A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? If x represents the speed of the wind, which expression represents the time it takes for the plane to travel the 640 miles against the wind?
1. 640/x
2. 640/(x+180)
3. 640/(180-x)

Answer:

[tex]x = 18[/tex]

[tex]y = 6\sqrt{3}[/tex]

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios. The longest side of a right triangle is called the hypotenuse and the other two sides are called the legs.  

Selecting any of the acute angles as a reference, it has an adjacent side and an opposite side. The trigonometric ratios are defined upon those sides as follows:

Cosine Ratio

[tex]\displaystyle \cos\theta=\frac{\text{adjacent leg}}{\text{hypotenuse}}[/tex]

Sine Ratio

[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]

Consider the angle of θ=30°, then we can write:

[tex]\displaystyle \cos 30^\circ=\frac{x}{12\sqrt{3}}[/tex]

Solving for x:

[tex]x=12\sqrt{3}\cos 30^\circ[/tex]

Since:

[tex]\cos 30^\circ=\frac{\sqrt{3}}{2}[/tex]

Then:

[tex]x=12\sqrt{3}\cdot \frac{\sqrt{3}}{2}[/tex]

[tex]x = 18[/tex]

Now apply the sine:

[tex]\displaystyle \sin 30^\circ=\frac{y}{12\sqrt{3}}[/tex]

Solving for y:

[tex]y=12\sqrt{3}\sin 30^\circ[/tex]

Since:

[tex]\sin 30^\circ=\frac{1}{2}[/tex]

Then:

[tex]y=12\sqrt{3}\cdot \frac{1}{2}[/tex]

[tex]y = 6\sqrt{3}[/tex]

Answer:

[tex]x = 18[/tex]

[tex]y = 6\sqrt{3}[/tex]

Answer:

A

Step-by-step explanation:

when the line is solid its greater, smaller or equal to

when the line is dashed its greater or smaller

When the shade is above the y is greater

When the shade is coming from down its less than

Answer:

(3x+21)(x-5)

Step-by-step explanation:

To solve this let's create an equation that has intercepts at -7 and 5

To do this we get the following

(x+7)(x-5)

Now we need to make sure that the line passes through (4,-33) To do so we will plug in 4 to see how far off we are

If you plug in 4 into x you should get -11

To make y= -33 we simply need to put a three in the front and then distribute it to the first bracket

So we have

3(x+7)(x-5)

then distribute the 3 to get

(3x+21)(x-5)

I doubled checked this answer on desmos and my math is correct

Answer:

x1 = 0.52

x2 = -10.1

x3 = 0.97

Step-by-step explanation:

From the question;

x1 = 1 - 3/(x0)^2

x0 = -2.5

x1 = 1- 3/(-2.5)^2

x1 = 1 -0.48

x1 = 0.52

x2 = 1 - 3/(x1)^2

x2 = 1 - 3/0.52^2

x2 = 1 - 11.1

x2 = -10.1

x3 = 1 - 3/(x2)^2

x3 = 1- 3/(-10.1)^2

x3 = 0.97

Answer:

x=1

2x+3=5

-3 -3

now the three gets canceled and 5-3 is 2

2x=2

now divide 2 on both sides

2x÷2=2÷2

x=1

Answer:

y=3.5572205

x=0.1114441

Step-by-step explanation:

Step-by-step explanation:

y = mx + c

When x = 0, y = 2.

=> (2) = m(0) + c, c = 2.

When x = 3, y = 8.

=> (8) = m(3) + 2, 3m = 6, m = 2.

Hence the answer is y = 2x + 2.

Answer:

24

Step-by-step explanation:

Using ratios, we know that PQ/PT = PR/PS = QR/TS

of course, we know this because of AA similarity.

PQ/PT = 1/2

so PR/PS = 1/2 => PS = 12*2 = 24

Answer:

24

Step-by-step explanation:

PQ is half of PT, therefore, if PR = 12, PS = 24  

Answer:

Y-intercept

Step-by-step explanation:

Because they both meet

Answer:

17

Step-by-step explanation:

6x7= 42

42 divided by 2 = 21

21 - 4 = 17

answer = 17

Answer:

1/4 of ur pens

Step-by-step explanation:

Answer:

a.) 94 cm^2

Step-by-step explanation:

3 x 4 = 12

5 x 3 = 15

4 x 5 = 20

12 + 12 + 15 + 15 + 20 + 20 = 94

Answer: 94 cm squared

Step-by-step explanation:

Answer:

m⁹

Step-by-step explanation:

In such questions , when any two or more numbers with exponents are multiplied and their bases are equal , the exponents of all the numbers add up . So ,

[tex]m^{5} \times m^{4} = m^{5+4} = m^{9}[/tex]

Answer:

3 feet per second isnt this really easy tho-

Step-by-step explanation:

Answer:

-29.988 or if you round up -30

Step-by-step explanation:

1) Convert fractions to decimals  

    3.6 x (-8.33) = -29.988

Answer:

I think its this but not sure

Answer:

a) [tex]5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]4(\sqrt{2} + \sqrt{7})[/tex]

Step-by-step explanation:

a) [tex]9\sqrt{3} - 4\sqrt{3} +\sqrt{5} + 2\sqrt{5}[/tex]

Taking √3 & √5 common respectively,

[tex]=> \sqrt{3} (9 - 4) + \sqrt{5} (1 + 2)[/tex]

[tex]=> 5\sqrt{3} + 3\sqrt{5}[/tex]

b) [tex]10\sqrt{2} + 4\sqrt{7} - 6\sqrt{2}[/tex]

Taking √2 common ,

[tex]=> \sqrt{2} (10-6) + 4\sqrt{7}[/tex]

[tex]=> 4\sqrt{2} + 4\sqrt{7}[/tex]

Taking 4 common ,

[tex]=> 4(\sqrt{2} + \sqrt{7})[/tex]

Answer: 5.25

Step-by-step explanation: .35*15=5.25

Answer:

5.25

Step-by-step explanation:

change the percent to a decimal by moving the dot to the left two places, then multiply it by the number

0.35*15=5.25

Answer:

[tex]m\angle WZY = 24^\circ[/tex]

Step-by-step explanation:

Angles and Lines

The figure shows two triangles WXZ and WYZ. Considering:

* Angles WXZ and WYZ are right (90°)

* Sides XW and YW are congruent (red marker on both)

* They share the side WZ.

We can conclude they are congruent. Thus, angles XZW and YZW are congruent or have the same measure:

5x + 4 = 6x

Subtracting 5x:

4 = x

Or, x =4

Thus:

[tex]m\angle WZY = 6x = 24^\circ[/tex]

[tex]\mathbf{m\angle WZY = 24^\circ}[/tex]

Answer:

4z:5p

4+5=9

10/9=1.11111...

1.11111*5=5.55555......or 50/9 or 5 5/9

Step-by-step explanation:

Answer:

guess what I don't know

Step-by-step explanation:

Answer:

Just look at the explanation

Step-by-step explanation:

My winter Break was really great. I got to spend time with my family! Looking back on 2020, I see that I would have iked to ask my parents for a dog before we figured out that they were allergic to them. But other than that, I am so glad that this year is over!

Answer:

877.40

Step-by-step explanation:

Answer:

A. y - 4 = 3(x + 2)

Step-by-step explanation:

Point slope form is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line

Plug in the slope and given point:

y - y1 = m(x - x1)

y - 4 = 3(x + 2) is the equation

So, A is the correct answer.

Answer:

y= -3x - 1

Step-by-step explanation:

The graph intercepts y at -3 and the slope is -1

Answer:

It's the 3rd answer. y = -x - 3

Step-by-step explanation:

Answer:

9/4 or 2 1/4

Step-by-step explanation:

2 7 /8 -5/8 which gives you 9/4

Answer:

the reasoning for 1 2 and 3 are given and then the statement for 4 is triangle abc = triangle cde and its reasoning is sss theorem (side-side-side)

Step-by-step explanation:

1, 2 and 3 are basically given and then 4 is SSS Theorem since all three sides of the first triangle are equal to all three sides of the second triangle

Step-by-step explanation:

Do you need answers to all of them of some of them?

1. (4.5×10¹²)÷(9×10^10)

(45×10^-1×10¹²)÷(9×10^10)

(45×10¹¹)÷(9×10^10)

(45÷9)×(10¹¹÷10^10)

5×10

if you need help with the others kindly let me know

Answer:

See below.

Step-by-step explanation:

The domain refers to the x values used in the equation/graph. The line appears to go from -10 to 10 on the x-axis. The dots above -10 and 10 are not shaded in meaning those x values do not count towards the domain meaning we will use parenthesis instead of brackets for interval notation or no equal to signs in inequality notation.

Interval Notation: (-10, 10)

Inequality Notation: -10 < x < 10