Answer:
2/5 hour is closest to 0 1/2 hours, 5/8 hour is closest to 1/2 hour. Therefore, the best estimate for the total time Maria spent with her sister is close to 1 hour
Step-by-step explanation:
We can represent the time Maria spends playing the game as 0.4, since 2/5 as a fraction is 0.4. This is closer to 1/2, which is 0.5 then it is to 0, because 4 is closer to 5 then 0. Then, we can represent the time Maria reads the book as 0.625, which is closer to 1/2 then it is to 1. Now we can add the estimated times. 
hour
Answer: tea = 15 rupees per kg
sugar= 3 rupees per kg
Step-by-step explanation:
Hi, to answer this question we have to write a system of equations with the information given:
<em>"Two kg of tea and 3 kg of sugar cost rupees 39 in january 1997":
</em>
2 t + 3 s =39 (a)
Where:
- t= price of 1 kg of tea
- s = price of 1 kg of sugar
<em>"in march 1997 the price of the tea increased by 25% (1.25)and the price of the sugar increased by 20%(1.20) and the same quantity of tea and sugar cost rupees 48.30.
"</em>
2(t1.25)+3(s1.2) = 48.30 (b)
- <em>Solving for t in (b)
</em>
2t =39-3s
t = (39 -3s)/2
t = 19.5-1.5s
- <em>Replacing the value of t in (b)
</em>
2 x ((19.5-1.5s)1.25)+ 3 ( 1.2s) =48.30
2x ( 24.375 -1.875s) +3.6s =48.30
48.75 -3.75s+3.6s= 48.30
48.75-48.30 = 3.75s-3.6s
0.45= 0.15s
0.45/0.15 =s
3 =s
- <em>Replacing the value of s in (a)
</em>
2 t + 3 (3) =39
2 t + 9 =39
2 t =39 -9
2 t =30
t = 30/2
t= 15
Prices in january:
tea = 15 rupees per kg
sugar= 3 rupees per kg
Feel free to ask for more if needed or if you did not understand something.
Answer:
y = 
Step-by-step explanation:
The function will be cubic. The x-intercepts are -4, -1, and 2
The constant factor is -1 because the graph falls on the right. So,
y = -(x + 4)(x + 1)(x - 2)
y = -
Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]
d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)
Evaluate the derivative at <em>x</em> = -1 :
d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4
This is the slope of the tangent line to the function at (-1, 4).
Use the point-slope formula to get the equation for the tangent line:
<em>y</em> - 4 = 4 (<em>x</em> - (-1)) → <em>y</em> = 4<em>x</em> + 8
Answer:
Step-by-step explanation:
The rate of change, slope, m is
m=(y2-y1)/(x2-x1), we have points (4,5) and (21,39) so
m=(39-5)/(21-4)
m=34/17
m=2
So the rate of change is 2
