algebra- you make a large pot of soup. You freeze the soup in small and medium containers. A small container holds 4 ounces and a medium container holds 6 ounces. The soup can fill 6 small containers and 10 medium containers.
A.Write an equation in standard form that models the possible combinations of small and medium containers that the soup can fill.
B. Graph the equation from part (a)
C. Find four possible combination.
Answers
A. Let us say that:
s = number of small containers
m = number of medium containers
From the given data, the total volume of soup is:
total soup = 4 ounces * 6 + 6 ounces * 10 = 84 ounces
So the equation is:
4s + 6m = 84
B. We rewrite the equation explicit to one variable, here we choose s:
4s = 84 – 6m
s = 21 – 1.5m
Then we assign several values for m starting at 0 to get the corresponding value of s then plot the graph. See the graph attached.
C. From the graph, we choose the pair of s and m that are whole numbers. The four possible combinations are:
21 small containers, 0 medium containers
15 small containers, 4 medium containers
9 small containers, 8 medium containers
3 small containers, 12 medium containers
Related Questions
What is the solution of the system? Use elimination.
-12x - y = 6
17x + y = 4
A. (-30, 2)
B. (-2, 30)
C. (2, -30)
D. (30, -2)
Answers
-12x-y+(17x+y)=6+4
5x=10
x=2
Substituting x=2 in either of the equations, we find the value of y.
Let's use the first equation:
-12x-y=6
-24-y=6
-y=24+6
-y=30, so y=-30.
Thus, the solution is (2, -30)
Answer: C
Answer:
C: (2, -30)
Step-by-step explanation:
Paulo scored "x" on his first math test, then scored 10 points higher on his second, scored 5 points lower on the third than the second, and scored half as well on the fourth test as the second. if his average for the four tests is 75 points, what did he score on the second test?
Answers
[tex] \frac{x+(x+10)+(x+10-5)+ \frac{x+10}{2} }{4} = 75 [/tex]
Then we simplify to get this:
[tex] \frac{(3x+15)+ \frac{x+10}{2} }{4} = 75[/tex]
Then we get common denominators and add:
[tex] \frac{ (\frac{6x+30}{2})+ (\frac{x+10}{2}) }{4} = 75[/tex]
[tex] \frac{ \frac{7x+40}{2} }{4} = 75[/tex]
Then reciprocalize the main denominator and simplify:
[tex]\frac{7x+40}{2} * \frac{1}{4} = 75[/tex]
[tex] \frac{7x+40}{8} = 75[/tex]
And then solve for x:
[tex]7x + 40 = 600[/tex]
[tex]7x = 560[/tex]
[tex]x = 80[/tex]
Since he scored ten points higher than x (x is what he earned in the first test), we can add:
[tex]80 +10 = 90[/tex]
So, he got 90 points on his second test.
What is the area of trapezoid ABCD? Enter your answer as a decimal or whole number in the box. Do not round at any steps
Answers
Let's split up the shape in a square and a triangle.
If you introduce point E at (5,1) you see a square ABED with area 5*5=25.
What remains is a triangle with straight sides 5 and √((11-5)² + (1--7)²) = 10. So the triangle's area is 5*10/2 = 25.
This means the total area is 25+25=50.
Find quadratic equation from 3 points calculator
Answers
Step 1:
We check to make sure that no pair of points is colinear (i.e. lie on the same line) by making that the slopes of the combinations of the line are not equal.
Slope of PQ = [tex] \frac{8-7}{6-(-2)} = \frac{1}{8} [/tex]
Slope of PR = [tex] \frac{-3-7}{-1-(-2)} = \frac{-10}{1} =-10[/tex]
Slope of QR = [tex] \frac{-3-8}{-1-6} = \frac{-11}{-7} = \frac{11}{7} [/tex]
Since, the slope of the lines are not equal, thus the points are not colinear nor parallel.
