9514 1404 393
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.Write down the equation that could be a correct equation for linear regression prediction function?
If the question meant that we should write a linear prediction function ;
Answer:
y = bx + c
Step-by-step explanation:
The equation for a linear regression prediction function is stated in the form :
y = bx + c
Where ;
y = Predicted or dependent variable
b = slope Coefficient
c = The intercept value
x = predictor or independent variable
Therefore, the Linear function Given represents a simple linear model for one dependent variable, x
b : is the slope value of the equation, whuch represents a change in y per unit change in x
if 18 : 6 = x : 3 then what is 5 + 3x
Answer:
32
Step-by-step explanation:
18 : 6 = 3
therefore, x : 3 has to equal 3.
X : 3 = 3
X = 3 × 3
X = 9
To verify:
18 : 6 = 9 : 3
3 = 3
It's true that X = 9, so now just replace the X with 9 in the next equation
5 + 3(9) = 32
Answer:
32
Step-by-step explanation:
18 : 6 = x : 3
Product of means = Product of extremes
6 * x = 3*18
x = [tex]\frac{3*18}{6}[/tex]
x = 3*3
x = 9
Now plugin x = 9 in the expression
5 + 3x = 5 + 3*9
= 5 + 27
= 32
can someone help with this
Answer:
[tex]\frac{8}{45}[/tex]
Step-by-step explanation:
'of' means 'multiply'
4/5 × 2/9 = 8/45
Solve the system of equations using the elimination method 5x+10y = 3
10x + 20y = 8
Answer:
No solution
Step-by-step explanation:
5x+10y=3 equation 1
10x+20y=8 equation 2
-2(5x+10y)=-2(3) multiply equation 1 by -2 to eliminate x
-10x-20y=-6 equation 1 multiplied by -2
10x+20y=8 equation 2
0 + 0 =2. Add above equations
0 =2
no solution
Find the image of the given point
under the given translation.
P(4, -7)
T(x, y) = (x+1, y + 3)
P' = ([?], []).
Answer:
P' (5, -4)
Step-by-step explanation:
P (4, -7)
x = 4 & Y =-7
T(4,. -7) = (4 + 1, -7 +3)
P' = (5, -4)
Solve a triangle with a =5, b =6, and c = 7. Round to the nearest tenth.
Answer:
<A ≈ 45 degrees
<B ≈ 57 degrees
<C ≈ 78 degrees
Step-by-step explanation:
Hi there!
1) Find <C with the law of cosines
Typically, we want to solve for the angle opposite the largest side first.
Law of cosines: [tex]cosC=\frac{a^2+b^2-c^2}{2(a)(b)}[/tex]
Plug in given values
[tex]cosC=\frac{5^2+6^2-7^2}{2(5)(6)}\\cosC=\frac{1}{5}\\C=cos^-^1(\frac{1}{5} )\\C=78[/tex]
Therefore, <C is approximately 78 degrees.
2) Find <B with the law of cosines
[tex]cosB=\frac{a^2+c^2-b^2}{2(a)(c)}[/tex]
Plug in given values
[tex]cosB=\frac{5^2+7^2-6^2}{2(5)(7)}\\cosB=\frac{19}{35}\\B=cos^-^1(\frac{19}{35})\\B=57[/tex]
Therefore, <B is approximately 57 degrees.
3) Find <A
The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:
180-57-78
= 45
Therefore, <A is 45 degrees.
I hope this helps!
What is the volume of the composite figure if both the height and the diameter of the cylinder are 3.5 feet? Give the exact answer and approximate to two decimal places.
Answer:
Volume of composite figure = 44.9 feet³
Step-by-step explanation:
Given:
Height of cylinder = 3.5 feet
Diameter of cylinder = 3.5 feet
Diameter of hemisphere = 3.5 feet
Find:
Volume of composite figure
Computation:
Radius of cylinder and sphere = 3.5/2 = 1.75 feet
Volume of composite figure = Volume of cylinder + Volume of hemisphere
Volume of composite figure = πr²h + (2/3)πr³
Volume of composite figure = (3.14)(1.75)²(3.5) + (2/3)(3.14)(1.75)³
Volume of composite figure = (3.14)(3.0625)(3.5) + (2/3)(3.14)(5.359375)
Volume of composite figure = 33.656875 + 11.2189583
Volume of composite figure = 44.8758
Volume of composite figure = 44.9 feet³
A Sociology instructor gives students points for each discussion-board post and points for each reply to a post. Ana wrote 6 posts and 8 replies and received 114 points. Jae wrote 5 posts and 4 replies and received 79 points. Determine how many points a discussion post is worth and how many points a reply is worth?
Answer:
5 points per post and 2 points per replies
Pls help quick:
The following figures are not drawn to scale but
AB and CD (if present in the picture) are straight lines. Find x:
Step-by-step explanation:
2x+60°= 110°
2x= 110-60
2x= 50
x= 25°
I need some help please!
Answer:
See below
Step-by-step explanation:
Given :-
y || zTo Prove :-
m∠5 + m∠2 + m∠6 = 180°Proof :-
Here we are required to prove that ,
[tex]\rm\implies m\angle 5 + m\angle 6 + m\angle 2 = 180^o [/tex]
And here it's given that , y || z . Therefore ,
∠3 = ∠6 ( alternate interior angles )∠1 = ∠5 ( alternate interior angles )Now we know that the measure of a straight line is 180°. Therefore ,
[tex]\rm\implies m\angle 1 + m\angle 2 + m\angle 3 = 180^o \\\\\implies\boxed{\rm m\angle 5 + m\angle 6 + m\angle 2 = 180^o} [/tex]
From 1 and 2 .Hence Proved !
How many outcomes (sample points) for a deal of two cards from a 52-card deck are possible? Report your answer as an integer.
Answer:
1326
Step-by-step explanation:
[tex]{52\choose2}=\frac{52!}{(52-2)!2!}=\frac{52!}{50!*2!}=1326[/tex]
help please i don't know how to do this
a pie chart is divided into four sectors in fig. 12.42. Each sector represents a percentage of the whole. The two larger sectors are equal and each represents x%. What is the angle subtended by one of those larger sectors ?
Answer:
Angle formed by the sector measuring x% will be 126°.
Step-by-step explanation:
Since, sum of all sectors formed in a circle is 100%.
By adding the measures of all the sectors,
x + x + 21 + 9 = 100
2x + 30 = 100
2x = 70
x = 35%
Now we know sum of all the central angles formed at the center of a circle = 360°
Therefore, angle formed by x% = 360° × 35%
= [tex]\frac{360\times 35}{100}[/tex]
= 126°
Solve the system by substitution.
y + 4 = x
10x + 2y = 16
Answer:
(2, -2)Step-by-step explanation:
Given system:
y + 4 = x 10x + 2y = 16Substitute x into the second equation:
10(y + 4) + 2y = 1610y + 40 + 2y = 1612y = -24y = -2Find x:
x = -2 + 4x = 2Answer:
x = 2 and y = -2
Step-by-step explanation:
Given system :-
y + 4 = x
10x + 2y = 16
Solve the system by substitution:-
Let,
y + 4 = x ...(1)
10x + 2y = 16 ...(2)
Solve for y;
Substitute y + 4 as x in the eq.(2)
10( y + 4 ) + 2y = 16
Distribute 10.10y + 40 + 2y = 16
Combine like terms.12y + 40 = 16
Move constant to the right-hand side and change their sign.12y = 16 - 40
Subtract 16 from -40.12y = -24
Divide both side by 12.12y / 12 = -24/12
Hence, y = -2
Solve for x.
Substitute the value of y in eq.(1)-2 + 4 = x
Add -2 and 4.Hence, 2 = x
27
78%
Work out the area of this circle.
Take a to be 3.142 and write down all the digits given by your calculator.
21
0
Type here to search
I
Answer: See explanation
Step-by-step explanation:
Your question isn't complete and well written but I'll give examples on the calculation of the area of a circle.
1. Let's assume that a circle has a radius of 14cm and we want to know the area.
Area of a circle = πr²
where π = 3.142
r = radius = 14cm
Area = πr² = 3.142 × 14²
= 3.142 × 196
= 615.382cm²
2. Let's assume that we are given a diameter of 10cm and told to calculate the area of the circle.
Note that Diameter is twice the radius.
Area of a circle = πr²
where π = 3.142
r = radius = Diameter/2 = 10cm/2 = 5cm
Area = πr² = 3.142 × 5²
= 3.142 × 25
= 78.55cm²
PLEASE HELP ASAP! So the answer I got for this problem is 50.26. Can someone make sure that is the correct answer? Please let me know how to solve this problem if it is wrong.
Answer:
Step-by-step explanation:
every thing looks good, except the question says "round" and soooooo, if you are rounding to the 2nd decimal place, then the next two decimal places are 54, or 50.2654 so, to round that, round up , so your final answer would look like 50.27 :) see?
9514 1404 393
Answer:
50.24 inches (or 50.2 inches)
Step-by-step explanation:
The formula for circumference in terms of radius is ...
C = 2πr
Using the given values for radius and for pi, the circumference is ...
C = 2(3.14)(8 in) = 50.24 in
__
Additional comment
If you use a more accurate value of pi, the rounded value is 50.27 in. That is not the value requested by this problem. It helps to follow directions.
If you like, you can round to 50.2, since only one decimal place is required in the result.
Find the square root of 1225 by Division method.
Answer:
35
Step-by-step explanation:
square root of 1225 is 35
Answer:
Write 1225 as 5 x 5 x 7 x 7
So, 52 x 72 = 1225
So (5 x 7)2 = 1225
So √1225 = 5 x 7 = 35
Why does it help to rearrange
addends in Example B to show that
2.5n +9.9+(-3n) is equal to
2.5n + (-3n) + 9.9?
Answer:
You don't really need to do it, but it helps you keep things more organized and easier to follow. Imagine if you're doing some multi-variable equation,
2a + 5b + 4d + 3c + b + a + 2d
that looks like a mess, it'll be easier to look at if you put all the similar variables next to each others like this:
a + 2a + b + 5b + 3c + 2d + 4d
(a + 2a) + (b + 5b) + 3c + (2d + 4d)
now you can add them up much easier.
Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire.
14 ft
15 ft
20 ft
29 ft
Based on the height that the wires attach, and the base length of the stakes, the length of the wire is 29 ft.
How long are the wires?This can be solved with the Pythagorean theorem because the height can be treated as the height of a right-angled triangle. The base as the base of the triangle.
The length of the wire is the hypothenuse.
Length:
c² = a² + b²
c² = 21² + 20²
c² = 841
c = √841
= 29 ft
Find out more on the Pythagorean theorem at https://brainly.com/question/343682.
#SPJ1
In the coordinate plane, two vertices of square ABCD are A (0,0) and B (0, m). What are the coordinates of points C and D? Do not introduce any new variables.
Answer:
Step-by-step explanation:
As shown in the graph,
A, B, C and D are the vertices of a square, all sides of the square will be equal in measure.
Coordinates of A → (0, 0)
Coordinates of B → (0, m)
Distance between point D and point A = m
Therefore, coordinates of point D → (m, 0)
Now point C will be equally distant from the points B and D.
Coordinates of C → (m, m)
(f⋅g) (x) = f(x) ⋅ g(x)
true
false**
Answer:
true
Step-by-step explanation:
(f×g)×x = f(x)×g(x)
3. Determine the Area and Perimeter of the
shape below.
13
5
12
Answer:
Perimeter: 30 Area: 30
Step-by-step explanation:
Perimeter of a triangle= Add all sides = 5+12+13 = 30
Area of a triangle= (B*H)/2 = (5*12)/2 = 60/2 = 30
Hope this helps! :)
PLEASE HELPP ITS AN EMERGENCY
Find the measure of angle A.
What value of x will make the equation true?
Answer:
5
Step-by-step explanation:
When a square root of an expression is multiplied by itself, the result is that expression
5=x
how do you find the angle?
What is the solution to the system of equations graphed below?
Answer:
D
Step-by-step explanation:
The 2 lines intersect at (1, 5)
Answer:
D
Step-by-step explanation:
the line intersects at 1（x-axis）and 5（y-axis）
Will marl brainliest! Please help :,)
Answer:
x= -4
Step-by-step explanation:
A line is 180 degrees. This means that we can use the equation
60+x+124=180
Simplify:
184+x=180
x= -4
We can check this answer by plugging it back in:
60 + (-4) +124 =180
180=180
I hope this helps!
Step-by-step explanation:
[tex]60 + 124 + x = 180 \\ 180 - 184 = x \\ x = - 4[/tex]
Fill in the blank.
The
numbers are {0, 1, 2, 3, 4, ...}.
Answer:
the answer is 5 and u know the rest
What is the value of h in the figure below? In this diagram, ABAD ~ ACBD.
Д.
С
0
20
А. 80
В. 16
ОО ооо
С. 60
D. 5
Е. 8
о
Е.
Answer:
[tex]h=\sqrt{16(4)}[/tex]
[tex]h=8[/tex]
[tex]ANSWER:E) 8[/tex]
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~HOPE IT HELPS
~HAVE A GREAT DAY!!
What is graph for the equation y=-4x+1
Answer: The line starts at 1 positive, then from there go -4 (so go to the left) then 1 down from that point.
Step-by-step explanation: the problem is supposed to have been Y= -4/1 +1