Solve for r.

√2/3r + 1 = 23

Solve For R. 2/3r + 1 = 23

Answers

Answer 1

Answer:

2nd option

Step-by-step explanation:

[tex]\frac{\sqrt{2} }{3}[/tex] r + 1 = 23 ( subtract 1 from both sides )

[tex]\frac{\sqrt{2} }{3}[/tex] r = 22 ( multiply both sides by 3 to clear the fraction )

[tex]\sqrt{2}[/tex] r = 66 ( divide both sides by [tex]\sqrt{2}[/tex] )

r = [tex]\frac{66}{\sqrt{2} }[/tex] × [tex]\frac{\sqrt{2} }{\sqrt{2} }[/tex] ( rationalising the denominator )

r = [tex]\frac{66\sqrt{2} }{2}[/tex] = 33[tex]\sqrt{2}[/tex]

Answer 2

Answer:

B) r=33*sqrt(2)

Step-by-step explanation:

sqrt(2)/3r+1=23

sqrt(2)/3r=23-1

sqrt(2)/3r=22

sqrt(2)r=22*3

sqrt(2)r=66

r=66/sqrt(2)

r=66*sqrt(2)/(sqrt(2)*sqrt(2))

r=(66*sqrt(2)/2

r=33*sqrt(2)


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It should be noted that mathematics is multicultural. This implies that mathematics applies to different cultures.

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A boat can travel 120 kilometers on 60 liters of gas. How far can it travel on 197 liters

Answers

Answer:

394 km

Step-by-step explanation:

197 is 197/60 times as much as 60

so the distance is also that much more: 120 km * 197/60 = 394

what is 2/3 x 9/8 as a fraction in simplest form

Answers

Answer: [tex]\frac{3}{4}[/tex]

Have attached the picture for explanation...

The product of the fraction in the simplest form is 3/4

What is a fraction?

A fraction is a figure that is not a whole number. A fraction usually has a numerator and a denominator. The numerator is the number above. While the denominator is the number below.

What is the product of the fraction?

2/3 x 9/8 = 18/24 = 3/4

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Answers

Step-by-step explanation:

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Answer: See below

Step-by-step explanation:

Isolate x for x-2y+2z=9

3x=9+2y

[tex]x=\frac{9+2y}{3}[/tex]....(1)

Substitute (1) into the 2nd equation

[tex]\begin{bmatrix}-\frac{9+2y}{3}+3y=-4\\ 2\cdot \frac{9+2y}{3}-5y+3z=16\end{bmatrix}[/tex]

[tex]\frac{3\left(-9+7y\right)}{3}=3\left(-4\right)[/tex]

7y=-3

y=-3/7

Substitute y=-3/7

[tex]\begin{bmatrix}3z+\frac{18-11\left(-\frac{3}{7}\right)}{3}=16\end{bmatrix}[/tex]

[tex]\begin{bmatrix}3z+\frac{53}{7}=16\end{bmatrix}[/tex]

Isolate z by substituting it

[tex]3z+\frac{53}{7}=16[/tex]

[tex]\frac{3z}{3}=\frac{\frac{59}{7}}{3}[/tex]

[tex]z=\frac{59}{21}[/tex]

For x =9+2y/3 substitute z=59/21 and y=-3/7

[tex]x=\frac{9+2\left(-\frac{3}{7}\right)}{3}[/tex]

[tex]x=\frac{19}{7}[/tex]

[tex]x=\frac{19}{7},\:z=\frac{59}{21},\:y=-\frac{3}{7}[/tex]

Answer:

(1, - 1, 3 )

Step-by-step explanation:

x - 2y + 2z = 9 → (1)

- x + 3y = - 4 → (2)

2x - 5y + 3z = 16 → (3)

Add (1) and (2) term by term to eliminate x

y + 2z = 5 → (4)

Multiply (2) by 2

- 2x + 6y = - 8 → (5)

Add (3) and (5) term by term to eliminate x

y + 3z = 8 → (6)

Subtract (6) from (4) term by term to eliminate y

- z = - 3 ( multiply both sides by - 1 )

z = 3

Substitute z = 3 into (4)

y + 2(3) = 5

y + 6 = 5 ( subtract 6 from both sides )

y = - 1

Substitute y = - 1, z = 3 into (1) and solve for x

x - 2(- 1) + 2(3) = 9

x + 2 + 6 = 9

x + 8 = 9 ( subtract 8 from both sides )

x = 1

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

See below

Step-by-step explanation:

Part A

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Part B

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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[tex]\huge \bf༆ Answer ༄[/tex]

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Answers

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Step-by-step explanation:

3x-6=4(2-3x)-8x

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Answers

Answer:

3x²-4

Step-by-step explanation:

1 distribute

(-4x²-2x-6)+7x²+2x+2

2 eliminate redudant parentheses

-4x² -2x - 6+7x² +2x+2

3 Add the numbers

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3x²-4

Answer:

[tex]3x^{2} -4[/tex]

Step-by-step explanation:

Before solving this you have to know that,

( - ) × ( - ) = ( + )

( + ) × ( + ) = ( + )

( - ) × ( + ) = ( - )

Let us solve now.

[tex](-4x^2-2x-6)-(-7x^2-2x-2)[/tex]

[tex](-4x^2-2x-6)+7x^{2} +2x+2[/tex]

[tex]-4x^2-2x-6+7x^{2} +2x+2[/tex]

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