Given:
The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex].
To find:
The least common multiple of given expressions.
Solution:
The expressions are [tex](x+1),\ (x-1)[/tex] and [tex](x^2-1)[/tex]. The factor forms of these expressions are:
[tex](x+1)=1\times (x+1)[/tex]
[tex](x-1)=1\times (x-1)[/tex]
[tex](x^2-1)=(x-1)(x+1)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
The least common multiple is the product of all distinct factors with its highest degree. So,
[tex]L.C.M.=1\times (x+1)\times (x-1)[/tex]
[tex]L.C.M.=(x+1)(x-1)[/tex]
[tex]L.C.M.=x^2-1^2[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]L.C.M.=x^2-1[/tex]
Therefore, the least common multiple of given expressions is [tex]x^2-1[/tex].
Las calificaciones de los alumnos en un examen de Estadística han sido: 6, 4, 4, 3, 6, 10, 1, 0, 2, 6 ,6, 8, 5. Calcula su media. Seleccione una: a. 4.6 b. 6.0 c. 5.0 d. 4.7
Which is the graph of y = |3x| – 2?
Answer:
It's the 3rd one, that you've selected in the picture.
Step-by-step explanation:
Used a graphing calculator to check,
Hope this is helpful.
I need help with this it's urgent!
Oh shucks man, I'm sorry bout that
Find all solutions to the equation in the interval [0, 2pie] Enter the solutions in increasing order.
sin 2x = sin x
=============================================
Work Shown:
sin(2x) = sin(x)
sin(2x) - sin(x) = 0
2*sin(x)*cos(x) - sin(x) = 0
sin(x)*(2cos(x) - 1) = 0
sin(x) = 0 or 2cos(x)-1 = 0
sin(x) = 0 or cos(x) = 1/2
Using the unit circle, the solutions to sin(x) = 0 are x = 0, x = pi, x = 2pi
Also, the solutions to cos(x) = 1/2 are x = pi/3, x = 5pi/3
So the entire solution set on the interval [0,2pi] is {0, pi/3, pi, 5pi/3, 2pi} when written in increasing order.
All solutions to the equation in the interval [0, 2[tex]\pi[/tex]] is {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}.
What is solution to an equation?A solution is an assignment of values to the unknown variables that makes the equality in the equation true.
As sin2x = 2 sinx cosx,
sin2x = sinx is equivalent to
2 sinx cosx = sinx or 2 sinx cosx − sinx = 0 or
sinx (2cosx − 1) = 0 i.e.
either sinx = 0 and x = 0, π, 2π
or 2cosx − 1 = 0 i.e. cosx = [tex]\frac{1}{2}[/tex] i.e. x = [tex]\frac{\pi }{3} , \frac{5\pi }{3}[/tex]
Hence, solution to an equation is x = {0, [tex]\frac{\pi }{3}, \pi , \frac{5\pi }{3} ,2\pi[/tex]}
Learn more about solution to an equation here
https://brainly.com/question/14603559
#SPJ2
PLZ ans have mocks plz
Answer:
The table will be:
x |-2 | -1 | 0 | 1 | 2
y | 1 | 4 | 5 | 4 | 2
Step-by-step explanation:
The function is:
[tex]y=5-x^{2}[/tex]
a) The x values of the table is:
x |-2 | -1 | 0 | 1 | 2
So, when x = -2, y will be:
[tex]y(-2)=5-(-2)^{2}=5-4=1[/tex]
Doing the same with the other x values we have:
[tex]y(-1)=5-(-1)^{2}=5-1=4[/tex]
[tex]y(0)=5-(0)^{2}=5[/tex]
[tex]y(1)=5-(1)^{2}=5-1=4[/tex]
[tex]y(2)=5-(2)^{2}=5-4=1[/tex]
The table will be:
x |-2 | -1 | 0 | 1 | 2
y | 1 | 4 | 5 | 4 | 1
I hope it helps you!
Which expression is equivalent to 4+2(1+3x)?
a. 24x
b. 6 + 18x
c. 6 + 6x
d. 4 + 8x
ps: any incorrect, irrelevant, plagiarized, or absurd answers will be reported ! sorry for the inconvenience !
