How do I factorise an expression

Jeff earned his pilot's license and flew to visit his brother 200 miles away. A headwind of 20 mph slowed down the plane's speed

lora16 [44]

<h2>Plane's speed without wind i s 117.68 mph</h2>

Step-by-step explanation:

We have speed of plane without wind is x.

Distance to brothers place = 200 miles.

A headwind of 20 mph slowed down the plane's speed on the first leg of the trip

Speed to brothers place = x - 20

We have

Distance = Speed x Time

$200=(x-20)\times t_1\\\\t_1=\frac{200}{x-20}$

A tailwind of 20 mph sped up the plane on the return trip

Speed of return trip = x + 20

We have

Distance = Speed x Time

$200=(x+20)\times t_2\\\\t_2=\frac{200}{x+20}$

The entire trip took 3.5 hours.

That is

$t_1+t_2=3.5\\\\\frac{200}{x-20}+\frac{200}{x+20}=3.5\\\\200x+4000+2000x-4000=3.5(x-20)(x+20)\\\\400x=3.5x^2-1400\\\\7x^2-800x-2800=0\\\\\texttt{x = 117.68mph or x =-3.40mph}$

Plane's speed without wind i s 117.68 mph

7 0

2 years ago

The gold bar has a trapezium cross-sectional area. Gold has a density of 19.3 grams per cm3. Work out the mass of the gold bar.

Varvara68 [4.7K]

Answer:

Mass of gold bar = 13.896 kg

Step-by-step explanation:

Volume of gold bar = Area of trapezium x Length of bar

Length of bar = 16 cm

Area of trapezium = 2 x Area of triangle + Area of rectangle

Area of triangle = 0.5 x 5 x 3 = 7.5 cm²

2 x Area of triangle = 2 x 7.5 = 15 cm²

Area of rectangle = 6 x 5 = 30 cm²

Area of trapezium = 15 + 30 = 45 cm²

Volume of gold bar = 45 x 16 = 720 cm³

Density of gold = 19.3 g/cm³

Mass of gold bar = 720 x 19.3 = 13896 g = 13.896 kg

Mass of gold bar = 13.896 kg

6 0

2 years ago

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A circle has a circumference of \blue{12}12start color #6495ed, 12, end color #6495ed. It has an arc of length \dfrac{8}{5} 5 8

Thepotemich [5.8K]

Answer:

Therefore,

The Central Angle is 48°.

Step-by-step explanation:

Given:

Circumference = 12 units

$Arc\ length = \dfrac{8}{5}= 1.6\ unit$

To Find:

Central angle = θ = ?

Solution:

If "θ" the central angle is in degree then arc of length is given by

$Arc\ length = \dfrac{\theta}{360}\times Circumference$

Substituting the values we get

$1.6 = \dfrac{\theta}{360}\times 12\\\\\theta = 48\°$

Therefore,

The Central Angle is 48°.

6 0

2 years ago

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Frank has 3 bags of birdseed. He wants to put the birdseed into 4 bird feeders equally.how much of the the bags will go in each

svp [43]

Hi!

To solve this, we simply divide.

$\frac{3 bags}{4feeders} = 0.75 bags per feeder$

The answer is 0.75

Hope this helps! :)

4 0

2 years ago

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A right triangle has side lengths a, b, and c as shown below.

Musya8 [376]

Answer:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Step-by-step explanation:

Given that

A right triangle has side lengths a, b, and c

Because you did not attached photo of the right triangle so I will assume that:

Side a is the adjacent (A)
Side b is the opposite (O)
Side c is the hypotenuse (H)

(Please have a look at the attached photo)

To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.

$\sin x = \frac{O}{H}\\\cos x = \frac{A}{H}\\\tan x = \frac{O}{A}$

EX: the sine of x is equal to the side opposite of angle x over the hypotenuse. Hence, we have the expressions of the trigonometric functions as shown below:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Hope it will find you well

4 0

2 years ago