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2 years ago

11

To take a taxi, it costs \$3.00 plus an additional \$2.00per mile traveled. You spent exactly \$20 on a taxi, which includes the

\$1 tip you left. How many miles did you travel

1 answer:

Alexeev081 [22]2 years ago

3 0

A taxi ride where the total fare is $3, $2 for every mile travelled plus a $1 tip and the original cost of $20.

First write a formula that expresses the cost of the ride:

Total cost= Flat fee + Mileage + Tip

Now let's drop in what we know:

20= 3+2 (miles) +1 - we know the total cost is 20, the fee of 3, the tip of 1 and the cost per mile of 2. The only thing we don't know is the number of miles. So let's solve for that.

Subtract 3 and 1 from both sides to get:

16=2(miles)

Divide both sides by 2:

8=miles
Therefore, you traveled 8 miles.

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3 years ago

Which shape has a line of symmetry that can be drawn through the figure?

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Step-by-step explanation:

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Then any figure that can be cutin exactly two halves, is a correct answer to this question.

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2 years ago

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2 years ago

The equation of function h is h... PLEASE HELP MATH

Flura [38]

Answer:

Part A: the value of h(4) - m(16) is -4

Part B: The y-intercepts are 4 units apart

Part C: m(x) can not exceed h(x) for any value of x

Step-by-step explanation:

Let us use the table to find the function m(x)

There is a constant difference between each two consecutive values of x and also in y, then the table represents a linear function

The form of the linear function is m(x) = a x + b, where

a is the slope of the function
b is the y-intercept

The slope = Δm(x)/Δx

∵ At x = 8, m(x) = 2

∵ At x = 10, m(x) = 3

∴ The slope = $\frac{3-2}{10-8}=\frac{1}{2}$

∴ a = $\frac{1}{2}$

- Substitute it in the form of the function

∴ m(x) = $\frac{1}{2}$ x + b

- To find b substitute x and m(x) in the function by (8 , 2)

∵ 2 = $\frac{1}{2}$ (8) + b

∴ 2 = 4 + b

- Subtract 4 from both sides

∴ -2 = b

∴ m(x) = $\frac{1}{2}$ x - 2

Now let us answer the questions

Part A:

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∴ h(4) = $\frac{1}{2}$ (4 - 2)²

∴ h(4) = $\frac{1}{2}$ (2)²

∴ h(4) = $\frac{1}{2}$ (4)

∴ h(4) = 2

∵ m(x) = $\frac{1}{2}$ x - 2

∴ m(16) = $\frac{1}{2}$ (16) - 2

∴ m(16) = 8 - 2

∴ m(16) = 6

- Find now h(4) - m(16)

∵ h(4) - m(16) = 2 - 6

∴ h(4) - m(16) = -4

Part B:

The y-intercept is the value of h(x) at x = 0

∵ h(x) = $\frac{1}{2}$ (x - 2)²

∵ x = 0

∴ h(0) = $\frac{1}{2}$ (0 - 2)²

∴ h(0) = $\frac{1}{2}$ (-2)² =

∴ h(0) = 2

∴ The y-intercept of h(x) is 2

∵ m(x) = $\frac{1}{2}$ x - 2

∵ x = 0

∴ m(0) = $\frac{1}{2}$ (0) - 2 = 0 - 2

∴ m(0) = -2

∴ The y-intercept of m(x) is -2

- Find the distance between y = 2 and y = -2

∴ The difference between the y-intercepts of the graphs = 2 - (-2)

∴ The difference between the y-intercepts of the graphs = 4

∴ The y-intercepts are 4 units apart

Part C:

The minimum/maximum point of a quadratic function f(x) = a(x - h) + k is point (h , k)

Compare this form with the form of h(x)

∵ h = 2 and k = 0

∴ The minimum point of the graph of h(x) is (2 , 0)

∵ k is the minimum value of f(x)

∴ 0 is the minimum value of h(x)

∴ The domain of h(x) is all real numbers

∴ The range of h(x) is h(x) ≥ 2

∵ m(8) = 2

∵ m(14) = 5

∵ h(8) = $\frac{1}{2}$ (8 - 2)² = 18

∵ h(14) = $\frac{1}{2}$ (14 - 2)² = 72

∴ h(x) is always > m(x)

∴ m(x) can not exceed h(x) for any value of x

<em>Look to the attached graph for more understand</em>

The blue graph represents h(x)

The green graph represents m(x)

The blue graph is above the green graph for all values of x, then there is no value of x make m(x) exceeds h(x)

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2 years ago

We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c

Kisachek [45]

We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

$\frac{dT}{dt}=k(T-a)$

We now separate the time and the temperature variables as follows,

$\frac{dT}{T-a}=kdt$

Integrating both sides of the differential equation, we obtain;

$ln(T-a)=kt +c$

This natural logarithmic equation can be rewritten as;

$T-a=e^{kt +c}$

Applying the laws of exponents, we obtain,

$T-a=e^{kt}\times e^{c}$

$T-a=e^{c}e^{kt}$

We were given the initial conditions,

$T(0)=4$

Let us apply this condition to obtain;

$4-20=e^{c}e^{k(0)}$

$-16=e^{c}$

Now our equation, becomes

$T-a=-16e^{kt}$

or

$T=a-16e^{kt}$

When we substitute a=20,
we obtain,

$T=20-16e^{kt}$

b) We were also given that,

$T(5)=8$

Let us apply this condition again to find k.

$8=20-16e^{5k}$

This implied

$-12=-16e^{5k}$

$\frac{-12}{-16}=e^{5k}$

$\frac{3}{4}=e^{5k}$

We take logarithm to base e of both sides,

$ln(\frac{3}{4})=5k$

This implies that,

$\frac{ln(\frac{3}{4})}{5}=k$

$k=-0.2877$

After 15 minutes, the temperature will be,

$T=20-16e^{-0.2877\times 15}$

$T=20-0.21376$

$T=19.786$

After 15 minutes, the temperature is approximately 20°C

6 0

2 years ago