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azamat
3 years ago
14

James has mapped his seat and his teacher's seat on the coordinate plane at (0,10) and (–4,6). Find the distance between their s

eats. A. 4√ 17 units B. 16 units C. 4√ 2 units D. 4 units
Mathematics
1 answer:
wlad13 [49]3 years ago
4 0

Answer:

Distance between their seats is 4√2 units.

Step-by-step explanation:

We are given that James mapped his seat and teacher's seat at (0,10) and (-4,6) on the coordinate plane.

So, distance between their seats= distance between the points (0,10) and (-4,6)

                                                     =\sqrt{(-4-0)^{2}+(6-10)^{2}}

                                                     =\sqrt{(-4)^{2}+(-4)^{2}}=\sqrt{16+16}

                                                     =\sqrt{32}=4\sqrt{2}units

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After 5 years, Rachel’s amount in her savings account is $7446.52. Her account earned interest at 4.32% APR and was compounded d
Katyanochek1 [597]
\bf \qquad \textit{Continuously Compounding Earned Amount}\\\\
A=Pe^{rt}\qquad 
\begin{cases}
A=\textit{accumulated amount}\to &7446.52\\
P=\textit{original amount deposited}\\
r=rate\to 4.32\%\to \frac{4.32}{100}\to &0.0432\\
t=years\to &5
\end{cases}
\\\\\\
7446.52=Pe^{0.0432\cdot 5}\implies \cfrac{7446.52}{e^{0.0432\cdot 5}}=P\implies 5999.92404\approx P
5 0
3 years ago
The average ticket price for a concert at the opera house was $50. The average attendance was 4000. When the ticket price was ra
kotegsom [21]

Answer

given,

opera house ticket = $50

attendance = 4000 persons

now,

opera house ticket = $52

attendance = 3800 person

assuming these are the points on the demand curve

(x, p) = (4000,50) and (x,p) = (3800,52)

using point slope formula

p-50 = \dfrac{50-52}{4000-3800}(x - 4000)

p-50 = \dfrac{-2}{200}(x - 4000)

p-50 = \dfrac{-x}{100}+ 40

p = \dfrac{-x}{100}+ 90

R(x) = x . p

R(x) = x (\dfrac{-x}{100}+ 90)

R(x) = \dfrac{-x^2}{100}+ 90x)

\dfrac{d}{dx}(R(x)) = \dfrac{d}{dx}(\dfrac{-x^2}{100}+ 90x))

\dfrac{d}{dx}(R(x)) = (\dfrac{-2x}{100})+90)

at \dfrac{d}{dx}(R(x)) = 0

\dfrac{-2x}{100}= -90

x = 4500

\dfrac{d^2}{d^2x}(R(x)) = -ve

hence at x =4500 the revenue is maximum

for maximum revenue ticket price will be

p = \dfrac{-4500}{100}+ 90

p = $45

6 0
4 years ago
A local hamburger shop sold a combined total of hamburgers and cheeseburgers on Thursday. There were fewer cheeseburgers sold th
myrzilka [38]

Answer:

the number of hamburgers sold on Thursday were 325.

Step-by-step explanation:

The total number of hamburger and cheese burger is missing

i will replace it with any figure, you can replace it wit your given data and you will get the solution.

A local hamburger shop sold a combined total of 593 hamburgers and cheeseburgers on Thursday

There were 57 fewer cheeseburgers sold than hamburgers

How many hamburgers were sold on thursday

Let h be the number of hamburgers and c be the number of cheeseburgers.

Using this information we can set up two equation as:

h+c=593\\c=h-57

Now we need to solve these two equations to get the value of number of hamburgers. For that we use substitution method as shown below:

h+h-57=593\\2h-57=593\\2h=650\\h=325

Therefore, the number of hamburgers sold on Thursday were 325.

6 0
3 years ago
Mathemat
Svetradugi [14.3K]
First 168 is with the discount
The tax is 11.76
168+ 11.76 is 179.76
7 0
3 years ago
Find the slope between the points (-5,1) and (-1,-6)
madam [21]

Answer:

- 7 / 4

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Slope = (1 - -6) / (-5 - -1)

Slope = - 7 / 4

6 0
3 years ago
Read 2 more answers
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