09.04.2022

How do I solve 5x=2/7;x step by step

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23.03.2022, solved by verified expert
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5x = 2/7 

multiplying both sides by 7

35x = 7(2/7) = 2 

35x = 2 

    x  = 2/35

therefore solution is 

x = 2/35  

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Mathematics
Step-by-step answer
P Answered by Master

Part 1) x=3

Part 2) x = −1.11 and x = 1.11

Part 3) 105

Part 4) a = −6, b = 9, c = −7

Part 5) x equals 5 plus or minus the square root of 33, all over 2

Part 6) In the procedure

Part 7) -0.55

Part 8) The denominator is 2

Part 9) a = −6, b = −8, c = 12

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

Part 1)

in this problem we have

x^{2} -6x+9=0  

so

a=1\\b=-6\\c=9

substitute in the formula

x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(9)}} {2(1)}

x=\frac{6(+/-)\sqrt{0}} {2}

x=\frac{6} {2}=3

Part 2) in this problem we have

49x^{2} -60=0  

so

a=49\\b=0\\c=-60

substitute in the formula

x=\frac{0(+/-)\sqrt{0^{2}-4(49)(-60)}} {2(49)}

x=\frac{0(+/-)\sqrt{11,760}} {98}

x=(+/-)1.11

Part 3) When the solution of x2 − 9x − 6 is expressed as 9 plus or minus the square root of r, all over 2, what is the value of r?

in this problem we have

x^{2} -9x-6=0  

so

a=1\\b=-9\\c=-6

substitute in the formula

x=\frac{-(-9)(+/-)\sqrt{-9^{2}-4(1)(-6)}} {2(1)}

x=\frac{9(+/-)\sqrt{105}} {2}

therefore

r=105

Part 4) What are the values a, b, and c in the following quadratic equation?

−6x2 = −9x + 7

in this problem we have

-6x^{2}=-9x+7  

-6x^{2}+9x-7=0  

so

a=-6\\b=9\\c=-7

Part 5) Use the quadratic formula to find the exact solutions of x2 − 5x − 2 = 0.

In this problem we have  

x^{2} -5x-2=0  

so

a=1\\b=-5\\c=-2

substitute in the formula

x=\frac{-(-5)(+/-)\sqrt{-5^{2}-4(1)(-2)}} {2(1)}

x=\frac{5(+/-)\sqrt{33}} {2}

therefore  

x equals 5 plus or minus the square root of 33, all over 2

Part 6) Quadratic Formula proof

we have

ax^{2} +bx+c=0  

Divide both sides by a

x^{2} +(b/a)x+(c/a)=0  

Complete the square

x^{2} +(b/a)x=-(c/a)  

x^{2} +\frac{b}{a}x+\frac{b^{2}}{4a^{2}} =-\frac{c}{a}+\frac{b^{2}}{4a^{2}}

Rewrite the perfect square trinomial on the left side of the equation as a binomial squared

(x+\frac{b}{2a})^{2}=-\frac{4ac}{a^{2}}+\frac{b^{2}}{4a^{2}}

Find a common denominator on the right side of the equation

(x+\frac{b}{2a})^{2}=\frac{b^{2}-4ac}{4a^{2}}

Take the square root of both sides of the equation

(x+\frac{b}{2a})=(+/-)\sqrt{\frac{b^{2}-4ac}{4a^{2}}}

Simplify the right side of the equation

(x+\frac{b}{2a})=(+/-)\frac{\sqrt{b^{2}-4ac}}{2a}

Subtract the quantity b over 2 times a from both sides of the equation

x=-\frac{b}{2a}(+/-)\frac{\sqrt{b^{2}-4ac}}{2a}

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

Part 7) in this problem we have  

3x^{2} +45x+24=0  

so

a=3\\b=45\\c=24

substitute in the formula

x=\frac{-(45)(+/-)\sqrt{45^{2}-4(3)(24)}} {2(3)}

x=\frac{-(45)(+/-)\sqrt{1,737}} {6}

x1=\frac{-(45)(+)\sqrt{1,737}} {6}=-0.55

x2=\frac{-(45)(-)\sqrt{1,737}} {6}=-14.45

therefore

The other solution is

-0.55

Part 8) in this problem we have

2x^{2} -8x+7=0  

so

a=2\\b=-8\\c=7

substitute in the formula

x=\frac{-(-8)(+/-)\sqrt{-8^{2}-4(2)(7)}} {2(2)}

x=\frac{8(+/-)\sqrt{8}} {4}

x=\frac{8(+/-)2\sqrt{2}} {4}

x=\frac{4(+/-)\sqrt{2}} {2}

therefore

The denominator is 2

Part 9) What are the values a, b, and c in the following quadratic equation?

