Answer:
Proved all parts below.
Step-by-step explanation:
As given ,
|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]
To prove- a) For any real number x , | x | ≥ 0 . Moreover, | x | = 0 ⇒ x = 0
b) For any two real numbers x and y , | x | ⋅ | y | = | x y | .
c) For any two real numbers x and y , | x + y | ≤ | x | + | y | .
Proof -
a)
As given x is a real number
Also , by definition of absolute value of x , we get
| x | ≥ 0
Now,
if |x| = 0
⇒ x = 0 and -x = 0
⇒ x = 0 and x = 0
⇒ x = 0
∴ we get
| x | = 0 ⇒ x = 0
Hence proved.
b)
To prove - | x | ⋅ | y | = | x y |
As we have,
|x| = [tex]\left \{ {{x , x\geq 0} \atop {-x, x< 0}} \right.[/tex]
|y| = [tex]\left \{ {{y , y\geq 0} \atop {-y, y< 0}} \right.[/tex]
|xy| = [tex]\left \{ {{xy , x,y > 0 and x,y < 0} \atop {-xy, x > 0, y< 0 and x <0 , y > 0}} \right.[/tex]
We have 4 cases : i) when x > 0 , y > 0
ii) when x > 0 , y < 0
iii) when x < 0, y > 0
iv) when x < 0, y < 0
For Case I - when x > 0 , y > 0
⇒ |x| = x, |y| = y
⇒|x|.|y| = xy
For Case Ii - when x > 0 , y < 0
⇒ |x| = x, |y| = -y
⇒|x|.|y| = -xy
For Case Iii - when x < 0 , y > 0
⇒ |x| = -x, |y| = y
⇒|x|.|y| = -xy
For Case IV - when x < 0 , y < 0
⇒ |x| = -x, |y| = -y
⇒|x|.|y| = (-x)(-y) = xy
∴ we get , from all 4 cases
| x | ⋅ | y | = | x y |
Hence Proved.
c)
To prove - | x + y | ≤ | x | + | y |
Let
|x| = |x + y - y|
≥ |x + y| - |y| ( Triangle inequality)
⇒ |x| + |y| ≥ |x + y|
Hence Proved.
Enter the perimeter of a 30°-60°-90° triangle with a hypotenuse of 20. Round your answer to the nearest tenth. You can leave the units off. *
Answer:
47.3
Step-by-step explanation:
as shown above ,this question can be solved using trigonometry and hence we get the perimeter to be 47.3
Explain how to find the greatest number of identical
arrangements that can be made with 54 roses and 42
tulips with no flowers left over.
(I will mark brilliant the correct answer)
Answer:
There are 6 identical arrangementsStep-by-step explanation:
The correct answer is found by getting the GCF of both numbers.
Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
The greater factor that is common between these is 6, which is the answer.
There are 6 identical arrangements.Graph the line through(-5,-10), m=3
Answer:
below
Step-by-step explanation:
first put it in point-slope then slope intercept:
y+10=3(x+5)
y+10=3x+15
y=3x+5
now graph it
Work out surface area of this sphere give your answer in to 1 DP
Answer:
84.9
Step-by-step explanation:
SA: 4×pi×r^2
the radius is the line (2.6cm)
f(x) is a function.
0
3
с а м а
7
12
f(x)Help
Answer:
It's a function
Step-by-step explanation:
Because non of the inputs have the same output
Determine the exact time from the first date to the second date. Assume the year is not a leap year.
March 27th to November 21rst
Answer:239 daya
Step-by-step explanation:
PLEASE ANSWER ASASP FOR BRAINLEST!!!!!!!!!!!!!!!!!!!!!
Answer:
n - 8 ≥ 10
Step-by-step explanation:
8 less than a number would be n - 8. At least means greater than or equal to so the answer is n - 8 ≥ 10.
In the right angle shown, what is the value of PQ
Answer:
8
Square 17 then Square 15
find the value of root 7 upto 4 decimal
Answer:
2.6458
Step-by-step explanation:
A root of 7 is definitely between the numbers 2 and 3. When you put this number on a calculator the number should be 2.6458 when rounded.
Answer:
the answer is 2.64575
Step-by-step explanation:
because √2 = 1.414, √3= 1.732, √4 = 2, √5 = 2.236, √6 = 2.449, and √7 = 2.64575 or 2.646
On the spinner below, what is the probability of spinning a 2 or a 3?
Answer:
2by1 or
3 by 1
depends on your questions
Step-by-step explanation:
hope it help you
What is the measure of the missing leg of a right triangle if the hypotenuse measures 10 ft and the other leg measures 8 ft?
