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2 years ago

Find the constant of variation k for the direct variation. 4x = -6y

Mathematics

1 answer:

ValentinkaMS [17]2 years ago

3 0

k = - $\frac{2}{3}$ → A

the equation for direct variation is y = kx ( k is the constant of variation )

thus k = $\frac{y}{x}$

given - 6y = 4x is a direct variation equation then

k = $\frac{4}{- 6}$ = - $\frac{2}{3}$

k =

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You pay $2.40 for 3/4 pound of grapes your friend buys a pound of grapes at the same time and estimates that he will pay $1.80 w

LenKa [72]

I would say your friends assumption is wrong. Why?

Because, if you payed $2.40 for 3/4 pounds of grapes, your friend should pay more for an entire pound, not less.

Hope this helped! c:

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3 years ago

Please help thanks in advance

Galina-37 [17]

Answer:

43.25

Step-by-step explanation:

Since sides DF and FE are congruent, their opposite angles D and E are also congruent.

m<D + m<E + m<F = 180

x + x + 93.5 = 180

2x = 86.5

x = 43.25

Answer: 43.25

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3 years ago

Carlo and Helen spend the same amount of money on art supplies. Carlo buys 4 glue sticks and spends $3 on glitter. Helen buys 2

Veseljchak [2.6K]

Answer:4.75

Since we don't have a total cost we will write an equation that will allow us to find the cost of x. The equation is 4x= 2x + $3 + $3.75 + $2.75. Now that we have our equation we are going to start by adding 3, 3.75, and 2.75. When added together, they come out with a total of 9.5. Now the equation becomes 4x= 2x + $9.50. Since we have our new equation we are going to subtract 2x from both sides of the equation. We now have the equation 2x= $9.50. Finally, you will divide both sides by 2. This leaves us with the final outcome x= $4.75. This means that one glues stick cost $4.75. Let's check by substituting $4.75 as the value of x in the expressions 4x is Carlo's total and 2x + $3 + $3.75 + $2.75 is Helen's total. First we do 4x, 4 multiplied by 4.75 equals 19, so Carlo spent $19 on art supplies. Now we do 2x + $3 + $3.75 + $2.75, which is 9.5 added to 9.5 and equals 19. So Helen spent $19 on art supplies. This proves that the cost of one glue stick, x, is equal $4.75.

4 0

2 years ago

manuel deposits $10000 for 12 yr in an account paying 4% compounded annually.He then puts this total amount on deposit in anothe

Naddik [55]

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$10000\\
r=rate\to 4\%\to \frac{4}{100}\to &0.04\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{annually, thus once}
\end{array}\to &1\\
t=years\to &12
\end{cases}
\\\\\\
A=10000\left(1+\frac{0.04}{1}\right)^{1\cdot 12}\implies A=1000(1.04)^{12}\\\\\\ A\approx 16010.32$

he then turns around and grabs that money and sticks it for another 9 years,

$\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
~~
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$16010.32\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2\\
t=years\to &9
\end{cases}
\\\\\\
A=16010.32\left(1+\frac{0.05}{2}\right)^{2\cdot 9}\implies A=16010.32(1.025)^{18}
\\\\\\
A\approx 24970.64$

add both amounts, and that's how much is for the whole 21 years.

6 0

3 years ago

A triangle has two sides of 7 and 12 what value could the length of the third side be

mezya [45]

It would be D:7
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3 years ago