Juan and his children went into a restaurant where they sell drinks for $2 each and
tacos for $4 each. Juan has $40 to spend and must buy a minimum of 11 drinks and
tacos altogether. If a represents the number of drinks purchased and y represents
the number of tacos purchased, write and solve a system of inequalities graphically
and determine one possible solution.
Answers
The number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
How to generate Inequality Graph?We are given that;
a represents the number of drinks purchased.
y represents the number of tacos purchased
He must buy a minimum of 11 drinks and tacos altogether. Thus, the inequality that describes this is;
2a + 4y ≤ 40
a + y ≥ 11
The inequality graph that represent the given system of inequalities is as shown in the atatched file.
From the given inequality graph, we can tell that one possible solution is; (a, y) = (2, 9)
Thus, the number of drinks purchased and the number of tacos purchased that will yield the inequality are; 2 and 9 respectively.
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Related Questions
A store is offering a 15 % discount on all items. Also, employees get a 20 % employee discount. Write composite functions
b. to model taking the 20 % discount and then the 15 % discount.
Answers
The composite functions of the model taking the 20 % discount and then the 15 % discount is (D ◦ E)(x) = 0.68x.
What is meant by function composition?
In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.
In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.
Let D(x) = cost after applying the 15% discount,
E(x) = cost after applying the 20% employee discount, and x = cost of item(s).
Then D(x) = 0.80x and E(x) = 0.85x.
(D ◦ E)(x) = 0.68x.
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Factor each expression.
9 x²-25
Answers
After factorization of the expression 9x²-25, the answer comes to:
(3x - 5)²What do we mean by an expression?An expression or mathematical expression is a finite mixture of symbols that is well-formed according to context-dependent rules. To help determine the order of operations and other aspects of logical syntax, mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping.Many authors differentiate between an expression and a formula, with the former referring to a mathematical object and the latter referring to a statement about mathematical objects.So,
The given expression is: 9x²-25
Then,
9x²-253²x²-5²(3x)²-(5)²(3x - 5)²Therefore, after factorization of the expression 9x²-25, the answer comes to:
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I really need help I will give you 5 stars and alike.
Answers
Answer:
the area is 935 square inches, and the perimeter is 39 inches
Step-by-step explanation:
Hey there!
In order to find the perimeter and area of the board, we must first list out the information we already know
----------------------------------------------------------------------------------------------------------
- The original board has a length of 44 - The original board has an area of 1496- The original board has a perimeter of 156- The new board has a length of 11----------------------------------------------------------------------------------------------------------
There is a tiny pattern in here:
The original board has a length of 44 while the new one has the length of 11
This means that, the original board had dimensions 4 times the length of the new board
In order to find the area or perimeter, we need to know the width of the new board
To do this, we divide 1496 by 44
That gets us 34
This means that the width of the old board is 34
Now we divide 34 by 4 which gets us 8.5
This means, 8.5 is the width of the new board
Now that we know this, we can easily find the area and the perimeter of the new board
8.5 + 8.5 + 11 + 11 = 39
This means, the perimeter is 39
8.5 x 11 = 935
This means, the area is 935
This brings us to the conclusion that the area is 935 square inches, and the perimeter is 39 inches!
-4x -5x
6x-(-3x)+x-6
-9x-y+1+5y+5x-10
6(x+3)
-5 (x-8)+2
7-(x-4)+5x-1
Answers
Step-by-step explanation:
1. -9x
2. 2(5x -3)
3.. -4x + 4y -9
4. 6x+18
5.-5x +42
6. (2x+5)
34. Marianne figured out that her father's age
is her age plus five to the power of four, less
365, minus 22, all divided by six. If her father
is 42, how old is Marianne?
ats true
Answers
Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Marianne figured out that her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six. If her father is 42.
Let x be the Marianne age
(x + 5⁴ - 365 - 22) (1/6) = 42
x + 238 = 252
x = 14 years
Thus, Marianne's age is 14 years old if her father's age is her age plus five to the power of four, less 365, minus 22, all divided by six.
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Expand each logarithm.
log₈8 √3a⁵
Answers
The expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
Given that the expression is log₈8 √3a⁵.
We are required to expand the expression.
The change of base formula is used to write a logarithm operation again as a fraction of logarithms with a new base.
The expression is log₈8 √3a⁵.
log₈8 √3a⁵= (log 8 +log [tex]\sqrt{3}[/tex] +log [tex]a^{5}[/tex])/log 8
=1+ log 3/2log 8 +5 log a/ log 8 (We know that log [tex]m^{n}[/tex]=n log m)
Hence the expansion of the expression log₈8 √3a⁵ is
1+ log 3/2log 8 +5 log a/ log 8.
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Find the inverse of each function. Is the inverse a function?
f(x)=x⁴
Answers
The domain of f(x) to be [0,∞).
If the domain R, f(x) is not one to one, so its inverse exists not a function.
If we restrict the domain of f(x) then we can define an inverse function.
What is meant by inverse function?An inverse function, even comprehended as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function exists denoted by ' f ' or ' F '.
In order to have an inverse function, a function must be one to one.
In the case of f(x) = x⁴ we find that f(1) = f(−1) =1.
If f(x) exists not one to one on its implicit domain R.
If we restrict the domain of f(x) to [ 0, ∞) then it does contain an inverse function, then [tex]f^{-1}(y)=\sqrt[4]{y }[/tex]
Let the given function be y = f(x) = x⁴
Taking the square root of both ends, then we get
± √y = x²
Let the real values be x, then
We require the left hand side to be non-negative, so assume the non-negative square root.
Take the square root of both sides of the equation then
±[tex]\sqrt[]{\sqrt{y} }[/tex] = x
⇒ x = ± [tex]\sqrt{\sqrt{y} }[/tex] = ± [tex]\sqrt[4]{y}[/tex]
It does not give us a unique value of x in terms of y.
So the inverse function exists not defined, then x ≥ 0,
i.e., restrict the domain of f(x) to be [0,∞).
If the domain R, f(x) exists not one to one, so its inverse exists not a function.
The domain of f(x) then we can describe an inverse function.
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Please tell me how its done, 25 points
1. There are 24% of boys in a school. If the number of girls is 456, find the total
number of students in the school.
Answers
Answer:
Heya genial Gracia dispute
A car tire has a radius of 1.5 feet. if the tire is rotating at 800 rpm, what is the speed of the car in miles per hour (1 mile = 5,280 feet)? round the answer to the nearest tenth. the car is traveling approximately miles per hour.
Answers
Answer:85.7 miles per hour
Step-by-step explanation:
The scale of a map is 2.6 ft = 89
miles
Map: 5.6 ft
Actual:
miles
Answers
Actual miles is [tex]\frac{2492}{13}[/tex]
According to the question,
Given that,
Map is 5.6 ft
scale of Map is 2.6 ft which is equal to 89 miles
Actual miles = [tex]\frac{5.6 * 89}{2.6}[/tex]
= [tex]\frac{498.4}{2.6}[/tex]
multiply both the numerator and denominator with the same integer
= [tex]\frac{4984}{26}[/tex]
= [tex]\frac{2492}{13}[/tex]
Actual miles is [tex]191\frac{9}{13}[/tex] ≈ 1.916923 ×[tex]10^{2}[/tex]
Definition of miles per hour unit: ≡ 1 mi / 3600 s = 1609.344 m / 3600 s. In American public life, this is the most commonly used speed unit. Cars speeds are measured in mpg. Interpretation: The speed at which the body moves 1 mile (or 1609.344 metres) in 1 hour.
Definition of feet per second unit: ≡ 1 ft / 1 s = 30.48 cm / 1 s. Abbreviation is fps. In America, perhaps this is the second most commonly used speed unit in public life (after miles per hour). Definition: The speed at which the body moves 1 foot (or 30.48 centimetres) in 1 second.
Convert Miles to Feet
Multiply your speed in miles per hour by 5,280. This is the number of feet in a mile. The result is your speed in feet per hour. For example, 60 miles per hour times 5,280 feet per mile is 316,800 feet per hour.
Convert to Feet per Minute
Divide your speed in feet per hour by 60. This is the number of minutes in an hour. Therefore, the result is your speed in feet per minute. For example, 316,800 feet per hour divided by 60 minutes per hour is 5,280 feet per minute.
Convert to Feet per Second
Divide your speed in feet per minute by 60. This is the number of seconds in a minute. Therefore, the result is your speed in feet per second. For example, 5,280 feet per minute divided by 60 seconds in a minute equals 88 feet per second.
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If you were George Washington, would you have put two VERY different people in your Cabinet to advise you? Do you think this was a wise decision by Washington? Explain.
Answers
If I were George Washington, I would have put two very different people to advise me because I would have a broader vision of government affairs.
Who was George Washington?George Washington (1732-1799) was an American politician and military man who stands out for being one of the most influential people in history and for having served as the first president of the United States between 1789 and 1797. He is considered the most important father of the Nation of the United States.
In 1789 he was unanimously elected by the other founding fathers as the first president of the United States. During his rule he tried to create a nation capable of maintaining peace with its neighboring countries, so he proclaimed neutrality to avoid any involvement in foreign conflicts.
Why have two very different advisers?For George Washington it was a challenge to occupy the position of the first president of the United States because he was going to lead a country that was just being formed. Due to the above, it was of vital importance to include all forms of thought and all visions in its government plan and way of governing.
Therefore, when assuming office as president of the United States, it would be of great importance to have advisers who would help him see from the point of view of other people so that his decisions would take into account the interests of all citizens to avoid uprisings and divisions.
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Put the correct number in each box
1/7=4/? = ?/56
Answers
Vertical 1.
3+ 12, an incomplete mathematical sentence.
Answers
Addition 3+ 12, an incomplete mathematical sentence. 1.3+ 12=13.3
Addition is a mathematical procedure that is used to add numbers. The sum of the given numbers is the result of adding the given numbers. For instance, if we add 2 and 3, (2 + 3), the result is 5. We used the addition function on two numbers, 2 and 3, to produce the sum, 5
Symbol for Addition
Different symbols are used in mathematics. One of the most used arithmetic symbols is the addition symbol. We read about adding two numbers, 2 and 3, in the definition of addition above. If we look at the addition pattern (2 + 3 = 5), the symbol (+) joins and completes the two integers.
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Eduardo started a business selling sporting goods. He spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. He earns $850 per week in sales. What is the minimum number of weeks it will take for Eduardo to make a profit?
Which inequality models this problem?
300w>7500+850w
850w≥7500+300w
850w<7500+300w
850w>7500+300w
Answers
The minimum number of weeks it will take for Eduardo to make a profit
850w > 7500 + 300w. Option D
This is further explained below.
What is the minimum number of weeks it will take for Eduardo to make a profit?Generally, the Total cost is mathematically given as
X= $7500+$300w
Where he is earning each week
=$850
Therefore,
He will be paid in n weeks=$850n
The information that has been presented states that the very bare minimum number of weeks that it will take for Eduardo to earn a profit is by.
Total revenue is more than total expenditures
850w > 7500 + 300w
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y varies directly with x .
If x=2 when y=4 , find y when x=5 .
Answers
After direct variation y =10 when x = 5.
What specifically do we mean by "direct variation"?Direct variation equations use the same phrase to give the reader a hint.The phrase is either "directly proportional" or "directly varies."The area of a square, for instance, is proportional to the square of its side.If y varies directly as x and y = 6 when x = 2, the variational constant is k = 3.As a result, the direct variation equation is y = 3x.So,
The initial statement is y = kx
Then to find y when x = 5.
K constant will be y/x ⇒ 4/2That is y = kx ⇒ y = 4/2 × xWhen x = 5:
y = 4/2 × 5 ⇒ y = 10Therefore, after direct variation y =10 when x = 5.
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please explain how you got it also
Answers
a WHOLE is always simplified to "1", and we can use any denominator for that, so 5/5 is 1, and 7/7 = 1, and [tex]\cfrac{4}{4}\implies \cfrac{113}{113}\implies \cfrac{1000000}{1000000}\implies \text{\LARGE 1}whole[/tex]
so hmmm for this case we'll be use thirds or namely the denominator of 3, so a whole bunch of basketballs was originally 3/3 of "b", "b" was the whole amount, so originally we had 3/3, but then during the day we sold 2/3 of them, so we were left with 3/3 - 2/3 = 1/3, and then 8 came back, because they were deflated or something, now the store has a total of 38 basketballs.
[tex]\stackrel{whole}{\cfrac{3}{3}b}~~ - ~~\stackrel{sold}{\cfrac{2}{3}b}\implies \cfrac{3b-2b}{3}\implies \cfrac{b}{3}\implies \stackrel{\textit{remaining in store}}{\cfrac{1}{3}b} \\\\\\ \stackrel{in~store}{\cfrac{1}{3}b}~~ + ~~\stackrel{coming~back}{8}~~ = ~~\stackrel{new~total}{38} \\\\\\ \cfrac{b}{3}+8=38\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( \cfrac{b}{3}+8 \right)=3(38)}\implies b+24=114\implies \stackrel{originally}{b=90}[/tex]
What is 3/4c - 1 = 1 + 3/4c? Thanks!
Answers
Answer:
False
Step-by-step explanation:
You want to know "what is 3/4c - 1 = 1 + 3/4c?"
SolutionSubtracting the left-side expression from both sides, we get ...
(3/4c -1) -(3/4c -1) = (1 +3/4c) -(3/4c -1)
0 = 2 . . . . a False statement
__
Additional comment
Since the equation is written without parentheses, we have to assume that c is in the numerator in each expression, and that its coefficient is (3/4).
please help!! 10 points+ brainlist!!
Answers
Answer:
Mean - 67 inches
Median - 67 inches
Mode - 68 inches
Step-by-step explanation:
Definitions of the words:
Mean - The average number of the data set.
Median - The middle number in the data set when ordered from least to greatest.
Mode - The value that appears most frequently.
Mean:
We can add them up and divide by the number of values in the set, 7.
469 / 7 = 67
Median:
We can order them from least to greatest and see which one is the 4th one.
60, 62, 66, 67, 68, 68, 78.
67 is in the middle, so that is our median.
Mode:
Only 68 is repeated twice in the set, so 68 is the mode.
Hope this helped! Have a great day!
Two water tanks 50 inches tall. tank a is empty and for each minute the water increases by 3.7 inches. tank b is draining and the water decreases 1.9 inchesveach minute. how many minutes will pass so the height of the water in each tank is the same
Answers
If two water tanks are 50 inches tall and tank a is empty and for each minute the water increases by 3.7 inches and tank b is draining and the water decreases by 1.9 inches each minute, then the minutes after which the height of the water in each tank is the same is equal to 9.
The time in minutes after which the height of the water in each tank is the same can be determined by using a linear equation.
The equation for this problem can be given as,
0 + 3.7(x) = 50 - 1.9(x)
Here x is equal to minutes. To find the minutes after which the water level will be the same can be determined by calculating the value of x in this linear equation.
3.7(x) + 1.9(x) - 50 = 0
5.6(x) = 50
x = 50 / 5.6
x = 8.92 ≈ 9
Hence, the height of the water in tank a and tank b is equal after 9 minutes.
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Evaluate the expression A=3, b=1/2.and c=4
8ab/2bc
Answers
Answer: 3
Step-by-step explanation:
First substitute values in :
8(3)(1/2)/ 2(1/2)(4)
Then simplify :
12/ 4
3
i need help with this
Answers
Answer:
y = 3x² + 2
Step-by-step explanation:
I'm help to number on more this, thank for subject on help for today.
In Problem 17, verify that the functions fand g are inverses of
each other by showing that (f o g) (x) = x and (g o f) (x) = x.
Problem 17:
f(x) = 1/x g(x) = 1/x
Answers
Answer:
you are very very very correct
Use a table to solve each equation. Round to the nearest hundredth.
2x⁺³=512
Answers
[tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.
