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2 years ago

What is the exact value of the cos F?

Mathematics

1 answer:

Galina-37 [17]2 years ago

7 0

Answer:

cos(F) = 9/41

Step-by-step explanation:

The triangles are similar, so you know that ...

... cos(D) = cos(A) = 40/41.

From trig relations, you know ...

... cos(F) = sin(D)

and

... sin(D)² +cos(D)² = 1

So ...

... cos(F) = sin(D) = √(1 -cos(D)²) = √(1 -(40/41)²) = √(81/1681)

... cos(F) = 9/41

_____

The ratio for cos(A) tells you that you can consider AB=40, AC=41. Then, using the Pythagorean theorem, you can find BC = √(41² -40²) = √81 = 9.

From the definition of the cosine, you know cos(C) = BC/AC = 9/41. Because the triangles are similar, you know

... cos(F) = cos(C) = 9/41

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destiny sells pencil cases for $5 each and mechanical pencils for $2 each at the school supply store. she sells p pencil cases a

Andrew [12]

Answer:

Step-by-step explanation:

5p + 2(p + 4) .......because pencil cases (p) sell for 5 bucks a piece....and mechanical pencils (p + 4), sell for 2 bucks a piece. She is basically selling 4 more mechanical pencils then she is pencil cases.

8 0

2 years ago

Two production lines produce the same parts per week of which 100 are defective. Line 2 produces 2,000 parts per week of which 1

Vikentia [17]

Answer:

(a) 0.0833 or 8.33%

(b) 0.40 or 40%

Step-by-step explanation:

Parts line one (n1) = 1,000 parts

Defects line one (d1) = 100 parts

Parts line two (n2) = 2,000 parts

Defects line two (d2) = 150 parts

Total number of parts (n) = 3,000 parts

a. Probability of a randomly selected part being defective:

$P(d) = \frac{d_1+d_2}{n_1+n_2}=\frac{100+150}{1,000+2,000}\\P(d) =0.0833=8.33\%$

The probability is 0.0833 or 8.33%

b. Probability of a part being produced by line one, given that it is defective:

$P(1|d)=\frac{P(1\cap d)}{P(1\cap d)+P(2\cap d)}\\P(1|d)=\frac{\frac{100}{3,000} }{\frac{100}{3,000}+\frac{150}{3,000}}\\P(1|d)=0.4 = 40\%$

The probability is 0.40 or 40%.

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2 years ago

If ΔOCD ≅ ΔJAL, then which of the following statements are true? Select True or False for each statement.

andrey2020 [161]

Answer:

true

false

true

Step-by-step explanation:

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2 years ago

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored f

AnnZ [28]

Volume of cube=side³
ok, so you need to know the difference or sum of cubes
a³+b³=(a+b)(x²-xy+y²)
so

(4p)³+(2q²)³=
(4p+2q²)((4p)²-(4p)(2q²)+(2q²)²)=
(4p+2q²)(16p²-8pq²+4q⁴)

3rd option

5 0

2 years ago

Simplify: StartRoot 64 r Superscript 8 Baseline EndRoot

patriot [66]

Answer:

8r^4

Step-by-step explanation:

$\sqrt{64r^8} =\sqrt{(8r^4)^2}=\boxed{8r^4}$

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2 years ago