Explanation: Zero Exponent
So far we have looked at powers of 10 with exponents greater than 0.
What would happen to our patterns if we included 0 as a possible exponent?
1. Write 10^12 × 10^0 with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning.
A. What number could you multiply 10^12 by to get this same answer?
Answers
Answer:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
Step-by-step explanation:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) In addition, we can use this property:
[tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex]
We can apply the property mentioned above:
[tex]10^{12}\cdot 10^{0} = 10^{12}\cdot (10^{n-n}) = 10^{12}\cdot \left(\frac{10^{n}}{10^{n}} \right) = 10^{12} \cdot 1 = 10^{12}[/tex]
In consequence, we conclude that [tex]10^{0} = 1[/tex]. [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
Related Questions
plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help
Answers
Answer:
p=18
Step-by-step explanation:
It is 18 because 5 times 18 will equal 90 and 90 +54 is 144
Answer:
it is b
Step-by-step explanation:
Which angles are alternate interior angles?
Answers
Answer:
∠JKH and ∠IHK
Step-by-step explanation:
∠JKH and ∠LHK are a linear pair
∠JKH and ∠IHK are supplementary
∠JKH and ∠IHK are same-side interior angles
The Snake river runs through the state of Idaho. It also runs through the city of
Idaho Falls, Idaho. I saw another river once. Many people enjoy the river for its beauty and recreation.
Which sentence doesn’t belong to the main idea?
1. The Snake river runs through the State of Idaho.
2. It also runs through the city of Idaho Falls, Idaho.
3. I saw another river once.
4. Many people enjoy the river for its beauty and recreation.
More help pls
Answers
Answer:
4. Many people enjoy the river for it's beauty and recreation.
Step-by-step explanation:
this sentence doesn't specify the river if it's snake or the other one
PLEASE HELP!!! I’ll give brainlest
Answers
Why are these two figures simaliar
Answers
Answer:
Se parecen porque son proporcionales.
Step-by-step explanation:
Si le das vuelta a la figura pequeña de manera que quede en forma horizontal, la figura es la misma, solo cambia el tamaño.
PLS IS NEEDED PLS HELP!!
Answers
Answer: 19°
Step-by-step explanation: 90+71= 161
180-161= 19
(correct me if i’m wrong):)
what is the x for this problem??
Answers
Answer:
Let's just find the value of the unknown degree next to 35 degrees.
180 - 35 = 145 degrees
Since 145 degrees is the unknown degree next to 35 degrees, it is vertical to the x it will be the same therefore your answer is 145 degrees.
Rectangle ABCD is reflected over the x axis to form rectangle A^ prime B^ prime C^ prime I)^ prime ' What is the length of side
Answers
Answer:if it’s a and d then 2 units other side too is 2 units
Step-by-step explanation: commen sense
NO LINKS !!! What are the measures of 21, 22, and 23? Enter your answers in the boxes.
р
23
60%
4 61°
9
m1 =
9. m 22 =
im_3 =
Answers
Answer:
4= 61+60=121
180-121=59
m<4= 59°
3=180-61= 119
m<3= 119°
2=180-119=61
m<2= 61°
1=61+60=121
180-121= 59
m<1= 59°
hey, I hope this was helpful:)
Danielle paid $5.57 for a fruit drink. She now has $27.53. How much money did she have before buying the fruit drink?
Answers
Answer:
$33.10
Step-by-step explanation:
BC is a diameter, m (HELP NEED TO TURN THIS IN 10 MINUTES)
Answers
Answer:
I would help, but there is no question.
Step-by-step explanation: Please give us the question and it might help us actually solve it for you.
Given the geometric sequence 42,16.8,6.72 find the next term
Answers
Answer:
I don't know
Step-by-step explanation:
because I don't understand which value it T1, T2, T4 etc
Five students are competing in a spelling bee for first second, and third places. How many different outcomes are possible?
Answers
Answer:
625
Step-by-step explanation:
This is a reoccurring permutation
so it is 5^3
Consider a circle centered at C(0,0). If the point P(3,5) lies on the circle, then which of the following points also lies on the circle?
A. (-2,6)
B. (6,-[tex]\sqrt{5}[/tex])
C. (1,[tex]\sqrt{33}[/tex])
D. (-2[tex]\sqrt{2}[/tex],4)
Answers
Answer:
C
Step-by-step explanation:
First find the equation of the circle
the general formula for a circle (x-h)² + (y-k)² = r² where (h=0, k=0) are the coordinates of the center and r is the radius that we do not know
the distance between the center (0, 0) and the point (3,5) is the radius
distance formula d² = (x2-x1)² +(y2-y1)² where (x1=0,y1=0) and (x2=3, y2=5)
d² = (3-0)² + (5-0)² = 3² +5² = 9+ 25 = 34 =r²
(x-0)² + (y-0)² = 34 ; x²+y² =34 is the equation of the circle
Second check if any of the points are on the circle by substituting x and y with de given coordinates.
A. for (-2, 6) we have (-2)²+6² =34 so 4+36 =34 false
B. for (6, -√5) we have 6²+(-√5)² =34 so 36+5=34 false
C. for (1, √33) we have 1²+(√33)² =34 so 1+33 =34 true
D. for (-2√2, 4) we have (-2√2)²+4² =34 so 8+16=34 false
ABCD is a parallelogram. Which statements are true?
Answers
Answer:
Final Answer: Statements 1, 2 and 4 are correct.
Step-by-step explanation:
Finding value of y:
2y + 3 = 15 => 2y = 12 => y = 6;
Finding value of x:
6x + 5 = 77 => 6x = 72 => x = 12;
Statement Number 1:
y² > 2x ? => 6² > 2 * 12 ? => 36 > 24 ?
Yes, 36 is bigger than 24, therefore statement one is correct.
Statement 2:
x = 2y ? => 12 = 2 * 6? => 12 = 12?
Yes, 12 is equal to 12. Statement 2 is correct.
Statement 3:
x + 2 = y + 10 ? => 12 + 2 = 6 + 10? => 14 = 16?
No, 14 is not equal to 16. Statement 3 is incorrect.
Statement 4:
y + 4 > x - 4 ? => 6 + 4 > 12 - 4 ? => 10 > 8 ?
Yes, 10 is bigger than 8. Statement 4 is correct.
If this helped you please rate
Final Answer: Statements 1, 2 and 4 are correct.
HELP ME HELP ME HELP ME PLEASE
Answers
Atriangle and square i think
Step-by-step explanation:
2.4x-9.1x+12.5x=39.44
x=
Answers
Answer:
x = 6.8
Step-by-step explanation:
2.4x - 9.1x + 12.5x = 39.44
5.8x = 39.44
x = 6.8
3 lan is buying a watch thal regularly
costs $75. It he plans to use a $15 gift
cord and sales tax is 6.4%, what will he
pay in total ?
Answers
Answer:
$63.84
Step-by-step explanation:
First, you subtract the gift card amount before taxing the new price.
75-15=60
then to calculate tax, use this equation:
.064×60=3.84
Add the tax to the price.
60+3.84=$63.84
Select the correct answer.
Which statement is true about this equation?
-9(x+ 3) + 12 = -3(2x + 5) - 3x
OA
The equation has one solution, x= 1.
OB.
The equation has one solution, x= 0.
O C.
The equation has no solution.
OD. The equation has infinitely many solutions.
Answers
D. the equation has infinitely many solutions
step-by-step explanation:
-9(x + 3) + 12 = -3(2x + 5) - 3x
-9x - 27 + 12 = -6x - 15 - 3x
-9x - 15 = -15 - 9x
+15 +15
-9x = -9x
the equation has infinitely many solutions
The measure of arc CD is 175°. Determine the measure of DBC.
1) 350 2) 87.5 3) 5 4) 175
Answers
Answer:
∠ DBC = 87.5°
Step-by-step explanation:
The inscribed angle DBC is half the measure of its intercepted arc, then
∠ DBC = [tex]\frac{1}{2}[/tex] CD = 0.5 × 175° = 87.5°
If someone can do this whole thing for me I will give brainiest.
Answers
Answer:
A= x r^2
A= x r x r
r means radius
The value of pi() is 3.14
r^2 means radius x radius
Substitute the radius for r: A= x 7^2
Square the radius: 7 x 7= 49
Area in terms of pi(): 49
Area in terms of square inches: 153.86 in^2
Divide the diameter by 2: 12 ÷ 2= 6
Substitute the radius for r: A= x 6^2
Square the radius: 6 x 6= 36
Area in terms of pi(): 36
Area in terms of square inches: 113.04 in^2
Step-by-step explanation:
What is the equation of the line?
Answers
Answer:
y = 3
Step-by-step explanation:
ILL GIVE BRAINLIEST ASAP AND PLEASE DONT PUT A LINK!!!
Answers
Answer:
A
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
the graph shows that it's greater than or equal to and the arrow going up represents at least 50
What is the value of x?
O 14
15
ООО
16
110
110
17
700
Answers
Answer:
⏩14°
Step-by-step explanation:
As we can see the opposite sides are equal and the opposite angles are equal so it is a parallelogram. Hence
5x = 70° { opposite angles of a parallelogram are equal }
x = 14°
Hope it will help :)⏩❤
The value of x in the given figure is 14, Option A is correct.
We need to find the value of x in the given figure.
The opposite angles in the given figure are equal.
So when we equate both the angles we get an equation
5x=70
Divide both sides by 5
x=70/5
x=14
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ7
Find the measures of the numbered angles in each rhombus
Answers
Answer:
angle 1 is 120
and I think angle 2 and 3 are 60
You have 143 toy farm animals.
Round that number to the nearest ten.
Answers
help please, what is the answer?
Answers
Answer:
sum of all angles in a triangle = 180
111 + 42 + x = 180
153 + x = 180
x= 180-153
x=27
Step-by-step explanation:
Answer:
27°
Step-by-step explanation:
All triangles are 180° therefore, you can add 111° and 42° then subtract that from 180°
13.El alquiler de un coche cuesta 20 € al día, más 0'50 € por kilómetro recorrido. Halla la ecuación que calcula lo que se cobra diariamente por el alquiler del coche en función de los kilómetros recorridos. Representa la función obtenida.
Answers
Answer:
La función es: f(x) = 20+0.5x
Step-by-step explanation:
La función que representa la condición sería:
f(x) = 20+0.5x
Donde:
20 € es el costo por díax es la cantidad de kilómetrosf(x) cobro por dia en función de los kilómetrosEspero te haya servido!
I dont think is that hard haha please help lol
Deandre deposits $400 into an account that pays simple interest at a rate of 6% per year. How much interest will he be paid in the first 4 years?
Answers
Answer:
$96 in interest
Step-by-step explanation:
400(0.06)(4) = 96
The length of one side of a square is 15 inches.
What is the area of the square?
OA. V60 in.2
B. 4V15 in.2
O C. 15 in?
D. 60 in.2
O E. 225 in.2
Answers
Answer:
O E. 225 in²
Step-by-step explanation: