Answers
where x is nonzero
=======================================================
Explanation:
We'll use two rules here
(a^b)^c = a^(b*c) ... multiply exponentsa^b*a^c = a^(b+c) ... add exponents------------------------------
The portion [ x^(a-b) ]^(a+b) would turn into x^[ (a-b)(a+b) ] after using the first rule shown above. That turns into x^(a^2 - b^2) after using the difference of squares rule.
Similarly, the second portion turns into x^(b^2-c^2) and the third part becomes x^(c^2-a^2)
-------------------------------
After applying rule 1 to each of the three pieces, we will have 3 bases of x with the exponents of (a^2-b^2), (b^2-c^2) and (c^2-a^2)
Add up those exponents (using rule 2 above) and we get
(a^2-b^2)+(b^2-c^2)+(c^2-a^2)
a^2-b^2+b^2-c^2+c^2-a^2
(a^2-a^2) + (-b^2+b^2) + (-c^2+c^2)
0a^2 + 0b^2 + 0c^2
0+0+0
0
All three exponents add to 0. As long as x is nonzero, then x^0 = 1
Related Questions
Find the number of possible outcomes. Seven books need to be placed
on a shelf. You randomly arrange the books on the shelf from left to right.
Answers
5040 possible outcomes.
Explanation:
There are 7 books, therefore you need to do 7! (factorial).
1x2x3x4x5x6x7 = 5040
Without simplifying, select all the expressions that represent a rational number. Group of answer choices LaTeX: 4\frac{2}{3}\times\frac{8}{\sqrt{3}} 4 2 3 × 8 3 4 2 3 × 8 3 4 2 3 × 8 3 LaTeX: 4\frac{2}{3}+\frac{\sqrt{3}}{9} 4 2 3 + 3 9 4 2 3 + 3 9 4 2 3 + 3 9 LaTeX: 4\frac{2}{3}-\frac{\sqrt{4}}{8} 4 2 3 − 4 8 4 2 3 − 4 8 4 2 3 − 4 8 LaTeX: 4\frac{2}{3}\times\frac{\sqrt{3}}{9} 4 2 3 × 3 9 4 2 3 × 3 9 4 2 3 × 3 9 LaTeX: 4\frac{2}{3}\div\frac{\sqrt{4}}{8} 4 2 3 ÷ 4 8 4 2 3 ÷ 4 8 4 2 3 ÷ 4 8
Answers
Answer:
Well the real answer is 1st 2nd and 5th
Step-by-step explanation:
Just took the quiz
I'm confused about what the expression is.
Answers
Answer:
4(x+y)
Step-by-step explanation:
x+y is one side length and there are 4 side lengths.
PLSSS HELP Which triangles are similar to triangle A?
Answers
Answer:
ΔB
Step-by-step explanation:
ΔA's angles are: 58º, 54º, and 68º
68º is found by 180 - (58 + 54)
ΔB's angles are: 54º, 68º, and 58º
58º is found by 180 - (68 + 54)
ΔA and ΔB have the same angles, therefore they are similar triangles
Answer:
triangle b
Step-by-step explanation:
i measured
.9 times what equals 1.5
Answers
Answer:
5/3
Step-by-step explanation:
x*0.9=1.5
x=15/9
x=5/3
Lets solve your question step by step:-
Given,
0.9*x = 1.5
0.9x = 1.5
=} 0.9x/0.9 = 1.5/0.9
x = 1.666667
So,
9 times 1.666667 (x) is 1.5
Hope it helps :)
Express the following fraction into a decimal
- 5/9
Answers
Answer:
5/9 = 0.5
Step-by-step explanation:
hope it helps leme know if u hab doubts
4b+4<4(5-3b) how do u break this down to get the right answer
Answers
4b+4<20-12b
16b<16
b<1 olur.
İYİ DERSLER!
Answer:
See answer in the image below.
please answer please!!!! Will mark brainliest for complete answer. -the first photo is to calculate the area. Just question number 7 a and b i). And question number 8.
Answers
Area = 1/2*b*h
= (1/2)*3*4
= 3*2
= 6 m^2
7a.
1cm^3
Or, 1cm * 1cm * 1cm
Or, 10mm * 10 mm * 10 mm
Or, 1000 mm^3
7b.i)
10 cm^3
Or, 10cm * 1cm* 1cm
Or, 100mm * 10mm * 10mm
Or, 10000 mm^3
8.)
