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navik [9.2K]
3 years ago
9

Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Mathematics
1 answer:
nydimaria [60]3 years ago
3 0

Answer: For 10 sessions, the cost of the two plans the same.

Step-by-step explanation:

Let x= Number of sessions.

Given: Christian’s Gym charges a one-time fee of $50 plus $30 per session for a personal trainer.

Total charge for x sessions = 50+30x

Nicole's fitness center charges a yearly fee of $250 plus $10 for each session with a  trainer.

Total charge for x sessions = 250+10x

When both plan charges the same, then

50+30x=250+10x\\\\\Rightarrow\ 30x-10x=250-50\\\\\Rightarrow\ 20x=200\\\\\Rightarrow\ x=10

i.e. For 10 sessions, the cost of the two plans the same.

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The function A=A_oe^{-0.01155x} A = A o e − 0.01155 x models the amount in pounds of a particular radioactive material stored in
vivado [14]

They are essentially asking us to solve:

357=900e^{-0.01155x} \implies\\ \frac{357}{900}=e^{-0.01155x} \implies\\ \ln{\frac{357}{900}}=-0.01155x \implies \\ x\approx 80.1

Solving this equation for x tells us that it will take around 80.1 years for the materials in the vault to reduce to 357 pounds.

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3 years ago
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Learning Task 3. Find the equation of the line. Do it in your notebook.
Wewaii [24]

Answer:

1) The equation of the line in slope-intercept form is y = 5\cdot x +9. The equation of the line in standard form is -5\cdot x + y = 9.

2) The equation of the line in slope-intercept form is y = \frac{2}{5}\cdot x +\frac{14}{5}. The equation of the line in standard form is -2\cdot x +5\cdot y = 14.

3) The equation of the line in slope-intercept form is y = 3\cdot x +4. The equation of the line in standard form is -3\cdot x +y = 4.

4) The equation of the line in slope-intercept form is y = 2\cdot x + 6. The equation of the line in standard form is -2\cdot x +y = 6.

5) The equation of the line in slope-intercept form is y = \frac{5}{6}\cdot x -\frac{7}{6}. The equation of the line in standard from is -5\cdot x + 6\cdot y = -7.

Step-by-step explanation:

1) We begin with the slope-intercept form and substitute all known values and calculate the y-intercept: (m = 5, x = -1, y = 4)

4 = (5)\cdot (-1)+b

4 = -5 +b

b = 9

The equation of the line in slope-intercept form is y = 5\cdot x +9.

Then, we obtain the standard form by algebraic handling:

-5\cdot x + y = 9

The equation of the line in standard form is -5\cdot x + y = 9.

2) We begin with a system of linear equations based on the slope-intercept form: (x_{1} = 3, y_{1} = 4, x_{2} = -2, y_{2} = 2)

3\cdot m + b = 4 (Eq. 1)

-2\cdot m + b = 2 (Eq. 2)

From (Eq. 1), we find that:

b = 4-3\cdot m

And by substituting on (Eq. 2), we conclude that slope of the equation of the line is:

-2\cdot m +4-3\cdot m = 2

-5\cdot m = -2

m = \frac{2}{5}

And from (Eq. 1) we find that the y-Intercept is:

b=4-3\cdot \left(\frac{2}{5} \right)

b = 4-\frac{6}{5}

b = \frac{14}{5}

The equation of the line in slope-intercept form is y = \frac{2}{5}\cdot x +\frac{14}{5}.

Then, we obtain the standard form by algebraic handling:

-\frac{2}{5}\cdot x +y = \frac{14}{5}

-2\cdot x +5\cdot y = 14

The equation of the line in standard form is -2\cdot x +5\cdot y = 14.

3) By using the slope-intercept form, we obtain the equation of the line by direct substitution: (m = 3, b = 4)

y = 3\cdot x +4

The equation of the line in slope-intercept form is y = 3\cdot x +4.

Then, we obtain the standard form by algebraic handling:

-3\cdot x +y = 4

The equation of the line in standard form is -3\cdot x +y = 4.

4) We begin with a system of linear equations based on the slope-intercept form: (x_{1} = -3, y_{1} = 0, x_{2} = 0, y_{2} = 6)

-3\cdot m + b = 0 (Eq. 3)

b = 6 (Eq. 4)

By applying (Eq. 4) on (Eq. 3), we find that the slope of the equation of the line is:

-3\cdot m+6 = 0

3\cdot m = 6

m = 2

The equation of the line in slope-intercept form is y = 2\cdot x + 6.

Then, we obtain the standard form by algebraic handling:

-2\cdot x +y = 6

The equation of the line in standard form is -2\cdot x +y = 6.

5) We begin with a system of linear equations based on the slope-intercept form: (x_{1} = -1, y_{1} = -2, x_{2} = 5, y_{2} = 3)

-m+b = -2 (Eq. 5)

5\cdot m +b = 3 (Eq. 6)

From (Eq. 5), we find that:

b = -2+m

And by substituting on (Eq. 6), we conclude that slope of the equation of the line is:

5\cdot m -2+m = 3

6\cdot m = 5

m = \frac{5}{6}

And from (Eq. 5) we find that the y-Intercept is:

b = -2+\frac{5}{6}

b = -\frac{7}{6}

The equation of the line in slope-intercept form is y = \frac{5}{6}\cdot x -\frac{7}{6}.

Then, we obtain the standard form by algebraic handling:

-\frac{5}{6}\cdot x +y =-\frac{7}{6}

-5\cdot x + 6\cdot y = -7

The equation of the line in standard from is -5\cdot x + 6\cdot y = -7.

6 0
2 years ago
Find slope of the line -12x+13y=-6
Burka [1]

Answer: 2 x - 3 y = 6 i think but let let me know if i'm wrong

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3 years ago
Svana wants to solve the equation x - 1.0675 = 3x - 4145.
AysviL [449]

Answer: D

Step-by-step explanation:

Given that Svana wants to solve the equation 1/2x - 1.0675 = 3x - 4145.

This equation is a system of equations which can be solved by using simultaneous equation methods.

But if she uses a graphing program to graph the equations y = 1/2x - 1.0675 and y = 3x - 4.145

The solution of 1/2x - 1.0675 = 3x - 4.145. Will be the point of intersection of the two equation.

Trace the point of intersection to the x - axis and also to the y - axis.

The solution to the system of equations is ( 1.231, - 0.452 )

3 0
3 years ago
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tom's baseball team wins 5 out every 12 games they play. If the team played 36 games, how many games did Tom's team win
atroni [7]

Answer:

15 games

Step-by-step explanation:

12X3=36 5X3=15

6 0
2 years ago
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