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solmaris [256]
3 years ago
7

There are two numbers that

Mathematics
1 answer:
GREYUIT [131]3 years ago
7 0
-3 x -2 = 6
-3 + -2= -5
answer is -2
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Alicia says the expression 2(m +4)+5 is equivalent to the expression 2m+13. Identify two properties that can be used to support
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Associative property and distributive property
6 0
3 years ago
As an estimation we are told 5 miles is 8 km.<br>Convert 100 km to miles​
dimulka [17.4K]

Answer: 100km = 62.5 miles.

Step-by -step explanation: given 5miles = 8km. now, 5miles — 8km. X miles — 100km. now do cross multiplication.

4 0
3 years ago
Which answer shows a correct order to solve this story problem?
Salsk061 [2.6K]
C is correct. 
1. You do 12.99 times 3
2. $0.69 times 2
3. Add $2.99 to the two prices above
4. Add the $2.52 tax to the prices
And you should get around $45 and some change
7 0
3 years ago
Fred the owl is looking down at a 67° angle from the top of a tree that is 15 ft tall, when he spots a bird on the ground. How f
guapka [62]

Answer:

Fred     C. 16.30 ft

Gary     B. 169.67 m

Step-by-step explanation:

Fred the owl...

Always <u>draw a diagram first</u> (see diagram below). We assume trees are perpendicular (at 90°) to the ground. The situation forms a right-angle triangle.

We need to <u>find "x"</u>, which is the direct distance between the owl and the bird. "x" is also the hypotenuse, which is the longest side in a right-angle triangle. Since we know a side and an angle, we can find the hypotenuse using primary trigonometry ratios.

∠B will be the angle of reference (the angle we are "talking" about). The side we know is opposite to ∠B (15ft). We know it's opposite because it's not touching the angle. The side we need to find is the hypotenuse.

<u>Use the trig. ratio sine</u> because it has opposite and hypotenuse in it. The general formula is:

sinθ = opp/hyp

θ means the angle, and we know it is 67°.

Replace all the information you know:

sinB = opp/hyp

sin67° = (15ft) / x     Isolate "x". Rearrange the equation.

xsin67° = (15ft)         Divide both sides by sin67°

x = (15ft) / sin67°

x = 16.295... ft   Exact answer in decimals

x ≈ 16.30 ft     Rounded to nearest hundredth

Therefore Fred the owl is 16.30 feet from the bird.

Gary spots a monkey...

Draw a diagram first (see below). G is Gary, M is the monkey, T is the bottom of the Sears Tower. We need to <u>find "x"</u>, which is the distance between the monkey and the bottom of the tower.

The angle of reference is M, which is 69°. We need to find the adjacent side and we know the opposite side. <u>The trig. ratio that has adjacent and opposite is tangent.</u>

tanθ = opp/adj

Replace all the information you know:

tanM = opp/adj

tan69° = (442m) / x    Rearrange the formula to isolate "x"

xtan69° = 442m         Divide both sides by tan69°

x = 442m / tan69°      Solve by dividing

x = 169.6679.... m    Exact decimal answer

x ≈ 169.67m            Rounded to the nearest hundredth

Therefore the monkey is 169.67 metres from the tower.

Remember all the trig. ratios using the acronym SohCahToa.

o = opposite side

a = adjacent side

h = hypotenuse side

S = sine, sin for short

C = cosine, cos for short

T = tangent, tan for short

The operation is always dividing the first side in the acronym by the second side.

sinθ = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

4 0
3 years ago
Evaluate the limit of tan 4x/ 4tan3x​
Brut [27]

Answer:

  1/3

Step-by-step explanation:

The ratio is undefined at x=0, so we presume that's where we're interested in the limit. Both numerator and denominator are zero at x=0, so L'Hôpital's rule applies. According to that rule, we replace numerator and denominator with their respective derivatives.

  \displaystyle\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\lim\limits_{x\to 0}\dfrac{\tan'{(4x)}}{4\tan'{(3x)}}=\lim\limits_{x\to 0}\dfrac{4\sec{(4x)^2}}{12\sec{(3x)^2}}=\dfrac{4}{12}\\\\\boxed{\lim\limits_{x\to 0}\dfrac{\tan{(4x)}}{4\tan{(3x)}}=\dfrac{1}{3}}

6 0
2 years ago
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