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3 years ago

On a map, 1cm represents 65 km. If two cities are 1950 km apart, how many centimeters apart would they be on this map?

Mathematics

1 answer:

kakasveta [241]3 years ago

7 0

Answer:

30 cm.

Step-by-step explanation:

We can solve this problem by making a proportion:

1 cm/65 km = x cm/1,950 km

By cross-multiplying, we can solve for x:

65x = 1,950

x = 30

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The table shows the distance Allison drove on one day of her vacation. Is the relationship between the distance and the time a p

Anuta_ua [19.1K]

Answer:

we conclude that the relationship between distance and time is NOT proportional.

Hence, she did not drive at a constant speed.

Step-by-step explanation:

We know that when 'y' varies directly with 'x', we get the equation

y ∝ x

y = kx

k = y/x

where 'k' is called the constant of proportionality.

In our case, the table shows the distance Allison drove on one day of her vacation.

Time (h) 1 2 3 4 5

Distance (mi) 55 100 165 280 250

using the equation

k = y/x

susbtitute y = 55, x = 1

k = 55/1 = 55

substitute y = 100, x = 2

k = y/x

k = 100 / 2 = 50

substitute y = 165, x = 3

k = y/x

k = 165 / 3 = 55

substitute y = 280, x = 4

k = y/x

k = 280 / 4 = 70

substitute y = 250, x = 5

k = y/x

k = 250 / 5 = 50

It is clear that the value of 'k' does not remain constant.

Therefore, we conclude that the relationship between distance and time is NOT proportional.

Hence, she did not drive at a constant speed.

6 0

3 years ago

Rules for subtracting integers with the same sign

klio [65]

Answer:

To subtract integers, change the sign on the integer that is to be subtracted. If both signs are positive, the answer will be positive. If both signs are negative, the answer will be negative.

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4 years ago

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OverLord2011 [107]

Therefore x intercept(a) is 3 and y intercept(b) is 3 .

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3 years ago

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A line passes through the origin and the point (3,5). What is the slope of the line?

masha68 [24]

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 0}}\quad ,&{{ 0}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ 5}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{5-0}{3-0}$

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3 years ago

Find the angle [OA] makes with the positive x-axis if the x-coordinate of the point A on the unit circle is 0.222

EastWind [94]

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

<h3>How to find an angle in an unit circle</h3>

Unit circles are circles with radius of 1 and centered at the origin of a Cartesian plane, which are used to determine angles and trigonometric functions related to them. If we use rectangular coordinate system and the definition of the tangent function, we find that the angle OA is equal to:

$\tan \theta = \frac{\sqrt{1 - x^{2}}}{x}$

$\tan \theta = \frac{\sqrt{1-0.222^{2}}}{0.222}$

tan θ ≈ 77.173°

By using the concepts of unit circle and trigonometric functions, we find that the angle OA, whose x-coordinate is 0.222, has a measure of approximately 77.173°.

To learn more on unit circles: brainly.com/question/12100731

#SPJ1

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2 years ago