Answer:
6+18x
Step-by-step explanation:
=6(1+3x)
=6×1+6×3x
=6+18x
What percent is represented by the shaded area?
Find the solution of the system of equations.
4x – 6y = 32
2x + 3y = 4
Answer:
(5,-2)
Step-by-step explanation:
4x – 6y = 32
2x + 3y = 4 (multiply everything by 2. This will allow for the elimination of one of the variables. In this case, the y. )
4x – 6y = 32
4x + 6y = 8 (Now add them together)
__________
8x = 40 (Divide by 8, both sides)
x = 5
4(5) - 6y = 32 ( Substitute the x value into one of the original equations)
20 - 6y = 32 (Subtract the 20 from both sides)
-6y = 12 Divide by the -6, both sides)
y = -2
\frac{1}{cos^{2} x}-(3+\sqrt{3} )tanx-3+\sqrt{3} =0
Step-by-step explanation:
pls type the question
properly and I swear I will solve it
HELP PLEASEEEE!!!!!!!
Answer:
The first one with the sequence 0.25,1,4,16
Answer:
the first one
Step-by-step explanation:
Gianna bought 6.2 pounds of berries. She used 4.8 pounds of the berries to make a pie. What equation can be used to find how many pounds of berries, b, Gianna has left over? A 6.2 + 4.8 = b
B b − 6.2 = 4.8
C 4.8 + b = 6.2
D b − 4.8 = 6.2
find the solution to the system of equations
Answer: (-2,1) deduced from graph
the point where the two lines intersect is the solution
Step-by-step explanation:
Answer:
(- 2, 1 )
Step-by-step explanation:
Given a system of equations graphically then the solution is at the point of intersection of the 2 lines.
The point of intersection = (- 2, 1 ) ← solution
The height y of a ball (in feet) is given by the function
y= -1/12^2+2+4
and x is the horizontal distance traveled by the ball. How high is the ball when it leaves the child’s hand?
Answer:
assuming that the problem was actually
-1/12 x ^ 2 + 2x + 4
height = 16
(12,16)
forty feet (40) feet
vertex = -b/2a = -2/(-1/6) = 12
f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4 = 16
Step-by-step explanation:
PQR is a triangle. PR = 13 cm, PQ = 12 cm and angle QPR = 30°
Calculate the length of QR.
Answer:
6.55 cm
Step-by-step explanation:
A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, acute, scalene, obtuse, right and equilateral triangle.
Cosine rule is used to show the relationship between sides and angles of a triangle. If a, b, and c are sides of a triangle, while A, B, and C are angles opposite to the corresponding sides. Then:
c² = a² + b² - 2ab*cos(C)
Given that PR = 13 cm, PQ = 12 cm and angle QPR = 30°, hence:
QR² = PR² + PQ² - 2(PR)(PQ)cos(∠QPR)
QR² = 13² + 12² - 2(13)(12)cos(30) = 169 + 144 - 270
QR² = 43
QR = 6.55 cm
Can someone help me? It's urgent and thank you!
Answer:
12
Step-by-step explanation:
Consider the series 1/4+1/6+1/9+2/27+4/81+....
Does the series converge or diverge?
Select answers from the drop-down menus to correctly complete the statements.
Answer:
The series converges as any two consecutive elements of the sum are monotonically decreasing.
Step-by-step explanation:
The series converges since the consecutive element is monotonically decreasing. That is:
[tex]\forall\,i\in \mathbb{N}\,a_{i} > a_{i+1}[/tex] (1)
Where:
[tex]a_{i}[/tex] - The i-th component of the sum.
[tex]a_{i+1}[/tex] - The (i+1)-th component of the sum.
Pls help will mark brainliest and 30 points
1. Answer is option 3
2. Answer is option 3
Answer:
for #1 it's the 3rd one and for #2 it's the 4th one (2.8 meters)
Element X is a radioactive isotope such that every 69 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 20 grams, how much of the element would remain after 30 years, to the nearest whole number?
Answer:
[tex]15\text{ grams}[/tex]
Step-by-step explanation:
Since the mass of the radioactive isotope is halved every 69 years, we want to multiply its initial mass by [tex]1/2[/tex] every 69 years.