Step 2:
Substitute the x-values and the y-values of the given points into the quadratic equation formular to have three system of equations as follows:
[tex]a(-2)^2+b(-2)+c=7\Rightarrow 4a-2b+c=7 \ .\ .\ .\ (1) \\ \\ a(6)^2+b(6)+c=8\Rightarrow36a+6b+c=8\ .\ .\ .\ (2) \\ \\ a(-1)^2+b(-1)+c=-3\Rightarrow a-b+c=-3\ .\ .\ .\ (3)[/tex]
Step 3:
We solve the system of equations as follows:
[tex]\left[\begin{array}{ccccc}4&-2&1&|&7\\36&6&1&|&8\\1&-1&1&|&-3\end{array}\right] \ \ \ R_1\leftrightarrow R_3 \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\36&6&1&|&8\\4&-2&1&|&7\end{array}\right] \ \ \ {{-36R_1+R_2\rightarrow R_2} \atop {-4R_1+R_3\rightarrow R_3}} \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\0&42&-35&|&116\\0&2&-3&|&19\end{array}\right] \ \ \ R_2\leftrightarrow R_3[/tex]
[tex]\left[\begin{array}{ccccc}1&-1&1&|&-3\\0&2&-3&|&19\\0&42&-35&|&116\end{array}\right] \ \ \ \frac{1}{2} R_2\leftrightarrow R_2 \\ \\ \left[\begin{array}{ccccc}1&-1&1&|&-3\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&42&-35&|&116\end{array}\right] \ \ \ {{R_1+R_2\rightarrow R_1} \atop {-42R_2+R_3\rightarrow R_3}} \\ \\ \left[\begin{array}{ccccc}1&0&\frac{-1}{2}&|&\frac{13}{2}\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&0&28&|&-283\end{array}\right] \ \ \ \frac{1}{28} R_3\leftrightarrow R_3[/tex]
[tex]\left[\begin{array}{ccccc}1&0&\frac{-1}{2}&|&\frac{13}{2}\\0&1&\frac{-3}{2}&|&\frac{19}{2}\\0&0&1&|&\frac{-283}{28}\end{array}\right] \ \ \ {{\frac{1}{2}R_3+R_1\rightarrow R_1} \atop {\frac{3}{2}R_3+R_2\rightarrow R_2}} \\ \\ \left[\begin{array}{ccccc}1&0&0&|&\frac{81}{56}\\0&1&0&|&\frac{-317}{56}\\0&0&1&|&\frac{-283}{28}\end{array}\right][/tex]
Thus,
[tex]a=\frac{81}{56}; \ \ \ b=\frac{-317}{56}; \ \ \ c=\frac{-283}{28}[/tex]
Therefore, the quadratic equation with the three given points is
[tex]y=\frac{81}{56}x^2-\frac{317}{56}x-\frac{283}{28}[/tex]
To find the quadratic equation from 3 points, use the method of substitution and solve the system of equations. Substituting the given points into the general quadratic equation will result in a system of equations that can be solved for the quadratic equation.
Explanation:To find the quadratic equation from 3 points, we can use the method of substitution. Let's say the three points are (x1, y1), (x2, y2), and (x3, y3). We can substitute these points into the general quadratic equation, y = ax^2 + bx + c, to get three equations. Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.
For example, let's say the three points are (1, 3), (2, 6), and (3, 11). Substituting these points into the general quadratic equation, we get the following equations:
3 = a(1^2) + b(1) + c
6 = a(2^2) + b(2) + c
11 = a(3^2) + b(3) + c
Solving this system of equations will give us the values of a, b, and c, and thus the quadratic equation.
Help me please thank you (:
Answers
The 24 students in Mr. Brown’s homeroom sold 72 magazine subscriptions. The 28 students in Mrs. Garcia‘s homeroom sold 98 magazine subscriptions. Whose homeroom sold more magazine subscriptions per student? Explain your reasoning.
Answers
What is the vertex form of f(x)=x^2+24x+138
Answers
f(x) = x^2 + 24x + (24/2)^2 + 138 - (24/2)^2
f(x) = (x+12)^2 - 6
Answer:
(x +12)^2 - 6
Step-by-step explanation:
d/dx x^2 + 24x + 138 = 2x + 24
when 2x + 24 = 0, the gradient = 0
x = -12
f(-12) = -6
therefore we have (x +12)^2 - 6.
With nothing but nick and pennies in his pocket , Rupert can afford 77 cents worth of candy. If he has 21 coins in his pocket how many coins does he have of each type
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Is this the correct way to fill out this deposit slip? (For an assignment) I have yet to put my name and date
Answers
Is this function even, odd, or neither?
Answers
when a function is odd, the symmetry is with respect to the origin, meaning, the graph to the right-side of the y-axis, is a mirror image of the one on the left-bottom-upside-down. So, you take a photo of the right-side graph,flip it over the x-axis, and then flip it again over the y-axis.
this one, doesn't show that either.
Generally speaking, using a ______ year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future. Part of a year or full year
Answers
By collecting full year's history of cash, we could determine the amount of expense that company might need to continue the operation in the future.
This projection is made on the assumption that the company won't make any major change on its way of operation in next year's period.
Generally speaking, using a FULL year's history of cash receipts and disbursements will be a satisfactory basis for projecting the future.
Explanation:
Though a rough projection can be made in half year's data as well, but a good and solid projection can be made using full year's data. Almost all business run for a full year, so its good to project on an yearly basis. Like in this particular year the profits are this much, so we can project that in the next year we can see a higher profit.
23: keith is driving from reno to kansas city to meet his girlfriend. the distance between the two cities is 1,650 miles. if keith can average 50 miles per hour, how many hours will it take him to complete his trip?
Answers
divide total miles by speed
1650 / 50 = 33
it will take 33 hours
How many real solutions does the equation have?
r2 – 94 = 0
Answers
The quadratic equation r² – 94 = 0 has two real solutions, as the discriminant is positive when applying the quadratic formula.
Explanation:The question deals with the quadratic equation r2 – 94 = 0. To determine how many real solutions this equation has, we can rearrange it into the standard quadratic form ar2 + br + c = 0, where a = 1, b = 0, and c = -94. The real solutions of a quadratic equation are found using the quadratic formula, which is r = −b ± √(b2 - 4ac) / (2a). In this case, the discriminant (b2 – 4ac) becomes (02 – 4(1)(-94)) which simplifies to 376. This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 0, and c = -94. To find the number of real solutions, we need to determine the discriminant, which is given by the formula: discriminant = b² - 4ac. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. In this case, the discriminant is: 0 - 4(1)(-94) = 376. Since the discriminant is greater than zero, the equation r² - 94 = 0 has two real solutions. Since the discriminant is positive, this equation has two real solutions.
The equation has two real solutions.
Explanation:This expression is a quadratic equation of the form where the constants are To find the number of real solutions, we can use the discriminant, which is given by . If Δ > 0, there are two real solutions. If Δ = 0, there is one real solution. If Δ < 0, there are no real solutions. Let's calculate the discriminant:
Δ = 0² - 4(1)(-94) = 376
Since Δ > 0, the equation has
Edna brought 4 pies to a party. At the end of the evening 1 and 5/8 pie was left over. How much pie did the guest eat?
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HELP!!
A vendor has 14 balloons for sale: 7 are yellow, 3 are red, and 4 are green. A balloon is selected at random and sold. If the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow?
7 over 14
7 over 13
6 over 14
6 over 13
Answers
Answer:
6 over 13
Step-by-step explanation:
its right i took the test
The metric system is easy to use because it is based on units of ten. how many centimeters are there in 100 meters?
