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3 years ago

A coffee shop sells lattes for $4 and

Mathematics

1 answer:

SVEN [57.7K]3 years ago

3 0

Answer: 54 lattes were sold

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations with the information given:

If each latte costs $4 , each cappuccino cost $3, and sales totaled $252:

4 x + 3y = 252

Where

x = number of lattes

y = number of cappuccinos

The number of lattes sold was 6 more than 4 times the number of cappuccinos. Mathematically speaking:

x = 4y +6

Now, we have the system:

a)4 x + 3y = 252

b)x = 4y +6

Replacing the value of x in a) for b):

4 (4y +6) +3y =252

16y +24 +3y =252

16y +3y =252 -24

19y = 228

y= 228/19

y = 12

Replacing the value of "y” in b ) for the value obtained:

b)x = 4y +6

x = 4 (12) +6

x = 48+6 = 54

x =54

So , 54 lattes were sold.

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Brian is a software salesman. His base salary is $2500 , and he makes an additional $50 for every copy of History is Fun he sell

QveST [7]

P = 50N + 2500 <== ur equation

for 23 copies...sub in 23 for N

P = 50(23) + 2500
P = 1150 + 2500
P = 3650 <==

6 0

3 years ago

Read 2 more answers

If f(x) = x-1/3 and g(x) = 3x+1 what is (fog)(x)

marin [14]

Answer:

if you meant f(x) = (x - 1) /3 then f (g(x) ) = x

of if you meant f(x) = x - (1/3) then f(g (x)) = 3x + 2/3

Step-by-step explanation:

f(x) = x-1/3 and g(x) = 3x+1 what is (fog)(x)

f ( g(x) ) = (3x + 1) - (1/3) = 3x + 2/3

if you meant f(x) = (x - 1) /3 then f (g(x) ) = x

of if you meant f(x) = x - (1/3) then f(g (x)) = 3x + 2/3

3 0

3 years ago

How do you find a vector that is orthogonal to 5i + 12j ?

Rashid [163]

$\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad \cfrac{a}{b}\\\\
slope=\cfrac{a}{{{ b}}}\qquad negative\implies -\cfrac{a}{{{ b}}}\qquad reciprocal\implies - \cfrac{{{ b}}}{a}\\\\
-------------------------------\\\\$

$\bf \boxed{5i+12j}\implies 
\begin{array}{rllll}
\ \textless \ 5&,&12\ \textgreater \ \\
x&&y
\end{array}\quad slope=\cfrac{y}{x}\implies \cfrac{12}{5}
\\\\\\
slope=\cfrac{12}{{{ 5}}}\qquad negative\implies -\cfrac{12}{{{ 5}}}\qquad reciprocal\implies - \cfrac{{{ 5}}}{12}
\\\\\\
\ \textless \ 12, -5\ \textgreater \ \ or\ \ \textless \ -12,5\ \textgreater \ \implies \boxed{12i-5j\ or\ -12i+5j}$

if we were to place <5, 12> in standard position, so it'd be originating from 0,0, then the rise is 12 and the run is 5.

so any other vector that has a negative reciprocal slope to it, will then be perpendicular or "orthogonal" to it.

so... for example a parallel to <-12, 5> is say hmmm < -144, 60>, if you simplify that fraction, you'd end up with <-12, 5>, since all we did was multiply both coordinates by 12.

or using a unit vector for those above, then

$\bf \textit{unit vector}\qquad \cfrac{\ \textless \ a,b\ \textgreater \ }{||\ \textless \ a,b\ \textgreater \ ||}\implies \cfrac{\ \textless \ a,b\ \textgreater \ }{\sqrt{a^2+b^2}}\implies \cfrac{a}{\sqrt{a^2+b^2}},\cfrac{b}{\sqrt{a^2+b^2}}
\\\\\\
\cfrac{12,-5}{\sqrt{12^2+5^2}}\implies \cfrac{12,-5}{13}\implies \boxed{\cfrac{12}{13}\ ,\ \cfrac{-5}{13}}
\\\\\\
\cfrac{-12,5}{\sqrt{12^2+5^2}}\implies \cfrac{-12,5}{13}\implies \boxed{\cfrac{-12}{13}\ ,\ \cfrac{5}{13}}$

4 0

4 years ago

Over the period of a year, Sam’s net worth increased. Which of the following could be true?

MAXImum [283]

Answer:

Sam's assets increased by more than his liabilities.

Step-by-step explanation:

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2 years ago

If f (x) = 3 [X-2] what is f(4.7) answer

Ipatiy [6.2K]

Answer:

Step-by-step explanation:

[x-2]=[4.7-2]=[2.7]=2

f(4.7)=3*2=6

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3 years ago