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zmey [24]
3 years ago
6

There are two numbers. The first number is 4/9 of the second number. If the difference between the two numbers is 375, find the

value of the second number.
Mathematics
1 answer:
erica [24]3 years ago
3 0
X and y
x=4/9 times y

y is bigger so
y-x=375
x=4/9y
y-4/9y=375
5/9y=375
times both sides by 9/5
y=675

the 2nd number is 675
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Find the area of the regular trapezoid. The figure is not drawn to scale. The top side is 4, the bottom side is 7, and both side
svp [43]
A regular trapezoid is shown in the picture attached.

We know that:
DC = minor base = 4
AB = major base = 7
AD = BC = lateral sides or legs = 5

Since the two legs have the same length, the trapezoid is isosceles and we can calculate AH by the formula:

AH = (AB - DC) ÷ 2
      = (7 - 5) ÷ 2
      = 2 ÷ 2
      = 1

Now, we can apply the Pythagorean theorem in order to calculate DH:
DH = √(AD² - AH²) 
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      = √(25 - 1)
      = √24
      = 2√6

Last, we have all the information needed in order to calculate the area by the formula:

A =  \frac{(AB + CD)DH}{2}

A = (7 + 5) × 2√6 ÷ 2
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The area of the regular trapezoid is 12√6 square units.

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