Answer:
4112
Step-by-step explanation:
When you plug in 3 for x you get 6.
Then you just do 4^6 which is 4096.
Then add 16 which gets you 4112.
write 3 ratios equivalent to 2:5. Show your work
Answer: 4/10, 6/15, 8/20
Hope this helps!
How would i kill a snake with fractions? it's on my homework question... i dont get it at all
Just me:
? I will just explain what I understand
Answer:
(Think hard) If you cut a snake in half you get 1/2 but if you cut it into 4's 1/5
I tried.
Find the missing length indicated.
The missing length of given right triangle is equal to 1500.
RIGHT TRIANGLEA triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: [tex]hypotenuse^2=(leg_1)^2+(leg_2)^2[/tex] . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse} \\ \\ tan (x)= \frac{opposite\ side}{adjacent\ side}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
Thus, if h²=m*n. You can write:
h²=900*1600
[tex]h=\sqrt{1440000}\\ \\ h=1200[/tex]
If h=1200, you can find x from Pythagorean Theorem.
x²=1200²+900²
x²=1440000+810000
x²=2250000
x=[tex]\sqrt{2250000}[/tex]
x=1500
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x² + y² if x = 7 and y = 5. What is the solution to this??
Step-by-step explanation:
x = 7
y = 5
[tex] = {x}^{2} + {y}^{2} [/tex]
[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]
= 7 × 7 + 5 × 5
[tex] = 49 + 25 [/tex]
[tex] = 74[/tex]
Hey there!
x^2 + y^2
= 7^2 + 5^2
= 7 * 7 + 5 * 5
= 49 + 25
= 74
Therefore, your answer should be: 74
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
can someone help me really quick
Answer:
-6
Step-by-step explanation:
Additive inverse is the number that when added to A gives a result of zero
A + inverse = 0
6 + inverse = 0
inverse = -6
5. Find the arc length on a circle with radius of 19 feet created by
an angle of 2(pie)/3radians.
19T
O
38
38T
O 19
O None of the above
**Disclaimer** Hi there! I am not fully sure what [ T ] represents. From the answer that I got [ 38π / 3 ], it does not match any one of them, so I choose none of the above. If there's a specific meaning of [ T ] and I am incorrect, please let me know and I will modify my answer.
Answer: None of above
Step-by-step explanation:
Given formula
S = r θ
S = arc lengthr = radiusθ = angle in radiansGiven information
radius = 19 ft
Angle = 2π / 3
Substitute values into the formula
S = r θ
S = (19) (2π / 3)
Simplify by multiplication
[tex]\Large\boxed{S=\frac{38\pi}{3} }[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to tariqareesha2, tysm for the help!
Please help answer my questions like these I have many more quick algebra 1 questions that are all due in 2 days so it would be much appreciated if you check them out. Once again, tysm!
Answer:
its the 4th one i think
Step-by-step explanation:
Find the term that must be added to the equation x2 4x=1 to make it into a perfect square.
The term that must be added to the equation x2+4x=1 to make it into a perfect square is 4.
What is Quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. Since there is no ax2 term, the equation is linear if a = 0, not quadratic.
Why is it called a quadratic equation?This is true because the Latin word quadratum, which means "square," plus the fact that the area of a square with side length x is equal to x2, make up what is known as the quadratic (or "square-like") definition of a polynomial equation with exponent two.
According to the given information:x²+4x=1
as, the x has coefficient 4.
so,
half the coefficient of x and add and subtract the square of the remaining.
x²+4x + 2 ² - 2² =1
Now,
make the whole square term
x²+4x + 2 ² - 4 - 1=0
( x + 2)² -5= 0
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Which value of y completes the proportion?
18/27 = 2/y
A. 1
B. 2
C. 3
D. 9
I picked c.) 3 am I right?
Answer:
c. 3
yes you are right, good job!!
Step-by-step explanation:
18 divided by what equals 2?
18 / 2 = 9 so 18 / 9 = 2
so 27 / 9 = y which y = 3
check: 9 x 3 = 27
Answer:
Yes, C
Step-by-step explanation:
18/2 = 9 so you need to divide 27 by 9 to get 3
Find the equation of the linear function represented by the table below in slope-intercept form.
x 0 1 2 3 4
y 7 15 23 31 39
Answer:
y = 8x+7
Step-by-step explanation:
firstly reduce the equation to an arithmetic series starting from the 0th term so:
7, 15, 23, 31, 39....
Secondly, identify the common difference: 8
we now know that the answer must contain 8x
Thirdly, form the equation 8x + c = y where y is a constant. Afterwards insert the values of any given x and y so:
8*0 + c = 7
c = 7
Thusly we now know that the series and thus equation is 8x+7 = y
Answer:
y = 8x + 7
Step-by-step explanation:
the equation of a linear function in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1,15) and (x₂, y₂ ) = (2, 23) ← 2 ordered pairs from the table
m = [tex]\frac{23-15}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
the ordered pair (0, 7 ) indicates c = 7
y = 8x + 7 ← equation of linear function
The equation for least regression line to this data set is ŷ = 76. 82x 88. 56. what is the predicted value (in dollars) for maintenance expenses when a truck is 7 years old?
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
In this question,
The equation for least regression line to this data set is
y' = 76.82x + 88.56 ------- (1)
Number of years, x = 7
The general form of equation for least regression line is
y' = a + bx
where y is the dependent variable, x is the independent variable, a is the intercept of regression line and b is the slope of regression line.
The predicted value (in dollars) for maintenance expenses when a truck is 7 years old can be calculated as
y' = 76.82x + 88.56
Substitute the value of x in the above equation, we get
y' = 76.82(7) + 88.56
y' = 537.74 + 88.56
y' = 626.3
Hence we can conclude that the predicted value (in dollars) for maintenance expenses when a truck is 7 years old is $626.3.
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A central role of members at this time is to recognize and deal with the many forms of?
Answer:
Resistance
Step-by-step explanation:
Question 2 (Essay Worth 10 points)
(08.02 MC)
A pair of equations is shown below:
y = 7x − 9
y = 3x − 1
Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points)
Part B: What is the solution to the pair of equations? (4 points)
Answer:
Step-by-step explanation:
part A: when you graph both y=7x-9 and y=3x-1 the two lines will intersect this is how you solve the graphing part of the system of equations.
Both of these lines are in slope form (y=mx+b) where m is the slope which is 7 and 3 and b is the y-intercept which is -1 and -9.
part B
7x-9=3x-1
subtract 3x from both sides
4x-9=-1
add 9 to both sides
4x=8
divide both sides by 4
x=2,
making y=3x-1 become:
y=3(2)-1=6-1=5,
the answer is (2,5)
A rental car company is running two specials. Customers can pay $50 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $40 the first day and $8 for every additional day beyond that. Camilla notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Camilla pay in total?
The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.
EquationCompact car:
Fixed price = $50Additional price per day = $6y = 50 + 6x
Another special:
Fixed price = $40Additional price per day = $8y = 40 + 8x
let
x = number of additional days
50 + 6x = 40 + 8x
collect like terms50 - 40 = 8x - 6x
10 = 2x
Divide both sides by 2x = 10/2
x = 5 days
Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.
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One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. which statements about the two rectangular solids are true? check all that apply.
The correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.What are solids?Solid geometry or stereometry is the standard name for the geometry of three-dimensional Euclidean spaces in mathematics. Stereometry is concerned with the volume measurements of various solid forms, such as pyramids, prisms, and other polyhedrons; cylinders; cones; truncated cones, and balls bordered by spheres.To find which statements are correct:
Congruent base: This is used to indicate that the triangles' bases are the same and that they have the same shape.
The volume of the first triangle is: [tex]2x^{2} h[/tex]
The volume of the second triangle is: [tex]x^{2} h[/tex]
Therefore, the correct statements about the solids are:
(A) The bases are congruent.(D)The volume of the first solid is twice as much as the volume of the second solid.(E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more.Know more about solids here:
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The complete question is given below:
One rectangular solid with a square base has twice the height of another rectangular solid with a square base with the same side length. Which statements about the two rectangular solids are true? Check all that apply.
A) The bases are congruent.
B) The solids are similar.
C) The ratio of the volumes of the first solid to the second solid is 8:1.
D)The volume of the first solid is twice as much as the volume of the second solid.
E) If the dimensions of the second solid are x by x by h, the first solid has 4xh more
surface area than the second solid.
PLS HELP ASAP! Ty
Let g(x)= 2x^2+3x-9 and h(x)=x^2+2x-6
Find (h-g)(2.1)
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve ~
[tex]\qquad \sf \dashrightarrow \: (h - g)(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: h(x) - g(x) [/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - (2 {x}^{2} + 3x - 9)[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + 2x - 6 - 2 {x}^{2} - 3x + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} - 2 {x}^{2} + 2x - 3x - 6 + 9[/tex]
[tex]\qquad \sf \dashrightarrow \: - {x}^{2} - x + 3[/tex]
For, (h - g)(2.1), put x = 2.1
[tex]\qquad \sf \dashrightarrow \: - {(2.1)}^{2} - (2.1) + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 4.41 - 2.1 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 6.51 + 3[/tex]
[tex]\qquad \sf \dashrightarrow \: - 3.51[/tex]
A Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. Which Equations Can Be Used To Find The Numbers Of Miles Driven For A Truck That Cost A Total Of $42.50 To Rent For One Day?
A)$25m + 0.35m = $42.50
B)$0.35 + $25m = $42.50
C)$42.50 + $0.35m = $25
D)$0.35 = $42.50
The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
According to the statement
we have given that the Rental Truck Is Company Charges $25 Per Day Plus A Fee Of $0.35 For Every Mile (m) Driven. and a Truck That Cost A Total Of $42.50 To Rent For One Day.
And we have to find the equation for this.
So, for given purpose,
we know that the A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.
And from the given values the equation formed that the
In the equation the charges per mile is added to the original charges is equal to the total charges per day.
So, The equation become
$25m + 0.35m = $42.50
And by this equation we represent the all given conditions related charges.
So, The Option A is correct. The Numbers of Miles Driven for A Truck That Cost a Total Of $42.50 To Rent for One Day $25m + 0.35m = $42.50
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The two lines y = 2x + 8 and y = 2x - 12 intersect the x-axis at the P and Q.
Work out the distance PQ.
Answer:
PQ = 10 units
Step-by-step explanation:
to find where the lines cross the x- axis let y = 0 and solve for x , that is
2x + 8 = 0 ( subtract 8 from both sides )
2x = - 8 ( divide both sides by 2 )
x = - 4 ← point P
and
2x - 12 = 0 ( add 12 to both sides )
2x = 12 ( divide both sides by 2 )
x = 6 ← point Q
the lines cross the x- axis at x = - 4 and x = 6
using the absolute value of the difference , then
PQ = | - 4 - 6 | = | - 10 | = 10 units
or
PQ = | 6 - (- 4) | = | 6 + 4 | = | 10 | = 10 units
Answer: [tex]\Huge\boxed{Distance=10~units}[/tex]
Step-by-step explanation:
Find the point PGiven expression
y = 2x + 8
Substitute 0 for the y value to find the x value
This is the definition of x-intercepts
(0) = 2x + 8
Subtract 8 on both sides
0 - 8 = 2x + 8 - 8
-8 = 2x
Divide 2 on both sides
-8 / 2 = 2x / 2
x = -4
[tex]\large\boxed{P~(-4,0)}[/tex]
Find the point QGiven expression
y = 2x - 12
Substitute 0 for the y value to find the x value
(0) = 2x - 12
Add 12 on both sides
0 + 12 = 2x - 12 + 12
12 = 2x
Divide 2 on both sides
12 / 2 = 2x / 2
x = 6
[tex]\large\boxed{Q~(6,0)}[/tex]
Find the distance between PQGiven information
[tex](x_1,~y_1)=(-4,~0)[/tex]
[tex](x_2,~y_2)=(6,~0)[/tex]
Substitute values into the distance formula
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]Distance=\sqrt{(6-(-4))^2+(0-0)^2}[/tex]
Simplify values in the parenthesis
[tex]Distance=\sqrt{(10)^2+(0)^2}[/tex]
Simplify values in the radical sign
[tex]Distance=\sqrt{100}[/tex]
[tex]\Huge\boxed{Distance=10~units}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Use the recursive formula to find the first five terms in the arithmetic sequence.
The first five terms of the given arithmetic sequence are:
54, 45, 36, 27, 18 (First option)
The arithmetic sequence is given as follows,
f(n) = f(n-1) - 9 ............ (1)
Also, f(1) = 54 .............. (2)
Now, for finding the first five term of this arithmetic sequence, we will substitute n as 1, 2, 3, 4, and 5 one by one. Using the above formula for the arithmetic sequence, we can deduce the first five terms.
f(1) is the first term of the sequence which is already provided as 54.
Now, putting n=2 in equation (1), we get,
f(2) = f(2-1) - 9
f(2) = f(1) - 9
Substitute f(1) = 54 from equation (2)
⇒ f(2) = 54 - 9
f(2) = 45
To find the third term of the arithmetic sequence, put n = 3 in equation (1)
f(3) = f(3-1) - 9
f(3) = f(2) - 9
⇒ f(3) = 45 - 9
f(3) = 36
Similarly, we can find the fourth and fifth terms of the arithmetic sequence by substituting n = 4 and n = 5 respectively.
∴ f(4) = f(3) - 9
⇒ f(4) = 36 - 9
f(4) = 27
Likewise, f(5) = f(4) - 9
⇒f(5) = 27 - 9
f(5) = 18
Thus, using the recursive formula, the first five terms of the arithmetic sequence are deduced to be:
54, 45, 36, 27, 18
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PLEASE HELP its math
Answer:
y = 3x + 6
Step-by-step explanation:
We are given a line.
We know this line is parallel to the line y=3x+2, and passes through (1, 9).
We want find the equation of this line.
Parallel lines have the same slopes.
So, let's find the slope of y=3x+2.
The line is written the format y=mx+b, where m is the slope and b is the value of y at the y intercept.
As 3 is in the place of where m (the slope) is, the slope of the line is 3.
It is also the slope of the line parallel to it.
We should write the equation of the line parallel y=3x+2 in slope-intercept form as well, however, before we do that, we can write the line in point-slope form, and then convert it to slope-intercept form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1,y_1)[/tex] is a point.
We can substitute 3 as m in the formula, as we know that is the slope of the line
[tex]y-y_1=3(x-x_1)[/tex]
Recall that we were given the point (1, 9), which also belongs to (it passes through) the line.
Therefore, we can use its values in the formula.
Substitute 1 as [tex]x_1[/tex] and 9 as [tex]y_1[/tex].
y - 9 = 3(x-1)
We can now convert the equation into slope intercept form.
Notice how y is by itself in slope-intercept form; this means we'll need to solve the equation for y.
Start by distributing 3 to both x and -1.
y - 9 = 3x - 3
Now add 9 to both sides.
y = 3x + 6
NEED HELP ASAP. :)))
The difference in mail handled between 195 and 1965 is -5.4 x 10
What is the difference in mail handled?The data on the pieces of mail handled by the United States Postal Service is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.
In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100
Difference in mail handled = mail handled in 1995 - mail handled in 1965
(1.8 x [tex]10^{11}[/tex]) - (7.2 x [tex]10^{10}[/tex])
(1.8 - 7.2) x [tex]10^{11 - 10}[/tex]
-5.4 x 10
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1 of 2. Very much apprexiated
Answer:x=5
Step-by-step explanation: 73+73+6x+4=180
150+6x=180
6x=30
x=5
If g(x)=-2x), which graph is the graph of function g?
Answer:
The graph of g(x) has a y-intercept at (0,0) and a slope of -2.
which number best represents the scope of the graphed line? a. -5 b. -1/5 c. 1/5 d.5
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
According to the given statement
we have given data set and we have to find the five number summary.
So, For this purpose,
the given data set is:
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Firstly we have to find the upper quartile means median for it.
So, Median = n /2
median = 12/2
median = 6th term.
So, Upper quartile range for this data set is 63.
And
Lower quartile for data set is the lower value of the data set.
So, That's why
Lower quartile range for this data set is 48.
And now, we have to find the Interquartile range
so, Interquartile range means maximum value of data.
So, That's why
Interquartile range of this data is 80.
So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
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10 points please help and marked brainlyist
Answer:
A.
Sample 1 mean: 6.375
Sample 2 mean: 6.375
Sample 3 mean: 6.625
B.
Range of sample means: 0.25
C.
The first and last boxes should be checked, as they are true.
Step-by-step explanation:
To calculate the mean you must add all of the numbers together and then divide the sum by the quantity of numbers. Ex: 3+7+8+3+7+9+6+8 = 51.
51/8 = 6.375.
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
I need to know how to solve it
The solution to the system of equations is x = 1, y = 10 and z = 4
How to solve the system of equations?The system of equations is given as:
3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
Multiply the second equation by 2
So, we have
4x - 2y + 6z = 8
Add this equation to the first equation
3x + 4x + 2y - 2y + 4z + 6z = 11 + 8
Evaluate the like terms
7x + 10z = 19
Multiply the second equation by 3
So, we have
6x - 3y + 9z = 12
Subtract this equation from the third equation
6x - 5x - 3y + 3y + 9z - 5z = 12 + 1
Evaluate the like terms
x + 4z = 13
Make x the subject
x = 13 - 4z
Substitute x = 13 - 4z in 7x + 10z = 19
7(13 - 4z) + 10z = 19
Expand
91 - 28z + 10z = 19
Evaluate the like terms
-18z = -72
Divide
z = 4
Substitute z = 4 in x = 13 - 4z
x = 13 - 4 * 4
Evaluate
x = 1
We have:
2x -y +3z = 4
This gives
2(1) - y + 3 * 4 = 4
Evaluate
2 - y + 12 = 4
This gives
y = 10
Hence, the solution to the system of equations is x = 1, y = 10 and z = 4
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graph the linear equation by plotting three points. 2y=-3+2
Answer:
Step-by-step explanation:
Convert 2y=-3x+2 into y=mx+b form
[tex]\frac{2y}{2} =\frac{-3x+2}{2}[/tex]
[tex]y=\frac{-3x}{2} +1[/tex]
Y intercept is 1, slope is -3/2
Graph looks like this:
I need help with this
Answer:
s = -24
Step-by-step explanation:
This is a 2-step linear equation, so can be solved the way all 2-step equations are solved.
SolutionStep 1
Identify the constant term on the side of the equation with the variable term, and add its opposite to both sides.
[tex]7 = \dfrac{1}{6}s+11\qquad\text{given}\\\\7-11=\dfrac{1}{6}s+11-11\qquad\text{add $-11$ to both sides}\\\\-4=\dfrac{1}{6}s\qquad\text{simplify}[/tex]
Step 2
Multiply both sides by the inverse of the coefficient of the variable.
[tex](6)(-4)=(6)\left(\dfrac{1}{6}s\right)\qquad\text{multiply both sides by 6}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]
Alternate solutionOften, when equations contain fractions, you are advised to "eliminate fractions" as a first step. That generally means you multiply both sides of the equation by a suitable common denominator.
Here, the only denominator is 6, so the fraction can be eliminated by multiplying both sides of the equation by 6.
[tex]7=\dfrac{1}{6}s+11\qquad\text{given}\\\\6(7)=6\left(\dfrac{1}{6}s+11\right)\qquad\text{multiply both sides by 6}\\\\42=s+66\qquad\text{simplify}\\\\42-66=s+66-66\qquad\text{add the opposite of 66 to both sides}\\\\\boxed{-24=s}\qquad\text{simplify}[/tex]
You will note this requires the same number of steps, but you don't have to mess with fractions after the first step.
CheckThe value we found for the variable can be checked in the original equation.
[tex]7=\dfrac{1}{6}(-24)+11\\\\7=-4+11\qquad\text{true}[/tex]
LOTS OF POUNT PLS HELP
Answer:
Option 2
Step-by-step explanation:
Using the quadrstic formula,
[tex]\tan \theta=\frac{-2 \pm \sqrt{2^2 - 4(\sqrt{3})(-\sqrt{3})}}{2\sqrt{3}} \\ \\ =\frac{-2 \pm 4}{2\sqrt{3}} \\ \\ =\frac{-1 \pm 2}{\sqrt{3}} \\ \\ = -\sqrt{3}, \frac{1}{\sqrt{3}}[/tex]
Case 1
[tex]\tan \theta=-\sqrt{3} \implies \theta=\frac{2\pi}{3}, \frac{5\pi}{3}[/tex]
Case 2
[tex]\tan \theta=\frac{1}{\sqrt{3}} \implies \theta=\frac{\pi}{6}, \frac{7\pi}{6}[/tex]