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maxonik [38]
3 years ago
8

From a pile of 100 pennies(P), 100 nickels(N), and 100 dimes(D), select 21 coins which have a total value of exactly $1.00. In y

our selection you must also use at least one coin of each type. How many coins of each of the three types(P, N, D) should be selected?
Mathematics
1 answer:
Murrr4er [49]3 years ago
4 0
So, you need 10 penny, 4 nickles and 7 dimes
Lets, check it.
According to the question,
total coins = 21
7 + 4 + 10 = 21
21 = 21.........................................true
Now,
their value should equal $1.00 = 100 cents
Penny = 1 cent
nickle = 5 cent
dime = 10 cent,
So,
(10 *1) + (4 * 5) + (7 * 10) = 100
10 + 20 + 70 = 100
100 = 100......................................true

 
So, you need 10 penny, 4 nickle, and 7 dimes
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Since BC is parallel to DE, triangles ABC and ADE are similar. What are the lengths of the unknown sides?
NikAS [45]

Answer:

C

Step-by-step explanation:

Step 1: find BC

Given Triangles ABC and ADE are similar,

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BC = \frac{AB}{AD} x DE

= \frac{8}{8 + 4} x 9

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Step 2: use Pythagorean theorem to find AC and / or AE

Consider triangle ABC,

by Pythagorean theorem,

AB² + BC² = AC²

AC² = 6² + 8² = 100

AC = √100 = 10 (answer... we can see that C is the only one with AC=10.

Step 3: Verify.. even though we know that it is C because AC  = 10,  you can verify that the ansewer is correct by finding CE and confirming that CE=5

By using similar triangles ABC and ADE,

AC/AE = AB / AD

AE = AD/AB x AC = 12/8 x 10 = 15

CE = AE - AC = 15 - 10 = 5 (answer confirmed)

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The product of two consecutive natural numbers is greater than their sum by 109. Find these numbers
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Answer:

The numbers will be "11 and 12".

i believe

Step-by-step explanation:

x(x + 1) > x + x + 1 + 109     where x and x+1 are the 2 numbers.

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(x - 11)(x + 10) > 0    The critical values are 11 and -10 but number must be natural

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8 0
3 years ago
When dividing exponents with the same base, what operation do we use
mario62 [17]

Answer:

To divide exponents (or powers) with the same base, subtract the exponents. Division is the opposite of multiplication, so it makes sense that because you add exponents when multiplying numbers with the same base, you subtract the exponents when dividing numbers with the same base.Quotient Rule: , this says that to divide two exponents with the same base, you keep the base and subtract the powers. This is similar to reducing fractions; when you subtract the powers put the answer in the numerator or denominator depending on where the higher power was located.

Step-by-step explanation:

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