Answer:
Try to understand by substitute a number in a and n.
Step-by-step explanation:
For example,
a=2, n=1
a^n= 2^1= 2
[tex]\frac{1}{2}[/tex] = 0.5
2^(-1)=0.5
Step-by-step explanation:
[tex] \frac{1}{ {a}^{n} } = {a}^{ - n} [/tex]
~Math Induction
[tex] \: [/tex]
—Prove that n = 1
[tex] \frac{1}{ {a}^{1} } = {a}^{ - 1} [/tex]
[tex] \frac{1}{a} = \frac{1}{a} \to \sf proved[/tex]
[tex] \: [/tex]
—Prove that n = k
[tex] \frac{1}{{a}^{n}} = {a}^{n} [/tex]
[tex] \frac{1}{{a}^{k}} = {a}^{-k} , k \in \mathbb{R}[/tex]
[tex] \: [/tex]
—Prove that n = k + 1
[tex] \frac{1}{ {a}^{k + 1} } = {a}^{ - (k + 1)} [/tex]
[tex] \frac{1}{ {a}^{k + 1} } = {a}^{ - k} \times {a}^{ - 1} [/tex]
[tex] \frac{1}{ {a}^{k + 1} } = \frac{1}{ {a}^{k} } \times \frac{1}{ {a}^{1} } [/tex]
[tex] \frac{1}{ {a}^{k + 1} } = \frac{1}{ {a}^{k + 1} } \: \: \rm proved[/tex]
[tex] \: [/tex]
Proved that 1/a^n = a^-n
Jenna gets an iTunes gift card for her birthday and decides to buy some games and some music the music she likes costs $1.99 per song and the games costs $0.99 each if she buys a total of 12 items and spends $18.88 how many of each item did she buy
Answer: 4 songs and 11 games
Step-by-step explanation:
Sorry if I’m wrong!
expanded form of (-p) ³
Answer:
(- p) × (- p) × (- p)
Step-by-step explanation:
(-p)³
(- p) × (- p) × (- p)
Can someone please help me?
Answer:
3.33×10^5 timesStep-by-step explanation:
Given
Mass of the Sun = 1.99×10^30Mass of the Earth = 5.97×10^24The mass of the Sun is greater than the mass of the Earth times:
1.99×10^30 / 5.97×10^24 =19.9×10^29 / 5.97×10^24 =19.9/5.97×10^(29 - 24) = 3.33×10^5How do you write an equation in standard form given the slope and one point in the graph? For example, slope = 9 and (-5, 2).
Answer:
Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
Step-by-step explanation:
hope this helps
Peter expected to earn $425 in a week. In fact, he earned $500. What was the percentage error? (Round to nearest percent)
Answer:
15%
Step-by-step explanation:
im almost certain its 15%
(©) For the members of the golf club the ratio men:children = 11:2.
The ratio women:children = 10:3.
(1) Find the ratio men: women.
Answer:
33:20
Step-by-step explanation:
Name the triangle congruent to ΔABC
ΔABC≅Δ
Answer:
QPR
Step-by-step explanation:
angle A=Q side AB=QP
B=P BC=PR
C=R CA=RQ
I needddd helppppp pleaseee
Answer:
51°
Step-by-step explanation:
Here is a circle, centre O, and the tangent to the circle at the point (8,15)
Answer:
y = -8/15x + 289/15
Explanation:
Given a circle with a radius of 17, and a centre at the origin (0,0), to find a line tangent to the point (8,15), there are a list of methods we could use to solve this problem. Instead of using derivatives (used to find the slope or gradient of a function at a given point), we can use the inverse tangent (goes from output to input, instead of input to output, but the inputs will still act as a function, which means you can only get one input for each output, this will get you from the side proportion to the angle, instead of angle to side proportion) as we know that a line connecting the origin to the point is always perpendicular to that line which is tangent to it. We can just take the opposite reciprocal (because when two lines are perpendicular, they always have opposite reciprocal slopes) of that, and then trace that slope back to the y-axis to find the it's y-intercept.
An opposite reciprocal just means to take that number, flip it's numerator, and denominator, and then make it negative.
So let's just use basic algebra to find the line going through points (0,0), and (8,15).
Because the line goes through the origin, we already know the y intercept is 0, so all we need to do is find the slope.
So slope [m] = (y2-y1)/(x2-x1).
Where (x1,y1) is the first point, and (x2, y2) is the second point. so m = 15-0/8-0 = 15/8.
Know that we have the slope of the first line, the perpendicular line will go through the same point, and have an opposite reciprocal -n^-1.
So 15/8 → 8/15 → -8/15 [this is the slope of the tangent].
Now since we know a point, and a slope, we can backtrack to find its y-intercept.
We can use point slope form:
y – y1 = m(x – x1)
(x1,y1) is the point we know [(8,15)], m is the slope we know [-8/15], and (x,y) is the point we are looking for. Also don't forget, since we are looking for a y-intercept, set x to zero because a y-intercept of anything is when x = 0.
Since we are only looking for y
y – y1 = m(x – x1) will become y = m(-x1) + y1.
This is because -y1 will cancel out when you add both sides by y1, and when x is 0, x1 will remain by itself in the form -x1.
So y = m(-x1) + y1 → y = (-8/15)(-8) + (15) →
64/15 + 15 = 64/15 + 15×15/15 = (64 + 225) / 15 = 289/15 [this is the y-intercept of the tangent line]
Now that we know the slope, and y- intercept of the tangent line, we can write the following equation in slope intercept:
m = -8/15, b = 289/15 → y = mx + b →
y = -8/15x + 289/15.
Answer:
y = -8/15x + 289/15
Need Help I'm A Good Person
Answer:
C
Step-by-step explanation:
I think thats what they are saying anyway
Oliver read for 450450450 minutes this month. His goal is to read for 10 percent more minutes next month.
If Oliver meets his goal, how many minutes will he read in all during the two months?
Answer:
94594945
Step-by-step explanation:
First we need 1105 of 450450450 we get this by multiply it by 1.10 we'll get 495495495 then we add that to his score of the first month to get 94594945
Answer: 945
Step-by-step explanation: since he is reading 10% MORE you would find the percentage of 450 PLUS 10%
110/100= 1.1
1.1 * 450= 495
495 + 450= 945
Hopefully this makes sense
Which of these expressions is equivalent to 0.03(x+80)?
A. 0.03x + 2.4
B. 0.03x + 80
C. 0.03x + 80.03
D. 0.03x + 24
43.9
44.3
45.7
46.2
Are possible answers.
Answer:
44.3 would be the correct answer if I looked at it correctly
Fill in the blank. If 9/24 =3/x , then x is .
Answer:
X=8
Hope I helped
Answer:
8
Step-by-step explanation:
Write it out: [tex]\frac{9}{24} = \frac{3}{x}[/tex] Cross multiply, then divide: 3 × 24 = 72, 72 ÷ 9 = 8So, the blank is 8I hope this helps!
distance between orlando and jacksonville
Answer:
Its about 140 miles
Step-by-step explanation:
it takes slight over 2 hours to get from point a to b
What is the interest on a loan of $2,500 that is borrowed at 9% for 7 months.
Answer:
$1575
Explanation:
Answer:
$131.25
Step-by-step explanation:
We'll need to review the simple interest formula for this:
I = P(1rt)
This is where P is the principal amount of money to be invested at an interest rate R% (put this in a decimal while calculating). The variable t is the amount of time in years.
Try to plug in these numbers and use my explanation as a checking tool. If you're having trouble, then no worries. Feel free to follow along :D
I = 2,500*(0.09)(7/12)
= 2,500 * 0.525
I = 131.25
So, the interest of a loan of $2,500 underneath those conditions is $131.25
Please let me know in the comments if anything is wrong. I'll be happy to update this answer!
Good luck and keep studying. I believe in you :D
Please help >.<
Which right prism would have the same volume as a square prism with a base area of 36 m2 and a height of 3 m?
A right triangular prism is shown. The triangle has side lengths of 6 meters and 3 meters. The height of the prism is 2 meters.
A rectangular prism is shown. The rectangle has side lengths of 18 meters and 2 meters. The height of the prism is 3 meters.
A triangular prism is shown. The triangle has a base length of meters and a height of 3 meters. The height of the prism is 4 meters.
B. 2 18 3
Step-by-step explanation:
on edg
In triangle ABC, ∠A = 55°, ∠B = 75°. Which statements are correct? You must select all correct answers.
Side BC is the longest side
Side AB is the shortest side
Side AC is the longest side
Side BC is the shortest side
Answer:
AC is the longest side
AB is the shortest
Step-by-step explanation:
Generally, the side that faces the smallest angle has the smallest side while the side that faces the largest angle has the largest side
The measure of the third angle C is 180 - 55 -75 = 50
Kindly note that A faces BC
B faces AC
C faces AB
So while AC is the longest side, AB is the shortest
So the correct answers are;
AC is the longest side
AB is the shortest side
guys i said it once but imma say it again i love lanie
also A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus?
4
Step-by-step explanation:
There are 400 students, and 100 buses, so number of student in each bus= 400/100
= 4
Someone plzz help it’s urgent!!
Answer:
hope it helps..
Step-by-step explanation:
If this helped please comment..
help meeeeeeeeeeeeeeeeeeee
Answer:
hm
Step-by-step explanation:
Given f(x) = x2 + 5x + k, and the remainder when f () is divided by x – 8 is
93, then what is the value of k?
By the remainder theorem, the remainder upon dividing a polynomial p(x) by x - c is equal to p(c).
Here, p(x) = x² + 5x + k and c = 8, which gives
p (8) = 8² + 5•8 + k
93 = 64 + 40 + k
k = -11
Rate this app 1/10 and explain why
plz help ASAP
solve for x in
1. sin x = cos 2x
2. cos 2x = sin 3x
3. sin x = cos x
thx
1. x = π/6 + 2πn/3, for any integer n
2. Is not possible to solve (I think)
3. x = π/4 + πn, for any integer n
How are 0.02 and 20 related
Answer:
No (unless you count them both being numbers then no!)
Step-by-step explanation:
Hope this helps! :)
i need some help.. fraction: {5⁷}{5²}
Step-by-step explanation:
[tex]\dfrac{5^7}{5^2}\qquad|\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\=5^{7-2}=5^5[/tex]
Describe the process for
graphing the equation
y – 4 = 2(x + 1)
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope: 2
y-intercept: (0,6)
Step-by-step explanation:
X y
−3 0
0 6
PLEASEEE HELPPPPP!!!! у
Test Scores in Relation to Homework
2.
100
How would you characterize the relationship
between the hours spent on homework and
the test scores? Explain.
90
80
70
60
Test Scores
50
3. Draw a line of best fit on the graph.
40
4.
30
Based on your line, what is the likely test
score of a student who does not study for
the test?
20
10
0
1
2
3
8
9
4 5 6 7
Hours of Homework
Answer:
2. The more hours spent doing homework the better the test scores.
3. Just draw a line that runs through (1,50) (2,55) (3,60) (4,65)
4. Dunno
Step-by-step explanation:
Answer:
Number 4 would be 45%
Step-by-step explanation:
Customers at an ice-cream shop took a survey. The results showed that 279 customers rates the shop as being "very satisfactory." This number represented 45% of the total number of customers who took the survey. What was the total number of customers who took the survey ? Explanation plz
Answer:
620 customers
Step-by-step explanation:
Customers at an ice-cream shop took a survey.
Let the total number of customers who took the survey be represented by x
We are told in the question that:
The results showed that 279 customers rates the shop as being "very satisfactory." This number represented 45% of the total number of customers who took the survey.
Hence:
45% of x = 279 customers
= 45/100 × x = 279 customers
45x /100 = 279
Cross Multiply
45x = 100 × 279
x = 27900/45
x = 620 customers
The total number of customers who took the survey is 620 customers
A wire is in the shape of square of side 12cm. if the wire is rebent into a
rectangle of length 14cm, find its breadth. Which figure encloses more area
and by how much?
Answer:
Breadth = 10 cm.
Difference in area = 4 cm^2 ( the square encloses more area).
Step-by-step explanation:
The perimeter of the square = 4*12 = 48 cm.
If the length of the rectangle is 14 then
2*14 + 2b = 48 where b is the breadth.
28 + 2b = 48
2b = 20
b = 10 cm.
A square encloses more area than a rectangle for a given length of wire.
Area of the square = 12^2 = 144cm^2 and
area of the rectangle = 14*10 = 140 cm^2.