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USPshnik [31]
3 years ago
7

On a​ map, 1 inch equals 20 miles. Two cities are 5 inches apart on the map. What is the actual distance between the​ cities?

Mathematics
1 answer:
astra-53 [7]3 years ago
3 0

Answer:

100 miles

Step-by-step explanation:

20x5

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80 is 50% of what number
KonstantinChe [14]

Answer:

80 is 50% of 160.

Step-by-step explanation:

In order to find this, we take the whole number and divide by the percentage that it represents. This gives us the number we are looking for.

80/50%

80/.50

160

3 0
3 years ago
Read 2 more answers
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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3 years ago
Which of the following cannot be used to state a postulate?
liubo4ka [24]
Among the four choices, theorems is the best possible answer. Postulate, by definition, is a statement that is assumed to be true without proof while theorems are true statements that can be proven. Both of these types of statements are used to justify geometrical equations, illustrations and statements.
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3 years ago
What is the circumference of this circle <br>​
Levart [38]

Answer:

31.4 cm

Step-by-step explanation:

Let C be the circumference and r be the radius of the circle.

\therefore \: C = 2\pi \: r  \\  \hspace{19 pt}= 2 \times 3.14 \times 5 \\ \hspace{19 pt} = 3.14 \times 10 \\ \hspace{19 pt} = 31.4 \: cm \\

8 0
3 years ago
Which of these is a binomial?<br> O A. 2x3 - 713<br> O B. 5xy<br> O c. x+2y2-7<br> O D. ab
V125BC [204]

Answer:

A.

Step-by-step explanation:

2x^3 - 713 is a binomial . It's a polynomial with 2 terms.

4 0
3 years ago
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