Answers
_________________________________________________
Note: 100 cm = 1 m (exact measurement); in which:
"cm" = centimeter(s) ;
"m" = meter(s) ;
_________________________________________________
100 m = ? cm ?
100 m * (100 cm / 1 m) = __?__ cm ;
The units of "m" cancel out; and we have:
(100)* (100 cm) = 10,000 cm .
_______________________________________
If the temperature is 64.4 degrees Fahrenheit, what is the temperature in degrees Celsius?
18
3.8
53.6
58.3
Answers
Answer:
[tex]18^{\circ}C[/tex]
Step-by-step explanation:
Given :The temperature is 64.4 degrees Fahrenheit
To Find : What is the temperature in degrees Celsius?
Solution:
The temperature is 64.4 degrees Fahrenheit
To convert in into Celsius
Formula : [tex]T(^{\circ}C) =(T(^{\circ}F)-32) \times \frac{5}{9}[/tex]
Substitute the vale
[tex]T(^{\circ}C) =(64.4-32) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =(32.4) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =18^{\circ}C[/tex]
So, Option A is true
Hence the temperature in degrees Celsius is [tex]18^{\circ}C[/tex]
A line contains the points (34, 12) and (32, 48) .
What is the slope of the line in simplified form?
Answers
( 34 , 12 ) and ( 32 , 48 )
48 - 12 / 32 - 34
36 / - 2
slope = - 18
Answer:
-18
Step-by-step explanation:
An investor wants to complain that the stock market continues to drop. What might they do to the graph shown to try to convince an audience that this is true?
A:) use a smaller range on the vertical scale
B:) use a larger range on the vertical scale
C:) omit numbers on the horizontal scale
Answers
Answer:
omit numbers on the horizontal scale
Lakshmi has had a checking account for over twenty years and has always gotten money from her bank by cashing a check. She would like a more convenient method of getting cash, without having to visit the bank each time she needs to withdraw money. What type of card would she get. A. Cash card. B. Credit card. C. Debit card. D. Store gift card
Answers
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle. if the measure of the vertex angle is 18, find the measure of each base angle.
Answers
The measure of each base angle is 81.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle.
An isosceles triangle is a triangle in which two sides are equal.
Given that the measure of the vertex angle is 18
We need to find the measure of each base angle.
By angle sum property the sum of three angles is 180 degrees.
x+x+18=180
2x+18=180
Subtract 18 from both sides
2x=180-18
2x=162
Divide both sides by 2
x=81
Hence, the measure of each base angle is 81.
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what is 13n-6p-11n=2p solve for n
Answers
2n - 6p (+6p) = 2p (+ 6p)
2n/2 = 8p/2
n = 8p/2
hope this helps
Your classmate is unsure about how to use side lengths to determine the type of triangle. How would you explain this to your classmate?
Answers
2) Isosceles Triangles: These triangles have two sides that have the same side length and one that is not the same. Given this, if the side lengths are all given, the triangle with two same sides are classified as isosceles triangle.
3) Scalene Triangles: These triangles have all sides associated with a different value. If all side lengths are given and they have different values, this triangle would classify as a scalene triangle.
Hope I helped :)
Answer:
First, look at the side lengths a, b, and c, where c is the longest. Then take the sum of a squared and b squared and compare it to c squared. If they are equal, the triangle is a right triangle. If c squared is less than a squared plus b squared, the triangle is acute. If c squared is greater than a squared plus b squared, the triangle is obtuse.
Graph 24x+25=−6y+7 .
Answers
24x+25+7= -6y
(24x+32)/-6=y
-3x-16/3=y (not too sure about the mental math here xp)
Knowing this, you know the y-intercept is (0, -16/3), the line is going downwards and you can easily find out another point.
If x= 1,
-3(1)-16/3=y
-9/3-16/3=y
-25/3=y
Ensure that at x=1, your graph passes through -25/3.
