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aksik [14]
3 years ago
11

On a Map, 1 inch equals 48 miles. If the if the distance between two cities on a map is 2.5 inches how many miles apart are they

Mathematics
2 answers:
erica [24]3 years ago
8 0

Answer:

120 Miles

Step-by-step explanation:

1 inch = 48 miles

Distance between two cities 2.5 inch

2*48 = 96

.5 = 24

96+24= 120 miles

statuscvo [17]3 years ago
6 0

Answer: 120 miles

2.5 x 48 = 120

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If you would like to solve 26/57 = 849/5x, you can do this using the following steps:

<span>26/57 = 849/5x          /*(5x)
</span>26/57 * (5x) = 849     /*57
26 * 5x = 849 * 57    /26
5x = 48393/26        /5
x = <span>48393/(26*5)
x = 372.25

The correct result would be </span><span>372.25.</span><span>
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Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 met
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The moment of inertia of a spherical shell is I = mr²

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I₁ = I₂
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A florist uses 10 red roses for every 4 white roses in her bouquets. What is the ratio of red roses to the total number of flowe
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3 years ago
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Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
Are the ratios 3:5 and 2:4 equivalent?<br> yes or no
jeyben [28]

Answer:

No, they are not.

Step-by-step explanation:

A ratio can be written as a fraction. So 3:5 is the same as 3/5 and 2:4 is the same as 2/4.

3/5 = 2/4

0.6 = 0.5 INCORRECT

As you can see, the both don't equal the same numbers, so they aren't equivalent.

4 0
2 years ago
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