Plz answer 1 and 2 for me plz plz plz

Based on the information given in the question, the inequality which can be used to determine x, the number of people who can go to the amusement park will be:

8 + 23(x) ≤ 100

8 + 23x ≤ 100

23x ≤ 100 - 8

23x ≤ 92

x ≤ 92/23

x ≤ 4

The number of people that can go to the amusement park will be at most 4

6 0

3 years ago

Complete the tables to determine if the expressions are equivalent. If the expressions are equivalent, name the properties that

jok3333 [9.3K]

I don’t know how to necessarily complete the tables but i know they are equivalent

1. 3(x-5)
3 (x) = 3x
3 (-5) = -15

that is the distributive property thus it equals

3x - 15

2. 3x - 15

they’re the same

5 0

2 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$