Lincoln has dimes and y quarters. He has no more than 24 coins worth at least $3.50 combined. Solve this system of inequalities graphically and determine one possible solution
Answers
Answer:
let's define:
x = number of dimes
y = number of quarters.
Then the total amount of money that he has is:
x*$0.10 + y*$0.25
Now we know that:
"He has no more than 24 coins"
Then:
x + y ≤ 24
"...worth at least $3.50 combined"
x*$0.10 + y*$0.25 ≥ $3.50
Then we have two inequalities:
x + y ≤ 24
x*$0.10 + y*$0.25 ≥ $3.50
To graph these, it is easier to write them as linear equations in the slope-intercept form.
Then we need to isolate the y-variable in both equations.
we will get:
y ≤ 24 - x
y ≥ $3.50/$0.25 - x*$0.10/$0.25
In the first equation we have:
"y is smaller or equal than the line"
Then this is graphed with a solid line, and we shade all the region below the line
For the second equation, we have the inverse case, then it will be graphed with a solid line and we need to shade all the region above the line.
The solutions for the system will be all these values that are in both shaded regions.
The graph can be seen below.
In the graph, we can see that one acceptable solution can be:
x = 5
y = 15
or
x = 6
y = 16
The only other restriction we should add is:
x ≥ 0
y ≥ 0
Because Lincoln can not have a negative number of coins, so we can only find solutions in the first quadrant.
Related Questions
Can anyone please help me with this!!! :(
Answers
Answer:
ano ba gagawin
parang Ang Dali pero ano gagawin dyan
Hi there!
For this problem, pretty much add all of them and then subtract with 22 to find how much Jen ran on Friday.
Monday+Tuesday+Wednesday+Thursday:
Simplify all terms and find all common denominators:
Common denominator: 8
[tex]4 \frac{3}{4} = 4 \frac{6}{8}[/tex]
[tex]5 \frac{1}{8} = 5 \frac{1}{8}[/tex]
[tex]6 \frac{1}{4} = 6 \frac{2}{8}[/tex]
Combine all terms:
[tex]4 \frac{6}{8} + 5 \frac{1}{8} + 6 \frac{2}{8} = 15 \frac{9}{8}[/tex]
Simplify 15 9/8 or else can’t subtract with 22.
[tex]9/8 = 1 \frac{1}{8}[/tex]
[tex]15 + 1 \frac{1}{8} = 16 \frac{1}{8}[/tex]
Turn 22 into 21 8/8...
Subtract: 21 8/8 with 16 1/8
[tex]21 \frac{1}{8} - 16 \frac{1}{8} = 5 \frac{7}{8}[/tex]
This means that 5 7/8 is how much mile Jen must run on Friday to reach her goal.
helpppppppppppppppppppppp
Answers
Answer:
t = 30
Step-by-step explanation:
[tex]\frac{6}{1} = \frac{t}{5}[/tex]
you can tell you need to multiple by 5 from the denominators. 1 *5 = 5. Then, just multiply 6 by 5 and get 30.
You want to put a 3 inch thick layer of topsoil for a new 23 ft by 24 ft garden. The dirt store sells by the
cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic
yards.
cubic yards
Answers
So first you need to find the area of the plot; 552. Then you need to find out how much soil you will need. There are 12 inches in a foot so if you have 3 inches you have .25 of a foot. So you multiply 552 by .25 and get 138. 138 is how many cubic feet you need. Therefore, you need to divide this number by 3 in order to convert this to yards (3 feet in a yard). This will bring you to 46. Finally, we need to multiply this number by 4 because they only sell in 1/4 cubic yards.
- 5x + 9y = - 32
-5x - 3y = 4
Answers
Answer: look at the picture
Step-by-step explanation: Hope this help :)
What is the perimeter?
Answers
Answer:
43
Step-by-step explanation:
add up each side
14 + 14 = 28
28 + 6 = 34
34 + 9 = 43
Round to the nearest ten thousand.
758,928
Answers
Answer:
760,000
Step-by-step explanation:
Ill give you brainliest and 5 stars help plz
Answers
Answer:
D
Step-by-step explanation:
It is going from top left to bottom right, so we now it is a negative slope. This leaves us with B or D. When the y axis decreases 1 (aka (x,-1)) the x axis is at 4. Rise/run is 1/4.
Find the value of x and the value of the given angle using the picture below?
Answers
Answer:
I think it is 81x
Step-by-step explanation:
It look the same as angle B which is 121 degree. 81x +40 = 121 degree.
1
Suppose f(x) = x2 - x - 12, g(x) = x + 3, and h(x) = 6x - 1. Which of the following function operations are
three that apply.
A (g x h)(x) = 6x2 + 17x-3
B (n + 1)(x) = x2 + 5x - 13
C (f = g)(x) = x - 4
D (f - h)(x) = x2 - 7x-13
E (g- h)(x) = 5x - 4
о
Answers
If you spend $400 on a new phone and it is depreciating about 50% per year , how much will it be worth by its third year?
Answers
Answer:
50$
Step-by-step explanation:
after 1 year: 200
after 2 years 100
after 3 years 50
Answer:
It will be worth $50 dollars after 3 years
hi what is 24/30 simplified to
Answers
Answer:
12/15 or .8
Step-by-step explanation:
So first you divide both the numerator and denominator by 2 because it’s the biggest number that goes into both 24 and 30
24 and 30 simplified by 2 gives us 12 and 15
you can’t simplify any further so your answer is 12/15
If you want a decimal, then you divide 24 by 30 and your answer is .8
The probability that Brian buys a sandwich is 0.1. The probability that Brian gets the bus is 0.6. Assuming the events are independent, what is the probability that Brian buys a sandwich and gets the bus?
Answers
Answer:
6% chance
Step-by-step explanation:
I think it would be 0.1 * 0.6 which is 0.06
Answer:
Step-by-step explanation:
The area of a rectangle 320in^2. The ratio of the length to the width is 5:4. Find the length and the width
Answers
Answer:
30 in length 24inches width
Step-by-step explanation:
Multiply the multiples if 5 and 4 together until you reach 720.
5*4=20
10*8=80
15*12=180
20*16=320
25*20=500
30*24=720
Your length is 30 in and your width is 24in.
the numerical coefficient in the expression -3×y² is
Answers
The numerical coefficient for the expression how much of the variables, in this case xy^2 there are in number form. There is only one number in this question so it makes it fairly straight forward. The answer is -3.
HELP ASAP!!!
Use Pythagorean Theorem to solve. Round to the nearest tenth •
33 cm
х
55 cm
Answers
Answer:
x= 44 cm
Step-by-step explanation:
[tex] {55}^{2} = {33}^{2} + {x}^{2} \\ {x}^{2} = 3025 - 1089 \\ {x}^{2} = 1936 \\ x = \sqrt{1936} = 44[/tex]
PLZ HELP!!!! WILL GIVE BRAINLIEST IF CORRECT! The social studies teacher wants to know whether the students in the entire school prefer a model United Nations activity or a student government activity. The teacher draws a random sample from the following groups:
All teachers in the school
All boys in each grade
All students in each grade
All students in the social studies club
Which group best represents the population he should take a random sample from to get the best results for his survey? (5 points)
Question 1 options:
1)
All teachers in the school
2)
All boys in each grade
3)
All students in each grade
4)
All students in the social studies club
Answers
3 is the answer
you're welcome
Step-by-step explanation:
4 is the answer since the question asks if the student would prefer so to get a better opinion you'd have to ask ever student in all grade
In fact, weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent events.With the weather forecast of the previous exercise, the probability that it rains over the weekend (either Saturday or Sunday) isA. 0.7516B. 0.3758 C. 0.2484D. Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.
Answers
Question is incomplete :
The weather forecast for the weekend is a 46% chance of rain for Saturday and a 54% chance of rain for Sunday. If we assume that consecutive days are independent events, What is the probability that it rains over the weekend (either Saturday or Sunday)? Please use 3 decimal places.
In fact, weather on consecutive days depends on similar atmospheric conditions and therefore consecutive days are not independent events.With the weather forecast of the previous exercise, the probability that it rains over the weekend (either Saturday or Sunday) isA. 0.7516B. 0.3758 C. 0.2484D. Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.
Answer:
0.7516 ;
D.) Because consecutive days are not independent, we cannot compute P(rain both days) with the information given.
Step-by-step explanation:
Let :
Saturday = A ; Sunday = B
P(A) = 0.46 ; P(B) = 0.54
If A and B are independent :
P(AuB) = P(A) + P(B) - P(AnB)
P(AnB) = P(A) * P(B) = 0.46 * 0.54 = 0.2484
P(AuB) = 0.46 + 0.54 - 0.2484
P(AuB) = 0.7516
If A and B are not independent, and how the weather on Saturday affect the weather on Sunday and vice versa. Hence, we cannot compute AuB
The measure of the second angle is 15 degrees more than the measure of the first angle the measure of the third angle is 45 degrees more than the measure of the first angle tine the measures of the interior angles in the triangle
Answers
Answer:
The measures of the three interior angles of the triangle are {40,55,85}.
Step-by-step explanation:
Let a = the measure of the first angle of the triangle.
Let b = the measure of the second angle of the triangle.
Let c = the measure of the third angle of the triangle.
The problem statement tells us that
(1) a = a
(2) b = a + 15 and
(3) c = a + 45
Now we (should) know that the sum of the three angles of a triangle is 180 degrees. Then we get
(4) a + b + c = 180 or by substitution we get
(5) a + (a + 15) + (a + 45) = 180 or
(6) a + a + 15 + a + 45 = 180 or
(7) 3*a + 60 = 180 or
(8) 3*a = 180 - 60 or
(9) 3*a = 120
Now divide both sides of (9) by 3 to get
(10) 3*a/3 = 120/3 or
(11) a = 40
Using (2) and (3) we get
(12) b = 40 + 15 or
(13) b = 55 and
(14) c = 40 + 45 or
(15) c = 55
Always check the answer. Use (4)
Is (40 + 55 + 85 = 180)?
Is (95 + 85 = 180)?
Is (180 = 180)? Yes
The measures of the three interior angles would be as follows:
40°,55°,85°
If we assume the first angle(∠1) to be [tex]x[/tex],
so, the second angle(∠2) [tex]= x + 15[/tex]
while the third angle(∠3) [tex]= x + 45[/tex]
Through the Angle Sum Property, we know:
∠1 + ∠2 + ∠3 = 180°
By applying the above expressions, we get
[tex]x + (x + 15) + (x + 45) = 180[/tex]°
⇒ [tex]3x + 60 = 180[/tex]
⇒ [tex]3x = 180 - 60[/tex]
⇒ [tex]x = 120/3[/tex]
∵ [tex]x = 40[/tex]°
Therefore,
∠1 = 40°
∠2 = 40° + 15°
= 55°
∠3 = 40° + 45°
= 85°
Thus, the measures of the angles are 40°,55°, and 85°
Learn more about "Angles" here:
brainly.com/question/11990585
When a number is decreased by 8.3%, the result is 50. What is the original number to the nearest tenth?
Answers
I'm pretty sure the answer would be 2.
Sorry if it's wrong
If a quantity is decreased by x% the new value of that quantity is (100 -x)% of the old one.The value of original number nearest to tenth is 55.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
To convert percentage into a fraction it is divided by 100.
Given that,
The percentage of decrease = 8.3%
The number obtained after decrease = 50
Since the number obtained after decrease is the original number minus the decrement in the number by 8.3%.
Thus, the expression for original number N is given by,
N - 8.3% of N = 50
=> N - (8.3 / 100) × N = 50
=> (91.7 / 100) × N = 50
=> N = 50 × (100 / 91.7)
=> N = 54.52
Nearest to tenth its value is 55.
Hence, the original number nearest to tenth is 55.
To know more about percentage click on,
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#SPJ5
Identify the y-intercept for the line 4x – 2y = 4
Give your answer as a coordinate.
PLEASE HELP ASAP
Answers
Answer: (0,-2)
Step-by-step explanation: uhdehdwhehehhH
the Johnson family went out to dinner and spent a total of $68.32 before tax. if tax is 6% of the total meal, how much will the family pay in total?
Answers
Answer:
72.68 would be your total.
Step-by-step explanation:
Can someone help me with this?
Answers
9514 1404 393
Answer:
x = 10y = 7.5Step-by-step explanation:
The ratio of the larger to the smaller corresponding sides is ...
12.5/5 = 2.5
That means ...
x = 2.5 × 4 = 10
y = 2.5 × 3 = 7.5
Solve the following system of equations using substitution, elimination, or elimination by multiplication
Answers
Answer: B
Step-by-step explanation:
Baldwin made a scale drawing of the town library. He used the scale 1 centimeter : 9 meters. The parking lot is 9 centimeters in the drawing. How long is the actual parking lot?
Answers
Answer:
81m
Step-by-step explanation:
1/9 = 9/x
x = 81
Because the ratio is 1:9 if you wanna change the centimeters you have to do it on both sides
So what times 1 equals 9? 9
So multiply the meters by 9.
Mrs. Beads grouped her students two different waysFirst, she students into groups with the same number of students in each group No students were leftover. Then she put students into 6 group with the same number of students in each group with none leftover
A) 14
B) 16
C) 18
D) 24
E) 30
Answers
Nancy bought a package of 4 spiral notebooks for a total cost of $18.25. Which equation represents p, the cost, in dollars, of each notebook?
Answers
Answer:
p=18.25/4
p=$4.56 (when you round)
Step-by-step explanation:
Brainliest?!?!?!?!?
Which expression is equivalent to -5(8x+9) -7x?
A. -33x+9
B. -47x-45
C. -33x - 45
D. 33x - 45
Answers
Hope this helps
Brainliest plzzzz
Answer:
b
Step-by-step explanation:
-5(8x+9)-7x
-40x-45-7x
-47x-45
A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the plane took 4 hours. Find the wind speed and the speed of the plane in still air. (5 marks)
Answers
Answer:
hxjdgetjettjittteitejetjetkrtir
The ratio of the number of girls to the number of boys in a classroom 6:5. After 16 girls left the room, the ratio became 2:3. How many girls were there at first?
Answers
Answer:
5/6 se eu não me engano.
Step-by-step explanation:
ajudareroesp
What is the value of the expression 42x3 - (2^4 - 1)/5
Answers
Answer:
The answer is 123.
Step-by-step explanation: