Answer:
30 Nickels and 188 Pennies
Step-by-step explanation:
okay, so to set up the equation first, we have to assign each coin a variable, let's call them p and n:
P= number of pennies
N= number of nickels
the value of a penny is 1 cent, so 1P, and the value of a nickel is 5 cents, so 5N
The problem states that he has 218 coins, meaning that the total number of pennies and nickels adds up to 218:
P + N = 218
the total value of the coins is $3.38, so that would mean that 1P + 5N has to equal $3.38:
1P + 5N = 338
Okay, so now that we have our equations let's solve them using elimination:
we have to get a common coefficient between both equations, so let's multiply our first equation by 5:
P x 5 = 5P
N x 5 = 5N
218 x 5 = 1090
so, now we can solve by elimination:
5P + 5N = 1090
1P + 5N = 338
the N's cancel out:
4P = 752
divide both sides by 4:
P = 188
okay, so if theres a total of 218 coins, subtract 188 from 218:
218 - 188 = 30
so, there are 30 nickels and 188 pennies.
check our work:
5 x 30 = 150
1 × 188 = 188
150 + 188 = 338
338 = 338
I hope this helps! :)
Finding the distance between (-4,2) and (146,52)
Use the distance formula<span> to determine the </span>distance<span> between the two </span>points<span>.
</span><span>Distance= </span>√<span>(<span>x2</span>−<span>x1</span><span>)^2</span>+(<span>y2</span>−<span>y1</span><span>)^2
</span></span>Substitute the actual values of the points<span> into the </span>distance formula<span>.
</span>√<span>((146)−(−4)<span>)^2</span>+((52)−(2)<span>)^2
</span></span>Simplify the expression<span>.
</span>√19400<span>
</span>Rewrite 19400<span> as </span><span><span><span>10^2</span>⋅194</span>.
</span>√10^<span>2⋅194
</span>
Pull terms<span> out from under the </span>radical<span>.
</span>10√<span>194
</span>The approximate<span> value for the </span>distance<span> between the two </span>points<span> is </span><span>139.28389.
</span>
10√<span>194≈139.28389</span>
Answer:
The prove is as given below
Step-by-step explanation:
Suppose there are only finitely many primes of the form 4k + 3, say {p1, . . . , pk}. Let P denote their product.
Suppose k is even. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
ThenP + 2 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 2 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠2. This is a contradiction.
Suppose k is odd. Then P ≅ 3^k (mod 4) = 9^k/2 (mod 4) = 1 (mod 4).
Then P + 4 ≅3 (mod 4), has to have a prime factor of the form 4k + 3. But pₓ≠P + 4 for all 1 ≤ i ≤ k as pₓ| P and pₓ≠4. This is a contradiction.
So this indicates that there are infinite prime numbers of the form 4k+3.
Answer:
1. y=3x-1
Step-by-step explanation:
y=mx+b
y=output
m=slope
x=input
b=y-intercept
Answer:
The age of the pottery bowl is 10523 years.
Step-by-step explanation:
Amount of substance:
The amount of a substance after t years is given by the following equation:
In which A(0) is the initial amount and r is the decay rate.
Half-life of C14.
Researching, the half-life of c-14 is 5730 years.
This means that:
We use this to find r. So
![\sqrt[5730]{(1-r)^{5730}} = \sqrt[5730]{0.5}](https://tex.z-dn.net/?f=%5Csqrt%5B5730%5D%7B%281-r%29%5E%7B5730%7D%7D%20%3D%20%5Csqrt%5B5730%5D%7B0.5%7D)
So
Age of the pottery bowl:
We have that:
We have to find t. So
So
The age of the pottery bowl is 10523 years.
