Hector is mixing fruit punch in a 40-cup punch bowl for a party. He plans to
add at least 24 cups of fruit juice to the bowl before adding ginger ale.
Identify the graph that represents the amounts of fruit juice and ginger ale he
can use, and then identify a valid solution. (The graph shows the overlapping
solution region only, not the shading for each inequality.)
Answers
The graph that represent the amounts of fruit juice and ginger ale he can use, and the valid solution is: A. valid solution (28, 8).
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of cups of fruit juice and number of hours clearing tables respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of cups of fruit juice.Let the variable y represent the number of cups of ginger ale.Since Hector is mixing fruit punch in a 40-cup punch bowl for a party, an inequality which models this situation is given by:
x + y ≤ 40.
Additionally, Hector plans to add at least 24 cups of fruit juice to the bowl before adding ginger ale:
x ≥ 24.
Based on the graph (see attachment), we can logically deduce that a valid solution to the given system of inequalities is the overlapping solution region, which is given by the ordered pair (28, 8).
Read more on inequality here: brainly.com/question/28748540
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Related Questions
How many gallons of a 20% antifreeze solution and a 15% antifreeze solution must be mixed to obtain 30 gal of a 18% antifreeze solution? Round to the nearest gallon
Answers
Answer:
20% antifreeze solution = 18 gal
15% antifreeze solution = 12 gal
Step-by-step explanation:
Let
20% antifreeze solution = x
15% antifreeze solution = y
x + y = 30
0.20x + 0.15y = 30 * 0.18
0.20x + 0.15y = 5.4
x + y = 30 (1)
0.20x + 0.15y = 5.4 (2)
From (1)
x = 30 - y
Substitute x = 30 - y into (2)
0.20x + 0.15y = 5.4 (2)
0.20(30 - y) + 0.15y = 5.4
6 - 0.20y + 0.15y = 5.4
- 0.20y + 0.15y = 5.4 - 6
-0.05y = -0.6
y = -0.6/-0.05
y = 12 gal
Substitute y = 12 into (1)
x + y = 30 (1)
x + 12 = 30
x = 30 - 12
x = 18 gal
20% antifreeze solution = 18 gal
15% antifreeze solution = 12 gal
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3,0) and (5, -3)
Answers
Identify the exponential function for the given graph.
A)
f(x) = (şs* +2
f(%) (şyx - 2
f(x) = (-3;* + 2
f(x) = (–33* - 2
9.
D)
Answers
Answer:
Step-by-step explanation:
C - 3(2^x).
⅕m - 12 = -32
could someone solve this
Answers
Answer:
m = -100
Step-by-step explanation:
(1/5)m -12 = -32
add 12 on both sides
(1/5)m = -20
multiply both sides by 5
m = -100
Answer:
m = -100
Step-by-step explanation:
So in order to solve this equation we are going to have to convert 1/5m to a decimal, this will make it easier to solve the equation:
1/5m = 0.2m
Next we are going to take our 0.2m and place it within the equation where 1/5m is:
⅕m - 12 = -32 or 0.2m - 12 = -32
So now we are going to add 12 to both sides of the equal sign in the equation to segregate the 0.2m within the equation:
0.2m - 12 = -32 or 0.2m + (-12 + 12) = (-32 + 12)
making the equation look like this:
0.2m = -20
now we are going to divide 0.2 from both 0.2m and -20 to get the value of m:
0.2m/0.2 = -20/0.2
Thus getting the answer:
m = -100
So how do we know that -100 is the value of m? well we check our work of course by substituting -100 in place of m!
⅕(-100) - 12 = -32 or 0.2(-100) - 12 = 32
0.2(-100) - 12 = 32
-20 - 12 = -32
-32 = -32
What is the value of the expression 11 - (34.48?
1) 3
O2) 5
O 3) 8
4) 9
Answers
Answer:
-23.48
Step-by-step explanation:
Hoped this helped!!
If A = 56° then find C.
Answers
Answer:
124
Step-by-step explanation:
If you are talking about angles, then the answer is 124 degrees. Question is a little open, though.
I hope this helps!
uM ANY help pls?
Hopely someone can help!
Answers
Answer:
He made 35% of his shots he did not make 65& of his shots
Step-by-step explanation:
7/20=35%, 20/7=65%
I need an explanation for the problem 4v2=-12v-9. I don't understand why it factors into 4v+3 and 4v+3
Answers
Answer:
The factors are [tex]2v+3,2v+3[/tex].
The factors are not [tex]4v+3,4v+3[/tex]
Step-by-step explanation:
Equation is [tex]4v^2=-12v-9[/tex].
This equation can be written as follows:
[tex]4v^2+12v+9=0[/tex]
Here,
[tex]12v=6v+6v[/tex]
Therefore,
[tex]4v^2+6v+6v+9=0\\2v(2v+3)+3(2v+3)=0\\(2v+3)(2v+3)=0[/tex]
So, the factors are [tex]2v+3,2v+3[/tex].
The factors are not [tex]4v+3,4v+3[/tex]
Amy and Darren each solved the following system of equations using a different method
y=0.5x + 1
4x -2y=4
Is either of them correct? Explain your reasoning and give the correct solution to the system.
Answers
Answer:
what is
Step-by-step explanation:
the the 3 4 4
Find the bank discount and proceeds using ordinary interest for a loan to michelle anders for 7,200 at 8.25% annual simple interest from august 8 to november 8
Answers
Answer:
$145.5
Step-by-step explanation:
Period, t = August 8.to November 8 = 3 months
Simple interest formula :
A = P(1 + rt)
A = final amount =. 7200
7200 = P(1 + (0.0825 * 3/12))
7200 = P(1 + 0.020625)
7200 = P(1.020625)
7200 = 1.020625P
P = 7200 / 1.020625
P = 7054.5009
Bank discount :
A - P
7200 - 7054.5009
= $145.4991
= $145.5
What is the conjugate of
(-5 + 4i)?
Answers
Answer:
the answer to that is -1i
Step-by-step explanation:
cause if you add negative and positve you get to subtract it and get the sign of the highest number
AI need help with this math homework ASAP I need the independent variable the dependent and the equation
Answers
Answer:
b is the independent variable
c is the dependent variable
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
A set of 25 two digit numbers are listed below 10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98. What is the probability of the sum of the number's digits is odd?
Answers
Answer:
0.48
Step-by-step explanation:
Given the data:
X:
10,17,20,23,24,28,32,39,42,25,26,52,55,58,61,65,66,72,75,78,79,85,94,97,98
Sum of each of the numbers :
1, 8, 2, 5, 6, 10, 6, 12, 6, 7, 8, 7, 20, 13, 7, 11, 12, 9, 12, 15, 16, 13, 13, 16, 17
Probability that sum of the number's digit is odd:
Number of odd sum / total numbers
Number of odd sum = 12
Total numbers = 25
12 / 25
= 0.48
In the number 8246315 what sigit is in the ones place
Answers
Answer:
5
Step-by-step explanation:
The ones place is the one most to the right that isn't after a decimal point.
Answer:
5, since it is all the way to the right
Step-by-step explanation:
if you ever have a big number, the number in thes ones place is ALWAYS on the far right, except if its a decimal !
i hope this helps !! :D
The area of circle can be expressed by the
formula A = ar?where r is a radius of circle.
express radius in terms of area of circle.
Answers
9514 1404 393
Answer:
r = √(A/π)
Step-by-step explanation:
Solve for r. Do this by dividing by the coefficient of the r² term, then taking the square root.
A = πr²
A/π = r²
r = √(A/π)
y-2=1/2(x-4) in slope intercept form
Answers
Answer:
y = 1/2x
Step-by-step explanation:
y - 2 = 1/2 (x-4)
y = 1/2x - 2 + 2
y = 1/2x
(The y - intercept is 0 because -2 and 2 cancels each other out)
Hope this helps :)
Let me know if there are any mistake!!
The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be
⇒ y = 1/2x
What is equation of line?
The equation of line in slope intercept form is defined as;
y = mx + b
Where, 'm' is slope of line and 'b' is y-intercept.
Given that;
The equation of line is;
y - 2 = 1/2 ( x - 4 )
Now,
We can change the equation of line in slope intercept form as,
y - 2 = 1/2 ( x - 4)
Solve as;
y - 2 = 1/2 x - 1/2 × 4
y - 2 = 1/2 x - 2
Add 2 both side,
y - 2 + 2 = 1/2 x - 2 + 2
y = 1/2 x
Thus, The slope intercept form of the equation y - 2 = 1/2 (x - 4) will be;
⇒ y = 1/2x
Learn more about the equation of line visit:
https://brainly.com/question/18555692
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PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
$67
Step-by-step explanation:
So 5x12+7=C
PEDMAS so:
5x12 = 60
60+7 = 67
67 = C
Find The Area of the parallelogram...
Answers
Answer:
162 ft^2
Step-by-step explanation:
the formula for finding the area of a triangle is [tex]\frac{b*h}{2}[/tex]
the base is 27 and the height is 12
[tex]\frac{27*12}{2}=\frac{324}{2} = 162[/tex]
(27 X 12)/2 = 324/2 = 162ft^2
Gabriella made 5 waffles for breakfast. She has 25 strawberries and 15 blueberries to put on top of the waffles. She will put a equal number of berries on each waffle.How many berries will gabrielle put on each waffle?
Answers
in each diagram, BD bisects
Answers
Answer:
26. ∠ABC=44
27. ∠ABC=86
28. ∠ABC=116
Step-by-step explanation:
Since BD bisects ∠ABC in each diagram, ∠ABD=∠DBC.
26.
∠ABD=∠DBC
5x+2=7x-6
2x=8
x=4
∠ABC=∠ABD+∠DBC
=5(4)+2+7(4)-6
=20+2+28-6
=44
27.
∠ABD=∠DBC
11x-12=8x+3
3x=15
x=5
∠ABC=∠ABD+∠DBC
=11(5)-12+8(5)+3
=55-12+40+3
=86
28.
∠ABD=∠DBC
9x-23=5x+13
4x=36
x=9
∠ABC=∠ABD+∠DBC
=9(9)-23+5(9)+13
=81-23+45+13
=116
The results of the first 100 students who voted are represented in the table. There are still 50 more students left to vote. Based on the early results, how many MORE votes do you expect Dan to get out of the 50 late voters?
Answers
Answer:
1-50
Step-by-step explanation:
, describe how a translation is different from a rotation.
Answers
Answer:Rotation is rotating an object about a fixed point without changing its size or shape. Translation is sliding a figure in any direction without changing its size, shape or orientation.
Step-by-step explanation:
Need answer pizza ???
Answers
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Surface areas and Volumes.
Since, we know that the lateral area of a Right circular cone is given as,
AL = πrl
here, l = slant height , r = radius of the circular base.
so now, we have to find first slant height to get the lateral surface area,
[tex]l \: = \sqrt{ {r}^{2} + {h}^{2} } [/tex]
here, r = 8 cm and h = 15,
hence,
[tex]l \: = \sqrt{64 + 225} = \sqrt{289} = 17cm[/tex]
hence, now we apply the formula,
AL = π(8) (17) cm^2
===> AL = 136 π cm^2
-3y>x+6 I need help w this math problem
Answers
Answer:
y< −x/3 −2
Step-by-step explanation:
I hope this is what you need if not let me know and ill edit the answer
Who ever get it right I will give Brainly thx u
Answers
It be 12 cause from the smaller one 2*4 would = to 8 and 5*4 also = to 20 so 3*4 = to 12.
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Use the definitions and theorems of this section to evaluate and simplify the following expression. Be sure to express answers with positive exponents.
(b^4)2
Answers
Answer:
[tex](b^4)^2 = b^{8}[/tex]
Step-by-step explanation:
Given
[tex](b^4)^2[/tex]
Required
Simplify
In indices, we have:
[tex](a^m)^n = a^{m*n[/tex]
So:
[tex](b^4)^2 = b^{4*2}[/tex]
[tex](b^4)^2 = b^{8}[/tex]
Find the slope of the line through the given points (4,-2),(-1,8)
Answers
Answer:
[tex]\displaystyle m=-2[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Slope Formula: [tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (4, -2)
Point (-1, 8)
Step 2: Find slope m
Simply plug in the 2 coordinates into the slope formula to find slope m
Substitute in points [Slope Formula]: [tex]\displaystyle m=\frac{8+2}{-1-4}[/tex][Fraction] Add/Subtract: [tex]\displaystyle m=\frac{10}{-5}[/tex][Fraction] Divide: [tex]\displaystyle m=-2[/tex]there are 5 red marbles, 7 green marbles, 4 black marbles, and 8 blue marbles in a bag. Find P(not yellow
Answers
Total number of Marbles is = 5 + 8 + 7 = 20
Total number of non-red marbles = 5 + 7 = 12.
P( Not yellow) 12/20 = 3/5.
The answer is 3/5.Answer:
3/5
Step-by-step explanation:
Which Triangle appears to be both right and isosceles?
Answers
Answer: B
Step-by-step explanation: An isosceles right triangle is an isosceles triangle and a right triangle. This means that it has two congruent sides and one right angle. Therefore, the two congruent sides must be the legs.
B
Step By Step Explanation:
The corner of the triangle is at 90 degrees making it a right angle. Both legs are congruent and has corresponding angles.
15x=12x+15 whats the angle measures.
Answers
Answer:
x = 5 (please read the step by step explanation)
Step-by-step explanation:
So, I'm just going to solve for x because the instructions aren't too clear. I believe there is supposed to be an image attached to it, but seeing as I don't have that, I'll just solve for x and you can plug in with the values.
15x = 12x + 15
Same to both sides:
3x = 15
Isolate x:
x = 5
Just plug in those values and you'll be good to go! Have a good day!