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oksian1 [2.3K]
3 years ago
15

Simplify 7.4z - 5 (-1.6z + 2.4) please

Mathematics
1 answer:
Sergeu [11.5K]3 years ago
8 0
The answer is 15.4z-12
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The graph of f (x) = x + 5 is a vertical translation 5 units
irakobra [83]

Answer:

A horizontal translation of 5 units to the left.

Step-by-step explanation:

Given the parent linear function:

\displaystyle f(x)=x

To shift vertically n units, we can simply add n to our function. Hence:

f(x)=x+n

So, a vertical shift of 5 units up implies that n=5. So:

f(x)=x+5

As given.

However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:

f(x-n)=(x-n)

Where n is the horizontal shift.

For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:

f(x-1)=(x-1)

Or:

f(x)=x-1

We notice that this is also a vertical shift of 1 unit downwards.

Therefore, we want a number n such that -n=5.

So, n=-5.

Therefore, it we shift our function 5 units to the left, then n=-5.

Then, our function will be:

f(x-(-5))=(x+5)\text{ or } f(x)=x+5

Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.

7 0
3 years ago
Find the negation of statement <br>2+5=5​
chubhunter [2.5K]

Answer:

Can u mark brainelst plz?

Step-by-step explanation:

x − 1  >  5

x  > − 6

x  +  1  ≥  9

7 0
3 years ago
The proportion of a population with a characteristic of interest is p = 0.37. What is the standard deviation of the sampling dis
lukranit [14]

The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.

<h3>What is a sample proportion?</h3>

A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.

Mathematically, sample proportion can be calculated by using this formula:

\hat{p} = \frac{x}{n}

Where:

  • x represent the number of individuals with a specified characteristic.
  • n represent the total number of individuals in a sample.

In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:

Standard deviation (SD) = √(p(1 - p)/n)

Substituting the given parameters into the formula, we have;

Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)

Standard deviation (SD) = √(0.37(0.63)/1,600)

Standard deviation (SD) = √(0.2331)/1,600)

Standard deviation (SD) = √0.0001457

Standard deviation (SD) = 0.0121.

Read more on standard deviation here: brainly.com/question/14467769

#SPJ1

8 0
1 year ago
the second term of a geometric sequence is 18 and the fourth term is 8 find the common ratio . And find the sum of the first 6 t
777dan777 [17]

Answer:

  • ratio: 2/3
  • sum: 73 8/9

Step-by-step explanation:

The general term of a geometric sequence is ...

  an = a1·r^(n-1)

You have the 2nd and 4th terms, so ...

  a2 = a1·r^(2-1) = a1·r

  a4 = a1·r^(4-1) = a1·r^3

We can find r from the ratio ...

  a4/a2 = (a1·r^3)/(a1·r) = r^2 = 8/18 = 4/9

Then r is ...

  r = √(4/9) = 2/3 . . . . the common ratio

The first term is ...

  a2 = 18 = a1·(2/3)

  a1 = (3/2)·18 = 27

__

The sum of the first 6 terms is ...

  Sn = a1·(r^n -1)/(r -1)

  S6 = 27·((2/3)^6 -1)/(2/3 -1)

  S6 = 27·(64/729-1)/(2/3-1) = (27)(665)/243 = 73 8/9

The sum of the first 6 terms is 73 8/9.

_____

<em>Check on the sum</em>

The first 6 terms are ...

  27, 18, 12, 8, 5 1/3, 3 5/9

Their sum is 73 8/9, as above.

8 0
3 years ago
Find the slope of 9x=3y+5
qaws [65]
<u>9x</u> = <u>3y + 5</u>
 9         9
x = 1/3y + 5/9
x - 5/9 = 1/3y + 5/9 - 5/9
x - 5/9 = 1/3y
3(x - 5/9) = 1/3y · 3
3x - 1 2/3 = y
y = 3x - 1 2/3
4 0
3 years ago
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