Answer: B
Step-by-step explanation:
To solve the system of equations, use substitution.
x+y =24
Subtract x on both sides
y=-x+24
We can now substitute -x+24 in for y in the second equation.
3x+5y=100
3x+5(-x+24)=100
Distribute the 5
3x-5x+120=100
Subtract the 120 on both sides
-2x=-20
Divide by 2 on both sides
x=10
Substitute 10 in for x in the first equation.
x+y=24
10+y=24
Subtract 10 inches on both sides
y=14
So there are 10 3point questions and 14 5 point questions, so choice B
Hope this helped!
<h3>
Answer: x = 1/2</h3>
=========================================================
Explanation:
Recall that quadratic form is ax^2+bx+c.
So we need an x^2 term followed by an x term, then a constant at the end.
It may not look it, but the given equation is nearly in quadratic form.
Rewrite 9^(2x) as (9^x)^2
We get this equivalent equation (9^x)^2 - 2*(9^x) - 3 = 0
From here, let's make w = 9^x. Replace every copy of '9^x' with 'w' and we end up with this new simpler equation: w^2 - 2w - 3 = 0
From here we can use the quadratic formula or factor. I'll factor.
w^2 - 2w - 3 = 0
(w - 3)(w + 1) = 0
w-3 = 0 or w+1 = 0
w = 3 or w = -1
---------------------
Now we use these values of w to find x
If w = 3, then,
w = 9^x
3 = 9^x
log(3) = log(9^x)
log(3) = x*log(9)
x = log(3)/log(9)
x = log(3)/log(3^2)
x = log(3)/(2*log(3))
x = 1/2
At the last step, we have the log(3) terms cancel.
Repeat for w = -1
w = 9^x
-1 = 9^x
log(-1) = log(9^x)
We run into a problem. The log of any negative number is not a real number output. In other words, 9^x is never negative. Raising any positive number to a real number output leads the result to be positive. Take a look at the graph of y = 9^x to confirm this.
In short, w = -1 is extraneous so it doesn't lead to any x value solution.
So only w = 3 is useful.
Ultimately, the only solution is x = 1/2.
Answer:
Hey! so glad you got this to help your child. I believe this will help them alot, but this is not like a social media app.... don't post things like this unless needed but i hope you enjoy your time here.
Step-by-step explanation:
Answer:
x=-1, x=3
Step-by-step explanation:
find the x intercepts
(x+1)(x-3)=0
x=-1
x=3
