Mathematics College

Juan and his children went into a movie theater and he bought $52.50 worth of bags of popcorn and pretzels. Each bag of popcorn costs $7.50 and each pretzel costs $3.75. He bought 5 more pretzels than bags of popcorn. Graphically solve a system of equations in order to determine the number of bags of popcorn, x,x, and the number of pretzels, y,y, that Juan bought.

Answers

Answer 1

Answer:

Juan bought 3 bags of popcorn and 8 bags of pretzel

Step-by-step explanation:

Given

$x = popcorn$

$y = pretzels$

$Amount = \$52.50$

Required

Solve graphically

First, we need to represent the cost as an equation.

If popcorn costs 7.50 per bag and pretzel costs 3.75 per bag

The cost is then represented as:

$7.50x + 3.75y = 52.50$

Next, we represent the quantity as an equation.

Bags of pretzel is 5 more than bags of popcorn

The quantity is then represented as:

$y = x + 5$

At this stage, we have:

$7.50x + 3.75y = 52.50$

$y = x + 5$

See attachment for graph

$7.50x + 3.75y = 52.50$ is represented by the $green\ line$ while the $blue\ line$represents $y = x + 5$

At the point of intersection of both lines, we have:

$(x,y) = (3,8)$

This implies that;

Juan bought 3 bags of popcorn and 8 bags of pretzel

Juan And His Children Went Into A Movie Theater And He Bought $52.50 Worth Of Bags Of Popcorn And Pretzels.

Related Questions

plz help me ASAP PLZ

Answers

Answer:

Supplementary angles add to 180 degrees.

Angles of a triangle add to 180 degrees.

So, the angles of this triangle are 2x, 3x, and 70.

This means we can have the equation: 5x+70=180, and 5x=110, meaning that x=22

Let me know if this helps!

Answer:

Step-by-step explanation:

So first things first we want to find the angle on the bottom right

That angle is supplementary to the one that is equal to 110 meaning that together they will add up to equal 180

180-110=70

We know that the angles of a triangle will add up to equal 180 so we set up an equation

180=70+2x+3x and solve for x

step 1 combine like terms

2x+3x=5x now we have

180=70+5x

step 2 subtract 70 from each side

180-70=110

70-70 cancels out

now we have

110=5x

step 3 divide each side by 5

110/5=22

5/5 cancels

x=22

so we can conclude that x=22

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Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3

Answers

The equivalent exponential equations are given as follows:

$2^{4x} = 2^{3(x - 3)}$

How to obtain the equivalent exponential expression?

The exponential expression for this problem is defined as follows:

$2^{4x} = 8^{x - 3}$

The number eight is the third power of 3, that is:

8 = 2³.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:

$8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}$

Meaning that the correct option is given by the fourth option.

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Find a primitive Pythagorean triplet (a, b, c) where c=a+50.

Answers

Answer:

Pythagorean triple (PT) can be defined as a set of three positive whole numbers that perfectly satisfy the Pythagorean theorem: a2 + b2 = c2.

theorem: a2 + b2 = c2.

This set of numbers are usually the three side lengths of a right triangle. Pythagorean triples are represented as: (a, b, c), where, a = one leg; b = another leg; and c = hypotenuse.

There are two types of Pythagorean triples:

Primitive Pythagorean triples

Non-primitive Pythagorean triples

Primitive Pythagorean triples

A primitive Pythagorean triple is a reduced set of the positive values of a, b, and c with a common factor other than 1. This type of triple is always composed of one even number and two odd numbers.

For example, (3, 4, 5) and (5, 12, 13) are examples of primitive Pythagorean triples because each set has a common factor of 1 and also satisfies the

Step-by-step explanation:

Pythagorean theorem: a2 + b2 = c2.

(3, 4, 5) → GCF =1

a2 + b2 = c2

32 + 42 = 52

9 + 16 = 25

25 = 25

(5, 12, 13) → GCF = 1

a2 + b2 = c2

52 + 122 = 132

25 + 144 = 169

169 = 169.

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20. Find the unknown angle measures.
51°
53°

Answers

The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

Finding the unknown angle measures.

From the question, we have the following parameters that can be used in our computation:

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

Answers

h(x)=2x-3
h(4)=2(4)-3=5
h(0)=2(0)-3=-3
h(-2)=2(-2)-3=-7
h(2)=2(2)-3=1
h(3)=2(3)-3=3
h(5)=2(5)-3=7

This graph shows a proportional relationship.
What is the constant of proportionality?

Answers

The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Convert the following equation into standard form: y=7/3x-10

Answers

Answer:

7/3x -y = 10

Step-by-step explanation:

do you want an explanation?

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Joyce paid $44.00 for an item at the store that was 60 percent off the original price. What was the original price?

Answers

Answer: 64

Step-by-step explanation: Joyce paid $64 for an item that was 60% off the original sale price. What was the original sale price? let x be the original sale price x(1-0.6) = 64

Answer:

Step-by-step explanation:

If Joyce paid $44.00 for an item that was 60% off the original price, then she paid only 40% of the original price. Let the original price be denoted by x.

40% of x can be expressed as (40/100)x, which simplifies to 0.4x.

We can set up the equation:

0.4x = 44

Solving for x, we divide both sides by 0.4:

x = 110

Therefore, the original price of the item was $110.

geomtry plzzz help 15 points

Answers

Answer:

Step-by-step explanation:

they give you xz, and they want half, so just divide 38 by 2

How to solve then length for h? Image below, please help

Answers

The length of h in the given figure is 25 cm.

In order to solve for the length of h in the given figure, we can make use of the Pythagorean theorem.

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite to the right angle) is equal to the sum of the squares of the other two sides

Let us label the three sides of the right triangle in the given figure:

a = length of side AB = 15 cmc = length of side BC = 20 cmh = length of side AC = ? cm

We know that the angle BAC is a right angle, so we can apply the Pythagorean theorem to solve for h.

According to the theorem:

h² = a² + c²h²

= (15)² + (20)²h²

= 225 + 400h²

= 625

Taking the square root of both sides, we get:h = 25

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Solve for x 3x+wx=20

Answers

Answer:

X=$\frac{20}{3+w}$

Step-by-step explanation:

We are to solve for x by factorizing the given expression

The value of x is $ \frac{20}{ 3 + w} $

Given:

3x + wx = 20

factorize

3x + wx = 20

x(3 + w) = 20

Divide both sides by 3+w

x = $ \frac{20}{ 3 + w} $

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Find the average rate of change for the function f(x)=3x+17
Using the intervals of x=3 to x=6

Show ALL your work to receive credit

Answers

Answer: what unit is this?

Step-by-step explanation:yeah I’ll need the unit to solve this question

which is the estimate quotient for 530÷9

Answers

59 ......................................................

Answer:

Step-by-step explanation:530 would be rounded to 550 and 9 would be rounded to 10

550 divided by 10 is 55

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I BELIVE ITS SINE BUT I NEED A SECOND OPINON
IM SO CONFUSED!! DUE SOON PLEASE HELP BEEN STUCK ON THIS FOREVER!
QUESTION DOWN BELOW!
MANY THANK!!

Answers

You're answer is (A) The cosine law only

What is the cosine law?

Law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.

Answer: The correct answer is (#1) the cosine law only.

Step-by-step explanation: Confirmed correct.

Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

Answers

The true statements about the circle are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

How to determine true statements about the circle?

Given: the equation is x²+y²–2x–8 = 0

In order to determine true statements about the circle, we have to rewrite the given equation and compare it with the standard form of the equation of a circle.

The standard form of the equation of a circle is

(x-a)² + (y-b)² = r²

where (a, b) is the center and r is the radius

using the completing square method on the given equation:

x²+y²–2x–8 = 0

x²-2x + (-1)² + y² + (0)²= 8 + (-1)²

(x-1)² + (y-0)² = 9

(x-1)² + (y-0)² = 3²

Thus, the center is (0, 1) and the radius is 3

Therefore, the options are the radius of the circle is 3 units, the center of the circle lies on the x-axis and the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

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Give both answers
Give both answers

Answers

Answer:

$\hat u = < -0.9439,-0.3303 >$

Step-by-step explanation:

To find the direction in which the maximum rate of change occurs for the function f(x,y)=2xsin(xy) at the point (1, 3), we need to find the gradient vector and normalize it to obtain a unit vector.

The gradient vector of a function f(x,y) is given as:

$\nabla f(x,y)=\Big < \dfrac{\partial f (x,y)}{\partial x},\dfrac{\partial f (x,y)}{\partial y} \Big >$

Taking the partial derivatives.

$\dfrac{\partial f}{\partial x} = 2\sin(xy)+2xy\cos(xy)\\\\\\\\\dfrac{\partial f}{\partial y} = 2x^2\cos(xy)$

Evaluate these at the point (1,3).