−6x2 − 8x + 12

in this problem we have

-6x^{2} -8x+12=0  

so

a=-6\\b=-8\\c=12

Mathematics
Step-by-step answer
P Answered by PhD
QUESTION 1

The given equation is

2.5(10 - x) + 10 = 72 - 1.5(5x + 12)
Clear the decimal by multiplying through by 10 to get,

25(10 - x) + 100 = 720 - 15(5x + 12)

Expand the bracket using the distributive property to get;

250 - 25x + 100 = 720 - 75x - 180

Group similar terms to get,

- 25x + 75x = 720 - 250 - 100 - 180

50x = 720 - 530

50x = 190

Divide through by 50 to get,

x = \frac{190}{50}

x = \frac{19}{5}

QUESTION 2

We want to solve the inequality,

16x \:  \: 12(2x - 6) - 24

We expand the bracket using the distributive property to obtain,

16x \:  \: 24x - 72 - 24

Group similar terms to get,

16x - 24x \:  \: - 72 - 24

Simplify to get,

- 8x \:  \: - 96

We divide both sides of the inequality by -8 and reverse the sign to obtain,

x \: < \: \frac{ - 96}{ - 8}

x \: < \: 12

QUESTION 3

Step 1.

Given:4(-6x – 3)+24x= -72x + 132

Step 2.

Distributive property:
-24x – 12 + 24x = -72x + 132

Step 3.

Combine like terms:
–12 = -72x + 132

Step 4.

Addition property of equality:

-144 = -72x

Step 5.

Division property of equality:

2=x

All the properties stated are correct.
Mathematics
Step-by-step answer
P Answered by Specialist
Question 1:

–6 + x = –3

x = -3 + 6

x = 3

Hence, the answer is C.

Question 2:

–2a + 2a + 7 = 8 

7 ≠ 8

Hence, the answer is C.

Question 3:

2(2y – 16) = 0

4y - 32 = 0

4y = 0 + 32

4y = 32

y = \frac{32}{4}

y = 8

Hence, the answer is C.

Question 4:

5p – 4p – 8 = –2 + 3 

p - 8 = 1

p = 1 + 8

p = 8

Hence, the answer is A.

Question 5:

4n – 2n + 4 = –1 + 17

2n + 4 = 16

2n = 16 - 4

2n = 12

n = \frac{12}{2}

n = 6

Hence, the answer is A.

Question 6:

2(4z – 3 – 1) = 166 – 46

8z - 6 - 2 = 120

8z = 12 + 8

8z = 20

z = \frac{20}{8} =  \frac{10}{4} =  \frac{5}{2}

z = 2.5

Hence, I think the question is wrong; it is missing a variable.

Question 7:

–x = 3 – 4x + 6

-x + 4x = 3 + 6

3x = 9

x = \frac{9}{3}

x = 3

Hence, the answer is C.

Question 8:

4n + 6 = 4 + 2 + 4n 

4n - 4n + 6 = 6

6 = 6

Hence, the answer is C.

Question 9:

6y + 4 = 8 + 2y + 2y

6y - 4y = 8 - 4

2y = 4

y = \frac{4}{2}

y = 2

Hence, the answer is B.

Question 10:

3(2x – 4) = 8 + 2x + 6

6x - 12 = 14 + 2x

6x - 2x = 14 + 12

4x = 26

x = \frac{26}{4} =  \frac{13}{2}

x = 6.5

Hence, the answer is A.

Question 11:

z – z + 1 = z + 1

1 = z + 1

z = 1 - 1

z = 0

Hence, the answer is B.

Question 12:

3.6m – 2.7 = –1.8m

3.6m + 1.8m = 2.7

5.4m = 2.7

m = \frac{2.7}{5.4} =  \frac{1}{2}

m = 0.5

Hence, the answer is B.
Mathematics
Step-by-step answer
P Answered by PhD
QUESTION 1

The given equation is

2.5(10 - x) + 10 = 72 - 1.5(5x + 12)
Clear the decimal by multiplying through by 10 to get,

25(10 - x) + 100 = 720 - 15(5x + 12)

Expand the bracket using the distributive property to get;

250 - 25x + 100 = 720 - 75x - 180

Group similar terms to get,

- 25x + 75x = 720 - 250 - 100 - 180

50x = 720 - 530

50x = 190

Divide through by 50 to get,

x = \frac{190}{50}

x = \frac{19}{5}

QUESTION 2

We want to solve the inequality,

16x \:  \: 12(2x - 6) - 24

We expand the bracket using the distributive property to obtain,

16x \:  \: 24x - 72 - 24

Group similar terms to get,

16x - 24x \:  \: - 72 - 24

Simplify to get,

- 8x \:  \: - 96

We divide both sides of the inequality by -8 and reverse the sign to obtain,

x \: < \: \frac{ - 96}{ - 8}

x \: < \: 12

QUESTION 3

Step 1.

Given:4(-6x – 3)+24x= -72x + 132

Step 2.

Distributive property:
-24x – 12 + 24x = -72x + 132

Step 3.

Combine like terms:
–12 = -72x + 132

Step 4.

Addition property of equality:

-144 = -72x

Step 5.

Division property of equality:

2=x

All the properties stated are correct.
Mathematics
Step-by-step answer
P Answered by Specialist

Step 1:  

✔ distributive property

Step 2:  

✔ combining like terms

Step 3:  

✔ addition property of equality

Step 4:  

✔ subtraction property of equality

Step 5:  

✔ division property of equality

Step-by-step explanation:

i just took the test

Mathematics
Step-by-step answer
P Answered by Specialist
Question 1:

–6 + x = –3

x = -3 + 6

x = 3

Hence, the answer is C.

Question 2:

–2a + 2a + 7 = 8 

7 ≠ 8

Hence, the answer is C.

Question 3:

2(2y – 16) = 0

4y - 32 = 0

4y = 0 + 32

4y = 32

y = \frac{32}{4}

y = 8

Hence, the answer is C.

Question 4:

5p – 4p – 8 = –2 + 3 

p - 8 = 1

p = 1 + 8

p = 8

Hence, the answer is A.

Question 5:

4n – 2n + 4 = –1 + 17

2n + 4 = 16

2n = 16 - 4

2n = 12

n = \frac{12}{2}

n = 6

Hence, the answer is A.

Question 6:

2(4z – 3 – 1) = 166 – 46

8z - 6 - 2 = 120

8z = 12 + 8

8z = 20

z = \frac{20}{8} =  \frac{10}{4} =  \frac{5}{2}

z = 2.5

Hence, I think the question is wrong; it is missing a variable.

Question 7:

–x = 3 – 4x + 6

-x + 4x = 3 + 6

3x = 9

x = \frac{9}{3}

x = 3

Hence, the answer is C.

Question 8:

4n + 6 = 4 + 2 + 4n 

4n - 4n + 6 = 6

6 = 6

Hence, the answer is C.

Question 9:

6y + 4 = 8 + 2y + 2y

6y - 4y = 8 - 4

2y = 4

y = \frac{4}{2}

y = 2

Hence, the answer is B.

Question 10:

3(2x – 4) = 8 + 2x + 6

6x - 12 = 14 + 2x

6x - 2x = 14 + 12

4x = 26

x = \frac{26}{4} =  \frac{13}{2}

x = 6.5

Hence, the answer is A.

Question 11:

z – z + 1 = z + 1

1 = z + 1

z = 1 - 1

z = 0

Hence, the answer is B.

Question 12:

3.6m – 2.7 = –1.8m

3.6m + 1.8m = 2.7

5.4m = 2.7

m = \frac{2.7}{5.4} =  \frac{1}{2}

m = 0.5

Hence, the answer is B.

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