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jok3333 [9.3K]
2 years ago
6

Fill in the blank. If necessary, use the slash mark ( / ) for a fraction bar.

Mathematics
2 answers:
kipiarov [429]2 years ago
8 0

Answer:

cos Ф = adj / hyp could be either 4/5 or -4/5.

Step-by-step explanation:

If sin Ф = 3/5, then we can assume that the opposite side is 3 and the hypotenuse is 5.  Using the Pythagorean Theorem, we find that the adjacent side is 4:  

√(5² - 3²) = √16 = ±4.

cos Ф = adj / hyp could be either 4/5 or -4/5.

iris [78.8K]2 years ago
6 0

Answer:

\frac{4}{5}

Step-by-step explanation:

Given,

sin \theta = \frac{3}{5}

\because sin \theta =\frac{\text{Opposite side of }\theta}{\text{Hypotenuse }}

By comparing,

Opposite side of \theta = 3

Hypotenuse = 5,

By pythagoras theorem,

Adjacent side of \theta = \sqrt{5^2 - 3^2}=\sqrt{25-9}=\sqrt{16}=4

Now,

cos \theta =\frac{\text{Adjacent side of }\theta}{\text{Hypotenuse }}

\implies cos \theta=\frac{4}{5}

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Susanne is going to college and was informed that she will get a grant to pay for
Yakvenalex [24]

Answer:

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2 years ago
Graph A line goes through the point (6,–2) and has a slope of –3. What is the value of a if the point (a,7) lies on the line?
3241004551 [841]

Answer:

The value of a is 3

Step-by-step explanation:

First you have to make an equation based on the point and slope that you were given. The formula for this is y-(y cordinate of point)=slope(x-x cordinate of slope)

y--2=-3(x-6), which simplifies to y+2=-3(x-6)

In (a,7), 7 is the y coordinate. We have to plug 7 in for the y in our equation.

7+2=-3(x-6),

Combine like terms on the left side to get to 9=-3(x-6)

Multiply out on the left to get 9=-3x+18

Subtract 18 from the left side to get -9=-3x

Divide both sides by negative 3 to get 3=x (remember x is a)

7 0
2 years ago
Write the equation of the line that passes through the points
anyanavicka [17]

Answer:

The equation that passes through (−7,−3)and (−2,−1) is y=2/5x-1/5

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=(-1)-(-3)/(-2)-(-7)

m=2/5

y-y=m(x-x¹)

y-(-1)=2/5(x-(-2)

y+1=2/5x+4/5

-1 -1

y=2/5x-1/5

7 0
3 years ago
Consider the function below. f(x) = 6x tan x, −π/2 < x < π/2 (a) find the vertical asymptote(s). (enter your answers as a
Molodets [167]

Answer: Does not exist.

Step-by-step explanation:

Since, given function,  f(x) = 6x tan x, where −π/2 < x < π/2.

⇒ f(x) = \frac{6x sin x}{cosx}

And, for vertical asymptote,  cosx= 0

⇒ x = π/2 + nπ where n is any integer.

But, for any n x is does not exist in the interval ( -π/2, π/2)

Therefore, vertical asymptote of f(x) where −π/2 < x < π/2 does not exist.


5 0
3 years ago
Read 2 more answers
I need help with coming up with equation
Natali5045456 [20]

Let's call a child's ticket c and an adult's ticket a. From this, we can say:

c + a = 116,

since 116 tickets are sold in total.


Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus

\$17000 \cdot (1 - \dfrac{1}{4}) = \$12750.


Given these values, we can say:

17000a + 12750c = 1653250,

since each adult ticket a costs 17,000 and each child's ticket c costs 12,750, and these costs sum to 1,653,250.


Now, we have two equations:

17000a + 12750c = 1653250

c + a = 116


Let's solve:

17000a + 12750c = 1653250

a = 116 - c

  • Find a on its own, which will allow us to substitute it into the first equation

17000(116 - c) + 12750a = 1653250

  • Substitute in 116 - c for a

1972000 - 17000c + 12750c = 1653250

  • Apply the Distributive Property

1972000 - 4250c = 1653250

  • Combine like terms

4250c = 318750

  • Subtract 1972000 from both sides of the equation and multiply both sides by -1

c = 75


We have now found that 75 child's tickets were sold. Thus,

75 + a = 116 \Rightarrow a = 116 - 75 = 41,

41 adult tickets were sold as well.


In sum, 41 adult tickets were sold along with 75 child tickets.

6 0
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