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Let Class 2 have x house points. Therefore, 

\(2x + x = 675\)

\(x = \boxed{225}\)

Class 2 has 225 points.

The formula is \(A = P(1 + \frac{r}{n})^{nt}\), where:

P = principal (starting amount)

r = annual rate

n = compound type (annually)

t = time in years

Plug in P = 10,000, r = 6%, n = 1, and t = 4 to get A = $12624.

Oh my bad. I'm really sorry for making you think you were wrong.

We can complete the square. After simplifying, we get x^2 + 9x.

This simplifes to \(x^2 + 9x = (x + \frac{9}{2})^2 - \frac{81}{4}\). So, the constant is 81/4.

We have \(4 - n \equiv 10 \quad (\mod 14)\)

So, \(n \equiv 8 \quad (\mod 14)\)

Therefore, \(m+n \equiv 4+8 \equiv \boxed{12} (\mod 14)\)

We have \(2 < \sqrt{t} < 35\)

\(4 < t < 1225\)

There are 1224 - 5 + 1 = 1220 values of t.

We can draw a Venn diagram.

office keys || both || wallet

       20       ||    5   ||    30

The probability that you forget your office keys or your wallet is 20 + 30 - 5 = 45%.

So, the answer is 1 - 45% = 55%

sorry how did you calculus t=-3/5 and 5 

The value of \(x\) is \(\boxed{\log_2{7}}\)

Use Simon's favorite factoring trick; it's going to make it so much easier:

\((a+2)(b+2)=-12\\ (a+2)(c+2)=30\\ (b+2)(c+2)=-10\)

Multiply all the equations to get:

\(((a+2)(b+2)(c+2))^2=3600\\ (a+2)(b+2)(c+2)= \pm 60\)

In the first case where the right-hand side of the equation above is positive, to solve for a, divide \((a+2)(b+2)(c+2)=60\) by \((b+2)(c+2)=-10\) to get \(a+2=-6 \rightarrow a=-8\). Do that the same with b and c to get \(b = 0\) and \(c=-7\).

In the second case where the right-hand side of the equation is negative, do the exact same thing mentioned above to get \(a = 4, b = -4, c = 3\).

Therefore, the solutions to this system of the equation are:

\(\boxed{a = -8, b = 0, c = -7 \text{ or } a = 4, b = -4, c = 3} \)

Let x be the number of one dollar bills and y be the number of five dollar bills. We can write a system of equations:

14 bills in total ==> x + y = 14                     . (1)

value of bills is $30 ==> x + 5y = 30           . (2)

Multiply equation (1) by 5.

5x + 5y = 70

x + 5y = 30

We get 4x = 40, so x = 10 and y = 4. Sharon has 10 $1 bills and 4 $5 bills.

Once again, we can use Vieta's equations. 

The sum of the roots is \(-\frac{b}{a} = -\frac{-10}{2} = 5\).

The product of the roots is \(\frac{c}{a} = \frac{5}{2}\).

Now, we can simplify: \((2a-3)(4b-6) = 8ab - 12(a+b) + 18 = 8(\frac{5}{2}) - 12(5) + 18 = \boxed{-22}\)

There is probably a formula for this, but I don't know any other method other than brute force.

\((8/5)^2 + (12/5)^2 + (16/5)^2 + \dots + (44/5)^2\)

\((64/25) + (144/25) + \dots + (1936/25)\)

The sum from 64 to 1936 is \((1^2 + 2^2 + \dots 45^2) - (1^2 + 2^2 \dots + 7^2) = \frac{(45)(46)(91)}{6} - 140 = 31225\).

Now, we have \(\frac{31225}{25} = \boxed{1249}\)

The ball hits the ground when the height is 0, so we are solving the equation \(-5t^2+22t+15=0.\)

Using the quadratic equation, we get \(t= -\frac{3}{5}, 5\). Time can't be negative, so the ball hits the ground after 5 seconds.

I am unsure about the second part, but I hope this gets you started.

Let x be the number of cupcakes and y be the number of cookies sold. We can write a system of equations:

total of 250 cupcakes and cookies ==> x + y = 250           . (1)

total cost was $506 ==> 3.5x + 1.25y = 506                       . (2)

We can multiply equation (1) by 5 and equation (2) by -4:

5x + 5y = 1250

-14x - 5y = -2024

Adding, we get -9x = -774, so x = 86 and y = 164.

You baked 86 cupcakes and 164 cookies.

Thank you!

We can use Vieta's Formulas. Simplifying, we get \(2y^2-11y+4\) and by Vieta's, we get \(\frac{11}{2}\)

The cost to rent each chair is c and the cost to rent each table is t. We can write the system of equations

cost to rent 6 chairs and 2 tables ==> 6c + 2t = 24       . (1)

cost to rent 3 chairs and 5 tables ==> 3c + 5t = 45       . (2)

Multiply equation (1) by 5 and equation (2) by -2:

30c + 10t = 120

-6c - 10t = -90

So, 24c = 30 and c = 1.25. Therefore, t = 8.25.

It's correct, thanks!!

Let  angle  ROB   = 3x

Let angle SOT  = x

Because   there are  central  angles,  the  arcs  they intercept  have  the   same measure

And  we  have  the  theorem  that

angle   RTB  =  (1/2)  ( arc  intercepted  by   ROB  - arc intercepted by  SOT)

So

29  = (1/2)  ( 3x  - x)     multiply  through by  2

58   = 3x  - x

58   =   2x

x =  29

Arc  ROB  = 3x  =  3(29)   =  87

Arc SOT  =  x     =  29

Minor arc  RS   =   180   -   87   -   29       =  64°

We can use Vieta's Formulas. The sum of the roots is \(-\frac{b}{a} = \frac{m}{2}\) and the product of the roots is \(\frac{c}{a} = \frac{n}{2}\).

The sum is 6, so \(\frac{m}{2}=6\) and m = 12.

The product is 10, so \(\frac{n}{a} = 10\) and n = 20.

So, \(m+n=12+20 = \boxed{32}\)

If we can repeat letters more than once, there are \(4^4 = \boxed{256}\) words that can be made.

19$ fortnite card is the answer

Thanks!