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Let’s start with the first one:
We can change this into a logarithm (click here if you’re confused):
Using the change of base rule, we can get it into log base 10:
And then find the answer:
Same for your second question:
For your final question:
We found the values of y and x, so we just need to plug them in:
I hope this helps :)
1. You need to multiple times 4 on both sides, so now you have 1 over sqrt x = 8
2. In order to know the value of the sqrt of x (so you can solve easier without any fractions), you can write sqrt x = (the number that is above the sqrt) / (the number that is in the other side). In this case, sqrt(x) = 1/8
3. To cancel the sqrt, you need to get the second power on both sides,
(sqrt(x))^2 = (1/8)^2
4. Now you have x = 1/64
I’m not sure if it’s clear. If not, let me know and I’ll try to solve it tomorrow morning. (Sorry if my english is terrible but it’s already 2am and I’ve been working for +10hrs straight and my bilingual brain can’t think straight)
We answered a similar question here.
Short answer: The differences between the numbers are increasing odd numbers. The next number should be 35+13=48.
Not a bother at all!
Simultaneous equations are pretty tricky if you’re new to them, the key thing to always remember is you have to eliminate a variable so you’re only left with one! How we can do this is by solving for one variable (making it so it’s x = …. or y = … ) and then substitute for that value! In any case you can always choose which equation you want to solve the variable for, since you have an option of two, we’ll choose the simpler one, the first one. It is only a first degree equation so it’s much easier to deal with.
We can solve for x or y, since we’re used to y = … in earlier classes, we’ll do it as such,
2x + 3y = 10 (We move the 2x to the other side so it changes integers to -2x)
3y = 10 - 2x (We divide the entire equation by 3 to isolate y)
y = [ 10/3 -2x/3 ]
Now that we have isolated for one variable we can substitute everything in the bracket as a representation for y. Now we bring in the other equation
4x^2 + y^2 =20
And put in the bracket where y is suppose to be.
so now we can solve for x alone.
4x^2 + [10/3 -2x/3]^2 = 20, (Expand and simplify)
4x^2 + 4x^2/9 - 40x/9 + 100/9 = 20 (To simplify we multiply everything by 9/1 to get rid of fractions)
36x^2 + 4x^2 - 40x +100 = 180 (make it into a quadratic to solve for the x’s)
40x^2 -40x +100 - 180 = 0
40x^2 -40x - 80 =0 (Divide by 40 to get the simplest equation possible)
x^2 -x - 2 = 0 (what has a sum of -1 and a product of -2? (-2, +1)
(x-2)(x+1) = 0
X = 2,
X = -1
So now that we have the x solutions, we can sub in the solutions to simplify either above equations and get the y.
Now you must note that we do this for BOTH x values as they will give us possibly different y values. The reason for having 2 solutions is because the 2nd equation given is a 2nd degree function meaning the original function will cross it twice.
2x + 3y = 10
2(2) + 3y = 10
4 + 3y = 10
3y = 10 -4
3y = 6
y = 2
So a solution is (2,2)
2(-1) + 3y = 10
-2 + 3y = 10
3y = 10 + 2
3y = 12
y = 4
And second one is (-1,4)
So the two solutions are (2,2) and (-1,4)
Hope this helps! :)
Can you help me with my homework? i have absolutely no idea what im doing and my teacher never answers any questions i have.
The first equation is in implicit form. This means that on one side (here: left) are all variables with their coefficients while on the other side of the equation you have a constant.
The second equation is in explicit form. This means you define one variable (here: y) as whatever’s on the other side of the equation.
"To graph an equation in implicit form the easiest way is to find the x-intercept and y-intercept.” Let’s look at the first equation: if you set x=0 you have y=2, so this graph cuts the y-axis at 2. If you then set y=0 you have x=4, so the graph cuts the x-axis at 4. You now only need to connect those points and you’re finished.
"Slope-intercept form is [I assume your teacher wants to hear y=mx+n but I’m not sure. Okay, I /am/ sure, but only 90% sure] where m is the slope and n is the y-intercept.” You get the slope by subtracting y- and x-coordinates from 2 different points and by dividing DELTA y / DELTA x. n is where the graph cuts the y-axis because when you set x=0 the first term is 0, thus you have y=n.
"The solution to the system is the interception point of the two lines.” How so? You are looking for a solution of this linear equations system that is x=~, y=~. Thus, it is implied that x and y have the same value in each equation; you are really looking for a point that both graphs have in common, which is their interception point.
You can now find the solution by drawing the graphs and then checking with the equations by first inserting one variable and then checking the value of the second one. The solution is x=4, y=0.
I hope that helped!
Domain is everything we can plug into x to make the function valid. For this, since it’s a fraction, the denominator can never be 0. Thus, x where the denominator is 0 is not possible, and is not in our domain!
2x + 8 = 0
2x = -8
x = -4
Any value of x, except for x = -4, is possible. In interval notation, this would look like this:
(-infinity, -4) U (-4, infinity)
Here is a site explaining it: (x)
Here is a nice video I found on it: (x)
So let’s separate this up, first looking at the house and then at the contents, and later combining them.
His house was valued at £50,000. Per £100 of that, he gets 20p. Thus, we need to find how many of those £100 fit into what it was valued at. Divide 50,000 by 100 = 500. Now we have 500 times 20p for the house = 10,000p.
The contents were valued at £20,000. Per £100, he gets 25p. £20,000 divided by 100 = 200. 200 times 25p = 5,000p.
The contents and house together = 10,000p + 5,000p = 15,000p. We can convert this into pounds by dividing it by 100 (there are 100 pence in a pound). So, Mr. Day’s total premium is £150 for his house and contents.