$\dfrac{\partial f}{\partial x}(1,3) = 2\sin((1)(3))+2(1)(3)\cos((1)(3))\\\\\\\ \Longrightarrow \boxed{\dfrac{\partial f}{\partial x}(1,3) =2\sin(3)+6\cos(3)}\\\\\\\\\dfrac{\partial f}{\partial y}(1,3) = 2(1)^2\cos((1)(3)) \\ \\ \\ \Longrightarrow \boxed{\dfrac{\partial f}{\partial y}(1,3) = 2\cos(3)}$

Thus, we have:

$\nabla f(1,3)=\Big < 2\sin(3)+6\cos(3), \ 2\cos(3) \Big >$

To obtain the unit vector in the direction of maximum rate of change, we need to normalize the gradient vector:

$\hat u =\dfrac{ \nabla f(1,3)}{||\nabla f(1,3)||}\\\\\\\\\Longrightarrow \hat u = \dfrac{\Big < 2\sin(3)+6\cos(3), \ 2\cos(3) \Big > }{\sqrt{(2\sin(3)+6\cos(3))^2+(2\cos(3))^2} } \\\\\\\\\Longrightarrow \hat u =\dfrac{ < -5.6577,-1.9800 > }{5.9942} \\\\ \\\\\therefore \boxed{\boxed{\hat u = < -0.9439,-0.3303 > }}$

Thus, the problem is solved.

a gift shop sells walnuts in three fourth pond bags . Ann wants to buy enough to have 4 pounds of walnuts. How many 3/4 pound bags will she need to buy?

Answers

Answer: 4 pounds is equal to 16 four-ounce (1/4 pound) increments.

To find the number of 3/4 pound bags Ann needs to buy, we can convert 16 four-ounce increments to three-fourth pound increments:

16 four-ounce increments = 16 x 4 = 64 ounces

64 ounces = 64/16 = 40 three-fourth pound increments

Therefore, Ann will need to buy 40 bags of walnuts, each weighing 3/4 of a pound.

Step-by-step explanation:

answer this whats 12*12

Answers

Answer:

144

Step-by-step explanation:

Answer:

12*12

Is 12 x 12

And 12 x 12 = 144

You are welcome :)

Which point is represented by 6 times the quantity cosine 11 pi over 6 plus i times sine 11 pi over 6 end quantity question mark

Answers

$6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}$

The cost of a newspaper subscription
includes a discounted initial week. Beatriz
pays $55 for 7 weeks of the newspaper
subscription and $100 for 12 weeks.

Answers

As a result, the original discounted price is $1 while the weekly normal price is $9.

How does arithmetic work with discounts?

The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.

From the given information, we have:

d + 6x = 55 (discounted price for 7 weeks)

d + 11x = 100 (discounted price for 12 weeks)

We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:

5x = 45

Dividing both sides by 5, we get:

x = 9

Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:

d + 6(9) = 55

d + 54 = 55

d = 1

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Please help ASAP!!! Thank you so much!!! Just want confirm my answer and it is A) -5. Consider the function f(x)= $x^{3}$ +4$x^{2}$-25x-50. (x^3+4x^2-25x-50). If there is a remainder of 50 when the function is divided by (x-a) what is the value of a? A) -5 B) -2 C)-3 D)

Answers

Answer:

Correct is A

Step-by-step explanation:

Correct is A , notice that when you perform synthetic division you get that the reminder is 50, please refer to the image I attach to see it.

Please help ASAP!!! Thank you so much!!! Just want confirm my answer and it is A) -5. Consider the function

Sally has made a cake (as shown on the right) and frosted the top and all sides but not the bottom of the cake. She cuts the cake into 9 pieces. How many pieces are frosted on only one side?

Answers

There are a total of 8 pieces on the outer edge with only one frosted side.

We have,

If Sally has frosted the top and all sides but not the bottom of the cake, then each piece will have one frosted side (the top) and three unfrosted sides (the bottom and two sides).

Out of the 9 pieces, only the pieces on the outer edge will have exactly one frosted side.

If we count the number of pieces on the outer edge, we can determine how many pieces are frosted on only one side.

For a cube-shaped cake, there are 8 pieces on the outer edge.

To see why, imagine slicing off the corners of the cube to create a smaller cube inside.

Each of the 6 faces of the smaller cube will have a piece missing from the corner.

Therefore, there are 6 pieces on the outer edge of the larger cube, and each of these pieces can be divided into two smaller pieces (with one frosted side each) by cutting along the diagonal.

This gives a total of 12 pieces, but we need to subtract the 4 corner pieces that have two frosted sides each.

So there are a total of 8 pieces on the outer edge with only one frosted side.

Therefore,

There are a total of 8 pieces on the outer edge with only one frosted side.

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