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3 years ago

Solve the following rational equation for x. 1/4x-3/4=7/x

Mathematics

1 answer:

Liula [17]3 years ago

6 0

Answer:

x1= -4, x2 = 7

Step-by-step explanation:

Move expression to the left-hand side:

1/4x-3/4-7/x=0

Write all the numerators above a common denominator:

x^2 - 3x - 28 /4x =0

When the quotient of expressions equal 0, the numerator has to be 0

x^2 + 4x - 7x - 28 = 0

x(x+4) - 7(x+4) =0

(x+4) × (x-7) =0

Separate into possible cases:

x+4=0

x-7=0

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Kenny's scores the first 5 times he played a video game are listed below. 38, 51, 64, 77, 90 Kenny's scores follow a pattern. If

gayaneshka [121]

Kenny's score on his 72nd game played is 961

Solution:

Given that the first 5 score of Kenny are listed below:

38, 51, 64, 77, 90

Kenny's scores follow a pattern

To find: Kenny's score on his 72nd game played

Let us first find the pattern followed

38, 51, 64, 77, 90

Find the difference between terms

51 - 38 = 13

64 - 51 = 13

77 - 64 = 13

90 - 77 = 13

So the difference between terms is constant

So the sequence is arithmetic sequence

An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant

The formula for nth term of arithmetic sequence is given as:

$a_n = a_1 + (n-1)d$

$a_n$ = the nᵗʰ term in the sequence

$a_1$ = the first term in the sequence

d = the common difference between terms

Here d = 13 and $a_1 = 38$

So we get,

$a_n = 38 + (n-1) \times 13$

To find the score of 72nd game, substitute n = 72

$a_{72} = 38 + (72-1) \times 13\\\\a_{72} = 38 + 71 \times 13\\\\a_{72} = 38 + 923\\\\a_{72} = 961$

Thus Kenny's score on his 72nd game played is 961

7 0

3 years ago

If the perimeter of a rectangle is 360 feet, and the length is twice the width, what is the length?

geniusboy [140]

Answer:

(P) =360

(l) =?

(b) =?

so, let the breadth be x

let the length be 2x

Perimeter of rectangle=2(l+b)

360 =2(2x+x)

360/2 =2x

180/2 =x

60 =x

x =60

ATQ

Breadth = 60

length= 60 ×2

=180

8 0

3 years ago

I need help with these two questions

Galina-37 [17]

Answer:

The first one: 19/15a

second one: b²-4ac = D

Step-by-step explanation:

for first one: take LCM and solve

for second one: you square the expression on both sides then b²= D + 4ac, then when you take 4ac to the left hand side, it becomes b²-4ac= D

6 0

2 years ago

Evaluate csc (3pi/14) and cot (5pi/12) using a calculator.

ELEN [110]

The drop down answers are
csc= 1.604
cot= .268

5 0

3 years ago

I needs some help pls

GrogVix [38]

Here is the order

- 6 2/3 ,- 1.3 , 29/8 , 7

5 0

3 years ago