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RideAnS [48]
2 years ago
7

A portion of the Quadratic Formula proof is shown. Fill in the missing statement.

Mathematics
1 answer:
Angelina_Jolie [31]2 years ago
8 0

x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 -4ac}}{2a}

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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
4 7/12 divided by 3/4 multipled by 3/11
Vlada [557]
Here is the answer With working

6 0
3 years ago
Six students earned a perfect score on a history quiz. Only 5% of the entire grade earned a perfect score. How many students are
stiks02 [169]

Answer:

120

Step-by-step explanation:

If 6 = 5%, then 6 = 1/20 of the total grade. 6×20= 120

5 0
2 years ago
There are 12 donuts in a box, and Claire at 2. Approximately what percent of the donuts remain in the box? (Round to the nearest
skelet666 [1.2K]

Answer:

83% remains in the box

Step-by-step explanation:

Here, we are interested in calculating the percentage of donuts remaining in the box.

From the question, we are told that 2 was eaten, the number of donuts left = 12-2 = 10 donuts

The percentage of donuts left would be;

Number of donuts left/Total no of donuts * 100%

= 10/12 * 100 = 83.33

Which is 83% to the nearest whole number percentage

5 0
3 years ago
Evaluate the expression when m=6 and n=33. <br><br> n-5m=
jok3333 [9.3K]
N = 33 and m = 6 substitute in the values in place of the variables to get 33 - 5*(6). distribute the five to get 33 - 30 =3. the answer is three
5 0
3 years ago
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