Hope I helped :)
What method would you choose to solve the equation 2x^2-7=9
Answers
Step 1) 2x^2-7=9
Step 2) 2x^2-7+7=9+7
Step 3) 2x^2=16
Step 4) (2x^2)/2=16/2
Step 5) x^2=8
Step 6) sqrt(x^2)=sqrt(8)
Step 7) |x|=sqrt(8)
Step 8) x=sqrt(8) or x=-sqrt(8)
-------------------------------------
Below are explanations/reasons to each of the steps above.
Step 1) Original equation
Step 2) Add 7 to both sides
Step 3) Combine like terms
Step 4) Divide both sides by 2
Step 5) Simplify
Step 6) Apply the square root to both sides. The notation "sqrt" is shorthand for "square root"
Step 7) Use the rule that sqrt(x^2) = |x| for all real numbers x
Step 8) Use the rule that if |x| = k then x = k or x = -k for some fixed number k.
-------------------------------------
The two solutions are
x = sqrt(8) or x = -sqrt(8)
After 2 1/4 h, a chainsaw has used 2 13/16 gal of fuel. How many gallons of fuel did the chainsaw use each hour? Enter your answer as a mixed number in simplest form in the box.
Answers
Answer:
1 1/4 or 5/4 gallon per hour.
Step-by-step explanation:
Fuel used in 2 1/4 hour = 2 13/16 gallon
Fuel used in 9/4 hour = 45 / 16 gallon
Fuel used in one hour = [tex]\frac{\frac{45}{16}}{\frac{9}{4}}[/tex]
= 5 / 4 gallon per hour = 1 1 /4 gallon per hour
Thus, teh fuel used in each hour is 1 1/4 gallon or 5 / 4 gallon.
Which expression is equivalent to 5 . 4 × 0 . 18 5.4×0.18?
A. ( 54 × 18 ) × ( 1 10 × 1 100 ) (54×18)×(110×1100)
B. ( 54 × 18 ) × ( 1 10 × 1 10 ) (54×18)×(110×110)
C. ( 5 . 4 × 0 . 18 ) × ( 1 10 × 1 10 ) (5.4×0.18)×(110×110)
D. ( 5 . 4 × 0 . 18 ) × ( 1 10 × 1 100 )
Answers
5.4 x 0.18 can be expressed as [tex](54 * 18) * (1/10 * 1/10)[/tex], where each 1/10 returns the decimal point stripped from 5.4 and 0.18 initially. So the correct answer is option B.
Explanation:The appropriate approach to solving this question is by acknowledging how numbers with decimal points function on multiplication. To express 5.4 x 0.18 in another form, we can take the decimal points away and multiply the resultant figures, 54 and 18. Then, we introduce the decimal points back using fractions equivalent to 0.1 and 0.01 (that is, 1/10 and 1/100, respectively). Hence, the correct equivalent is option B: [tex](54 * 18) * (1/10 * 1/10).[/tex] The 1/10 accounts for the decimal in 5.4, and the other 1/10 accounts for the decimal in 0.18.
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Mary made $126 for 7 hours of work
At the same rate, how much would she make for 18 hours of work?
Answers
126 divided by 7 = 18
18*18 = 324
What is the measure of angle a
Answers
Here 110 and A are "straight angles," and so 110 + A = 180 (degrees).
Then A = 70 degrees.
Answer:
m∠A = 70°
Step-by-step explanation:
The given figure is nothing but parallel lines cut by a transversal.
We use property of transversal to find the value of angle A.
Here ∠A and 110° are pair of interior angles on the same side.
The pair of interior angles on the same side add upto 180 degrees.
Therefore, ∠A + 110 = 180
Subtract 110 from both sides, we get
∠A + 110 - 110 = 180 -110
∠A = 70°
m∠A = 70°
Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. the students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. researchers found that visually impaired students averaged 8.14 hours of sleep, with a standard deviation of 1.78 hours. assume that the number of hours of sleep for these visually impaired students is normally distributed.