2) as sin x + (1/2) bs sin x
Equating the two equations gives us:
ab cos x = (1/2) as + (1/2) bs
Solving for s
s = 2 ab cos x / (a + b)
Answer:
$836.8
Step-by-step explanation:
Average price = mean = $965
Standard deviation, = $100
Given that distribution is approximately normal ;
The least expensive 10% of the laptops :
We Obtain the Zscore that corresponds to P(Z ≤ 0.1) ; this means the least 10% of the laptops ;
From, a normal probability distribution table ;
P(Z ≤ 0.1) = - 1.282
We substitute this into the Zscore formula :
Zscore = (x - mean ) / standard deviation
x = price
-1.282 = (x - 965) / 100
-128.2 = (x - 965)
x = - 128.2 + 965
x = $836.8
Hence, price is $836.8
Answer:
4/5 frames/h
Step-by-step explanation:
Find the ratio frames per hour by dividing frames by hours:
(4 frames)/(5 hours) = (4/5) frames/hour