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Hello,
We'll solve this by taking the Logarithm of both sides like this:
3^x = -2
Log3 3^x = Log3 -2 (Notice: we're using log3 for both sides because this gives the left side of the "=" leaving just x)
x=log3 -2 Now we need change of base formula.
x=log -2/ log 3
From here with the scientific calculator you can find the values. (Note: Log -2 is not defined)
RJ
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Hello,
Let's expand this out first.
x(4x-11)=3 rewritten as:
4x^2-11x=3 Subtract 3 from both sides to be:
4x^2-11-3=0 Now we can factor this to give us:
(4x+1)(x-3)=0 Sovingxwillbe:
4x+1=0 Subtract 1 and divide 4 into both sides to result in:
x=-1/4
x=3
This can be by plugging the answers intothe original equation.
RJ
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Hello,
Well, we got a problem here because this is not an equation. It's an expression. Are you sure you copied it correctly?
This can be simplified if that's what's needed.
( x- 3) + 5x - 11 Rewritten as:
6x-14
RJ
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Hello,
I'll march you through the steps so you can do future problems like this.
4x + 7y = 21, Find y when x = 14. Plug in 14 for x like this:
4(14)+ 7y = 21 Rewritten as:
56+7y = 21 Now we subtract 56 from both sides to be:
7y=-35 Then we divide each side by 7 to result in:
y=-5
We can check to see if this is right by plugging the answer into the original problem. I'll let you do that.
RJ
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Hello,
When we have fractions in the equation,the first thing we want to do is get rid of them. So in the case we can multiply by 12 to get:
12x+3+12x-4= x Now we can combine like terms like this:
24x-1=x Then add 1 to each side and subtract x from both sides to give us:
23x=1 Now divide both sides by 23 to result in:
x=1/23 There we go. to check to see if this is correct just plug the answer into the original equation.
RJ
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Hello,
To find the average of anything, we first add everything up and divide it by the number of items. For example:
36+70=106 Then we divide the total by 2 to give us:
53km/h
Make sense?
RJ
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Hello,
Since we're looking for the length of AC we would add the two smaller lengths like this:
(8x - 3)+(6x + 7)= combine like terms to be:
14x+4 is the answer.
Make sense?
RJ
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Hello,
Let's have "x" be the first number. Now we can set up an equation to look like:
x+(x+4)=56 Combine like terms to be:
2x+4=56 Subtract 4 from both sides:
2x=52 Divide both sides by 2 to give us:
x=26 There we go, so the second number is? Right. 30! Do they add up to 56?
RJ
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Hello,
We can let x be the number of hours so an equation can be set up as:
150 + 30x<1500 Subtract 150 from both sides will give us:
30x<1350 Now divide 30 into both sides to give us:
x<45 There we go. The person can't work over 45 hours. Check it out in the equation above to see if it works.
RJ
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Hello,
The cube root of 8xy^3 is:
2xy
Another way to look at this is 2*2*2=8 so going backwards the cube root of 8 is 2. And y^3 is brought to y when cube root is found.
RJ
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Hello,
Let's have "x" represent the first angle. The second angle will be shown as 3x and the third angle will be x+55. We know all triangles have 180 degrees so the equation we can set up will look like this:
x+3x+(x+55)=180 Combine like terms and we'll get:
5x+55=180 Now subtract 55 from both sides to get:
5x=135 Divide both sides by 5 to result in:
x=27 OK this is the smallest angle.
Make sense?
RJ
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Hello,
Let's represent x as one integer and x+1 as the next integer. Now we can set up and equation.
x(x+1)=[x+(x+1)]8-8 Rewritten it will look like:
x^2+x=16x+8-8 Let's put all this on one side of the "=" so subtract 16x from both sides to result in:
x^2-15x=0 We can solve x by using the quadratic formula.
{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}
Plugging in the numbers gives us:
x = 15
So the 2 consecutive numbers are:
15 & 16
Check it out in the above equation.
RJ
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Hello,
First off, complementary angles are when 2 angles add up to 90 degrees.
So if one angle is 82 degrees the other is 8 degrees.
That was easy,huh?
RJ
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Hello,
Let's get rid of the fractions in this (-15 / x = x+16/ 4) by multiplying both sides by 4x which will give us:
-15(4) = x(x+16) Rewrite this as:
-60=x^2+16x Add 60 to both sides will be:
0=x^2+16x+60 Now we can factor this to be:
0=(x+10)(x+6) Now we can solve x which are:
x=-10
x=-6
You can check these by plugging the answer into the original problem.
Make sense?
RJ
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Hello,
First, let's get rid of the fractions by multiplying each side by (y-8)^2 which will give us:
7(y-8) = 51 Now expand it out to be:
7y-56=51 Add 56 to both sides will result in:
7y=107 Divide both sides by 7:
y = 15.285714 (approx) Pretty wild answer, huh?
Plug this answer into the original equation and it will work out.
RJ
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Hello,
The key to finding the answer is getting r all alone in this: 12,000(1+r)^2=27,000
This can be rewritten as:
12,000(r^2+2r+1)=27,000 and rewritten again as:
12,000r^2+24,000r+12,000=27,000 Now let's subtract 27,000 from both sides to give us:
12,000r^2+24,000r-15,000=0 Now take out 3000 to be:
3000(4r^2+8r-5)=0 Now use the quadratic formula to solve x:
{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }} Plugging in the values we get:
{{r = (-8 +- sqrt( 8^2+80))/(8) }}This works out to .5 the other value is negative so we have:
rate = .5 or 50% Good return for that investment!
This can be checked by plugging the answer into the original equation.
RJ
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Hello,
2(x-1)+3(2+-3)-(4x-5) First let's multiply out this in expanded form:
2x-2+6-9-4x+5 Now we can combine like terms to be:
-2x
There we go. Make sense?
RJ
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Hello,
Not sure what you want since you didn't write out what's needed. If it's supposed to be expanded out it would look like this:
6(3x - 6y + 4z - 3) Rewritten as:
18x-36y+24z-18
RJ
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Hello,
Let's set up two equations and solve it from there.
x+y=18
xy=20
There are a couple ways to solve this. Let's set the first one like this:
x+y=18 Subtract y from both sides to give:
x=18-y Replace this into the second equation as:
(18-y)y=20 rewritten as
18y-y^2=20 Move these so they equal zero.
0=y^2-18y+20 Now we use the quadratic equation to solve:
y = (-b +- sqrt( b^2-4*a*c ))/(2*a) }
y = (18 +- sqrt( 324-80)/(2) Rewritten as:
y = (18 +- sqrt 244)/2 (Sqrt of 244 is approx 15.65)
y = 1.18975 (Approx)
Now solve for x
I'm doing basically the same as I solved for y but won't show all the steps here.
x= 16.81024 (approx)
Now we can add these and multiply these answers and it will work out.
Very good Problem.
RJ
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Hello,
Let's find the volume of the rectangular dish first by multiplying:
12x16x2=384 cubic inches
Now let's find the circular volume:
V=3.14(pi)r^2*3 (r is the radius and given is the diameter so r=6.5
V=3.14(6.5)^2*3 Do the calculations and:
V=397.995 Cubic inches
OK there we go. Looks like the rectangle dish wins the cake!:-)
RJ
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Hello,
Let's set it up so x will represent scott's money. Alice get 3/4(x) and Tricia gets 1/2(x). So the equation will be:
x+1/2(x)+3/4(x)=900,000 Combine like terms will result in:
2 1/4(x)=900,000 Let's convert the fraction so it's 2.25 and divide each side by it to give us:
x=400,000
There we go--Scot gets 400,000 dollars
Tricia gets 200,000
Alice gets 300,000
This should all add up to the total. Right?
RJ
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Hello,
First, we can plug -4 for "x" into the equation.
3x+y=-8
3(-4)+y=-8 Then add 12 to both sides to give us:
y=12-8 now combine like terms:
y=4 Therefore:
k would be 4
Sometimes letters confuse students but k here is showing the y value.
RJ
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Hello,
Here's a hint for you. Understanding miles per hour is the key. "per" means "in each" so we could say "miles in each hour" so "63 miles in each hour."
Then we just multiply 63 times 3 hours and you'll have the answer.
I'll let you do the calculation here.
Make sense?
RJ
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Hello,
The whole key to algebra equations is get the variable "x" all alone. So when we have an equation like this: x^2=40
The only way to get it to be "x" is square root both sides. When we sq rt x^2 it just becomes "x". But we need to sq rt the other side too so to keep it balanced.
(sq rt)x^2=(sq rt)40
x=6.3246 Rounded off (Also a minus 6.32)
Now we can check this to see if it's right by putting the answer back into the original equation.
RJ
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Hello,
We know the perimeter of a square is 4 times a side--right? OK, let's have x represent the side. Therefore we can set up an equation like this:
4x=40 Divide each side by 4 to give us:
x=10
Therefore we know the sides are 10 inches long.
Now we can multiply each side to get the area of the top.
10*10=100 square inches is the area.
RJ
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Hello,
We can set this up as a proportion as follows:
A couple things are needed before we set it up. One is x will represent the speed of the car and we need to know how many seconds in an hour. there are 3600 seconds in one hour. so here it is:
5/62=x/3600 Cross multiply gives us:
62x=18000 Divide 62 into both sides will be:
x=290.32 miles an hour (fast)
RJ
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Hello,
First, let's state the formula for the area of a circle
Area = pi radius squared. Now we can plug in the numbers.
1250=3.14r^2 Divide both sides by 3.14
398.089=r^2 Now square root each side to give us:
radius = 19.95 inches (Note: these numbers are rounded off)
Hey--thanks for the expanded calculation of pi
RJ
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Hello,
We can plug in the values that we have into the equation like this:
w=Cr^-2
100=C3963^-2 (r represents the radius of earth)
First let's get rid of the negative exponent like this:
100=C/3963^2 Multiply both sides by 3963^2 or 15705369
1,570,536,900=C
RJ
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Hello,
The key to this is the sum of "EVEN" integers. For example 2+4+6 etc.
So to show this in an equation it would need to be set up as:
x+(x+2)+(x+4)=72
Another helpful hint: the word "is" in math problems usually mean "equal".
RJ
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Hello,
First off we want to see if we can eliminate one of the variables.
7r-4s=33
4r+7s=56
Let's go for getting rid of "s". To do this we need to multiply the first equation by 7 and the second equation by 4 so it would turn out like this:
49r-28s=231
16r+28s=224
Now we can add both of these to be:
65r=455 Divide each side by 65 to result in:
r=7
Now we can plug 7 into either original equation to find "s".
49-4s=33 Subtract 49 from both sides to be:
-4s=-16 Now divide -4 into both sides to give us:
s=4
You can check to see if this is right by plugging s=4 and r=7 into both equations.
Make sense?
RJ
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Hello,
Since this has been factored out (21 - 0.8x)(5 - 0.4x) = 0 we can solve both x's.
(21 - 0.8x)=0 Subtract 21 from both sides to give us:
-.8x=-21 Divide both sides by -.8 to be:
x=26.25 Now let's do the other x
(5 - 0.4x) = 0 Subtract 5 from both sides to be:
-.4x=-5 Divide both sides by -.4 to be:
x=12.5
Plug these answers into the original to see if it works.
RJ
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