who was often called the father of modern mathematics because he created analytic geometry and the cartesian coordinate system?

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:

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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the height of the box is 9 inches

Answer:

solution given:

total surface area of a box=160 square inches

let length, width, and height be l,b, and h respectively.

according to the question:

l=2b

∴b =[tex]\frac{l}{2}[/tex]

l=h-4

∴ h=l+4

we have

total surface area of a box=160 square inches

2(lb+lh+bh)=160

[tex]2(l*\frac{l}{2}+l(l+4)+\frac{l}{2}*(l+4))=160[/tex]

[tex]2*\frac{l^2+2l^2+8l+l^2+4l}{2}=160[/tex]

[tex]4l^2+12l=160[/tex]

[tex]4(l^2+3l)=160[/tex]

[tex]l^2+3l=\frac{160}{4}[/tex]

[tex]l^2+3l-40=0[/tex]

doing middle term factorization

[tex]l^2+(8-5}l-40=0[/tex]

[tex]l^2+8l-5l-40=0[/tex]

taking common from each two terms

l(l+8)-5(l+8)=0

(l+8)(l-5)=0

either

l=-8[neglected as length is always positive]

or

l=5

now

b=[tex]\frac{5}{2} =2.5[/tex]

h=5+4=9

Step-by-step explanation:

Answer:

-5/4

Step-by-step explanation:

4x-5y=10

-5y=-4x-10

-5y/-5=-4/-5-10/-5

y=4/5+2

perpendicular slope is -5/4

Answer:

B.  y = -2x-25 These lines will intersect

Step-by-step explanation:

y = 2x+25  Which line has one solution to this equation:

A.  y = 2x+25   [This is the same line!  The solutions are infinite.]

B.  y = -2x-25 [These lines will intersect.  They'll meet at the corner of -12.5th and Zero streets (-12.5,0)]

C.  y = 2x-25  [Same slope, 2.  They, also, will never meet.  Pity]

D.  y = 2x [OMG.  Didn't parallel lines ever get the message.  Get with the slope and focus on the bliss of intersection.]

===============

[Extra Credit]

y = 2x + 25

y = –2x – 25

-----------

y = 2x + 25

y = -2x - 25

2y =  0

y = 0

--

y = 2x + 25

0 = 2x + 25

2x = -25

x = -12.5

The single solution is (-12.5,0)

If system of two linear equations has one solution. One of the equations is y = 2x + 25 then y = –2x – 25 is the other equation.

Two or more expressions with an Equal sign is called as Equation.

A system of two linear equations has one solution.

One of the equations is y = 2x + 25

We need to find the other equation which has one solution

y = 2x+25  

This is the same line

The solutions are infinite.

y = -2x-25

These lines will intersect.

The other equation is y = –2x – 25 because this equation is interacting with y = 2x + 25

Hence, if system of two linear equations has one solution. One of the equations is y = 2x + 25 then y = –2x – 25 is the other equation.

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Answer:

arc MP = 88°

Step-by-step explanation:

The measure of the inscribed angle MQP is half the measure of its intercepted arc MP , then

arc MP = 2 × ∠ MQP = 2 × 44° = 88°

Answer:

55

Step-by-step explanation:

As you can see, the length of the outer angle is 125. So, 180 - 125 = 55.

Answer:

(0,-2)

Step-by-step explanation:

Answer:

1. yes, both lines are straight

2. domain: (-∞ ∞)

3. range: (-∞ ∞)

Answer:

6.5 x 10^(-7)

Step-by-step explanation:

When multiplied by 10, it is like multiplying by 10^1. We can use the exponent rule: 10^(-8) * 10^1 = 10^(-7).

Example:

1.3 x 10^2 multiplied by 10

This is the same as 130 multiplied by 10 which is equal to 1300.

1300 written in scientific notation is 1.3 x 10^3, which adds one more onto the exponent.

