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Explanation:
Your question covers a good bit of the material in an algebra course. The short answer is, "the same way you solve a numerical equation." The point of algebra is that literals can stand for numbers, and so be manipulated the same way numbers are.
Expressions are evaluated according to the Order of Operations. For equations involving a single variable, the equation specifies what operations are being performed on that variable. To find the vale of the variable (solve for that literal), you need to "undo" the operations that are performed on it. As with many problems that have layers, you work down through the layers from the outside in. Generally, that means working through the list of operations "backwards," undoing the last one first.
Simple example
y = mx + b . . . . . . solve for x
In this equation, the operations performed on x are ...
multiplication by maddition of b to the productIn accordance with the above, the first thing we do is "undo" the addition of b. (Note that this could be a number or literal--or even a complicated expression--and the process would be exactly the same.) To "undo" addition, we add the opposite.
y -b = mx +b -b ⇒ y -b = mx
Next, we "undo" the multiplication by m. That is, we divide by m, or multiply by the reciprocal of m. Either is the same as the other.
(y -b)(1/m) = (mx)(1/m) ⇒ (y -b)/m = x
Now, we have solved this literal equation for x.
_____
Throughout this process you must adhere strictly to the properties of equality. That is, anything you do to one side of the equation must also be done to the other side.
The reason you study inverses and identity elements is so you understand that addition of an additive inverse produces the additive identity element:
x + (-x) = 0
Similarly, multiplication by the multiplicative inverse (reciprocal) produces the multiplicative identity element.
x · (1/x) = 1
When other operations are involved, such as raising to a power, trig functions, roots, logs, exponentiation, each of these has an associated inverse function that produces an identity:
(x^a)^(1/a) = x^1 = x
arcsin(sin(x)) = x
(√x)^2 = x
10^(log(x)) = x or log(10^x) = x
Some of these inverse functions have restricted domains, so care must be used when solving equations involving them.
When a variable of interest appears on both sides of the equal sign, then you must figure a way to rearrange the equation so the terms with the variable can be combined.
Example:
ax + b = cx +d . . . . . solve for x
ax -cx = d -b . . . . . . subtract (cx+b). (Of course, this is subtracted from both sides of the equation.)
x(a -c) = d -b . . . . . combine x-terms
x = (d -b)/(a -c) . . . . divide by the coefficient of x
Note that we had to divide the entire right-side expression by the x-coefficient, so had to enclose it in parentheses.
More Complicated Example:
A recent Brainly problem asked for the solution to ...
T = 2π√(L/g) . . . . solve for L
Here, L is divided by g, a root taken, and that multiplied by 2π. Undoing these in reverse order, we first divide by 2π, square both sides to undo the root, then multiply by g to undo the division:
[tex]T=2\pi\sqrt{\dfrac{L}{g}}\\\\\dfrac{T}{2\pi}=\sqrt{\dfrac{L}{g}}\\\\\left(\dfrac{T}{2\pi}\right)^2=\dfrac{L}{g}\\\\\boxed{L=g\left(\dfrac{T}{2\pi}\right)^2}[/tex]
The problem posted on Brainly had numbers where some of these variables are. That does not affect the solution method, except that sometimes numerical values can be combined where literal values cannot.
_____
Key Points
The equal sign is sacred, and its truth must be preserved at every step.Literal equations are solved the same way numerical equations are solved.Inverse operations and functions are used to "undo" operations and functions.The Order of Operations can be helpful when considering what to do first.Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
The half-life of a radioactive substance is 20 years. If you start with some amount of this substance, what fraction will remain in 180 years?
Answer:
1/512
Step-by-step explanation:
Let staring fraction = x
Half-life = 20 years ; this is the time taken for an element to decrease to half of its original size
Hence,
After 20 years - - - > x/2
After 40 years - - - - > x/2 ÷ 2 = x/2 * 1/2 = x /4
After 60 years - - - - > x/4 ÷ 2 = x/4 * 1/2 = x/8
After 80 years - - - - -> x/8 ÷ 2 = x/8 * 1/2 = x / 16
After 100 years - - - > x/16 * 1/2 = x/32
After 120 years - - - - > x/32 * 1/2 = x/64
After 140 years - - - - -> x / 64 * 1/2 = x / 128
After 160 years - - - - - > x / 128 * 1/2 = x/256
After 180 years - - - - > x/256 * 1/2 = x / 512
Hence, the fraction after 180 years = 1/512
Help me plz will mark brainliest
Step-by-step explanation:
Given,
the bigger triangle (∆GFH), <HGF = 90° and <GFH = 60° and GF = 4
In the 30-60-90 triangle, FH = 4×2 = 8
or you can find it like this,
cos60 = 4/FH
FH = 4/cos60 = 8
Now, I is the midpoint of FH, so, FI = 8/2 = 4
now for ∆FGI,
<GFI = 60°, GF = 4, FI = 4, it's a equilateral triangle, so we can say GI = 4
Now we need to find the height of ∆FGI, for that,
area of ∆FGI = (√3/4)×4² = 4√3 = 6.92820323..
So height (GJ) = 2×area/side = 2×4√3/4 = 2√3 = 3.46410162.. [height of ∆GFI (Because altitude is perpendicular distance from a point) = GJ, given]
now, in ∆GJI, GJ = 2√3, GI = 4 and <GJI = 90° (since itsy altitude, the angle will be a right angle, i.e. 90°)
So, JI = √{4²-(2√3)²} = 2
Area = 2×2√3/2 = 2√3 = 3.46410162.. = 3.46 (rounded to the nearest hundredth)
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
Answer:
f^-1 (-15) = -6
f^-1(4) + f(9) = 0
Step-by-step explanation:
f^-1 (-15) =
Look where the output is -15 and find the x value ( x=-6)
Since where are using the inverse function, the input becomes the output and the output and the output becomes the input
f^-1 (-15) = -6
f^-1 (4) = -11 (inverse function)
f(9) = 11 ( regular function)
f^-1(4) + f(9) = -11+11 = 0
Please help explanation if possible
Answer:
18.84 feet. let me know if you have ay other questions.
Step-by-step explanation:
The way to find the formula for circumference is kinda complicated so it is best to ust memorize the formula, which is 2πr. or 2 times pi times the radius.
Your problem gives you the formula, but instead of 2 and r in it you have d, which is the diameter.
The diameter of the circle is 2 times the radius, so that's why it is replaced.
the radius is the distance from the center fo the circle to one edge, and the diameter is the distance through the circle passing through its center. so it's the center to one end plus the center to another end. or r+r which is also 2r.
So d = 2r, so in this problem d =6 feet.
So now the formula πd = 3.14*6 feet = 18.84 feet
Find the slope of the line
Slope=m=_______
Answer:
[tex]\displaystyle m = \frac{3}{4}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Reading a coordinate planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]Step-by-step explanation:
Step 1: Define
Identify points from graph.
Point (4, 0)
Point (0, -3)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m = \frac{-3 - 0}{0 - 4}[/tex]Simplify: [tex]\displaystyle m = \frac{3}{4}[/tex]Find the surface area of the figure round your answer to the nearest tenth if necessary
Answer:
.kpokojj8nvchrfhuthuvu9jeuvh
Step-by-step explanation:
j8tguhrhfgzhedh8ugh8euweuhujdhhruehf hhcufe7fhd fu y in my as 08ygrt8hthts8hewhrs8h8h8
(5, 4)
11-5-2)
16.nat's the slope-intercept form of the equation of the line graphed in this figure?
O A. y = 5/3x + 1
O B.y=-3x + 1
O C. y = 3x + 1
O D.y = -5/3X - 1
Answer:
The answer is B. y=3/5x+1When a 0.42 tax was added to the price of a ticket, the total bill come to $7.03. Describe the above situation as a linear equation.
Answer:
P = 7.03 - 0.42T
Step-by-step explanation:
Let the price of a ticket be P.
Let the ticket be T.
A linear equation can be defined as an algebraic equation that's typically written for two (2) independent variables, in which each of them has an exponent of one (1) and they make a straight line when plotted on a graph.
Given the following data;
Tax = 0.42
Total bill = $7.03
Translating the word problem into an algebraic expression, we have;
0.42T + P = 7.03
P = 7.03 - 0.42T
The entrance ticket for a carnival costs $89.97, which includes a royal meal
that costs $10.85, 1 play station game, and 3 water rides (Each water ride
costs the same price). The cost of a water ride is twice as that of a play
station game. Find the cost of a water ride. Estimate to the nearest tenths.
Subtract the meal:
89.97- 10.85 = 79.12
Let the play station game = x
A water ride is twice that so a water ride is 2x
There is 3 water rides : 3 x 2x =6x
The PlayStation game and water rides = 79.12
6x + x = 79.12
Simplify:
7x = 79.12
Divide both sides by 7:
X = 11.30
The PlayStation game is 11.30
The water ride = 2 x 11.30 = 22.60
please help me
find x
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Answer:
x = 6√2
Step-by-step explanation:
The side ratios in an isosceles right triangle are ...
1 : 1 : √2
These will be the same as ...
x : x : 12
so, ...
x = 12/√2
x = 6√2
In performing a one-way ANOVA, ________ measures the variability of the observed values around their respective means by summing the squared differences between each observed value of the response and its corresponding treatment mean.
Answer: SS Error
Step-by-step explanation:
The SS Error refers to the sum of the squares of the deviations of the observations, from their mean. It is simply the total variance from the observations on the study.
In performing a one-way ANOVA, the SS Error measures the variability of the observed values around their respective means and this is done through the summation of the squared differences between each observed value of the response and its corresponding treatment mean.
Người ta chiếu xạ liều 3000 Rơn ghen vào một quần thể ruồi dấm ở thế hệ F1: Chiếu xạ 1000 con ruồi dấm không cho ăn đường thì có 80 con bị đột biến và chiếu xạ 1000 con ruồi dấm có cho ăn đường thì có 120 con bị đột biến. Cho ăn đường có ảnh hưởng đến tỉ lệ đột biến của ruồi giấm không, với mức ý nghĩa 5%? Giá trị kiểm định là
Answer:
gggggggggggggggggggggrrrrrrrrrrrttyuuiiiii
Please helpppppp i need help…
///..
ASAP!!!!
!!!,,!!!!!!
Answer:
True
Step-by-step explanation:
64 - x^2
Rewriting as
8^2 - x^2
(8-x)(8+x)
This is the difference of squares
Evaluate this |-2+3|
[tex]\displaystyle \Large \boldsymbol{} |-2+3| =|1|=1[/tex]
Si una mujer gana más que su marido
Answer:
nada está bien gana bien.
The productivity of a country is given by f(x, y) = 600x^2/3 y^1/3, where x and y are the amount of labor and capital.
a) Compute the marginal productivities of labor and capital when x = 125 and y = 64.
b) Use part (a) to determine the approximate effect on productivity of increasing capital from 64 to 66 units, while keeping labor fixed at 125 units.
c) What would be the approximate effect of decreasing labor from 125 to 124 units while keeping capital fixed at 64 units?
15 points PLEASE ANSWER
Answer:
D. (25π - 50) sq m
Step-by-step explanation:
Since ABCD is a square with the area of 100, we know that the dimensions are 10 by 10. With that, we can find that triangle ABC = 50 sq m because of (h*l)/2. Since A is the center of the circle that contains arc BD, we know that 10 is the radius of the quarter-circle ABC. Using (πr^2)/4 to get the area of the quarter-circle, we get that the quarter-circle ABC = 25π sq m. But the original triangle ABC in the quarter-circle is not shaded. Therefore, we subtract 50 from 25π, which leads to (25π - 50) sq m.
I hope this helped! :D
4. (08.02 MC)
Factor completely 2x3 + 10x2 + 14x + 70. (5 points)
(2x^2 + 14)(x + 5)
(x^2 + 7)(2x + 10)
2(x^3 + 5x2 + 7x + 35)
2[(x^2 + 7)(x + 5)]
Answer:
2[(x^2 + 7)(x + 5)]
Step-by-step explanation:
Note that the ratio of the first and second terms is the same as that between the third and fourth terms. So this cubic will factor by grouping, but first we can separate out the common scalar factor 2...
2x3+10x2+14x+70=
2(x3+5x2+7x+35)
2((x3+5x2)+(7x+35))
2(x2(x+5)+7(x+5))
2(x2+7)(x+5)
Answer:
The answer is D. 2[(x2 + 7)(x + 5)]
Step-by-step explanation:
PLEASE HELP!!!
Find the equation of the line with an x intercept of 4 and a y intercept of -1.5
Answer:
y = 4x - 1.5
Step-by-step explanation:
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = 4x - 1.5
trigonometric identities
1/tan x = cot x
Cot x + tan x = 1/ sin x cos x
The answer is D.
Ms. Lowder has 2 children, one in first grade and one in fifth grade. Both children need paper for school. Paper costs $2.29 per pack. If the first grader needs 2 packs of paper and the fifth grader needs 6 packs of paper, how much money will Ms. Lowder spend on paper?
the answer is she spend $18.32
-8=8(-3+a) plz help me and show work simply
Answer:
[tex] - 8 = 8( - 3 + a) \\ - 8 = - 24 + 8a \\ 8a = 16 \\ a = 2[/tex]
Answer:
2
Step-by-step explanation:
-8 = 8a - 24
16 = 8a
a =2
I hope this helps! :)What is the order of rotational symmetry for the figure?
A. 3
B. 2
C. 4 or more
D. 1
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Answer:
C. 4 or more
Step-by-step explanation:
Rotating the figure in increments of 90° will give the same figure. There are 4 such rotations in a full turn. The order of rotational symmetry is 4.
The TV weatherman says "there's a 30% chance of rain tomorrow ". Explain what this statement means?
Write an equation for the graph below in terms of x
Answer:
x = -2
Step-by-step explanation:
the line goes through -2 on the x-axis
the line also goes through -3 on the y-axis
Which functions represent a vertical stretch of the parent function, f(x) = 1/x? Check all that apply.
g(x) = 3/x
g(x) = -2/x
g(x) = 1/4x
g(x) = 5/2x
g(x) = 1/2x
Answer:
[tex]g(x) = \frac{3}{x}[/tex]
[tex]g(x) =-\frac{2}{x}[/tex]
[tex]g(x) =\frac{5}{2x}[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\frac{1}{x}[/tex]
Required
Which represents vertical stretch of f(x)
The transformation is represented as:
[tex]g(x) = a* f(x)[/tex]
Where:
[tex]|a| > 1[/tex]
So, the functions are:
[tex]g(x) = \frac{3}{x}[/tex] ---- [tex]|3| > 1[/tex]
[tex]g(x) =-\frac{2}{x}[/tex] --- [tex]|-2|>1[/tex]
[tex]g(x) =\frac{5}{2x}[/tex] --- [tex]|\frac{5}{2}| > 1[/tex]
Answer:
the other person is correct if you need them quick it is a b and d
Step-by-step explanation:
muscle max gym charges a $30 fee to join plus $2 each day that you go workout. Capital cross-fit charges $10 to join and $4 each day you use the gym. After how many days of workouts would the two gyms have cost you the same amount of money?
Set up equations for each gym.
multiply daily cost by number of days(x) and add the fee:
Muscle max: 2x + 30
Capital: 4x + 10
Now set them
Equal to each other and solve for x:
2x + 30 = 4x + 10
Subtract 2x from both sides :
30 = 2x + 10
Subtract 10 from both sides :
20 = 2x
Divide both sides by 2:
X = 10
It will take 10 days
Factors and rewrite the expression 25x-15
Answer:
5(5x-3)
Step-by-step explanation:
The common factor in this expression is 5 so divide 5 to all the values
25/5=5
-15/5= -3
Put these values into parenthesis and leave the 5 on the left side and out of the parenthesis
5(5x-3)
Answer:
5(5x - 3)
Step-by-step explanation:
The greatest common factor here is 5. Divide each term by 5 and simplify.
25x/5 = 5x
15/5 = 3
Therefore, the answer is 5(5x - 3).
Find all real zeros of the function y = 2x - 4.
a.
2
C.
-4
b. 2, -4
d. -2
Answer:
x = 2
Step-by-step explanation:
To find the zeroes of the function, substitite 0 for y.
0 = 2x - 4
~Add 4 to both sides
4 = 2x
~Divide 2 to both sides
2 = x
Best of Luck!