Volume = 50 cm^3
Base area= 5 cm^2
Now,
Volume = area * height
Or, 50 = 5 * height
Or, height = 50/5
Or, height = 10 cm
Plz mark this as the brainiest. :)
4m-3/4= -9+4m/8 helppp
Answers
Answer:
m=− 33/14 =−2.357
Step-by-step explanation:
if you search up you question the first thing will come up is an answer from tiger algebra is may not be you question but click on it is will take to to this search bar area clear it and put you question in it then it will give your answer and step by step explanation
Which of the following is the correct formula for distance?(1 point) d=(x2−x1)+(y2−y1)−−−−−−−−−−−−−−−−−√, where d is the distance between points (x1,y1) and (x2,y2). d=(x2+x1)2+(y2+y1)2−−−−−−−−−−−−−−−−−−√, where d is the distance between points (x1,y1) and (x2,y2). d=(x2−x1)2+(y2−y1)2, where d is the distance between points (x1,y1) and (x2,y2). d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√, where d is the distance between points (x1,y1) and
Answers
Answer:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Step-by-step explanation:
Which of the following is the set of all real number x such that x-2 < x-4?
Answers
If you subtract x from both sides, then you go from
x-2 < x-4
to
-2 < -4
which is a false statement. The value -2 is not smaller than -4. It's the other way around. I recommend looking at a number line to compare the two values.
This means that x-2 < x-4 is never true regardless of what x value you pick. So there are no solutions.
I’m mainly looking for help with #15 for this one please
Answers
Answer:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}=1[/tex]
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
Step-by-step explanation:
So we want to left and right hand limits of the function:
[tex]f(x)=\sin{\frac{\pi}{\floor[x]}[/tex]
as x approaches 3.
Note that the [x] means the floor function a.k.a the greatest integer function. In other words, the value of the function will be the greatest integer less than or equal to x.
1) Left
So we have the limit:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}[/tex]
Note that since we're coming from the left, the values are 2.9, 2.99, and 2.999...
As I mentioned previously, the floor function outputs the greatest integer less than or equal to x.
With 2.9, 2.99, and 2.999, the greatest integer less than or equal to x is 2.
Therefore:
[tex]=\sin{\frac{\pi}{2}[/tex]
Simplify:
[tex]=1[/tex]
So:
[tex]\lim_{x\to3^-}\sin{\frac{\pi}{\floor[x]}=1[/tex]
2) Right:
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}[/tex]
Since we're coming from the right this time, the values are going to be 3.01, 3.001, 3.001.
And, the greatest integer less than or equal to 3.01, 3.001, and 3.001... is 3.
Therefore:
[tex]=\sin{\frac{\pi}{3}[/tex]
Simplify:
[tex]=\frac{\sqrt3}{2}[/tex]
So:
[tex]\lim_{x\to3^+}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
At 3:
So we have:
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}[/tex]
The greatest integer of 3 is just 3. So:
[tex]=\sin{\frac{\pi}{3}\\[/tex]
Simplify:
[tex]=\frac{\sqrt3}{2}[/tex]
So:
[tex]\lim_{x\to3}\sin{\frac{\pi}{\floor[x]}=\frac{\sqrt3}{2}[/tex]
given:x+2<-5. choose the solution set.
Answers
Step-by-step explanation:
x+2<−5
Step 1: Subtract 2 from both sides.
x+2−2<−5−2
x<−7
Answer:
x<−7
What is the solution to the inequality below?
X^2>=81
Answers
A. x ≤ - 9 or x ≥ 9
Step-by-step explanation:x² ≥ 81
| x | ≥ 9
x ≥ 0 => x ≥ 9 => x ∈ [ 9 ; + oo)
x < 0 => x ≤ - 9 => x ∈ ( -oo ; - 9 ]
x ∈ ( -oo ; - 9 ] ∪ [ 9 ; + oo)
+3х2+3x2
What is that answer simplified?
Answers
20 POINTS !!!
Find the distance between the points (3,-4) and (5, 4)
Answers
Answer:
[tex]d=2\sqrt{17}\approx8.2462[/tex]
Step-by-step explanation:
To find the distance between two points, use the distance formula.
The distance formula is:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2[/tex]
Let (3,-4) be x₁ and y₁ and let (5,4) be x₂ and y₂. Therefore:
[tex]d=\sqrt{(5-3)^2+(4--4)^2[/tex]
Simplify:
[tex]d=\sqrt{(2)^2+(8)^2[/tex]
Square:
[tex]d=\sqrt{4+64}[/tex]
Add:
[tex]d=\sqrt{68}[/tex]
Simplify:
[tex]d=\sqrt{4\cdot17}=\sqrt4\cdot\sqrt{17}[/tex]
Simplify:
[tex]d=2\sqrt{17}\approx8.2462[/tex]
Answer:
[tex]\boxed{2\sqrt{17}}[/tex]
Step-by-step explanation:
To find the distance between two points, we use the distance formula. The distance formula is:
[tex]\boxed{d=\sqrt{(x_{2}-x_{1})^{2}+({y_{2}-y_{1})^{2}}}}[/tex]
Therefore, we can label our coordinate pairs and solve for d.