What is exponentiation?Exponentiation is a mathematical operation that involves the base number (b) and the exponent (or power) number (n), and is represented as [tex]b^n[/tex]. Its pronunciation is "b (raised) to the (power of) n."Now,
[tex]2^{(x + 3)} = 512[/tex]
=> [tex]2^{(x + 3)} = 8^3 = (2^3)^3[/tex]
As [tex](a^b)^c = a^{bc}[/tex],
=> [tex]2^{(x + 3)} = 2 ^9[/tex]
=> x + 3 = 9
=> x = 6
Hence, [tex]2^{(x + 3)} = 512[/tex] => x = 6, by properties of exponentiation.
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There are 100 people on the swim team.today, they are going to a big swim meet on the other side of town. if each minivan can take 15 people how much minivans will they need.
Answers
Using the mathematical operation such as division, the swim team, which has 100 people on it, needs 7 minivans to take them on the other side of town.
If there are 100 people on the swim team that will be divided into minivans that can only occupied by 15 people, divide 100 by 15 to know how many vans they will need.
100 people ÷ 15 people/minivan
100 ÷ 15 = 6 r 10
This means that the swim team will need 6 minivans and still, 10 people don't belong to any minivan yet. So, 1 additional minivan will be needed for the remainder of 10 people.
Hence, the swim team will be needing 7 minivans to cater 100 people on their team.
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what is 209.3 ÷ 80 without a remainder
Answers
Answer:
2.61625
Step-by-step explanation:
209.3 divided by 80
Miles caught a fish that weighed 4 1/6 pounds and then caught another that weighed 6 5/8 pounds. How much more did the second fish weigh? Create an expression to represent this situation.
Answers
Answer: 2 11/24
Step-by-step explanation: First we have to subtract it, so 6 5/8 - 4 1/6 which is 2 11/24
WHAT I SHOULD HAVE DONE
1 CUP MILK
4 SCOOPS
CHOCOLATE
WHAT I DID
1 CUP MILK
5 SCOOPS
CHOCOLATE
Answer the questions on each slide.
Use complete sentences. You do not have to show your work.
If it asks to explain, please provide an explanation.
How should I fix this to equal 1/4?
Answers
Answer:
just add more to the milk and another scoop of chocolate
Step-by-step explanation:
1.5 cups milk
6 scoops of chocolate
Find the coordinates of the point where y - 4x = 1 crosses the y-axis
Answers
Step-by-step explanation:
to cross the y-axis x must be 0.
so,
y - 4×0 = 1
y = 1.
so, the point is
(0, 1)
Get into form….y =mx +c
y=4x+1
The c is where it crosses the y axis…(y intercept)
Therefore ans= 1
Elena’s father put $460 into a savings account for her. The account pays 2.5% simple interest each year. If he neither adds nor withdraws money from the account, how much interest will the account earn after 4 years? Round to the nearest cent.
Answers
$46
Step-by-step explanation:
Give that Elena's father put $460 into a savings account.
So, the principal amount, P= $ 460
Yearly simple interest , R= 2.5% = 0.025
Time, t = 4 years.
The interest, I, for the principal amount, P, at the rate of R yearly, after t years,
By using the given values, we have
Hence, the account will earn $46.
Answer:
$46
Step-by-step explanation:
So, the principal amount, P = $460
Yearly simple interest, R = 2.5% which equals 0.025
Time(T) which is 4 years.
The interest(I) for the amount, P at the rate of R yearly, after T years,
Elena's account will earn $46.
HELP!! The slope of the line below is 3. Write the equation of the line in point-slope form, using the coordinates of the labeled point. Do not use parenthesis on the y-side. (-1,1)
Answers
The equation of the line in point-slope form is y-1 = 3 ( x + 1)
Equation of a line:
The equation of a line, in point-slope form, is designated using:
y-y0= m( x - x0)
In which the point is given by(x0,y0) and m is the slope.
Slope of the line below is 3 (given in the question).
This means that m = 3
(-1,1)
This means x= -1 and y =1
equation of the line
y - y0 = m( x- x0)
y-1 =m(x-(-1))
y-1=m(x + 1)
substituting the value of m is 3
y-1= 3 ( x + 1)
Therefore, The equation of the line in point-slope form is y-1= 3 (x + 1)
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