The school purchased 35 tickets for the ballet. Adult tickets were $10, and student tickets were $7. The total cost was $266.
If x represents the number of adult tickets purchased, and y represents the number of student tickets purchased, which system of equations represents this situation?
Answer:
Not too sure, but maybe this is what you need.
(Students = S, Adults = A) So, Ax + Sy = 266?
Or
x10 + y7 = $266
Step-by-step explanation:
I think the second one is the most accurate one, ignore the first equation. T^T
A system of equations is made up of an ellipse and a hyperbola.
Part A: Create the equation of an ellipse centered at the origin, with a vertical major axis of 8 units and a minor axis of 6 units. Show your work. (3 points)
Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (–4, 0), and asymptotes of y equals plus or minus seven fourths x period Show your work. (4 points)
Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points)
The equation of the ellipse and the equation of the hyperbola can be
derived from the given information and the general form of the equations.
[tex]Part \, A: The \ equation \ of \ the \ ellipse \ is; \displaystyle \frac{x^2}{3^2} + \frac{y^2}{4^2} = 1[/tex]
[tex]Part \, B: The \ equation \ of \ the \ hyperbola \ is; \displaystyle \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1[/tex]
Part C: The domain of the ellipse is; [-3, 3]
The domain of the hyperbola is; (-∞, -4]
The domains of the ellipse and the hyperbola do not intersect, therefore, the system of equation has no solution.Reasons:
Part A: The center of the ellipse = At the origin;
The vertical major axis = 8 units
The minor axis = 6 units
The general equation for an ellipse is presented as follows;
[tex]\displaystyle \frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
Where;
[tex]\displaystyle a = The \ \mathbf{ semi \ major \ axis} = \frac{8}{2} = 4[/tex]
[tex]\displaystyle b = The \ semi \ \mathbf{ minor} \ axis = \frac{6}{2} = 3[/tex]
The equation of the ellipse is therefore;
[tex]\displaystyle \underline{\frac{x^2}{3^2} + \frac{y^2}{4^2} = 1}[/tex]Part B: center of the hyperbola = The origin
The transverse axis = Horizontal
The vertex of the hyperbola = (-4, 0)
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{ \pm\frac{7}{4} \cdot x}[/tex]
The general equation of an hyperbola is presented as follows;
[tex]\displaystyle \mathbf{\frac{x^2}{a^2} - \frac{y^2}{b^2}} = 1[/tex]
[tex]\displaystyle The \ asymptote \ are; \ y = \mathbf{\pm\frac{b}{a} \cdot x}[/tex]
The vertices = (a, 0), (-a, 0)
Therefore, by comparison, we have;
a = -4
b = -7
Which gives the equation of the hyperbola as follows;
[tex]\displaystyle \underline{ \frac{x^2}{(-4)^2} - \frac{y^2}{(-7)^2} = 1}[/tex]The above equation can be written as follows;
[tex]\displaystyle \frac{x^2}{(4)^2} - \frac{y^2}{(7)^2} = 1[/tex]
Part C: Given that both equations are equal, we have;
The covertices of the ellipse are; (-3, 0) and (3, 0)
The domain of the ellipse = [-3, 3]
The domain of the hyperbola = x < The negative vertex
∴ The domain of the hyperbola = x < -4 = (-∞, -4]
The above domain of the ellipse does not extend to the hyperbola, therefore there is no solution to the system.Learn more about ellipse and hyperbola here:
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Which three points are collinear?
according to defination of collinear points :Three or more points are said to be collinear if they all lie on the same straight line.
therefore, A,B,C points are collinear.
At the beginning of the month you have $1500 in your bank account. Each time you visit the ATM you take $60 out. What is the rate at which your balance is changing each time you visit the ATM?
Group of answer choices
$3
-$60
$60
-$63
-$1500
-$3
Alright I need help.. I will mark brainliest .
;-;
Answer:
x - y = 9
Step-by-step explanation:
When x goes up by 1, y goes up by 1. That means there is a constant difference between the values. That difference is x1 -y1 = 1 -(-8) = 9.
An equation relating the values is ...
x - y = 9
_____
Some folks like to see the relation in "y =" form. You can add y-9 to both sides to get that form:
y = x -9
PLEASE help, I'm begging, this was due to all the way back at November 12th, please help!!! Finding the Inverse of a Function Algebraically Practice Pt. 2
Answer:
19
Step-by-step explanation:
What is the y-intercept of a line that passes through the points (1,-7) and (5,-15)?
Answer: (0,-5) or just -5
Step-by-step explanation:
gradient = change in y/change in x = (-7+15)/(1-5) = -2
y = -2x + c
-7 = -2 x 1 + c
c = -7 + 2 = -5
y intercept is (0, -5)
A local pizza shop has a membership program for frequent buyers. The membership costs $25 per month and members get a discounted price of $1.25 per slice of pizza. Tristan purchased a membership to this pizza shop. How much would Tristan have to pay the pizza shop if he bought 9 slices of pizza this month? What would be the monthly cost for xx slices of pizza?
Answer:
Step-by-step explanationcvm
Answer:
25
25+1.25x
Step-by-step explanation:
At least you got an actual answer this time hope this helps
What’s the an and the a10
Answer:
an = -6 + n
a10 = -6+ 10 =4
Step-by-step explanation:
an should start at one behind the first number so it should be -6. Then we add whatever the sequence is increasing by, which is 1 in this case, multiplied by n.
an = -6 + n
a10 = -6+ 10 =4
What is the equation of the line in slope-intercept form?
Line on a coordinate plane. The line runs through points begin ordered pair negative 5 comma 0 end ordered pair and begin ordered pair 0 comma 3 end ordered pair.
Enter your answer in the boxes.
y =
x +
Step-by-step explanation:
Use the slope formula
Taking two points on the line:
(0,3) and (-5,0)
3-0/0+5
You will get: 3/5 as your slope
The y-intercept is (0,3)
Therefore:
y = 3/5x + 3
box and whisker plots please help!
Sam runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?
Answer:
4.8
Step-by-step explanation:
6/55= ~0.109
0.109*44=4.8
if 10 seeds are planted, what is the probability that exactly 3 don't grow?
Answer:
10:7
Step-by-step explanation:
take 10 as it is and it becomes 10
then,10-3 it is because when 3 don't grow it subtracts and becomes 7
Asha bought 60 fruit baskets.
25% of the fruit baskets have 12 pieces of fruit in each basket.
The remaining 75% of the baskets have 15 pieces of fruits in each basket.
Answer:
Answer: 855
Step-by-step explanation:
I take it you want the total number of fruit? You should state the question. I will assume I am correct.
So 25% of 60 baskets = 25/100 * 60 = 15 baskets.
Each basic contains 12 pieces of fruits 12 * 15 = 180
And 75% of 60 baskets = 0.75 * 60 = 45 baskets.
Each contains 15 pieces 45 * 15 = 675
The total number of fruit in all is 855
How many groups of are there in 30?
Answer:
6
Step-by-step explanation:
divide or multiply by 5 to get 30
Answer:
??????????????????????
A TV has a listed price of $900.99 before tax. If the sales tax rate is 6.75%, find the total cost of the TV with sales tax included.
Round your answer to the nearest cent, as necessary.
Segment AB and CD intersect at point E, measure of angle ABC =6x+20 and measure of angle DEB=10x. What is the value of x?
Answer:
x = 5
Step-by-step explanation:
6x + 20 = 10x
I hope this helps!
I need help please? ????????
Answer:
ummmmm i really don't get it but I think its 17/66
Step-by-step explanation:
multiply in to each fraction
how to calculate fractions without a calculator
Answer:
Step-by-step explanation:
all you need to do is divide that number by the denominator of the fraction, then multiply your result by the numerator of the fraction
Write a function for the line with a slope of 5 that passes through the point (2, 1). Enter the correct equation in the box.
Answer:
brainly
Step-by-step explanation:
find the circumference of a cd that has an diamater of 5 round your andwer to the nereast tenth
Answer:
15.7
Step-by-step explanation:
C = 2πr
C = 2(3.14)(2.5)
C = 15.7
Write an expression that represents the perimeter of the figure below. Write your answer in simplified form. P=??
The perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s
How to find the Perimeter of a FigureTo find the perimeter of any figure, add all the side lengths of the figure together.
Thus, the given side lengths of the figure are:
p, p, q, q, r, r, s, s, s, and s.
To find the perimeter add them together.
Perimeter of the figure = p + p + q + q + r + r + s + s + s + s
Perimeter = 2p + 2q + 2r + 4s
Therefore, the perimeter of the figure in simplified form is expressed as: P = 2p + 2q + 2r + 4s
Learn more about perimeter on:
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Write the word sentence as an equation. Then solve the equation.
The quotient of a number and -1.5 is 21.
a
Equation:
Solution: x=
Answer:
Step-by-step explanation:
"The quotient of a number and -1.5 is 21."
Let X be the "number."
X/-1.5 = 21
X = -1.5*(21)
X = - 31.5
does anyone have an answer to this question?
Answer:
8.9 cm to 1 dec. place.
Step-by-step explanation:
First, use Pythagoras to find the length of BD.
BD^2 = 6^2 + 7^2 = 85
BD = √85.
BM = √85 / 2.
Consider the triangle TBM, by Pythagoras:
TB^2 = BM^2 + MT^2
MT^2 = 10^2 - (√85 / 2 )^2
= 100 - 21.25
= 78.75.
MT = 8.874
Find the product:
[tex] \frac{1}{8} \times \sqrt{8} [/tex]
Answer:
≈ 0.35
Step-by-step explanation:
First simplify [tex]\sqrt{8}[/tex] and [tex]\frac{1}{8}[/tex] :
[tex]\sqrt{8}[/tex] ≈ 2.83
[tex]\frac{1}{8}[/tex] = 0.125
Now multiply them as shown in the original equation:
0.125 x 2.83 = 0.35375 ≈ 0.35
find x and y for this triangle
Answer:
x = 1.25
x = 1.75
Step-by-step explanation:
I marked the points of this triangle in the attached image so it's easier to explain.
ΔABC is similar to ΔADE, and all pairs of corresponding sides are proportional as a result.
[tex]\frac{DE}{BC}=\frac{AD}{AB}=\frac{AE}{AC}[/tex]
The length of the sides BC and DE is given, so I'll start with that and set it equal to the proportion between AB and AD.
[tex]\frac{DE}{BC}=\frac{AD}{AB}\\\\\frac{10}{8}=\frac{x+5}{5}\\\\10\times5=(x+5)\times8\\50=8x+40\\10=8x\\x=1.25[/tex]
Now, you can do the exact same thing for y:
[tex]\frac{DE}{BC}=\frac{AE}{AC}\\\\\frac{10}{8}=\frac{y+7}{7}\\\\10\times7=(y+7)\times8\\70=8y+56\\14=8y\\y=1.75[/tex]
can anyone please help?
Answer:
-1 or 1.
Step-by-step explanation:i hope thats what your looking for.
Which equation could have been used to create this table? need answer fast
y = x + 6
y = x + 5
y = 6x
y = 7x
Answer:
y=6x
Step-by-step explanation:
Each value for y is can be divided by 6 for the value of x
Answer:
y=6x
Step-by-step explanation:
A medication with an initial concentration of 1. 5 milligrams per liter is administered to a
patient, and the decay rate of the drug is 10% per hour. Which equation can be used to model
the concentration, C, of the drug in the patient’s body as a function of time, t, in hours since the
drug was administered?
Answer: Exponential decay model:
y
=
x
(
1
−
r
)
t
, half life of tablet is about
2
hours and after
t
=
3
hours , remaining drug on patient's system is
42.875
mg.
Step-by-step explanation: Initial drug
x
=
125
mg ; rate of decay
r
=
30
100
=
0.3
gm/hour
Exponential model:
y
=
x
(
1
−
r
)
t
=
125
(
1
−
0.3
)
t
=
125
⋅
0.7
t
Half life:
y
=
125
2
=
62.5
mg
∴
62.5
=
125
⋅
0.7
t
or
0.7
t
=
1
2
. Taking logarithm on both sides we get ,
t
log
(
0.7
)
=
log
(
0.5
)
∴
t
=
log
(
0.5
)
log
(
0.7
)
≈
1.94
(
2
d
p
)
hour
The half life of tablet is about
2
hours.
After
t
=
3
hours , remaining drug on patient's system is
y
=
125
⋅
0.7
t
=
125
⋅
0.7
3
=
42.875
mg [Ans]
which polynomial function in factored form represents the given graph below?
Answer:
Question:which polynomial function in factored form represents the given graph below?
Answer:If a polynomial of lowest degree p has zeros at x=x1,x2,…,xn x = x 1 , x 2 , … , x n , then the polynomial can be written in the factored form: f(x)=a(x−x1)p1(x−x2)p2⋯(x−xn)pn f ( x ) = a ( x − x 1 ) p 1 ( x − x 2 ) p 2 ⋯ ( x − x n ) p n where the powers pi on each factor can be determined by the behavior of the graph
Step-by-step explanation:
CARRY ON LEARNING
BRAINLILEST NA LANG KUNG TAMA SALAMAT