Because we are given two coordinate pairs, we will follow the standard naming system for coordinate pairs. This is [tex](x_{1}, y_{1}) \text \: {and} \: (x_{2}, y_{2})[/tex]. Therefore, we can implement the distance formula and solve.
[tex]\sqrt{(5-3)^{2}+(4-(-4))^{2}}\\\\\sqrt{(2)^{2}+(8)^{2}}\\\\\sqrt{4 + 64} \\\\\sqrt{68} \\\\\boxed{2\sqrt{17} }[/tex]
Huda evaluated the expression below. Negative 3 (8 minus 5) squared minus (negative 7) = negative 3 (3) squared minus (negative 7) = negative 3 (9) minus (negative 7) = 27 minus (negative 7) = 34. What was Huda's error? Huda evaluated (3) squared incorrectly. Huda found the product of –3 and 9 as positive. Huda subtracted –7 from 27 incorrectly. Huda did not follow the order of operations.
Answers
Answer:
Huda found the product of –3 and 9 as positive.
Step-by-step explanation:
Given the expression and result below :
Huda evaluated the expression below. Negative 3 (8 minus 5) squared minus (negative 7) = negative 3 (3) squared minus (negative 7) = negative 3 (9) minus (negative 7) = 27 minus (negative 7) = 34
-3(8 - 5)² - (-7) =
Step 1:
- 3(3)² - (-7)
Step 2:
-3(9) - (-7)
Step 3:
27 - (-7) = 34 (error in the third step)
-3(9) = - 27
Hence,
-27 - (-7) = - 27 + 7 = - 20
Answer:
its B on edge
Step-by-step explanation:
I just took the test
Spackle paint supply had a beginning inventory of 10 cans of paint at 25 per can. They purchased 20 at 30 per can. They had an ending inventory valued 500. How much paint in dollars was used for the month
Answers
Answer:
The total number of paints used for the month = $350
Step-by-step explanation:
Given that:
Spackle paint had a beginning inventory of 10 can of paint at $25 per can =
10× $25 = $250
They purchased 20 at $30 per can.
The amount of the 20 purchased can = 20 × $30 = $600
The total inventory for this supply = $600 + $250
= $850
They had an ending inventory valued 500.
∴
The total number of paints used for the month = total inventory - ending inventory
The total number of paints used for the month = $850 - $500
The total number of paints used for the month = $350
Example of a function and why?
Answers
Answer:
f(x) = x + 2
Step-by-step explanation:
If we graph x + 2, we can see that it passes the Vertical Line Test. Each x-value only has 1 y-value.
Factorise a2 -10a-24
Answers
Answer:
(a+2)(a-12)
Step-by-step explanation:
[tex]a^2-10a-24\\\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(a^2+2a\right)+\left(-12a-24\right)\\\\\mathrm{Factor\:out\:}a\mathrm{\:from\:}a^2+2a\mathrm{:\quad }a\left(a+2\right)\\\\\mathrm{Factor\:out\:}-12\mathrm{\:from\:}-12a-24\mathrm{\\:\quad }-12\left(a+2\right)\\=a\left(a+2\right)-12\left(a+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}a+2\\=\left(a+2\right)\left(a-12\right)[/tex]
Answer:
(a + 2)(a - 12)
Step-by-step explanation:
a^2 - 10a - 24
using splitting method
a^2 - 12a + 2a - 24
taking separate common from both pairs
a(a - 12) + 2(a - 12)
(a + 2)(a - 12)
Something that represent today’s culture ( sum that isn’t tech or social media)
Answers
It depends on which culture you're looking at to be honest. But in the current environment, one item that is fairly prevalent is the coronavirus facemask. You could say it symbolically represents the idea of trying to stay safe and it represents a new norm (that many may consider strange since people are used to seeing each other's faces).
E={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} A={x:x is a multiple of 3} B={x:x is a factor of 24} C={x:x is an odd number} (i) Find (a) n(B),
Answers
B={1,2,3,4,6,8,12,24}
n(B)=8
Answer:
[tex] \boxed{ \huge{ \bold{ \boxed{ \sf{3 \: , \: 6 \: , \: 12}}}}}[/tex]
Step-by-step explanation:
Given,
E = { 1 , 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 }
Here, E is the universal set.
A = { x : x is a multiple of 3 }
Here, we have to list the multiples of 3 less than 16
A = { 3 , 6 , 9 , 12 , 15 }
B = { x : x is a factor of 24 }
Here, we have to list the factors of 24 less than 16 }
Factor of 24 means the numbers that can divide 24 easily.
