A graphics designer is designing an advertising brochure for an art show. Each page of the brochure is rectangular with an area of 30 in^2 and a perimeter of 22 in. Find the dimensions of the brochure.The longer side is nothing in.The shorter side is nothing in.
Answers
Recall that one page of the brochure would be a rectangle of the form
We are told that the area of this rectangle is 30 squared inches. For this rectangle, the area would be
\(x\cdot y\)So we have the equation
\(x\cdot y=30_{}\)Also, we are told that the perimeter of the figure is 22 in. Recall that the perimeter of the rectangle is obtained by adding the lengths of the sides of the figure. So we have the equation
\(x+y+x+y=22=2x+2y\)Dividing both sides by 2, we get
\(x+y=11_{}\)Using the first equation we have
\(y=\frac{30}{x}\)So if we replace this in the second equation, we have
\(x+\frac{30}{x}=11\)If we multipy both sides by x, we get
\(x^2+30=11x_{}\)Subtracting 11x from both sides, we get
\(x^2-11x+30=0\)Recall that given an equation of the form
\(ax^2+bx+c=0\)The solutions are given by the formula
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)In this case we have a=1, b= -11 and c=30
\(x=\frac{-(-11)\pm\sqrt[]{(-11)^2-4\cdot1\cdot30}_{}}{2\cdot1}=\frac{11\pm\sqrt[]{121-120}}{2}=\frac{11\pm1}{2}\)From where we get
\(x_1=\frac{11+1}{2}=\frac{12}{2}=6\)and
\(x_2=\frac{11-1}{2}=\frac{10}{2}=5\)So, if x=6, we have that
\(y=\frac{30}{6}=5\)and if x=5, we have that
\(y=\frac{30}{5}=6\)This means that the longer side is 6 inches long and the shorter side is 5 inches long
Related Questions
The base of a parallelogram with area 154.5 cm² and height 15 cm is
(a) 10 cm
(b) 12 cm
(c) 10.3 cm
(d) 13 cm
Answers
Answer:
▶ (c) 10.3 cmStep-by-step explanation:
\( \space\)
A = b × h
=> 154.5 = b × 15
=> b = \( \sf{\frac{154.5}{15} }\)
=> 10.3 cm
\( \space\)
Hope it helps!
Have a great day! :)
Using the points in this table, write the equation of the line in slope-intercept form
Answers
Firsr, we need to calculate the slope, given two points. We will use (3,2) and (4,4)
\(m=\frac{4-2}{4-3}=\frac{2}{1}=2\)Having the slope, we can calculate the equation
\(\begin{gathered} y-4=2(x-4) \\ y=2x-8+4=2x-4 \end{gathered}\)here is a list 31 29 33 37 43 38 33 40 find the mode in number of list and work out on mean
Answers
Answer: Mode = 33, Mean = 35.5
Step-by-step explanation: The mode is whatever number appears the most.
To find the mode, first put the numbers in order from least to greatest.
29, 31, 33, 33, 37, 38, 40, 43
In this case, 33 appears the most, so the mode is 33.
The mean is the average of all of the numbers.
Firstly, add up all of the numbers:
29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284
Now that you have all of them added up, divide the final sum by the number of numbers you have in the list. In this case, you have 8 numbers.
284/8 = 35.5
Your mean is 35.5
Answer:
Mode = 33
Mean = 35.5
The mode is whatever number appears the most.
to find the mean:
add all the numbers:
29 + 31 + 33 + 33 + 37 + 38 + 40 + 43 = 284
divide that by the number of numbers you have in the list.
284/8 = 35.5
mean = 35.5
Consider the situations.
i. The value of an investment increases by $30 every year.
ii. The value of an investment decreases by 10% every year.
In which situation(s) is (are) the investment(s) changing at a constant rate?
both i and ii
only i
only ii
neither i norii
Answers
If the value is changing by a certain dollar amount every year, this means it is a constant rate of change. If it is changing by a certain percentage every year, this means it is changing at a non uniform, specifically exponential, rate.
solve the PDE using separation of variables method Uxx = 1/2 Ut 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Answers
The general solution of the partial differential equation is:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
How to solve Partial Differential Equations?The partial differential equation (PDE) is given as:
Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)
Assume that the solution can be written as a product of two functions:
U(x, t) = X(x)T(t)
Substituting this into the PDE, we have:
X''(x)T(t) = (1/2)X(x)T'(t)
Dividing both sides by X(x)T(t), we get:
(X''(x))/X(x) = (1/2)(T'(t))/T(t)
Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:
(X''(x))/X(x) = -λ²
(1/2)(T'(t))/T(t) = -λ²
Simplifying the second equation, we have:
T'(t)/T(t) = -2λ²
Solving the second equation, we find:
T(t) = Ce^(-2λ²t)
Applying the boundary condition U(0, t) = 0, we have:
U(0, t) = X(0)T(t) = 0
Since T(t) ≠ 0, we must have X(0) = 0.
Applying the boundary condition U(3, t) = 0, we have:
U(3, t) = X(3)T(t) = 0
Again, since T(t) ≠ 0, we must have X(3) = 0.
Therefore, we can conclude that X(x) must satisfy the following boundary value problem:
X''(x)/X(x) = -λ²
X(0) = 0
X(3) = 0
The general solution to this ordinary differential equation is given by:
X(x) = Asin(λx) + Bcos(λx)
Applying the initial condition U(x, 0) = 5*sin(4πx), we have:
U(x, 0) = X(x)T(0) = X(x)C
Comparing this with the given initial condition, we can conclude that T(0) = C = 5.
Therefore, the complete solution for U(x, t) is given by:
U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)
where:
Σ represents the summation over all values of n
λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).
To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):
X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0
X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0
From the first equation, we have Bₙ = 0.
From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.
This implies that 3λₙ = nπ, where n is an integer.
Therefore, λₙ = (nπ)/3.
Substituting the eigenvalues into the general solution, we have:
U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)
where Aₙ are the coefficients that can be determined from the initial condition.
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Which triangle is a reflection of the green triangle
Answers
Tthe triangle that is a reflection of the green triangle is figure 1
Which triangle is a reflection of the green triangleFrom the question, we have the following parameters that can be used in our computation:
The figures
Where, we have:
Figure 1 and the green figure have the opposite orientationFigure 1 and the green figure have the same sizeThis means that the triangle that is a reflection of the green triangle is figure 1
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Calcular los 3/5 de los 2/3 de las 3/4 de 560
Answers
For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.
How to solve fractions?To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:
Step 1: Calculate 3/4 of 560:
3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420
Step 2: Calculate 2/3 of the result from Step 1:
2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280
Step 3: Calculate 3/5 of the result from Step 2:
3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168
Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.
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I’ll give points and brainalist for correct answer / explanation
Answers
Answer:
i think you forgot to attach the image lol
Step-by-step explanation:
Suppose that a bike rents for 50php plus 8php per hour. Write an equation in slope-intercept form that models this situation.
Answers
Answer: C(x) = (8 php)*x + 50 php.
Step-by-step explanation:
In a linear equation:
y = a*x + b
a is the slope.
x is the variable
b is the y-intercept.
In this case, we have
The rent is 50 php fixed, plus 8 php per hour.
Then we will pay the 50php only one time, and it does not depend on the number of hours that we rent, then this is the y-intercept.
then if we rent the bike for x hours, we will pay a plus of x*8 php.
Then the total cost for x hours, C(x), will be
C(x) = (8 php)*x + 50 php.
Then the slope is 8 php, and the y-intercept is 50 php.
What is the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰?
Answers
Given:
a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰.
To find:
The GCF of given terms.
Solution:
Greatest common factor (GCF): To find the GCF of two or more numbers, we need to find the product of their prime factor with their maximum powers.
The given terms are
\(a^{12}b^{4},a^{4}b^8, a^{24}b^{16}, a^{12}b^{20}\)
Here, each term has two prime factors a and b. The highest power of a is 24 and the highest power of b is 20. So, the GCF of given terms is
\(GCF=a^{24}\times b^{20}\)
\(GCF=a^{24}b^{20}\)
Therefore, the GCF of a¹²b⁴, a⁴b⁸, a²⁴b¹⁶ and a¹²b²⁰ is a²⁴b²⁰.
How do I find how many times a line intersects?
Answers
Answer:
you should count how many time two or more line touches each other
Answer:
If you want to know where a line intercepts the y axis then you make substitute x for 0 and solve for y. If you want to know the intercepts for the x axis, then substitute y for 0 and solve for x.
Step-by-step explanation:
Choose True or False for each statement.
Column A
1.
If the distance from 0 to x on a number line is equal to 2, then -2 + X = 0.:
If the distance from 0 to x on a number line is equal to 2, then -2 + X = 0.
2.
If the distance from 0 to x on a number line is less than 2, then -2 + X = is negative.:
If the distance from 0 to x on a number line is less than 2, then -2 + X = is negative.
3.
If the distance from 0 to x on a number line is greater than 2, the -2 + X is positive.:
If the distance from 0 to x on a number line is greater than 2, the -2 + X is positive.
4.
If the distance from 0 to x on a number line is greater than 0, then -2 + X is positive.:
If the distance from 0 to x on a number line is greater than 0, then -2 + X is positive.
Answers
Does the graph represent a function? Why or why not ?
Answers
Answer:
A.
Step-by-step explanation:
The vertical line test is a way of finding out if a relation is a function.
Graph the relation.
Then imagine a vertical line moving from left to right over the graph of the relation.
If the vertical line intersects at most one point of the graph in any position you place the vertical line, then the relation is a function.
This function passes the vertical test since it never intersects more than one point on the vertical line at a time.
Answer: A.
This may be hard to put together, but I need help with an angle equation. I'm looking for example equations and how to do these types of equations. *please note that this equation is completely random and probably ends with an ugly number. it's just an example of a type of problem*
Answers
Example: (2x - 4) x=7 so (2x (x=7) - 4) =18
Natural number is subset of whole number. Mark True / False
Answers
Answer: This is false statement.
because, whole numbers belong to the set of integers and rational numbers. But, they are not the set of natural numbers
Step-by-step explanation:
I want brainliest
Juan buys candy that costs $8 per pound. He will spend at least $48 on candy. What are the possible numbers of pounds he will buy?
Use p for the number of pounds Juan will buy.
Write your answer as an inequality solved for p.
Answers
In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).
How can these number be determined?Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.
From the question, p = number of pounds Juan will buy.
candy=costs $8 per pound
$20/$4 = 5 pounds
p>5
at least 5 pounds
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Find the radius of a circle with a circumference of 4/3 pi.
Answers
The radius of a circle with circumference of 4π/3 is equal to 2/3
What is the circumference of a circleThe circumference of a circle is the same as the total length of the circle boundary. It can also be called the perimeter of a circle.
The circle in question have its circumference as
4π/3.
circumference of circle = 2πr
4π/3 = 2πr
divide through by π
4/3 = 2r
r = 4/(3×2) {by cross multiplication}
r = 4/6
radius = 2/3.
Therefore, the radius of a circle with circumference of 4π/3 is equal to 2/3
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The radius of a circle with a circumference of 4π/3 is equal to 2/3 units.
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Substituting the given parameters into the circumference of a circle formula, we have the following;
Circumference of circle, C = 2πr
4π/3 = 2πr
4π = 6πr
Radius, r = 4/6 = 2/3 units.
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This table shows a proportional relationship between x and y.
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у
0
1
ANO
2
الا
6
Find the constant of proportionality (r). Using the value for r, enter an equation in the form of y = rx.
Answers
Answer:
2
Step-by-step explanation:
I just did this like a few days ago
Y (4)
+4y ′′
+4y=0 A general solution with x as the independent variable is y(x)=
Answers
Answer:
Step-by-step explanation:
We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.
For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,
y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0
(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.
Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get
yp″=a1+2a2x....yp‴=2a2+3a3x+....
Substituting the general solution into the non-homogeneous equation, we get
a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)
So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:
a(n+1)=Y(n-2)/n^2
From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.
9(2n+1) help please brooooooo
Answers
Answer:
18n + 9
Step-by-step explanation:
Distribute 9 into the expression.
9*2n = 18n
9*1 = 9
18n + 9
Read the article below carefully and answer the question that follows.
On the morning of July 15, 2006, fourteen school buses were vandalized. The buses, property of Walt Whitman Middle School, were parked in the "bus barn" on campus. The vandals spray-painted the buses with pictures of dogs. Dogs happen to be the mascot of rival school Edgar Allan Poe Academy. This has led some to believe that some students from EAPA may be the culprits in the incident. Says the mother of one Walt Whitman student, "Oh, yeah, the [Edgar Allan] Poe [Academy] kids are definitely responsible. Those kids don't have any discipline, and they're still stewing over the loss of last week's football game." Police, however, say that they currently have no suspects.
This article is probably NOT from a mainstream news source.
True
False
Answers
The cost, c(x), for a taxi ride is given by c(x) = 3x + 2.00, where x is the
number of minutes.
On a piece of paper, graph c(x) = 3x + 2.00. Then determine which answer matches the graph you drew, including the correct axis labels,
Answers
Answer:
Graph D is the correct answer
Step-by-step explanation:
The graph of is attached.
The y-axis of the graph represents the cost, and the x-axis represents the number of minutes.
Also, the slope of is 2, and the y-intercept is 2.
Now let us look at the choices given and determine which graph represents the function .
The first graph has the slope of 2, and a y-intercept of 2, but the y-axis represents minutes, and the x-axis represents cost—this does not match our graph.
The second graph has y-intercept of 3—also not our graph.
The third graph also has a y-intercept of 3—this does match our graph either.
The fourth graph has a y-intercept of 2 and a slope of 2, and its y-axis represents the cost and x-axis represents the minutes—this perfectly matches our graph.
Therefore, the graph that matches our graph is D.
The ESS Ravens bought pizza for $900 to sell at the football game. They kept 10 pizzas to feed the players after the game and sold the rest for $1040. There were 8 slices in each pizza. Their profit was 50 cents a slice.
a) How many pizzas were in the original order?
Answers
Answer: 45
Step-by-step explanation:
The total profit in all was \(1040-900=\$ 140\).
The total profit per pizza was \((0.50)(8)=\$4\).
This means they sold \(\frac{140}{4}=35\) pizzas.
Adding this to the 10 pizzas held back, there were \(35+10=45\) pizzas in the original order.
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answers
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
Solve the equation
2^2x+1 +5(2^x) -3=0
Please help
Answers
Answer:
The answer is -1
Step-by-step explanation:
2^(2x+1) = 2^2x × 2^1 = 2^2x × 2
after this we can make appointments
2^x = t
and then solve it :)
40% of 250 students have part-time jobs. How many students have
part-time jobs?
Answers
Answer:
100 students
Step-by-step explanation:
40/100 x 250 = 100Answer:
100 Students
Step-by-step explanation:
\(\frac{250*40}{100} =100 students\)
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.
Step 1 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.
give thanks for more! your welcome!
Step-by-step explanation:
5. Which of the following is a pair of alternate exterior angles?
Angles 1 and 4
Angles 2 and 8
Angles 1 and 7
Angles 4 and 7
Answers
Answer: angle 1 and 7
Step-by-step explanation: you just do it
Find the ordered pair (x, y) that is a solution to the equation.
2x+y=7
(x, y) = (_ , _)
Answers
Answer:
(1, 5)
Step-by-step explanation:
There are many possible solutions, but one would be (1, 5)
What is needed to get accurate measurement of distance/length? Explain
Answers
Explanation: It is more accurate than a ruler when it comes to measuring long distances.
I hope this helps. :)