The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $6.50 and each adult ticket sells for $10. The auditorium can hold no more than 140 people. The drama club must make at least $1100 from ticket sales to cover the show's costs. If x represents the number of student tickets sold and y
y represents the number of adult tickets sold, write and solve a system of inequalities (in y= form) graphically and determine one possible solution.
The system of inequalities is 6.50x + 10y ≥ 1100 and x + y ≤ 140.
The graph is attached below
How to plot the graph of the inequalitiesTo plot the system of equations, we can first plot the lines for each equation on the same coordinate plane.
The first inequality is 6.50x + 10y ≥ 1100.
We can rewrite this in slope-intercept form as
y = (-6.50/10)x + (1100/10).
The slope of the line is -6.50/10 = -0.65
And the y-intercept is (1100/10) = 110.
The second inequality is x + y ≤ 140.
We can rewrite this in slope-intercept form as y = (-1/1)x + (140/1).
The slope of the line is -1/1 = -1
And the y-intercept is (140/1) = 140.
We can now plot these lines on the same coordinate plane.
The points of intersection are the solutions to the system of equations.
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I’m confused and I just need a little help understanding
Answer:
3,3
Step-by-step explanation:
Answer:
Step-by-step explanation:
The term "about the origin" means that the origin is "the center of rotation".
Our coordinate right now is (3, 2).
90 degrees clockwise means we need to rotate to the left by 90 degrees. So if you rotate your image:
We now get (2, 3).
(I had some trouble reading the numbers, I'm reading them as (1, 2, 3, 4, 5,) for the X and Y axis, I hope I read them right.)
Mathematics verified
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asd
sda
ss
das
ds
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dasdasd
Factorise 3c squared-4c+1
Answer:
(c-1)(3c-1)
Step-by-step explanation:
3c² - 4c +1
get rid of square and write like this : (3c ... )(3c.... )
you need to din what multiplies to (3 x 1) = 3 but also adds to -4
-3 + -1 = -4
-1 x -1 = 3
put into the brackets
(3c -3 )(3c-1 )
simplify
(c-1)(3c-1)
Find the area of the triangle 15 m and 34 m
Answer:
255m^2
Step-by-step explanation:
You multipliy 15 and 34. Then you divide by 2
PLZ dont ignore me! I need help on this :(
Answer: should be the last answer! to the right.
Step-by-step explanation:
You have 30 coins and the d are dimes and q are quarters
Calculate the volume of iron needed to create a rectangular prism with a base area of
2250 square cm. The prism has a cylinder missing through the center of the prism. The
radius of the cylinder is 25 cm and the height of the cylinder and the prism are both
100cm. Find the volume to the nearest tenth of a cubic cm.
The volume of iron needed to create the rectangular prism is approximately 28650.5 cubic cm.
what is volume?
Volume is the amount of space occupied by a three-dimensional object. It is a measure of how much an object can hold or how much space it takes up. The volume of a solid object is typically measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³).
The volume of the rectangular prism without the cylinder can be calculated as:
\($$V_1 = A \times h$$\)
where A is the base area and h is the height
\($$V_1 = 2250 \times 100$$\)
\($$V_1 = 225000 \ \text{cubic cm}$$\)
The volume of the cylinder can be calculated as:
\($$V_2 = \pi r^2 h$$\)
where r is the radius and h is the height
\($$V_2 = \pi \times 25^2 \times 100$$\)
\($$V_2 = 196349.54 \ \text{cubic cm}$$\)
The volume of the rectangular prism with the cylinder missing can be calculated as:
\($$V = V_1 - V_2$$\)
\($$V = 225000 - 196349.54$$\)
\($$V = 28650.46 \ \text{cubic cm}$$\)
Therefore, the volume of iron needed to create the rectangular prism with a base area of 2250 square cm, a cylinder missing through the center of the prism with a radius of 25 cm, and the height of the cylinder and the prism being 100 cm, is approximately 28650.5 cubic cm (rounded to the nearest tenth of a cubic cm).
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Parallelogram JKLM is reflected across a horizontal line through its center and then translated down and to the left to produce parallelogram QTSR
K
110°
R
S
9 ft
70°
M 12 ft
L
T
m
What is true about the angles and side lengths of parallelogram QTSR?
Enter the correct answers in the boxes
Answer:
\(\huge\boxed{Q = 110 \textdegree, \ ST = 9 \ \text{ft}}\)
Step-by-step explanation:
When we reflect and transform a figure, the angle lengths nor the side lengths are touched. The side length only changes if we dilate or stretch the figure, and the angle length only changes if we stretch the figure.
Therefore, we know the information is going to be the exact same. We just have to figure out what corresponds to what from JKLM to QTSR.
If we reflect a figure across a horizontal reflection line through its center, the figure will just flip sides. M will be J, L will be K, etc.
When we translate this down, nothing changes except its position. So we can pretend these two shapes are right on top of each other for now.
When we move these right on top of each other, we can see that Angle J overlaps with Angle Q. Since they don't have any weird intersects, we know that angle J will be equal to Angle Q. Since we already know J is 110°, we know Q is also 110°.
When we move it on top, we also see that KL overlaps with ST perfectly. Since we know KL is 9, that must mean ST is also 9.
Hope this helped!
DUE FRIDAY HELP!!!!!! WELL WRITTEN ANSWERS ONLY!
Use the following information for questions 2 and 3:
Here is a unit circle with points marked at the following locations: A (1, 0), B π/3, C 4π/3, D 7π/4, E 5π/2, and F 6π/2.
2. What do you think the cosine value at 5π/2 radians is? At 6π/2 radians?
3. What do you think the sine of 4π radians is? 6π radians? 10π radians?
2. At 5π/2 radians, the cosine value is 0, and at 6π/2 radians, the cosine value is 1.
3. The sine of 4 radians is 0. As the angle is on the x-axis and has made two full revolutions, the sine of 6 radians is equal to 0. The sine of two radians, or a whole revolution, is equal to the sine of ten radians, which is likewise zero.
Circle explained in what way?
A circular shape is a sphere with no borders or edges. In mathematics, a circle is a closed form, a two-dimensional shape, and a curved shape. Our immediate environment has a number of circular things, including a car tyre, a wall clock that tells the time, and lollipops.
2. At 5π/2 radians, the cosine value is 0, and at 6π/2 radians, the cosine value is 1.
3. As the angle lies on the x-axis, the sine of 4 radians is 0. As the angle is on the x-axis and has made two full revolutions, the sine of 6 radians is equal to 0. The sine of two radians, or a whole revolution, is equal to the sine of ten radians, which is likewise zero.
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You have $135 and you want to give the money to 5 of your friends. You want each friend to have the same amount of money. How much money will you give each of your friends?
Given:
Total amount = $135
Total friends = 5
Each friend to have the same amount of money.
To find:
The money you will give each of your friends.
Solution:
We know that,
\(\text{Money for each friend}=\dfrac{\text{Total money}}{\text{Total number of friends}}\)
Substituting the given values, we get
\(\text{Money for each friend}=\dfrac{135}{5}\)
\(\text{Money for each friend}=27\)
Therefore, each friend will get $27.
Please help!!! Thank you!!!!!
Answer:
Its the third answer choice
Step-by-step explanation:
Hope this helps
The set B 1 t2, t t 2 t t2) is a basis for P2. Find the coordinate vector of p(t) 1 3t 6t2 relative to B. That is, find [p t)]
The coordinate vector of p(t) = 1 + 3t + 6t^2 relative to the basis B = {1 + 2t, t + 2t^2} is [p(t)]_B = (1, 1).
The coordinate vector of p(t) = 1 + 3t + 6t^2 relative to the basis B = {1 + 2t, t + 2t^2}, we need to express p(t) as a linear combination of the basis vectors.
Step 1: Write p(t) as a linear combination of the basis vectors.
p(t) = c1(1 + 2t) + c2(t + 2t^2)
Step 2: Equate the coefficients of the terms in p(t) to the coefficients in the linear combination.
