Answers
Answer: see proof below
Step-by-step explanation:
Use the following Product to Sum Identities:
2 sin A · cos B = sin (A + B) + sin (A - B)
2 cos A · cos B = sin (A + B) + sin (A - B)
Given: cos A + cos B = 1/2 and sin A + sin B = 1/4
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \tan\dfrac{A+B}{2}[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}[/tex]
[tex]\text{Multiplication:}\qquad \quad \dfrac{\sin\frac{(A+B)}{2}}{\cos\frac{(A+B)}{2}}\bigg(\dfrac{2\cos\frac{A-B}{2}}{2\cos \frac{A-B}{2}}\bigg)[/tex]
[tex]\text{Simplify:}\qquad \qquad \quad \dfrac{2\sin \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}{2\cos \frac{A+B}{2}\cdot \cos \frac{A-B}{2}}[/tex]
[tex]\text{Product to Sum:}\qquad \dfrac{\sin A+\sin B}{\cos A+\cos B}[/tex]
[tex]\text{Given:}\qquad \qquad \qquad \quad \dfrac{\frac{1}{4}}{\frac{1}{2}}[/tex]
[tex]\text{Simplify:}\qquad \qquad \qquad \dfrac{1}{2}[/tex]
LHS = RHS: 1/2 = 1/2 [tex]\checkmark[/tex]
Related Questions
0.3(10-5x)=31.5(8x+9)
Answers
Answer:
x = - 1.106Step-by-step explanation:
0.3(10-5x)=31.5(8x+9)
Expand the terms in the bracket
That's
3 - 1.5x = 252x + 283.5
Subtract 3 from both sides
3-3 - 1.5x = 252x + 283.5 - 3
-1.5x = 252x + 280.5
Subtract 252x from both sides
That's
- 1.5x - 252x = 252x - 252x + 280.5
- 253.5x = 280.5
Divide both sides by -253.5
We have the final answer as
x = - 1.106
Hope this helps you
passes through (-4, 11) and (2,8)
Answers
Are you looking for slope?
if u r the slope is -6/3
A slope of line will be "[tex]-\frac{1}{2}[/tex]".
Slope of line:According to the question,
(-4, 11) = (X1, Y1)(2,8) = (X2, Y2)We know,
Slope of line:
= [tex]\frac{Y2-Y1}{X2-X1}[/tex]
By substituting the values, we get
= [tex]\frac{8-11}{2-(-4)}[/tex]
= [tex]\frac{-3}{6}[/tex]
= [tex]-\frac{1}{2}[/tex]
Thus the answer above is correct.
Find out more information about slope here:
https://brainly.com/question/3493733
what quadrant would (0,4) be in
Answers
Answer:
Step-by-step explanation:
Answer:
the answer is
36(thirty six)
The scale of a map is 1cm : 70km. What is the actual distance between two towns that are 3cm apart on the map
Answers
Answer:
210 km
Step-by-step explanation:
1cm : 70km
3 x 70 = 210
3cm : 210km
Hopefully this helps you :)
pls mark brainlest ;)
HELP PLZ!!! A, B, C,or D.
Answers
Answer:
D
Step-by-step explanation:
Find the value of X in this equation.
g=c+x
Answers
x=g-c
Explanation:
You want to get x by itself, so you need to subtract c on both sides. Then, you are left with x=g-c.
Help meeeee !!!!!!!!!
Answers
Answer:
3n²+3n-60
Step-by-step explanation:
Area of rectangle= L*W
A=3(n-1)(n+2)
A=3(n²+n-2)
A=3n²+3n-6
54=3n²+3n-6
3n²+3n-6-54=0
3n²+3n-60=0
Answer:
3, 3, - 60
Step-by-step explanation:
Area = lw
Therefore 54=(3n-3)(n+2)
Expand and we get:
3n^2+6n-3n - 6=54
Combine terms and move 54 to left side:
3n^2+3n-60
Hope this helped!
After being treated with chemotherapy, the radius of the tumor decreased by 23%. What is the corresponding percentage decrease in the volume of the tumor
Answers
Answer:
The volume of the tumor experimented a decrease of 54.34 percent.
Step-by-step explanation:
Let suppose that tumor has an spherical geometry, whose volume ([tex]V[/tex]) is calculated by:
[tex]V = \frac{4\pi}{3}\cdot R^{3}[/tex]
Where [tex]R[/tex] is the radius of the tumor.
The percentage decrease in the volume of the tumor ([tex]\%V[/tex]) is expressed by:
[tex]\%V = \frac{\Delta V}{V_{o}} \times 100\,\%[/tex]
Where:
[tex]\Delta V[/tex] - Absolute decrease in the volume of the tumor.
[tex]V_{o}[/tex] - Initial volume of the tumor.
The absolute decrease in the volume of the tumor is:
[tex]\Delta V = V_{o}-V_{f}[/tex]
[tex]\Delta V = \frac{4\pi}{3}\cdot (R_{f}^{3}-R_{o}^{3})[/tex]
The percentage decrease is finally simplified:
[tex]\%V = \left[1-\left(\frac{R_{f}}{R_{o}}\right)^{3} \right]\times 100\,\%[/tex]
Given that [tex]R_{o} = R[/tex] and [tex]R_{f} = 0.77\cdot R[/tex], the percentage decrease in the volume of tumor is:
[tex]\%V = \left[1-\left(\frac{0.77\cdot R}{R}\right)^{3} \right]\times 100\,\%[/tex]
[tex]\%V = 54.34\,\%[/tex]
The volume of the tumor experimented a decrease of 54.34 percent.
30. When asked his age, the algebra teacher said, "If you
square my age, then subtract 23 times my age, the
result is 50. How old is be?
F. 23
G. 25
H. 27
J. 46
K. 50
Answers
Answer:
25 years old
Step-by-step explanation:
Let the teacher's age be a.
Then:
a^2 - 23a = 50
In standard form, this quadratic is
x^2 - 23a - 50 = 0
Factoring this, we get (x - 25)(x + 2) = 0
So a is either 25 or a is -2. Only a = 25 is relevant here.
The teacher is 25 years old (Answer G)
Is 253/10 a rational or irrational
Answers
Answer:
irrational
Step-by-step explanation:
did I do this right also how should I finish it?
Answers
it depends on what your supposed to do i would finish it myself
Jack's bank statement shows an account balance of $25 50 Which descubes the magnitude or size of the debt in dollars? $50 50 $25 50 SO 0-$25 50
Answers
Answer:
it’s B. $25.50
The mean of four numbers is 70. When a fifth number is included, the mean of the five numbers is 80. What is the fifth number?
Answers
=============================================
Explanation:
S = sum of the first four values
S/4 = 70 since we divide the sum by 4 to get the mean of the first four values
S = 280 is the result after multiplying both sides by 4
Let x be the fifth unknown value. Adding it onto S leads to S+x = 280+x. This represents the sum of all five values.
Dividing that sum 280+x over 5 leads to the new mean 80, which leads to...
----------
(280+x)/5 = 80
280+x = 5*80
x+280 = 400
x = 400-280
x = 120
The fifth number is 120
The fifth number is 120
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the four numbers be = a , b , c , d
Let the fifth number be = e
Now , the mean of 4 numbers is m = 70
So , the equation will be
( a + b + c + d ) / 4 = 70
Multiply by 4 on both sides , we get
a + b + c + d = 280 be equation (1)
Now , the mean of 5 numbers is m = 80
So , the equation will be
( a + b + c + d + e ) / 5 = 80
Multiply by 5 , we get
a + b + c + d + e = 400 be equation (2)
Substitute the value of equation (1) in equation (2) , we get
a + b + c + d + e = 400
280 + e = 400
Subtracting 280 on both sides , we get
e = 400 - 280
e = 120
Therefore , the value of e is 120
Hence , The fifth number is 120
To learn more about equations click :
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Can you pls help me solve this?
Answers
Answer:
x=−9
Step-by-step explanation:
i hope this helps you
Answer:
x=-9
Step-by-step explanation:
Subtracting 53 from both sides, you get -2/3x=6.
-9*2/3x=6
x=-9
what is the standerd form of number shown in this calculater display. 1.46e-6
Answers
Answer:
scientific notation
Step-by-step explanation:
This number is shown in scientific notation.
Answer:
0.00000146
Step-by-step explanation:
I took the test
lX – 12.2l= 0.3 gives the minimum and maximum acceptable lengths of the wires in centimeters. What is the minimum acceptable length of a wire?
Answers
Work Shown:
|x-12.2| = 0.3
x-12.2 = -0.3 or x-12.2 = 0.3
x = -0.3+12.2 or x = 0.3+12.2
x = 11.9 or x = 12.5
The min length is 11.9 cm and the max length is 12.5 cm
Subtracting 12.2 from either x value leads to a positive difference of 0.3 which is the margin of error.
The surface area of the side of a right cylinder can be found by multiplying twice the number π by the radius times the height. If a circular cylinder has radius r and height h, write an expression that represents the surface area of its side.
Answers
Answer:
2[tex]\pi[/tex]rh
Step-by-step explanation:
A little easier way to see:
2 * [tex]\pi[/tex] * r * h
0.15(y-0.2)=2-0.5(1-y)
The answer is -153/35 I just need to know how to get that
Answers
Answer:
[tex]y=-\dfrac{153}{35}[/tex].
Step-by-step explanation:
The given equation is
[tex]0.15(y-0.2)=2-0.5(1-y)[/tex]
Using distributive property, we get
[tex]0.15(y)+0.15(-0.2)=2-0.5(1)-0.5(-y)[/tex]
[tex]0.15y-0.03=2-0.5+0.5y[/tex]
[tex]0.15y-0.03=1.5+0.5y[/tex]
Isolate variable terms.
[tex]0.15y-0.5y=1.5+0.03[/tex]
[tex]-0.35y=1.53[/tex]
Divide both sides by -0.35.
[tex]y=\dfrac{1.53}{-0.35}[/tex]
[tex]y=-\dfrac{1.53}{0.35}\times \dfrac{100}{100}[/tex]
[tex]y=-\dfrac{153}{35}[/tex]
Therefore, [tex]y=-\dfrac{153}{35}[/tex].
i need seven please help
Answers
Answer:
3n + 6
Step-by-step explanation:
7.
three times a number: 3n
six more than three times a number: 3n + 6
If HJ = 7x27 find the value of x. 3x-5. x-1
•———————-•——•
H. I. J
Answers
Answer:8.6
Step-by-step explanation:
Solve the equation for W
Answers
Answer:
fourth option
Step-by-step explanation:
Given
[tex]\frac{2x-1}{y}[/tex] = [tex]\frac{w+2}{2z}[/tex] ( cross- multiply )
y(w + 2) = 2z(2x - 1) = 4xz - 2z ( divide both sides by y )
w + 2 = [tex]\frac{4xz-2z}{y}[/tex] ( subtract 2 from both sides )
w = [tex]\frac{4xz-2z}{y}[/tex] - 2
. Sonya buys four pairs of shoes on
sale for buy one, get one 50% off.
The sales tax is 6.5%. If the
original price for each pair of shoes
was $35, how much does Sonya
pay for the four pairs altogether?
A. $74.55
B. $105.00
C. $111.83
D. $149.10
________________
Answers
Answer:
c
Step-by-step explanation:
35/2=17.5 *2= 35+35+35= 105
6.5% of 105 is 6.83, so 105+ 6.83= 111.83
Simplify this equation 2x³y³/4y²
Answers
Is the correct answer
I need help on this giving brainlist ASAP
Answers
Answer:
no solution
Step-by-step explanation:
|x| = -10
Absolute value means that it is positive or 0
It cannot be negative
There is no solution
Step-by-step explanation:
There is no solution
|A|
can be only 0 or positive number
can't be -
from the rule of Mathematics
what is 1xy+3x-(23y+3)
Answers
Answer:
[tex]xy+3x-23y-3[/tex]
Step-by-step explanation:
[tex]1xy+3x-(23y+3)\\[/tex]
Multiply ; 1× x =x
[tex]=xy+3x-\left(23y+3\right)\\[/tex]
Use - to open the bracket
[tex]-\left(23y+3\right):\quad -23y-3\\\\=xy+3x-23y-3[/tex]
Solve this system of equations and enter an ordered pair (x,y). y = x + 3 y = -x - 5
Answers
Answer:
(x,y). y = x + 3 y = -x - 5
Step-by-step explanation:
add it up cowgirl howdey with PHOTOT MATHSAnswer:
(-4,-1)
Step-by-step explanation:
I graphed the two lines using a graphing tool. When graphed, the lines intercept at (-4,-1). Therefore, (-4, -1) is the solution.
Please see the graph attached.
Hope this helps.
Solve for x: −4x − 4 = −4(x + 2)
Answers
Answer:
Step-by-step explanation:
-4x - 4 = -4x - 8
=4 ≠ -8
no solution
undefined
Answer:
no solution
Step-by-step explanation:
-4x - 4 = -4(x + 2)
Distribute
-4x -4 = -4x -8
Add 4x to each side
-4x+4x - 4 = -4x+4x -8
-4 = -8
This is never true so there is no solution
Solve for x.
y= 2x
y=20
Simplify your answer as much as possible.
Answers
Answer:
20=2x
20/2=x
X=10
Step-by-step explanation:
Answer:
x=10
Step-by-step explanation:
20 divided by 2 equals 10.
If 8b-9=b then 7b=?
Please answer if you can!
Also it’s NOT 1.5
Answers
Answer:
9 is your answer.
Step-by-step explanation:
Solve for b. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
First, add 9 to both sides:
8b - 9 (+9) = b (+9)
8b = b + 9
Next, subtract b from both sides:
8b (-b) = b (-b) + 9
8b - b = 9
7b = 9
Divide 7 from both sides:
(7b)/7 = (9)/7
b = 9/7
Plug in 9/7 for b in the equation given:
7(b) = 7(9/7) = 9
9 is your answer.
~
Find the perimeter of each polygon created by the coordinates.
A(-2, 3), B(3, 1), C(-2, -1), D(-3, 1)
a) 16.7
b) 14
c) 15.2