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3 years ago

3(negative 2-3x)=negative 9x-4

Mathematics

1 answer:

Andreyy893 years ago

3 0

Answer:

x = -2

Step-by-step explanation:

3(-2 - 3x) = -9x - 4 (Given)

3(-2) + 3(-3x) = -9x - 4 (Distributive Property of Equality)

-6 + 9x = -9x - 4 (Simplify)

-6 + 4 -9x= -9x - 4 + 4 (Addition Property of Equality)

-2 + 9x = -9x (Simplify)

-2 + $\frac{-9x}{-9} = \frac{-9}{-9}$ (Division Property of Equality)

-2 = x (Simplify)

x = -2 (Symmetric Property of Equality)

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Find the least common multiple of x² + x – 12 and x² + 2x – 15.

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The LCM is (x+4)(x-3)(x+5)

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A radio manufacturer believes that the length of life of WPPX model radio is normal with µ=12 years and σ=2.5 years. (a) What pe

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Answer:

(a) 5.48%

(b) 17.82 years

(d) 15.21 years

Step-by-step explanation:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

µ=12 years and σ=2.5 years.

(a) What percent of the radios will function for more than 16 years?

For x = 16

z = 16 - 12/2.5

z = 1.6

Probability value from Z-Table:

P(x<16) = 0.9452

P(x>16) = 1 - P(x<16)

1 - 0.9452

= 0.054799

Converting to percentage = 0.054799 × 100

= 5.4799%

Approximately = 5.48%

(b) Suppose the company decides to replace 1% of the radios. Find the length of the guarantee period. i.e. find X.

find the z score of the 99th percentile = 2.326

Hence:z = (x-μ)/σ

2.326 = x - 12/2.5

Cross Multiply

2.326 × 2.5 = x - 12

5.815 = x - 12

x = 12 + 5.815

x = 17.815

Approximately = 17.82 years

When x < 10

Hence,

z = 10 - 12/2.5

z = -0.8

Probability value from Z-Table:

P(x<10) = 0.21186

Converting to percentage

0.21186 × 100

= 21.186%

Approximately = 21.19%

(d) If 10% of the radios will function for more than X years, find X.

The z score would be : 100 - 10%

= 90th percentile z score

We find the z score of the 90th percentile = 1.282

Hence:z = (x-μ)/σ

1.282 = x - 12/2.5

Cross Multiply

1.282 × 2.5 = x - 12

3.205 = x - 12

x = 12 + 3.205

x = 15.205

Approximately = 15.21 years

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3 years ago

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines. Then she cuts off 5 of the sections to make into p

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Answer:

3/8

Step-by-step explanation:

Let us represent the total fabric as an integer = 1

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines.

= 1/8, hence each section = 1/8

Then she cuts off 5 of the sections to make into placemats.

This is written as: 5 sections × 1/8 = 5/8

The fraction of the fabric that is left is calculated as:

1 - 5/8

Lowest Common Denominator = 8

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The value of x is 9.

We have : - 25 = 7 - (5x - 13)

We have to find the value of x.

<h3>If f(x) = g(x), than what do you understand by true solution of this equation?</h3>

The true Solution of the equation is the value of x for which LHS = RHS.

For example - if ax + b = cx + d , then

ax - cx = d - b

x = $\frac{d-b}{a-c}$ is the true solution of the equation.

In the question given -

- 25 = 7 - (5x - 13)

- 25 = 7 - 5x + 13

5x = 45

x = 9

Hence, the value of x for which LHS = RHS is 9.

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2 years ago

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Answer:

110

Step-by-step explanation:

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