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anyanavicka [17]
2 years ago
11

PLZ HURRYSolve for z.z3–3≤–2

Mathematics
2 answers:
nika2105 [10]2 years ago
7 0
I’m so confused

I’m so confused
Nimfa-mama [501]2 years ago
5 0

Answer:

z ≤ 1/3

Step-by-step explanation:

3z - 3 ≤ -2        Add 3

3z ≤ 1               Divide by 3

z ≤ 1/3

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Determine whether the Mean Value Theorem applies to the function f(x)=2x^1/5 on the interval [-32, 32]
Anettt [7]

Answer

given,

f(x) = 2 x^{1/5}

interval = [-32, 32]        

differentiating the given equation

f'(x) = \dfrac{d}{dx}(2 x^{1/5})

f'(x) = \dfrac{2}{5x^{4/5}}

hence, the above solution is not defined at x = 0

and x = 0 lie in the given interval i.e. [-32, 32]

so, at x = 0 the function is not differentiable.

Hence, mean value theorem does not apply to the given function.

5 0
3 years ago
The sum of 5 consecutive integers is 110, what is the fourth number in this sequence?
Xelga [282]

The answer is:  " 23 " .

    →  The fourth number in the sequence is:  " 23 " .

_____________________________________

Explanation:

To solve:

 " x + (x + 1) + (x + 2) + (x + 3)  + (x + 4) = 110 " ;

in which:

 "x" = The first number in these sequence;

 "(x + 1 )" = the second number in the sequence;

 "(x + 2)" = the third number in the sequence;

 "(x + 3)" = the fourth number in the sequence;

 "(x + 4)" = the fifth number in the sequence;

_____________________________________

Solve for the "fourth number in the sequence" ; or:  "(x + 3)" ;

_____________________________________

Given:  " x + (x + 1) + (x + 2) + (x + 3) + (x + 4) = 110 " ;

                     ↔   " x + x + 1 + x + 2 + x + 3 + x + 4 = 110 " ;

→  Solve for "x" ;  

→  then,  solve for "(x + 3)" ;  

     →  which is the fourth number in this sequence;

_____________________________________

→  " x + x + 1 + x + 2 + x + 3 + x + 4= 110 " ;

      "5x + 1 + 2 + 3 + 4= 110 " ;

      " 5x + 10 =  110 " ;

Solve for "x" :

     Subtract "10" from EACH SIDE of the equation; as follows:

      " 5x + 10 - 10 =  110 - 10 " ;

 to get :

      "  5x = 100 " ;

Now, divide EACH SIDE of the equation by "5" ;

to isolate "x" on one side of the equation; & to solve for "x" ;  as follows:

         5x / 5  = 100 / 5 ;

to get:

         "  x  = 20 "  .

_____________________________________

Now, to find the fourth number in the sequence:

 →  " (x + 3) " ;

→  Substitute "20" for "x" ;

    " x + 3 = 20 + 3 = 23" ;

_____________________________________

The answer is:  " 23 " .

The fourth number in the sequence is:  " 23 " .

_____________________________________

Let us check our work:

If there are five "5" numbers in the sequence, and "23" is the "fourth number" , then:  "24" is the "fifth number" .

As such:  "22" is the "third number" ;  "21" is the "second number" ; and "20" is the "first number" .  Is this consistent with:  "x = 20" as the "first number" ?  Yes!

Thus,  "20 + 21 + 22 + 23 + 25 = ?  110 ?  ? ;

→  20 + 21 = 41 ;

→  41 + 22 = 63 ;

→  63 + 23 = 86 ;

→  86 + 24 = 110 .    Yes!

_____________________________________

Hope this answer is helpful!

Best wishes in your academic pursuits—

 and within the "Brainly" community!

_____________________________________

5 0
3 years ago
Find an explicit rule for the nth term of the sequence.
Sphinxa [80]

Step-by-step explanation:

in a geometric sequence there is a constant factor x that is multiplied with every previous term to create the next one.

a2 = 20

a5 = 1280 = a2×x×x×x = a2×x³ = 20x³

64 = x³

x = 4

=> a1 = 5

therefore

an = an-1×4 =

a1 \times  {4}^{n - 1}

n > 1

7 0
2 years ago
Find the equation of the line passing through the point (–1, –2) and perpendicular to the line y = –1∕2x + 5. Question options:
tankabanditka [31]

Answer:

<h3>The answer is option C</h3>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

y = - 1/2x + 5

Comparing with the general equation above

Slope / m = -1/2

Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line

That's

Slope of the perpendicular line = 2

Equation of the line using point (–1, –2) and slope 2 is

y + 2 = 2( x + 1)

y + 2 = 2x + 2

y = 2x + 2 - 2

We have the final answer as

<h3>y = 2x</h3>

Hope this helps you

4 0
2 years ago
Which angles are pairs of corresponding angles? Check all that apply
AleksAgata [21]

Answer:

B and D people. Your welcome.

Step-by-step explanation:

6 0
3 years ago
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