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3 years ago

What is x if the equation is, 4 - (2x-3) = 3?

Mathematics

1 answer:

user100 [1]3 years ago

4 0

Answer:

x = 2

Step-by-step explanation:

4 - (2x-3) = 3

Distribute the minus sign

4 -2x+3 = 3

Combine like terms

7 -2x = 3

Subtract 7 from each side

7 -2x-7 = 3-7

-2x = -4

Divide by -2

-2x/-2 = -4/-2

x = 2

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Evaluate 12 x (4^-2/4^-4) A 1/4 B 3/4 C 16 D 192

MrMuchimi

12 ×4^4/4^2
=12×4^2
=12×16
=192

7 0

3 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

2 years ago

Evan’s family drove to a theme park for vacation.

zhuklara [117]

Answer:

They drove 150 miles on the third day

They drove 50 miles per hour so if you multiply that by 3 (since they drove 3 hours on the third day) you would get 150 miles.

5 0

3 years ago

A six-sided fair die and an eight-sided fair die are rolled together. What is the probability of getting numbers whose sum is a

aalyn [17]

There are 48 possible outcomes in this situation, and of those outcomes, the ones whose sums are a multiple of three are;
12, 21, 15, 51, 24, 42, 33, 18, 27, 36, 63, 45, 54, 48, 57, and 66. So, that is 16 out of 48 possibilities, or 16/48, which simplifies to 1/3. Written as a percent, the probability of getting numbers whose sum is a multiple of three is 33.33%.

Hope this is helpful! :)

3 0

3 years ago

Read 2 more answers

Optimal-Eats blender has a mean time before failure of 40 months with a standard deviation of 6 months, and the failure times ar

GarryVolchara [31]

Answer:

The warranty period should be of 32 months.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean time before failure of 40 months with a standard deviation of 6 months.

This means that $\mu = 40, \sigma = 6$