[tex]\stackrel{\textit{Half-Angle Identities}}{cos\left(\cfrac{\theta}{2}\right)=\pm \sqrt{\cfrac{1+cos(\theta)}{2}}} \\\\[-0.35em] ~\dotfill\\\\ \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos\left( \cfrac{45^o}{2} \right)\implies \sqrt{\cfrac{1+cos(45^o)}{2}}~~ = ~~cos(22.5^o)[/tex]
I have a bag with 6 marbles numbered from 1 to 6. mathew has a bag with 12 marbles numbered from 1 to 12. matthew chooses one marble from his bag and i choose two from mine. in how many ways can we choose the marbles (where the order of my choices does matter) such that the sum of the numbers on my marbles equals the number on his?
Answer:
It would be 30.
Step-by-step explanation:
If we make a list of all the sums that we can get, we have:
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways, since order matters, and we could do 2+1 instead of 1+2.
That gets us to 15x2 which is 30.
The number of ways that we can choose the marbles such that the sum of the numbers on my marbles equals the number on his would be 30.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
I have a bag with 6 marbles numbered from 1 to 6.
Mathew has a bag with 12 marbles numbered from 1 to 12.
1+2, 1+3, 1+4, 1+5, 1+6, 2+3, 2+4, 2+5, 2+6, 3+4, 3+5, 3+6, 4+5, 4+6, 5+6
These 15 sums can be chosen in two ways,
Since order matters, and we could do 2+1 instead of 1+2.
15 x 2 which is 30.
Learn more about the unitary method;
https://brainly.com/question/23423168
#SPJ1
Slope of (1,-4) and (0,-5)
Answer:
Slope is 1
Step-by-step explanation:
use slope formula: m= [tex]\frac{y2-y1}{x2-x1}[/tex]
m= [tex]\frac{-5+4}{0-1}[/tex]
[tex]\frac{-1}{-1}=1[/tex]
m=1
Hope this helps!
If not, I am sorry.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the slope of
[tex]\star\mathrm{(1,-4)}[/tex]
[tex]\star\mathrm{(0,-5)}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Use the slope formula.Here's the slope formula:
[tex]\star\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}[/tex]
Input the values, which are:
y2=-5
y1=-4
x2=0
x1=1
[tex]\star\mathrm{\cfrac{-5-(-4)}{0-1}}[/tex]
Simplify!
[tex]\star\mathrm{\cfrac{-5+4}{-1}}[/tex]
[tex]\star\mathrm{\cfrac{-1}{-1}}[/tex]
[tex]\star\boxed{\mathrm{1}}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
[tex]\bf{\overline{\underline{\overline{\underline{Maribel\:Peri}}}}[/tex]
Find the value of 8power of five
Answer:
the answer is 32,768 hopes this helps
Step-by-step explanation:
8^5 = 8x8x8x8x8 = 64x8x8x8= 64x64x8 = 4096x8= 32,768
Consider this sphere with a diameter of 12 cm. a sphere with diameter 12 centimeters. what is the volume of the sphere? sphere v = four-thirds pi r cubed 24pi cm3 48pi cm3 288pi cm3 2,304pi cm3
Answer: 200 pi
Step-by-step explanation:
the multiplication law of exponents says that for any numbers b, n, and m,
b^n.b^m=b^n+m
a. true
b. false
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
Law of indicesIndices are written in term of exponents. Some of the laws of indices;
[tex]a^m\times a^n=a^{m+n}[/tex] (product law of indices)
For the quotient law of indices
[tex]\dfrac{a^m}{a^n} =a^{m-n}[/tex]
According to the given expression, we are to determine if it is true or false
Check:
[tex]b^n.b^m=b^{n+m[/tex]
Since the exponents were added based on the product rule, hence the multiplication law of exponents is TRUE
Learn more on multiplication law of exponents here: https://brainly.com/question/847241
#SPJ1
Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
The function h(x) is increasing on the interval (–∞, 3).
The function h(x) is increasing on the interval (–3, ∞).
The function h(x) is decreasing on the interval (–∞, 3).
The function h(x) is decreasing on the interval (3, ∞).
Using translation concepts, it is found that the correct option regarding the function is:
The function h(x) is decreasing on the interval (3, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is given by:
[tex]f(x) = \sqrt{x}[/tex]
Which increases on (0, ∞).
The translated function is given by:
[tex]g(x) = -2\sqrt{x - 3}[/tex]
With the translation, the domain is now (-3, ∞), and the function is decreasing, hence the correct option is given by:
The function h(x) is decreasing on the interval (3, ∞).
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
If Sammy starts drinking his tea at 11:25 P.M. and he finishes it at 12:20 A.M., how long does it take him to drink his tea?
Answer:
55 minutes
Step-by-step explanation:
add 35 to 11:25 should equal to 12AM then add 20 to it should give you the answer of 12:20AM combining the 35 and 20 should give you 55
Answer:
55 Minutes
Step-by-step explanation:
Assuming the start time is on the previous day, the time between 11:25:00 PM and 12:20:00 AM is:
0 hour, 55 minutes, and 0 second
0.917 hour
55 minutes
3,300 seconds
Hope this helps!
