Katie has a collection of nickels, dimes, and quarters with a total value of $4.35. There are 3 more dimes than nickets and 5 more quarters than
nickels. How many of each coin is in her collection?

What’s the equation

Step-by-step explanation:

So you know that some number of nickels, dimes and quarters will add up to 490 cents. Every nickel is worth 5 cents, so some number of nickels can be 5n. In the same way, some number of dimes can be 10d, and some number of quarters can be 25q. So the general equation is going to be 5n + 10d + 25q = 490 But since the dimes and quarters are also explained in relation to the number of nickels, think of everything as nickels: the number of dimes (d) = the number of nickels + 7, so d = n + 7 And in the same way, you can arrive at the number of quarters (q) is nickels + 4, so q = n + 4 So re-write the equation, but each time you see d, write n + 7 instead and each time you see q, write n + 4. you'll end up with lots of chunks of n: 5n + 10(n + 7) + 25(n + 4) = 490 when you do all the multiplying, you get: 5n + 10n + 70 + 25n + 100 = 490 combine all those terms and you get 40n + 170 = 490. Subtract 170 from both sides and you get 40n = 320. Divide both sides by 40 and you get n = 8. Which means you have 8 nickels, then add 7 to get 15 dimes, and for the quarters it was the nickels plus 4, so you have 12 quarters. When you double check by multiplying out how much each pile of coins is worth, it will add up to 490 cents, or $4.90

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

b. 18

step-by-step explanation:

so the equation for this is:

ab^2=ac⋅ad

ab being the top length of 6 and ac being the length of 2 and ad being the length of x. let's plug into the equation:

6^2 = 2x

now lets just solve for x:

36 = 2x

18 = x

i hope that !