Answer:
The circumcenter of the triangle with vertices (0,0), (2,4), and (5,1) is located at (3,2).
To find the circumcenter, use the formula:
Cx = (x1 + x2 + x3)/3
Cy = (y1 + y2 + y3)/3
In this case, Cx = (0 + 2 + 5)/3 = 3
Cy = (0 + 4 + 1)/3 = 2
Therefore, the circumcenter of the triangle is located at (3,2).
The orthocenter of the triangle with vertices (0,0), (2,4), and (5,1) is located at (2.5, 2.5).
To find the orthocenter, use the following equation:
Hx = (x1 + x2 + x3)/3
Hy = (y1 + y2 + y3)/3
In this case, Hx = (0 + 2 + 5)/3 = 2.5
Hy = (0 + 4 + 1)/3 = 2.5
Therefore, the orthocenter of the triangle is located at (2.5, 2.5).
Step-by-step explanation:
The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, …
Let n represent the term number and f(n) the term in the sequence. The function ____ represents the sequence
A: f(n)=-3n+23
B: f(n)=-3n +61
C: f(n)= 20-3n
D: f(n) =20n-3
Click or tap the graph to plot a point.
Function representing the sequence will be f(n) = (23 - 3n
The first five terms of an arithmetic sequence are as 20, 17, 14, 11, 8....
Let n represents the number of term and f(n) the the term in the sequence.
Then we have to find the function that represents the sequence.
As we know explicit formula of an arithmetic sequence is given by
Or the function representing the sequence will be
f(n) = a + (n-1)d
where a represents first term of the sequence a = 20
and common difference d = 17-20 = (-3).
Now the function which represents this sequence will be
f(n) = 20 + (n-1)(-3) = 20 - 3n + 3 = 23 - 3n
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Sadie is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Sadie will earn $40 every time one of her songs is played in a commercial and she will earn $120 every time one of her songs is played in a movie. Sadie's songs were played on 3 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $440. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Sadie's songs were played. Define the variables that you use to write the system.
The number of commercials and movies on which the songs were played are 5 and 2.respectively
How to determine the number of commercials and movies on which the songs were played.From the question, we have the following parameters that can be used in our computation:
Earnings from songs played in commercial = $40Earnings from songs played in movie = $120Total earnings = $440The number of commercials is x, and the number of movies is y
The above parameters when represented as an equation is as follows
40x + 120y = 440
x = y + 3
Substitute x = y + 3 in 40x + 120y = 440
40(y + 3) + 120y = 440
Expand
40y + 120 + 120y = 440
Evaluate the like terms
160y = 320
Divide by 160
y = 2
Recall that
x = y + 3
So, we have
x = 2 + 3
x = 5
Hence, the number of commercials is 5 times
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solve the system by graphing y=-x+10 y=x+8
Answer:
Step-by-step explanation:
I graphed this system on Desmos because it's easier. The solution they have (the intersection- the point where they both touch at the same time-) is at point (1,9) ...
Johnny bought 4 adult tickets and 8 children tickets for $81. Leslie bought 2 adult
tickets and 2 children tickets for $28.50. How much was each type of ticket.
Adult tickets cost $8.25 and children ticket is $6.
How to illustrate the 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 written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
Let adult tickets = a
Let children tickets = c
Since Johnny bought 4 adult tickets and 8 children tickets for $81. Leslie bought 2 adult
tickets and 2 children tickets for $28.50.
This will be:
4a + 8c = 81 ....i
2a + 2c = 28.50... ii
From equation ii a + c = 14.25
a = 14.25 - c
Put this into equation I
4a + 8c = 81 .
4(14.25 - c) + 8c = 81
57 - 4c + 8c = 81
4c = 81 - 57.
c = 6
Since a = 14.25 - c
a = 14.25 - 6.
a = 8.25
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read the picture plsss
Answer:
Step-by-step explanation:
x^4-2x^2-16x-15=0 find the zeros with work please
ANSWER : -1 , 3 , (-1 - 2i) , (-1 + 2i)
steps
find the zeros JUST MEANS SOLVE FOR X
x⁴-2x²-16x-15=0
break it up
let u = x²
x⁴ = (x²)² = u²
-16x+u²-2u-15=0
hold off on -16x
u²-2u-15=0
what 2 numbers when multiplied give you -15 & when added give you -2?
-5 and 3
(u-5) (u+3)
-16x + (u-5) (u+3) = 0
go back x
-16x + (x²-5) (x²+3) = 0
factor -1 out
( looks horrible so far lol )
-1 ((- x²+ 5) (x²+3) + 16x) = 0
multiply (- x²+ 5) with ( x² + 3 )
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² ( x² + 3 ) + 5 ( x² + 3 ) ) + 16x ) = 0
-1 (( - x² * x² + -x² * 3 ) + 5x² + 15 ) + 16x ) = 0
-1 (( - x⁴ + -2x² + 15 ) + 16x ) = 0
PLEASE HELP ME I TOOK A PICTURE
The inequality to describe the possible side length for the third side is 5 < x ≤ 23.
What is the inequality of a triangle?
According to the triangle inequality theorem, the sum of any two sides of a triangle is greater than or equal to the third side of a triangle. This statement can symbolically be represented as; a + b > c. a + c > b.
The triangle inequality tells that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.
We have given,
Two sides of a triangle have lengths 9 and 14.
The third side is represented by x.
So by triangle inequality, we have the following inequality:
x ≤ 9 + 14
x ≤ 23
Also, the difference between the lengths of any two sides of a triangle is less than the length of the third side.
14 - 9 < x
5 < x
Hence, the inequality to describe the possible side length for the third side is 5 < x ≤ 23.
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passes through (-2,6) with a slope of - 1/4
The equation of the line is y = x/4 + 13/2 .
What is a slope?A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1/4
And (x₁ ,y₁) = (-2,6)
then the equation of line is
y - y₁ = m (x - x₁)
y - 6 = (1/4) (x +2)
y = x/4 + 13/2
Therefore, the equation is y = x/4 + 13/2.
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Evaluate each function
The function is given as g(n) = -n + 5 then the value of g(1) is 4. the correct option is B.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output. . Simplification usually involves making the expression simple and easy to use later.
The procedure in mathematics to utilize and analyze the function or expression to make the function or expression uncomplicated or more coherent is called simplifying and the process is called simplification.
From the given function, g(n) = -n + 5
By plugging in the value of 'x' in the bracket, we have;
g(n) = -n + 5
g(1) = -1 + 5
g(1) = 4
Therefore, the value of function is 4.
Hence, the correct option is B.
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Mitchell's family is slow cooking 2 and 3-fourths pounds of meat. The recipe says to cook the meat 1 and 1-half hours per pound.
How long should Mitchell's family cook the meat?
Mitchell's family will take 4 1/8 hours of time to cook the meat.
Multiplication:Maltiplication is reffered as adding multiple times. It is a one of the fundamental Mathematical operation. The symbol '×' used to denote the Maltiplication.
We use Multiplication to simplify the addition of the same number multiple times.
Here in this problem we use multiplication to solve the problem.
Here we have
Mitchell's family is slow cooking 2 and 3-fourths pounds of meat.
=> 2 and 3-fourth = 2 3/4 = 11/4 pounds of meat
The recipe says to cook the meat for 1 and a half hours per pound
For 1 pound of meat = 1 and 1/2 hours = 3/2 hours
The time required to cook 11/4 pounds = (11/4)(3/2) hours
= [tex]\frac{11}{4} (\frac{3}{2})[/tex] = [tex]\frac{33}{8}[/tex] = 4 (1/8) hours
Therefore,
Mitchell's family will take 4 1/8 hours of time to cook the meat.
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Solve for c.
4(c + 17) = 16
C =
Please help
3 ft
5 ft
4 ft
5 ft
Find the area of this figure.
Round your answer to the
nearest hundredth. Use
3.14 to approximate ™.
A = [?] ft²
The area of the given figure is 52.26 ft².
What is a triangle?A triangle is a geometric figure with three edges, three angles and three vertices. It is a basic figure in geometry.
The sum of the angles of a triangle is always 180°
In the given question,
The radius of semicircle r = 3 ft.
Height of the triangle = 4 ft.
Lateral side of triangle = 5 ft.
And the base of triangle = 2 x 3 = 6 feet
To find the area of the given figure, individually find area of semicircle and triangle.
Area of semicircle = π x r² = 3.14 x 3 × 3 = 28.26 square feet.
Area of triangle having height 4 feet and base 6 feet.
Area of triangle = base x height = 4 x 6 = 24 square feet.
The Area of the whole figure = Area of semicircle + area of triangle
= 28.26 +24
= 52.26 ft²
The required area of figure is 52.26 ft².
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one and four seventh plus three and two fifths equals blank
a
five and thirty four thirty fifths
b
four and six twelfths
c
four and thirty four thirty fifths
d
four and eight thirty fifths
Answer:
a. four and thirty four thirty fifths
Suppose a batter has an average of .303 for the season (this player's experimental probability of hitting the ball). How many hits would you predict that the player will get in his next 9 at-bats?
On closely observing and solving the Probability it can be stated that the batter will hit around 3 balls out of the next nine balls
What is Probability?
The ratio of the number of outcomes in an exhaustive collection of equally probable options that create a particular event to the entire number of conceivable outcomes.
Solution:
Average of Batter is 0.303 which means that the batter hits 303 shots of 1000 balls
So, in the next nine balls he will hit 9 * 303/1000 = 2.7 balls
Which means the batter will hit around 3 balls
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The temperature in Tampa, Florida, is 15 degrees warmer than twice the temperature in Chicago, Illinois. The temperature in Tampa is 75 degrees. Write an equation to determine
the temperature in Chicago.
January has an overnight average temperature of 52.4°F, making it the coldest month in Tampa. The average daytime temperature increases to 90.0°F in August, the warmest month.
What's it like to live in Tampa, Florida?
This Florida city, which is a part of the Tampa Bay region, has reasonable housing options, wonderful tropical weather, easy access to the beach, and more, making it one of the greatest locations to live in the Southeast.
How far away from the beach is Tampa?
The beach lottery has been won by Tampa visitors. You can reach more than a dozen of the world's most stunning beaches in less than 30 minutes by car from downtown Tampa. You need only select one.
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8. The quadratic function below models the flight of a model rocket, where
the height, h(t) is in metres, and the time, t is in seconds. When does the
rocket hit the ground?
h(t) = -5t² +42t + 54
The rocket hit the ground is 6.3 sec.
The quadratic equation y = -x2 - 12x, where y is the height of the rocket in metres at time x seconds after launch, may be used to describe the trajectory of a model rocket. The rocket's highest point should be noted, along with the time it was at that height.
A rocket's height is a function of time, h(t), where h is measured in metres and t is measured in seconds. 9.8 m/s2 is the rate of change of velocity (d2h dt2 - t). The rocket is catapulted into the air, reaching a speed of 50 m/s at time t0.
To find the rocket's height at t = 2 sec, we just have to substitute 2 into the equation for t and then solve for h:
h = -5*t2 + 30*t + 10
h = -5(2)2 + 30(2) + 10
h = -5(4) + 30(2) + 10
h = -20 + 60 +10
h = 50 m
The height of the rocket 2 seconds after launching it is 50 meters.
To find the x-coordinate of the vertex of a parabola, we use the formula:
t - 3 = ± √(11)
t = 3 ± √(11)
t = 3 ± 3.3
Solving for t, we get two solutions:
t = 3 - 3.3
t = -0.3 sec
and
t = 3 + 3.3
t = 6.3 sec
Remember that the rocket takes off from an elevated platform (the roof of a building), not from the ground, in order to comprehend the two alternatives we came up with. Even though we have two x-intercepts, only one of them, tground = 6.3 seconds, is related to when the rocket touches down. The other x-intercept, t = -0.3 sec, only has theoretical significance and is therefore irrelevant in our actual situation.
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what is the volume of the shape
Answer:
Step-by-step explanation:
Hope it helps!
is there good evidence that the mean percentage tip left by patrons who have received a bad weather forecast is less than 19%?
At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.
After getting excellent news, people often behave more generously. After receiving negative news, do they become less giving? Adult Americans tip 20% of the whole bill on average. Give 20 diners a notice on their bill informing them that the weather is going to be poor tomorrow, and then keep track of the tip % they left. The tips are shown in Table 1 as a percentage of the total bill.
Table : 18.0 19.1 19.2 18.8 18.4 19.0 18.5 16.1 16.8 18.2 14.0 17.0 13.6 17.5 20.0 20.2 18.8 18.0 23.2 19.4
Suppose that tip percentage is Normal with ? = 2 and assume that the patrons in this study are a random sample of all patrons of this restaurant. Is there good evidence that the mean tip percentage for all patrons of this restaurant is less than 20 when they receive a message warning them of tomorrow’s bad weather? State [tex]H_{o}[/tex] and [tex]H_{a}[/tex] and carry out a significance test. Use significance level 0.05.
The given data is :
18.0, 19.1, 19.2, 18.8, 18.4, 19.0, 18.5, 16.1, 16.8, 18.2, 14.0, 17.0, 13.6, 17.5, 20.0, 20.2, 18.8, 18.0, 23.2, 19.4
Therefore, sample mean,
X = ∑x / n
X = [tex]\frac{18+19.1+19.2+19.3+....19.5}{20}[/tex]
X = 18.19
Now test : μ < 20 with normal distance
Hypothesis test:
[tex]H_{o}[/tex] = μ ≥ 20
[tex]H_{a}[/tex] = μ ≤ 20
This is the lower tailed test.
X = 18.19
σ = 2
n = 20
Significant level, α = 0.05
Test statistics,
z = ( X-μ ) / (σ / [tex]\sqrt{n}[/tex] )
z = [tex]\frac{18.19-20}{2\sqrt{20} }[/tex]
z = -4.05
P value is in direction of alternative hypothesis or [tex]H_{a}[/tex]
Since, [tex]H_{a}[/tex] ≤ 20 P value = P(Z<-4.05)
P value is the area to the left of the test statistics = -4.05 (from the figure)
P value = P(Z< -4.05) = 0.000 (from z table)
P value = 00000
Rejection rule : Reject [tex]H_{o}[/tex] if P value < α
Using excel functional normdist ( [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] , 0 , 1 , TRUE ) or TI's function normaldf ( 1E-99 , [tex]\frac{18.19-20}{2\sqrt{20} }[/tex] ) answer is 0.0000259078
Decision : Since 0.0000 < 0.05, we reject the null hypothesis
Therefore,
At 5 percentage significance level, we have sufficient evidence to conduct that μ is less than 20.
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** h(x) = 2f(x).g(x)
Find the value of h’(1), if f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1.
The value of h’(1) is = 22
How may the chain rule example be used?
Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.
Given that :
h(x) = 2f(x).g(x)
f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1
h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule
h’(1) = 2 f'(1)g(1) + g'(1)f(1)
= 2 * (4 * 2 + 1 * 3)
= 2* (11)
= 22
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Write the coordinates of the vertices after a reflection over the line y=-5.
The coordinates of the vertices after a reflection over the line y = -5 is given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
How to obtain the coordinates of the vertices after the reflection?The vertices of the original quadrilateral are given as follows:
T(-2,-5), U(2,-3), V(-2,-1), W(-3,-3).
The reflection line y = -5 is an horizontal line, meaning that after the reflection:
The x-coordinate remains constant.The y-coordinate will be equidistant to y = -5, however in an opposite direction.For example, the distance of the y-coordinate of the vertex U from -2 is of:
2 units above.
Then the y-coordinate of the vertex U' will be also 2 units from -5, just two units below, hence:
U'(2,-7).
Applying this rule for all the other vertices, they will be given as follows:
T'(-2,-5), U'(2,-7), V'(-2,-9), W'(-3,-7).
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Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Then
find the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8
the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.
What is the area under the curve?The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.
The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.
The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve
2y = 4√x
Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x
so, 4√x + 4x = 8
or, √x + x = 2
or, √x = (2 - x)
or, x = (2 - x)²
or, x = x² - 4x + 4
or, x² - 5x + 4 = 0
or, ( x - 4) ( x - 1) = 0
or, x = 4, 1
when x = 4 then y = 2√4 = 4
when x = 1 then y = 2 √1 = 2
when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.
Thus, only intersection point is: (1,2)
This is the type (II) region.
So, integrate the region with respect to y.
Now, area =
= [tex]\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy[/tex]
= [tex]\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy[/tex]
= [tex]\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2[/tex]
= [tex]\frac{117}{12} - 6 + \frac{21}{4}[/tex]
= [tex]\frac{108}{12}[/tex]
= 9
Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.
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AB and CD bisect each other at E m/CAE 80 and m/BDE 60 Amy says that mZCEA = 20°, Brent says that it is 30", Carlos says that it is 40", and Debra says that it is 50" Which
student is correct?
The only person that is correct with respect to the measurement of ∠CEA of the congruent triangles is; Carlos
How to Interpret Congruent Angles?From the diagram attached, we are given that;
The measure of ∠CAE = 80°
∠BDE = 60°
Amy says that m∠CEA = 20°
Brent says that it is 30°
Carlos says that it is 40°
Debra says it is 50°
Now, by inspection, it is clear that ΔCAE is congruent to ΔBDE by SAS Congruency postulate and as such we can say that;
∠A = ∠B and ∠C = ∠D
Thus;
∠B = 80° and ∠C = 60°
Sum of angles in a triangle is 180 degrees and so;
∠CEA = 180 - (80 + 60)
∠CEA = 180 - 140
∠CEA = 40°
Which means that Carlos is correct.
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Rachel van Dressler earns 3% commission on all sales. What was her total sales amount if she earns a commission of $3652
Answer:
Van Dressler's total sales amount is $12,166.6666667
Step-by-step explanation:
3% = $365
365/3*100 =$12,166.6666667
write the equation of the line in slope intercept form
(-5, -11) and (-2, 1)
Answer:
Step-by-step explanation
The slope intercept form is M=y2-y1 over x2-x1.
The answer for the equation is 12/3. 3 goes into 12 four times, so the answer is 4.
can you please help me
The equivalent exponential expression for the radical expression [tex]\sqrt{2 + 3}[/tex]
is [tex](2 +3)^{\frac{1}{2} }[/tex].
How to find equivalent expression ?Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
Equivalent expression may not look the same but substituting the variables will result to the same values.
Therefore, let's find the equivalent exponential expression for the radical expression can be found as follows:
[tex]\sqrt{2 + 3}[/tex]
Using exponential law,
[tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
Therefore,
[tex]\sqrt{2+3} = (2 +3)^{\frac{1}{2} }[/tex]
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if <1 and <2 form a linear pair, and m<1 = (7x - 3) and m<2 = (12x - 7), draw and label a diagram of the problem, then find the m<2.
The value of the variable 'x' is 10. Then the measure of angle ∠2 is 113°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Linear angle - If the total of two angles is 180 degrees, they are said to be linear angles.
If angles ∠1 and ∠2 form a linear pair, m∠1 = (7x - 3) and m∠2 = (12x - 7). Then the equation is given as,
∠1 + ∠2 = 180
7x - 3 + 12x - 7 = 180
Simplify the equation, then we have
7x - 3 + 12x - 7 = 180
19x = 190
x = 10
Then the measure of angle ∠2 is calculated as,
∠2 = 12(10) - 7
∠2 = 120 - 7
∠2 = 113°
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how is (-7.5)-21.04 and (-7.5)+21.04 the same value?
The values (-7.5)-21.04 and (-7.5)+21.04 are not the same
What is a decimal?A decimal can be defined as a number consisting of a whole number and also a fractional part.
These numbers are separated by a dot known as the decimal point
The decimal numeral system is seen as a standard system that denotes integer and non-integer numbers.
It is important to note the following operations;
+ × + = ++ × - = -- × + = -- × - = +From the information given, we have;
(-7.5)-21.04
Multiply the operation
+ 157. 8
Then,
(-7.5)+21.04
Multiply the operation
- 157. 8
Hence, the values are either negative or positive.
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Help fast I can’t figure this out
Answer:
100
Step-by-step explanation:
x^3 = 1,000,000 Find the cube root of 1,000,000
x^3 = 1.0x10^6 Using scientific notation, we can split the 1,000,000 into a 1.0 and a factor of 10*10*10*10*10*10 or 10^6
x = 1.0x10^2 The cube root of 1.0 is 1.0. The cube root of 10^6 is found by dividing the exponent by 3: 10^2
The cube root of 1,000,000 is 1.0X10^2, or 100.
x = 100
a company makes wax candles in the shape of a cylinder. each candle has a diameter of 4 inches and a height 8 of inches. if the company used of wax, how many candles did it make? use for , and do not round your answer.
If the company has made 6732.16 in³ wax , Total number of candles made is 67
According to the question,
It is given that a wax candle is in cylindrical shape
Diameter of candle = 4 in
Radius will be = 4 / 2
=> 2 in
Height of each candles = 8 in
Company has used 6732.16 in³ of wax
We have to calculate number of candles company has made
Volume of cylinder = πr²h
Where r is radius and h is height
Substituting all the values,
Volume of candle = π (2)² (8)
=> V = 3.14 × 4 × 8 (putting π = 3.14)
=> V = 100.48
Therefore , Number of candles made = Total volume /volume of one candles
=> 6732.16 / 100.48
=> 67 candles are made by company
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6x-7=1-3x[tex]6x-7=1-3x[/tex]
Answer:
x=8/9
Step-by-step explanation:
step one: move x to one side. to do this, we are going to use inverse operations which means adding 3x to both sides.
3x+-3x cancels itself out and 3x+6x=9x.
now, the equation looks like: 9x-7=1
step two: isolate the variable, x. we want to just get x to be by itself so we need to get rid of the -7 next to it by using inverse operations again. this means we're going to add 7 to both sides.
7+-7 cancels itself out and 7+1=8.
now, the equation looks like 9x=8
step three: divide to get x by itself. we want to know what x alone is, not 9x. to do this we are going to use inverse operations one last time. this means dividing each side by 9, because 9x means "9 times x".
9x/9= x, 8/9
so the answer is x=8/9
hope this helped!!
