4)

What is the fraction of 0.897

Harman [31]

Answer:

897/1000

Step-by-step explanation:

Source: Google

7 0

3 years ago

In the diagram, ABCD is a part of a right angled triangle ODC. If /AB/= 6 cm,

Andreas93 [3]

Answer:

1) 13.3 cm

2) 48.3 cm

Step-by-step explanation:

1) Right angled triangle ODC and right angled triangle OAB are similar because AB//DC. The two triangles have the same proportion and are equiangular (having equal angles) but have different lengths.

Let OB = x, OC = OB + BC = x + 8

Therefore:

$\frac{OC}{OB}=\frac{DC}{AB} \\\frac{x+8}{x}=\frac{15}{6}\\15x=6(x+8)\\15x=6x+48\\15x-6x=48\\9x=48\\x=5.3\ cm$

The height of triangle ODC = OC = x + 8 = 5.3 + 8 = 13.3 cm

2) Using Pythagoras theorem:

OD² = OC² + DC²

OD² = 13.3² + 15²

OD² = 401.89

OD = √401.89 = 20 cm

2) perimeter of triangle ODC = OD + OC + DC = 20 + 13.3 + 15 =48.3 cm

3 0

3 years ago

Please help ASAP! The terminal side of an angle θ in standard position passes through the point (2,-5). calculate the values of

Troyanec [42]

Answer:

$sin(x)=\frac{opp}{hyp}=\frac{5}{\sqrt{21}}=\frac{5\sqrt{21}}{21}\\cos(x)=\frac{adj}{hyp}=\frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\\tan(x)=\frac{opp}{adj}=\frac{5}{2}\\csc(x)=\frac{hyp}{opp}=\frac{\sqrt{21}}{5}\\sec(x)=\frac{hyp}{adj}=\frac{\sqrt{21}}{2}\\cot(x)=\frac{adj}{opp}=\frac{2}{5}$

Step-by-step explanation:

Start by drawing out the triangle on the graph:

(See picture)

(By the drawing you can judge me that I am a really bad artist)

Theta and the side lengths are labeled, the hypotenuse has a length of √21 by Pythagora's theorem. Now, time to put everything to the trigonometric functions:

$sin(x)=\frac{opp}{hyp}=\frac{5}{\sqrt{21}}=\frac{5\sqrt{21}}{21}\\cos(x)=\frac{adj}{hyp}=\frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}\\tan(x)=\frac{opp}{adj}=\frac{5}{2}\\csc(x)=\frac{hyp}{opp}=\frac{\sqrt{21}}{5}\\sec(x)=\frac{hyp}{adj}=\frac{\sqrt{21}}{2}\\cot(x)=\frac{adj}{opp}=\frac{2}{5}$

(Suppose that x is theta as I can't type it)

By some basic understanding that's all that I can do.

3 0

2 years ago

Charles buys 30 packs of pens.

kompoz [17]

Answer:

£159

Step-by-step explanation:

Charles buys 30 packs of pens.

There are 15 pens in each pack.

Each pack costs £2.80.

Charles sells each pen for 90p but he only manages to sell 3/5 of the pens.

How much profit did he make?

Step 1

Charles buys 30 packs of pens.

There are 15 pens in each pack.

The total number of pens in the pack is

30 packs × 15 pens

= 450 pens

Each pack costs £2.80

Hence:

1 pack = £2.80

30 packs = x

Cross Multiply

x = 30 × £2.80

x = £84

Step 2

The total number of pens in the pack is

30 packs × 15 pens

= 450 pens

He only manages to sell 3/5 of the pens

The amount of pens Charlie sells =

3/5 × 450 pens

= 270 pens

Charles sells each pen for 90p

100p = £1

90p = x

Cross Multiply

100 × x = 90 × £1

x = 90/100

x = £0.9

The amount he sells each pen =

1 pen = £0.9

270 pens = x

Cross Multiply

x = 270 pens × £0.9

x = £243

Step 3

The profit that he made is calculated as:

£243 - £84

= £159

8 0

3 years ago

30 lbs of potatoes cost $360. How much would 13 lbs cost?

gregori [183]

Answer:

$156

Step-by-step explanation:

To find how many pounds of potatos an amount is, it's valuable to find how much *one* pound is

With just dividing both sides by 30, we can get that one pount of potatos costs $12

Since we want how much 13 pounds we cost, simply multiple 12 by 13 which gives us an amount of $156

6 0

3 years ago

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