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ehidna [41]
3 years ago
7

Rosita and Garth are saving up for a vacation, and begin with a certain amount saved each. If Rosita works 5 hours, she will hav

e $128. If she works 7 hours, she will have $164. If Garth works 3 hours, he will have $124. If he works 8 hours, he will have $194. They want to know when they will have saved the same amount of money and how much each will have saved.
Mathematics
1 answer:
noname [10]3 years ago
7 0
Treat each (time, money) pair as an (x, y) pair, and get the slope of the line:
For Rosita, (5, 128), (7, 164): m = (y2 - y1)/(x2 - x1) = (164 - 128)/(7 - 5) = 18, implying that she earns $18/hr. The y-intercept is calculated as: y = 18x + b, 128 = 18*5 + b, b = $38, meaning that she started with $38. Rosita's equation is y = 18x + 38.
For Garth, (3, 124), (8, 194): m = (194 - 124)/(8 - 3) = 14. For 124 = 14*3 + b, b = $82. Garth's equation is y = 14x + 82

To find out when they will have saved the same amount, both equations would have the same y-value:
18x + 38 = 14x + 82
4x = 44
x = 11 hours
y = 18*11 + 38 = $236 (alternatively, y = 14*11 + 82 = 236)
This means that Rosita and Garth will have both saved $236 after 11 hours of working.
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Please help!! (Number 73)
Rasek [7]
So hmm notice the picture below

one is 7x5x1.75 the volume of a rectangular prism is V = length * width * height

so 7*5*1.75 gives us 61.25 ft³

the second one, is larger by some width and length we dunno, but we know that it required that 61.25 plus an extra 17.5 to fill it up, so its volume is 61.25 + 17.5 or 78.75

the height is the same... so \bf V=l\cdot w\cdot h\qquad 
\begin{cases}
l=length\\
w=width\\
h=height\\ --------\\
h=1.75\\
V=78.75
\end{cases}\implies 78.75=lw\cdot 1.75
\\\\\\
\cfrac{78.75}{1.75}=lw\implies 45=lw

so.. if you factor 45, to two factors, one will be the length, the other the width

3 0
3 years ago
Which equation represents a line that passes through (4,1/3) and has a slope of 3/4?
scoray [572]

Step-by-step explanation:

With this kind of problem, we're looking at an equation in the form

y - y1 = m(x - x1)

(m = slope)

so we can substitute m, y1, and x1 with the values we're given.

y - y1 = m(x - x1)

y - 1/3 = 3/4(x - 4)

Answer:

y - 1/3 = 3/4(x - 4)

6 0
3 years ago
If y is 20 when x is 5 find x when y is 60
Verdich [7]

Answer:

15

Step-by-step explanation:

If y is 20 when x is 5 then x is always 1/4 of y

60*(1/4)=15

5 0
3 years ago
Read 2 more answers
Will give 5 stars on your answer and a thank you.
DENIUS [597]

Answer:

the variable term is (t)

the answer is 13.50t

4 0
2 years ago
Read 2 more answers
A skyscraper has 49 floors there are 26 offices on each of the bottom 31 fours the top 18 floors each have 38 officers about how
Anettt [7]

Answer:

903 offices

Step-by-step explanation:

Total number of officers in the sky scraper

= 26 + 31 + [(49-2)×18]

= 26 + 31 + 846

= 903 offices

3 0
2 years ago
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