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3 years ago

Julius and Walt are finding the product of 25 and 18.

1 answer:

7 0

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An account earns simple interest. (a) Find the interest earned. (b) Find the balance of the account.

Lubov Fominskaja [6]

1. The interest would be $332.80 and the balance of the account would be $2,932.80.

2. The interest would be $1,912.50 and the balance of the account would be $9,412.50

5 0

3 years ago

What is the value of X? x=

Sever21 [200]

Answer:

$x=12$

Step-by-step explanation:

All of the sides are the same length.

$5x-22=4x-10=3x+2$

$5x-22=4x-10$

$x=12$

3 0

4 years ago

Write any two necessary condition for collinearity.

Zolol [24]

Collinear points: Three points A, B and C are said to be collinear if they lie on the same straight line.

There points A, B and C will be collinear if AB + BC = AC as is clear from the adjoining figure.

In general, three points A, B and C are collinear if the sum of the lengths of any two line segments among AB, BC and CA is equal to the length of the remaining line segment, that is, either AB + BC = AC or AC +CB = AB or BA + AC = BC.

In other words,

There points A, B and C are collinear if:

(i) AB + BC = AC i.e.,

Or, (ii) AB + AC = BC i.e. ,

Or, AC + BC = AB i.e.,

6 0

2 years ago

OAB is a triangle. OPM and APN are straight lines. Mis the midpoint of AB.

Kryger [21]

9514 1404 393

Answer:

ON : NB = 5 : 4

Step-by-step explanation:

It may be helpful to refer to the attached figure.

We have divided the triangle into pieces so that we can refer to specific areas and sums of areas. For example, the area of triangle AMO is a+b1. That is half the total area, due to segment AM being half the total length AB.

We have found it convenient to choose a total area of 126 square units. The labels in the figure show how that total area is divided among the different triangles.

Here's one way to get there.

a + b1 = 1/2 the total, so is 63

Similarly,

d + c + b2 = 63

The given segment ratio OP : PM = 5 : 2 tells us ...

a : b1 = 5 : 2 ⇒ a = 45, b1 = 18

Since PM is the median of ∆ABP, we have ...

b1 = b2 = 18 ⇒ d + c = 45

So far, we know

d + c = ∆BOP = 45 and ∆BOA = 126

which means AN : PN = 126 : 45 = 14 : 5.

Applying that ratio to triangles to the right of AN, we have ...

c / (c + b1 + b2) = 5 : 14

14c = 5(c +36) ⇒ c = 20

Since c + d = 45, this means d = 25.

The ratio of d to c is the ratio of ON to NB:

d : c = 25 : 20 = 5 : 4 = ON : NB

_____

Additional comment

We have made extensive use of the fact that triangles with the same base have areas proportional to their height. In the final conclusion, we have also used the fact that triangles with the same height have bases proportional to their areas.