In 8 years Jamie will be three times as old as she is now. How old is Jamie?
Answer:
x=4
Step-by-step explanation:
Based on the given conditions, formulate:
x+8=3×x
Rearrange unknown terms to the left side of the equation:
x-3x=-8
Combine like terms:-2x=-8
Divide both sides of the equation by the coefficient of variable:x=-8/-2
Rewrite the fraction:8/2
Cross out the common factor:x=4
get the result:x=4
Answer: 4
rodea la fracción que sigue y escribe el patrón que corresponde en cada sucesion
If f(x)=3x+5/x, what is f(a + 2)?
a. 3a + 5/a + 2
b. 3(f(a)) + 5/f(a)+2
c. 3(a+2) + 5/a+2
Answer:
Answer C is correct
Step-by-step explanation:
1. We replace x as (a + 2)
2. Then we just rewrite this function with the new value
3. Result: 3(a+2) + 5/(a+2)
Need the correct answers to select asap! Will give brainliest for correct answers
Answer:
first 2 options and 5th option are true
Step-by-step explanation:
locate y = - 4 on the y- axis. then a horizontal line through y = - 4 intersects the curve at x = - 2 and x = 1
----------------------------------------------------------
the axis of symmetry is a vertical line through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex )
vertex = ( - [tex]\frac{1}{2}[/tex], - 6 )
equation of axis of symmetry is x = - [tex]\frac{1}{2}[/tex]
------------------------------------------------------------
the minimum value is the y- coordinate of the vertex
that is the minimum value of f(x) is - 6
------------------------------------------------------------
given a parabola in standard form
ax² + bx + c ( a ≠ 0 )
• if a > 0 then graph opens up
• if a < 0 then graph opens down
Here the graph opens up , then coefficient of f(x) is positive
-------------------------------------------------------------
the solutions to f(x) = 0 are the values of x on the x- axis where the graph crosses.
the solutions are x = 2 and x = - 3
Find the area of a trapezoid shown:
The area of this trapezoid is A = 55
We know that the application formula for calculating the area of a trapezoid is given by:
[tex] \boxed{ \large \sf A = \dfrac{(b + b) \times h}{2} } \\ \\ [/tex]
⚘ Then, the resolution will be:
[tex]{ \large \sf A = \dfrac{(7 + 15) \times 5}{2} } [/tex]
[tex]{ \large \sf A= \dfrac {22 \times 5}{2} } [/tex]
[tex]{ \large \sf A= \dfrac {110}{2} } [/tex]
[tex]\pink{ \boxed{ \purple{ \boxed{ \large \sf A= 55 }}}} \\ \\ [/tex]
Therefore, the area of this trapezoid will be, A = 55
11. Courtney removes a colored tile from a bag containing 12 red tiles, 10 blue tiles, and
8 yellow tiles. Without replacing the first tile, she removes a second tile from the bag.
What is the probability that both tiles that Courtney removed are blue? Identify
whether removing the second tile from the bag is an independent event of a
dependent event. Justify your response.
Answer:
whos courtney
Step-by-step explanation:
whos courtney??
For the complex number z = (5sqrt(3))/4 - 5/4 * i what is the polar form
The complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6). (Correct choice: C)
How to transform a complex number in rectangular form into polar formComplex numbers are elements of the form z = a + i b, where [tex]a, b \in \mathbb{R}[/tex]. In other words, represents a generalization from real numbers. The polar form of a complex number is shown below:
[tex]z = r\cdot (\cos \theta + i \,\sin \theta)[/tex] (1)
Where:
r - Normθ - Direction, in radians.The norm is determined by Pythagorean theorem and the direction by inverse trigonometric reason. If we know that z = (5√3 / 4) - i 5/4, then its polar form is shown below:
Norm
[tex]r = \sqrt{\left(\frac{5\sqrt{3}}{4} \right)^{2}+\left(-\frac{5}{4} \right)^{2}}[/tex]
r = 5/2
Direction
[tex]\theta = \tan^{-1} \left[\frac{\left(-\frac{5}{4} \right)}{\left(\frac{5\sqrt{3}}{4} \right)} \right][/tex]
θ = 11π/6 rad
Thus, the complex number in rectangular form z = (5√3 / 4) - i 5/4 is equivalent to the complex number in polar form z = 5/2 · (cos 11π/6 + i sin 11π/6).
To learn more on complex numbers: https://brainly.com/question/10251853
#SPJ1
PLEASE HELP I’LL MAKE YOU THE BRAINIEST
find the area of the trapezoid to the nearest tenth
Answer:
2.7m
Step-by-step explanation:
1.0m
0.5m
+1.2m
2.7m - answer
Are you good at maths?????????????????????????
The probability that a student, chosen at random, does not study chemistry is 20/41.
What is Probability?
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
Here, Total number of student = 41
Student who does not study chemistry = 20
So, the probability = favorable outcome / total outcomes
P(not studying chemistry) = 20 / 41
Thus, The probability that a student, chosen at random, does not study chemistry is 20/41.
Learn more about Probability from:
https://brainly.com/question/11234923
#SPJ1
Q). Express each of the following recurring decimal as a rational numbers . 1) 0.5 2) 0.13 3) 0.341
The following recurring decimal as a rational number are 1/2, 13/100 and 341 / 1000
What is rational number?A rational number is a number that is expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator such as;
3/4. where,
Numerator = 3Denominator = 4Therefore,
0.5
= 5/10
= 1/2
0.13
= 13/100
0.341
= 341 / 1000
Learn more about rational number:
https://brainly.com/question/12088221
#SPJ1
3. How many solutions does the equation have?
−8x+6+20x = 2/3(18x + 9)
O No Solutions
○ Two Solutions
O One Solution
An infinite number of solutions
C Explain why it is not possible to fill out the frequency distribution table below without additional information.
What is 4 times 4(5+7)
Answer:
192
Step-by-step explanation:
so you basically make an equation like this:
4*4(5+7)
4*4(12)
4*48
=192
Translate the shape A two squares right and one square up.What are the coordinates of the vertices of the image?
Answer:
(3, 5) (3, 2) , (5, 2)
Step-by-step explanation:
Analysis:
(1) Translate square A two squares right
(a, b) ⇒ ( a + 2, b)
{ (1, 4) {(3, 4)
{ (1, 1) ⇒ { (3, 1)
{ (3, 1) { (5, 1)
(2) ... one square up:
(a, b) ⇒ (a, b + 1)
{ (3, 4) { (3, 5)
{ (3, 1) ⇒ { (3, 2)
{ (5, 1) { (5, 2)
Which point best represents √10?
0
1
R
P
+2
P Q R
11111
3
Q
S45
4
S
Done ->
Answer:
Point Q best represents the square root of 10.
The radius of a circle is 2 centimeters. What is the length of a 45° arc?
Answer:
1.57 cmStep-by-step explanation:
the circle has a radius of 2.
Then
The circumference of the circle = 2πr = 2π(2) = 4π
…………………………………
Since , 45/360 = 1/8
Then, the arc is 1/8 of the entire circle.
…………………
Therefore,
the length of a 45° arc = 4π/8 = π/2 cm ≈ 1.57 cm
Find the derivative using the first principles.
[tex]~~~~\dfrac{d}{dx} \left( \sqrt[5]{1+x} \right)\\\\\\=\dfrac{d}{dx} (1+x)^{\tfrac 15}\\\\\\=\dfrac 15 \left(1 + x\right)^{\tfrac 15 -1} \cdot \dfrac{d}{dx}(1+x)\\\\\\=\dfrac 15 (1+x)^{-\tfrac 45} \cdot(0+1)\\\\\\=\dfrac{1}{5(1+x)^{\tfrac 45}}[/tex]
if a= 2x - 3 and b= 2x+5
find the value of a+b
help pleaseeee i would really appreciate
Answer:
4x+2
Step-by-step explanation:
a= 2x - 3 and b= 2x+5
a+b = 2x-3 + 2x+5
Combine like terms
a+b = 4x+2
Answer:
a + b = 4x + 2
Step-by-step explanation:
a = 2x - 3
b = 2x + 5
a + b = (2x-3) + (2x+5)
a + b = 2x + 2x - 3 + 5
a + v = 4x + 2
Pls help I will give brainliest!!
Answer:
A. (-8, 0)
Step-by-step explanation:
The side of the line that is shaded contains the solutions to the inequality. (-8, 0) is in the shaded part of both graphs.
Also, 0 > -15 and 0 [tex]\geq[/tex] -9
I hope this helps :)
please help me thank you :)
The function on the table is decreasing on the interval [-2, 0).
Over what interval is the function shown in the table decreasing?
A function is decreasing if, as x increases, f(x) decreases.
We can see that at x = -2, f(-2) = 12.
Then at x = 0, f(0) = 0.
And for the value after that:
x = 1, f(1) = 3
So now the function increases. Then we conclude that the function is decreasing on the interval [-2, 0), and after that the function increases.
If you want to learn more about decreasing functions:
https://brainly.com/question/1600302
#SPJ1
4 cups is equivalent to ____ quart
Answer:
1 quart is equal to 4 cups
Step-by-step explanation:
4 cups is equivalent to __1__ quart
find this expression in square form with process pls help me !!!!
Answer:
(p -3q )(p -3q )
Step-by-step explanation:
p'2 - 6pq + 9q'2
(p -3q )(p -3q )
find two values that add to give 6 and multiply to 9
p x p =p'2
-3q x p = -3pq -3 x pq = -3pq ...... -3pq - 3pq = -6pq
-3q x - 3q = 9q'2
Which matrix multiplication is possible?
Answer:
second 0ne
Step-by-step explanation:
3×-1+-2 ×0
3×0+-2×3