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1 year ago

What is the the answer for 2(x - 4)=6x

Mathematics

2 answers:

anzhelika [568]1 year ago

7 0

Answer:

x = -2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

2(x−4)=6x

(2)(x)+(2)(−4)=6x (Distribute)

2x + −8 = 6x

2x − 8 = 6x

Step 2: Subtract 6x from both sides.

2x −8 − 6x = 6x − 6x

−4x − 8 = 0

Step 3: Add 8 to both sides.

−4x − 8 + 8 = 0 + 8

−4x = 8

Step 4: Divide both sides by -4.

−4x/−4

= 8/−4

x = −2

katrin2010 [14]1 year ago

3 0

Answer:

x=-2

Step-by-step explanation:

first distribute the 2 through x-4 you get 2x-8=6x then subtract 2x from both sides of the equation now you have 4x=-8 then divide 4 from both sides of the equation and you x=-2

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Step-by-step explanation:

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2 years ago

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On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter

andrezito [222]

Answer:

1) The common ratio = 1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio = 1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

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2 years ago

The pet store has 20 mice: 11 are white, five are

luda_lava [24]

Answer:

The answer is: 5/20 or a 25% chance

4 0

2 years ago

a school principal orders 75 boxes of chalk. each box has 12 sticks of chalk, the school has 23 teachers. Does the principal hav

Zolol [24]

Well 75x12=900 so 900 divided by 40 is 22.5 so 22 teachers can have 40 chalks but the principal needs to order another 20 :)

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2 years ago

In Pennsylvania the average IQ score is 101.5. The variable is normally distributed, and the population standard deviation is 15

blsea [12.9K]

Answer:

We conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 101.5

Sample mean, $\bar{x}$ = 106.4

Sample size, n = 30

Alpha, α = 0.05

Population standard deviation, σ = 15

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 101.5\\H_A: \mu > 101.5$

We use one-tailed z test to perform this hypothesis.

Formula:

$z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}} }$

Putting all the values, we have

$z_{stat} = \displaystyle\frac{106.4 - 101.5}{\frac{15}{\sqrt{30}} } = 1.789$

Now, $z_{critical} \text{ at 0.05 level of significance } = 1.96$

Since,

$z_{stat} > z_{critical}$

We reject the null hypothesis and accept the alternate hypothesis.

Thus, we conclude that the Pennsylvania school district have an IQ higher than the average of 101.5

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