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4 years ago

George and Bella are asked to solve −3x − 30 = 5x + 18. Identify where one of them made an error.

Mathematics

2 answers:

scZoUnD [109]4 years ago

7 0

Answer:

Bella made an error in step 2

Step-by-step explanation:

The given equation is:

-3x-30=5x+18

Rearranging the like terms, we get

⇒-3x-5x=18+30

⇒-8x=48

⇒x=-6

Thus, the correct value of x is -6.

Now, Bella made a mistake in her solution as:

-3x-30=5x+18

⇒−3x − 30 − 3x = 5x + 18 − 3x (she should add 3x on both sides rather than subtracting)

⇒− 30 = 2x + 18

⇒−30 − 18 = 2x + 18 −18

⇒− 48= 2x

⇒x=-24

Anika [276]4 years ago

4 0

For the second,
In the first step, instead of adding 3x for both sides, they subtract 3x instead.

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In a village the number of houses and the number of flats are in the ration9:5 the number of flats and the number pf bungalows a

Dmitry_Shevchenko [17]

Answer: 180 houses

Step-by-step explanation:

From the question, we are informed that in a village the number of houses and the number of flats are in the ratio 9:5 while the number of flats and the number of bungalows are in the ratio 10:3 and that there are 30 bungalows in the village.

Since the ratio of the number of flats and the number of bungalows are in the ratio 10:3 and there are 30 bungalows in the village, the number of flats will be:

= 10/3 × 30

= 10 × 10

= 100 flats

Since we are told that the ratio of the number of houses to the number of flats are in the ratio 9:5 and we've gotten the number of flats as 100, then the number of houses will be:

= 9/5 × 100

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6 0

3 years ago

A flagpole is 12 feet tall. Its shadow is 14 ft long. How far is it from the top of the

Kisachek [45]

Answer:

Step-by-step explanation:

AC = length of flagpole = 12 ft

AB = length of shadow = 14 ft

BC = length from the top of the flagpole to the end of the shadow = x ft

Use Pythagorean theorem to find the length of x,

x² = AC² + BC²

= 12² + 14²

= 144 + 196

= 340

x = √340

x = 18.4 ft

3 0

2 years ago

8. A substance has a half life of 2.347 minutes.

mina [271]

Answer:

a.) 4 half lives have passed

b) 9.388 minutes

Step-by-step explanation:

Formula for exponential growth / decay is given as:

$A=A_0b^{\frac{t}{c}}$

Where $A$ is the final population

$A_0$ is the initial population

$b$ is the growth factor

$c$ is the time taken for the growth 'b'

$t$ is the amount of time

Here, we are given that:

$A$ = 6. 9 grams

$A_0$ = 110.4 grams

$b = \dfrac{1}{2}$

$c = 2.347$ min

To find:

a.) Number of half lives taken for the decay.

b.) Total time in the decay.

Solution:

a.) Number of half lives taken for the decay is nothing but equal to $\frac{t}{c}$ .

Putting the values in the formula, we get:

$6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4$