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3 years ago

Liliana solved the equation below. When she tried to verify her answer, she realized she made an error.

Mathematics

2 answers:

katrin2010 [14]3 years ago

6 0

It should be :
1/3(x + 18) = 7
1/3x + 6 = 7
1/3x + 6 - 6 = 7 - 6
1/3x = 1
x = 3

Softa [21]3 years ago

4 0

Answer:

(B)

Step-by-step explanation:

The given expression is:

$\frac{1}{3}(x+18)=7$

Upon solving the above expression, we get

$\frac{1}{3}(x+18)=7$

Step 1. Solving the above equation, we get

$\frac{1}{3}x+6=7$

Step 2. Subtracting 6 on both the sides of the above equation, we have

$\frac{1}{3}x+6-6=7-6$

Step 3. The equation can be written as:

$\frac{1}{3}x=1$

Step 4. Cross multiplying the above equation , we have

$x=3$

She made an error in step 2 as she added 6 on right hand side but in actual we have to subtract 6 on that side.

Thus, option (B) is correct.

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4(2x-3)=0.2(x+5)÷5.72

rusak2 [61]

Answer:

x=1.528534

Explanation:

Simplify both sides of equation

4(2x-3)=0.2(x+5)/5.72

(4)(2x)+(4)(−3)=0.034965x+0.174825(Distribute)

8x+−12=0.034965x+0.174825

8x−12=0.034965x+0.174825

Step 2: Subtract 0.034965x from both sides.

8x−12−0.034965x=0.034965x+0.174825−0.034965x

7.965035x−12=0.174825

Step 3: Add 12 to both sides.

7.965035x−12+12=0.174825+12

7.965035x=12.174825

Step 4: Divide both sides by 7.965035.

7.965035x/7.965035=12.174825/7.965035

x=1.528534

4 0

3 years ago

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in s

Norma-Jean [14]

The positions when the particle reverses direction are:

$s(t_1)=55ft\\\\s(t_2)=28ft$

The acceleraton of the paticle when reverses direction is:

$a(t_1)=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=18\frac{ft}{s^{2}}$

Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

Also, when the particle reverses its direction, the velocity is equal to 0.

We are given the following function:

$s(t)=2t^{3}-21t^{2}+60t+3$

So,

- Derivating to get the velocity function, we have:

$v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60$

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

$v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s$

We know that the particle reversed its direction two times.

- Derivating the velocity function to find the acceleration function, we have:

$a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42$

Now, substituting the times to calculate the accelerations, we have:

$a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}$

Now, substitutitng the times to calculate the positions, we have:

$s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft$

Have a nice day!

3 0

3 years ago

Please help me with this again

dimaraw [331]

$( {x}^{2} -2x + 3)(x + 1) \\ {x}^{3} - 2 {x}^{2} + 3x + {x}^{2} - 2x + 3 \\ {x}^{3} - {x}^{2} + x + 3$

Therefore, the answer is the first choice.

3 0

3 years ago

Read 2 more answers

if the cost of a movie ticket now averages $11.50 , interpret the meaning of the expression 11.50(1.083)

LUCKY_DIMON [66]

I believe the correct expression is: 11.50(1.083)^t where t is the time.

Now, we are given that the average price of the ticket is $11.5
The given expression means that this average value is dependent on the variable t. Therefore, the average price of the ticket increases exponentially with the time with the rate of growth equals 1.083

Now, to better understand this, we will get the price of the ticket at different times:
At t = 1: price = 11.50(1.083)^1 = $12.4545
At t = 2: price = 11.50(1.083)^2 = $13.4882235
At t = 3: price = 11.50(1.083)^3 = $14.60774605
We can notice that the price of the ticket increases exponentially as the time increases.

Hope this helps :)

5 0

3 years ago

I need help on this one too

zysi [14]

Answer:

C.. is the answer.........

6 0

3 years ago

Read 2 more answers