Answer:

he didnt subtract each equations on both sides

5y-6=4y+1

-4       -4

y  -6=1

  +6=+6

y=7

Step-by-step explanation:

hope that wrk

Answer: C

Pt. C is at coordinate point (2,1)

The distance between A and C is 4 units (or boxes).

Answer:

x=12

Step-by-step explanation:

4x-6+2x=18

2x-6=18

2x=24

x=12

Answer:

For easy way

convert to decimals first

3.5h - 3 (5h - 3.5)

Open brackets

3.5h - 15h + 10.5

Answer = 10.5 - 11.5h

Answer:

39, 44, 48

Step-by-step explanation:

Add 5 to the following terms.

Please mark me as the Brainliest, Thank you!

Answer:

(f-g)(x) = f(x) - g(x)

         = x-3 - (3[tex]x^{2}[/tex])

          = x- 3 - 3[tex]x^{2}[/tex]

domain is all real number

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

Sequence: 1,2,2,4,8,32,256

After the first digit, the repeated pattern for the last digit is  2,2,4,8,2,6

So, the 35 term's final digit will be 8

Answer:

0.1

Step-by-step explanation:

hope this helps

Answer: 0.1 / 0.10

Step-by-step explanation:

since the 2 is lower than 5 - it turns into 0

hope this helped ! :>

Answer:

The story is not clear enough to provide the answer

Step-by-step explanation:

First of all we do not know how many childen are in the Martin Family

[tex]20 \times 8[/tex]

=$160

So depending on how each child sends and how many children will determine which kid will have most of the money left

Answer:

D) r=-0.9

Step-by-step explanation:

Recall that when [tex]|r|[/tex] is closest to 1, the stronger the correlation between the variables. In this case, while [tex]|0.8|=0.8[/tex], [tex]|-0.9|=0.9[/tex] is actually larger and shows a stronger negative correlation between random variables. Therefore, D is correct.

Answer:

$17.30

Step-by-step explanation:

6 (video games) multiplied by $2.25 equals $13.50

or

(2.25 + 2.25 + 2.25 + 2.25 + 2.25 + 2.25) = 13.50

and

1 (DVD) is $3.80

$13.50 + $3.80 = $17.30

$17.30

Answer:

C. w = 4t

Step-by-step explanation:

Let's examine the way t and w are related to each other, one point at a time starting with (0, 0). This point really doesn't tell us much, but we do know that this relationship must be proportional since any line that goes through the origin (the point (0, 0)) is proportional. we can rule out B. 2 + t and D. 4 + t since neither of these go through the origin. 2 + t goes through the point (0, 2) and 4 + t goes through the point (0, 4).

Now, we have two options left: A. w = 2t and C. w = 4t. Which one is correct? Well, let's look at the point (1, 4). 1 × 2 is not equal to 4, but 1 × 4 is equal to 4, so C. w = 4t must be the correct option.

We can test this on the rest of the points as well: 2 × 4 = 8 and 3 × 4 = 12. Hopefully that's helpful! If you have questions or need clarification on anything, let me know. :)

2(4+3)  yw     OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

Answer:

  0.4 kg

Step-by-step explanation:

A proportion can be used to find the amount of sugar.

  x/(1.1 L) = (0.1 kg)/(0.275 L)

  x = (1.1)(0.1)/0.275 kg = 0.4 kg

Angela needs 0.4 kg of sugar for her biscuits.

Answer:

y = 2x - 4.

Step-by-step explanation:

2x - y = 4

Subtract 2x from both sides

- y = -2x + 4

Multiply both sides by -1:

y = 2x - 4.

Answer:

y=-2x+4

Step-by-step explanation:

2x-y=4  -  move the 2x to the right side by subtracting 2x from both sides

2x - y = 4

-2x       -2x =

-y=-2x+4  -   negative variable turns into y, since the negative isn't relevant

y=-2x+4

Answer:

It would be y=0.5x+1

Step-by-step explanation:

1/2 is the x which is the slope and it starts at 1 so that is the the y-intercept