A restaurant charges different amounts for each drink, entrée, and side order.
• Each side order costs $2 more than each drink.
• Each entrée costs $5 more than each side order.
• A total of 2 drinks, 1 side order, and 2 entrées costs $26.
How much does each entrée cost?
Answers
Each entrée costs $9.80. The total cost of 2 drinks, 1 side order, and 2 entrées is $26, 2D + S + 2E = $26.
Let's assign variables to represent the costs of each item:
Let D represent the cost of each drink.
Let S represent the cost of each side order.
Let E represent the cost of each entrée.
Based on the given information, we can create a system of equations:
Each side order costs $2 more than each drink:
S = D + $2
Each entrée costs $5 more than each side order:
E = S + $5
The total cost of 2 drinks, 1 side order, and 2 entrées is $26:
2D + S + 2E = $26
To solve for E, we can substitute the expressions for S and E from equations (1) and (2) into equation (3):
2D + (D + $2) + 2(D + $5) = $26
Simplifying this equation:
2D + D + $2 + 2D + $10 = $26
D + $12 = $26
Subtracting $12 from both sides:
5D = $14
Dividing both sides by 5:
D = $2.80
Now, we can substitute the value of D into equations (1) and (2) to find the values of S and E:
From equation (1):
S = D + $2
S = $2.80 + $2
S = $4.80
From equation (2):
E = S + $5
E = $4.80 + $5
E = $9.80
Therefore, each entrée costs $9.80.
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Related Questions
Identify the slope and explain
Answers
Use the following function rule to find f(1.5).
f(x) = 5.97/x + 0.48
Write your answer as a decimal or whole number.
f(1.5) = ________
Answers
Answer:
f(1.5) = 4.46
Step-by-step explanation:
f(x) = 5.97/x + 0.48 f(1.5)
f(1.5) = 5.97/1.5 + 0.48
f(1.5) = 3.98 + 0.48
f(1.5) = 4.46
So, the answer is f(1.5) = 4.46
Are the ratios 3:6 and 2:4 equivalent? ) yes no
Answers
Answer:
Yes, the ratios 3:6 and 2:4 are equivalent because they represent the same proportion. To confirm, we can simplify both ratios to their simplest form:
3:6 can be simplified by dividing both terms by 3: 3/3 : 6/3 -> 1:2
2:4 can be simplified by dividing both terms by 2: 2/2 : 4/2 -> 1:2
Since both ratios simplify to the same ratio, 1:2, they are equivalent.
Answer: yes !!
Step-by-step explanation: 3:6 and 2:4 are equivalent b/c of their common factors.
may i have some help with 9? thanks :)
Answers
#9. C
A negative sign on the outside of the function indicates a reflection in the y-axis.
A negative sign on the inside of the function (attached to the x) indicates a reflection in the x-axis.
Hope this helps!
PLEASE HELP ASAP
What is the area of the real object that the scale drawing models?
A. 20 sq cm
B. 180 sq cm
C. 120 sq cm
D. 60 sq cm
Answers
Answer:
B. 180 sq cm
Step-by-step explanation:
if the area of the scale drawing is 20 cm then the width must be 5cm and the length is 4cm.
Since the scale factor is 1:3 you multiply the side lenghts by 3. So the width of the real object is 15 cm and the length is 12 cm.
Multiply L x W to get area, 15 x 12 = 180
Michael Fenton sells plumbing supplies to contractors. He earns 3% commission on the first $15,000
in sales, 5% on the next $15,000, and 8% on sales over $30,000. Last month he sold $52,000 worth
of plumbing supplies. What was his total commission?
Answers
Answer:
His total commission was: $2,960
Step-by-step explanation:
The commissions that Michael Fenton earns by selling plumbing supplies to contractors has three levels:
On the first $15,000 in sales, he earns 3%
On the next $15,000 in sales, he earns 5%
Over $30,000 in sales, he earns 8%.
Last month he sold $52,000 worth of plumbing supplies. His commissions will be calculated according to the levels reached:
The first $15,000 gave him 3%*15,000=0.03*15,000=$450
From the $52,000 sales, there remains $52,000 - $15,000 = $37,000 for the next levels.
The next $15,000 gave him 5%*15,000=0.05*15,000=$750
Now $37,000 - $15,000 = $22,000 remain for the last level.
Michael earned 8% of $22,000 = 0.08*22,000 = $1,760
His total commission was: $450 + $750 + $1,760 = $2,960
From the city A to C, there are two options: through city B or not. From A to B there are 3 different routes, from B to C there are 4 different routes, and there are 2 ways from A to C, directly. How many possible ways can a person choose,from A to C ?
Answers
Answer:
36
Step-by-step explanation:
You add all of them together which is 9
Then you take the combination of A to C
Which is 9C2
Suppose it takes 4 hours for a certain strain of bacteria to reproduce by dividing in half. If 45 bacteria are present o begin with the total number present after a days is f(x) = 45 - 64* Find the total number present after 1, 2 and 3 days. There will be bacteria present after 1 day, after 2 days and after 3 days.
Answers
A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
The problem can be solved using the exponential growth model.
In the given problem, the formula for the growth model is given, that is:
f(x) = 45 (64)^(x)
Where:
f(x) = total number of bacteria present after x days
To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.
f(1) = 45 (64)¹ = 2,880
f(2) = 45 (64)² = 184,320
f(3) = 45 (64)³ = 11,796,480
Hence,
after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.
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There is a line whose
y-intercept is 1 and whose slope is -2. What is its equation in slope intercept-form?
Answers
Answer:
1 = -2x + b
Step-by-step explanation:
slope intercept forms= y = mx+ b
your "Y" is 1 and you "M" is your slope which is -2
Find the equation of the line that
- is perpendicular to the line y=3x-1
and
-passes through the point (7,4)
Answers
Answer:
y = -1/3x + 19/3
Step-by-step explanation:
let the equation of the line be y = mx + b
since it is perpendicular to y = 3x - 1, these two lines's gradient when producted gives -1.
hence, 3 x m = -1
m = -1/3
sub m = -1/3 and (7, 4):
4 = -1/3(7) + b
b = 19/3
therefore, equation of the line is y = -1/3x + 19/3
Topic: coordinate geometry
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Express 43% as a fraction or mixed number in simplest form
Answers
Answer: 43/100
Step-by-step explanation:
43%=
43/100 * 100%=
43/100 * 1=43/100
GALOIS THEORY
Let F be a field. Prove that if a0 + a1x + ...\begin{matrix} & & \\ & & \end{matrix}+ anxn\inF[x] is irreducible, then so is an + an-1x + ... + a0xn.
Answers
We have shown that a0 + a1x + ... + anxn is irreducible if and only if xn + an-1xn-1 + ... + a1x + a0 is irreducible.
We will use the fact that the polynomial a0 + a1x + ... + anxn is irreducible if and only if its reciprocal polynomial xn + an-1xn-1 + ... + a1x + a0 is irreducible.
First, assume that a0 + a1x + ... + anxn is irreducible. We will show that its reciprocal polynomial xn + an-1xn-1 + ... + a1x + a0 is also irreducible.
Suppose, for the sake of contradiction, that xn + an-1xn-1 + ... + a1x + a0 is reducible. Then we can write it as a product of two non-constant polynomials f(x) and g(x) in F[x].
We can assume without loss of generality that f(x) and g(x) are monic (i.e. have leading coefficient 1), since we can always factor out a non-zero constant.
Since f(x) and g(x) are monic, their constant terms are non-zero. Let's write f(x) = x^k + b1x^(k-1) + ... + bk and g(x) = x^l + c1x^(l-1) + ... + cl, where k and l are positive integers.
Since f(x)g(x) = xn + an-1xn-1 + ... + a1x + a0, we know that the constant term of f(x) times the constant term of g(x) is equal to a0. Since a0 is non-zero, both the constant term of f(x) and the constant term of g(x) are non-zero.
Without loss of generality, let's say that the constant term of f(x) is non-zero. Then we can write f(x) = (x - d)h(x), where d is a non-zero element of F and h(x) is a polynomial in F[x].
Substituting x = d into the equation f(x)g(x) = xn + an-1xn-1 + ... + a1x + a0, we get (d - d)h(d)g(d) = a0, which implies that h(d)g(d) = a0. Since a0 is irreducible, it can only be factored as a product of a constant and a unit in F. Since h(d) and g(d) are both non-zero (because f(x) and g(x) are monic and have non-zero constant terms), we conclude that h(d) and g(d) are both units in F.
Therefore, we can write f(x) = (x - d)u(x) and g(x) = v(x), where u(x) and v(x) are both units in F[x].
Substituting these expressions into the equation f(x)g(x) = xn + an-1xn-1 + ... + a1x + a0 and simplifying, we get
(x - d)^ku(x)v(x) = xn + (a_n-1 - da_n)x^(n-1) + ...
This implies that d is a root of the polynomial xn + (a_n-1 - da_n)x^(n-1) + ..., which contradicts the assumption that a0 + a1x + ... + anxn is irreducible.
Therefore, xn + an-1xn-1 + ... + a1x + a0 must be irreducible.
Conversely, assume that xn + an-1xn-1 + ... + a1x + a0 is irreducible. We will show that a0 + a1x + ... + anxn is also irreducible.
Suppose, for the sake of contradiction, that a0 + a1x + ... + anxn is reducible. Then we can write it as a product of two non-constant polynomials f(x) and g(x) in F[x].
Let's write f(x) = c0 + c1x + ... + cx^k and g(x) = d0 + d1x + ... + dx^l, where k and l are positive integers.
Since f(x)g(x) = a0 + a1x + ... + anxn, we know that the constant term of f(x) times the constant term of g(x) is equal to a0. Since a0 is non-zero and irreducible, we know that either the constant term of f(x) or the constant term of g(x) is a unit in F.
Without loss of generality, let's say that the constant term of f(x) is a unit in F. Then we can write f(x) = u(x) and g(x) = v(x), where u(x) is a unit in F[x].
Substituting these expressions into the equation f(x)g(x) = a0 + a1x + ... + anxn and simplifying, we get
u(x)v(x) = (a0/c0) + (a1/c0)x + ... + (an/c0)x^n
Since c0 is a unit in F, we can write a0/c0, a1/c0, ..., an/c0 as elements of F.
Therefore, we have expressed a0 + a1x + ... + anxn as a product of two non-constant polynomials in F[x], contradicting the assumption that it is irreducible.
Therefore, a0 + a1x + ... + anxn must be irreducible.
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What is the distance between the points X(-4,3) and Y(2, -7) rounded to the nearest tenth? show your work.
O 11.7 units
O 8.0 units
O 16.0 units
O 4.5 units
Answers
Answer:
11.7 units
Step-by-step explanation:
sq root(2--4)^2+(-7-3)^2
sq root(6)^2 + (-10)^2
sq root (36)+(100)
sq root 136
equals 11.66 which rounds up to 11.7
A factory produces 90 packages of mixed nuts in 1 min. A quality control manager selected 10 of these 90 packages at random and then counted the number of nuts in each package. The manager recorded the results.
30, 31, 36, 32, 35, 35, 35, 33, 31, 36
What is the estimated median number of nuts in all 90 packages?
Enter your answer in the box.
nuts =
Answers
34
explanation:
First of all, put the numbers in order
30, 31, 31, 32, 33, 35, 35, 35, 36, 36
Then, find the middle number.
In this case, there is an even amount of numbers so, we have to pick the 2 middle numbers which is 33 and 35.
Now all you have to do is add these two numbers together then divide by 2 which will give you 34.
or, in simpler questions like this one, you can just say 34 as you know it is between 33 and 35.
In other questions, it might have and odd amount of numbers, for example:
3, 3, 5, 8, 10
so all you would do here is pick the middle number which would be 5. (it has 2 numbers on each side of it)
Answer:
34
Step-by-step explanation:
just because its 34 add my
A person invests $350 in an account that earns 3.65% annual interest compounded
semiannually. Find when the value of the investment reaches $5675.
Answers
M = C(1+r)^t
5675 = 350(1+0.0365/2)^t
5675=350×1.01825^t
t = 154.04
Answer:
Approximately 77 years
Step-by-step explanation:
V(t)=P(1+r/n)^nt
5675=350(1+.0365/2)^2t
16.214=1.01825^2t
log16.214=log1.01825^2t
log16.214=2t(log1.01825)
log16.214/2log1.01825=t
77=t
Any whole number that can be represented in base 10 can also be represented in base 2, although it may take ____ digits.
Answers
Answer:
More
Step-by-step explanation:
Any whole number that can be represented in base 10 can also be represented in base 2, although it may take more digits.
construct a box plot from the given data. diameters of cans in an assembly line: 5.7,5.6,5.1,5.4,5.2,5.6,5.7,5.3,5.8,5.2
Answers
The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4.
A box plot, also known as a box-and-whisker plot, is a graphical representation of numerical data that displays the distribution of a dataset. It provides a visual summary of the minimum, first quartile, median, third quartile, and maximum values, as well as any outliers that may be present.
To construct a box plot from the given data (diameters of cans in an assembly line: 5.7, 5.6, 5.1, 5.4, 5.2, 5.6, 5.7, 5.3, 5.8, 5.2), follow these steps:
1. Sort the data in ascending order: 5.1, 5.2, 5.2, 5.3, 5.4, 5.6, 5.6, 5.7, 5.7, 5.8.
2. Find the median (middle value) of the dataset, which is 5.4.
3. Determine the first quartile (Q1), which is the median of the lower half of the data. In this case, it is the median of the numbers below 5.4: 5.2.
4. Find the third quartile (Q3), which is the median of the upper half of the data. In this case, it is the median of the numbers above 5.4: 5.7.
5. Calculate the interquartile range (IQR) by subtracting Q1 from Q3: 5.7 - 5.2 = 0.5.
6. Identify any outliers in the dataset. Outliers are values that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. In this case, there are no outliers.
7. Construct the box plot using a number line. Draw a box from Q1 to Q3, with a line inside representing the median. Add whiskers (lines) extending from the box to the minimum value (5.1) and the maximum value (5.8).
The resulting box plot for the given data would show a box ranging from 5.2 to 5.7, with the median at 5.4. The whiskers would extend from 5.1 to 5.8. This visual representation provides an overview of the distribution and key statistical measures of the diameters of cans in the assembly line.
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the tickets for the field trip were purchased yesterday for both students and instructors. children tickets cost $11, adult tickets cost $13. the number of children tickets purchased was one more than ten times the number of adults tickets purchased. how many of each were purchased if all of the tickets cost a total of $995 dollars?
Answers
42 adult tickets and 421 children tickets were purchased for the field trip, based on the given information that the total cost of the tickets was $995 and the children tickets cost $11 while the adult tickets cost $13, and the number of children tickets purchased was one more than ten times the number of adults tickets purchased.
Let's use variables to represent the unknown quantities in the problem:
Let x be the number of adult tickets purchased
Then the number of children tickets purchased is 10x + 1 (since it is one more than ten times the number of adults tickets purchased)
Using these variables, we can set up an equation based on the total cost of the tickets:
13x + 11(10x + 1) = 995
Simplifying and solving for x, we get:
23x + 11 = 995
23x = 984
x = 42.7826087 (rounded to 9 decimal places)
Since we can't purchase a fraction of a ticket, we'll round x down to the nearest whole number, which means 42 adult tickets were purchased. Then the number of children tickets purchased is:
10x + 1 = 10(42) + 1 = 421
So, 42 adult tickets and 421 children tickets were purchased.
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A pumpkin farm sells small pumpkins in bags of n pumpkins each. Helen buys 3 bags of pumpkins. Which expression can be used to find the total number of pumpkins Helen bought.
Answers
Answer:
3n
Step-by-step explanation:
this question is asking for multiplication because to figure out how many are in the bag you need to multiply 3 times the numbers of pumpkins in the bag
-2x-7+9-2= Please can i have an answer
Answers
Answer:
-2x
Step-by-step explanation:
-2x-7+9-2
Combine like terms
-2x +0
-2x
Answer:
-2x
Step-by-step explanation:
from the question
-2x-7+9-2=
step 1
collect the like terms
we have,
-2x-7+9-2
-2x + 2 -2
-2x + 0
-2x
therefore the answer to the question -2x-7+9-2 is equal to -2x
____ : referring to the fact that the distance between two or more points is equal.
Answers
The term that refers to the fact that the distance between two or more points is equal is "equidistant".
In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.
Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.
The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.
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one half of negative five eights in numerical epression
Answers
Answer:
The answer is in the picture
Step-by-step explanation:
hope it helps!
The proof shown needs several statements and reasons filled in.
Answers
Given the angle bisector, the statements and reasons for the proof are explained.
What is an angle bisector?A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.
The statements and reasons for the proof are given below;
STATEMENT REASONS
1. MK bisects <HKO and <HMO Given
2. m<HMK = m<OMK and m<HKM = m<OKM Definition of angle bisector
3. HK ≅ KO, and HM ≅ OM Congruent side property
4. ΔHMK ≅ ΔOMK Angle-Angle-Side theorem
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Without graphing, determine the x-intercepts and vertex of the quadratic function f(x)=x²+11x+18. Show all of your work.
Answers
Answer: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/ex3-completing-the-square
Step-by-step explanation: This will help you a lot
Sebastian learned a total of 220 appetizer recipes over the course of 44 weeks of culinary school. After 88 weeks of culinary school, how many total appetizer recipes will Sebastian know? Assume the relationship is directly proportional.
Answers
Answer:
Sebastian will know 440 recipes.
Step-by-step explanation:
Since we can assume that the relationship of the situation is directly proportional, proportional relationships are described as:
\(y=kx\)Then, if he learned 220 appetizers in 44 weeks, after 88 weeks;
\(\begin{gathered} \frac{220}{44}=\frac{x}{88} \\ x=\frac{88\cdot220}{44} \\ x=440\text{ } \\ \text{ Sebastian will know 440 recipes} \end{gathered}\)expand the given function in a fourier series. (give the fourier series that is the periodic extension of f with period 2.) f(x) = x2, 0 < x < 2
Answers
By evaluating the integrals and expressing the Fourier series as a sum of the constant, cosine, and sine terms, we can obtain the complete Fourier series representation of f(x) = x² with a period of 2.
To expand the function f(x) = x^2 into a Fourier series with a period of 2, we can represent it as a combination of sine and cosine terms. The Fourier series will consist of a constant term, cosine terms with frequencies that are multiples of the fundamental frequency, and sine terms with frequencies that are also multiples of the fundamental frequency.
The given function f(x) = x² is defined for 0 < x < 2. To extend it periodically with a period of 2, we can consider it as a periodic function defined for all real numbers x. The period is extended by repeating the function values after every interval of 2.
The Fourier series representation of f(x) will consist of a constant term, cosine terms, and sine terms. The constant term represents the average value of the function over one period. In this case, since f(x) = x² is an even function, the constant term is given by the average value of the function over half a period, which is 1/2 times the integral of x² from 0 to 2, divided by 2.
The cosine terms in the Fourier series represent the even components of the function. The coefficients of the cosine terms can be obtained by integrating the product of the function and the cosine functions with frequencies that are multiples of the fundamental frequency. In this case, the fundamental frequency is 2π/2 = π. So the cosine terms will have frequencies of nπ, where n is an integer. The coefficients of the cosine terms can be obtained by integrating x² multiplied by cos(nπx/2) over the interval from 0 to 2.
The sine terms in the Fourier series represent the odd components of the function. The coefficients of the sine terms can be obtained by integrating the product of the function and the sine functions with frequencies that are multiples of the fundamental frequency. In this case, the sine terms will have frequencies of nπ, where n is an integer. The coefficients of the sine terms can be obtained by integrating x^2 multiplied by sin(nπx/2) over the interval from 0 to 2.
By evaluating the integrals and expressing the Fourier series as a sum of the constant, cosine, and sine terms, we can obtain the complete Fourier series representation of f(x) = x² with a period of 2.
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Can someone help? Show work
Answers
Answer:
5\(\sqrt{2}\)
Step-by-step explanation:
\(\sqrt{50}\)
\(\sqrt{25} = 5^{2}\)•\(2\)
\(\sqrt{5^{2} }\)×\(\sqrt{2}\)
since 5 is squared the square root cancels out
so 5\(\sqrt{2}\)
Evaluate (3n)! for n=2.
Answers
A public park is the shape of a triangle. The side of the park that forms the base of the triangle is 200 yd long, And the area of the park is 7500 yd squared. What is the length of the side of the park that forms the height of the triangle?
Answers
The height of the triangular shaped park is 75 yd.
Given that, base of the triangle = 200 yd and the area of the park = 7500 yd squared.
What is area of a triangle?The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
Now, the area of a triangle = 1/2 × 200 × h
⇒ 7500 = 1/2 × 200 × h
⇒ 15000 = 200 × h
⇒ h = 15000/200
⇒ h = 75 yd
Therefore, the height of the triangular shaped park is 75 yd.
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(9x-54)/(x-6) rational equation
Answers
By taking 9 as a common factor in the numerator we can write the rational equation as:
(9x-54)/(x-6) = 9
So it is just a scalar.
How to solve the rational equation?Here we have the following rational equation:
(9x-54)/(x-6)
And we want to simplify this, so let's do that.
First, we can rewrite the numerator, it is:
(9x - 54)
We also know that 54 = 9*6
So we can write:
(9x - 54) = (9x - 9*6)
And now we can take 9 as a common factor to get.
(9x - 9*6) = 9*(x - 6)
Replacing that in the rational equation we will get:
(9x-54)/(x-6) = 9*(x - 6)/(x - 6) = 9
So we have a constant.
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