ANSWER
The exact solution are:
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
EXPLANATION
The given quadratic equation is
[tex] {(5y + 6)}^{2} = 24[/tex]
We use the square root method to solve for y.
We take square root of both sides to get:
[tex] \sqrt{{(5y + 6)}^{2}} = \pm\sqrt{24} [/tex]
This gives us:
[tex]5y + 6 = \pm 2 \sqrt{6} [/tex]
Add -6 to both sides to get:
[tex]5y = - 6 \pm 2 \sqrt{6} [/tex]
Divide through by 5:
[tex]y = \frac{ - 6 \pm2 \sqrt{6} }{5} [/tex]
[tex]y = \frac{ - 6 - 2 \sqrt{6} }{5} \: \: or \: \: y = \frac{ - 6 + 2 \sqrt{6} }{5} [/tex]
when walking home from school during the summer months, Harold buys either an ice-cream or a drink from the corner shop. If Harold bought an ice-cream the previous day, there is a 30% chance that he will buy a drink the next day. If he bought a drink the previous day, there is a 40% chance that he will buy an ice-cream the next day. On Monday, Harold bought an ice-cream. Determine the probability that he buys an ice-cream on Wednesday.
To determine the probability that Harold buys an ice-cream on Wednesday, we consider the probabilities for each day. Given that he bought an ice-cream on Monday, there is a 40% chance that he will buy an ice-cream on Wednesday.
Explanation:To determine the probability that Harold buys an ice-cream on Wednesday, we need to consider the probabilities for each day.
Given that he bought an ice-cream on Monday, there is a 30% chance that he will buy a drink on Tuesday and a 40% chance that he will buy an ice-cream on Tuesday.
Using the probabilities, we can calculate the probability that Harold buys an ice-cream on each day:
Monday: 1 (since he bought an ice-cream)
Tuesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)
Wednesday: 0.4 (40% chance of buying an ice-cream based on previous ice-cream purchase)
How do I do rate of change???
Answer:
12
Step-by-step explanation:
For our problem since we only in 10 am:
I'm going to let x=4 represent the time 10:04 am
which means I'm going to let x=17 represent 10:17am.
So when x=4, y=23 miles and when x=17,y=179 miles.
You have two points.
You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].
Or just line the points up vertically and subtract them vertically, then put 2nd difference over first difference. Like this:
( 17 , 179)
-( 4 , 23)
-----------------------
13 156
So the slope is 156/13=12 miles/hour.
What is the explicit formula for this sequence?
2, 10, 50,250, 1250....
Answer:
Explicit formula is 2(5)^(n-1).
Step-by-step explanation:
This is a Geometric Sequence with common ratio 10/2 = 50/10 = 250/50 = 5.
The nth term an = a1 r^(n - 1)
= 2(5)^(n-1).
Formula for sequence tells about getting its specific term by putting its index. The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]
What is a geometric sequence and how to find its nth terms?There are three parameters which differentiate between which geometric sequence we're talking about.
The first parameter is the initial value of the sequence.
The second parameter is the quantity by which we multiply previous term to get the next term.
The third parameter is the length of the sequence. It can be finite or infinite.
Suppose the initial term of a geometric sequence is [tex]a[/tex] and the term by which we multiply the previous term to get the next term is [tex]d[/tex]
Then the sequence would look like
[tex]a, ad, ad^2, ad^3, ad^4,...[/tex] (till the terms to which it is defined)
Thus, the nth term of such sequence would be
[tex]T_n = ad^{n-1}[/tex]
For the given sequence, it can be seen that each previous term is multiplied by 5 to get the next term to that term.
Like, we got
[tex]10 = 2 \times 5\\50 = 10 \times 5[/tex] and so on.
This shows that there is single constant used which is multiplied to previous terms to get the next term. This is the property of a geometric sequence. Here, we got
[tex]a = 2\\d = 5[/tex]
Thus, sequence is
[tex]a, ad, ad^2, ad^3, ...\\\\or\\\\2, 2\times 5, 2 \times 5^2, 2 \times 5^3 ...\\\\or\\2, 10, 50, 250, 1250,...[/tex]
Its nth term is given as: [tex]T_n = ad^{n-1} = 2(5)^{n-1}[/tex]
A sequence with n terms, and its nth term formula being [tex]a_n[/tex] is written as [tex]\{a_i\}_{i=1}^n[/tex] (showing that put i = 1, 2, ... n) to get its terms.
Here, sequence is not limited, so infinite terms.
or, we get the formula for the sequence as: [tex]\{a_i\}_{i=1}^n = \{2(5)^{i-1}\}_{i=1}^\infty[/tex]
Thus, The formula for considered sequence is [tex]\{2(5)^{i-1}\}_{i=1}^\infty[/tex]
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Solve the system using Elimination
2x +6y=-12
5x-5y=10
A) 2,1
B) 0,-2
C) -2,0
D) 1,2
Answer:
B) 0,-2 (x = 0 , y = -2)
Step-by-step explanation by elimination:
Solve the following system:
{2 x + 6 y = -12 | (equation 1)
{5 x - 5 y = 10 | (equation 2)
Swap equation 1 with equation 2:
{5 x - 5 y = 10 | (equation 1)
{2 x + 6 y = -12 | (equation 2)
Subtract 2/5 × (equation 1) from equation 2:
{5 x - 5 y = 10 | (equation 1)
{0 x+8 y = -16 | (equation 2)
Divide equation 1 by 5:
{x - y = 2 | (equation 1)
{0 x+8 y = -16 | (equation 2)
Divide equation 2 by 8:
{x - y = 2 | (equation 1)
{0 x+y = -2 | (equation 2)
Add equation 2 to equation 1:
{x+0 y = 0 | (equation 1)
{0 x+y = -2 | (equation 2)
Collect results:
Answer: {x = 0 , y = -2
{c, f , j, k}={j, k, f , c }
Answer:
True.
Step-by-step explanation:
These are sets containing the same exact elements so they are the same set of elements.
They both contain 4 elements.
The 4 elements in each are c, f , j , and k.
It matters not of the arrangement. It also doesn't matter if they repeat an element.
For example these sets are also the same:
{a,a,b} and {a,b}.
They both contain 2 elements and those elements are a and b.
People don't normally write something like {a,a,b} because it is redundant (because of the repetition of a).
Here is an example of some sets that are equal:
{1,2,3}={1,3,2}={2,1,3}={2,3,1}={3,1,2}={3,2,1}.
These are all the same because they all contain the elements: 1 , 2 , and 3. It doesn't matter the order in a set.
What is the cube root of 512m12n15
Could anyone plz help me?
Answer:
[tex]8m^4n^5[/tex]
Step-by-step explanation:
cube root is basically taking to the power of [tex]\frac{1}{3}[/tex]
Also, there is a property that is [tex](x^m)^n=x^{mn}[/tex]
We can use these and find the cube root of the expression:
[tex](512m^{12}n^{15})^{\frac{1}{3}}\\=(512)^{\frac{1}{3}}*(m^{12})^{\frac{1}{3}}*(n^{15})^{\frac{1}{3}}\\=8*m^{\frac{12}{3}}*n^{\frac{15}{3}}\\=8*m^4 * n^5[/tex]
Thus, third answer chioce is right.
Answer:
C. 8m^4n^5[/tex]
Step-by-step explanation:
We are given [tex]\sqrt[3]{512m^{12}n^{15} }[/tex]
The cube root is nothing but the power of [tex]\frac{1}{3}[/tex]
Now we have to write 512 as the power 3.
512 = 8.8.8 = [tex]8^{3}[/tex]
So, [tex]\sqrt[3]{512m^{12}n^{15} }[/tex] = [tex](8^{3}.m^{12}.n^{15}) ^{\frac{1}{3}}[/tex]
We know that the exponent property: [tex](a^{m} )^n= a^{mn}[/tex]
Using this property, we can simplify the exponents.
= [tex]8.m^{4} .n^5 = 8m^4n^5[/tex]
If a rectangle is not a square, what is the greatest number of lines of symmetry that can be drawn
Answer:
B
Step-by-step explanation:
what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry
Answer:
B) 2
Step-by-step explanation:
Given that a rectangle is not a square.
Hence we find that opposite sides are equal.
If we mark midpoints on all sides then the vertical line joining mid points and horizontal lines joining next pair of midpoint of opposite sides are the lines of symmetry
There can be no other line of symmetry
Hence no of lines of symmetry for a rectangle = 2
What is the cube root of -729a^9b^6?
A. -9a^3b^2
B. -9a^2b^3
C. -8a^3b^2
D. -8a^2b^3
Answer:
[tex]\large\boxed{A.\ -9a^3b^2}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{-729a^9b^6}\qquad\text{use}\ \sqrt[n]{xy}=\sqrt[n]{x}\cdot\sqrt[n]{y}\\\\=\sqrt[3]{-729}\cdot\sqrt[3]{a^9}\cdot\sqrt[3]{b^6}\\\\=-9\cdot\sqrt[3]{a^{(3)(3)}}\cdot\sqrt[3]{b^{(2)(3)}}\qquad\text{use}\ (x^n)^m=x^{nm}\\\\=-9\cdot\sqrt[3]{(a^3)^3}\cdot\sqrt[3]{(b^2)^3}\qquad\text{use}\ \sqrt[3]{x^3}=x\\\\=-9a^3b^2[/tex]
Answer: A
Step-by-step explanation:
-9•9•9= -729a 9/3= 3
6/3=b^ 2
Given:
BC⊥AC
m∠BAC = 32°
Use the given information to determine m∠CDE.
32°
58°
68°
90°
Answer: 32°
Step-by-step explanation:
m∠BAC = m∠CDE, therefore m∠CDE = 32°
Answer:
Option B, 58°
Step-by-step explanation:
In the given figure AB ║ CD and BC ║ DE ( given )
Since BC ║ DE and BC ⊥ AC
So DE will also be perpendicular to CE
m ∠ BAC = 32° [given]
Since AB ║ CD and line AE is transverse
Then ∠BAC ≅ ∠DCE ≅ 32°
Now in ΔDEC.
∠DCE + ∠CED + ∠EDC = 180°
32° + 90° + ∠EDC = 180°
122° + ∠EDC = 180°
∠EDC = 180 -122
= 58°
Option B, 58° is the answer.
If fx) - 3x2 and g(x) - 4x + 1, what is the degree of (fºg)(x)?
оооо
Answer:
The degree is 2.
Step-by-step explanation:
We are given f(x)=-3x^2 and g(x)=-4x+1.
(f o g)(x)
f(g(x))
f(-4x+1)
This means the old x in f will be replaced with -4x+1 like so:
-3(-4x+1)^2
-3(-4x+1)(-4x+1)
Use foil!
-3(16x^2-4x-4x+1)
-3(16x^2-8x+1)
-48x^2+24x-3
The degree is 2. The degree is the highest exponent on the variable if you only have one variable and your polynomial is written in standard form.
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?
O f(x) = -x2 - 8x – 16
O f(x) = -x2 + 8x – 16
o f(x) = -x2 – 8x + 16
Of(x) = _x2 + 8x + 16
Answer:
[tex]f(x)=-x^{2} +8x-16[/tex]
Step-by-step explanation:
we know that
A polynomial function that has a leading coefficient of -1 and root 4 with multiplicity 2 is equal to
[tex]f(x)=-(x-4)^{2}[/tex]
Expand the function
[tex]f(x)=-(x^{2}-8x+16)\\ \\f(x)=-x^{2} +8x-16[/tex]
Answer: B
Step-by-step explanation:
If the measure of arc XY plus the measure of arc YZX equals 360°, and the
arcs do not overlap, then the arcs form a _
A. square
B. polygon
C. circle
D. parallelogram
Answer:
The arcs form a circle ⇒ answer C
Step-by-step explanation:
* Lets explain some facts in the circle
- The chord in a circle is a segment whose endpoints lie on the circle
- Any chord of a circle intersects it into 2 arcs
- The minor arc which its measure lies between 0° and 180°
-The major arc which its measure lies between 180° and 360°
- The sum of the measures of the minor arc and the major arc is equal
to the measure of the circle
- The measure of the circle is 360°
* Lets solve the problem
∵ The measure of arc XY + the measure of arc YZX = 360°
∵ The arcs do not overlap
- That means the endpoints of the arcs are X and y
∵ The measure of the circle is 180°
∴ The arcs form a circle
Answer:circle
Step-by-step explanation:
im lookin it on a question rn
The variable z is inversely proportional to x. When x is 12, z has the value 1.5833333333333. What is the value of z when x= 18?
Answer:
Z=1.055
Step-by-step explanation:
Z is inversely proportional to X: [tex]Z=\frac{K}{X}[/tex] Where K is a constant
X=18, Z=1.583333333333 we can find K value
K=Z*X =1.58333333333*12= 19
So, Using X=18 We have the following
[tex]Z=\frac{19}{18}[/tex]= 1.055
Find the area of triangle ABC.
A = 34.5°, b = 13.2 in., c = 5.3 in.
Answer:
=19.81 in²
Step-by-step explanation:
We use the sine formula to find the area of the triangle in question.
In this formula we find the product of two adjoined sides with the sine of the angle between them.
The sides b and c are bound by the angle A.
Therefore area=1/2bcSin A
A=1/2×13.2 in×5.3 in× Sin 34.5
=19.81 in²
Answer:19.812
Step-by-step explanation:
Given
angle A=34.5
b=13.2 in.
c=5.3 in.
Area of triangle when two sides and angle between them is given
[tex]A=\frac{1}{2}bcsina[/tex]
[tex]A=\frac{1}{2}\left ( 13.2\right )\left ( 5.3\right )sin\left ( 34.5\right )[/tex]
[tex]A=19.812 in.^2[/tex]
Which Platonic solid has twenty faces that are equilateral triangles?
Answer:
Icosahedron
Step-by-step explanation:
Icosahedron has 20 faces and all the faces are equilateral triangle. Also the faces are congruent and the Icosahedron is one of the five Platonic solids.
Icosahedron has twenty faces that are equilateral triangles.
What is Icosahedron?Icosahedron is one of the 5 Platonic solid which has 20 faces, 12 vertices, 30 edges.
All the faces of Icosahedron is an equilateral triangle at each vertex. also all the faces are congruent and are of the same size.
From the picture given below, it is also clear that
Icosahedron has twenty faces that are equilateral triangles.
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Factor the expression.
15n−18
Enter your answers in the boxes to complete the factored expression.
(
n − 6)
Answer:
3(5n -6)
Step-by-step explanation:
15n -18
Both 15 and 18 can be divided by 3
Factor out a 3
3(5n -6)
Anwser
3(5n -6)
Step-by-step explanation:
15n -18
Both 15 and 18 can be divided by 3
Factor out a 3
3(5n -6)
The slope of a given line is -2. What is the slope of a line that is parallel to the given line?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given the slope of a line m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
A school sells pencils to student for 25 cents each.If a student has $5, how many pencils can the student buy?
With $5 and pencils priced at 25 cents each, the student can buy 20 pencils. This is obtained by dividing $5 by $0.25 (the cost of one pencil).
Let's break down the calculation step-by-step:
Identify the given information.
The student has $5 to spend.
Each pencil costs 25 cents, which is equivalent to $0.25.
Set up the formula for the number of pencils.
Number of pencils = Total money / Cost per pencil
Substitute the given values into the formula.
Number of pencils = $5 / $0.25
Simplify the expression.
Dividing $5 by $0.25 is the same as multiplying $5 by the reciprocal of $0.25, which is 4.
Number of pencils = 5 * 4
Calculate the result.
Number of pencils = 20
So, the student can buy 20 pencils with $5.
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Solve
-10 + 3x + 5 = 18 - 2
Answer:
x = 7
Step-by-step explanation:
-10 + 5 + 3x = 16
-5 + 3x = 16
3x = 21
x = 7
How many degrees is angle b?
Answer:
b =45
Step-by-step explanation:
A full circle is 360 degrees
b+315 = 360
Subtract 315 from each side
b+315-315 = 360-315
b =45
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the expression below.
(- 6)(x+ 2)
For (x - 6)(x + 2) to equal ,either (X - 6) or (x+2) must equal____
The values of x that would result in the given expression being equal to 0, in order from least to greatest___are
and____
The values of x that make the expression (x - 6)(x + 2) equal to zero are -2 and 6. This is based on the Zero Product Property in Mathematics, which states that if the product of two factors is zero, then at least one of the factors must equal zero.
Explanation:In Mathematics, the Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Applying this property in the expression (x - 6)(x + 2) = 0, one can conclude that either (x - 6) = 0 or (x + 2) = 0.
The expression (x−6)(x+2) equals 0 when either (x−6)=0 or (x+2)=0. Solving each equation separately:
For (x−6)=0, add 6 to both sides to get x=6.
For (x+2)=0, subtract 2 from both sides to get x=−2.
So, the values of x that make (x−6)(x+2)=0 are x=−2 and x=6.
Solving both equations, we get two possible solutions, x = 6 or x = -2. So, the values of x that would result in the expression being equal to zero are -2 and 6, listed in order from least to greatest.
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What is the sum of the angle measures of 24 - gon
[tex]\bf \textit{sum of all \underline{interior angles} in a polygon}\\\\ S=180(n-2)~~ \begin{cases} n=\textit{number of sides}\\ \cline{1-1} n=24 \end{cases}\implies \begin{array}{llll} S=180(24-2)\\\\ S=3960 \end{array}[/tex]
What is the slope of a line perpendicular to line A?
Answer:
-7/4
Step-by-step explanation:
Line A is the blue one.
I see two points they have identified for me:
(-7,0) and (0,4).
To find the slope of the line A given two points we could use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
We could also line up the points vertically and subtract, then put 2nd difference over 1st difference.
Like this:
(-7,0)
-(0,4)
-------
-7 -4
So the slope is -4/-7=4/7
So the slope of a line that is perpendicular will have opposite reciprocal slope. That is the opposite reciprocal of 4/7 is -7/4.
Therefore the slope of a line that is perpendicular to A will have slope -7/4.
Answer:
[tex] - \frac{7}{4} [/tex]
Step-by-step explanation:
We use the slope formula to fine the slope of line A.
[tex] m = \frac{y_2-y_1}{x_2-x_1} [/tex]
Line A passes through (-7,0) and (0,4)
[tex]m = \frac{4 - 0}{0 - - 7} [/tex]
[tex]m = \frac{4}{7} [/tex]
The slope of a line that is perpendicular to line A is the negative reciprocal of the slope of line A
[tex] - \frac{7}{4} [/tex]
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function? (x – 11)2 + 58 (x + 22)2 – 121 (x + 7)2 – 47 (x – 15)2 + 94
Answer:
Option C is correct.
Step-by-step explanation:
The given function f(x) is:
f(x) = x^2 + 22x + 58
To find the vertex find [tex](\frac{-b}{2a} )^2[/tex] and add and subtract it from both sides of the given function
b= 22, a= 1
Putting values:
[tex](\frac{-b}{2a} )^2 = (\frac{-22}{2(1)})^2\\=(\frac{-22}{2})^2\\= (-11)^2\\=11^2[/tex]
Adding (11)^2 on both sides
f(x) = x^2 + 22x + 58 +(11)^2 -(11)^2
f(x) = x^2+22x+(11)^2 +58-(11)^2
a^2 +2ab+b^2 = (a+b)^2 Using this formula:
f(x)=(x+11)^2+58-121
f(x)=(x+11)^2-63
The vertex of the given function is (-11,-63)
The function is translated 4 units to right and 16 units up
The vertex of new function will be:
(x+4,y+16) => (-11+4,-63+16)
=> (-7,-47)
So, the vertex of new function is (-7,-47)
The function will be
(x+7)^2 -47
So, Option C is correct.
Answer:
C
Step-by-step explanation:
What is the value of f-1(3)
Answer: C.
Step-by-step explanation:
The value of inverse function f⁻¹(3) is 13, option (D) is correct.
What is function?Function is a combination of different types of variable and constants.
A function is generally denoted by f(x).
The given function is,
f(x) = (2x+1)/(x-4)
To find the value of f⁻¹(3),
Let f⁻¹(3) = y
⇒3 = f(y)
⇒3 = (2y+1)/y-4
⇒3(y-4) = 2y+1
⇒3y-12 = 2y+1
⇒ y = 13
⇒ f⁻¹(3) = 13
Therefore, the value of f⁻¹(3) is 13.
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I WILL GIVE BRAINLIST if I get enough answers how do i find the radius someone help me please
Answer:
r=7
Step-by-step explanation:
We have the equation
(x+5)^2 + (y+8)^2 =
We know that this is equal to the radius squares
(2+5)^2 + (-8+8)^2 = r^2
We know a point on the circle (2,-8)
Substitute this point into the equation
(2+5)^2 + (-8+8)^2 = r^2
(7)^2 + (0)^2 = r^2
7^2 = r^2
The radius is equal to 7
What is the length of EF in the right triangle below?
Answer:
F 24
Step-by-step explanation:
This is a right triangle, so we can use the Pythagorean theorem
a^2 +b^2 = c^2 where a and b are the legs and c is the hypotenuse
10^2 + EF^2 = 26^2
100 + EF^2 = 676
Subtract 100 from each side
100-100 + EF^2 = 676-100
EF^2 = 576
Take the square root of each side
sqrt(EF^2) = sqrt(576)
EF = 24
Answer:
F 24
Step-by-step explanation:
You have to use the Pythagorean Theorem
a²+b²=c²
(a and b are the legs of the triangle and c is always the hypotenuse)
a²+10²=26²
a²+100=676; now isolate the a² by subtracting 100 from both sides.
a²=576; now square root each side (gets rid of the squared)
a=24
Which formula would be used to find the measure of
angle 1?
1/2 (aº + bº).
1/2(a-cº).
1/2 (b° +cº).
1/2(aº – bº).
Check the picture below.
The formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
To get the measure of angle 1, the circle theorem below will be used as shown:
The angle at the vertex of the circle is equal to half of the difference of the intercepted arc.
Angle at the vertex = m<1 Angles at the intercepted arc ar m<a and m<bThe formula that would be used to find the measure of angle 1 will be
m<1 =12(a - b)
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Going into the final exam, which will count as two tests, Brooke has test scores of 75, 82, 70, 65, and 90. What score does Brooke need on the final in order to have an
average score of 80?
If tan0=-3/4 and 0 is in quadrant IV, cos20= (33/25, -17/25, 32/25, 7/25, 24/25?) and tan20= (24/7, -24/7, 7/25, -7/25, 13/7, -13/7?) PLEASE HELP. More information in the picture
Answer:
cos(2θ) = 7/25tan(2θ) = -24/7Step-by-step explanation:
Sometimes, it is easiest to let a calculator do the work. (See below)
__
The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.
You can also use the identities ...
cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)
cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)
cos(2θ) = 7/25
__
tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)
tan(2θ) = -24/7
Answer: tan(2θ) = -24/7
Step-by-step explanation: N/A