Answer:
2?
Step-by-step explanation:
A production company spent 45
1
2 days filming its first movie. The company's second movie was filmed in 7
3
4 weeks. Find the ratio of the first movie's filming time to the second movie's filming time. Compare in weeks.
Answer:
26 /33
Step-by-step explanation:
Given that :
Number of days taken filming first movie = 45 1/2
Number of weeks spent filming second movie = 8 1/4
Concerning days to weeks ;
45 1/2 days = 91/2 days = 91/2 ÷ 7 ;
91 / 2* 1/7 = 91/14 = 6. 5 weeks
Hence,
Ratio of first week fuming to second week filming ;
6.5 weeks : 8 1/4 weeks
6 1/2 : 8 1/4
13 / 2 : 33 /4
13 / 2 * 4 /33
52 / 66
26 / 33
HELP I’m being timed!!
Answer:
A 1/4
Step-by-step explanation:
Answer:
A. There is a 1/4 chance.
Step-by-step explanation:
There are 8 outcomes if a coin is flipped 3 times.
Of these, 4 start with tails.
Since 4 is the denominator here, C (3/8) is out.
Also 4 doesn't have 3 as a factor, so B (1/3) is also out.
After the tails flip, two heads follow.
That's one of four of the combinations starting with tails (THH, THT, TTH, TTT, so D is out, leaving A as our answer! (We would need two for A to work)
Use the distributive property.
Simplify the expression below.
5(x - 2) =_-_
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Hey there!
Do you remember what the Distributive property states? If not, no worries! Here's what this property states:
a(b+c)=ab+ac
In this formula, a, b, and c can be
Constants. These are numbers like 1, 2, 3, or -1, -2, -3... or even fractions, decimals... (all real numbers)Variables. These are letters like d, a, s, e, t, k, a...Variables can have a number next to them; it's called a coefficient.Now that we know what this property states, let's simplify this expression.
5(x-2)
First, multiply 5 times x:
5x (5 is the coefficient of x, by the way)
Then, multiply 5 times -2 (please pay attention to the sign) :)
-10
Put both terms together.
Hence, the simplified expression is
[tex]\boxed{\boxed{\bold{5x-10}}}[/tex]
Is it possible to simplify the expression any further? No.
Why? Because 5x and -10 aren't like terms, so we cannot combine them.
Hope everything is clear.
Let me know if you have any questions!
#ILoveLearning
:-)
(13x+2)+(3x-4)+(5x-7)
Answer:
13x+2+3x-4+5x-7=180
Step-by-step explanation:
I WILL GIVE BRAINLIEST AND 50 POINTSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Calculate the rate of change for the following data:
x y
-1 7
2 -2
7 -17
10 -26
HELP!!!!
Answer:
we get Rate of change = -3
Step-by-step explanation:
We need to calculate the rate of change for the following data:
x y
-1 7
2 -2
7 -17
10 -26
The rate of change can be calculated using slope formula: [tex]Rate\:of\:change=\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table, we can take any 2 points
Suppose we take (-1,7) and (2,-2)
We have: [tex]x_1=-1, y_1=7,x_2=2, y_2=-2[/tex]
Putting values in formula and finding rate of change
[tex]Rate\:of\:change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:change=\frac{-2-7}{2-(-1)}\\Rate\:of\:change=\frac{-9}{2+1}\\Rate\:of\:change=\frac{-9}{3}\\Rate\:of\:change=-3[/tex]
So, we get Rate of change = -3
Will mark brainliest!!!Please find the value of each variable in the parallelogram!!
Answer:
a=9
b=11
Step-by-step explanation:
opposite sides of a parallelogram are congruent(aka equal)
so, a=9
b=11
Answer:
A is 9 units and B is 11 units.
Step-by-step explanation:
In a parallelogram, there are 2 parallel line. And they are congruent. So whatever their parallel line is equal to, it is the measure of that variable.
-4/7p + (-2/7p) +1/7
Answer:
-6/7p+1/7
Step-by-step explanation:
I NEED HELP!! Please
Answer:
Step-by-step explanation:
P represents the original price of the sandwich
1.5 represents the discount
This is a solid bounded by a curved lateral surface and two
circular bases.
Answer:
Cylinder
Step-by-step explanation:
...
Can someone please explain how to do number 9.
Answer:
x<15, probably
Step-by-step explanation:
maybe multiply 2 to each side to eliminate the fraction. so 3x+15<60. subtract 15 to isolate the variable term so 3x<45. divide by 3 to isolate x so x<15. check the work. is the inequality true for all values of x less than 15? let's try the first possible integer value, 14, to be sure. 3(14)+15= 57. so 57/2<30. now 57/2 is 28.5 and 28.5<30 so it seems right
Question:
A store had 600 pounds of feed. After delivering equal amounts to 4 farmers, there are 60 pounds left. How many pounds did each farmer receive?
Answer:
135
Step-by-step explanation:
I am not sure if you have to use the substitution method but I just did (600 - 60) then divided by 4
Graph the line
Through (6, 0), m= -1/2
Answer:
The equation of the line would be y = -1/2x + 3. You can use this to make a graph that looks like this:
question:find the angle measure of the missing angle
if you can pls explain
Answer:
85°
Step-by-step explanation:
So in geometry, the formula to find the sum of all interior angles is denoted as follows:
n = number of sides in the polygon
( n - 2 ) × 180° = sum of the interior angles
Using that formula, a triangle has 3 sides, so
n = 3 , therefore:
= ( 3 - 2 ) × 180°
= 1 × 180°
= 180°
Since the total sum of the interior angles of a triangle all have to add up to 180°, you can create the following equation and solve:
34° + 61° + x = 180°
Solve for x.
Calories consumed by members of a track team the day before a race are normally distributed, with a mean of 1,600 calories and a standard deviation of 100
calories. If a normal curve is sketched using these data, what is the range for 3 standard deviations to the right and to the left of the mean?
O 1,400-1,800
O 1,500-1,700
O 1,300-1,900
O 0-3,200
20 POINTS
plz help
Thank you
Answer:
The solution is 1,300-1,900
Step-by-step explanation:
Simply put:
The standard deviation is 100. Because the range is 3 standard deviations, you add and subtract 300 from 1,600 instead of the normal 100.
So,
1,600 - 300 = 1,300
1,600 + 300 = 1,900
So, your answer is the third option: Between 1,300 and 1,900
The correct answer is 1,300 - 1,900.
I messed up somewhere I think ugh
Answer:
¯\_(ツ)_/¯
Step-by-step explanation:
Answer:
Step-by-step explanation:
n≤-2
n≥-4
or -4≤n
combining
-4≤n≤-2
let f(x) = x^3+3x^2-x-3. Find the polynomial function each of whose roots are two less than the roots of f(x)
Step-by-step explanation:
f(x) = x³ + 3x² - x - 3 = x²(x + 3) - (x + 3)
= (x² - 1)(x + 3) = (x + 1)(x - 1)(x + 3).
The roots of f(x) are x = -3, -1 and 1.
=> The new roots are x = -5, -3 and -1.
=> g(x) = (x + 5)(x + 3)(x + 1) = x³ + 9x² + 23x + 15.
What is the solution to the gaming systems of linear equations 2X plus 3Y equals 13 for a 6+ 6Y equals 14
Answer:
(9/2, 4/3) or just x = 9/2, y = 4/3. (it's the same thing)
Step-by-step explanation:
First, multiply the first equation 2x + 3y = 13 by 2, so that you get 4x + 6y = 26. Now you have the same coefficient for y. Now, subtract the second equation 6y = 8 (i simplified it first) from the first one that is doubled. After that, you would have just one equation, 4x = 18. So x = 18/4 = 9/2. Substitute x to solve for y, and you'd get 4/3.
9514 1404 393
Answer:
(x, y) = (-6, 8 1/3)
Step-by-step explanation:
The system of equations appears to be ...
2x +3y = 136x +6y = 14Dividing the first equation by 2 gives ...
3x +3y = 7
Subtracting the first equation from this, we get ...
(3x +3y) -(2x +3y) = (7) -(13)
x = -6
Then substituting for x in the first equation, we have ...
2(-6) +3y = 13
3y = 25 . . . . . . . . add 12
y = 25/3 = 8 1/3 . . . . divide by 3
The solution is (x, y) = (-6, 8 1/3).
Select all the expressions that are equivalent to 15n – 10.
8n – 23 – 3n + 11 + 10n + 2
20n – 5 + 15n – 5
3(5n – 2)
5(3n – 2)
35 – 3n + 10
Answer:
Step-by-step explanation:
the expression is equivalent with
5(3n-2)=15n-10
Add a noun of direct address to the sentence below, along with proper punctuation.
“I like your new haircut."
Answer:
I like your new haircut, dad.
Step-by-step explanation:
I'm pretty sure