Factor of 24 includes :
B = { 1 , 2 , 3 , 4 , 6 , 8 , 12 }
C = { x : x is an odd number }
Here, we have to list the odd numbers which are less than 16
C = { 1 , 3 , 5 , 7 , 9 , 11 , 13 , 15 }
Finding A ∩ B
Here, We have to find the common elements that are present in both A and B
{ 3 , 6 , 9 , 12 , 15 } ∩ { 1 , 2 , 3 , 4 , 6 , 8 , 12 }
= { 3 , 6 , 12 }
Hope I helped!
Best regards!!
If one bus takes 15 minutes to refill diesel in the tank than 4 buses will take how many minutes to refill
Answers
Answer:
1-->15 min
4-->x min
Step-by-step explanation:
x=15×4=60
4 buses will take 60 min to refill
In hours, 60min÷60=1 hour
Answer:
Step-by-step explanation:
x=15×4=60
4 buses will take 60 min to refill
In hours, 60min÷60=1 hour
For all integer values of x and constant k, if (x+6)(x+k)=x^2+14x+48, what is the value of k?
Answers
Answer:
8
Step-by-step explanation:
The product of terms on the left of the equal sign is ...
(x+6)(x+k) = x^2 +(6+k)x +6k
So, you have two clues to the value of k. The coefficient of x must match, and the constant must match.
6+k = 14 ⇒ k = 8
6k = 48 ⇒ k = 8
The value of k is 8.
X² + 9x + 4 = FACTORISE
Answers
Answer:
[tex]$-\frac{1}{4} (-2x-9+\sqrt{65})(2x+9+\sqrt{65})$[/tex]
Step-by-step explanation:
We have a second-degree polynomial:
I will find the roots (y = 0) completing the square:
[tex]$x^2+9x+\frac{81}{4}-\frac{81}{4}+4=0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +4 =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{81}{4} +\frac{16}{4} =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 -\frac{65}{4} =0$[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 =\frac{65}{4} $[/tex]
[tex]$\left(x+\frac{9}{2} \right)^2 =\pm \sqrt{\frac{65}{4} } $[/tex]
[tex]$x =-\frac{9}{2} \pm \frac{\sqrt{65} }{2} $[/tex]
[tex]$x =\frac{-9 \pm \sqrt{65} }{2} $[/tex]
[tex]$\boxed{x_1 =\frac{-9 + \sqrt{65} }{2}} $[/tex]
[tex]$\boxed{x_2 =\frac{-9 - \sqrt{65} }{2}} $[/tex]
-9(2+3x) distributive property
Answers
Answer: -18 - 27x, or -27x - 18
1. Solution Steps
[tex]-9(2+3x)[/tex]
Use the distributive property to multiply −9 by 2+3x.
[tex]-18-27x[/tex]
Expand
[tex]-27x-18[/tex]
2. Solution Steps
[tex]-9(2+3x)[/tex]
Use the distributive property to multiply −9 by 2+3x.
[tex]-18-27x[/tex]
What is the value of the expression below when z = 2? 4z2 – 3z – 4
Answers
Answer:
6Step-by-step explanation:
[tex]4z^2 - 3z - 4\\z =2[/tex]
Substitute 2 for z in the given equation
[tex]4(2)^2 - 3(2) -4\\[/tex]
Follow the PEMDAS order of operations
[tex]\mathrm{Calculate\:exponents}\:\left(2\right)^2\::\quad 4\\=4\cdot \:4-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:4\times\:4\::\quad 16\\=16-3\left(2\right)-4\\\\\mathrm{Multiply\:and\:divide\:\left(left\:to\:right\right)}\:3\left(2\right)\::\quad 6\\=16-6-4\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:16-6-4\::\quad 6[/tex]
Answer:
Step-by-step explanation:
Plug in z = 2 in the expression
4z² - 3z - 4 = 4*2² - 3*2 -4
= 4*4 - 6 - 4
= 16 - 6 - 4
= 10 - 4
= 6
The sum of only negative numbers.
Is it positive or negative
Answers
Answer: negative
Step-by-step explanation: Whenever you are adding negative
numbers together, you will always get a negative number.
For example, (-1) + (-1) will give you -2.
In the same way, (-5) + (-4) gives you -9.
Answer: negaitive
When you add a negative plus a negative you always get another negative
A new car costs $8000 at full price. With a sales tax of 5.75%, how much will the car cost in total?
Answers
Answer:
$8460
Step-by-step explanation:
So for this problem we will use the base price of $8000 and add the additional cost of the 5.75% to find the total cost for the car.
So, to find the 5.75%, we simply multiply 8000 by .0575 to get 460.
So 8000 + 460 = 8460.
Thus, the total price of the car would be $8460.
Cheers.
Answer: $8,460
Step-by-step explanation: If you multiply the cost of the car by the sales tax you get your answer. Hope this helps!
Solve for x.
45+ Go +1) =
2x
Answers
Answer:
x= [tex]\frac{1}{2}[/tex]go+23
Step-by-step explanation: