1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
stiv31 [10]
3 years ago
10

Write each of the following expressions without using absolute value: |z−6|−|z−5|, if z<5

Mathematics
1 answer:
abruzzese [7]3 years ago
6 0

Answer:

The answer is <em>1</em>.

Step-by-step explanation:

Given the expression:

|z-6|-|z-5|,\ if\ z

To find:

The expression without absolute value.

Solution:

First of all, let us learn about the absolute value function:

y = f(x) = |x| =\left \{ {{x\ if\ x>0} \atop {-x\ if\ x

i.e. value is x if x is positive

value is -x if x is negative

Here the given expression contains two absolute value functions:

|z-6| and |z-5|

Using the definition of absolute value function as per above definition.

|z-5| =\left \{ {{(z-5)\ if\ z>5} \atop {-(z-5)\ if\ z

|z-6| =\left \{ {{(z-6)\ if\ z>6} \atop {-(z-6)\ if\ z

Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6

So, given expression |z-6|-|z-5|,\ if\ z will be equivalent to :

-(z-6) - (-(z-5))\\\Rightarrow -z+6 +z-5 = \bold{1}

So, the expression is equivalent to <em>1</em>.

You might be interested in
The price of bananas went from $0.20 per lb to $0.60 per lb in four years. Find the rate of change of the price of bananas
MrMuchimi
$0.10 a year
$0.20-$0.60
=.40
.40/4=10
6 0
3 years ago
Read 2 more answers
Rearrange the equation so u is the independent variable,<br> 4u + 8w = -3u + 2w<br><br> W=
Katyanochek1 [597]

Answer:

w=-1.16u

Step-by-step explanation:

first you want to put the W's on one side and the U's on the other. we can do this by subtracting 4u from the left side and the right side making the equations 8w=-7u+2w.

next we want to subtract 2w from both sides making the equation 6w=-7u then we divide by 6 to get w=-1.16u

3 0
2 years ago
What is the trigonometric ratio for cosn? enter your answer, as a simplified fraction, in the boxes. $$ triangle l m n with righ
hjlf

The trigonometric ratio will be Cos(n)=12/13

<h3>What will be the trigonometry ratio?</h3>

Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.

Given are the sides LM = 15, MN = 36, and LN = 39.

It says to find cos(n) = ?

So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.

We know that the cosine ratio is given by :-

Cos(n)=\dfrac{adjacent}{Hypotenuse}

Cos(n)=\dfrac{MN}{LN}

Cos(n)=\dfrac{36}{39}

Cos(n)=\dfrac{12}{13}

Hence the required ratio will be   Cos(n)=\dfrac{12}{13}

To know more about trigonometry, follow

trigonometry

3 0
2 years ago
Help pls its just math :( <br><br>Ik it sucks I hate math too, pls help tho
Umnica [9.8K]

Answer:

x = - 1

Step-by-step explanation:

Given

- 4(3x - 7) = 40 ( divide both sides by - 4 )

3x - 7 = - 10 ( add 7 to both sides )

3x = - 3 ( divide both sides by 3 )

x = - 1

6 0
3 years ago
Read 2 more answers
Find the side lengths ! help pls
sergeinik [125]

(a) the given triangle is a isosceles triangle, therefore the two leg sides will be congruent, as well as the two base angles. It is given that one of the base angles ∠XYW is 70°, therefore, due to the law of a isosceles triangle, the measurement of ∠XWY is also 70°. Remember, a triangle's interior angles add up to 180°, so:

180 - (70 + 70) = 180 - 140 = 40

40° is your answer.

m∠X = 40°

(b) All sides are congruent, making it a equilateral triangle. If it is a equilateral triangle, then all the angles also have the same measurement. The total of the interior angle's measurement is 180°. Divide by the amount of angles, 3:

180/3 = 60

60° is your answer.

m∠V = 60°

~

7 0
3 years ago
Other questions:
  • A box contains four bowling balls numbered 2, 4, 6, and 10 according to their weight. Two are drawn randomly without replacement
    8·1 answer
  • Determine which system below will produce infinitely many solutions.
    12·1 answer
  • abdul bought 3 cds that were each the same price. including sales tax, he paid a total of $47.40. of that total, $2.70 was tax.
    6·1 answer
  • Please help me out with this!!!!!!!!!!!!
    10·1 answer
  • Kevin buys the items listed below at a grocery store. 3 packages of chicken priced at $12.36 per package 12 pound of broccoli pr
    6·1 answer
  • 3/4 divided by 6/7<br> Please help me
    10·1 answer
  • A circle has center at C(-10,7). A point on the circle is P(-12, 15). What is the
    6·1 answer
  • Number of College Faculty The number of faculty listed for a variety of private colleges that offer only bachelor’s degrees is l
    10·1 answer
  • A factory robot recently examined some bulbs, of which 12 were flawed and 48 were not. Considering this data, how many flawed bu
    15·1 answer
  • Car X weighs 136 pounds more than car Z. Car Y weighs 117 pounds more than car Z. The total weight of all three cars is 9439 pou
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!