3x −4 = 11 what is the answer

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of t

Yuliya22 [10]

The original are would be 48.

Since we know that the length and width are two consecutive even integers, we can model them as follows:

Width = x

Length = x + 2

This works because no matter what even number is put in for x, the length will also be even.

Now we know if we subtract 3 from the width, we have a new rectangle that gives us an area of 24 inches. Therefore, our new triangle has the following:

Width: x - 3

Length: x + 2

Area: 24

And we can plug this into the equation.

Length* Width = Area

(x + 2)(x - 3) = 24

x^2 - x - 6 = 24

x^2 - x - 30 = 0

This is not a quadratic that we can factor to show the following:

(x - 6)(x + 5) = 0

This gives us the answers of x = 6 and x = -5. Since a side can't be negative, we throw out the x = -5 and the answer is x = 6.

So if we go back to the original rectangle, we know:

Width = x = 6

Length = x + 2 = 8

Area = 6*8 = 48

7 0

3 years ago

To study the population of consumer perceptions of new technology, sampling of the population is preferred over surveying the en

Gennadij [26K]

Because It is quicker and fast.

Sampling:

Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling.

Sampling is the selection of a subset of the population of interest in a research study. In the vast majority of research endeavors, the participation of an entire population of interest is not possible, so a smaller group is relied upon for data collection.

Learn more about Sampling on:

brainly.com/question/24466382

#SPJ4

6 0

2 years ago

A group of retailers will buy 104 televisions from a wholesaler if the price is $300 and 144 if the price is $250. The wholesale

stepladder [879]

Answer:

The required equilibrium point is (356.538,58.769)

Step-by-step explanation:

The two points on your demand equation are : (300,104) and (250,144)

Take the number of televisions on y-axis and the price of the television on x-axis

Now, to find the demand equation for the given problem, find slope using the above two points :

$\implies Slope=\frac{144-104}{250-300}\\\\\implies Slope = -\frac{4}{5}=-0.8$

And the y - intercept is : y = -0.8x + b

Find the value of b using any point. Let us take (250,144)

144 = -0.8 × 250 + b

⇒ b = 144 + 200

⇒ b = 344

So, the y-intercept is : y = -0.8x + 344

The two points on your supply equation are : (225,88) and (315,68)

Take the number of televisions on y-axis and the price of the television on x-axis

Now, to find the supply equation for the given problem, find slope using the above two points :

$\implies Slope=\frac{68-88}{315-225}\\\\\implies Slope = -\frac{2}{9}$

And the y - intercept is :

$y = -\frac{2}{9}x + b$

Find the value of b using any point. Let us take (225,88)

$88 = -\frac{2}{9}\times 225 + b\\\\\implies b = 88 + 50\\\\\implies b = 138$

So, the y-intercept is :

$y = -\frac{2}{9}x + 138$

To find the equilibrium point, solve both the y-intercepts of the demand equation and the supply equation :

⇒ x = 356.538 and y = 58.769

Hence, the required equilibrium point is (356.538,58.769)

8 0

3 years ago

The coordinate grid shows the plot of four equations.

Rom4ik [11]

Answer:

Your answer would be A and B

Step-by-step explanation:

Simply look for the coordinates on the graph and look for the name of the lines that intersect there.

5 0

3 years ago

A random sample of 7 fields of durum wheat has a mean yield of 29.8 bushels per acre and standard deviation of 3.62 bushels per

meriva

Answer:

CI = 29.8 ± 3.53

Critical value is z = 2.58

Step-by-step explanation:

First of all let's find margin of error. It is given by the formula;

ME = zσ/√n

We are given;

Standard deviation; σ = 3.62

Sample size; n = 7

Mean; x¯ = 29.8

Now, z-value for 99% Confidence level is 2.58

Thus;

ME = (2.58 × 3.62)/√7

ME = 3.53

CI is written as;

CI = x¯ ± ME

CI = 29.8 ± 3.53

Critical value is z = 2.58

5 0

3 years ago