1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Soloha48 [4]
3 years ago
11

An electrician charges a $50 fee to make a service call plus $25 per hour he works. write an equation to represent the relations

hip between the two variables and tell whether or not it is proportional. explain your reasoning.
Mathematics
1 answer:
Kay [80]3 years ago
4 0
If x is the number of calls he makes and y is the number of hours he works;
the total amount he charges is termed as C
C = (50 * x) + (25 * y )
C = 50x + 25y
25y = C - 50x
the 2 variables are not proportional.
For 2 variables to be proportional, they need to be in the form y = mx 
Where m is a constant. When x increases, y too should increase by the same amount. 
The question given x and y are not proportional. As the number of hours he works and number of calls he charges are not dependent on each other. Therefore the 2 variables are not proportional.
You might be interested in
PLEASE HELP!! Algebra 2
lawyer [7]

Answer:

No

Edit:

Yes, based on original equation. (Credit to greenpumpkin for correction)

Step-by-step explanation:

For this problem, we simply need to find the values of x that can make the equation true.  So, let's begin by isolating the "x" variable.

sqrt(2x + 13) = x + 5

[sqrt(2x + 13)]^2 = (x + 5)^2

2x + 13 = x^2 + 10x + 25

0 = x^2 + 8x + 12

Note, we can remove the sqrt method by squaring both sides of the equation.  Doing this, we see we have a quadratic equation meaning we can apply the quadratic formula to find solutions for x.

[-b +/- sqrt( b^2 - 4(a)(c) ) ] / 2a

Let a = 1, b = 8, and c = 12

[-8 +/- sqrt( (8)^2 - 4(1)(12) ) ] / 2(1)

= [-8 +/- sqrt( 64 - 48 ) ] / 2

= [-8 +/- sqrt(16) ] / 2

= [ -8 +/- 4 ] / 2

So, x = [ -8 + 4 ] / 2  and x = [-8 - 4 ] / 2

x = [-4] / 2 = -2  and x = [-12] / 2 = -6

Hence, the two values of x that can solve this quadratic equation are x = -2 and x = -6.

Therefore, we know that x = -6 is not extraneous, meaning it is a solution to our equation.

Cheers.

----------------------------------------------------

Edit:

Plugging the value of -6 back into the original equation, we get the following:

sqrt(2x + 13) = x + 5

sqrt(2(-6) + 13) = (-6) + 5

sqrt (1) = -1

1 != -1

Given that 1 cannot equal negative 1, we can say that x = -6 is an extraneous solution. (Credit to greenpumpkin for correction)

8 0
3 years ago
Write an equation to describe the proportional relationship in this table. Explain your thinking and how you got your answer.
creativ13 [48]

Focus on the values in red outside the table (on the left and right sides). As the output increases by 4, the input increases by 1. This leads to the slope being rise/run = 4/1 = 4. The slope is the number just to the left of the x variable. So that's how they ended up with the equation y = 4x.

You can think of it as y = 4x+0, and note how it's in the form y = mx+b

m = 4 = slope

b = 0 = y intercept

The y intercept is the value of y when x = 0.

--------

Now because x = 0 and y = 0 pair up together, we can find the slope a different way: Pick any row other than the first row. Divide the y value over its paired x value. So let's say we pick on row two and we'd get a slope of y/x = 4/1 = 4.

Or we could pick on row three and get y/x = 8/2 = 4.

Picking on the fourth row gets us the slope to be y/x = 12/3 = 4. We end up with the same slope value each time. Again, this trick only works if (x,y) = (0,0) is on the line. Otherwise, you'll need to use the first method or use the slope formula.

For equations like this, we consider them a direct proportion. As x increases, so does y. As x increases by 1, y increases by 4. This is the same throughout the table.

----------

A real world example of this could be that x represents the number of sodas you buy, and if each soda is $4, then y = 4x represents the total cost of buying x number of sodas.

For instance, if you bought x = 10 sodas, then y = 4*x = 4*10 = 40 dollars is what you spend overall.

7 0
3 years ago
Write the number four million, two hundred thirty, seven thousand, three hundred and four hundredths
Anit [1.1K]

There are no tens, ones, or tenths.

4,237,300.04

6 0
3 years ago
F(1)=_________________________
olga nikolaevna [1]

Answer:

f(1) = 1

Step-by-step explanation:

The value of f(1) simply means what is the corresponding output we would get for an input of 1.

This also implies that for what of y is x equal to 1?

From the graph, when x = 1, y = 1.

Thus:

f(1) = 1

7 0
3 years ago
Avery can run at 10 uph. The bank of a river is represented by the line 4x + 3y = 12, and Avery is at (7, 5). How much time does
Reil [10]
The minimum distance will be along a perpendicular line to the river that passes through the point (7,5)

4x+3y=12

3y=-4x+12

y=-4x/3+12/3

So a line perpendicular to the bank will be:

y=3x/4+b, and we need it to pass through (7,5) so

5=3(7)/4+b

5=21/4+b

20/4-21/4=b

-1/4=b so the perpendicular line is:

y=3x/4-1/4

So now we want to know the point where this perpendicular line meets with the river bank.  When it does y=y so we can say:

(3x-1)/4=(-4x+12)/3  cross multiply

3(3x-1)=4(-4x+12)

9x-3=-16x+48

25x=51

x=51/25

x=2.04

y=(3x-1)/4

y=(3*2.04-1)/4

y=1.28

So now that we know the point on the river that is closest to Avery we can calculate his distance from that point...

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(7-2.04)^2+(5-1.28)^2

d^2=38.44

d=√38.44

d=6.2 units

Since he can run at 10 uph...

t=d/v

t=6.2/10

t=0.62 hours  (37 min 12 sec)

So it will take him 0.62 hours or 37 minutes and 12 seconds for him to reach the river.




8 0
3 years ago
Other questions:
  • 7x + 14 - 17-3x = 6x - 4z + 2 - 5 find the value of x<br> 3 5 3
    9·1 answer
  • Please help with this question
    11·1 answer
  • There is no overlap between the graphs of y&lt; x+ 2 and y&gt; x-2.
    11·1 answer
  • Help me please Nd thankyou
    13·1 answer
  • WILL GIVE BRAINLIEST!!Soro bought a $50.00 bus card at the beginning of the week. Each bus ride costs $2.50. He needs to have at
    15·2 answers
  • The perimeter of a rectangle is 24 inches. If the length of
    12·1 answer
  • You are planning to buy a house for $800,000. City bank offers a 30 year loan at 4.9 % apr ( Annual percentage interest rate) if
    10·1 answer
  • What is the area of a square with h=3in l=5in w=6in
    5·1 answer
  • F(x) = 6x + 3<br> g(x) = 3x - 2<br><br> help ASAP PLS
    6·1 answer
  • Evaluate b-(-1/8)+c where b=2 and c=-7/4
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!