Answer:
[tex]S = -\dfrac{1}{3}P+\dfrac{740}{3}[/tex]
Step-by-step explanation:
Given that:
Number of seats sold is 180 with ticket price $200.
Number of seats decreases by one when the ticket price is increased by $3.
To find:
The formula for the number of seats sold (S) when the ticket price is P dollars.
Solution:
It is linear dependency of number of seats sold, S on ticket price, P.
[tex]S\propto P[/tex]
It can be written as:
[tex]S = kP+C[/tex]
Where [tex]k[/tex] is the constant of proportionality and
[tex]C[/tex] is a constant.
Now, putting the given values:
[tex]180 = 200k +C ..... (1)[/tex]
[tex]179 = 203k+C[/tex] ...... (2)
Subtracting (1) from (2):
[tex]3k = -1\\\Rightarrow k =-\dfrac{1}{3}[/tex]
Putting the value in (1):
[tex]\Rightarrow C = 180+\dfrac{200}{3} = \dfrac{740}{3}[/tex]
Therefore the equation becomes:
[tex]S = -\dfrac{1}{3}P+\dfrac{740}{3}[/tex]
Connor is working two summer jobs, making $8 per hour walking dogs and making $12 per hour landscaping.
What is the slope and y intercept for 14X - 7Y = 28
Answer:
y = 2x - 4 (the slope is 2 or 2/1 and the y-intercept is -4)
Step-by-step explanation:
Subtract 14x from both sides of the equation.
This should get you -7y = 28 - 14x.
Then you need to divide by -7 on both sides.
y = -4 + 2x is the result
which you can switch around if you like and get y = 2x - 4
-1.64 as a mixed number
:)
Why is it essential to know how to solve Exponential equations in order to solve Logarithmic equations? (Make sure to fully explain).
Answer:
Because you need it for your later life and for your GCSES and if you dont want to fail then you will need it.
Step-by-step explanation:
Given an exponential equation in which a common base cannot be found, solve for the unknown. Apply the logarithm of both sides of the equation. If one of the terms in the equation has base 10, use the common logarithm. If none of the terms in the equation has base 10, use the natural logarithm.
What is the answer for 4(2p-8)-6p=20+4(p+6)
Hello! :)
[tex]\large\boxed{p = -38}[/tex]
4(2p - 8) - 6p = 20 + 4(p + 6)
Distribute the coefficients outside of the parenthesis:
4(2p) + 4(-8) - 6p = 20 + 4(p) + 4(6)
8p - 32 - 6p = 20 + 4p + 24
Combine like terms:
2p - 32 = 44 + 4p
Subtract 2p from both sides:
-32 = 44 + 2p
Subtract 44 from both sides:
-76 = 2p
Divide both sides by 2:
p = -38.
Answer p = -4
6p + 2(4 + -2p) = 3(p + 4)
6p + (4 * 2 + -2p * 2) = 3(p + 4)
6p + (8 + -4p) = 3(p + 4)
8 + 6p + -4p = 3(p + 4)
8 + 2p = 3(p + 4)
8 + 2p = 3(4 + p)
8 + 2p = (4 * 3 + p * 3)
8 + 2p = (12 + 3p)
8 + 2p = 12 + 3p
8 + 2p + -3p = 12 + 3p + -3p
8 + -1p = 12 + 3p + -3p
8 + -1p = 12 + 0
8 + -1p = 12
8 + -8 + -1p = 12
0 + -1p = 12 + -8
-1p = 12 + -8
-1p = 4
p = -4
There are currently 73 million cars in a certain country, decreasing by 1.7% annually.
How many years will it take for this country to have 54 million cars? Round to the
nearest year.
Answer:
17.6 years
Step-by-step explanation:
There are currently 73 million cars in a certain country, decreasing by 1.7% annually.
How many years will it take for this country to have 54 million cars? Round to the
nearest year.
We use the formula
y = a(1 - r)^t
a = Initial amount = 73 million cars
y = Future amount = 54 million cars
r = decreasing rate = 1.7 % = 0.017
t = time is unknown
54,000,000 = 73,000,000(1 - 0.017)^t
Divide both sides by 73,000,000
54,000,000/73,000,000 = (0.983)^t
0.7397260274 = (0.983)^t
Take the logarithm of both sides
log 0.7397260274 = Log (0.983)^t
log 0.7397260274 =t log (0.983)
t = log 0.7397260274/log 0.983
t = -0.13092910029/-0.00744648216
t = 17.5826783005 years
Approximately = t = 17.6 years
by rounding each number to 1sf estimate the answers to 8.2*6.7/ 0.46
Answer:
Please check the explanation.
Step-by-step explanation:
Given the function
[tex]8.2\times \frac{6.7}{0.46}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \:a\times \frac{b}{c}=\frac{a\:\times \:b}{c}[/tex]
[tex]=\frac{6.7\times \:8.2}{0.46}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:6.7\times \:8.2=54.94[/tex]
[tex]=\frac{54.94}{0.46}[/tex]
[tex]=100[/tex] (Round to 1 significant number)
Step-by-step explanation
80+80=1660 so we add the number together then agter times then after take away the number and use the nu
first to help gets brainliest
$300 at 2.5% for 16 months
Answer:
Total: $420 (growth of $120)
Step-by-step explanation:
Multiply $300 by 0.025 (2.5%) which is equal to 7.5. Then multiply that by 16 months which gives you $120 added to your $300.
what is the value of |4.75|
A square plastic tarp has sides that are 7 meters long. What is the tarps area?
Answer:
49 square meters
Step-by-step explanation:
The formula for finding the area of a surface is [tex]area=length*breadth[/tex] Since the tarp is square, all of its sides have the same lengthSo the length equals the breadthThat means the area is [tex]area=(7meters)*(7meters)=49meters^{2}[/tex]Simplify ratio 10 :200
Answer:
Step-by-step explanation:
10 : 200
Both have table of 10 in common
1 : 20
What is the multiples of 46
Answer:
0, 46, 92, 138, 184, 230, 276, 322, 368, 414, 460, 506, 552
Step-by-step explanation:
multiples up until 12
Answer:
46,92,138,184,230,276,322,368,414,460
Step-by-step explanation:
w
S
Tim
elaps
V
00
07
Smarts
out of 10
U
50
Statement
Reason
1
ASTV is equilateral
Given
2
SW & TU
Given
3
ZUTV - ZVSW
Given
4
SV & TV
Definition of equilateral triangle
5
ATUV W ASWV
Answer:
HELP me with my last qu3estion
Step-by-step explanation:
Find the distance between the two points in simplest radical form.
(-9,8) and (-3,-1)
Answer:
[tex]d = 3\sqrt{13}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra II
Distance Formula: [tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-9, 8)
Point (-3, -1)
Step 2: Find distance d
Substitute: [tex]d = \sqrt{(-3+9)^2+(-1-8)^2}[/tex]Add/Subtract: [tex]d = \sqrt{(6)^2+(-9)^2}[/tex]Evaluate: [tex]d = \sqrt{36+81}[/tex]Add: [tex]d = \sqrt{117}[/tex]Simplify: [tex]d = 3\sqrt{13}[/tex]And we have our final answer!
What is the value of X
D=X°
F=103°
A. 51.5°
B. 128.5°
C. 77°
D. 38.5°
Write the difference of two algebraic expressions modeled by the algebra tiles. Let $x$ be the variable. Then use the algebra tiles to simplify the expression. Two groups of algebra tiles. The second is subtracted from the first. The first group has two positive variables tiles and seven positive unit tiles. The second group has two positive variable tiles and four negative unit tiles.
Answer:
3
Step-by-step explanation:
Who cares? just copy down the answer.
Which of the ratios below has a unit rate of 50? Select all that apply.
A) 250:5
B) 100:2
C) 75:25
D) 300:6
E) 600:12
{(1,2), (2,4), (1,-3), (4,6)}
<
Is the relation a function? [Select ]
State the domain. [Select]
State the
range.
[ Select]
Answer:
That is not a function ( because of the repeating number which is the 1.)
Domain: 1,2,4
Range:2,4,-3,6
Answer:
domain first no.before comma
1 2 1 4
range send no. after comma
2 4 -3 6
Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape of a right rectangular
prism and the dimensions, in inches, are 367 x 19 x 24. During the set-up, Alex fills the aquarium with 6,039
ins of water.
What percent of the volume of the aquarium is filled with water? Round your answer to the nearest whole percent.
Enter your answer in the space provided.
Answer:
4%
Step-by-step explanation:
Formula for volume of a right rectangular prism is;
V = lwh
Where;
l is length
w is width
h is height
We are given l = 367; w = 24; h = 19
Thus;
Volume is;
V_full = 367 × 24 × 19
V_full = 167352 in³
We are told that Alex filled the aquarium with 6039 in³ of water.
Thus, percentage of the aquarium filled with water is;
(6039/167352) × 100% = 3.61%
Approximating to nearest percent gives; 4%
So if he reads 147 pages of a book and he has completed 70% of the book how much would be left
Answer:
63 pages
Step-by-step explanation:
147/x=70/100
147=x(70/100)
x = 147/(70/100)
x = 210
210-147=63
Answer:
63 pages
Step-by-step explanation:
147 100
---- * ---- = 210 and then 210-147=63
1 70
Which of these division problems have the same quotient as 12.3 divided by 0.4? Check all that apply.
1. 123 ÷ 4
2. 1.23 ÷ 0.4
3. 1,230 ÷ 40
4. 123 ÷ 0.04
Answer:
1 and 3
Because if you move the decimal point for one number you also have to move it for the other.
six Notebooks cost 720 find the cost of 44 note books
Explanation:
720/6 = 120
44 x 120 = 5280
Answer:
$5280
Hope this helps!!!!!
Step-by-step explanation:
Cost of 6 notebooks = 720
Then, cost of 1 notebook = 720/6
Therefore, cost of 44 notebooks = 720/6 x 44
= 120 x 44
= 5,280
Therefore, the cost of 44 notebooks will be 5,280
Which equation has a center at (2, 1) and a point on the circle of (2, -3)?
O (x + 2)2 + (y + 1)2 = 16
O x - 2)2 + (y - 1)2 = 4
O(x - 2)2 + (y - 1)2 = 16
O (x + 2)2 + (y + 1)2 = 4
Answer:
Option 3: [tex](x-2)^2+(y-1)^2 = 16[/tex] is the correct answer
Step-by-step explanation:
We will find the equation of the circle with given information and then compare with the choices given.
Given
Center = (h,k) = (2,1)
And point on circle = (2,-3)
The equation of circle is given as:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
The distance between center and point on circle is the radius. So using the distance formula:
[tex]r = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\r = \sqrt{(2-2)^2+(-3-1)^2}\\r = \sqrt{(0)^2+(-4)^2}\\r = \sqrt{0+16}\\r = \sqrt{16}\\or\\r = 4[/tex]
Putting the values in equation of circle
[tex](x-2)^2+(y-1)^2 = 4^2\\(x-2)^2+(y-1)^2 = 16[/tex]
Hence,
Option 3: [tex](x-2)^2+(y-1)^2 = 16[/tex] is the correct answer
Answer:
c on edge
i got it right
The table shows the outputs y, for different inputs ,x
Input x: 3,7,11,15
Output y: 4,6,8,10
Part A: Do the data in this table represent a function? Justify your answer.
Part B: Compare the data in the table with the relation f(x) = 5x-21. Which relation has a greater value when x=11
Part C: Using the relation in part b, what is the value of x if f(x) =99
Part A: Yes, the data represent a function. The definition of a function is a relation in which no value of x will have two different values of y.
(Every time you plug in 3 as x, you will always get 4 as y; it's ok if you plug in 3 and 5 as x and get the same y, you just can't get two different y's for one x; sorry, it is pretty confusing). None of the numbers in the table repeat, so we can safely say that the relation is a function.
Part B: All we have to do is plug in 11 for x in the function given to find the answer:
In the table, y = 8 when x = 11, but in the function given, y = 34 when x = 11, so the function given is greater.
Part C: To find the answer to C, just plug in 99 for f(x), as it tells you to do:
Whats The RiGhT answer giving brainliest
Answer:
D is correct because its the only graph that displays the first set of data correctly.
536+248 anweser please
Answer:
784
Step-by-step explanation:
Kite LMNO is shown below.
What is the measure of angle M
Answer:
the answer is 78
Step-by-step explanation:
It is the largest one that i can see. The other options are cut off. If you could repost again....
In a circle with radius 2, an angle measuring pi/3 radians intercepts an arc. Find the
length of the arc in simplest form.
Answer:
2pi/3
Step-by-step explanation:
Using the formula s = r(theta), where s is arc length, r is radius, and theta is the central angle,
s = 2(pi/3)
s = 2pi/3
Please help ASAP. What is the value of x
Answer: X = 2
Step-by-step explanation: