Step-by-step explanation:
Algebra is a topic that covers linear equations, system of equations, sequences, exponential functions, polynomials, quadratic, exponents, radicals, functions, and more. I'm going to give use algebraic formulas and not all the topics.
Like Terms Rule: If two terms that share the same variable are separated by a binary operation, we can combine them.
For example, look at
[tex]6 + 7x + 9x[/tex]
We can combine 7x and 9x.
[tex]7x + ( + 9x) = 16x[/tex]
Add the coeffceint and keep the variable.
16x+6
Solving Algebraic Equations:
Alot questions in Algebra asks you to isolate a variable. For example,
[tex] \frac{x}{2} + 6 = 9[/tex]
First step, is to get the x variable by itself. To do this subtract 6 by both sides. Why? Because Subtraction is a inverse operation off addition. Remeber the Golden Rule of Algebra,
WHAT WE DO TO ONE SIDE. WE DO TO THE OTHER.
[tex] \frac{x}{2 } = 3[/tex]
Now, we multiply both sides by 2 because multiplying is the inverse operation of division and vice versa.
[tex]x = 6[/tex]
If we plug this in, it is indeed true.
[tex] \frac{6}{2} + 6 =[/tex]
[tex]3 + 6 = 9[/tex]
Some other rules are
If we multiply a term by a one term, we only affect the term that is being multiplied, for example
[tex]2x \times 3[/tex]
2 and 3 are both real numbers so we just multiply 2 and 3. and put x behind the answer.
[tex]2 \times 3 = 6(x)[/tex]
[tex]2x \times 3 = 6x[/tex]
When we multiply 2 variables, we put the variable near each other. For example,
[tex]x \times y = xy[/tex]
When we add term, we add the coeffcient parts
[tex]y + y = 1y + 1y = 2y[/tex]
Know that
[tex]y = 1y[/tex]
When we multiply same term variables, we get
[tex]x \times x = {x}^{2} [/tex]
There is more formulas for Algebra. But these are the basicis.
Completing the Square
2. Solve the equation by completing the square. Show your work.
x2 – 30x = –125
Step 1: Add (b/2)^2 to both sides of the equation. (2 points)
Step 2: Factor the left side of the equation. Show your work. (2 points)
Hint: It is a perfect square trinomial.
Step 3: Take the square root of both sides of the equation from Step 2. (1 point)
Step 4: Simplify the radical and solve for x. Show your work. (1 point)
Answer:
See below
Step-by-step explanation:
Step 1
x^2 – 30x = –125
-30/2 = -15
(-15)^2 = 225
Step 2
x^2 -30x+225 = -125+225
(x-15)^2 = 100
Step 3
Take the square root of each side
sqrt((x-15)^2) = sqrt(100)
Step 4
x-15 = ±10
x-15 =10 x-15 = -10
x= 10+15 x = -10 +15
x = 25 x = 5
Solve the system by elimination
− 7x+ 9y =− 18
4x+ 9y =− 18
Answer:
x= 0
y= -2
Step-by-step explanation:
− 7x+ 9y =− 18
4x+ 9y =− 18
7x- 9y =+ 18
4x+ 9y =− 18
11x=0
x=0
y=-2
The cost price of an electric fan is Rs. 2800. If the shopkeeper marks its price 30℅ above the cost price and sells it at 10℅ discount, how much should a customer pay for it with 15℅ VAT?
Answer:
The customer will pay along with VAT = Rs 3767.4
Step-by-step explanation:
Cost price of an electric fan = 2800
Pirce after 30% above the cost price = 2800 + (30% of 2800 = 3640
Selling price after 10% discount = 3640 - (10% of 3640) = 3276
Now 15% VAT = 3276 x 15%
15% VAT = 491.4
The customer will pay along with VAT = 3276 + 491.4
The customer will pay along with VAT = Rs 3767.4
: Đẳng thức nào sau đây đúng ?
A. cos4x – sin4x = 2-cos2x B. cos4x – sin4x = 1+2sin2x
Step-by-step explanation:
A. cos4x-sin4x=2-cos2x
Solve for t. 4=1/2gt^2
Answer:
[tex]4=1/2gt^{2}[/tex]
Multiply equation by 2/g
4(2/g) = t²
t = √(8/g)
t = 2√(2/g)
[tex]answer:t=\sqrt{\frac{8}{g} }[/tex]
OAmalOHopeO
Using the given image and congruency markings ,type in the triangle that is congruent with the given triangle below.
Answer:
GHI is congruent to HGW
Step-by-step explanation:
The demand function for Widgets is given by the equation P = 14 – 0.39Q, and the supply function is
given by the equation P = 0.61Q + 12. Find the market equilibrium price for Widgets.
Answer:
Equilibrium price for widgets = 13.22
Step-by-step explanation:
At equilibrium, quantity demand, Qd = quantity supplied, Qs
Demand
P = 14 – 0.39Q
P - 14 = - 0.39Q
Q = (P - 14) / - 0.39
Supply
P = 0.61Q + 12
P - 12 = 0.61Q
Q = (P - 12) / 0.61
Qd = Qs
(P - 14) / - 0.39 = (P - 12) / 0.61
Cross product
(P - 14) * 0.61 = - 0.39 * (P - 12)
0.61P - 8.54 = - 0.39P + 4.68
0.61P + 0.39P = 4.68 + 8.54
P = 13.22
Check
Q = (P - 14) / - 0.39
= (13.22 - 14) / - 0.39
= -0.78 / -0.39
= 2
Q = (P - 12) / 0.61
= (13.22 - 12) / 0.61
= 1.22 / 0.61
= 2
Therefore,
Equilibrium price for widgets = 13.22
Equilibrium quantity = 2
Rate of Change: Based on the equation determine the rate of change by looking at the coefficients.
Hint: Remember: y=mx+b (m=slope)
1. y=-x+ 3
2. y=3x-1
3. y= 8 + x2
Answer:
1) -1
2) 3
3) 2
please help me (geometry)
Answer:
True
Step-by-step explanation:
When two lines are parallel, the corresponding angles formed by the transversal (intersecting line) are congruent. This is called the corresponding angles postulate. It can be used in reverse: if two corresponding angles are congruent, then the non-transversal lines are parallel.
Answer:
Step-by-step explanation:
Angles 4 and 5 are corresponding; this means that they are sitting in the same places within their angle "bunch" for lack of a better word. We are then told that they are are congruent which means that they have the exact same measure. Corresponding angles can exist without being congruent, but because they are, that means that A and B HAVE to be parallel. So true.
what is the value of i^n if the remained of n/4 is 2
A. i
B. -i
C. -1
D. 1
Answer:
5
Step-by-step explanation:
Pls help me in this question
Answer:
3
Step-by-step explanation:
since the diagonal are equal in length
6x-8=2x+4
4x=12
x=3
Instructions: Find the measure of the indicated angle to the nearest
degree
21
?
40
?=
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.
Remember: SOH-CAH-TOA
Looking from the angle, we know the opposite side and the hypotenuse. Therefore, we should use the sine function.
sin(x) = 21/40
x = sin^-1(21/40)
x = 32 degrees
Hope this helps!
combine like terms and simplify (−3 + 4x2 − 4x) + (−1 − 3x2− 4)
Answer:
x² - 4x - 8
General Formulas and Concepts:
Algebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(-3 + 4x² - 4x) + (-1 - 3x² - 4)
Step 2: Simplify
Combine like terms (x²): x² - 3 - 4x - 1 - 4Combine like terms: x² - 4x - 8Determine the axis of symmetry and the vertex of the given function.
The axis of symmetry always passes through the vertex of the parabola . The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola. For a quadratic function in standard form, y=ax2+bx+c , the axis of symmetry is a vertical line x=−b2a .
If a = -5, then 2a = -10
Answer:
That is correct
Step-by-step explanation:
To get from a to 2a we multiply by 2, so we also need to multiply -5 by 2:
2(a)=2(-5)
2a=-10
Happy learning!
--Applepi101
ASAPPPPPPPPPPPPPPPPPPPPPPPPPP HELPPPPPPPPPPPPPPPPPPPPP PLEASEEEEEE
Answer:
- 3 / 10
Step-by-step explanation:
- 9 / 10 - ( - 3 / 5 )
= - 9 / 10 + 3 / 5
= 3 / 5 - 9 / 10
= 6 / 10 - 9 / 10
= ( 6 - 9 ) / 10
= - 3 / 10
A) If {3,1,-1,-3} is the range of the function f(x) =2x+3/5, find its domain.
B) Which element in the range has pre-image 8 under the function of f:x->3x+1/5?
Answer:
64
Step-by-step explanation:
1=879=96889=
What is the area of the trapezoid below
Answer:
A = 60 in ^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 (b1+b2) h where b1 and b2 are the lengths of the bases
The bottom base is 8+2+2 = 12
A = 1/2 ( 8 + 12) *6
A = 1/2( 20)6
A = 60 in ^2
Rose’s checking account has a balance of Negative 54 dollars. She makes no more withdrawals but deposits $15 per day in her account over the next five days. On the sixth day, she makes no deposits, but the bank charges a maintenance fee of $5. What is the balance in her account on the sixth day? $16 $26 $124 $134
Answer:
16
Step-by-step explanation:
Her account balance on the sixth day is sixteen. This is because -54 +75 is 21 then you subtract 5 and get 16. (15 times 5 is 75)
Answer:
16
Step-by-step explanation:
Starting balance: -54
Deposits +15
+15
+15
+15
+15
for a total of +75
-54+75 = 21
Maintenance fee: - 5
21 - 5 = 16
what is the value of x?
Answer:
x= 25 degree
I think this one is the answer
How many solutions will each system of equations have? y=-2x+5 and 2x + y = -7
Answer:
no solution
Step-by-step explanation:
Y=-2x + 5 equation 1
2x + y = -7 equation 2
2x + (-2x+5)=-7 substitute y value from equation 1 into equation 2
2x + -2x + 5 = -7
0 +5=-7
5=-7
no solution
Find XY given the base?
Answer:
XY = 12
Step-by-step explanation:
The midsegment XY is half the length of the base CE , that is
XY = [tex]\frac{1}{2}[/tex] × 24 = 12
Determine which quadratic equation has two
non-real solutions.
Answer:
Hello,
answer C : -3x²-3x-2=0 (or 3x²+3x+2=0)
Step-by-step explanation:
A: delta=12²-4*2*18=0 not negative
B: delta= 5²+4*3*1=37 not negative
C: 3x²+2x+2=0, delta=2²-4*3*2=16-24=-8 is negative: roots are complex
D: delta 16²-4*2*2=240 not negative
Solve the inequality.
X-5 < 16
A. X> 21
B. x<21
C. x< 11
D. x> 11
Answer:
x < 21
Step-by-step explanation:
x - 5 < 16
x < 21 Add 5 to both sides
Answer:
B. x < 21
Step-by-step explanation:
x - 5 < 16
+5 +5
x < 21
The answer would be B.
1. Shoe B was created by rotating Shoe A counterclockwise about a fixed point. How many degrees was the shoe rotated?
Answer:
90°
Step-by-step explanation:
Rotation counterclockwise means the rotating an object over a fixed point in the opposite direction of our normal wall clock.
To get exact position of shoe B, shoe A would be rotated in about 90° in the opposite direction of a clock.
Thus, shoe A was rotated 90° about a fixed point to create shoe B.
Write an absolute value equation to salsify the given solution set shown on a number line -1/2 1/2 a Plz help me
Answer:
The absolute value equation is |x| =[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The standard form of absolute value equation is |x-a| =b
Where 'b' is distance from midpoint to one of the end point.
'a' is midpoint.
Here we need to write absolute value equation for the solution -[tex]\frac{1}{2}[/tex] to [tex]\frac{1}{2}[/tex] .
The midpoint of -[tex]\frac{1}{2}[/tex] to [tex]\frac{1}{2}[/tex] is 0. Because [tex]\frac{\frac{-1}{2} +\frac{1}{2} }{2} =0[/tex]
The distance from 0 to [tex]\frac{1}{2}[/tex] is [tex]\frac{1}{2}[/tex]
The absolute value equation is
|x-0 | =[tex]\frac{1}{2}[/tex]
We can simplify it as
|x| =[tex]\frac{1}{2}[/tex]
Answer:
-
Step-by-step explanation:
Hi ConcepcionPetillo,
Sorry to bother you. Can you help me with my question please? Thank you so much!
https://brainly.com/question/26223588
I NEED HELP IM LATE PLEASE
Answer:
9x, 8x+12
Step-by-step explanation:
x(2x+7)-2x(x-1)
=> 9x
2d+5(-6z-4) use z=3 d=9 .. Its between -92 and 1 .. I need help !! Thanks for whoever doing this for me . <3
Answer:
Step-by-step explanation:
Filling in the values we were given:
[tex]2(9)+5(-6(3)-4)[/tex] and we start inside the parenthesis first:
[tex]2(9)+5(-18-4)[/tex] and
[tex]2(9)+5(-22)[/tex] and by order of operations, we do multiplication or division, whichever we come to first:
18 - 110 = -92
PLEASE HELP!! what is the value of x?
Answer:
[tex]\frac{3x}{4x} =\frac{3x+7}{5x-8}[/tex]
[tex]\frac{3}{4} =\frac{3x+7}{5x-8}\: (cross\: multiply)[/tex]
[tex]3(5x-8)=4(3x+7)[/tex]
[tex]15x-24=12x+28\\+24~~~~~~~~~~~~+24[/tex]
[tex]15x=12x+52\\-12x~~~~-12x\\-------\\3x=52[/tex]
[tex]\frac{3x}{3} =\frac{52}{3}[/tex]
[tex]x=52/3[/tex]
[tex]Answer:C[/tex]
-------------------------
Hope it helps...
Have a great day!!
what is the answer to this question
Step-by-step explanation:
here's the answer to your question
Answer:
x = 45. the option is C
Ihope its right
