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sergey [27]
3 years ago
13

Solve the Equation. Show work and explain steps. 2(x +4) +2 = 3(x − 2) +x

Mathematics
2 answers:
Sophie [7]3 years ago
6 0

Answer:

X = 8

Step-by-step explanation:

A breakdown of the calculation is attached. I hope you find it helpful, thanks.

kolbaska11 [484]3 years ago
5 0

Answer:

first step.

Multiply everything in the brackets by the number outside of the brackets.

then; 2x + 8 = 3x - 6

second step.

Collect the like terms, pronumerals on one side and numbers on one side .

2x - 3x = -6 - 8

-x = -14

therefore divide each side by -1 to make it look good then we end up with

x = 14

that's the answer.

You might be interested in
Rewrite the expression $6j^2 - 4j 12$ in the form $c(j p)^2 q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$
solniwko [45]

Rewrite the expression  6j^2 - 4j + 12$ in the form $c(j + p)^2 + q$, where $c$, $p$, and $q$ are constants. What is $\frac{q}{p}$

The ratio of \frac{q}{p}  = - 34

How to solve such questions?

Such Questions can be easily solved just by some Algebraic manipulations and simplifications. We just try to make our expression in the form which question asks us. This is the best method to solve such questions as it will definitely lead us to correct answers. One such method is completing the square method.

Completing the square is a method that is used for converting a quadratic expression of the form ax^{2} + bx + c to the vertex form

a(x - h)^{2} + k. The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^{2} + n, such that the left side is a perfect square trinomial

$6j^2 - 4j +12$

=  $6(j^2 - \frac{2}{3} j )+12$

= $6(j^2 - \frac{2}{3} j  +  \frac{1}{9}  )+\frac{102}{9}                   (Completing Square method)

=6( j- \frac{1}{3} )^{2}  +  \frac{34}{3}

On comparing with the given equation we get

p = - \frac{1}{3}     and q = \frac{34}{3}

∴ \frac{q}{p} = \frac{\frac{34}{3} }{\frac{-1}{3} }

= - 34

Learn more about completing the square method here :

brainly.com/question/26107616

#SPJ4

7 0
2 years ago
In order to ensure efficient usage of a server, it is necessary to estimate the mean number
juin [17]

Answer:

a. [36.19;39.21]

b. Reject the null hypothesis. The population mean of users that are connected at the same time is greater than 35.

Step-by-step explanation:

Hello!

Your study variable is,

X: "number of users of one server at a time"

The objective is to estimate the mean, for this, a sample of n=100 times was taken and the standard deviation S= 9.2 and the sample mean is X[bar]= 37.7 were calculated.

You need to study the population mean, for this you need your variable to have at least normal distribution. Since you don't have information about its distribution, but the sample is big enough (n≥30) you can apply the Central Limit Theorem and approximate the distribution of the sample mean X[bar] to normal:

X[bar]≈N(μ;σ²/n)

a. With this approximation, you can construct the 90% Confidence Interval using the approximate Z

[X[bar] ± Z_{1-\alpha /2} * S/√n]

Z_{1-\alpha /2} = Z_{0.95} = 1.64

[37.7± 1.64* 9.2/√100]

[36.19;39.21]

b. You need to test if the population mean is greater than 35 with a level of significance of 1%.

The hypothesis is:

H₀: μ ≤ 35

H₁: μ > 35

α: 0.01

This is a one-tailed test so you have only one critical level (right tail):

Z_{1\alpha } = Z_{0.99} = 2.33

This means that if the value of the calculated statistic is equal or greater than 2.33 you will reject the null Hypothesis.

If the value is less than 2.33 you will support the null hypothesis.

The statistic is:

Z=<u> X[bar] - μ </u>= <u> 37.7 - 35 </u> = 2.93

       S/√n           9.2/10

The value 2.93 > 2.33, so you reject the null hypothesis. This means that the population mean of users that are connected at the same time is greater than 35.

<u><em>Note: </em></u><em>To make the decision using the interval calculated on a), the hypothesis should have been two-tailed and the confidence and significance levels complementary.</em>

I hope it helps!

7 0
3 years ago
Lacy pays $15 for each hour of golf lessons and $10 for equipment rental. If the lesson is more than 3 hours long, she only pays
Ghella [55]

Answer:

60

Step-by-step explanation:

15x3=45

5x3=15

15+45=60

4 0
3 years ago
Read 2 more answers
If,
lora16 [44]

Answer

What is the question?

Explanation

Thanks for the free points

Have a great day/night ❤

6 0
3 years ago
Addison's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold 70 espressos in all
Valentin [98]

Answer:

The number of single-shot espressos sold by the cafe was 49.

Step-by-step explanation:

It is provided that Addison's Cafe offers two kinds of espresso: single-shot and double-shot.

Total number of espressos sold by the cafe yesterday afternoon was,

<em>N</em> = 70

The proportion of single-shot espresso sold was, <em>p</em> = 0.70.

Let <em>X</em> = number of single-shot espressos sold.

Compute the number of single-shot espressos sold by the cafe as follows:

E(X)=N\times p

         =70\times 0.70\\=49

Thus, the number of single-shot espressos sold by the cafe was 49.

6 0
3 years ago
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