Mrs. Gibbs goes to the store to buy AA and 9V batteries. She needs at least 6 AA batteries. In all, she wants to buy at least 20 batteries. The store has 12 AA batteries and 15 9V batteries in stock.
The graph shows the feasible region, where x represents the number of AA batteries and y represents the number of 9V batteries.
Which ordered pairs meet all the constraints and make sense in the context of the situation?
Select each correct answer.
(7, 13)
(8,11)
(10,16)
(12,12)
Answers
Take a look at the snip for proof ;)
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Let
x------> represents the number of AA batteries
y------> represents the number of 9V batteries
we know that
The constraints are
[tex]x\geq 6[/tex]
[tex]x\leq 12[/tex]
so
[tex]6\leq x\leq 12[/tex] --------> inequality A
[tex]y\leq 15[/tex] --------> inequality B
[tex](x+y)\geq 20[/tex]
[tex](x+y)\leq 27[/tex]
so
[tex]20\leq (x+y) \leq 27[/tex]-----> inequality C
The solution of the system of inequalities is the shaded area in the attached figure
If a ordered pair meet all the constraints and make sense in the context of the situation, then the ordered pair is a solution of the system of inequalities
let's check each of the ordered pairs
case A) point [tex](7,13)[/tex]
[tex]x=7\ y=13[/tex]
Verify inequality A
[tex]6\leq 7\leq 12[/tex]--------> is true
Verify inequality B
[tex]13\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (7+13) \leq 27[/tex]
[tex]20\leq (20) \leq 27[/tex]------> is true
The ordered pair [tex](7,13)[/tex] meets all restrictions, therefore the ordered pair is a solution of the system of inequalities
case B) point [tex](8,11)[/tex]
[tex]x=8\ y=11[/tex]
Verify inequality A
[tex]6\leq 8\leq 12[/tex]--------> is true
Verify inequality B
[tex]11\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (8+11) \leq 27[/tex]
[tex]20\leq (19) \leq 27[/tex]------> is not true
The ordered pair [tex](8,11)[/tex] does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.
case C) point [tex](10,16)[/tex]
[tex]x=10\ y=16[/tex]
Verify inequality A
[tex]6\leq 10\leq 12[/tex]--------> is true
Verify inequality B
[tex]16\leq 15[/tex] -------> is not true
Verify inequality C
[tex]20\leq (10+16) \leq 27[/tex]
[tex]20\leq (26) \leq 27[/tex]------> is not true
The ordered pair [tex](10,16)[/tex] does not meet all the restrictions, therefore the ordered pair is not a solution of the system of inequalities.
case D) point [tex](12,12)[/tex]
[tex]x=12\ y=12[/tex]
Verify inequality A
[tex]6\leq 12\leq 12[/tex]--------> is true
Verify inequality B
[tex]12\leq 15[/tex] -------> is true
Verify inequality C
[tex]20\leq (12+12) \leq 27[/tex]
[tex]20\leq (24) \leq 27[/tex]------> is true
The ordered pair [tex](12,12)[/tex] meets all restrictions, therefore the ordered pair is a solution of the system of inequalities
the answer is
[tex](7,13)[/tex]
[tex](12,12)[/tex]
Related Questions
19.25 tons=_______lbs. Show work
Answers
1 Tons - Short =2,000 Pounds
Just multiply 2,000 and 19.25 and get 38,500.
Hoped I helped!
Joe works full time as a carpenter and brings home $3,000 per month. He owes a total of $1,500 in fixed expenses every month, which includes items such as rent and insurance. If Joe had $1,000 in variable expenses such as groceries and entertainment, what would be his ending balance?
Answers
Answer:
The answer is $500.
Step-by-step explanation:
Joe works full time as a carpenter and brings home $3,000 per month.
He owes a total of $1,500 in fixed expenses every month.
Joe had $1,000 in variable expenses.
Total expenses are = [tex]1500+1000=2500[/tex] dollars
So, his ending balance will be = [tex]3000-2500=500[/tex] dollars
Therefore, the answer is $500.
rule add 15, subtract 10 first term4
Answers
4 + 15 = 19
19 - 10 = 9
9 is your answer
hope this helps
Simplify by collecting like terms: 2x-4-6x+8
Answers
-4x + 4
The expression 2x - 4 - 6x + 8 is simplified as 4(1 - x).
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ 2x - 4 - 6x + 8
Simplify the expression, then the value of the expression will be
⇒ 2x - 4 - 6x + 8
⇒ - 4x + 4
⇒ 4(1 - x)
The expression 2x - 4 - 6x + 8 is simplified as 4(1 - x).
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How many 3/4-foot lengths of pipe can be cut from a 6 1/3-foot pipe?
Answers
To find how many 3/4-foot lengths of pipe can be cut from a 6 1/3-foot pipe, you need to divide the length of the pipe by the length of each piece. The answer is 8 4/27 lengths of pipe.
Explanation:To find how many 3/4-foot lengths of pipe can be cut from a 6 1/3-foot pipe, we need to divide the length of the pipe by the length of each piece. To do this, we convert both the length of the pipe and the length of each piece to the same unit of measurement. Here's how:
Convert 6 1/3 feet to improper fraction: 6 1/3 = 19/3 feet.Convert 3/4 foot to improper fraction: 3/4 = 9/12 feet.Divide the length of the pipe by the length of each piece: 19/3 / 9/12 = (19/3) x (12/9) = 228/27 = 8 4/27.Therefore, you can cut 8 4/27 lengths of pipe from a 6 1/3-foot pipe.
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A gardener brought 5 rabbits, after 2 months rabbits became 10, and after 4 months they became 20. If the growth continues on the same ratio, what would be the amount of rabbits after 1 year?
(a) 300 (b) 435
(c) 535 (d) 635
Answers
Answer:
Initial population of Rabbit = 5 rabbit
After 2 months
Population of Rabbit = 10
After 4 months
population of rabbit = 20
Formula for growth is :
G = [tex]G_{0}[1 + R]^n[/tex], where G is final population and [tex]G_{0}[/tex] is initial population, and R is growth rate.
1. 10 = 5 [1 +R]²
Dividing both sides by 5 , we get
2 = (1 + R)²
→ R + 1 = √2 ⇒ taking positive root of 2
→R = √2 -1
Amount of rabbit after 1 year = [tex]20(1 + \sqrt2 -1)^8= 20 \times (\sqrt2)^8= 20 \times 2^4= 20 \times 16= 320[/tex]
The amount of rabbits after 1 year is[tex]\boxed{635}[/tex].
Further explanation:
The terms of the geometric sequence can be written as,
[tex]a,ar,a{r^2},a{r^3}[/tex], ..
Here, is the first term and is the common ratio.
If the first term and the second term is known then, the value of can be obtained.
Now, the value of any term can be easily obtained with the help of a and r.
Explanation:
The initial population of the rabbit is 5.
After two months the population of the rabbit is 10.
After four months the population of the rabbit is 20.
After six months the population of the rabbit is 40.
After eight months the population of the rabbit is 80.
After ten months the population of the rabbit is 160.
After twelve months the population of the rabbit is 320.
The series can be formed as,
[tex]5,{\text{10, 20, 40, 80, 160, 320}}[/tex]
Now find the sum of all the population.
[tex]\begin{aligned}{\text{Sum}} &= 5 + 10 + 20 + 40 + 80 + 160 + 320\\&= 685 \\\end{aligned}[/tex]
The amount of rabbits after 1 year is [tex]\boxed{635}[/tex].
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Geometric progression
Keywords: Rabbit, gardener, same ratio, amount of rabbits, growth, continues, 1 year, Five rabbits, after two months,
When one-fifth of the boys left, there were still b boys and g girls who stayed to see a program. What was the total number of boys and girls at the beginning of the program?
Answers
To find the total number of boys and girls at the beginning of the program, use the equations b2 = (1/5)b1, b = (4/5)b1, and g = g1. Then, the total number of boys and girls at the beginning is b1 + g1.
Explanation:To find the total number of boys and girls at the beginning of the program, we need to first determine the number of boys that left. Let's say the total number of boys at the beginning was b1 and the number of boys that left was b2.
Given that one-fifth of the boys left, we can write the equation: b2 = (1/5)b1.
Then, the number of boys remaining is: b = b1 - b2 = b1 - (1/5)b1 = (4/5)b1.
Similarly, the number of girls remaining is: g = g1, where g1 is the initial number of girls. Therefore, the total number of boys and girls at the beginning is: b1 + g1.
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The total number of boys and girls at the beginning of the program is represented by 5b + g, where 'b' represents the remaining boys after one-fifth left and 'g' represents all the girls who stayed for the program.
Explanation:To answer this, we must first understand that 'b' represents the number of boys left after one-fifth of them have exited. If we let 'B' denote the total number of boys initially present, then according to the prompt, B - 1/5*B = b. Simplifying this, we get B = 5b.
Now, along with the girls, the total number of children initially present would be B + g (since all girls stayed throughout the program). Plugging in the value of 'B' we found, we get the total as 5b + g.
So, the total number of boys and girls at the beginning of the program is represented by 5b + g.
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Simplify. 25√+35√−5√
Answers
Answer:
4√5
Step-by-step explanation:
i did the quiz
Answer:
4√5
Step-by-step explanation:
Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line. Which line segment in the image corresponds to EH in the pre-image?
A.) AD
B.) AB
C.) BC
D.) CD
Answers
Answer: A) AD
Step-by-step explanation:
Given: Quadrilateral ABCD is the result of a reflection of quadrilateral EFGH over the line.
We know that after reflection each point on the pre-image has a corresponding point on its image that is equidistant from a given line of reflection.
Since, EH shows the first and the last character of the name .
Thus, the line segment in the image corresponds to EH in the pre-image is AD because A is the first and D is the last character of the pre-image.
math question down below
Answers
9,791 rounded to the nearest hundred
Answers
9,791 rounded to the nearest hundred is 9,800 because the tens digit (9) is closer to 0 than 100.
Rounding 9,791 to the nearest hundred means finding the closest multiple of 100 to 9,791. To do this, we look at the tens digit, which is 9, and determine if it's closer to 0 or 100. Since 9 is closer to 0 than to 100, we keep the hundreds digit the same (9) and change all digits to the right to 0. So, rounding 9,791 to the nearest hundred gives us 9,800.
DO NOT COPY FROM ANOTHER ANSWER! I Will know!!
A stone was thrown into a pond from 8 feet above the surface of the water in the pond. Justin wrote +8 feet to represent the height from which the stone was thrown. What does 0 represent in this situation?
the depth of water in the pond
the level at which the stone fell
the surface of the water in the pond
the level from which the stone was thrown
Answers
depth is height of ground to surface.
level it fell was 8 ft
if level it was thrown was 0 then the surface would be -8ft
C is the right answer
Dritown received 0.135 inches of rain in the spring of 2011. Write this decimal as a fraction in simplest form.
A: 7/50
B: 1/8
C: 13/100
D: 27/200
Answers
Answer:
[tex]\frac{27}{200}[/tex]
Step-by-step explanation:
Dritown received 0.135 inches of rain in the spring of 2011.
Convert 0.135 in fraction form
0.135 can be written as 0.135/1
To remove decimal multiply top and bottom by 1000
[tex]\frac{0.135 \cdot 1000}{1000} =\frac{135}{1000}[/tex]
Divide both top and bottom by 5
[tex]\frac{135}{1000}[/tex] becomes [tex]\frac{27}{200}[/tex]
Mal downloads 4 songs each week for 5 weeks.Then he sorts the songs into equal groups.There are 10 songs in each group.How many groups are there?
Answers
20/10= 2
There are 2 groups of songs.
Hope this helps!
Two lines intersect to form a linear pair with equal measures. One angle has the measure 9x° and the other angle has the measure (9y − 54)°. Find the values of x and y.
Answers
Which number line shows the graph of -0.7
Answers
-0.7 is 0.7 units on the left from 0 on number line
hope it helps
Fractions and decimals are all around us. For example, you might have seen those oval stickers on the back of people’s cars that say 26.2. That is the length of a modern marathon, 26.2 mi. As a fraction, that would be 2 26 10 mi or, in simplest form, 1 26 5 mi. A. Find three examples of fr actions or decimals in the real - world. You can use videos, magazines, newspapers, books, or the In ternet. Don't take more than two examples from the same source. Also, get a mix of fractions and decimals. Don't choose all fractions or all decimals. B. List your examples. Explain each example and list the source. C. Convert each example either from a fraction to a decimal or from a decimal to a fraction. Don’t forget to show your work and simplify.
Answers
Fraction form: 1/4 Decimal form: 0.25
Example 2: BOGO 1/2 off (Sale at shoe store, buy one get one half off)
Fraction form: 1/2 Decimal form: 0.50
Example 3: Gas prices
$2.63 per gallon
Fraction form: 2 63/100 Decimal form: 2.63
9th grade Algebra 1 help! PLEASE HELP ME! EXPLAIN YOUR ANSWERS :)
Answers
find and intrepret the Slope
Answers
0.42 inch of rain fell in 3 hours. How many inches of rain fell per hour?
Answers
divide total amount (0.42) by number of hours (3)
0.42 / 3 = 0.14 inches per hour
0.42/3= 0.14
what are the common factors of 16a and 20ab
Answers
Hope this helped! :)
-9u - 5 + 6u = 19
What is u?
Answers
Then you add 5 to both sides to get -3u =24
Finally you divide by -3 to get u=-8
What is the equivalent ratio of 5/9?
Answers
Luis purchased 24 purple plants and 8 pink plants. He wants to plant them in equal groups in his garden. What the largest number of groups he can make?
Answers
24/8=3
Three groups. One pink in each, three purple in each.
Hope this helps :)
You use a microscope to look at bacteria that is 0.0034 millimeter long. The microscope magnifies the bacteria 430 times. How long does the bacteria appear to be when you look at it through the microscope?
Answers
move the decimal point of 0.0034 to the right to make it a whole number which is 34. Then multiply 34 times 430 which is 15,620.
move the decimal point (which is at the end) 4 times to the left
the answer will be 1.562
Answer:
1.462 millimeters.
Step-by-step explanation:
You use a microscope to look at bacteria that is 0.0034 millimeter long.
The microscope magnifies the bacteria 430 times.
So the bacteria appears 430 times long through the microscope.
We will multiply the length of bacteria by 430.
The size of bacteria appear = 430 × 0.0034
= 1.462 millimeters
The length of the bacteria would appear 1.462 millimeters through microscope.
Kendall recently received a job offer which required him to move his house full of furniture across the country from Columbia, South Carolina, to Riverside, California. To manage his moving expenses, Kendall kept track of the amount of gasoline used by the moving truck he rented. The truck used 109 gallons of gas to drive 1,092 miles from Columbia to Des Moines, Iowa. On the next leg of the drive, the truck used 67 gallons of gas to drive 671 miles from Des Moines to Denver, Colorado. Finally, he used 99 gallons of gas to drive 985 miles from Denver to Riverside, California. Using x to represent the number of miles and y to represent the number of gallons, create a table of values to represent this relation.
Answers
1092, 109
671, 67
985, 99
The rate is 10.02 and I found that by dividing x with y
Answer:
Step-by-step explanation:
A table of values is generally used when there are few values of the independent variable "x" and their corresponding values of the dependent variable "y".
x = Number of miles (Independent variable)
y = Number of gallons (dependent variable)
The table of values can be represented as follows:
x ------------------- y ------- Relationship (x / y)
1,092 ------------ 109 --------- 10.02
671 -------------- 67 ---------- 10.02
985 ------------- 99 ----------- 9.95
--------------------------------------------------
Total 2,748 ----------- 275 ---------- 9.99
Hope this helps!
The sum of 2 and three times a number equals 14. Find the number
Answers
14-2=12
12/3=4
answer in correct fashion
2+3×4=14
2 times the number is 2Y
3 times the number is 3Y
The sum of two and three times the number is 14. That is represented as;
2Y+3Y=14
5Y=14
Divide both sides by 5
Y=14/5
Y=2.8
The number is 2.8
Have a nice day
A used electronics store pays $40 for each cell phone, spends $25 refurbishing the phone, and sells the refurbished phone to a customer for $100.
Answers
Answer:
h
Step-by-step explanation:
e
In a Toy store, the ration of dolls to teddy bears is 9:3. If the store has 240 dolls, how many teddy bears are in the store
Answers
Hope this helps
There are 80 teddy bear in the store.
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
The ratio of dolls to teddy bears is,
⇒ 9 : 3
Number of dolls in the store = 240
Now,
Since, The ratio of dolls to teddy bears is,
⇒ 9 : 3
⇒ 3 : 1
So, Number of dolls = 3x
And, Number of teddy bears = x
We can formulate;
⇒ 3x = 240
Solve for x as;
⇒ x = 240 / 3
⇒ x = 80
Thus, Number of teddy bears = x
= 80
So, There are 80 teddy bear in the store.
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Quincy needs 322 yards of ribbon to decorate quilts for a craft fair. The ribbon comes in rolls of 15 yards. How many rules of ribbon should Quincy buy? Alice needs twice as many yards of ribbon as Quincy. How many rules of ribbon does Alice need?