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8.52 x 10^7
10^7 means to multiply 8.52 by 10^7
To do this move the decimal point seven places to the right. When you run out of numbers fill in the places with zeros.
85,200,000 is the answer

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(x + 7)^2 = 81
Take the square root of both sides
x+7=9 and x+7=-9
solve each equation
x=2 and x=-16

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x^2 – 6x = -8
rewrite in standard form X^2 -6X+8=0
factor (x-4)(x-2)=0
set each factor =0 x-4=0 x-2=0
solve each equation x=4 x=2

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AB IS THE DIAMETER OF THE CIRCLE WHOSE CENTER IS O .IF THE COORDINATES OF O ARE (2,1) AND THE COORDINATES OF B (4,6). WHAT ARE THE COORDINATES OF A . PLEASE SEND ME ANSWER
O is the center of the circle. The diameter is a segment with endpoints A and B. This makes O the midpoint of segment AB. The Midpoint formula is:
M=(X1 +X2)/2, (Y1 +Y2)/2
You are given the coordinates of the midpoint and one endpoint. Adapt the formula:
X coordinate of Midpoint=(X1 +X2)/2, Y coordinate of Midpoint=(Y1 +Y2)/2
Substitute the numbers:
2=(X+4)/2 , 1=(Y+6)/2 Now solve each equation to find the X and Y coordinates of point A.
2=(X+4)/2 , 1=(Y+6)/2
cross multiply 4=X+4 , 2=Y+6 cross multiply
X=0 , Y=-4
A( 0,-4)

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if a 5 foot 6 person cast a 11 foot shadow and a nearby tree casts a 20 foot shadow how tall is the tree
5 feet 6 means 5 feet and 6 inches. Change 6 inches to .5 ft (1/2 foot)
Write a proportion with the given information. There is more than one way to write this proportion. I will write it as:
person's height /person's shadow = tree's height/tree's shadow
5.5/11 = x/20 I used x for the unknown height of the tree.
Cross multiply
11x = 110 Now divide both sides by 11
x=10

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-7 squared = 294 or -294
if -7^2=-49 because 7 times 7=49 and - is carried on but
if (-7)^2=49 because -7times-7=49

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9(^2x-1)= (81^(x+1)(27^-x)
(3^2)^2x-1=(3^4)^x+1(3^3)^-x Change 9,81and 27 to bases of 3
3^4x-2=3^4x+4(3^-3x) power to power: multiply exponents
3^4x-2=3^x+4 multiply like bases:add exponents
4x-2=x+4 equate exponents
3x=6
x=2

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Write the ratio of 10 1/2 to 25 1/5 as a fraction in simplified form.
10 1/2 =21/2 and 25 1/5 = 126/5
(21/2) / (126/5) means 21/2 divided by 126/5
to divide fractions 21/2 multiply 5/126 = 105/252 reduce to 5/12

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(5x + 2x - 7x – 3) – (6x + 3x – 11)
Combine like terms gives: (-3)-(9x-11)
A "-" in front of ( ) means to mulyiply by -1 which just changes the signs.
-3-9x+11
Now combine like terms -9x+8

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"multiplicative inverse"
Example: Find the multiplicative inverse of 5.
Write 5 as 5/1
The multiplicative inverse is the reciprocal of 5/1.
5/1 x 1/5 =1 When you multiply a number by its multiplicative inverse the product is always 1.

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The formula for the Area is A=lw
Substitute 24 for A and 2 for l.
A=lw
24=2w
w=12 Divide both sides by 2 Solve for w
Perimeter Formula P=2l+2w
Substitute 2 for l and and 12 for w
P=2(2) + 2(12)
P+4+24
P=28

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The complement is one of two angles whose degree measures added together =90.
Complementary angles add up to 90. Corners are 90 degree angles. Complemantary and corner both start with a "c"
If you know that one angle =10, then subtract 10 from 90 to get the other angle.
90-10=80 so 80 is the measure of the other angle.
The supplement is one of two angles that add up to 180 degrees.
Supplementary angles add up to 180 degress.
Straight angle = 180 degrees.
Supplementaty and straight both start with an "s".
To find the other angle, subtract the angle that you know fromm 180 to find the other angle. 180-10=170

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What is one half of 14?
one half can be written as 1/2.
"of" means to multiply. This gives this problem 1/2x14
1/2 x 14/1 Make 14 a fraction by writing it over 1.
Now this equals 14/2 To get 14/2 multiply the numerators(top numbers) together then multiply the denominators(bottom numbers) together. Then reduce the fraction to get 7. To reduce, divide the top and the bottom by 2.
1/2 x 14 = 7

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36x^2=100
x^2=100/36 Isolate the variable term( get x^2 by itself)
sqrtx^2=sqrt(100/36) Take the sqrt of both sides.
x=10/6 Take the sqrt of both sides.
x=5/3 Reduce the fraction

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9x^2=6
x^2=6/9 Isolate the variable expression(get x^2 by itself)
x=sqrt(6/9) Take the sqrt of both sides.
x=sqrt6/3 The sqrt of 9=3
x=sqrt6/3 So this is the final answer.

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The terms that are multiplied together are called factors.
(x+6)is a factor and (x-8)is a factor because they are multiplying each other.
Set each factor = 0 This gives (x+6)=0 and (x-8)=0. Solve these two one- step equations.

(x+6)=0
x=-6
(x-8)=0
x=8

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Use a proportion to solve this problem:
amount of change/beginning amount=%/100.
"From 1950" means this population is the beginning amount.
The amount of change is the positive difference between the beginning amount and the ending amount(means subtract the smaller number from the larger number)
620500000/426000000=%/100 Change % to a variable
620500000/426000000=x/100
426000000x=62050000000 Cross multiply and solve for x.
x=145.66 %

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P=2l+2w
64=2l+2w substitute 64 for P
A=lw substitute 240 for A
240=lw Solve for either l or w. I will solve for w.
w=240/l Divide both sides by l
64=2l+2(240/l) Substitution of (240/l) for w
64=(2l^2 +480)/l find common denominator of l and combine like terms
64/1=(2l^2 +480)/l Write the left side over 1 to form a proportion.
64=2l^2+480 Cross multiply
2l^2-64l+480 =0 Standard form of quadratic equation
2(l^-32l+240)=0 Factor out a common factor of 2
2(l-20)(l-12)=0 Factor the trinomial
l-20=0 and l-12=0 Set each variable factor equal to zero and solve each equation
l=20 and l-12 Let one answer be the width and one answer be the length
For example length = 20 and width =12

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Rewrite as (3^2)^x=1/3(3^1/2)
power to power: multiply exponents: 3^2x=1/3(3^1/2)
multiply both sides by 3: 3(3^2x)=1/3(3^1/2)(3)
like bases -add exponents 3^2x+1=3^1/2
equate exponents 2x+1=1/2
solve equation x=-1/4

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problem 1.
y=2/3x+0 slope =2/3 b=o
y=mx+b slope intercept formula: m=slope b=y intercept
2x-y=-4 solve for y, this puts the equation in y=mx+b form
-y=-2x-4 subtracted 2x from both sides
y=2x+4 divided both sides by -1 m=2 b=4
Therefore one solution because:
Different slopes means the graphs will intersect in one point. If the m's are = and the b's different then no solution because the graphs will never intersectbecause the lines are parallel. You have infinitely many solutions when the m's are the same and the b's are the same because one line will graph on top of the other line. This means the two lines intersect at all points.
problem 2 The first equation
x/2+2y=9 solve for x begin by subtracting 2y from both sides
x/2=-2y+9 multiply both sides by 2 to get rid of the denominator
x=-4y+18
The second equation
2x-y=18 solve for x, add y to both sides
2x=y+18 now divide both sides by 2
x=(y+18)/2
Equate your two answers resulting from both equations solved for x
-4y+18=(y+18)/2 you could make it a proportion by placing a 1 under the
left side
(-4y+18)/1=(y+18)/2 now cross multiply
-8y+36=y+18 solve this equation
-9y=-18
y=2
Take either one of the original equations and substitute 2 for y and solve for x.
2x-y=18
2x-2=18
x=10
problem 3. Have you typed this problem in correctly?
Problem 4. Using y=mx+b the slope of the first equation is 2 and the slope of the second equation is also 2. This means the lines are parallel and there is no point of intersection, hence no solution.

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I am not sure which way to read this problem. I will work it both ways.
If it is 7^x-2/6=sqrt7
change sqrt7 to 7^1/2
equate the two exponents x-2/6=1/2
solve for x x=1/2+2/6 get commom denominator
x=3/6+2/6
x=5/6
or if the problem is
7^(x-2)/6=7^1/2
equate exponents and solve the equation for x
(x-2)/6=1/2 This is a proportion, so cross multiply.
2x-4=6
2x=10
x=5

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The domain is the x value. The range is the y value. Alphabeticly domain comes before range. Alphabaticly, x comes before y. Therefore x=domain and y= range.
x-2y=1
x=2y+1 Solve equation for x.
x=2(-2) +1
x=-4+1=-3 Substitute the first value in the range for y and solve for x.
Continue this process for each number in the range.
x=2(0)+1
x=1
x=2(5)+1
x=11
x=2(8)=1
x=17
Domain is -3,1,11,17

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9+5x=7x-3 nine more than five times a number-rewrite as 9+5x
is equal to- rewrite as =
3 less than seven times the number-means 3 subtracted from 7x
rewrite as 7x-3 . Now you have the equation to be solved.
Subtract 7x from both sides of the equation
9-2x=-3
Subtract 9 from both sides.
-2x=-12
Divide both sides by -2
x=6

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use the formula: part/total=%/100 The total number must follow the
word "of"
The part number is next to the word "is".
4/50=%/100 You now have a proportion. Cross multiply.
50%=400 Replace % with any variable.
50x=400 Now divide both sides of the equation by 50.
x=8

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(-y)^-8/6(y)^5 To raise a power to a power ---Multiply exponents. If you
do not see exponent, it is one.
1/6y^5(-y^8) Move the term in the numerator with the negative exponent
to the denominator. Changing sides of the fraction line
changes the sign of the exponent.
1/-6y^13 Multiply the coefficients of the variables first.
Then multiply the y terms together. Remember,to
multiply like bases, you add the exponents.

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1/2(3a=1)-1/3(a-5)=
(3a+1)/2-(a-5)/3= Use distributive property to multiply
Now fine the common denominator of 2 and 3 which is 6.
Change each complex fraction into an equivalent one
with a denominator of 6.
3(3a+1)-2(a-5)/6 Use distributive property to multiply the numerator.
9a+3-2a+5/6 The result after multiplying.
7a+8/6 Combine like terms in the numerator.
7a/6 +4/3 Divide each term of the numerator by the 6 in the
denominator and reduce where possible.

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5i-(-15i)=20i
Two negative signes together without any number between them equals a positive sign. This problem becomes 5i+15i which equals 20i.