Answer:
Step-by-step explanation:
I'm assuming that you meant: x^(-11)*x^2. Here there's a common base: x.
Then this expression becomes x^(-11*2)*x^2. We need only combine (add up) the exponents of x: x^(-11*2)*x^2 = x^(-11 + 2) = x^(-9). Use of parentheses as shown is important here.
Note that x^(-9) is the same as
1
------------
x^9
Which equation has no real solutions?
Answer:
C is the answer
Step-by-step explanation:
What is the answer to 10 to the power of 8
Answer:
Step-by-step explanation:
10^8
it means multiply 10 8 times so
10*10*10*10*10*10*10*10
=100000000
Verify that:
1. (CosX)(CotX) = CscX - SinX
2. (Csc X - CotX)^2 = 1-CosX/1+CosX
These were the last two questions on my Homework that I couldn’t figure out after many tries! Thank you to anyone who helps!
Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to verify that:
[tex]\displaystyle \left(\cos(x)\right)\left(\cot(x)\right)=\csc(x)-\sin(x)[/tex]
Note that cot(x) = cos(x) / sin(x). Hence:
[tex]\displaystyle \left(\cos(x)\right)\left(\frac{\cos(x)}{\sin(x)}\right)=\csc(x)-\sin(x)[/tex]
Multiply:
[tex]\displaystyle \frac{\cos^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Recall that Pythagorean Identity: sin²(x) + cos²(x) = 1 or cos²(x) = 1 - sin²(x). Substitute:
[tex]\displaystyle \frac{1-\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Split:
[tex]\displaystyle \frac{1}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}=\csc(x)-\sin(x)[/tex]
Simplify:
[tex]\csc(x)-\sin(x)=\csc(x)-\sin(x)[/tex]
Problem 2)
We want to verify that:
[tex]\displaystyle (\csc(x)-\cot(x))^2=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Square:
[tex]\displaystyle \csc^2(x)-2\csc(x)\cot(x)+\cot^2(x)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Convert csc(x) to 1 / sin(x) and cot(x) to cos(x) / sin(x). Thus:
[tex]\displaystyle \frac{1}{\sin^2(x)}-\frac{2\cos(x)}{\sin^2(x)}+\frac{\cos^2(x)}{\sin^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out the sin²(x) from the denominator:
[tex]\displaystyle \frac{1}{\sin^2(x)}\left(1-2\cos(x)+\cos^2(x)\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (perfect square trinomial):
[tex]\displaystyle \frac{1}{\sin^2(x)}\left((\cos(x)-1)^2\right)=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Using the Pythagorean Identity, we know that sin²(x) = 1 - cos²(x). Hence:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{1-\cos^2(x)}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor (difference of two squares):
[tex]\displaystyle \frac{(\cos(x)-1)^2}{(1-\cos(x))(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Factor out a negative from the first factor in the denominator:
[tex]\displaystyle \frac{(\cos(x)-1)^2}{-(\cos(x)-1)(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Cancel:
[tex]\displaystyle \frac{\cos(x)-1}{-(1+\cos(x))}=\frac{1-\cos(x)}{1+\cos(x)}[/tex]
Distribute the negative into the numerator. Therefore:
[tex]\displaystyle \frac{1-\cos(x)}{1+\cos(x)}=\displaystyle \frac{1-\cos(x)}{1+\cos(x)}[/tex]
Consider the series One-fourth, StartFraction 1 Over 16 EndFraction + StartFraction 1 Over 64 EndFraction + StartFraction 1 Over 256 EndFraction + ellipsis
Which expression defines Sn?
Answer:
C, I got it right
Step-by-step explanation:
The two major types of series are the arithmetic series and the geometric series. The arithmetic series is characterized by common difference, while the geometric series has common ratio between two successive terms.
