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3 years ago

Find two consecutive even integers such that five times the smaller integer is ten more than three times the larger integer.

Mathematics

1 answer:

quester [9]3 years ago

8 0

5n = 3(n + 2) + 10
5n = 3n + 16
12n = 16
n = 8

8 is smaller integer and 10 is the larger.

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How can -6.75 + (10.25) be expressed as the sum of its integer and decimal parts

ArbitrLikvidat [17]

Answer:

-6.75 + (10.25) = ( (-6) + (10)) + ( (-0.75) + (0.25))

Here, the integer part = ( (-6) + (10))

Decimal part = ( (-0.75) + (0.25))

Step-by-step explanation:

Here, the given expression is: -6.75 + (10.25)

Now, -6.75 = (-6) + (-0.75)

Also, (10.25) = (10) + (0.25)

So, the expression can be written as

-6.75 + (10.25) = (-6) + (-0.75) + (10) + (0.25)

= ( (-6) + (10)) + ( (-0.75) + (0.25))

or, -6.75 + (10.25) = ( (-6) + (10)) + ( (-0.75) + (0.25))

Where the integer part is ( (-6) + (10))

and the decimal part is ( (-0.75) + (0.25))

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3 years ago

Given a line passes through point (5,8) and the origin, find the equation of the line.<br> y=

SOVA2 [1]

Answer:

y = 8/5x

Step-by-step explanation:

I'm assuming that they're asking for the equation in point-slope form.

The formula is y=mx+b where:

m = slope

b = y intercept

However, the y intercept is just (0,0) so b = 0

To find the slope we already have 2 given points: (0,0) and (5,8)

To find slope you do rise/run and you get 8/5

Substitute the slope & y intercept in the formula:

y = 8/5x

Let me know if I'm wrong!!

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How to construct a triangle with side lengths 10 cm and 14 cm and an angle between them of 60 degrees.

Yuliya22 [10]

Answer:

We draw line AB which is perpendicular to the 14 cm side

Since Angle C is 60 degrees that makes angle CAB = 30 degrees

Triangle CAB is a 30 60 90 triangle so line CB is half the hypotenuse or 5 cm

Line BD equals 9 cm

Line AB^2 = 10^2 - 5^2 = 75

Line AD^2 = AB^2 + BD^2

Line AD^2 = 75 + 81

Line AD^2 = 156

Line AD = 12.4899959968

Line AB = Sqr root (75) = 8.6602540378

Angle D = arc sine (8.6602540378 / 12.4899959968)

Angle D = 43.898 degrees

Angle A = 180 - 60 - 43.898 = 76.102 degrees

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Actually this could have been done a little easier by using the Law of Cosines and then the Law of Sines, but I just thought I'd show another way to solve this.

Step-by-step explanation:

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