Answers
Answer: see proof below
Step-by-step explanation:
Use the following Sum Identities:
cos (A + B) = cosA · cosB - sinA · sinB
sin (A + B) = sinA · cos B - cosA · sinB
Use the Unit Circle to evaluate the following:
cos 30 = √3/2 sin 30 = 1/2
cos 45 = √2/2 sin 45 = √2/2
cos 120 = -1/2 sin 120 = √3/2
cos 240 = -1/2 sin 240 = -√3/2
cos 315 = √2/2 sin 315 = -√2/2
cos 330 = √3/2 sin 330 = -1/2
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \dfrac{\cos 285+\cos 345}{\sin 435-\sin 375}[/tex]
[tex]\text{Expand:}\qquad \quad \dfrac{\cos (240+45)+\cos (315+30)}{\sin (315+120)-\sin (330+45)}[/tex]
[tex]\text{Sum Identity:}\qquad \dfrac{\cos 240\cdot \cos 45-\sin 240\cdot 45+\cos 315\cdot \cos 30-\sin 315\cdot 30}{\sin 315\cdot \cos 120+\cos315\cdot \sin 120-(\sin330\cdot \cos45+\cos 330\cdot \sin 45) }[/tex]
[tex]\text{Unit Circle:}\quad \dfrac{(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{-\sqrt3}{2}\cdot \frac{\sqrt2}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{3})-(\frac{-\sqrt2}{2}\cdot \frac{1}{2})}{(\frac{-\sqrt2}{2}\cdot \frac{-1}{2})+(\frac{\sqrt2}{2}\cdot \frac{\sqrt3}{2)}-(\frac{-1}{2}\cdot \frac{\sqrt2}{2})-(\frac{\sqrt3}{2}\cdot \frac{\sqrt2}{2})}[/tex]
[tex]\text{Simplify:}\qquad \dfrac{-\sqrt2+\sqrt6+\sqrt6+\sqrt2}{\sqrt2+\sqrt6+\sqrt2-\sqrt6}\qquad =\dfrac{2\sqrt6}{2\sqrt2}\qquad =\sqrt3[/tex]
LHS = RHS: [tex]\sqrt3 = \sqrt3\qquad \checkmark[/tex]
Related Questions
2
3(9x-6) = 4x + 10
What is the value of x that makes the equation true?
Answers
The value of [tex]x[/tex] is 7.
Important information:
The given equation is [tex]\dfrac{2}{3}(9x-6)=4x+10[/tex].Solve the equation:The given equation can be written as:
[tex]\dfrac{2}{3}(9x)-\dfrac{2}{3}(6)=4x+10[/tex]
[tex]6x-4=4x+10[/tex]
[tex]6x-4x=4+10[/tex]
[tex]2x=14[/tex]
Divide both sides by 2.
[tex]x=\frac{14}{2}[/tex]
[tex]x=7[/tex]
Therefore, the value of [tex]x[/tex] is 7.
Find out more about 'Solve the equation' here:
https://brainly.com/question/14338212
In a small company's accounting department, the accounts receivable
coordinator often takes the role of the
O A. bookkeeper
B. credit and collection manager
C. payroll administrator
D. accounting manager
SUBMIT
Answers
Answer:
The correct option is;
D. Accounting manager
Step-by-step explanation:
Mid level managers such as accounting managers in a large establishment can comprise three different managers, including accounts payable manager, account receivables manager, and the payroll administrator. However, in a small firm the accounting manager can be responsible for the above accounting duties
In a large establishment, the financial controller has three accounting managers reporting directly to her, which are the accounts receivable manager, the payroll manager, and the account payable manger. In a small firm however all the above named accounting functions will be performed the accounting manager.
Let p: A car has automatic windows. Let q: A car has automatic seats. p v q is true for a total of how many cars?
Answers
Answer:
d 80
Step-by-step explanation:
Urgent ! Use a table to compress the function y=f(x) vertically by 1/2 . Identify the graph of the function and its transformation . A-B-C- or D ?
Answers
The third one is the right answer
Answer:
The first one is right. (A)
Step-by-step explanation:
Whenever we talk about compressions we just need to compress one of the axes in this case we are asked to compress the y-axis which means that the only values that will change are the y-values, don't get confused the x values have to stay the same.
Simplify the exponential expression. 5 4 =
Answers
Answer:
???
Step-by-step explanation:
what the expression just 5 and 4 i dont get it
Ingrid traveled to Jacksonville, texas, to watch baskets being made. she saw six shelves with 19 baskets on each shelf. how many baskets were on the shelves in all?
Answers
Use the figure shown to the
right to write a polynomial
that represents the areatof
the shaded region. Express
the polynomial in standard
form, that is, in descending
powers of x.
The polynomial that represents the area of the shaded region is ]
(Simplify your answer. Type your answer in standard form.)
Answers
Answer:
4x + 16
Step-by-step explanation:
The area of the shaded region = area of the outer rectangle - area of the inner rectangle
Area of rectangle = l*w
Area of outer rectangle, where length (l) = (x + 5), and width (w) = (x + 4):
Area = (x + 5)(x + 4)
Expand
x(x + 4) +5(x + 4)
x² + 4x + 5x + 20
area of outer rectangle = x² + 9x + 20
Area of inner rectangle, where length (l) = (x + 4), and width (w) = (x + 1):
Area = (x + 4)(x + 1)
Expand
x(x + 1) +4(x + 1)
x² + x + 4x + 4
Area of inner rectangle = x² + 5x + 4
Area of shaded region = (x² + 9x + 20) - (x² + 5x + 4)
x² + 9x + 20 - x² - 5x - 4
Collect like terms together
x² - x² + 9x - 5x + 20 - 4
4x + 16
Area of the shaded region = 4x + 16
-5y+15=3x i really need help on this question! 10 points! please explain.
Answers
Answer:
Step-by-step explanation:
-5y +15 = 3x
divide both sides by 3 to find x
-5y/3 + 5 = x
to find Y you have to isolate it so you add 5y to both sides and subtract 3x from both sides to get
-3x + 15 = 5y
then to find y divide both sides by 5
-3x/5 + 5 = y
The ones in bold are your answers and they are in their simplest form.
Suppose two quantities, A and B, have different dimensions. Determine which of the following arithmetic operations could be physically meaningful.
a. B-A
b. A-B
c. A+B
d. AB
e. A/B
Answers
Answer:
d. AB
e. A/B
Step-by-step explanation:
From the concept of homogeneity of dimension. The principle is that if two quantities occurs in the same direction, addition and subtraction of those two variable tends to occur but if two quantities occur in different direction, then we can only have either the division and multiplication of those quantities.
From the given information;
Suppose two quantities, A and B, have different dimensions.
The arithmetic operations that could be physically meaningful are :
d. AB
e. A/B
Select the correct choice that completes the sentence below -5(x-3) = -5x +15 illustrates the ____ property of multiplication over addition 1. Additive 2. Inverse 3. Distributive 4. Commutative 5. Multiplication
Answers
Answer: 3. Distributive
Step-by-step explanation:
Distributive property of multiplication over addition is the only property that is require to multiply an expression to the other expression with two or more than two terms.
For example: a (b+c)= a b+ac , where a,b,c can be any expression.
Given expression: -5(x-3) = -5x +15 , which illustrates the distributive property of multiplication over addition.
Hence, the correct option is 3. Distributive.
The rest of properties cannot work for multiplication over addition as they are used for one operation.
Gordon took a panoramic picture that is 2 inches tall. The picture is 4 1/2 times as long as it is tall. How long is Gordon's picture?
Answers
Answer:
9 inches
Step-by-step explanation:
4 1/2 = 9/22 = 2/19/2 x 2/1 = 18/218/2 = 9inSteve had 48 chocolates but decided to give 8 chocolates to each of his coworkers. How many chocolates does Steve have left? Write your answer as an expression.
Answers
Answer:
y = 48 - (8x)
Step-by-step explanation:
x = unknown number of coworkers
y = number of chocolates left over
y = 48 - (8x)
Example: If you were to plug in the number 5 for x:
y = 48 - (8(5))
y = 48 - 40
y = 8
The answer is 48-8f
Ccffcxdfcve
factor (difference of squares) the binomial 25x^2-4 and find one of its factors
Answers
Step-by-step explanation:
Hey, there!
Here,
Given that:
[tex] = 25 {x}^{2} - 4[/tex]
we need to find factor,
As it is in a^2-b^2 form as per its factor (a+b) (a-b), keeping same formula here,
25x^2 means (5x)^2
and 4 means 2^2
Now, it would be,
[tex] = ( {5x)}^{2} - {2}^{2} [/tex]
[tex] = (5x + 2)(5x - 2)[/tex]
Therefore, it's factor would be (5x+2)(5x-2).
Hope it helps....
find the area of the figure
Answers
Answer:
This is the answer i hope
We have to find the area of rectangle or triangle if triangle
Equation =1/2*length*Breadth
That is 1/2*13*8
=52
Answer:
104 sq. ft.
Step-by-step explanation:
Add the to heights and then multiply your base times height:
6+7=13
13x8= 104
SOMEONE PLEASE ANSWER THESE!!! ASAP!!
1.) why isn’t -8 a irrational number?
2.) why isn’t 4.349 a irrational number?
3.) why isn’t -9.7 a irrational number?
4.) why isn’t 7 a irrational number?
5.) why isn’t 3/7 a irrational number?
6.) why isn’t 0 a irrational number?
7.) why isn’t 18 a irrational number?
8.) why isn’t -8/9 a irrational number?
Answers
Answer:
1. Because it is an integer.
2. Because it is a terminating decimals.
3. Because it is a terminating decimal as well as an integer.
4.Because it is a natural number.
5.Because it is a terminating decimal when divided.
6. Because it is a whole number.
7. Because it is a natural number.
8. Because it is a terminating negative decimal when divided(simplified basically).
Step-by-step explanation:
Irrational numbers include:
Non terminating,and non recurring decimals.
Example: 1.2345677854903421......so on.
Hope this helps... :-)
In ΔLMN, \overline{LN}
LN
is extended through point N to point O, \text{m}\angle MNO = (5x-13)^{\circ}m∠MNO=(5x−13)
∘
, \text{m}\angle NLM = (x-4)^{\circ}m∠NLM=(x−4)
∘
, and \text{m}\angle LMN = (2x+19)^{\circ}m∠LMN=(2x+19)
∘
. Find \text{m}\angle NLM.m∠NLM
Answers
Answer:
[tex]\bold{\angle NLM = 10^\circ}[/tex]
Step-by-step explanation:
Given a ΔLMN.
Line LN is extended to point O.
such that:
[tex]\text{m}\angle MNO = (5x-13)^{\circ}[/tex]
[tex]\text{m}\angle NLM = (x-4)^{\circ}[/tex] and
[tex]\text{m}\angle LMN = (2x+19)^{\circ}[/tex]
To find:
[tex]\text{m}\angle NLM=?[/tex]
Solution:
Kindly refer to the attached image for the given triangle and dimensions of angles.
Let us recall the external angle property of a triangle:
The external angle of a triangle is equal to the sum of two opposite internal angles.
i.e.
[tex]\angle MNO = \angle NLM + \angle LMN\\\Rightarrow 5x-13 = x-4+2x+19\\\Rightarrow 5x-13 = 3x+15\\\Rightarrow 5x-3x = 13+15\\\Rightarrow 2x=28\\\Rightarrow x =14[/tex]
Putting the value of [tex]x[/tex] in [tex]\angle NLM[/tex].
[tex]\angle NLM=14-4 \\\Rightarrow \bold{\angle NLM = 10^\circ}[/tex]
- 4(x + 2) = - 2x + 1
HELP MEEEEE
Answers
please help i don’t know if i got the right answer
Answers
ooooh lemme drive da bus
Solve -17 + n over 3 = 33
Answers
Answer:
n=82
Step-by-step explanation:
[tex] \frac{17 + n}{3} = 33 \: \: \: \frac{17 + n}{3} = \frac{33}{1} \: \: \: 17 + n = 99 \: \: \: n = 99 - 17 \: \: \: n = 82[/tex]
Proof:
17+n/3=33
17+82/3=33
99/3=33
33=33
Hope this helps ;) ❤❤❤
please someone help me... i need full answer
Answers
Answer: see proof below
Step-by-step explanation:
Use the following Sum to Product Identities:
[tex]\sin x-\sin y=2\cos\bigg(\dfrac{x+y}{2}\bigg)\sin\bigg(\dfrac{x-y}{2}\bigg)\\\\\\\cos x-\cos y=2\cos\bigg(\dfrac{x+y}{2}\bigg)\cos\bigg(\dfrac{x-y}{2}\bigg)[/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \qquad \dfrac{\sin 2A+\sin 5A-\sin A}{\cos A+\cos 2A+\cos 5A}[/tex]
[tex]\text{Regroup:}\qquad \qquad \qquad \dfrac{\sin 2A+(\sin 5A-\sin A)}{\cos 2A+(\cos 5A+\cos A)}[/tex]
[tex]\text{Sum to Product:}\qquad \dfrac{\sin 2A+2\cos\bigg(\dfrac{5A+A}{2}\bigg)\sin\bigg(\dfrac{5A-A}{2}\bigg)}{\cos2A+\cos\bigg(\dfrac{5A+A}{2}\bigg)\cos\bigg(\dfrac{5A-A}{2}\bigg)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{\sin 2A+2\cos 3A\sin 2A}{\cos 2A+2\cos 3A\cos 2A}[/tex]
[tex]\text{Factor:}\qquad \qquad \qquad \dfrac{\sin 2A(1+2\cos 3A)}{\cos 2A(1+2\cos 3A)}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{\sin 2A}{\cos 2A}\\\\.\qquad \qquad \qquad \qquad =\tan 2A[/tex]
LHS = RHS: tan 2A = tan 2A [tex]\checkmark[/tex]
If -2/1 = 6/7x , what is x?
Answers
Answer:
7/3
Step-by-step explanation:
Answer:
x =-7/3Step-by-step explanation:
[tex]-\frac{2}{1}=\frac{6}{7}x\\\\\frac{6}{7}x=-\frac{2}{1}\\\\\mathrm{Apply\:rule}\:\frac{a}{1}=a\\\frac{6}{7}x=-2\\\\\mathrm{Multiply\:both\:sides\:by\:}7\\7\times\frac{6}{7}x=7\left(-2\right)\\\\Simplify\\6x=-14\\\\\mathrm{Divide\:both\:sides\:by\:}6\\\frac{6x}{6}=\frac{-14}{6}\\\\Simplify\\x=-\frac{7}{3}[/tex]
Evaluate 6t -20-32u when t=6 and u=1/4
Answers
Answer:
[tex]8[/tex]
Step-by-step explanation:
[tex]6t - 20 - 32u = 6(6) - 20 - 32( \frac{1}{4} ) = 36 - 20 - 8 = 16 - 8 = 8[/tex]
Hope this helps ;) ❤❤❤
Then multiply first. 36-20-8.
Then go left to right for subtracting.
36-20= 16; 16-8=8
So your answer would be 8.
Which expressions are equivalent to 4b?
Answers
Step-by-step explanation:
5b-b,4b^2/b,...and so on
there are infinite number of equivalent expression..
among them five are here
4*b,
6b-2b,
2*2b,
((5b^3-b^3)/b^2),
2b+2b,etc
Evaluate 6|5 - c| + 2c when c = 6. 6 18 48 -24
Answers
Answer:
18
Step-by-step explanation:
The solution is Option B.
The value of the modulus function is A = 18
What is Modulus Function?Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x
If x = 0, then f(x) = 0
If x < 0, then f(x) = -x
Given data ,
Let the modulus function be represented as A
Now , the value of A is
A = 6 | 5 - c | + 2c be equation (1)
Now , when the value of c = 6
Substituting the value of c in the equation , we get
A = 6 | 5 - 6 | + 2 ( 6 )
A = 6 | -1 | + 2 ( 6 )
The value of the modulus function always returns a positive value ,
So , A = 6 ( 1 ) + 2 ( 6 )
A = 6 + 12
A = 18
Therefore , the value of A is 18
Hence , the modulus function is A = 18
To learn more about modulus function click :
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The following diagrams show two rectangles.Given the perimeter of diagram A is 12cm while the perimeter of diagram B is twice the perimeter of diagram A.Find the values of x and y.
Answers
Step-by-step explanation:
i tried to solve one question. if it is correct then u can try another also same like this.
Twice a number increased by seven is twenty-five.
Answers
2x = 25-7
2x = 18
2x /2 = 18/2
X = 9
2(9) + 7 = 25
18 + 7 = 25
25 = 25
10 + 10 is what!? I’ll give you guys some points
Answers
Answer:
20
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
IF my scientific calculations are correct the answer is 20
can u please help me with this question
Answers
Answer:
D
its the big clix
Answer:
B
Step-by-step explanation:
Higher temps. shows lower altitude, therefore lowering temps. shows an increase in altititude
When you have a division problem, what do you do to the exponents?
Answers
Answer:
you work out the exponents before you divide,
Step-by-step explanation:
Enter the mixed number as an improper fraction. 3 3/5 =
Answers
Answer:
18/5
Step-by-step explanation: