He is correct, the answer is B.
Answer:
a) 1/7 liters of petrol is used for each mile
Step-by-step explanation:
Justin fills his car with 40 litres of petrol. After travelling 35 miles it's down to 35 litres.
From the above statement:.
The difference is :
40 litres - 35 liters = 5 liters
Hence:
After travelling 35 miles he used 5 liters
(a) How much petrol does the car use each mile?
This is calculated as:
35 miles = 5 Liters
1 mile = x liters
Cross Multiply
35x = 5 Liters
x = 5/35
x = 1/7 liters
Hence, for each mile, 1/7 liters of petrol is used
Answer:
x = 40
m∠Q = 105°
m∠R = 40°
m∠P = 35°
Step-by-step explanation:
Sum of Angles in a Triangle: 180°
Step 1: Define variables
m∠Q = 2x + 25
m∠R = x
m∠P = x - 5
Step 2: Set up equation
m∠Q + m∠R + m∠P = 180°
2x + 25 + x + x - 5 = 180°
Step 3: Solve for <em>x</em>
4x + 20 = 180
4x = 160
x = 40
Step 4: Solve for measure angles.
m∠Q = 2x + 25
m∠Q = 2(40) + 25 = 80 + 25 = 105°
m∠R = x
m∠R = 40°
m∠P = x - 5
m∠P = 40 - 5 = 35°
Answer:
Theoretical probability. 1/13
Step-by-step explanation:
probablility = number of favorable outcomes/number of possible outcomes
Since there are four 5's in a deck, this will be the numerator and since there is 52 cards in a deck this will be the denominator.
(p of drawing a 5) = 4/52
Simplify the fraction by dividing the numerator and denominator by 4
4/52 ÷ 4/4 = 1/13
This is theoretical probability because you are not actually drawing the cards.
The trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
<h3>
How to solve the trigonometric identity?</h3>
Since (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
Using the identity a² - b² = (a + b)(a - b), we have
(cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = [(cos²θ)² - (sin²θ)²]/[1 - (tan²θ)²]
= (cos²θ - sin²θ)(cos²θ + sin²θ)/[(1 - tan²θ)(1 + tan²θ)] =
= (cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] (since (cos²θ + sin²θ) = 1 and 1 + tan²θ = sec²θ)
Also, Using the identity a² - b² = (a + b)(a - b), we have
(cos²θ - sin²θ) × 1/[(1 - tan²θ)sec²θ] = (cosθ - sinθ)(cosθ + sinθ)/[(1 - tanθ)(1 + tanθ)sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)/cosθ × (cosθ + sinθ)/cosθ × sec²θ]
= (cosθ - sinθ)(cosθ + sinθ)/[(cosθ - sinθ)(cosθ + sinθ)/cos²θ × 1/cos²θ]
= (cosθ - sinθ)(cosθ + sinθ)cos⁴θ/[(cosθ - sinθ)(cosθ + sinθ)]
= 1 × cos⁴θ
= cos⁴θ
So, the trigonometric identity (cos⁴θ - sin⁴θ)/(1 - tan⁴θ) = cos⁴θ
Learn more about trigonometric identities here:
brainly.com/question/27990864
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