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galina1969 [7]
4 years ago
9

1) A decorator charges a $75 consultation fee, plus $50 per hour. Another decorator chargers a $50 consultation fee, plus $60 pe

r hour. When do the decorators charge the same amount? How much is it?
1st decorator: y = __x + __
2nd decorator: y = __x + 50
Mathematics
1 answer:
Leviafan [203]4 years ago
3 0
1st decorator : y = 50x + 75
2nd decorator : y = 60x + 50

when do they charge the same ?
50x + 75 = 60x + 50
75 - 50 = 60x - 50x
25 = 10x
25/10 = x
2 1/2 = x.....so they charge the same at 2 1/2 hrs or 2.5 hrs <==

they both charge :
50x + 75.....50(2.5) + 75 = 125 + 75 = 200 <==
60x + 50....60(2.5) + 50 = 150 + 50 = 200 <==

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A sequence can be generated by using an = an-1 + 4, where a1 = 6 and n is a whole number greater than 1. What are the first four
Firlakuza [10]

<u>Answer:</u>

  • The first four terms are <u>4</u><u>,</u><u>8</u><u>,</u><u>1</u><u>2</u><u>,</u><u>1</u><u>6</u>

<u>Step-by-Step </u><u>Explanation</u><u>:</u>

The given relation between the nth term and it's previous term is given by:

\boxed{an = an - 1 + 4}

GiveN:

  • a1 = 4

Now finding the other three terms of the AP with the given relation.

a2 = a1 + 4

Putting a1 = 4,

a2 =  4 + 4 = 8

Now, Third term:

a3 = a2 + 4

Putting a2 = 8,

a3 = 8 + 4 = 12

Now, Fourth term:

a4 = a3 + 4

Putting a3 = 12,

a4 = 12 + 4 = 16

Hence, The first four terms of the AP is 4, 8, 12 & 16.

7 0
3 years ago
Emily Elizabeth has $1.50 in dimes and nickels. She has 22 coins in all. How many nickels does she have?
Marat540 [252]

Answer:

14

Step-by-step explanation:

We can set up the following system of equations:

\begin{cases}10d+5n=150\\d+n=22\\\end{cases}, where d is the number of dimes she has and n is the number of nickels she has.

Multiplying the second equation by -5 and adding both equations lets us isolate and solve for d:

10d+5n+(-5(d+n))=150+(-5(22)),\\5d=40,\\d=8

Plugging d=8 into any of the two equations will let us solve for n:

8+n=22,\\n=\fbox{$14$}.

Therefore, she has 14 nickels.

6 0
3 years ago
Evaluate the function g(x) = 8x+16 when x=-3,0, and 8
andriy [413]

Answer:

g(x)=8x+16 for x= -3, 0, and 8.

g(-3) = -8

g(0)= 16

g(8)= 80

Step-by-step explanation:

Step 1. Plugin the given numbers.

g(-3)= 8(-3) + 16

g(0)= 8(0) + 16

g(8)= 8(8) + 16

Step 2. Solve the equations.

g(-3)= -24 + 16   Multiplied -3 and 8.

g(-3)= -8             Added -24 and 16

g(0)= 0+16         Multiplied 0 and 8.

g(0)= 16             Added 16 and 0.

g(8)= 64+16      Multiplied 8 and 8.

g(8)= 80            Added 64 and 16.

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