The bus trip takes 30 minutes. If the bus arrives at 5:00 P.M., what time did the
bus leave?
P.M.

How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.

#3

Let's start with sin here. [tex]\frac{2\sqrt{5}}{5} = \frac{2}{\sqrt{5}}[/tex] Therefore, because sin is y/r, r = [tex]\sqrt{5}[/tex] and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.

cos = [tex]\frac{-1}{\sqrt{5}} = \frac{-\sqrt{5}}{5}[/tex]

#4

Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = [tex]4\sqrt{2}[/tex]. Now, to find csc, we have to do r/y.

csc = [tex]\frac{9}{4\sqrt{2}} = \frac{9\sqrt{2}}{8}[/tex]

The pythagorean identities are

sin^2 + cos^2 = 1,

1 + cot^2 = csc^2,

tan^2 + 1 = sec^2.

#5

Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.

sin^2 + (-3/4)^2 = 1

sin^2 + 9/16 = 1

sin^2 = 7/16

sin = [tex]\sqrt{7/16}[/tex] = [tex]\frac{\sqrt{7}}{4}[/tex]

Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.

tan^2 + 1 = (-4/3)^2

tan^2 + 1 = 16/9

tan^2 = 7/9

tan = -[tex]\sqrt{7/9} = \frac{-\sqrt{7}}{3}[/tex]

#6

Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.

1 + cot^2 = [tex](\frac{-\sqrt{6}}{2})^{2}[/tex]

1 + cot^2 = 6/4

cot^2 = 2/4

cot = [tex]\frac{\sqrt{2}}{2}[/tex]

tan = [tex]\sqrt{2}[/tex]

Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.

[tex](\frac{2}{\sqrt{2}})^2[/tex] + 1 = sec^2

4/2 + 1 = sec^2

2 + 1 = sec^2

sec^2 = 3

sec = -[tex]\sqrt{3}[/tex]

cos = [tex]\frac{-\sqrt{3}}{3}[/tex]

Hope this helps!! :)

Answer:

sin(θ)=√7/4

tan(θ)= - √7/3

Step-by-step explanation:

c^2= √(4^2-(-3^2))

c^2= √(16-9)

c^2= √7

sin(θ)= opp/hyp=√7/4

tan(θ)= (opp )/adj= - √7/3

Answer:

I dont know what sin is

Step-by-step explanation:

Answer:

You may have gotten the opposite and adjacent mixed up.

[tex]\frac{24}{7}[/tex]

Step-by-step explanation:

An easy way to remember these trigonometric ratios is by using SOHCAHTOA, where:

SOH stands for-

[tex]Sine=\frac{Opposite}{Hypotenuse}[/tex]

CAH stands for-

[tex]Cosine=\frac{Adjacent}{Hypotenuse}[/tex]

TOA stands for-

[tex]Tangent=\frac{Opposite}{Adjacent}[/tex]

We are asked to find tan 74° given the right triangle. To find this, we must find the lengths of the opposite side and the adjacent side of the 74° angle. From looking at the triangle, we can see that the side opposite from the 74° angle is 24, and the adjacent is 7. So plugging it into the trigonometric ratio that we found using SOHCAHTOA, we find that:

[tex]tan74=\frac{24}{7}[/tex]

So the answer would be [tex]\frac{24}{7}[/tex]

Seeing as how you picked [tex]\frac{7}{24}[/tex] as your answer, it seems that you may have gotten the opposite and the adjacent mixed up or used [tex]tangent=\frac{adjacent}{opposite}[/tex] as your trigonometric ratio.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

Triangular prism

Step-by-step explanation:

A triangular prism has 9 edges, 6 vertices and 5 faces. I don't think there is any other shape which fits 9 edges and 6 faces.

Answer:

arc XY = 46°

Step-by-step explanation:

the arc of an inscribed angle is equal to 2 x the inscribed angle

mXY

Answer:

64*x^-6

Step-by-step explanation:

Simplify Using Laws of Exponent (4x^-2)^3

Given data

(4x^-2)^3

Let us open the bracket

=4^3*x^-2*3

=64*x^-6

=64x^-6

Hence the equivalent is

64*x^-6

Answer:

0 = -16t² + 3200 → 16t²= 3200 → t² = 200 → t = 10√2 s ≈ 14 s

The time taken by the skydiver to reach the ground is 14.1 second.

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

Given that, the height of a skydiver jumping out of an airplane is given by n = -16t² + 3200.

Here, n=0

-16t² + 3200=0

-16t²=-3200

t²=200

t=√200

t=14.14

t=14.1 second

Therefore, the time taken by the skydiver to reach the ground is 14.1 second.

To learn more about the solution of quadratic equation visit:

https://brainly.com/question/18305483.

#SPJ3

Answer:

so simple pls follow up..

Inbox me

Answer:

24-18=6+6+12

hope this helps you!!

Step-by-step explanation:

Answer: $117,000

Step-by-step explanation:

The maximum that Arianna may borrow is 2.5 times her annual income.

First step therefore, would be to calculate her annual income:

= 900 * 52 weeks

= $46,800

She may borrow 2.5 times this:

= 46,800 * 2.5

= $117,000

Answer:

Not enough information.

Step-by-step explanation:

AB + BC + CD + DA = 46

In a parallelogram, opposite sides are congruent.

AB + DA + AB + DA = 46

2AB + 2DA = 46

We have two unknowns and only one equation.

There is not enough information to answer the question.

Answer:

1152

Step-by-step explanation:

Answer:

Percent of change each year = 5%

Step-by-step explanation:

P.S - The exact question is -

Given - The number of carbon atoms in a fossil is given by the function,

             y (x)= [tex]5100(0.95)^{x}[/tex], where x represents the number of years since

             being discovered.

To find - What is the percent of change each year? Explain how you arrived

              at your answer

Proof -

Given that, the number of carbon atoms in a fossil is y(x) = [tex]5100(0.95)^{x}[/tex]

Initially, the number of fossils be

y(0) = [tex]5100(0.95)^{0}[/tex] = 5100

After 1 year, The number of fossils be

y(1) = [tex]5100(0.95)^{1}[/tex] = 5100(0.95) = 4845

Now,

Change in 1 year = y(0) - y(1) = 5100 - 4845 = 255

Now,

Percent of chance  = [tex]\frac{255}{5100}[/tex] × 100%

                                = 0.05 × 100%

                                = 5%

⇒Percent of chance = 5%

∴ we get

Percent of change each year = 5%

Answer:

y=0.5x-3

Step-by-step explanation:

m=(-12+14)/(-18+22)=0.5

y+14=0.5(x+22)

y=0.5x-3

Answer:

18t-72

Step-by-step explanation:

Answer:

[tex]\frac{2x+y}{w}[/tex]

Answer:

6-12.

Step-by-step explanation:

Between 6 to 12 two numbers must the third side of the card fall.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that Sarah is creating a triangular birthday card for her teacher.

Thus in order to glue lace around the outside of the card, Sarah needs to know the length of each side.

It should be known that two of the sides measure 4 inches and 9 inches.

Therefore, in between 6 to 12 the third number must be lie.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

Answer:

7 feets

Step-by-step explanation:

Volume of shed, V = 357 feet³

Height of shed, H= 8 1/2 fts

Width of shed, W = 6 ft

Using the relation :

Volume = Length * width * height

357 = L * 6 ft * 17/2 feets

357 feets³ = L * 51 feets²

L = 357 feets³ / 51 feets²

Length, L = 7 feets

Answer:

7.0

Step-by-step explanation:

Right angled triangle. To find the hypotenuse, use Pythagorean theorem.

Hypotenuse² =  base² + altitude²

                      = 6.5² + 2.7²

                      = 42.25 + 7.29

                     = 49.54

hypotenuse = √49.54 = 7.04 = 7

Step-by-step explanation:

by using Pythagoras law

h²=p²+b²

missing angle =h let

h²=(2.7)²+(6.5)²

h=√(49.50)=7.03=7

Answer:

15x^2+3x-2

Step-by-step explanation: Just like regular math but with negatives!

Answer:

[tex]\frac{10\sqrt{6} }{3}[/tex] and [tex]\frac{11\sqrt{3} }{3}[/tex]

Step-by-step explanation:

(a)

A = [tex]\frac{1}{2}[/tex] × 4[tex]\sqrt{2}[/tex] × [tex]\frac{5}{\sqrt{3} }[/tex]

   = 2[tex]\sqrt{2}[/tex] × [tex]\frac{5}{\sqrt{3} }[/tex]

   = [tex]\frac{10\sqrt{2} }{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ← rationalise the denominator

= [tex]\frac{10\sqrt{6} }{3}[/tex] units²

(b)

Using Pythagoras' identity in the right triangle

let hypotenuse be h , then

h² = (4[tex]\sqrt{2}[/tex] )² + ([tex]\frac{5}{\sqrt{3} }[/tex] )²

    = 32 + [tex]\frac{25}{3}[/tex]

    = [tex]\frac{96}{3}[/tex] + [tex]\frac{25}{3}[/tex]

    = [tex]\frac{121}{3}[/tex] ( take the square root of both sides )

h = [tex]\sqrt{\frac{121}{3} }[/tex] = [tex]\frac{11}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex] ← rationalise the denominator

h = [tex]\frac{11\sqrt{3} }{3}[/tex]

Answer:

x = 22

Step-by-step explanation:

19+23=2X-2

42 = 2x - 2

-2x = -2 - 42

-2x = -44

x = 22

hope this helps

Responda:

21 dias

Explicação passo a passo:

Total de dias necessários = 70 dias

Dias usados ​​no mês 1 = 25 dias

Dias usados ​​no mês 2 = 24 dias

Dias usados ​​no total = 24 + 25 = 49 dias

Dias restantes :

70 dias - 49 dias

= 21 dias

Answer:

Here, it's ratio

Step-by-step explanation:

4/9: 2 and 2/9

simplify

1:5

6/7:x

6/7 x 5 is....

30/7

Mixed number is 4 2/7

BLAM!!!

Answer:

y=-2x+5

Step-by-step explanation:

y=mx+b where m=slope and b=y-intercept

Answer:

Answering so you can give other person branliest

Answer:

B) ΔGRS ≈ ΔART by SAS Similarity

Step-by-step explanation:

Given:

The graph of a parabola.

To find:

The equation for the parabola.

Solution:

The vertex form of a parabola is:

[tex]y=a(x-h)^2+k[/tex]       ...(i)

Where, a is a constant and (h,k) is the vertex.

From the given graph it is clear that the vertex of the parabola is at point (-1,6). So, h=-1 and k=6.

Putting h=-1 and k=6 in (i), we get

[tex]y=a(x-(-1))^2+(6)[/tex]

[tex]y=a(x+1)^2+6[/tex]         ...(ii)

The y-intercept of the graph is at point (0,3). Putting x=0 and y=3 in (ii), we get

[tex]3=a(0+1)^2+6[/tex]

[tex]3-6=a[/tex]

[tex]-3=a[/tex]

Putting a=-3 in (ii), we get

[tex]y=-3(x+1)^2+6[/tex]

Therefore, the equation of the parabola is [tex]y=-3(x+1)^2+6[/tex].