All categories

2 years ago

If CDE ~ GDF, find ED

Mathematics

1 answer:

qaws [65]2 years ago

7 0

Answer:

Step-by-step explanation:

$\triangle CDE \sim \triangle GDF.. (given) \\\\\therefore \frac{CD}{GD} =\frac{DE}{DF}.. (csst) \\\\\therefore \frac{15}{x+3} =\frac{3x+1}{4}\\\\ \therefore \: 15 \times 4 = (x + 3)(3x + 1) \\ \\ \therefore \: 60 = 3 {x}^{2} + x + 9x + 3 \\ \\ \therefore 3 {x}^{2} + 10x + 3 - 60 = 0 \\ \therefore 3 {x}^{2} + 10x - 57 = 0 \\ \therefore 3 {x}^{2} + 19x - 9x - 57 = 0 \\ \therefore \: x(3x + 19) - 3(3x + 19) = 0 \\\therefore \: (3x + 19)(x - 3) = 0 \\ \therefore \: 3x + 19 = 0 \: \: or \: \: x - 3 = 0 \\ \therefore \: x = - \frac{19}{3} \: \: or \: \: x = 3 \\ \because \: x \: can \: not \: be \: - ve \\ \therefore \: x = 3 \\ ED = 3x + 1 = 3 \times 3 + 1 \\ \huge \red{ \boxed{ ED= 10}}$

You might be interested in

Amelia and Elliott are collecting empty soda cans for recycling. Amelia has 13 less than 5 times the cans that Elliott has. Toge

xeze [42]

Answer:

D.) Elliott has 212 cans, Amelia has 45 cans

Step-by-step explanation:

257 = x + (5x - 12)

257 = 6x - 13

+13 +13

270 = 6x

/6 /6

45 = x (the amount of Amelia's cans)

257 - 45 = 212 (the amount of Elliott's cans)

please rate and thank : )

6 0

2 years ago

A low-strength children’s/adult chewable aspirin tablet contains 81 mg of aspirin per tablet. How many tablets may be prepared f

Svetlanka [38]

Answer:

12,345 tablets may be prepared from 1 kg of aspirin.

Step-by-step explanation:

The problem states that low-strength children’s/adult chewable aspirin tablets contains 81 mg of aspirin per tablet. And asks how many tablets may be prepared from 1 kg of aspirin.

Since the problem measures the weight of a tablet in kg, the first step is the conversion of 81mg to kg.

Each kg has 1,000,000mg. So

1kg - 1,000,000mg

xkg - 81mg.

1,000,000x = 81

$x = \frac{81}{1,000,000}$

x = 0.000081kg

Each tablet generally contains 0.000081kg of aspirin. How many such tablets may be prepared from 1 kg of aspirin?

1 tablet - 0.000081kg

x tablets - 1kg

0.000081x = 1

$x = \frac{1}{0.000081}$

x = 12,345 tablets

12,345 tablets may be prepared from 1 kg of aspirin.

4 0

2 years ago

A company has two office buildings that hold 30,000 employees. Their headquarters contains 14 times as many employees as their o

VikaD [51]

Answer:

Their headquarters contains <u>420000</u> employees.

Step-by-step explanation:

The company has two office buildings which hold 30,000 employees.

The headquarters contains 14 times as many employees as the overseas branch.

Therefore, the number of employees in the headquarters is:

14 * 30000 = 420000 employees

Their headquarters contains 420000 employees.

7 0

2 years ago

Read 2 more answers

In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?

gizmo_the_mogwai [7]

<h3>Answer: 56/65</h3>

Work Shown:

sin(angle) = opposite/hypotenuse

sin(F) = EG/FE

sin(F) = 56/65

Refer to the diagram below.

5 0

2 years ago

A copper smelting process is supposed to reduce the arsenic content of the copper to less than 1000 ppm. let μ denote the mean a

Hitman42 [59]

The rejection region is give by

$|z_{test}|\ \textgreater \ z_{\alpha/2}$

where the test statistics is given by

$\frac{\bar{x}-\mu}{\sigma/\sqrt{n}} = \frac{980-1000}{100/\sqrt{75}} \\ \\ = \frac{-20}{100/8.6603} = \frac{-20}{11.5470} =-1.73$

i.e. $|z_{test}|=|-1.73|=1.73$

Thus, $z_{\alpha/2}=1.73$

Using the statistical table, the level of the test is 0.04.

6 0

2 years ago