You have two unknown integers. Double the larger integer increased by triple the smaller integer is 46. Squaring the larger number and increasing it by four times itself gives the same result as multiplying the smaller number by 20 and adding 5. Use a system to solve for the integers by graphing
The two unknown integers can be found by graphing the given equations. The larger integer is 10, and the smaller integer is 8.
Let's represent the larger integer as 'x' and the smaller integer as 'y.' According to the given information, we have two equations:
Equation 1: 2x + 3y = 46
Equation 2: x^2 + 4x = 20y + 5
To solve this system of equations, we can graph both equations on the same coordinate plane. The point where the two graphs intersect will give us the values of 'x' and 'y' that satisfy both equations simultaneously.
For equation 1, we rearrange it to y = (46 - 2x)/3. Plotting this equation on the graph, we see a straight line.
For equation 2, we rearrange it to x^2 + 4x - 20y - 5 = 0. Plotting this equation, we get a quadratic curve.
By examining the graph, we can see that the two lines intersect at a point where 'x' is approximately 10 and 'y' is approximately 8. Therefore, the larger integer is 10, and the smaller integer is 8.
By substituting these values back into the original equations, we can verify that they satisfy both equations.
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A coach ordered 20 practice jerseys for her soccer team. Six of the jerseys she ordered arrived late. What decimal represents the fraction of jerseys that arrived late?
Answer: 0.3
Step-by-step explanation:
There are 20 practice jerseys in total.
Six of those 20 jerseys arrived late.
The fraction of jerseys that arrived late is therefore:
= 6 / 20 jerseys
Convert them to decimal form by dividing the numerator with the denominator:
= 6 ÷ 20
= 0.3
You might need: Find the area of a circle with a circumference of 12.56 units.
Answer:
The area is 12.56 units^2 (same as circumference?)
Step-by-step explanation:
Assuming pi is 3.14, the equation for the circumference is C = 2 pi r
Fill it out for the radius (r)
12.56 = 2 3.14 r
12.56 = 6.28 r
r = 2
With the radius, the equation for the area is A = pi r^2
Fill it out for the area
A = 3.14 2^2
A = 3.14 4
A = 12.56
If JKLM is a rectangle, solve for x.
For this project, you will research setting up a food cart that sells one item (like hot dogs in buns) along with any condiments (like catsup, mustard, relish, onions, etc.) and necessary serving products (like napkins, plates, containers/wrapping foil, etc.) You may pick any food item of your choice. You will determine your total cost function, revenue function, profit function, and find your break-even point(s).
Variable(s): Very clearly define your variable(s) and be specific. For example, if you say "x
2. Total Cost: Research and determine your total cost function. Your cost function should include the cost of the cart, cost of paying employees, cost of the food and supplies for the cart, etc. Fully explain how you arrived at your cost function. Provide information/links in how you determined what your supplies and materials cost. (You may ignore the cost of permits, taxes, and city fees.)
3. Marginal Cost: Determine your marginal cost function. In your own words, explain what your marginal cost function tells you. How is this different from what your total cost function tells you?
4. Revenue: Determine your revenue function. Explain how you arrived at this function.
5. Profit: Determine your profit function. Explain how you arrived at this function.
For this project, I will choose the food item to be "Gourmet Burgers." Now let's go through each step as outlined.
1. Variable(s):
- x: Number of gourmet burgers sold
2. Total Cost:
The total cost function includes various components:
- Cost of the food ingredients for each gourmet burger
- Cost of the buns, condiments, and other toppings
- Cost of the cart and any necessary equipment
- Cost of paying employees
- Cost of serving products like napkins, plates, and containers
To determine the cost function, I would research the prices of the food ingredients, condiments, buns, and other supplies needed for each gourmet burger. I would also consider the cost of the cart, equipment, and estimated wages for the employees. By summing up all these costs, I can derive the total cost function.
3. Marginal Cost:
The marginal cost function represents the change in total cost when one additional gourmet burger is produced and sold. It can be calculated by taking the derivative of the total cost function with respect to the variable x (number of burgers sold). The marginal cost function provides insights into how the cost per unit changes as the production level increases.
The marginal cost function tells us how much it costs to produce and sell one additional gourmet burger, considering factors like additional ingredients, labor, and supplies required. It helps in making decisions regarding production levels and pricing.
4. Revenue:
The revenue function is determined by multiplying the price per gourmet burger by the number of burgers sold. The price per gourmet burger can be determined based on market research, competition, and desired profit margin. Multiplying this price by the number of burgers sold gives the revenue generated from sales.
5. Profit:
The profit function is obtained by subtracting the total cost function from the revenue function. It represents the financial gain or loss from selling a certain number of gourmet burgers. The profit function helps in assessing the profitability of the food cart business and making decisions related to pricing, cost management, and production levels.
To find the break-even point(s), we set the profit function equal to zero and solve for the number of gourmet burgers sold that result in zero profit. The break-even point is the production level where the revenue equals the total cost, indicating that no profit or loss is incurred.
It's important to note that the specific values and calculations for the cost, revenue, and profit functions would require extensive research, market analysis, and consideration of various factors such as local market conditions, ingredient prices, labor costs, and other operational expenses.
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Find a curve that passes through the point (1,5) and has an arc length on the interval [2,6] given by:
6
S2 V1 + 16x dx.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx. To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x).
To find a curve that passes through the point (1, 5) and has an arc length on the interval [2, 6] defined by the expression 6S²V1 + 16x dx, we can follow these steps:
Step 1: Determine the general form of the curve equation.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
Step 3: Solve the resulting equation to find the specific curve.
Let's proceed with each step:
Step 1: Determine the general form of the curve equation.
Let's assume the curve equation is y = f(x), where f(x) represents the unknown function describing the curve.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
The arc length formula for a curve defined by y = f(x) is given by:
S = ∫[a,b] √(1 + (f'(x))²) dx
We are given that the arc length on the interval [2, 6] is defined by the expression 6S²V1 + 16x dx. Substituting the formula for arc length, we have:
6∫[2,6] (√(1 + (f'(x))²))²dx + 16∫[2,6] x dx
Simplifying, we get:
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx
Step 3: Solve the resulting equation to find the specific curve.
Since the expression 6S²V1 + 16x dx represents the arc length on the interval [2, 6], we need to equate it to the arc length formula obtained in Step 2.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx
To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x). Without such information, it is not possible to determine the specific curve. Please provide additional constraints or information if available to proceed further in finding the specific curve.
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QUICK! WHOEVER GIVES CORRECT ANSWER GETS BRAINLIEST
Let P(n) be the set of all partitions of the positive integer n. For all (a₁,..., ak), B = (B₁, ...) = P(n), define (a) Show that (P(n), ≤) is a partially ordered sets (b) Draw its Hasse diagram of (P(6),≤). Is (P(n), ) a lattice for all n?
The set of all partitions of a positive integer n, denoted as P(n), forms a partially ordered set (poset) under the relation of set inclusion (≤).
In part (a), we show that (P(n), ≤) satisfies the properties of a poset. In part (b), we draw the Hasse diagram for P(6) to illustrate the partial order. Whether (P(n), ≤) forms a lattice for all n depends on the specific values of n.
a) To show that (P(n), ≤) is a poset, we need to verify three properties:
Reflexivity: Every partition is included in itself, so for any partition A in P(n), A ≤ A.
Antisymmetry: If A ≤ B and B ≤ A, where A and B are partitions in P(n), then A = B.
Transitivity: If A ≤ B and B ≤ C, where A, B, and C are partitions in P(n), then A ≤ C.
These properties hold for the relation of set inclusion, thus establishing that (P(n), ≤) is a poset.
b) The Hasse diagram for P(6) represents the partial order of the partitions of 6. The partitions are depicted as nodes, with an upward-directed edge connecting A to B if A is included in B (A ≤ B). The diagram illustrates the hierarchy of partitions based on the inclusion relation.
Whether (P(n), ≤) forms a lattice for all n depends on whether it has both a least element (bottom element) and a greatest element (top element). For P(n), if n is greater than 1, there is no unique greatest element since there can be multiple ways to partition n. Therefore, (P(n), ≤) is not a lattice for all values of n.
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Just need the answer thank you
Answer:
The multiplicative rate of change is 3/4
Step-by-step explanation:
Here, we want to get the multiplicative rate of change
In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change
mathematically, we have this as;
81/128 divided 27/32
= 81/128 * 32/27
= 3/4
please help I will mark 5 stars and worth 30 pts
Answer:
25
Step-by-step explanation:
I took the test 2021!!!
Plz help I’ll mark brainliest:$
(1) x = -2 y = -8
(2) x = -1 y = -4
(3) x = 0 y = 0
(4) x = 1 y = 4
(5) x = 2 y = 8
Those are the answers for what y is so now i think you have to plug it in to the right side of the chart
Solve by completing the square.
x2 - 4x – 20 = 0
A. x = {-2±6√2}
B. x = {2+6√2}
C. x = {2+2√6}
D. x = {-2±2√6}
Show your work.
Step-by-step explanation:
Subtract
20
from both sides of the equation.
x
2
−
4
x
=
−
20
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
−
2
)
2
Add the term to each side of the equation.
x
2
−
4
x
+
(
−
2
)
2
=
−
20
+
(
−
2
)
2
Simplify the equation.
Tap for more steps...
x
2
−
4
x
+
4
=
−
16
Factor the perfect trinomial square into
(
x
−
2
)
2
.
(
x
−
2
)
2
=
−
16
Solve the equation for
x
.
Tap for more steps...
x
=
2
±
4
i
Legs are 5ft and 25ft what is the hypotenuse round to the nearest tenth
Answer:
15ft
Step-by-step explanation:
I need help thank you
Answer:
A & C
Step-by-step explanation:
If you substitute the first coordinate (which is the x coordinate) for x in the function and set it equal to the y, options A and C should satisfy the function.
-12 x (1/3)? what is this equal to!
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
-12 times 1/3.
It's pretty much just -12x1, then divided by 3.
-12x1 is equal to -12.
Your equation is now simplified, making it easier to solve.
Your equation is: [tex]\frac{-12}{3}[/tex]
-12 divided by 3 is -4, because when a negative number is divided (or multiplied) by a positive number, the quotient (or product) is negative.
-12 x (1/3) = -12/3 = -4.
Find the area of a circle if the diameter is l6 meters.
PLEASE EXPLAIN AND DO THE PROBLEM IN THE ANSWER!!!!
Answer:
Step-by-step explanation:
the formula for a circle is pi(r^2) where r is the radius. the diameter is 16 so 16/2 =8. substitute 8 for the radius to get pi(8^2). 8^2=64 so you have pi(64).
pi(64)= approximately 201.06
Find the value of $x$ .
A circle with center Q has four points L, M, N, and P lie on the circle. Diameter L N and chord M P intersect perpendicularly. The diameter divides the chord M P into two parts with measures 5 x minus 6 and 2 x plus 9.
Answer:
What
Step-by-step explanation:
I dont understand what you are asking
Mr. Piper's plumbing needed
repairs. The plumber charged
$98 for parts plus $45 per hour
for labor. If the bill totaled $458,
how many hours of labor were
required?
Answer:
8 hours of labor at 45 dollars an hour, plus the 98 dollars for parts equal 458
A company advertises on a website
Answer:
I'm not that good at math sorry for waiting your time:)
A neighborhood in Shiloh is building a treehouse. It has a rectangle floor of 6 ft by 4 ft. What is the area of the tree house floor?
Answer:
24
Step-by-step explanation:
Shiloh is building a tree house
It's measurement is 6ft by 4ft
Therefore the area can be calculated as follows
= 6×4
= 24
Hence the area of the rectangle is 24
The cook at the Elmview School cafeteria made grilled chicken and fried chicken yesterday for lunch. He made 5 pieces of grilled chicken for every 2 pieces of fried chicken.
Pick the diagram that models the ratio in the story.
If the cook made 80 pieces of fried chicken, how many pieces of chicken did he make altogether?
The cook made 280 pieces of chicken altogether.
the diagram is like this :
Grilled chicken: [#####] [#####] [#####] [#####] [#####] ,
Fried chicken: [##] [##]
The ratio of grilled chicken to fried chicken is 5:2, which means for every 5 pieces of grilled chicken, the cook made 2 pieces of fried chicken.
To model this ratio, we can use a bar diagram with five sections for the grilled chicken and two sections for the fried chicken,
If the cook made 80 pieces of fried chicken, we can use this ratio to calculate the number of pieces of grilled chicken.
First, we need to find out how many sets of 5:2 there are in 80. We can do this by dividing 80 by 2 and then multiplying by 5:
80 ÷ 2 = 40
40 × 5 = 200
So the cook made 200 pieces of grilled chicken.
To find the total number of pieces of chicken, we just need to add the grilled and fried chicken together: 200 + 80 = 280 .
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Kora and Wallace planted a garden bed the size of the red square. How big is their garden bed? (Finding the area)
Answer: no sol
Step-by-step explanation:
bro there is no pic to do so im just going to say...
What is an equation of the line that passes through the point (3,-1) and is parallel to the line 5.2 + 3y = 6?
Answer: Its y=-1.
Step-by-step explanation:
Find the area of the trapezoids
Answer:
48 square units
Step-by-step explanation:
Each square on the grid is 2 units by 2 units.
Bases: AT = 8; RS = 4
Height: 8
area = (b1 + b2)h/2
area = (8 + 4)(8)/2
area = 48 square units
Answer:
The area of trapezoid is 48 sq units.
Step-by-step explanation:
According to the question,
➻ Trapezoid is consist of many square shapes. Each grid square equals 2 units. We need to find the area of trapezoid.
➻ To find area we need to find the length if base and height of trapezoid.
Calculate the square grids to find base and height. we get.
Base ; SR = 4 units and TA = 8units
Height = 8 units.
Finding the area of trapezoid.
We know that,
Area of trapezoid = ( Base1 + Base2 ) ×Height / 2
plug the values of both base and a height.
Area of trapezoid = ( 4 + 8 ) × 8 / 2
Add the numbers which are in bracket and multiply by 8.
Area of trapezoid = 12 × 8 / 2 = 96/2
Divide 96 by 2.
Area of trapezoid = 48 sq units.
Hence,
The area of trapezoid is 48 sq units.
Which of the following best describes the vertical cross-section of the cylinder ?
A.
cone
B.
rectangle
C.
triangle
D.
circle
The shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.
What is a vertical cross section?When you slice a given object vertically (perpendicular to the ground level), then the sliced surface is called vertical cross section.
For a cylinder, usually it sits on its base and we take a right circular cylinder. When we slice it vertically, we obtain a rectangle, as shown in the figure attached below.
It can be proven that this shape is always going to be rectangular.
Thus, the shape that best describes the vertical cross-section of the cylinder is given by: Option B: Rectangle.
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How can this expression be written another way?
32k + 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes
32k + 24 = __ (__)
There are 40 batteries in 10 packs.
Gavin wants to know how many batteries are in 1 pack.
Kylie wants to know how many batteries are in 5 packs.
Drag an expression to answer each question.
Answer:
1.40/10
2.40/2
Step-by-step explanation:
Answer: For a 1 pack you would divide 40 by 10 and for a 5 pack youd divide 40 by 5
Step-by-step explanation:
Please help me, it's due today. I'll give 86 points to someone who answers and writes the problem step by step.
A 14 -in. diameter pizza is cut into 6 equal sides. About how many square inches of pizza are on each slice? Round to the nearest square inch.
Answer:
here go the answer hope it help
Step-by-step explanation:
Please awnser correctly! I will mark you as Brainliest!
it is 20 miles from the airport to the hotel. The driver says that there is 1/8 of the total distance left to travel. What distance has already been driven?
Answer:
2.5mi
Step-by-step explanation:
?/20 = 1/8
^ If you turn into a percentage you get 1/8 = 12.5%
so now the question is v
what is 12.5 percent of 20?
which is 2.5
I WOULD CHECK FIRST, NOT 100 PERCENT SURE