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23-2t=15-t
23-15= -t+2t
8=t
Answer:t=8

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6x+3=2x+11
6x-2x=11-3
4x=8
divide both sides by 4
x=2

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Point-Slope Form::
where (x1, y1) is a point through which the line passes.
so given:
x1=1
y1=1
m= 1/4




Standard Form , where A =1, B =-4,and C=-3
====================================================================
I hope this helps!

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Basic Properties of Logs
= .
so
=
take antilog to cancel the log
we get

x = 5

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log(5x+1)=log(2x+3)+log2
log(5x+1)-log(2x+3)=log2
property of Logarithms

=
Take antilog of both sides to cancel the log

(5x+1) = 2(2x+3)
5x + 1 = 4x +6
5x-4x = 6-1
x = 5

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4X-Y=3

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To find the mean you add up all the numbers and divide the answer by how many numbers you have.
mean= = = 18.5

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A series such as 3 + 7 + 11 + 15 + ··· + 99 or 10 + 20 + 30 + ··· + 1000 which has a constant difference between terms. The first term is a1, the common difference is d, and the number of terms is n. The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.

Formula: sum =

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90km/h in 20minutes
Given speed =90 km/h
Time= 20 mins= hrs= hrs
distance= speed* time
== 30km

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divide both sides by 3 we get

squaring both sides


so

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3x + 3y + ax + ay
3(x+y)+a(x+y)
taking(x+y) comman
(x+y)(a+3)

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f(x)=5x-1
plugin the value of x equal to (a-2)in the above equation
f(a-2)=5(a-2)-1
= 5a-10-1
=5a-11

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f(x)=-2x-5

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(a) f(0)
plugin x=0 in the equation


(b) f(5)
plugin f(5) in the equation we get



(c) f(-2)
plugin x=-2

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Cross multiplying we get


Divide both sides by 3 we get

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ax - bx -4a + 4b

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Compare the above equation with standard quadratic equation
we get
a = 3
b = 15
c = 18

Discriminant:
Discriminant (9) is greater than zero. The equation has two solutions.


or

or


Equation factored:

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comparing the above equation with standard quadratic equation
we get
a = 3
b = 10
c = 7
Discriminant:
Discriminant (16) is greater than zero. The equation has two solutions.

or



or



Equation factored:

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y = x-4
to get the coordinates to plzot the graph substitute the values of x (x=0,-1,1,2,3...) in the equation to get corresponding value of y
x=0 we get y=-4
for x=-1 we get y=-5
for x=2 we get y= -2

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this is a quadratic equation...if you need thevalues of t we have to factor this quadratic equation as :

we get
and

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Adding like terms we get


.

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question :: y-1 divided by 5 equals 6 .what is y?

------>(1)
cross multiplying we get
=
=
Adding 1 to both sides of the equation we get
=
=

check ::
substitute the value of y in the equation (1)
=
=
= thatz true!

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–3(x + 2) + 4x = 5x + 18
-3x-6+4x=5x+18
Taking like terms to one sides of the equation
-3x+4x-5x=18+6
-4x=24
divide both sides by 4 we get
x=-6

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Multiply.
times
A) B) C) D)
Solution:
*
=
Answer: (B):

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Solve. 3x – 0.11 = 2(x – 0.66)
A) –1.07 B) –1.21 C) –1.42 D) –0.87
Solution: 3x – 0.11 = 2(x – 0.66)
3x-0.11 = 2x- 1.32
Taking like terms to one side of the equation
3x-2x= -1.32 + 0.11
x=-1.21
ANSWER: B)-1.21

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x-intercept:-3
slope :undefined
equation of line :x=-3
To avoid the problems of lines that have infinite slopes, don't use
the equation y = mx + b; instead use the equation
ax + by + c = 0
All lines (even with infinite slopes) can be represented using that
equation.

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Let central angle be θ, and the radius be r.
θ = 60 degrees
r = 16 in
60 degrees = 60 pi/180 radians = pi/3 radians
arc length = s = rθ= pi/3 *16in =

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Compare above equation with standard quad equation
we get
a = 14
b = -20
c = 6

Discriminant: =
Discriminant (64) is greater than zero. The equation has two solutions.

or

or
x1,2 = (20 ± 8) / 2*14
or
x1 = 28 / 28 = 1
x2 = 12 / 28 = 3/7
or
x1,2 = 1, 0.428
Equation factored:
14(x-1)(x-0.428)

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Compare the above equation with standard quadratic equation
we get
a = -3
b = -10
c = 8

Discriminant: =
Discriminant (196) is greater than zero. The equation has two solutions.

or

or
x1,2 = (10 ± 14) / 2*-3
or
x1 = 24 / -6 = -4
x2 = -4 / -6 = -2/-3=2/3=0.666
or
x1,2 = -4, 0.666

Equation factored:
-3(x+4)(x-0.666)

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Sqrt(2)-sqrt( 8)
we can write sqrt(8) =2*sqrt(2)
So sqrt(2) - 2*(sqrt(2))
Taking the common term out we get,
= sqrt(2)*(1-2)
= (-sqrt(2))

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The width of a rectangle is 7 ft less than the length. The area of the rectangle is 120 ft2(square). Find the width of the rectangle.
If we let the length = L
Then, the width, or w, will be L-7
We know that the area of a rectangle is length times width.
So, L(L-7)=120



(L-15)(L+8)
So, L=15,-8 length can't be negative, so L=15
So width w=L-7=15-7=8
So width of the rectangle is 8 ft.