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lapo4ka [179]
3 years ago
10

A collection of nickels, dimes, and quarters consist of 18 18 coins with a total of $ 2.05 $2.05. if the number of dimes is equa

l to the number of nickels, find the number of each type of coins.
Mathematics
1 answer:
ladessa [460]3 years ago
6 0
The first thing we must do for this case is to define variables.
 We have then:
 x = the number of nickels
 y = the number of dimes
 z = the number of quarters
 We write the system of equations:
 0.05x + 0.1y + 0.25z = 2.05
 x + y + z = 18
 x = y
 Solving the system we have:
 x = 7
 y = 7
 z = 4
 Answer:
 
nickels = 7
 
dimes = 7
 
quarters = 4
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If a varies directly as b and a=3 when b=12, what is the value of a when b=18?
Zepler [3.9K]

Answer:

a is proportional to b

a=kb

k is proportionality constant

k =a/b =3/12 =1/4

k=1/4 = a/b=a/18

1/4=a/18

a=18/4 =9/2 =4.5 answer

4 0
3 years ago
Expand the number 1120 into its corresponding exponential form. 25 · 5 · 7 52 · 8 22 · 53 · 7 2 · 5 · 7
Eduardwww [97]

Answer:

(A) 2^{5} * 5 * 7

Step-by-step explanation:

Your question formatting made it very complicated to understand the possible answers.  Please use some notation or the equation editor next time.

So, the exponential form a way to write a number using multiplications and powers.

Let's examine the various options (if I read them correctly)

(A) 2^{5} * 5 * 7 - YES!

2^{5} is 32, so 32 * 5 * 7 = 160 * 7 = 1120

(B) 5² · 8  - NO

= 25 * 8 = 200

(C) 2² * 5³ * 7 - NO

= 4 * 125 * 7 =500 * 7 = 3500

(D) 2 · 5 · 7 - NO

= 10 * 7 = 70

5 0
3 years ago
Given the diagram below. If G is the circumcenter of ABC. DC = 16, GB = 21 and AZ = 19, find each measure.​
Jlenok [28]

Answer:

Step-by-step explanation:

Properties of a circumcenter;

1). Circumcenter of a triangle is a point which is equidistant from all vertices.

2). Point where perpendicular bisectors of the sides of a triangle meet is called circumcenter of the triangle.

From the picture attached,

9). AG = GB = GC = 21

10). BC = 2(DC)

            = 2×16

            = 32

11). By applying Pythagoras Theorem in ΔGFB,

     GB² = GF² + FB²

     (21)² = GF² + (19)²

     441 = GF² + 361

     GF² = 441 - 361

     GF = \sqrt{80}

     GF = 8.9

12). By applying Pythagoras theorem in ΔGDB,

     GB² = DG² + BD²

     (21)² = (DG)² + (16)² [BD = DC = 16]

     DG² = 441 - 256

     DG = √185

     DG =  13.6

7 0
3 years ago
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bearhunter [10]
$52 - $16= $36
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Answer:

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