A little confused here!
Hey guys. I just need someone's help to clarify things with me.
As I was doing the equations, I got to:
x^-1
-----
x^13
I moved the x^-1 down to x^13 so they'd subtract. But when I did, x^-1 became positive.
So it became x^13 times x^1
Radical Rule: a^n x a^m is pretty much a^n+m
So my answer was 14.
How did x^-1 become positive in this case?
Step-by-step explanation:
Given [tex]\frac{x*x^{-2} }{x^{13}}[/tex]
= [tex]\frac{x*x^{-2} }{x^{13}} = \frac{x^{-1} }{x^{13}}[/tex]
According to the Negative Exponent Rule, [tex]a^{-n} = \frac{1}{a^{n}}[/tex]
Therefore, [tex]\frac{x^{-1} }{x^{13}} = \frac{1}{x^{1}*x^{13}} = \frac{1}{x^{13+1}}= \frac{1}{x^{14}}[/tex]
In other words, [tex]x^{-1}[/tex] became positive because of the Negative Exponent Rule. Once you bring [tex]x^{-1}[/tex] down towards the denominator, you're essentially removing its negativity and turning its exponent into a positive value. Once that takes place, then you could apply the Product Rule of Exponents onto the exponents in the denominator, where it states, [tex]a^{m}a^{n} = a^{m+n}[/tex].
Please mark my answers as the Brainliest if you find my explanations helpful :)
a line parallel to the graph of 3x+2y=6 and contains the point (6,-3)
Find the intercepts of the following equation
7x^2+y=7
Lashonda exercises at least 50 minutes per day. Use t to represent Lashonda's amount of exercise (in minutes per day).
The question is an illustration of inequalities.
The inequality that represents Lashonda's amount of exercise is: [tex]\mathbf{t \ge 50}[/tex]
The given parameter is:
[tex]\mathbf{Minutes = At\ least\ 50}[/tex]
In inequality, at least means greater than or equal to.
So, the above equation becomes:
[tex]\mathbf{Minutes \ge 50}[/tex]
From the question, we understand that the number of minutes should be represented with t.
So, we have:
[tex]\mathbf{t \ge 50}[/tex]
Hence, the inequality is: [tex]\mathbf{t \ge 50}[/tex]
Read more about inequalities at:
https://brainly.com/question/15137133
5) Find the numbers:
a. 0.75 of what number is 9?
b. 0.8 of what number is 8?
Answer:
12
10
Step-by-step explanation:
A bottle of milk is 63% full and contains 1260ml of milk.
How much milk did the carton contain when it was full?
9514 1404 393
Answer:
2 liters
Step-by-step explanation:
The applicable proportion can be written ...
amount/percentage = 1260 mL/63% = x/100%
2000 mL = x = 2 liters
The full carton held 2 liters of milk.
Find the derivatives.
f ' (0) exists if the limit,
[tex]\displaystyle \lim_{h\to0}\frac{f(0+h)-f(0)}h[/tex]
exists, and f ' (0) has the value of this limit.
In order for this limit to exist, both limits from either side of h = 0 must exist.
Suppose h < 0. Then 0 + h is also negative, so by definition of f(x) we have
f (0 + h) = ((0 + h) + 1)² = h ² + 2h + 1
Then in the limit, if h is approaching 0, it must be from below or from the left:
[tex]\displaystyle \lim_{h\to0^-}\frac{f(0+h)-f(0)}{h} = \lim_{h\to0^-}\frac{(h^2+2h+1)-1}{h} = \lim_{h\to0^-}(h+2) = 2[/tex]
Now suppose h > 0, so that 0 + h is positive and h approaches 0 from above or from the right. Then
f (0 + h) = 2 (0 + h) + 1 = 2h + 1
and
[tex]\displaystyle \lim_{h\to0^+}\frac{f(0+h)-f(0)}h = \lim_{h\to0^+}\frac{(2h+1)-1}{h} = \lim_{h\to0^+}2 = 2[/tex]
Both one-sided limits match, so f ' (0) = 2.
Please help me with this math
If 1/4 of a gallon is enough for 1/3 of a room, how much paint would you need to paint four rooms?
Answer:
you would use 3/4 of a gallon per room, so you would multiply 3/4 x 4., which equals 3 gallons
A polynomial of degree at least 3 where one or more of the roots are fractions
#1 p(x)=(x-3)*(x-5)*(x-1)=x3-9x2+23x-15
You try the next one...a fractional root would look like (x-3/2)
Using the Factor Theorem, it is found that an example of a polynomial of degree at least 3 where one or more of the roots are fractions is given by:
[tex]f(x) = x^3 - \frac{7}{2}x^2 + \frac{1}{2}x - 1[/tex]Factor Theorem: The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.In this problem:
A polynomial of degree 3 will be built, hence it will have 3 roots.A leading coefficient of a = 1 is supposed.Two non-fractional roots, which are x = 1 and x = 2, hence [tex]x_1 = 1, x_2 = 2[/tex].The fractional root is [tex]x_3 = \frac{1}{2}[/tex].Hence:
[tex]f(x) = (x - x_1)(x - x_2)(x - x_3)[/tex]
[tex]f(x) = (x - 1)(x - 2)\left(x - \frac{1}{2}\right)[/tex]
[tex]f(x) = (x^2 - 3x + 2)\left(x - \frac{1}{2}\right)[/tex]
[tex]f(x) = x^3 - \frac{7}{2}x^2 + \frac{1}{2}x - 1[/tex]
To learn more about the Factor Theorem, you can take a look at https://brainly.com/question/24380382
What is the equation of a line that passes trough (6,-1) and is parallel to the line that has a slope of -2/3?
Answer:
y=-2/3x+3
Step-by-step explanation:
First, identify the slope you need for your equation. The keyword here is "parallel" so the slope you need is the same as the given slope (-2/3).
Next, use the ordered pair (6,-1); it's on the line that you need to find the equation for. Using slope-intercept form (y=mx+b), plug the -1 in for y, plug the 6 in for x, and plug in your slope of -2/3 for m. Solve for b, your y-intercept. You should get 3.
You have your slope and y-intercept now. Create your equation:
y=-2/3x+3.
Mandy is making a bouqet of flowers. She goes to a flower shop and finds 3 types of rose, 2 types of peony, 3 types of lily and 5 types of carnation. She only wants to buy 2 flowers. How many possible flower combinations can she choose from?
Answer:
Mandy is making a bouqet of flowers. She goes to
Answer:
possible flower combinations can she choose from?
Step-by-step explanation:
possible flower combinations can she choose from?
Write each decimal as a fraction or mixed number.
1. 0.61
2. 3.43
3. 0.009
4. 4.7
5. 1.5
6. 0.13
7. 5.002
8. 0.021
Plz help
Answer:
1. 61/100
2. 3 43/100
3. 9/1000
4. 4 7/10
5. 1 1/2
6. 13/100
7. 5 1/500
8. 21/1000
Simplify: qp - 8m - m + 1 - m; use m = -3, p = 9, and q = 5
Answer:
The answer is 76
Step-by-step explanation:
qp - 8m - m + 1 - m; m = -3, p = 9, and q = 5
(5)(9) - 8(-3) - (-3) + 1 - (-3)
45 + 24 + 3 + 1 + 3 = 76
Thus, The answer is 76
-TheUnknownScientist 72
look at the photo.
Which expression is equivalent to the given expression? 10q +5
due at 5:30 pls help asap
A side of a square is 10 cm longer than the side of an equilateral triangle. The perimeter of the square is 3 times the perimeter of the triangle. Select the equation that represents the scenario when x represents the side of the triangle.
Here's the solution :
Side of the equilateral triangle = x Side of square = x + 10perimeter of equilateral triangle = 3 × x = 3x
perimeter of square = 4 × (x + 10)
now, according to above statement :
permission (square) = 3 × perimeter (triangle)
that is :
[tex]4(x + 10) = 3 \times 3x[/tex][tex]4x + 40 = 9x[/tex][tex]9x - 4x = 40[/tex][tex]5x = 40[/tex][tex]x = 8[/tex]therefore, side of triangle = 8 cm
perimeter (triangle) = 8 × 3 = 24 cmside of square = 8 + 10 = 18 cmperimeter of square= 18 × 4 = 72 xmAnswer:
Let the side of the equilateral triangle = x
so the side of the square = x+10
The perimeter of the triangle = 3x
and the perimeter of the square = 4(x+10)
condition : the perimeter of the square is 3 times the perimeter of the triangle.
so, 4(x+10) = 3*(3x)
Step-by-step explanation:
Which of the following is the area of a rectangle with a length of 7 feet and a width of 5 feet?
Answer:
D) 35 sq ft
Step-by-step explanation:
The options are:
A) 24 sq ft B) 70 sq ft C) 12 sq ft D) 35 sq ft
So, when calculating the area of a regular rectangle or square, you need to multiply the base by the height (area=base*height)
So it is as simple as 7 multiplied by 5 which is 35 (7*5=35), so the answer is D) 35 square feet.
Help plssssssssssssssss
Answer:
both
Step-by-step explanation:
The mean and the median give the same information, so it doesn't matter which one she chooses.
1. Which of the following should you do first when solving the equation 3x + 2 = 4x – 5(x + 6)?
A. divide both sides by 3
B. subtract 2 from both sides
C. distribute the - 5 through the parenthesis (x+6)
D. subtract 4x from both sides
Answer:
(x+6)
Step-by-step explanation: remember gemdas
Groups
Exponents
Multipy
Divide
Add
Ssubtract
NO LINKS PLEASE HURRY I REALLY NED HELP!!!
Answer:
The answer is D
Step-by-step explanation:
-7.6+4.17= -3.43x
3.54-1.32= 2.22
Neeeed asapppp!!!!!!!!!
Answer:
NM
Step-by-step explanation:
The hypotenuse is always the longest side.
Explanation:
For any triangle, the longest side is always opposite the largest angle.
Twix bars cost $1.29.each. If you buy 10 bars, how much
change will you receive from $20?
Answer:
$7.10
Step-by-step explanation:
1 bar = $1.29
10 bars = 10 x $1.29 = $12.90
Change received = $20 - $12.90 = $7.10
Answer:
7.1
Step-by-step explanation:
1 twix bar = $1.29
10 twix bar = $12.9
change = 20 - 12.9
= $7.1
hyun is on a game show. points are added for the correct answer and subtracted for incorrect answers. at the end of the second round he has five points and the third round he loses 5 points how many points does hyun have after the third round ?show your work
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The number of points at the end of second round is :
5 pointsand if he loses all the 5 five points in the third round then the number of point he is left with is :
5 - 5 0 pointsA cereal box manufacturer changes the size of the box to increase the amount of cereal it contains. The expressions 13+7.9n and 10+8.2n, where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains. How many smaller boxes equal the same amount of cereal in the larger box? The larger box of cereal has as much cereal as nothing smaller boxes.
Answer: 10.5 small boxes
Step-by-step explanation:
Evaluate. 4^3⋅(100÷25)−5^0
[tex]4 {}^{3} .(100 \div 25) - 5 {}^{0} [/tex]
Solution[tex] {4}^{3} \times (100 \div 25) - {5}^{0} \\ \\ = 64 \times 4 - 1 \\ \\ = 256 - 1 \\ \\ = 255[/tex]
[tex] \fbox \red{Hope This Helps }[/tex]
Answer:
255
Step-by-step explanation:
1) Simplify 100 ÷ 25 to 4.
4³ × 4 - 5⁰
2) Use Rule of Zero: x⁰=1
4³ × 4 - 1
3) Use Product Rule
4⁴ - 1
4) Simplify 4⁴ to 256
256 - 1
5) Simplify
255
help plz help
send photo
plz
Answer:
See belowStep-by-step explanation:
9 a)
8 + 3/4 = 8.75 cmb)
10 + 5 + 3 = 18 kgc)
1 + 1/5 = 1.2 l10 a)
65 - 1 = 64 cmb)
100 + 100 * 2.5/4 = 162.5 mlc)
20 + 4.2 = 24.2° CEach unit in the graph above is one block. How far would you have to walk from the harbor to the magic shop and then return to the harbor?
Question 3 options:
A)
5 blocks
B)
9 blocks
C)
3 blocks
D)
6 blocks
John's phone bills for the last five months are $24.71, $22.13, $19.87, $27.33, and $26.76.
Find John's mean phone bill over this period.
Answer:
$24.16
Step-by-step explanation:
What is the distance between the points (1,-6) and (5,-3)?
Answer: 5 is the answer
Use the distance formula to determine the distance between two points.
Answer:
[tex]\displaystyle d = 5[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinate Planes
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
Point (1, -6)
Point (5, -3)
Step 2: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(5 - 1)^2 + (-3 + 6)^2}[/tex][Order of Operations] Evaluate: [tex]\displaystyle d = \sqrt{25}[/tex]Simplify: [tex]\displaystyle d = 5[/tex]Simplify (23)-2
- -13
2
ОО
O 64
DONE
9514 1404 393
Answer:
(b) (correct choice is marked)
Step-by-step explanation:
The expression can be evaluated according to the Order of Operations and the rules of exponents.
(2^3)^-2 = 8^-2 = 1/8^2 = 1/64
__
The applicable rule of exponents is ...
a^-b = 1/a^b
Answer:
The correct answer choice is option b. 1/64
Step-by-step explanation:
(2^3)^-2
= 2^3(^-2)
= 2^-6
= 1/2^6
= 1/64