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3 years ago

19 = 15 w- 4(3 w-1) solve for w

Mathematics

1 answer:

Gnom [1K]3 years ago

8 0

Step-by-step explanation:

Simplifying

19 = 15w + -4(3w + -1)

Reorder the terms:

19 = 15w + -4(-1 + 3w)

19 = 15w + (-1 * -4 + 3w * -4)

19 = 15w + (4 + -12w)

Reorder the terms:

19 = 4 + 15w + -12w

Combine like terms: 15w + -12w = 3w

19 = 4 + 3w

Solving

19 = 4 + 3w

Solving for variable 'w'.

Move all terms containing w to the left, all other terms to the right.

Add '-3w' to each side of the equation.

19 + -3w = 4 + 3w + -3w

Combine like terms: 3w + -3w = 0

19 + -3w = 4 + 0

19 + -3w = 4

Add '-19' to each side of the equation.

19 + -19 + -3w = 4 + -19

Combine like terms: 19 + -19 = 0

0 + -3w = 4 + -19

-3w = 4 + -19

Combine like terms: 4 + -19 = -15

-3w = -15

Divide each side by '-3'.

w = 5

Simplifying

w = 5

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3 years ago

Just need the equation

Anna007 [38]

$a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}$

Each of the equations can be solved as shown below:

a. $3x + 7 = - x - 1$

$3x + 7 + x = - x - 1 + x$ (addition property of equality)

$4x + 7 = - 1\\4x + 7 - 7 = -1-7$ (Subtraction property of equality)

$4x = -8\\\frac{4x}{4} = \frac{-8}{4}$ (Division property of equality)

$x = -2$

b. $1 - 2x + 5 = 4x - 3\\$

Add like terms

$6 - 2x = 4x - 3\\\\6 - 2x - 6 = 4x - 3 - 6$ (Subtraction property of equality)

$- 2x = 4x - 9\\-2x - 4x = 4x -9 - 4x$ (Subtraction property of equality)

$-6x = -9 \\\frac{-6x}{-6} = \frac{-9}{-6}$ (Division property of equality)

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

c. $4x - 2 + x =-2 + 2x\\$

$5x - 2 = -2 + 2x\\5x - 2x = -2 + 2\\3x = 0\\ x = \frac{0}{3} \\x = 0$

d. $3x - 4 + 1 = - 2x -5 + 5x\\$

$3x - 3 = - 7x -5\\3x + 7x = 3 - 5\\10x = -2\\x = \frac{-2}{10} \\x = -\frac{1}{5}$

The value of x in each equation are:

$a. $ x = -2\\b. $ x = \frac{3}{2} \\c. $ x = 0\\d. $ x = -\frac{1}{5}$

Learn more here:

brainly.com/question/1527981

5 0

3 years ago

PLEASE HELP! The table shows the number of championships won by the baseball and softball leagues of three youth baseball divisi

Irina18 [472]

Answer:

Question 1: $P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16}}{ \frac{4}{16}} = \frac{1}{2}$

Question 2:

A. $P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

B. $P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

C. $P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

Step-by-step explanation:

Conditional probability is defined by

$P(A|B)= \frac{P(A and B)}{P(B)}$

with P(A and B) beeing the probability of both events occurring simultaneously.

Question 1:

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( B | Y ) = \frac{ P ( B and Y)}{ P (Y)} = \frac{ \frac{2}{16} }{ \frac{4}{16} } = \frac{1}{2}$

Question 2.A:

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( B and Y)= \frac{ 2 }{ 16 }[/tex]

By definition,

$P ( Y | B ) = \frac{ P(Y and B) }{ P(B) } = \frac{ \frac{2}{16} }{ \frac{6}{16} } = \frac{1}{3}$

Question 2.B:

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

then

P( Z and B)= \frac{ 1 }{ 16 }[/tex]

By definition,

$P( Z | B ) = \frac{ P ( Z and B)}{ P (B)}= \frac{ \frac{1}{16} }{ \frac{6}{16} } = \frac{1}{6}$

Question 3.B

Y: Championships won by the 10 - 12 years old, beeing

$P ( Y)= \frac{ 4 }{ 16 }$

Z: Championships won by the 13 - 15 years old, beeing

$P ( Z)= \frac{ 1 }{ 16 }$

then

$P (Y or Z) = P(Y) + P(Z) = \frac{6}{16}$

B: Baseball League Championships won, beeing

$P ( B ) = \frac{ 6 }{16}$

$P((YorZ) and B)= \frac{3}{16}$

By definition,

$P((Y or Z)|B) = \frac{ P ((Y or Z) and B)}{P(B)}= \frac{ \frac{3}{16}}{ \frac{6}{16}}= \frac{1}{2}$

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago