Rashaad has
x
x dimes and
y
y nickels, having no less than 18 coins worth at most $1.50 combined. At least 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Answers
Answer:
see attached for a graph4 dimes, 22 nickelsStep-by-step explanation:
You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.
InequalitiesAn inequality can be written for each of the constraints:
x + y ≥ 18 . . . . . . . no less than 18 coins
0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value
x ≥ 4 . . . . . . . . . . at least 4 dimes
GraphA graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.
One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50
What is System of Linear InequalitySystems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.
In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.
Let;
x = dimesy = nickelx + y ≥ 18
0.1x + 0.05y ≤ 1.50
x ≥4
Using a graphing calculator to solve this,
The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
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Related Questions
A farmer has 240 acres to plant. He needs to decide how many acres of corn to plant and how many of oats. He can make $40 per acre profit for corn and $30 per acre for oats. However, the corn takes 2 hours of labor per acre to harvest and the oats only take 1 hour per acre. He only has 320 hours of labor he can invest. To maximize his profit, how many acres of each should he plan
Answers
Answer:
The acres of each the farmer must plant to obtain the maximum profit is:
160 acres of oat.80 acres of corn.Step-by-step explanation:
First, we're gonna take the data of the exercise:
Area: 240 acres.Profit of the corn: $40/acreProfit of the oat: $30/acreTime spent by corn: 2 hour per acre.Time spent by oat: 1 hour per acre.Total working time available: 320 hours.Now, we're gonna suppose that all the area could be planted with corn (the most profitable), in this form, we obtain the highest profit to take this how reference:
Total profit with corn = area * profit of the cornTotal profit with corn = 240 acres * $40/acreTotal profit with corn = $9600How you can see, $9600 is the highest profit that the farmer can obtain, but, as each acre of corn needs 2 hours, the farmer would need 480 hours of labor to plant all the area with corn, with the 320 hours availables, the farmer just could plant 160 acres of corn, therefore, the real profit would be:
Total profit with corn = 160 * $40Total profit with corn = $6400Now, we're gonna make the same exercise but with the oats, to obtain the total profit with this:
Total profit with oat = area * profit of the oatTotal profit with oat = 240 acres * $30/acreTotal profit with oat = $7200Taking into account the hours of labor availables, the oat gives $800 more profit than the corn, but in that case we'd lose 80 hours of labor that could be used to make a better profit, but, as the oat per hour of labor is more profitable, we're gonna use 2/3 of the area to plant oat and 1/3 to plant corn:
Area used for oat = 240 acres * 2/3Area used for oat = 160 acresArea used for corn = 240 acres * 1/3Area used for corn = 80 acresHow you can see, with 160 acres of oat, the farmer would need 160 hours of labor and, with 80 acres of corn, the farmer would need 160 hours of labor too, by this, we know all the available time will be used, now, we're gonna calculate the profit in each case:
Real profit with oat = used area * profit of the oatReal profit with oat = 160 acres * $30/acreReal profit with oat = $4800Real profit with corn = 80 acres * $40/acreReal profit with corn = $3200The total profit to the farmer with this plan is:
Total profit = Corn profit + Oat profitTotal profit = $3200 + $4800Total profit = $8000The profit with the given plan is $8000, that is better than the profit only with oat or corn separately and, this is the maximum profit the farmer can make.
The owner-manager of Good Guys Enterprises obtains utility from income (profit) and from having the firm behave in a socially conscious manner, such as making charitable contributions or civic expenditures. Can you set up the problem and derive the optimization conditions if the owner-manager wishes to obtain a specific level of utility at the lowest possible cost? Do these conditions differ from the utility maximizing conditions?
Answers
Answer:
Step-by-step explanation:
Certainly! To set up the problem, we can consider the owner-manager's utility as a function of two variables: income (profit) and charitable contributions or civic expenditures. Let's call these variables x and y, respectively.
The owner-manager utility is given by the function U(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.
The cost of obtaining this utility is given by the function C(x,y), where x is the income (profit) and y is the charitable contributions or civic expenditures.
To find the lowest possible cost at which the owner-manager can obtain a specific level of utility, we can use the following optimization conditions:
The cost function C(x,y) should be minimized subject to the constraint U(x,y) = k, where k is the specific level of utility that the owner-manager wishes to achieve.
The first-order necessary conditions for a minimum are:
∂C/∂x = λ ∂U/∂x
∂C/∂y = λ ∂U/∂y
where λ is a Lagrange multiplier.
These conditions are known as the Karush-Kuhn-Tucker (KKT) conditions.
These optimization conditions differ from the utility-maximizing conditions in that we are minimizing the cost function instead of maximizing the utility function. In addition, we have the constraint U(x,y) = k, which means that we are trying to achieve a specific level of utility rather than trying to maximize it.
The two-way table shows the number of students in a class who play basketball and/or football.
What is the missing number in the table?
A) 2
B) 10
C) 34
D) 46
will mark BRAINLIEST*
Answers
40 - 30 = 10
Or
16 - 6 = 10
What is XZ to the nearest tenth?
7
51°
77
Answers
PLS HELP ASAP!!!!! WILL GIVE 30 POINTS TO WHOEVER ANSWERS CORRECTLY
Describe a sequence of transformations that maps Figure A to Figure B.
Answers
Answer:
Reflection across the Y axis and you would have to translate figure a down by some units. I dont know the units because i cant see the grid/graph so this is the farthest I can tell you
Step-by-step explanation:
Hope this helps :)
For what values of k are the graphs of 8y=4x+3 and 4y=k(x+5) parallel? perpendicular?
parallel k= __
perpendicular k= __
Answers
The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
what is slope ?A line's slope determines how steep it is. A mathematical expression for the gradient is called "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical change (rise) between two points to the horizontal change (run) between those same two points. When a straight line's equation is written as y = mx + b, the slope-intercept form of an equation is used to represent it. The y-intercept is located at a point where the line's slope is m, b is b, and (0, b). For instance, the slope of the equation y = 3x - 7 and the y-intercept (0, 7).
given
for parallel their slope will be equal
y1= 1x/2 + 3/8 .... eq1
y2= kx/4 + 5k/4 ..... eq2
y1 = y2
1x/2 + 3/8 = kx/4 + 5k/4
1/2 + 3/8 = k/4 + 5k/4
7/8 = 6k/4
k = 7/12
for perpendicular product of their slope is 1
y1 * y2 = 1
1x/2 + 3/8 * kx/4 + 5k/4 = 1
1/2 + 3/8 * k/4 + 5k/4 = 1
k = 1/21
so The values of k for parallel and perpendicular in the equations 8y=4x+3 and 4y=k(x+5) are 7/12 and 1/21, respectively.
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Supplementary for solving x
Answers
Answer:
sorry
Step-by-step explanation:
Answer:
M<3 is 49 degrees, M<4 is 131 degrees
Step-by-step explanation:
This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees
First, we know that M<1 and M<2 added together is 180. We know M<1 is 11x-38 and M<2 is 19x+8, so then, we have:
(11x-38) + (19x+8) = 180
30x - 30 = 180
30x = 210
x = 7
Now, we plug in 7 for x to find M<1 and M<2.
M<1 is (11x-28), so it would be 49 degrees.
M<2 is (19x+8), so it would be 131 degrees (or just do 180-49).
Now, we can find M<3 and M<4 easily. M<3 and M<2 are supplementary, so 131 + M<3 must equal 180. Thus, M<3 is 49.
M<4 and M<1 are supplementary, so 49 + M<4 must equal 180. Thus, M<3 is 131.
AN EASIER WAY TO FIND M<3 AND M<4:
Vertical angles are angles directly opposite each other, created by two intersecting lines. A pair of vertical angles holds the same degree measurements. In this problem, M<2 and M<4 are a pair of vertical angles, and M<3 and M<1 are a pair. Thus, M<2 and M<4 must are the same degree and M<3 and M<1 must are the same degree. Thus, if M<2 is 131, M<4 is 131 degrees as well. If M<1 is 49 degrees, M<3 is 49 degrees as well.
can somebody help me with this one question i’m stuck on?? ;^(
Answers
Answer:
The answer is 2.27mm
Step-by-step explanation:
help it’s due today and i haven’t done it since wensday
Answers
Answer:
135
Step-by-step explanation:
:)
Answer:
When you convert them both you get 135
Solve x^3 + x - 4 = 0, leaving your answers correct to 2 decimal places.
Answers
The solution to the equation x³ + x - 4 = 0 is x = 1.38
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
x^3 + x - 4 = 0
Express the exponents as proper superscript
So, we have the following representation
x³ + x - 4 = 0
Next, we solve the equation using a graph
i.e. we plot the graph of x³ + x - 4 = 0
See attachment for the graph of x³ + x - 4 = 0
The points where the graph of x³ + x - 4 = 0 crosses the x-axis are the solution
In this case, the point is 1.38
Hence, the solution is x = 1.38
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Layla has 29 carnival ride tickets and it takes for tickets to ride the roller coaster how many times can she ride the coaster how many tickets does she have left over
Answers
Answer:
7 times with 1 left over
Step-by-step explanation:
29/4=7
(28)
Remainder 1
how to horizontally stretch a cubic fucnction
Answers
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
Can you please help me What is 2/3 x 1/2
Answers
Answer:
2/6 lol
Step-by-step explanation:
hope this helps :3
Evaluate x−25 when x=35.
Answers
Answer: 5
Step-by-step explanation:
1. Since you are told x=35. Plug it into x.
35-25
2. Simplify
35-25=5
Answer: 10
Step-by-step explanation:
x-25
substitute 35 for x
35-25 = 10
Given U(-6, 7), V (1, -7), W (6, 4), and X (10, y). Find y such that
UV LWX.
Answers
The coordinates of U and V are (-6,7) and (1,-7), respectively. The vector UV connecting these two points is given by (1-(-6), -7-7) = (7, -14).
The coordinates of W and X are (6,4) and (10,y), respectively. The vector WX connecting these two points is given by (10-6, y-4) = (4, y-4).
For the sides UV and WX to be parallel, the vector UV must be proportional to the vector WX. This means that the ratio of the x-components must be equal to the ratio of the y-components. In other words, we have the following equation:
(7/4) = (-14)/(y-4)
Solving for y, we get:
y = -7
Therefore, the value of y such that the quadrilateral UVLWX is a parallelogram is y = -7.
what is the domain of y=2(x+1)-(3x-2)
Answers
Answer:
Domain is all real numbers (basically any number)
Step-by-step explanation:
Step 1: Simplify the expression first
y = 2(x+1)-(3x-2)
y = 2x + 2 -3x + 2
y = -x + 4
Step 2: Observe the graph
y = -x + 4 is simply a linear graph with a negative fixed gradient of -1, with a y-intercept of 4.
Step 3: Identify the domain
For linear graphs, domain is all real numbers.
(No restrictions on the graph according to question)
Describe the congruence transformation that maps ΔABC onto ΔA′B′C′ in the given figure.
Question 2 options:
A)
Reflection along x-axis; Translation: (x, y) → (x, y – 3)
B)
Reflection along y-axis; Translation: (x, y) → (x, y – 3)
C)
Reflection along y-axis; Translation: (x, y) → (x, y + 3)
D)
Reflection along x-axis; Translation: (x, y) → (x, y)
Answers
Reflection along y axis
Translation: [tex](x,y) \to (x,y-3)[/tex] which means we shift 3 units down
===========================================================
Explanation:
Let's track point A to see how it could move to point A'.
If we were to reflect point A over the vertical y axis, then A(-4,4) would move to (4,4). The x coordinate flips in sign, but the y coordinate stays the same.
The diagram shows that A' is located at (4,1) instead of (4,4). So a y-axis reflection isn't enough to move A to A', but we can shift that reflected point three units down. That will move (4,4) to (4,1) which is exactly where we want to end up. Note how we subtract 3 from the y coordinate and x stays the same. So that explains the notation [tex](x,y) \to (x,y-3)[/tex]
Overall, this points to choice B as the final answer. If we apply these steps to points B and C, you should find that they'll land on B' and C' respectively. Apply this to all of the points on the triangle ABC, and it will move everything to triangle A'B'C'.
HELP PLS
I’m rly confused
Answers
bro use a photo math...................
HELLPPPP ASAP PLEASE I NEED HELP WHOEVER GETS FIRST GETS BRAINLIEST AND 100 coinss
Answers
This is a simple cross multiplication problem! Any time you're given a ratio and then the actual quantity of something, you can use cross multiplication to figure out the quantity of the other thing!
We know that the ratio of toads to frogmen is 7 : 2. We also know there were 98 actual toads. Therefore we can set up our equations!
[tex]ratio_{toads}=ratio_{frogmen}\\actual_{toads}=actual_{frogmen}\\\\7=2\\98 = x\\\\7x=196\\x=28[/tex]
The first two equations above everything is how you would have everything set up! The second equations under them are the numbers plugged in, and the rest is just simplification.
So, your final answer should be 28 frogmen!
40 pupils in class 4A scored 380 points in a contest. Each girl scored
10 points and each boy scored 8 points. How many girls are there in
class 4A?
Answers
There are 30 girls and 10 boys
One fifth of the animals at the shelter are stray cats. If there are 13 stray cats at the shelter, how many animals are there in total?
Answers
Answer:
1/5 x X = 13
x5 x5
x = 65 in total
Please help me!
Please!
Answers
Answer:
27
Step-by-step explanation:
9/1/3=9*3=27
Answer:
D. 27
Step-by-step explanation:
This is a simple division
[tex]9[/tex] ÷ [tex]\frac{1}{3}[/tex] =
[tex]\frac{9}{1}[/tex] ÷ [tex]\frac{1}{3}[/tex] =
Cross multiply
[tex]1[/tex] × [tex]1 = 1[/tex]
[tex]9[/tex] × [tex]3 = 27[/tex]
Set it up
[tex]\frac{27}{1}[/tex]
Then, the model represents 27
Help
Fjfjdjfjdjdjdjdjjfjfjfhfjd
Answers
Answer:
A. 69°
Step-by-step explanation:
Given:
m<FED = 179°
m<NED = 19x - 4
m<FEN = 12x - 3
Required:
m<FEN
Solution:
m<NED + m<FEN = m<FED (angle addition postulate)
19x - 4 + 12x - 3 = 179 (substitution)
Add like terms
31x - 7 = 179
31x - 7 + 7 = 179 + 7
31x = 186
31x/31 = 186/31
x = 6
✔️m<FEN = 12x - 3
Plug in the value of x
m<FEN = 12(6) - 3 = 72 - 3
m<FEN = 69°
HELP ME !! AND EXPLAIN HOW YOU GOT IT.
PLEASE ANSWER !! ILL GIVE BRAINLIEST !!
50 POINTS !!
FAKE ANSWERS WILL GET REPORTED .
Answers
Answer:
<5=39
Step-by-step explanation:
<2=48
<3=93
<2 and <4 are equal to each other because they are alternate interior angles
93+48=141
180-141=39
Answer:
∠5 = 39º
Step-by-step explanation:
∠1 + ∠2 + ∠3 = 180
∠1 + 48 + 93 = 180
∠1 = 180 - 48 - 93
∠1 = 39
Corresponding angles are congruent
∠5 = ∠1
∠5 = 39º
Round the number to the given place value.
In a town in California, the average consumption of soft drinks per day per elementary school
student is 15.766 ounces. Round this value to the nearest tenth.
Answers
Find the volume.
Pls NO links
Answers
Explanation: V=lwh/3
There are two ways of finding the volume of a pyramid.
1. [tex]\large\tt V =\frac{lwh}{3}[/tex]
[tex]\tt V=\frac{lwh}{3}[/tex][tex]\tt V=\frac{(4in)(2in)(5in)}{3}[/tex][tex]\tt V=\frac{40in}{3}[/tex][tex]\tt V={13.33^3}[/tex]Therefore, the volume of a pyramid is 13.33in³
2. [tex]\large\tt V = \frac{Bh}{3}[/tex]
Where [tex]\longrightarrow\tt B = l \times w[/tex]
[tex]\longrightarrow\tt B = 4in \times 2in[/tex]
[tex]\longrightarrow\tt B = {8in^2}[/tex]
[tex]\tt V = \frac{Bh}{3}[/tex][tex]\tt V = \frac{4in^2 \times 5in}{3}[/tex][tex]\tt V = \frac{40in}{3}[/tex][tex]\tt V = {13.33^3}[/tex]Therefore, the volume of a pyramid is 13.33in³
#CarryOnLearningWhat are the exact values of a and b ?
CORRECT ANSWER
PROVIDE EXPLANATION
Answers
Answer:
b
Step-by-step explanation:
i think i say c because a is 30 degrees and c is 90 the whole triange needs to be 180 so b would be 60 also you see one side is 10 the other side also known as b is also 10 they have to be the same length and a is five because half of 10 is 5
Could somebody please help it’s due in a couple of minutes, and please no links
Answers
Answer:
no solution
Step-by-step explanation:
reduce the fraction 3×15×24 /16×20×6 no links or files
Answers
Answer:
1 38888888889/50000000000
Step-by-step explanation:
The answer to the first part equation is 1080 ( 3*15*24). The answer to the second question ( 16*20*6) is 1920. Then you divide 1920/ 1080= 1 38888888889/50000000000
help me pls the question is in the picture
Answers
Answer:
Step-by-step explanation: