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 situation could this graph represent?
a. speed of a car starting from a stop sign and then approaching a stoplight
b. riding your bike slowly up a steep hill and then quickly down the other side
c. total rainfall during a rainy day
d. temperature as the weather changes from rainy to snowy
Answer:
A because the other answer choices are not associated with what is in the graph
what is the y-intercept of y=5?
Answer:
The slope is 0, and the y-intercept is (0,5)
Step-by-step explanation:
I've had this question before.
Answer:
Step-by-step explanation:
y= x+ 5
anybody help please hm
Answer: [tex]2^{21}[/tex]
Step-by-step explanation:
PLEASE HELP!
A park charges $16 for one round of miniature golf and a reduced fee for each additional round played. If Tom paid $51 for 6 rounds of miniature golf, what is the reduced fee for each additional round played?
Which is the better buy 31 once bottle of katchup for $2.53 Or a 64 once bottle for $5.05
Answer:
64 once bottle for $5.05
A store sells four printers for every five computers. The store sells 40 computers on Saturday. How many printers did it sell on Saturday?
Which table could be a partial set of values for a linear function?
Answer:
I think it might be the bottom right one but not sure
someone please help, will give branliest
consider a sequence with the common difference of 5 and whose fiftieth term is 259. what are the first three terms of this sequence?
A- 15,20,25
B- 13,18,23
C- 9,14,19
D- 14-19,24
E- 10,15,20
Greg has entered a cycle race of 125 km. he rides the first 85 km in 2.5 hours. he rides the rest of the way in 2 hours. How much faster did he ride during the first part of the journey compared to the second?
Answer:
He rides 14km/hr faster
Step-by-step explanation:
Speed = distance/ time
In the first part,
Speed= 85/2.5
= 34km/hr
In the second part,
Distance= 125-85
=40km
Speed= 40/2
=20km/hr
How much faster did Greg ride ?
34-20= 14km/hr
Question 2
1 pts
Directions: Include the inequality symbol and solution. If you need less than or equal
to, use "<" and for greater than or equal to use ">".
A taxi charges a flat rate of $7.50 plus an additional $0.35 per mile. If Aliana has at most
$25 to spend on the cab ride, how far could she travel?
She could travel
Answer:
17.85 answer
Step-by-step explanation:
u add the following and the ans u get u take it away from 25
The inequality representing the given statement is 25 ≥ 7.5 + 0.35 x and Aliana can travel a total of 50 miles.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
A taxi charges a flat rate of $7.50 plus an additional $0.35 per mile,
Aliana has at most $25 to spend on the cab ride,
Write the equation as shown below,
The total charges of the taxi = flat rate + rate per mile × number of mile
The total charges of the taxi = 7.5 + x × 0.35
Here, x is the number of miles
The total charge should be equal to $25 or less than $25 then,
25 ≥ 7.5 + 0.35x
Solve for x
0.35x = 25 - 7.5
x = 17.5 / 0.35
x = 50 miles
Thus, she can travel a total of 50 miles.
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pls help
Determine if each pair of ratios is equivalent or not. 6/8 21/36
Answer:
Not
Step-by-step explanation:
6/8 In Simplest Form 3/4
21/36 In Simplest Form 7/12 May Be The Answer Will Be Not Equivalent
Hope To Help!!!
The following circular spinner has 10 sections of equal size. If the spinner is spun twice, what is the probability that the spinner lands on an odd number both times?
Answer:
The chance of anding on A for one spin is 90+45360=38. So the probability of that happening twice in a row is 38×38=964.
Step-by-step explanation:
hope this helps you mark me brinilylist
How i can answer this question?, NO LINKS, if you answer correctly i'll give u brainliest!
Answer:
6t+4
Step-by-step explanation:
Answer:
answer is 6t+4 other person is correct too
Solve for x (thank you!)
5/8 = 21/ (21+y)
there’s the equation, just solve for “y” from there!
hellpppppppppppppppp
Answer:Its probably c
Step-by-step explanation:
Answer:
Future Farmers of America
Step-by-step explanation:
Tamir bought 2 1/2 pounds of fish at $5.50 per pound, and two bananas at the price shown
Answer:
8.50
Step-by-step
Use the figure below to determine the relationship between _DBE and BED
Olivia reads 72 pages in 40 minutes. How many pages can she read per minute?
Answer:
1.8 pages a minute
Step-by-step explanation:
3/5 of a number is 30. What’s the number?
Therefore, the number is 50.
Hoped this helped.
[tex]-BrainiacUser1357-[/tex]
Can someone please take the time out of they’re day and help me with this
Answer:
30 in
Step-by-step explanation:
18^2 + 24^2 = x^2
324 + 576 = x^2
900 = x^2
30 = x
Answer:
30 in
Step-by-step explanation:
With maths problems, first thing to do is to identify clearly the information that you have (from the question) and what you want to find;
Here, we have a right-angle triangle and given 2 of the sides, we are asked to find the other;
Considering this, if you've learnt it well and done plenty of practice, then you should realise pythagoras theorem can be applied to get the unknown side;
The square of the two given sides added will give the square of the unknown side:
(24)² + (18)² = x²
576 + 324 = x²
x² = 900
x = sqrt(900)
x = 30
.pleseee help so important
my answer with solving steps
#CARRYONLEARNING
LOVEUALL
What is the equation of the line that has a slope of 1/5 and a y-intercept of -1
A y = 1/5x — 23/5
B y = 1/5x — 1
C y = 1/5x + 1
D y = 1/5x + 23/5
Answer:
C y = 1/5x - 1
Step-by-step explanation:
Slope intercept form: y = mx + b where m = slope and b = y-intercept.
Substitute into the slope intercept form m= 1/5 and b = -1
y = 1/5x - 1
The diagram shows a square pizza box with side lengths of 12 inches. In the box is a circular pizza with a radius of 5 inches. What is the difference between the area of box and the pizza?
Use π = 3.14 and round your answer to the nearest hundredth.
Nevermind give the points to the another guy
Step-by-step explanation:
the area of the box (as a square) is
side length × side length = side length ²
that is here 12² = 144 in²
the area of a circle is
pi×r²
that is here
pi×5² = pi×25 = 3.14×25 = 78.50 in²
the difference is
144 - 78.5 = 65.50 in²
Find x- and y-intercepts of 4x + 2y = 10
Answer:
Below is the graph
Hope This Helps!!!
Answer:
( 5/2 , 0 ) x- intercept , ( 0 , 5 ) y- intercept
Step-by-step explanation:
To find x- intercept , set y = 0
4x + 2(0) = 10
x = 5/2
To find y- intercept , set x = 0
4(0) + 2y = 10
y = 5
How can i answer this question
Answer: 10g+6h+8
So none of the above I think
Step-by-step explanation:
Answer:
It should be C none of the above
Alejandro uses the steps below to convert StartFraction 5 over 8 EndFraction to a percent. Five-eighths right arrow 8. 0 divided by 5 = 1. 6. 1. 6 = 160 percent. Which best explains Alejandro’s error? The division was computed incorrectly. The division was completed in the incorrect order. The decimal was moved to the right too many times. The decimal was moved to the right instead of the left.
Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100 and it can be determined by using fraction or percentage.
Given that,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
We have to determine,Which best explains Alejandro's error?
According to the question,Alejandro uses the steps below to convert 5/8 to a percent.
8 divided by 5 = 1.6.,
1.6 = 160 percent
The division was computed incorrectly.
The division was completed in the incorrect order. The decimal was moved to the right too many times.
The decimal was moved to the right instead of the left.
Alejandro uses the steps below to convert 5/8 to a percent.
To convert 5/8 into percentages following all the steps given below.
Step1; Firstly 5 is divided by 8,[tex]= \dfrac{5}{8} \\\\ = 0.625[/tex]
Step2; To convert 0.625 into percentage multiplied by 100,[tex]\rm = 0.625 \times 100\\\\= 62.5 \ percent[/tex]
Hence, Alejandro makes an error in the first steps he divides 8 by 5 which is incorrect he has to divide 5 by 8, and in the second step, he does not multiply the term by 100.
For more details about the Equation refer to the link given below.
https://brainly.com/question/18187260
Answer:
Just tell me the letter.
Step-by-step explanation:
Someone please help no need to show work just answer (I will give brainliest)
Answer:
image 1 : 3.78
image 2 : 10.20
Step-by-step explanation:
I haven't done geometry in a bit but I'll try to help!
How do I graph 2x-3?
Please find the surface area of the prism... I will mark you brainliest
Answer:
The surface area = 548 in²
Step-by-step explanation:
The surface Area = 2lw + 2lh + 2wh using l = 10 in, w = 7 in, and h = 12in.
Substitute into the formula and solve
2lw + 2lh + 2wh
= 2· 10·7 + 2· 10 · 12 + 2 ·7 ·12
= 140 + 240 + 168
= 548 in²
Find the equation of the axis of symmetry
for this function.
f(x) = 8x2 + 6x + 19
X=?