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mote1985 [20]
2 years ago
5

Which are solutions of the equation 4x2 – 7x = 3x + 24? Check all that apply.

Mathematics
1 answer:
Andreyy892 years ago
3 0

Answer:

x = -3/2, x = 4

Step-by-step explanation:

4x² - 7x = 3x + 24, first put everything on one side

4x² - 10x - 24 = 0, factor 2 out

2(2x² - 5x - 12) = 0 then factor. You need two numbers that multiply to be -24 and add to be -5, so -8 and 3 are the factors.

(2x² - 8x) + (3x - 12) group them either way and then factor out GCF

2x(x - 4) + 3(x - 4) = 0

(2x + 3)(x - 4) = 0, set each factor = 0 and solve

2x + 3 = 0, 2x = -3, x = -3/2

x - 4 = 0, x = 4

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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

Therefore, the answer is:

<em>4 half lives </em>have passed.

b.) Total time of decay. We have to find the value of t here.

From answer of part a.):

\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}

7 0
2 years ago
What is the volume of a rectangular prism when the measures are multiplied by 4?
koban [17]

Answer: A. 3072 cm³

Step-by-step explanation:

The formula for determining the volume of a rectangular prism is expressed as

Volume = length × width × height

Looking at the diagram,

Length = 6 cm

Width = 4 cm

Height = 2 cm

When the measures are multiplied by 4, then

Length = 6 × 4 = 24 cm

Width = 4 × 4 = 16 cm

Height = 2 × 4 = 8 cm

Therefore,

Volume = 24 × 16 × 8 = 3072 cm³

6 0
2 years ago
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40% of a nurse 's time is spent dispensing medicine to patients. If 16 hours per a week is spent dispending medicine, how many h
GarryVolchara [31]

Answer:

40

Step-by-step explanation:

16/.4=40

7 0
3 years ago
Find the area of the figure. Round your answer to the nearest hundredth.
Vlad1618 [11]

Answer:

Total area = 98.26 ft²

I didn't do the math for this, credit goes to: https://brainly.in/question/16592416

3 0
2 years ago
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The movie started at 11:45 and ended at 1:20 how long was the movie
igor_vitrenko [27]
11:45 ---> 01:20

11:45 + (00:15 + 01:00 + 00:20)

= 01:20

So your answer is:

01:35 which is 1 hr, 35 mins.
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