MATHEMATICS HIGH SCHOOL

DEFG is a rectangle. DF = 5x - 3and EG = x + 5. Find the value of x and the length of each diagonal.a. x = 1, DF = 6, EG = 6
b. x = 2, DF = 7, EG = 12
c. x = 2, DF = 6, EG = 6
d. x = 2, DF = 7, EG = 7

Answers

Answer 1
Answer: d. x = 2, DF = 7, EG = 7
 
DF is equivalent to EG; Therefore, the equation would be like this:

5x - 3 = x + 5
Transfer 3 and x to their opposite side and change their signs.

5x - x = 5 + 3
4x = 8
Find x. Divide both sides by 4.

4x / 4 = 8 / 4
x = 2

Subsitute x in the equation to find the length of each diagonal.

DF = 5x - 3 = 5(2) - 3 = 10 - 3 = 7 ; DF = 7
EG = x + 5 = 2 + 5 = 7 ; EG = 7
Answer 2
Answer: Answer: d. x = 2, DF = 7, EG = 7
Solution:
by ratio:  DF : EG
                5x - 3 = x + 5
Solving for x:
                5x -x = 5 + 3
                 x = 2
Substituting x=2 in the expression
               DF = 5x -3 = 5(2) - 3 = 7
               EG = x + 5 = 2 + 5 = 7

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Solve for x. 2003-05-04-00-00_files/i0060000.jpg

How many different arrangements can be made with the letters in the word POWER?100
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120
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Answers

120 different arrangements

Answer:120

Step-by-step explanation:

Simplify the following expression:
-9(14p - 8) - 4p

Answers

Step-by-step explanation:

-126p + 72 - 4p

-130p + 72

Simplify the expressions. Show your work.
(x+6^2)

Answers

(x+6*6)
x+36

Or 
(x+6)^(2)
=x^(2) +12x+36

Solve the equation X^2 +10x+24=0

Answers

Answer:x= -4 and -6

Step-by-step explanation:

To solve the equation x²+10x+24=0, we need to factorize. Factorizing this using the general formula,

x = -b+/-√b²-4ac/2a

Generally, quadratic equation are of the form ax²+bx+c=0

Comparing the coefficients;

a= 1, b=10 and c=24

Substituting this into the general formula,

x = -10+/-√10²-4(1)(24)/2(1)

x = -10 +/-√100-96/2

x = -10 +/-√4/2

x = -10 +/- 2/2

x = -10 + 2/2 and -10-2/2

x = -8/2 and -12/2

x = -4 and -6
(x+6) (x+4) thats the answer

If a runner covers 400 meters in 50 seconds, what is the runners average speed? What if the runner takes 60 seconds to cover the same distance?

Answers

400/50 = 8 m/s;
400/60 = 6,(3) m/s;

Answer:

400/50 = 8 m/s 400/60 = 6,(3) m/s

Step-by-step explanation:

Choose the correct simplification of x to the 3rd power over y to the 5th power all raised to the 2nd power.x to the 5th power over y to the 7th power
x over y to the 3rd power
x to the 6th power over y to the 10th power
x6y10

Answers

Answer:

Option 3 - x to the 6th power over y to the 10th power

Step-by-step explanation:

Given : Expression x to the 3rd power over y to the 5th power all raised to the 2nd power.

To find : Choose the correct simplification of the expression?

Solution :

Writing the expression in value form,

x to the 3rd power = x^3

y to the 5th power= y^5

x to the 3rd power over y to the 5th power all raised to the 2nd power =

((x^3)/(y^5))^2

Now applying identity,

((x)/(y))^a=(x^a)/(y^a)

=((x^3)/(y^5))^2

=((x^3)^2)/((y^5)^2)

Using identity,(x^a)^b=x^(a.b)

=(x^(3.2))/(y^(5.2))

=(x^(6))/(y^(10))

In word form, x to the 6th power over y to the 10th power.

Therefore, Option 3 is correct.
\left( \cfrac{x^3}{y^5} \right)^2=\cfrac{(x^3)^2}{(y^5)^2}=\cfrac{x^(3*2)}{y^(5*2)}=\cfrac{x^(6)}{y^(10)}
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