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nordsb [41]
3 years ago
15

Which two properties of equality could Zoe use to finish solving for x

Mathematics
1 answer:
7nadin3 [17]3 years ago
4 0
3x-4= - 10
add both side 4 so its a addition property 
3x=- 6
now divide both side 3 so it is a  <span>division property.
so x=-2</span>
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A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)= at² + bt + c, where t is the
frutty [35]

Answer:

<h2>a) a = -3, b = 18, c = 48; </h2><h2>s(t) = -3t²+18t+48</h2><h2>b) 48m</h2><h2>c) 8secs</h2>

Step-by-step explanation:

The question is incomplete. Here is the complete question.

'A rock was thrown from the top of a cliff such that its distance above sea level was given by s(t)=at²+bt+c, where t is the time in seconds after the rock was released. After 1 second the rock was 63 m above sea level, after 2 seconds 72 m, and after 7 seconds 27 m. a. Find a, b and c and hence an expression for s(t). b. Find the height of the cliff. c. Find the time taken for the rock to reach sea level.'

Given the equation of the distance modelled as s(t)=at²+bt+c

If after 1 second the rock was 63 m, then 63 = a+b+c

If after 2 seconds, the distance was 72 m then 72 = 4a+2b+c

Also if after 7 seconds, the distance is 27 m, then 27 = 49a+7b+c

i) Solving the 3 equations simultaneously to get a, b and c we have;

a+b+c = 63 ... 1

4a+2b+c = 72 ...2

49a+7b+c = 27 ...3

Subtracting 2 from 1 and 3 from 2 we will generate 2 new equations as shown;

eqn 2- eqn1: 3a + b = 9...4

eqn 3- eqn 2: 45a + 5b = -45

eqn 3- eqn 2: 9a+b = -9 ... 5

solving 4 and 5 simultaneously

3a + b = 9 ...4

9a+b = -9 ... 5  

Taking the difference of 4 and 5 we have

6a - -9-9

6a = -18

a = -3

substituting a = -3 into equation 4 to get b we have;

3(-3)+b = 9

-9 + b = 9

b = 9+9

b = 18

substituting a = -3 and b = 18 into equation 1 to get c we have;

-3+18+c = 63

15+c = 63

c = 48

a = -3, b= 18 and c = 48

The distance function will be s(t) = -3t²+18t+48

ii) If the height of the cliff is modelled by the equation  s(t)=at²+bt+c

The height of the cliff is at when t = 0

s(0) = -3(0)²+18(0)+48

s(0) = 48m

The height of the cliff is 48m

iii) At the sea level, the height of the rock will be 0m, substituting this into the modeled equation for the height to get the time we have;

s(t)=at²+bt+c

0 = -3t²+18t+48

3t²-18t-48 = 0

t² - 6t - 16 =0

t² - 8t+2t - 16 = 0

t(t-8)+2(t-8) = 0

(t+2)(t-8) = 0

t = -2 or 8

Taking the positive value of the time, t = 8secs

Time taken for the rock to reach sea level is 8secs

7 0
3 years ago
What is the median of 10 31 36 36 38 42 47 48 49 52
Anna11 [10]
It could be 36 because its been shown multiple times
3 0
3 years ago
What is another way to write 2 7/5 as a fraction with the same denominator
lukranit [14]

Answer:

\frac{17}{5}

Step-by-step explanation:

As an improper fraction

4 0
2 years ago
Read 2 more answers
I need help with 9/2 divided by 2/9 =
taurus [48]
<h2>Answer: 81/4</h2><h2>______________________________________</h2><h3>Simplify the expression.</h3><h3>Exact Form:</h3><h3>81/4</h3><h3>Decimal Form:</h3><h3>20.25</h3><h3>Mixed Number Form/Simplified Form:</h3><h3>20 1/4</h3><h3>__________________________________________________</h3>

Hope this helps! 

Also can I please have Brainliest...?

<em>Only if I'm right of course...</em>

5 0
3 years ago
What is the STANDARD FORM of the following:<br> y-8= 2(x + 3)
bearhunter [10]

Answer:

-2x+y=14

Step-by-step explanation:

Standard = ax+by=c

y-8=2x+6.

-2x+y=14.

Hope this helps :D

3 0
3 years ago
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