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
dsp73
3 years ago
12

FILL IN THE BLANK

Mathematics
2 answers:
IgorLugansk [536]3 years ago
3 0
Now, we know that he's charging $12 per session to each of his students, and he has 14 students currently, so his revenue is just 14 * 12 or 168 bucks.

now, let's take a peek as the session price goes up in jumps of 2, from 12, to 14, 16, 18 and so on, as each jumps happen, the students drop by 1, from 14, to 13, to 12 and so on.

\bf \begin{array}{ccccllll}
\stackrel{increase}{x}&\stackrel{new}{price}&students&\stackrel{revenue}{y}\\
------&------&------&------\\
0&12&14&168\\
1&14&13&182\\
2&16&12&192\\
3&18&11&198\\
\boxed{4}&20&10&\boxed{200}\\
5&22&9&198\\
6&24&8&192\\
7&26&7&182\\
8&28&6&168\\
..&..&..&..
\end{array}

notice, the revenue starts off at 168, goes up up, reaches 200 bucks and then starts to drop back down.

thus, that means the U-turn or vertex of that revenue function is at 4,200, namely h = 4, and k = 200

\bf \qquad \textit{parabola vertex form}\\\\
\begin{array}{llll}
\boxed{y=a(x-{{ h}})^2+{{ k}}}\\\\
x=a(y-{{ k}})^2+{{ h}}
\end{array} \qquad\qquad  vertex\ ({{ h}},{{ k}})\\\\
-------------------------------\\\\
\stackrel{c(x)}{y}=a(x-\stackrel{h}{4})\stackrel{k}{+200}
\\\\\\
\textit{now, we also know that }
\begin{cases}
x=2\\
y=192
\end{cases}\implies 192=a(2-4)^2+200
\\\\\\
-8=a(-2)^2\implies -8=4a\implies \cfrac{-8}{4}=a\implies -2=a
\\\\\\


\bf therefore\qquad \stackrel{ c(x)}{y}=-2(x-4)^2+200\impliedby \textit{let's expand that}
\\\\\\
y=-2(x^2-8x+16)+200\implies y=-2x^2+16x-32+200
\\\\\\
\stackrel{y}{c(x)}=-2x^2+16x+168
s344n2d4d5 [400]3 years ago
3 0

Answer:

c(x)= <u>-2 </u>x2 + <u>16</u>x + <u>168</u>

Step-by-step explanation:

#PLATOFAMILY

You might be interested in
Suppose that y varies directly with x, and y=15 when x=24. Write a direct variation equation that relates x and y. Find y when x
Lapatulllka [165]

Just set up a proportion with the original numbers and then the numbers you want to find like so: (x1/y1)=(x2/y2) and since you want to find the second y value, just leave y as a variable like so: (15/24)=(3/y) after this just cross multiply and get the answer: 15y=72.....y=4.8


4 0
3 years ago
Read 2 more answers
Question below. Please answer it, its math.
AleksAgata [21]

Answer:

- 0.8

Step-by-step explanation:

The first thing we want to do here is simplify the expression -

\frac{3}{5}( 2x + 5 ) - 2x, Distribute the " \frac{3}{5} " to elements within the parenthesis

= \frac{3}{5} * 2x + \frac{3}{5} * 5 - 2x, Focus on simplifying the expression " \frac{3}{5} * 2x + \frac{3}{5} * 5 "

= 2\cdot \frac{3}{5}x+5\cdot \frac{3}{5} - 2x

= \frac{6x}{5}+3 - 2x, Combine fractions

= -\frac{4x}{5} + 3

= -\frac{4}{5}x + 3

So we have our simplified expression "  -\frac{4}{5}x + 3, " with -\frac{4}{5} being the coefficient of x. Our requirements are that this fraction should be expressed as a decimal, so we can simply divide the numerator by the denominator to figure that out,

- 4 / 5 = - 0.8,

Solution = - 0.8

4 0
3 years ago
The perimeter of a triangle is 70 in. The shortest side is 11 in. less than the longest side. The middle side is 24 in. less tha
kondor19780726 [428]

Answer:

The sides are

6

inches,

8

inches and

10

inches

Explanation:

I'd suggest that the question should read 'The perimeter of a triangle is 24 inches. The longest side is 4 inches longer than the shortest side, and the shortest side is three-fourths the length of the middle side. How do you find the length of each side of the triangle?'

In this case the question can be answered. If

x

is the length of the middle side, then the shortest side is 3/4x and the longest side is 3/4x+4

x+3/4x+3/4x+4=24

10/4x=20

x=8

Then the shortest side is 6and the longest side is 10

Step-by-step explanation:

4 0
3 years ago
Which do you pick and why? How much money do you end up with in each case?
Mademuasel [1]

Answer:

1. Start with $1 and then double the money you have everyday for 30 days. You would end up with 1,073,741,824 on the 30th day.

Step-by-step explanation:

Why you should choose the first option:

1 x 2 = 2

2 x 2 = 4

4 x 2 = 8

8 x 2 = 16

16 x 2 = 32

32 x 2 = 64

64 x 2 = 128

128 x 2 = 256

256 x 2 = 512

512 x 2 = 1024

1024 x 2 = 2048

2048 x 2 = 4096

4096 x 2 = 8192

8192 x 2 = 16384

16384 x 2 = 32768

32768 x 2 = 65536

65536 x 2 = 131072

131072 x 2 = 262144

262144 x 2 = 524288

524288 x 2 = 1048576

1048576 x 2 = 2097152

2097152 x 2 = 4194304

4194304 x 2 = 8388608

8388608 x 2 = 16777216

16777216 x 2 = 33554432

33554432 x 2 = 67108864

67108864 x 2 = 134217728

134217728 x 2 = 268435456

268435456 x 2 = 536870912

536870912 x 2 = 1073741824

7 0
2 years ago
Write a number sentence that does not involve regrouping using this sum and two 2- digit addends
melisa1 [442]
Using the sum (addition) and two 2-digit addends, 12 + 34 can be answered without regrouping.
5 0
3 years ago
Other questions:
  • There are 26.2 miles and a marathon write the number of miles using a fraction
    14·2 answers
  • Find the average rate of change of the function f(x) equals -1X^2-4x-3 from x=-1 to x=5
    14·1 answer
  • Simplify 0.4(−4.5)......................................
    12·1 answer
  • What is the difference between a rate and a unit rate? Show an example
    12·1 answer
  • Please help me to solve it
    15·1 answer
  • Translate the sentence into an inequality. The product of C and 9 is at most -28
    13·1 answer
  • Need help with number 11 ASAP!!!!
    12·2 answers
  • How do I find the function rule???<br> x: 0, 1, 2, 3<br> y: 5, 4, 3, 2
    13·1 answer
  • Multiply 3.4x and 1.2x.<br><br> 4.08x2<br> 4.6x2<br> 4.08x<br> 4.6x
    12·1 answer
  • Interpreting Points on Graphs of Proportional Relationships
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!