Answer:
In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many people mistakenly call this a 'square root' symbol, and many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol. For example, 3√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.
The term underneath the radical symbol is called the radicand.
I hope it's helpful!
prove it please
answer only if you know
Part (c)
We'll use this identity
[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\[/tex]
to say
[tex]\sin(A+45) = \sin(A)\cos(45) + \cos(A)\sin(45)\\\\\sin(A+45) = \sin(A)\frac{\sqrt{2}}{2} + \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\[/tex]
Similarly,
[tex]\sin(A-45) = \sin(A + (-45))\\\\\sin(A-45) = \sin(A)\cos(-45) + \cos(A)\sin(-45)\\\\\sin(A-45) = \sin(A)\cos(45) - \cos(A)\sin(45)\\\\\sin(A-45) = \sin(A)\frac{\sqrt{2}}{2} - \cos(A)\frac{\sqrt{2}}{2}\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]
-------------------------
The key takeaways here are that
[tex]\sin(A+45) = \frac{\sqrt{2}}{2}(\sin(A)+\cos(A))\\\\\sin(A-45) = \frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\[/tex]
Therefore,
[tex]2\sin(A+45)*\sin(A-45) = 2*\frac{\sqrt{2}}{2}(\sin(A)+\cos(A))*\frac{\sqrt{2}}{2}(\sin(A)-\cos(A))\\\\2\sin(A+45)*\sin(A-45) = 2*\left(\frac{\sqrt{2}}{2}\right)^2\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = 2*\frac{2}{4}\left(\sin^2(A)-\cos^2(A)\right)\\\\2\sin(A+45)*\sin(A-45) = \sin^2(A)-\cos^2(A)\\\\[/tex]
The identity is confirmed.
==========================================================
Part (d)
[tex]\sin(x+y) = \sin(x)\cos(y) + \cos(x)\sin(y)\\\\\sin(45+A) = \sin(45)\cos(A) + \cos(45)\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}\cos(A) + \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\[/tex]
Similarly,
[tex]\sin(45-A) = \sin(45 + (-A))\\\\\sin(45-A) = \sin(45)\cos(-A) + \cos(45)\sin(-A)\\\\\sin(45-A) = \sin(45)\cos(A) - \cos(45)\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}\cos(A) - \frac{\sqrt{2}}{2}\sin(A)\\\\\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\[/tex]
-----------------
We'll square each equation
[tex]\sin(45+A) = \frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\\\\\sin^2(45+A) = \left(\frac{\sqrt{2}}{2}(\cos(A)+\sin(A))\right)^2\\\\\sin^2(45+A) = \frac{1}{2}\left(\cos^2(A)+2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
and
[tex]\sin(45-A) = \frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\\\\\sin^2(45-A) = \left(\frac{\sqrt{2}}{2}(\cos(A)-\sin(A))\right)^2\\\\\sin^2(45-A) = \frac{1}{2}\left(\cos^2(A)-2\sin(A)\cos(A)+\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\frac{1}{2}*2\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
--------------------
Let's compare the results we got.
[tex]\sin^2(45+A) = \frac{1}{2}\cos^2(A)+\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\\sin^2(45-A) = \frac{1}{2}\cos^2(A)-\sin(A)\cos(A)+\frac{1}{2}\sin^2(A)\right)\\\\[/tex]
Now if we add the terms straight down, we end up with [tex]\sin^2(45+A)+\sin^2(45-A)[/tex] on the left side
As for the right side, the sin(A)cos(A) terms cancel out since they add to 0.
Also note how [tex]\frac{1}{2}\cos^2(A)+\frac{1}{2}\cos^2(A) = \cos^2(A)[/tex] and similarly for the sin^2 terms as well.
The right hand side becomes [tex]\cos^2(A)+\sin^2(A)[/tex] but that's always equal to 1 (pythagorean trig identity)
This confirms that [tex]\sin^2(45+A)+\sin^2(45-A) = 1[/tex] is an identity
B. Solve;
1. Find a number such that three times the sum of that number
and 5 is greater than 33.
2. The sum of two consecutive integers is less than 81. Find the
pair of integers with the greatest sum.
This means that each point where the two lines intersect is a
Answer: When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.
I think this the answer♀️
The linear combination method is applied to a system of equations as shown.
4(.25x + .5y = 3.75) → x + 2y = 15
One-fourth(4x – 8y = 12) → x – 2y = 3
2x = 18
What is the solution of the system of equations?
Answer:
hi
Step-by-step explanation:
Option 4th is correct
The solution of the system of equations is, (9, 3)
Step-by-step explanation:
Given the system of equations:
⇒ .....[1]
⇒ .....[2]
Add equation [1] and [2] we have;
Divide both sides by 2 we have;
Substitute x = 9 in [1] we have;
Subtract 9 from both sides we have;
2y = 6
Divide both sides by 2, we have;
y = 3
Therefore, the solution of the system of equations is, (9, 3)
Givereasons
a) The image gives all the details of an object.
b) The shadow of a translucent material is not clear.
Answer:
a
Step-by-step explanation:
In each of the following graphs, the two given polygons are similar. Write precisely a single dilation (coordinates of center and coefficient) by which the image (labeled with primed letters) was obtained. C
What is the answer?
here is the image
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
What is dilation?Dilation is the increase or decrease in the size of a figure by a scale factor of k, thereby creating an image.
From the diagram:
Scale factor = A'B' / AB = 6/3 = 2
Center = (6, -6)
Polygon ABCD was dilated by a scale factor of 2 to create A'B'C'D'.
Find out more on dilation at: https://brainly.com/question/10253650
Need help as fast as possible please
I will mark BRAINLIST only for correct answers babes :)
Thank you!
Answer:
What is ur book called
I will edit my answer after this
Answer:
1. you move a shape to somewhere else by a number of units
2. the position of the book changes
3. no you are just moving the shape
If a + b = c, which of the following statements is true?
c – a = b
b – c = a
a – c = b
c + b = a
Answer:
c-a=b
Step-by-step explanation:
Plz help me I don’t het this a question !!!
Answer:
C=50.24
Step-by-step explanation:
Formula for circumference with radius: 2[tex]\pi[/tex]r
r= radius
C=circumference
Now subsitute the variables with the values given.
Formula: 2[tex]\pi[/tex]r -> 2(3.14)(8)
C=50.24
HELP ILL MARK YOU BRAINLIST PLZ
Answer:
Step-by-step explanation:
Answer:
An = A + (n - 1) ×d
hope it helps
The Basketball team sets a goal of having at least a 7:2 Win Loss Ratio. If they play 36 games in a season, how many games must they win to achieve their goal?
What is the amount of sales tax owned in a $39 jacket if the tax rate is 5%
Answer:
$1.95
Step-by-step explanation:
3. What are the factors in the expression 4(5 + x)?
Answer:
Step-by-step explanation:
The factors are the parts that are being multiplied together.
4 and (5+x) are the two that are being multiplied and also the expression you get when you factor the distributed expression.
So the factors of 4(5+x) are:
4 and (5+x)
a right angled triangle has sides which are 2cm and 7cm shorter than its hypotenuse find the length of the hypoenuse
Answer:
The length of the hypotenuse side is (9 + 2·√7) cm
Step-by-step explanation:
The given parameters of the triangle are;
The type f triangle = Right triangle
The length of the sides 2 cm and 7 cm shorter than the hypotenuse
Let 'h' represent the length of the hypotenuse side of the triangle, in centimeters we have;
The length of one side of the right triangle = (h - 2) cm
The length of the other side of the right triangle = (h - 7) cm
By Pythagoras's theorem, we have;
h² = (h - 2)² + (h - 7)²
Using search function on the internet, we have;
h² = (h - 2)² + (h - 7)² = 2·h² - 18·h + 53
∴ h² = 2·h² - 18·h + 53
∴ 2·h² - 18·h + 53 = h²
h² - 18·h + 53 = 0
53 is a prime number, therefore, by the quadratic formula, we have;
h = (18 ± √((-18)² - 4×1×53))/(2 × 1)
h = 9 + 2·√7 cm ≈ 14.29 cm or h = 9 - 2·√7 ≈ 3.71
However, given that one of the side is 7 cm shorter than the hypotenuse, for all the sides to remain positive, we have h = 9 + 2·√7 cm ≈ 14.29 cm , because for h ≈ 3.71 cm, we have;
The length of the other side = (h - 7) cm ≈ (3.71 - 7) cm ≈ -3.29 cm which is not possible for a real triangle
Therefore, the length of the hypotenuse side, h = 9 + 2·√7 cm ≈ 14.29 cm.
the yearly income of a person is rs 90000.It is increased by 15%what is the income of person after one year
Answer:
13,500.00 yearly is the raise + 90000.00 original salary= 103500.00 a year
Rs 103500
Sorry hazy little bit
Find the measure of the following:
m arcTR =
m arcTL =
m ∠L =
m ∠R =
m ∠RTV =
Answer:
you have to do that we don't know k sorry bro
A rectangular prism has a volume of 360 in3. If the height measures 6in. which base measurements could the prism have?
Answer:
Both sides that are parallel ( 6 inches I believe ) would be 12 in total for both sides. Then the top and bottom would be 3 inches ( I believe ) which would be 6. I think you need to do 6 times 12 until you get 360 and then see how many times you multiplied it and that is your answer. But I am not FULLY sure. Hope this helps somehow!
Step-by-step explanation:
Which of the following shapes is concave?
OA)
OB)
OC)
OD)
Answer:
A is a concave polygon,....,.
Answer:
the answer will be A.
Step-by-step explanation:
I need help with Geometry
Answer:
Me too
Step-by-step explanation:
Answer: hello
your answer will be C
Step-by-step explanation:
Help ASAP Glven the system of equations, what is the value of the system determinant?
2x+y=8
X-y=10
A single card is drawn at random from a standard 52 card deck. Work out the following probabilities in their simplest form: P(7) = P(not 7) =
Answer:
[tex]1) \frac{1}{13} \\ 2) \frac{12}{13} [/tex]
Step-by-step explanation:
to understand thisyou need to know about:simple probabilityPEMDAStips and formulas:there are 4 "7" cards in a decklet's solve:according to the question
P(7)=4/52P(7)=1/13according to the question
P(not 7)=1-[tex]\frac{1}{13}[/tex]P(not 7)=12/13Answer:
no of 7=4
total no of card =52
total not no.7=52-4=48
Step-by-step explanation:
probability of getting 7=4/52=1/13
probability of not getting 7=48/52=12/13
1/4 + 1/8= ????????????
Answer:
3/8!! hope i helped :))
I need help with this one please and can yall explain this because I try to do but I can't just figure it out
Answer:
9
Step-by-step explanation:
because the FIM and LAK are similar, then
FI/LA=IM/AK=MF/KL
MF/KL=2/3
The diagonal of a rhombus are 14cmand 10 cm find the area of
rhombus.
What is 1,050/55 What is the answer.
Answer: 19.0909090909 or 19
a) X -Y =10 y = 5
b) X = 20 , y = 6
c) X = 14, y = 4
Answer:
a) X - Y = 10
and,
X - 5 = 10
or, X = 10 + 5
or, X = 15
And i don't get the other two questions
Hope this helped
Hope this helped ALL THE BEST !!
Frederick's brother is going on a hike. He has his backpack filled with supplies. His backpack weighs 400 ounces. How many pounds is Frederick's backpack? Note: 1 pound = 16 ounces
Answer:
25
Step-by-step explanation:
Do 400 divided by 16 to convert to pounds
400/16=25
Hope this helped :)
Answer:
25 pounds
Step-by-step explanation:
1 Pound=16 ounces
? Pounds=400 ounces
400 divided by 16=25
25 pounds=400 ounces
PLZZZZZZZZ HELPPPP!!!!!!!!!!!!!!
Answer:
1 135
2 80
3 145
4 45
Step-by-step explanation:
Thats the answer
.
.
.
Which algebraic expression represents “Marcus practiced the trumpet twice as long this week”?
2 + p
2p
p minus 2
StartFraction p Over 2 EndFraction
Please Help!
Answer:
2p should be the correct answer!
Answer:
2p is the answer
Step-by-step explanation:
I took the answer edg2021
What is the slope of the line represented by the equation y=-2/3-5x?
-5
-2/3
2/3
5
Answer:
-5
Step-by-step explanation:
y=-2/3-5x
Rewriting the equation in the form y = mx+b where m is the slope and b is the y intercept
y = -5x -2/3
The slope is -5 and the y intercept is -2/3
