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3 years ago

Show that the proportions a+b/b=c+d/d and a/b=c/d are equivalent. Pls I need help!

Mathematics

1 answer:

LiRa [457]3 years ago

3 0

Answer: c=d/d

Step-by-step explanation: Realize that b/b= d/d= 1 And also a/b= c/d

a/b+ 1= c/d +1

a/b+ b/b= c/d+ d/d

a+b/b= c=d/d

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Find value of P and Q

ch4aika [34]

Answer:

$P= 6 \frac{1}{7}\\\\Q = 4 \frac{2}{7}$

Step-by-step Explanation

$\frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } = P+Q\sqrt 2 \\ \\ \frac{(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2}) } \times \frac{(5 + 3 \sqrt{2}) }{(5 + 3 \sqrt{2} )} = P+Q\sqrt 2 \\ \\ \frac{ {(5 + 3 \sqrt{2} )}^{2} }{ {(5)}^{2} - (3 \sqrt{2})^{2} } = P+Q\sqrt 2 \\ \\ \frac{ {5}^{2} + {(3 \sqrt{2} )^{2} + 2.5.3 \sqrt{2} } }{25 - 9 \times 2} = P+Q\sqrt 2 \\ \\\frac{ 25 + 18 + 30 \sqrt{2} }{25 - 18} = P+Q\sqrt 2 \\ \\\frac{ 43 + 30 \sqrt{2} }{7} = P+Q\sqrt 2 \\ \\ \frac{43}{7} + \frac{30 }{7} \sqrt{2} = P+Q\sqrt 2 \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ P = \frac{43}{7} \\ \\ \huge \red { \boxed{ P= 6 \frac{1}{7}}} \\ \\ Q = \frac{30}{7} \\ \\ \huge \orange { \boxed{ Q = 4 \frac{2}{7} }}$

4 0

3 years ago

(PLZ HELP STAT) The lengths of three sides of a trapezoid are shown below:

balandron [24]

Hey there :)

The perimeter formula of a trapezium is:
P = a + b + c + d ( adding all sides )

Perimeter is given : P = 17z³ + 60z² + 2z - 5

Part A :

Total lengths of sides 1, 2 and 3 will be just adding the given lengths :
1 → 16z² - 4z + 2
2 → 7z² - 2z + 21
3 → 18z² - 3z + 2

side 1 + side 2 + side 3
( 16z² - 4z + 2 ) + ( 7z² - 2z + 21 ) + ( 18z² - 3z + 2 )

Combine like terms together:

16z² + 7z² + 18z² - 4z - 2z - 3z + 2 +21 + 2
41z² - 9z + 25

Part B:

Length of 4th side will be the total perimeter minus the total length of sides 1, 2 and 3:

( 17z³ + 60z² + 2z - 5 ) - ( 41z² - 9z + 25 )

Combine like terms

17z³ + 60z² - 41z² + 2z + 9z - 5 - 25
17z³ + 19z² + 11z - 30

Part C:

Addition of polynomials result in polynomials as well as subtraction of polynomials result in polynomials.

Therefore, this polynomial is closed under addition and subtraction.

3 0

3 years ago

Ethan's car can drive 30 miles per gallon of gasoline. Gasoline costs $4 per gallon, including tax. Ethan drove 180 miles on a t

Advocard [28]

24$ I believe is the answer You divide the total number of miles driven, to the number of miles per gallon . 180 divided by 30 = 6. Then multiply the answer 6 times dollars per gallon 4$ • 6 = 24 Your answer is 24 :)

3 0

4 years ago

Solve: 4x² = 32 A. x = 4 B. x = ±8 C. x = ± √4 D. x = ± √8

son4ous [18]

Answer:

Step-by-step explanation:

4x²= 32

x²= 32 ÷4 (÷4 on both sides)

x²= 8

x= ±√8 (square root bith sides)

☆ A '±' symbol has to be added whenever we introduce a square root as the square of any number, positive or negative, would result in a positive number.

5 0

3 years ago

In complete sentences explain why you can sometimes add square roots with different radicands. Give an example where you can add

Ghella [55]

Answer:

Some square roots are negative while others are positive. :)

Step-by-step explanation:

5 0

4 years ago