Step-by-step explanation:
First factor out the negative sign from the expression and reorder the terms
That's
[tex] \frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \cot(6A) - \cot(2A) } [/tex]
Using trigonometric identities
That's
[tex] \cot(x) = \frac{1}{ \tan(x) } [/tex]Rewrite the expression
That's
[tex]\frac{1}{ - (( \tan(2A) - \tan(6A) )} - \frac{1}{ \frac{1}{ \tan(6A) } } - \frac{1}{ \frac{1}{ \tan(2A) } } [/tex]
We have
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{ \tan(6A) \tan(2A) } } [/tex]Rewrite the second fraction
That's
[tex] - \frac{1}{ \tan(2A) - \tan(6A) } - \frac{ \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]Since they have the same denominator we can write the fraction as
[tex] - \frac{1 + \tan(6A) \tan(2A) }{ \tan(2A) - \tan(6A) } [/tex]
Using the identity
[tex] \frac{x}{y} = \frac{1}{ \frac{y}{x} } [/tex]Rewrite the expression
We have
[tex] - \frac{1}{ \frac{ \tan(2A) - \tan(6A) }{1 + \tan(6A) \tan(2A) } } [/tex]Using the trigonometric identity
[tex] \frac{ \tan(x) - \tan(y) }{1 + \tan(x) \tan(y) } = \tan(x - y) [/tex]Rewrite the expression
That's
[tex] - \frac{1}{ \tan(2A -6A) } [/tex]Which is
[tex] - \frac{1}{ \tan( - 4A) } [/tex]Using the trigonometric identity
[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]Rewrite the expression
That's
[tex] - \cot( - 4A) [/tex]Simplify the expression using symmetry of trigonometric functions
That's
[tex] - ( - \cot(4A) )[/tex]Remove the parenthesis
We have the final answer as
[tex] \cot(4A) [/tex]As proven
Hope this helps you
Answer: see proof below
Step-by-step explanation:
Use the following identities:
[tex]\cot\alpha=\dfrac{1}{\tan\alpha}\\\\\\\cot(\alpha-\beta)=\dfrac{1+\tan\alpha\cdot \tan\beta}{\tan\alpha-\tan\beta}[/tex]
Proof LHS → RHS
Given: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\cot 6A-\cot 2A}[/tex]
Cot Identity: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}-\dfrac{1}{\tan 2A}}[/tex]
Simplify: [tex]\dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{1}{\tan 6A}\bigg(\dfrac{\tan 2A}{\tan 2A}\bigg)-\dfrac{1}{\tan 2A}\bigg({\dfrac{\tan 6A}{\tan 6A}\bigg)}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{1}{\dfrac{\tan 2A-\tan 6A}{\tan 6A\cdot \tan 2A}}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}-\dfrac{\tan6A\cdot \tan 2A}{\tan 2A-\tan 6A}\bigg(\dfrac{-1}{-1}\bigg)[/tex]
[tex]= \dfrac{1}{\tan 6A-\tan 2A}+\dfrac{\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
[tex]= \dfrac{1+\tan6A\cdot \tan 2A}{\tan 6A-\tan 2A}[/tex]
Sum Difference Identity: cot(6A - 2A)
Simplify: cot 4A
cot 4A = cot 4A [tex]\checkmark[/tex]
Complete the point slope equation of the line through (0,-2) and (3,4). y-4 = *
Answer:
y-4=4/5(x-0)
or, 5y-20=4x
or, 4x-5y+20=0 is the required equation
What is the product? Two-thirds times eight-ninths StartFraction 10 over 27 EndFraction StartFraction 16 over 27 EndFraction Two-thirds Five-sixths
Answer:
16/27
Step-by-step explanation:
First let's convert this info an equation and then we will solve.
(2/3) * (8/9) = ?
( 2 * 8 ) / ( 3 * 9 ) = ?
( 16 ) / ( 27 ) = ?
16 / 27 = ?
So our fractional answer is 16/27.
In words this would be sixteen over twenty seven.
Cheers.
Answer:
15/9
Step-by-step explanation:
In math the words transformation means to blank, blank, blank, or blank a figure
Answers:
TranslateReflectRotateDilateThis can be stated in any order
============================================
Explanation:
In geometry, a translation is where you slide a point or figure some distance left, right, up or down.
A reflection will mirror a point over a line, or you could mirror a point over another point.
A rotation turns a point around a fixed center point.
A dilation scales the figure to be larger or smaller.
The first three transformations mentioned (translation, reflection, rotation) are known as rigid transformations. They keep the figure the same size and shape. A dilation will keep the same shape, but the size will be different, so the before and after figures are not congruent when you apply a dilation.
Which equation could be used to create the graph? y=x−2 y=x−4 y=x3 y=3x
Answer:
y=3x
Step-by-step explanation:
If I am wrong sorry.
Answer:
y=3x
Step-by-step explanation:
i just took the test
-0.6 irrational or rational
Answer:
Rational
Step-by-step explanation:
If you can write it as a fraction (=ratio), it is rational.
-6/10 = -0.6
In the image below, lines n and mare parallel. What is the measure of angle 4?
a.98
b.82
c.164
d.122
help me asap pls
Answer:
a.) 98°
Step-by-step explanation:
Angle 5 and angle 8 (82°) are supplementary angles. This means that their sum will make a straight angle of 180°. Make an equation:
[tex]82+x=180[/tex]
Solve for x, the value of angle 5:
[tex]x=180-82\\\\x=98[/tex]
Angle 5 has a measure of 98°.
Now we know the measure of angle 5. Angle 4 and angle 5 are alternate interior angles, so they are congruent. Therefore, angle 4 has a measure of 98°.
:Done
what are you really changing when you change the length of the segment?
Answer: how much you have done
Step-by-step explanation:
Find the measure of ∠e, if m∠g = x + 17 and m∠f = 4x + 3. Answer choices: 131 49 4.6 15
Answer:
Step-by-step explanation:
∠g and ∠f are the interior angles on the same side of the transversal, therefore they're supplementary.
g + f = 180
4x + 3 + x + 17 = 180
5x + 20 = 180
5x = 180 − 20
5x = 160
x=1605=32
g = x + 17 = 32 + 17 = 49
Since ∠g and ∠e are corresponding angles, they're congruent.
g = e = 49
G. Write the equation of the line in slope-intercept form.
1. The line containing (3,1) and is perpendicular to the y=-x+1.
2. The line passes through (-1,7) and is parallel to the 5y = 4x + 5.
Answer:
y= x-2y = 4/5 x+39/5Step-by-step explanation:
1.
[tex](3,1) and\:perpendicular \:to \: y = -x+1\\(3,1) = (x,y)\\m = -1\\In\: perpendicularism ; m_2 = \frac{-1}{m_1} \\m_2 = \frac{-1}{-1} \\m_2 =1\\y = mx+c\\1 = 1(3) +c\\1=3+c\\1-3=c\\-2 =c\\Substitute \:new \:values\:into\\y =mx+c\\y = 1x -2\\y = x-2[/tex]
2.
[tex](-1,7) =(x_1,y_1)\\\\5y = 4x+5\\\\Write\:in\:y=mx+c\:form\\\frac{5y}{5} = \frac{4}{5} x + \frac{5}{5} \\y = \frac{4}{5} x +1\\m = \frac{4}{5} \\\\y -y_1=m(x-x_1)\\y-7=\frac{4}{5} (x -(-1)\\y -7 = 4/5(x+1)\\y -7 = 4/5x +4/5\\\\y = \frac{4}{5} x+\frac{4}{5} +7\\\\y = \frac{4}{5} x +39/5[/tex]
What is the factors of 5.1x
Answer:
1, 5.1, x, 5.1x
Step-by-step explanation:
5.1x can be split into 5.1 * x, therefore, we know that two of the factors are 5.1 and x. Keep in mind that 2 factors of a number are always 1 and the number itself, so we know that 1 and 5.1x are also factors. The final answer is 1, 5.1, x, 5.1x.
Suppose mr. Swanson turns in a late order for 1 veggie sandwich and 1 chicken sandwich. what is the new ratio of chicken sandwiches to veggie sandwiches
Answer:
6 chicken sandwiches to 4 veggie sandwiches
Step-by-step explanation:
I took the quiz.
Answer:
c
Step-by-step explanation:
where's the trust?
what is federal state?
Step-by-step explanation:
A federation (also known as a federal state) is a political entity characterized by a union of partially self-governing provinces, states, or other regions under a central federal government (federalism).
Will give brainliest! I need help with those three questions! Please :)))
15-29=
(I need the explanation most importantly)
14+(-4) - 8 =
(Explanation please)
12. -8.4 - (19.5.) =
(Explanation)
-15 + 8 - (-19.7) =
(Explanation)
29.45 - 56.009 - 78.2
(Explanation)
LAST ONE
45.9 - (-9.2) + 5
Answer:
15-29= -14
(I need the explanation most importantly)
14+(-4) - 8 =10-8=2
(Explanation please)
-8.4 - (19.5.) = - 27.9, (just add them to each other and write -, because both have - in front of them)
(Explanation)
-15 + 8 - (-19.7) = - 7+19,7=12,7 (there is + and - so it will became - 7, and at next there is two - which will turn them into +)
(Explanation)
29.45 - 56.009 - 78.2=−104,759 (all you have to is to put them all together, and than make it 29.45 less, writing - in front of them)
(Explanation)
LAST ONE
45.9 - (-9.2) + 5= 45.9+9.2+5=55.1+5=60.1 (because when there is 2 minus next to each other it will became plus)
"Construct c=a+b by drawing and calculating the direction and magnitude of c. The direction should be measured from the +x-axis" how do you do this problem?
Answer:
The question seems to be incomplete, so i will answer in a general way.
Ok, i guess that here we have two vectors:
a = (Ax, Ay) and b = (Bx, By).
Now we have that:
c = a + b = (Ax, Ay) + (Bx, By) = (Ax + Bx, Ay + By).
Now, to calculate the magnitude of a vector (x, y) we have:
√(x^2 + y^2)
Then the magnitude of c will be:
IcI = √( (Ax + Bx)^2 + (Ay + By)^2)
And for the direction:
First, the direction is already defined by the vector c.
But a more exact (and easy to read) way is:
When we have a vector (x, y).
The angle between this vector and the x-axis is given by:
Tan(θ) = y/x.
Then in the case of c.
Tan(θ) = (Ay + By)/(Ax + Bx)
θ = ATan( (Ay + By)/(Ax + Bx) )
Simplify.
6y-2y
Help please
Answer:
4y
Step-by-step explanation:
youd have to combine like terms..
Answer:
4y
Step-by-step explanation;
since they have something in common which is y,it is possible to subtract.we would be focusing more on the numbers than letters.The like term which is y just paves a way for these numbers to be subtracted.Hence, 6y -2y= 4y
or you can do it this way also
they have something in common which is y,so we factorise
y(6-2)
y(4)
hence y(4) also means 4 x y= 4y
Help needed ASAP will give brainliest It’s just a small problem pls
Answer: 1/7
Step-by-step explanation:
Just divide the numbers to convert it to decimal.
Answer:
1/7
Step-by-step explanation:
1 divided by 7 using long division is 0.142857 repeated. Please give brainliest thanks
how to move a parallel line next to the origin
Answer:
Write its y-intercept as zero:
[tex]y=m\,x[/tex]
Step-by-step explanation:
If the line is given in slope-intercept form:
[tex]y=m\,x+b[/tex]
make sure that you keep the value of the slope (m) as it is (because you want a line parallel to this one so it has to have the same slope "m", and change the value of "b" to zero, leaving the line with the following form:
[tex]y=m\,x+0\\y=m\,x[/tex]
This forces the line to have its y-intercept at the value zero (origin of coordinates)
Inverse operation of f(x)=x/2+1
Answer:
the inverse is f(x) = 2x - 2
Step-by-step explanation:
Inverse operation in this equation is basically switching the x and y:
y = x/2 + 1
x = y/2 +1
x - 1 = y/2
2x - 2 = y
In the Venn diagram, the blue circle represents when p is true, and the orange represents when q is true. A conjunction is true in region . A disjunction is true in region(s) . A disjunction is false in region(s) .
Answer:
A conjunction is true in region
✔ B <--- Answer
A disjunction is true in region(s)
✔ A, B, and C <--- Answer
A disjunction is false in region(s)
✔ D <--- Answer
Step-by-step explanation:
I took the assaignment aswell
A conjunction is true in the region
✔ B ← Answer
A disjunction is true in the region(s)
✔ A, B, and C ← Answer
A disjunction is false in the region(s)
✔ D ← Answer
What is a Venn diagram?A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.
Learn more about the Venn diagram here: brainly.com/question/2099071
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Find the area of each figure below. Round to the nearest hundredth.
Answer:
Area of rectangle=9×17=153 SQ.ft
Area of semi-circle=π9'2/2
Area of traingle=(1/2)×7×9=31.5
The area of the composite figure is 325.17 square feet
How to determine the area of the figure?The figure is a composite figure with the following shapes
RectangleTriangleSemicircleThe dimension of the shapes are:
Semicircle: Radius = 9 ftRectangle: Length = 9 ft; Width = (26 - 9)ftTriangle: Base = 9ft; Height =(26 -9 - 7) ftThe area of each shape is:
Semicircle
A = 0.5πr²
This gives
A = 0.5 * 3.14 *9^2 = 127.17
Triangle
A = 0.5 * base* height
This gives
A = 0.5 * 9 * (26 -9 - 7) = 45
Rectangle
A = Length * Width
This gives
A = 9 * (26 - 9) = 153
The area of the figure is the sum of the areas of the individual shapes.
So, we have:
Total = 127.17 + 45 + 153
Evaluate
Total = 325.17
Hence, the area of the composite figure is 325.17 square feet
Read more about areas at:
https://brainly.com/question/14137384
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Bob thought of an even and odd number, multiplies the numbers together, added 6, divided by 5, and subtracted 3 to give an answer of 1. What was the odd number he started with?
Answer:
7
Step-by-step explanation:
Working backward, we can find Bob's initial product.
We subtracted 3 to get 1, so we had 4.
We divided by 5 to get 4, so we had 20.
We added 6 to get 20, so we had 14
After Bob multiplied the two numbers together, he had 14. We know that 14 is the product of 2 and 7. The odd number is 7.
Answer two questions about Equations A and B: A=3(x+2)=18 B=x+2=6 1) How can we get Equation B from Equation A? do they have the same solution?
Answer:
see below
Step-by-step explanation:
A:3(x+2)=18
Divide each side by 3
3/3(x+2)=18/3
x+2 = 6
This is the same equation as equation B
They will have the same solution since they are the same equation
x+2-2 = 6-2
x = 4
Answer:
You need to multiply/divide both sides by the same constant- they're both equivalent as well.
Step-by-step explanation:
You need to multiply/divide both sides by the same constant- they're both equivalent as well.
This is because solving it you get this
3(x+2)=18
3(x+2) over 3 = 18/3
x+2=6.
That's dividing by a non-zero constant (3).
Kind of new to this so I hope you can understand my answer-
The equation f = v + at represents the final velocity of an object, f, with an initial velocity, v, and an acceleration rate,
a, over time, t. Which is an equivalent equation solved for a?
O f-v=a
+
o-v=a
t
Of+V = a
o(+va
Answer: [tex]a = \frac{f-v}{t}[/tex]
This can be written as a = (f-v)/t
============================================
Work Shown:
[tex]f = v + at\\\\v + at = f\\\\at = f-v \ \text{ Subtract v from both sides}\\\\a = \frac{f-v}{t} \ \text{ Divide both sides by t}\\\\[/tex]
----------
Note
[tex]a = \frac{f-v}{t}[/tex] is the same as [tex]\frac{f-v}{t} = a[/tex]
Please help I cover the bottom half on purpose please help ASAP 100 points
Answer:
see explanation
Step-by-step explanation:
The first multiplier is the number of terms being added.
The second multiplier is one more than the first multiplier, that is
2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus
2 + 4 + 6 + 8 + 10 = 5 × 6
Answer:
The first multiplier is the number of terms being added.
The second multiplier is one more than the first multiplier, that is
2 + 4 + 6 + 8 + 10 ← has 5 terms being added and 6 is one more than 5, thus
2 + 4 + 6 + 8 + 10 = 5 × 6
What is the distance between the two numbers on this number line? -13 and 28
Answer:
41
Step-by-step explanation:
Points are:
-13 and 28Distance between these points:
28 - (-13) = 28+13 = 41Answer is 41
Answer:
[tex]\Huge \boxed{41}[/tex]
Step-by-step explanation:
Easy way to find the distance between the two numbers is by taking the sum of the absolute values of these numbers.
[tex]|-13| + |28|[/tex]
The absolute value tells the distance of the numbers from zero.
Solving for absolute value.
[tex]13+28[/tex]
Adding the numbers.
[tex]41[/tex]
The distance between -13 and 28 on the number line is 41.
a wall of a building is 36 inches wide. Fourteen inches is concrete 12 inches is brick and 10 inches limestone what fraction of the wall is limestone?
Answer:
10/36 or 5/18 is the fraction of the wall that is limestone. In percentage form it would 27.77..% or could be rounded to 27.8%
vertical translation
please help me on this
Answer:
8in
Step-by-step explanation:
The correct answer is eight inches
Describe the opposite of a positive integer, the opposite of a negative integer, and the opposite of zero.