We can model this using the following equation:
The remaining mass, [tex]f(x)[/tex], is equal to the initial mass multiplied by [tex]\frac{1}{2}^{(\frac{t}{69})}[/tex], where [tex]t[/tex] is the number of years that have passed from the initial mass. The reason why the exponent is [tex]\frac{t}{69}[/tex] is because we only want to half the mass every 69 years, so [tex]\frac{69}{69}=1[/tex] and [tex]\frac{1}{2}^1=\frac{1}{2}[/tex].
Thus, we have:
[tex]f(x)=20\cdot \frac{1}{2}^{(t/69)}[/tex]
Substituting [tex]t=30[/tex], we get:
[tex]f(x)=20\cdot \frac{1}{2}^{(30/69)}=20\cdot 0.73980522316=14.7961044632\approx \boxed{15\text{ grams}}[/tex]
Hurry I need answers to this problem
Pleasee help me, I might give brainliest to the best answer. I urgently need a answer
Answer:
1<1.35<2
Step-by-step explanation:
Answer:
1.35 is closer to 1 than 2
So the bag of nuts weighed about 1 pound.
Step-by-step explanation:
The decimal is closer to the whole number 1 when plotted on a number line, so it rounds to 1.
please help asap ill give brainliest
Answer:
is 0.24 yards in the option, becausw i am getting this as my answer
The record for the largest scoop of ice cream was made in Wisconsin. Thebscoop of ice cream was 3,010 pounds! How many ounces of ice cream is that?
Answer:
48160
Step-by-step explanation:
What is the correct solution set for the following graph?
Answer: i do not see a graph
Step-by-step explanation:
Slopes of parallel lines
Answer:
2
Step-by-step explanation:
Parallel lines have the same slopes
If the slope of line a is 2, the slope of line b is 2
Answer:
slope of line b = 2
Step-by-step explanation:
The slopes of parallel lines are equal
Given slope of line a = 2 and parallel to line b , then
slope of line b = 2
The figure represents a doorstop in the shape of a triangular prism. What is the volume of the doorstop in cubic inches?
Answer:
7 times 5
35
divided by two
17.5
times 3
52.5 cubic inch
In ΔJKL, KL = 14, LJ = 11, and JK = 4. Which list has the angles of ΔJKL in order from smallest to largest?
Answer:
m<L, m<K, m<J
Step-by-step explanation:
The angle that sees the longest side length has the biggest measurement
so
for listing the angles from smallest to largest
m<L, m<K, m<J
Answer:K J L
Step-by-step explanation:
Which inequality can be used to explain why these
three segments cannot be used to construct a triangle?
Answer:
Iliana cannot construct a triangle because the sum of the two smaller sides will not be greater than the third side.
The distance between the parallel lines x – 2y = 3 and 2x – 4y = 12 is
Answer:
???????????????????????
Step-by-step explanation:
sorry di ko po alam yung sagot pasensiya na po
Given :
Parallel lines are
x – 2y = 3 and 2x – 4y = 12
Step-by-step explanation:
Lets write the given lines in slope intercept form y=mx+b
[tex]x -2y = 3 \\-2y=-x+3\\Divide \; both \; sides \; by -2\\y=\frac{x}{2} -\frac{3}{2}[/tex]
From the above equation , y intercept of first line is [tex]\frac{-3}{2}[/tex]
Solve the second equation for y and find out y intercept
[tex]2x-4y=12\\-4y=-2x+12\\Divide \; by \; -4\\y=\frac{1}{2} x-3[/tex]
y intercept of second line is -3
To find the distance between parallel lines, we subtract the y intercepts
[tex]\frac{-3}{2} -(-3)=\frac{-3}{2} +\frac{6}{2} =\frac{3}{2} =1.5[/tex]
Answer:
The distance between the parallel lines = 1.5
Reference:
https://brainly.com/question/24145911
Find y.
Round to the nearest tenth:
31°
у
х
400 ft
y = [ ? ]ft
What is the name of the function f(x)=|x|
A. Linear Function
B. Absolute value Function
C. Quadratic Function
D. Cubic Function