The sum of the given series is:
[tex]\lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
The given series is a geometric series. So, we first calculate the common ratio (r) using:
[tex]r = T_2 \div T_1[/tex]
From the series, we have:
[tex]T_1 = \frac{1}{4}[/tex]
[tex]T_2 = \frac{1}{16}[/tex]
So, the equation becomes
[tex]r = \frac{1}{16} \div \frac{1}{4}[/tex]
Rewrite as product
[tex]r = \frac{1}{16} * \frac{4}{1}[/tex]
[tex]r = \frac{1}{4}[/tex]
The formula to calculate the sum of a geometric series of is:
[tex]S_n = \frac{a(1 - r^n )}{1-r}[/tex]
Where
[tex]a = T_1 =\frac{1}{4}[/tex] -- the first term
[tex]S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{1-\frac{1}{4}}[/tex]
Simplify the denominator
[tex]S_n = \frac{\frac{1}{4}(1 - \frac{1}{4}^n )}{\frac{3}{4}}[/tex]
Divide 1/4 by 3/4
[tex]S_n = \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
We can conclude that, the sum of the series is:
[tex]S_n = \lim_{n \to \infty} \frac{1}{3}(1 - \frac{1}{4}^n )[/tex]
Read more at:
https://brainly.com/question/21087466
Tres amigos han corrido una carrera de 20 corredores, sus 3 dorsales eran números de 2 cifras consecutivos y su producto era 2.730 ¿que número llevavan los tres amigos ne sus dorsales?
Answer:
Los números son: 13, 14, y 15.
Step-by-step explanation:
Un número de dos cifras puede escribirse como:
a*10 + b
Donde a y b son números entre 0 y 9.
3 números consecutivos entonces se escribe como:
a*10 + b
a*10 + b + 1
a*10 + b + 2
El producto de esos 3 números será:
(a*10 + b)*(a*10 + b + 1)*(a*10 + b + 2) = 2,730, pero sabemos que hay 20 corredores, entonces el máximo número de dos cifras posibles es 20.
Esto nos obliga a tomar a = 1 (porque si a fuera igual a dos, tendríamos números mayores a 20)
Entonces la ecuación es:
(1*10 + b)*(1*10 + b + 1)*(1*10 + b + 2) = 2,730
(10 + b)*(11 + b)*(12 + b) = 2,730
(110 + 21b + b^2)*(12 +b) = 2,730
1,320 + 110*b + 252*b + 21*b^2 + 12*b^2 + b^3 = 2,730
b^3 + 33*b^2 + 362*b + 1,320 - 2,730 = 0
b^3 + 33*b^2 + 362*b - 1,410 = 0
Ahora, sabemos que b tiene que ser un número entero entre 0 y 9, entonces simplemente podemos ir probando con distintos valores de b y ver cuál es solución de esa ecuación.
b = 0
0^3 + 33*0^2 + 362*0 - 1,410 = 0
-1,410 = 0
b = 0 no es una solución.
b = 1
1^3 + 33*1^2 + 362*1 - 1,410 = 0
-1,014 = 0
b = 1 no es una solución.
b = 2
2^3 + 33*2^2 + 362*2 - 1,410 = 0
-546 = 0
b = 2 no es una solución
b = 3
3^3 + 33*3^2 + 362*3 - 1,410 = 0
27 + 297 + 1,086 - 1,410 = 0
0 = 0
b = 3 es una solución.
Entonces los 3 números consecutivos son:
10 + 3 = 13
10 + 3 + 1 = 14
10 + 3 + 2 = 15
What is the 9th row of Pascal's Triangle?
Group of anwers
1,10,45,120,200,252,200,120,45,10,1
1,8,28,56,70,56,28,8,1
1,9,36,84,126,126,84,36,9,1
Pascal's Triangle does not have 9 rows.
Answer:
Pascal triangle is infinite, and the answer to this question is the 1,9,6,84,126,126,84,36,9,1
Step-by-step explanation:
in the pascal triangle the first row start with 0.
4.
Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3
A. Graph c
B. Graph b
C. Graph d
D. Graph a
Answer: Graph D (bottom right corner)
======================================================
Explanation:
The equation y = 3x+3 is in slope intercept form y = mx+b
m = 3 = slope
b = 3 = y intercept
In this case, both the slope and y intercept are the same (though in general they tend not to be).
The positive slope value means the line goes uphill as you move from left to right. The positive y intercept means the diagonal line crosses the y axis somewhere above the horizontal x axis. Specifically, it crosses the y axis at y = 3
Graph D is the only graph that has such a line on it. Graphs A, B and C have the positive slope line where they have a negative y intercept, so we can rule them out.
You can use graphing tools such as Desmos or Geogebra to help confirm this answer. You could also make a table of values, and plot each point, to form the lines. Two points is the minimum amount needed to form any line.
Answer:
Step-by-step explanation:
Answer:
See picture attached below.
Step-by-step explanation:
To graph the system, graph each line separately.
y = 3x + 3 ha slope 3 and y-intercept 3.
Start at 3 on the y-axis and mark a point. Then from this point move up 3 units and to the right 1 unit. Mark a point and connect.
y=-x - 3 has slope -1 and y-intercept -3.
Start at -3 on the y-axis and mark a point. Then from this point move down 1 unit and to the right 1 unit. Mark a point and connect.
This graph is represented in the picture attached.
...............................................................................................................................................
Which graph represents the following system of equations?
y = 3x + 3
y = –x – 3
...............................................................................................................................................
y=x−8
y=12x−5
...............................................................................................................................................
Graph of 2 lines that intersect at one point. Both lines are solid. One line passes through (-2,2) and (0,3) and is shaded below the line.
y < = 1/2x + 3...(-2,2) y < = 1/2x + 3....(0,3)
2 < = 1/2(-2) + 3 3 < = 1/2(0) + 3
2 < = -1 + 3 3 < = 0 + 3
2 < = 2 (correct) 3 < = 3 (correct)
The other line passes through points (0,1) and (1,-2) and is shaded above the line.
y > = -3x + 1...(0,1) y > = -3x + 1...(1,-2)
1 > = -3(0) + 1 -2 > = -3(1) + 1
1 > = 0 + 1 -2 > = -3 + 1
1 > = 1 (correct) -2 > = -2 (correct)
...............................................................................................................................................
we have
using a graph tool
see the attached figure
The solution of the system is the shaded area
we know that
The line is solid
The line passes through points and and is shaded above the line.
The line is solid
The line passes through points and and is shaded below the line
The two lines intersect at one point
therefore
the answer is the option
B) Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.
Help me!!!!!!!!! For 10 points
Answer: Hope this helps!
XYW=48 degrees
X=16
Step-by-step explanation:
So the angles are on a straight line. A straight line is 180 degrees. If you subtract 132 by 180 you get 48. Now to solve for x I divided 48 by 3. And I got 16.
Step-by-step explanation:
1). m∠ XYW = 180° - 132°
= 48°
2). 3x + 132 = 180°
3x = 180° - 132°
3x = 48°
x = 48/3
x = 16°
#CMIIWEllise has 4 times as much money as her sister. If Ellise has php 10.40, how much money does her sister have?
Answer:Ellise's sister has php 2.4
Step-by-step explanation:
Let the amount of money Ellise sister has be = x
and amount Ellise has be =4x
since Ellise has php 10.40
her sister will have php 10.40/4 = php 2.4
when the “a” value is negative in any quadratic what do you know about the graph?
Answer:
when a is negative, the parabola opens downward
Step-by-step explanation:
ASAP can one of y’all help me do surface how do you do it
Answer:
false
Step-by-step explanation:
solid A surface area-112
solid B surface area-136
to find the surface area of a rectangular prism the equation is 2(lw + lh + wh)
Solid A 4*8+4*2+8*2
32+8+16
56*2=112
Solid B 2*2+2*16+2*16
4+32+32
68*2=136
Point s is locaded 5 units to the right of point t plot the point that represents the location of point s select the place on the coordinate plane to plot the point
Answer:
See attachment for plot
Step-by-step explanation:
Given
[tex]t = (-1,2.5)[/tex] ---- coordinates of t
s = 5 units to the right of t
Required
Plot s
First, we determine the coordinate of s
The rule to translate a point to the right is:
[tex](x,y) \to (x + h,y)[/tex]
Where h is the number of units
i.e.
[tex]h= 5[/tex]
So, we have:
[tex]s = (-1 + 5, 2.5)[/tex]
[tex]s = (4, 2.5)[/tex]
See attachment for plot
A die is rolled. The set of equally-likely outcomes is {1, 2, 3, 4, 5, 6}. Find the probability of rolling a number greater than 4.
Answer:
33.33 percent or 2:4
Step-by-step explanation:
AABC has vertices at (1,5), (4,8), and (16, 12). A second triangle, ADEF, has vertices at (4, 20), (16, 32), and (64, 48). If the two triangles are related by a dilation factor, which of the following could be a rule for the dilation?
Select one:
O (I,y) → (4x, 4y)
0 (x,y) → (6x, 6y)
O (x,y) → (2, y)
0 (r,y) → (16x, 16y)
Answer: the first one
Step-by-step explanation:
(x,y)->(4x, 4y)
which of these figures has rotational symmetry
Answer: The answer is C
Step-by-step explanation:
The reason is because if you make a line in between it would be symetrical (up, down, left, right).
Find the value of x.
Answer:
18
Step-by-step explanation:
all angles of a triangle adds up to 180
90 + 25 + (3x+11) = 180
3x + 11 = 65
3x = 54
x = 18
Answer:
x= 18
90+25= 115
115-180= 65
65-11=54
54/3=18
Step-by-step explanation:
:)
PLEASE HELP ASAP NOO LINKS!!!
Answer:
b
Step-by-step explanation:
help! (equivalent fractions)
it has three questions, please awnser the three! thank you!!!
Answer:
1. answer is 12
2. answer is 18
3. answer is 2
1) A museum charges different rates for adults and students. Adult
tickets are $14.50 and student tickets are $8.00. Ms Olivis class went
to the museum last week and spent $232.50 on 25 tickets. How
many students and how many adults went to the museum?
Answer:
Step-by-step explanation:
Order the following in ascending order.
A library labels each book with a six-character code to identify the book in its computer system. The first character is either a letter or digit, and this is followed by three digits, then two letters. How many different codes are possible
Answer: There are 24336000 different codes that are possible.
Step-by-step explanation:
We know that,
Total alphabets = 26
Total digits = 10
Choices for First place = 26+10=36
Choices for next 3 places = 10 x 10 x 10 = 1000
Choices for last 2 places = 26 x 26 = 676
Total different codes are possible = 36 x 1000 x 676
=24336000
Hence, there are 24336000 different codes that are possible.
Can someone tell me what I did wrong?
Answer:
The answer is 12 feet. .
Step-by-step explanation:
You have to multiply 3/4 or 0.75 by the number of tiles. So you would go, 0.75 x 10 and then 0.75 x 6 and add the answers together.
Can you answer the question in the picture please?
Answer:
D)
Step-by-step explanation:
5x5+5=30
8x9+7=79
24x3+28=100
The slope of the line that contains the points (4, 10) and (5, 13) is 3. Find the y-intercept.
A. -26
B. -2
C. 8
D. 34
The slope of the line that contains the points (-2, -1) and (3, 19) is 4. Find the y-intercept.
A. -7
B. -2
C. 2
D. 7
Answer:
B
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 3 , then
y = 3x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation.
Using (4, 10 ) , then
10 = 12 + c ⇒ c = 10 - 12 = - 2 → B
D
Given m = 4 then
y = 4x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (3, 19 ), then
19 = 12 + c ⇒ c = 19 - 12 = 7 → D
Mr. Cobb is carpeting a 17.7 m long hallway. He has a piece of carpet 22 m long. How much does Mr. Cobb need to cut off the length of the piece of carpet?
Answer:5.7
Step-by-step explanation:
Help! How do I find AC in this equation?
Answer:
33
Step-by-step explanation:
add 25 & 8 together
Answer:
SEE IMAGE FOR SOLUTION
Hope it helps
Have a great day
Which experiment has a uniform probability model? Select all that apply.
HELP ME WITH THIS ASAP
Answer:
13) non-regular pentagon (5-sides, all sides not equal)
14) regular hexagon (6-sides, all appear to be equal)
15) two pair of parallel sides without right angles is a parallelogram
16) two pair of parallel sides with four right angles is a rectangle; if all sides are equal then it is a square
Step-by-step explanation:
Pls answer quick 45 points :))
Answer:
5
Step-by-step explanation:
PLEASE HELP ME I'LL APPRECIATE IT!!!!
Simplify the expression. Write your answer in positive exponent form:
9^5/9^4
Answer:
The answer is 9^1 or simply 9.