1 = c1
3 = 2c1 + c2
6 = 2c2
Step 3: Solve the system of equations for c1 and c2.
From the first equation, we know that c1 = 1.
Now substitute c1 into the second equation:
3 = 2(1) + c2
c2 = 1
Step 4: Substitute c2 into the third equation:
6 = 2(1)
This confirms that our values for c1 and c2 are correct.
Step 5: Write the coordinate vector with the coefficients c1 and c2.
[p(t)]_B = (c1, c2) = (1, 1)
In conclusion, the coordinate vector of p(t) = 1 + 3t + 6t^2 relative to the basis B = {1 + 2t, t + 2t^2} is [p(t)]_B = (1, 1).
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As an estimation we are told 5 miles is 8 km.
Convert 52 km to miles.
Answer:
32.5 miles
Step-by-step explanation:
We can convert 52 km to miles using the given estimation.
To convert 52 km to miles, create a proportion where x is how many miles are in 52 km:
\(\frac{5}{8}\) = \(\frac{x}{52}\)
Cross multiply and solve for x
8x = 260
x = 32.5
So, in 52 km, there are approximately 32.5 miles
52 km is approximately equal to 32.5 miles.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
If we are given the estimation that 5 miles is approximately 8 km, we can use this ratio to convert 52 km to miles.
Let's set up a proportion:
5 miles / 8 km = x miles / 52 km
Cross-multiplying, we get:
5 miles × 52 km = 8 km × x miles
260 miles = 8x
To solve for x, divide both sides of the equation by 8:
260 miles / 8 = x
x ≈ 32.5 miles
Therefore, 52 km is approximately equal to 32.5 miles.
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Select the correct answer.
What is the greatest common factor of the numerator of 9x^3 - 3x^2 + 12x / 3x
A. 3x2
B. 12x
C. 3x
D. 9x3
Answer:
D is right
Step-by-step explanation:
Solve for x. Round to the nearest tenth.
Answer:
18.5
Step-by-step explanation:
You want the length x of the leg in a right triangle that is opposite an angle of 51°, given the adjacent leg is 15 units.
TangentThe tangent ratio is ...
Tan = Opposite/Adjacent
In this triangle, that means ...
tan(51°) = x/15
Multiplying by 15, we have ...
x = 15·tan(51°)
x ≈ 18.5 . . . units
is my answers correct?
Answer:
Saleh is x years old. And 10 years ago he was 100 years old.
Suha is x years old. Saleh is 10 years younger than Suha. Saleh is 100 years old.
The product of 6 and a number is the same as 40 less than twice that same number. Find the number.
Answer:
-10
Step-by-step explanation:
let the number=x
6x=2x-40
6x-2x=-40
4x=-40
x=-40/4=-10
I need help. Someone please figure it out
Answer:
\(\frac{1}{2^{n} }\)
Step-by-step explanation:
The rules of exponents state that
\(a^{-m}\) = \(\frac{1}{a^{m} }\) and \(a^{0}\) = 1
Thus
\(2^{-5}\) = \(\frac{1}{2^{5} }\) = \(\frac{1}{32}\)
\(2^{-4}\) = \(\frac{1}{2^{4} }\) = \(\frac{1}{16}\)
\(2^{-3}\) = \(\frac{1}{2^{3} }\) = \(\frac{1}{8}\)
and so on , to
\(2^{0}\) = 1
Suppose the commuting time on a particular train is uniformly distributed between 40 and 90 minutes. What is the probability that the commuting time will be between 50 and 60 minutes? Linked below is
The probability of the commuting time being between 50 and 60 minutes is determined for a train with a uniformly distributed commuting time between 40 and 90 minutes.
In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. In this case, the commuting time is uniformly distributed between 40 and 90 minutes. The PDF for a uniform distribution is given by:
f(x) = 1 / (b - a)
where 'a' is the lower bound (40 minutes) and 'b' is the upper bound (90 minutes) of the distribution.
To find the probability that the commuting time falls between 50 and 60 minutes, we need to calculate the area under the PDF curve between these two values. Since the PDF is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.
The width of the range between 50 and 60 minutes is 60 - 50 = 10 minutes. The total width of the distribution is 90 - 40 = 50 minutes.
Therefore, the probability that the commuting time will be between 50 and 60 minutes is:
P(50 ≤ x ≤ 60) = (width of range) / (total width of distribution) = 10 / 50 = 1/5 = 0.2, or 20%.
Thus, there is a 20% probability that the commuting time on this particular train will be between 50 and 60 minutes.
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Which values are solutions to the inequality below? Check all that apply.
√x <10
A. 100
B. 25
C. -100
D. 105
E. 36
F. 9
Answer:
The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v
Step-by-step explanation:
its E and A
Answer:
The solutions to the inequality are B, E, and F: 25, 36, and 9.
Step-by-step explanation:
The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:
√x < 10
x < 10^2 = 100
So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:
A. 100 (not a solution)
B. 25 (solution)
C. -100 (not a solution)
D. 105 (not a solution)
E. 36 (solution)
F. 9 (solution)
Help for points please!
Answer:
A) 0
Step-by-step explanation:
15/21 simplifies to 5/7. 5/7-5/7 (itself) is 0.
Answer:
0
Step-by-step explanation:
= \(\frac{5}{7}-\frac{5}{7}\)
= \(\frac{5-5}{7}\)
= \(\frac{0}{7}\)
= \(0\)
PLZZZZZZZZZZ HELP MEEEEEEEE
Answer:
D
Step-by-step explanation:
\(2x^2+2x+12=3x^2-x+2\\2x+12=x^2-x+2\\x^2-3x-10=0\\(x-5)(x+2)=0\\x=5, -2\)
The correct answer is choice D. Hope this helps!
Answer:
{-5, 2}
Step-by-step explanation:
\(2x^{2} + 2x + 12 = 3x^{2} -x + 2\) move everything to the right side
\(-2x^{2} -2x-12=-2x^{2} -2x-12\) add line 1 and 2 to get the below equation
\(0 = x^{2} -3x -10\) find multiples of -10 that add to give you -3
to get -10 we have to have (+)(-)
{-5, 2}
Just onve more question
same as the other one
Answer:
x = 2
Step-by-step explanation:
4(5 - 2x) + 3 = 7
Distributive property , multiply (5-2x) by 4:
20 -8 x + 3 = 7
Combine like terms:
23 - 8x = 7
Inverse add and subtract:
23 - 7 - 8x + 8x = 7 - 7 + 8x
16 = 8x
Inverse divide:
16/8 = 8x/8
x = 2
I will mark first answer who showed their work brainliest
Solve (2x-3)^5 Using pascal's triangle
Answer: (2x+3)5
Step-by-step explanation:
convert this equation into standard form
y=-0.25(x+0)(x-8)
I need help with this someone very smart in math this is algebra 2
Answer:
D
Step-by-step explanation:
The interest is compounded annually, which means that interest from the previous year earns you even more money next year.
It should be obvious that after one year Alexis will have
$475 + $475 * 1.25% = $475 * 100% + $475 * 1.25% =
= 101.25% * $475 = 1.0125 * $475
Then, next year she would have
1.0125 * $475 + (1.0125 * $475) * 1.25% =
= (1.0125 * $475) * 1.0125 = 1.0125^2 * $475
See the pattern?
Alexis will have $475 * 1.0125^x after x years.
A boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 6^{\circ} ∘ , before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 22^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
Using the slope concept, it is found that the distance from point A to point B is of 887 feet.
What is a slope?The slope is given by the vertical change divided by the horizontal change.
It's also the tangent of the angle of depression.
In this problem, the vertical change is of 126 feet.
At point A, the angle is of 6º, while the horizontal position is of \(x_A\), hence:
\(\tan{6^\circ} = \frac{126}{x_A}\)
\(x_A = \frac{126}{\tan{6^\circ}}\)
\(x_A = 1198.8\)
At point B, the angle is of 22º, while the horizontal position is of \(x_B\), hence:
\(\tan{22^\circ} = \frac{126}{x_B}\)
\(x_B = \frac{126}{\tan{22^\circ}}\)
\(x_B = 311.9\)
Hence, the distance in feet is of:
\(d = x_A - x_B = 1198.8 - 311.9 \approx 887\)
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Answer:
621.4
Step-by-step explanation:
I got the question right
I have taken a picture of the question I am needing help with. Thank you.
Answer:
Width: 20 in
Length: 25 in
Explanation:
We can represent the situation with the following figure
Where x is the width of the rectangular piece of metal, (x + 5) is the length of the rectangular because it is 5 in longer than its wide, and the corners have squares of side 1 in.
Therefore, the volume of the box will be equal to
Volume = Length · Width · Height
Volume = (x + 5 - 1 - 1) · (x - 1 - 1) · (1)
Volume = (x + 3)(x - 2)(1)
Volume = (x + 3)(x - 2)
Because the length of the box will be the length of the rectangle less the length of the squares and the width of the box will be the length of the rectangle less the width of the squares.
The volume is 414 in³, so we need to solve the following equation:
414 = (x + 3)(x - 2)
414 = x² + 3x - 2x + 3(-2)
414 = x² + x - 6
414 - 414 = x² + x - 6 - 414
0 = x² + x - 420
Factorizing x² + x - 420, we get:
(x + 21)(x - 20) = 0
Then
x + 21 = 0
x + 21 - 21 = 0 - 21
x = -21
or
x - 20 = 0
x - 20 + 20 = 0 + 20
x = 20
Since x = -21 doesn't have sense, the width is x = 20 and the length is:
x + 5 = 20 + 5 = 25 in.
So, the original width is 20 in and the original length is 25 in
find the function P defined by a polynomial of degree 3 with real coefficients that satisfy the given conditions. The zeros are -3,-1, and 4. The leading coefficient is -4.
Given:
Degree of polynomial = 3
Zeros are -3,-1, and 4.
The leading coefficient is -4.
To find:
The polynomial.
Solution:
The general form of a polynomial is
\(P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}\)
where, a is a constant, \(c_1,c_2,...,c_n\) are zeros with multiplicity \(m_1,m_2,...,m_n\) respectively.
Zeros of the polynomial are -3,-1, and 4. So,
\(P(x)=a(x-(-3))(x-(-1))(x-4)\)
\(P(x)=a(x+3)(x+1)(x-4)\)
\(P(x)=a(x^2+3x+x+3)(x-4)\)
\(P(x)=a(x^2+4x+3)(x-4)\)
\(P(x)=a(x^3+4x^2+3x-4x^2-16x-12)\)
\(P(x)=a(x^3-13x-12)\)
\(P(x)=ax^3-13ax-12a\)
Here, leading coefficient is a.
The leading coefficient is -4. So, a=-4.
\(P(x)=(-4)x^3-13(-4)x-12(-4)\)
\(P(x)=-4x^3+52x+48\)
Therefore, the required polynomial is \(P(x)=-4x^3+52x+48\).
Carmen suele ir a la biblioteca de su barrio cada 28 días, Rafael cada 25 y Teresa cada 22. El día 12 de septiembre se encuentran los 3 amigos. ¿Qué día volverán a coincidir?
Responder:
7.700
Explicación paso a paso:
Dado que:
Carmen va a la biblioteca cada 28 días
Rafael va a la biblioteca cada 25
Theresa cada 22 días.
Si todos se reunieron el 12 de septiembre, ¿cuándo volverán a reunirse?
Para obtener la fecha de su próxima reunión, multa el mínimo común múltiplo de los diferentes días en que Theresa, Rafael y Carmen van a la biblioteca
____28__25__22
__2_14__25___11
__2_7__25___11
__5_7__5____11
__5_7__1____11
__7_1__1____11
_ 11_1__1 ____1
Por lo tanto, el múltiplo común más bajo:
(2 * 2 * 5 * 5 * 7 * 11) = 7700
Por lo tanto, todos se volverán a encontrar en el nido 7.700 días