Taking into account the definition of a system of linear equations, the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.
A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
In this case, a system of linear equations must be proposed taking into account that:
x: price of each bag of popcorn. y: the price of each pretzel.On one hand, Julia went into a movie theater and bought 2 bags of popcorn and 5 pretzels, costing a total of $37.25. This is expressed by 2x+5y= 37.25
Zoe went into the same movie theater and bough 8 bags of popcorn and 9 pretzels, costing a total of $102.25. This is expressed by 8x+9y=102.25
So, the system of equations to solve is:
[tex]\left \{ {{2x+5y=37.25} \atop {8x+9y=102.25}} \right.[/tex]
There are various methods to solve a system of equations, it is decided to solve by the substitution method, which consists of solving one of the two variables in one of the equations of the system and substituting its value in the other equation.
So, isolating the variable x from the first equation:
2x+5y= 37.25
2x= 37.25 - 5y
x= (37.25 - 5y)÷2
x= 18.625 - [tex]\frac{5}{2}[/tex]y
Replacing in the second equation:
8×(18.625 - [tex]\frac{5}{2}[/tex]y)+9y=102.25
Solving:
8×18.625 - 8×[tex]\frac{5}{2}[/tex]y+9y=102.25
149 - 20y + 9y=102.25
149 -11y= 102.25
-11y= 102.25-149
-11y= -46.75
y= (-46.75)÷ (-11)
y= 4.25
Finally, replacing in x= 18.625 - [tex]\frac{5}{2}[/tex]y and solving you get:
x= 18.625 - [tex]\frac{5}{2}[/tex]×4.25
x= 18.625 - 10.625
x=8
Remembering that x represents the price of each bag of popcorn and y represents the price of each pretzel, you get that the price of each bag of popcorn is $8 and the price of each pretzel is $4.25.
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Which of the following ordered pairs are solutions to the system of equations below?
Answers:
A.) (3.5, 5.8)
B.) (3.5, -5.8)
C.) (-3.5, -5.8)
D.) (-3.5, 5.8)
The answer is B. 3.5, -5.8
A 12 ounce Starbucks latte costs $3.36. What is the constant of proportionality that relates the cost in dollars, y, to the number of ounces, x, in a Starbucks latte?
Answer:
Y = X times 0.28
Step-by-step explanation:
1. You set it up as a proportionality
12/1 and 3.36/x
The x stands for how much money it takes to get 1 ounce
2. You do the old man line.
12 times x = 3.36 times 1
12x = 3.36
3. Now you divide 3.36 by 12
3.36 divided by 12
.28
4. You insert 0.28 into the problem
12 times 0.28 = 3.36
X = 0.28
So 1 ounce costs $0.28
So Y = X times 0.28
Answer:
Step-by-step explanation:
PLEASE HELP QUESTION IN PICTURE
Answer:
y=4x+5
Step-by-step explanation:
. .. . . . . . .. . .. . so easy
Answer: 7
Step-by-step explanation: if it's so easy, why do you need brainly? (not judging, just confused why you'd waste points)
What is the area of a rectangle with the following measurements:
Answer:
24x^5
Step-by-step explanation:
3 x 8 = 24
x multiplied by x^4 = x^5
(the exponents add to each other when multiplied)
Given that f(x) = 10 - 3x and g(x) = x-3/2 find the value of fg(4)
Answer:
-1
Step-by-step explanation:
(fg)(x) is the product of f(x) and g(x).
We can find (fg)(4) by first finding f(4) and g(4) and then multiplying the results together:
f(x) = 10 - 3x, so f(4) = 10 - 3(4) = -2, and
g(x) = x - 3/2, so g(4) = 4 - 3/2 = 1/2
Then (fg)(4) = (-2)(1/2) = -1
Zack buys some potatoes from a store. The potatoes cost $6.78 for 3 pounds. He wants to buy more vegetables, but at the same price per pound as the potatoes. Which of the following vegetables could Zack buy?
Answer:
well we dont know other vegis are going for each pound is 2.26 but any vegtable thats is going 2.26 per pound works
Step-by-step explanation:
im having a mental breakdown can someone please just do this for me
Answer:
it only changes the magnitude.
for any general a let f(x) be =a|x| , a>0
so for any x say ±3 your function will throw out a×3.
Can someone please give me the (Answers) to this? ... please ...
A man has 25 sweets and his son has 55 sweets.find the number of sweets that the man has to give to his son so that his son would have 4times as many sweets as him.
Answer:
9sweets
Step-by-step explanation:
sweets man has to give to his son=x
mans sweets=25-x
child's sweets=55=x
55+x=4(25-x)
55+x=100-4x
4x+x=100-55
5x=45
x=45/5
x=9
Answer: The man has to give nine sweets for his son to have four times as many sweets as him.
A 26 foot ladder is set against the side of a house so that it reaches up 24 feet. If Mila grabs the ladder at its base and pulls it 12 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 12 ft.) Round to the nearest tenth of a foot.
Answer:
13.9 ft
Step-by-step explanation:
What is another word for change in y
When finding the slope of real-world situations, it is often referred to as rate of change. change in y Rate of change = change in x change in height change in time The average rate of change or a rider between 0 and 5 seconds is —24 ft/s. magnitude relation. Another synonym is "velocity".
Hope this helps
Which expression is equivalent to 24 1/3?
Answer:
2∛3
Explanation:
∛24=(∛8)(∛3)=2∛3
Hopes This Helps :)
One serving of ice cream has 320 calories. If there are 6 servings in the container and you ate of the container, how many calories did you eat?
Answer: You ate 1920 calories
Step-by-step explanation:
It’s pretty simple,
all you have to do is multiply 6 by 320.
this then gets you 1920
Answer:
1920 calories
Step-by-step explanation:
6servings*320cal/servings = 1920cal (servings cancel)
pls answer don’t scam
Answer:
y=x
step by step:
graph equation is y=mx+c
y intercept (c) is 0
gradient (m) is 1
gradient is represented as (m), so the equation is just y=1x, simplified-> y=x
Answer:
money = 2×tickets
Step-by-step explanation:
For 1 ticket sold, $2 is collected. for 8 tickets sold, $16 is collected. The relationship appears to be proportional with a constant of proportionality of $2 per ticket.
The axes are labeled "money" and "tickets", so we can write the equation ...
money = 2×tickets . . . . . where money is in dollars
__
If you like, you can use y to represent dollars collected, and x to represent tickets sold. Then the equation is ...
y = 2x
HELP PLZ I NEED THIS DONE ASAP
[tex]\text{Given that,}\\\\y^2 +9y +3 \\\\\text{when}~ y = -2,\\\\(-2)^2 +9(-2) +3 = 4-18+3 = 7 -18 = -11,[/tex]
I have three bits of tinsel measuring the following: 2.3m, 45cm and 750mm. How long is my tinsel altogether in metres?
Write the equation of the line, in slope-intercept form, with the
following information:
slope:
3
point: (6,-1)
Answer:
y=3x-19
Step-by-step explanation:
y-y1=m(x-x1)
y-(-1)=3(x-6)
y+1=3(x-6)
y=3x-18-1
y=3x-19
7363626x726=???? Helpppppp
Answer:
The answer is 5345992476
Step-by-step explanation:
33 + 55 = __ (3+5)
Help me with this
Answer:
11 I think and hi how are u ::):):):):):):):):):):):):):
Does anybody know how to does this pleaseee helppppp. The first 2 my teacher did them for me but I’m still confused pleaseee helpppp
Answer:
below
Step-by-step explanation:
A triangle can only be a triangle if the two shortest sides add up to be greater than the longest side.
For example on the first one, the segments 1 2 and 3 will not make a triangle as 1 + 2 = 3 and if the two smallest sides of a triangle are equal to the longest side it will not be a triangle at all.
So to make this easy, out of the three numbers given: add the two smallest numbers. This number has to be greater than the third number given, and it cannot be equal.
For question three: 3+9 = 12
And 12 is greater than 11, therefore this can make a triangle.
3. The sum of the second term and the ninth term of an arithmetic sequence is -5. The sum of the third and fourth terms of the same sequence is 7. Find the first term of the sequence.
Answer:
First term of the sequence is [tex]11[/tex]
Step-by-step explanation:
Let [tex]a[/tex] be the first term and [tex]d[/tex] be the common difference
We have
The sum of the second term and the ninth term of an arithmetic sequence is [tex]-5[/tex]
[tex]a+(2-1)d+a+(9-1)d=-5\\\\2a+9d=-5---eqn1[/tex]
The sum of the third and fourth terms of the same sequence is [tex]7[/tex]
[tex]a+(3-1)d+a+(4-1)d=7\\\\2a+5d=7---eqn2[/tex]
eqn 1 - eq2
[tex]4d=-12\\\\d=-3[/tex]
Substituting in eqn 1
[tex]2a+9\times -3=-5\\\\2a=22\\\\a=11[/tex]
First term of the sequence is [tex]11[/tex]
Simplify Simplify 6 - 23 + (-9 + 5) · 2.
Answer:
The answer is −42
What is the perimeter of a rectangle whose length is twice the width? Width = 7 cm.
Answer:
42 cm is the perimeter
Step-by-step explanation:
Brainleast answer mo nalang
Answer:
P = 42 cm
Step-by-step explanation:
The perimeter (P) is the sum of the 4 sides of the rectangle with opposite sides being congruent.
Given width = 7 cm then length = 2 × 7 = 14
P = 7 + 7 + 14 + 14 = 42 cm
can you help me solve 4^3/4^4?
Answer:
64/256
Step-by-step explanation:
4*4*4=64/4*4*4*4=256
20x+10x-8=0 solution set of equation
Answer:
0.2666666666Step-by-step explanation:
20x+10x-8=0
first of all, you will +8 on both sides so there are no negative numbers onany side
20x+10x=8
now gather everything up
30x=8
divide everything by 30 now to get the value of 1x
30x/30=x
8/30=0.2666666666
What is the product? (x 3)(2 x minus 1) 2 x squared minus 3 2 x squared 6 x 2 x squared 5 x minus 3 2 x squared 6 x minus 3.
The product of the function is 2x^2+ 5x - 3
We are to find the product of the functions x + 3 and 2x -1
let f(x) = x+ 3g(x) = 2x - 1Taking the product:
f(x)g(x) = (x+3)(2x -1)
f(x)g(x) = x(2x) - x(1) + 3(2x) + 3(-1)
f(x)g(x) = 2x^2 - x + 6x - 3
f(x)g(x) = 2x^2+ 5x - 3
Hence the product of the function is 2x^2+ 5x - 3
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Answer:
c
Step-by-step explanation:
Samuel has 52 marbles in a bag. Fourteen are red, 13 are green and 25 are blue. If a marble is chosen at random, what is the probability that it is green?
A car is 12 feet long. Levi makes a scale model of the car at 1:8 of its actual size. How long is the model
Answer:
1.5 feet
Step-by-step explanation:
Answer:
1.5 feet or 3/2 feet
Step-by-step explanation:
WILL GOVE 50 POINTS AND BRAINLIEST PLZZZZZZZZZZZZZZZZZ HELP
Examine the diagram of a chloroplast.
Which choice best describes the function of the part labeled B?
enclosed space containing proteins used in ATP formation
membranes enclosing open space
layered stacks of membranes
fluid space that contains DNA, ribosomes, and other enzymes
Answer:
fluid space that contains DNA, ribosomes, and other enzymes
Step-by-step explanation:
B is points towards the "empty" space, meaning its Stroma.
Stroma defintion: involved in the synthesis of organic molecules from carbon dioxide and water or the fluid of the chloroplast surrounding the thylakoid membrane;
Let's look at the answer choices.
A. enclosed space containing proteins used in ATP formation
B. membranes enclosing open space
C. layered stacks of membranes
D. fluid space that contains DNA, ribosomes, and other enzymes
Obviously not C.
A is Synthase.
B is the whole thing.
It is D.
(BTW THIS IS MATH!! Not science!! Just in case you have more questions!)
Answer:
raw
Step-by-step explanation: