If \( y \) varies directly as \( x \) and inversely as \( z \) and \( y=24 \) when \( x=120 \) and \( z=16 \), then what is the value of \( y \) when \( x=4 \) and \( z=15 \) ?

Two families attended a baseball game bought popcorns and souvenir, the cost of each pack of popcorn is $4 and cost of each pack of souvenir is $7.

An expression that depicts the relationship between two or more variables and numbers is called an equation. The provided information can be represented as, using equations:

let x be the price of popcorn and y be the price of souvenir.

First family:

[tex]3x+4y=40[/tex](equation 1)

Second family:

[tex]8x+4y=60[/tex] (equation 2)

We have a system of 2 equations with 2 variables.

3x + 4y = 40

8x + 4y = 60

We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.

from equation 2,

[tex]8x+4y=60\\4y=60-8x[/tex]

divide both sides by 4

[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=15-2x[/tex]

now putting the value of y in equation 1

[tex]3x+4(15-2x)=40\\3x+60-8x=40\\-5x=-20\\x=4\\[/tex]and [tex]y=7[/tex]

Hence, the cost of popcorn is $4 and cost of souvenir is $7.

Learn more about equation at:

brainly.com/question/29174899

#SPJ4

The function that represents an exponential growth would be = f(X) = 0.3 ( 1.05) ^x. That is option C.

An exponential growth of a function is defined as the growth that shows increase rates with respect to a given time.

There are two types of exponential functions: exponential growth and exponential decay.

The function that shows an exponential growth has the formula = f (x) = b^x, when b > 1.

From the examples given in the options above, the correct option that represents the exponential growth is f(X) = 0.3 ( 1.05) ^x. Thai so because 1.05 is greater than 1.

Learn more about growth here:

https://brainly.com/question/25630111

#SPJ1

The correct answer to this question is 7/220. To calculate this answer, divide the number of students who preferred the turkey club (7) by the total number of seventh-grade students (220). The fraction form of this answer is 7/220, the decimal form is 0.0318, and the percentage form is 3.18%.

Proportion is a mathematical concept that compares two values, which can be the same or different, using division. It is used to identify the relationship between two or more values. It can also be used to compare the parts of a whole or to compare two different wholes. Proportions can be expressed as a fraction, a decimal, or a percentage.

This answer can be used to estimate the number of students who preferred the turkey club. To do this, multiply the total number of seventh-grade students (220) by the proportion (7/220). This calculation results in 7 students. In other words, approximately 7 of the 220 seventh-grade students preferred the turkey club.

The proportion 7/220 can also be used to estimate the number of students who preferred the turkey club if the total number of seventh-grade students changes. For example, if the total number of seventh-grade students increases to 250, the estimated number of students who preferred the turkey club can be calculated by multiplying the new total (250) by the proportion (7/220). This calculation results in 8 students.

Therefore, the correct answer to the question is 7/220.

For more questions related to numbers

https://brainly.com/question/28223520

#SPJ1

The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

To calculate the height of the sunflower after 10 weeks, we can use the formula:

=>height = starting height + growth rate * time elapsed

where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.

So the height after 10 weeks would be:

=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches

Therefore, the sunflower would be 30 inches tall after 10 weeks.

To calculate the height after w weeks, we can use the same formula:

=>height = 25 + 0.5 * w

So the height after w weeks would be:

=>height = 25 + 0.5 * w inches

To learn more about expression refer the below link

https://brainly.com/question/112703

#SPJ1

Perimeter would not be used to solve the problem of determining the cost of replacing a linoleum floor with a wood floor. Perimeter is a measure of the boundary of a two dimensional shape, such as a square, rectangle, or triangle. This measure would not be useful in calculating the cost of replacing a floor, as the cost of the flooring materials will depend on the total area of the floor, rather than its perimeter.

Area is the measure of the two dimensional space of a shape, and would be the correct measure to use when calculating the cost of replacing a floor. Area is calculated by measuring the length and width of the floor, then multiplying them together. The cost of the flooring materials can then be calculated by multiplying the area of the floor by the cost of the materials per square foot. This would give an accurate figure for the total cost of the flooring materials.

Know more about Perimeter here

https://brainly.com/question/6465134#

#SPJ11

Answer:

Step-by-step explanation: I don’t know

Answer:

You are distributing (multiplying) the three to all the terms in the parentheses.

Start:

3(x-2) = 4x + 2

Next:

3x - 6 = 4x +2

After that simplify:

-8 = x

Hope this helps!

Answer:

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The property we use,

→ Distributive property.

The equation is,

→ 3(x - 2) = 4x + 2

Then the value of x will be,

→ 3(x - 2) = 4x + 2

→ 3(x) - 3(2) = 4x + 2

→ 3x - 6 = 4x + 2

→ 3x - 4x = 2 + 6

→ -x = 8

→ [ x = -8 ]

Hence, the value of x is -8.

The medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.

To prove that the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC, we can use the following steps:
Draw triangle ABC and label its vertices as A, B, and C.

Find the midpoints of the sides of triangle ABC. Let's call these midpoints D, E, and F.

Draw the medial triangle DEF, connecting the midpoints of the sides of triangle ABC.

We need to prove that the sides of triangle DEF are parallel to the sides of triangle ABC. To do this, we can use the fact that the midpoints of the sides of a triangle divide the sides into two segments of equal length.

Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.

We can also use the fact that if two lines are parallel and the corresponding angles are equal, then the corresponding sides are also parallel.

Since AD = DB and BE = EC, we know that angle ADB = angle BEC and angle BDE = angle CEF.

Therefore, we can conclude that the sides of triangle DEF are parallel to the sides of triangle ABC.

To prove that the sides of triangle DEF are half the length of the sides of triangle ABC, we can use the fact that the   midpoints of the sides of a triangle divide the sides into two segments of equal length.

Since the midpoints of the sides of triangle ABC are D, E, and F, we know that AD = DB, BE = EC, and CF = FA.

Therefore, we can conclude that the sides of triangle DEF are half the length of the sides of triangle ABC.

So, the medial triangle of a given triangle ABC has sides parallel to and half the length of the sides of triangle ABC.

Learn more about Triangle

brainly.com/question/2773823

#SPJ11

Answer:

[tex] - \frac{5x}{34} + 14y + 9[/tex]

Step-by-step explanation:

Just making sure. If the way the equation is written is

[tex]1 + 1 - \frac{5}{34} x + 14y + 7[/tex]

then yeah, that's the answer. If it's formatted differently, send a comment so that I could give you the proper answer.

The roots of equation A are  2 and 0.25.

The roots of equation B are 3.14 and -0.64.

To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation.

For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:

x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8

This gives us two possible values for x:

x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25

Therefore, the roots of equation A are 2 and 0.25.

For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:

x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4

This gives us two possible values for x:

x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64

To know more about quadratic equation click on below link:

https://brainly.com/question/30098550#

#SPJ11

The polyhedron that can be constructed using this net is a triangular pyramid.

A triangular pyramid is a polyhedron that has four faces, with one of the faces being a square and the other three faces being equilateral triangles. The given net shows a square in the center, with three equilateral triangles attached to each of its sides. When the net is folded along the edges, the square becomes the base of the pyramid and the three equilateral triangles become the sides of the pyramid. Therefore, the polyhedron that can be constructed using this net is a triangular pyramid.

Learn about Polyhedron

brainly.com/question/28718923

#SPJ11

The coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0

The coefficient of a term in a polynomial is the number that is multiplied by the variable. The degree of a term is the exponent of the variable. In the polynomial 8x^(2)+6x+8, there are three terms:

- The first term is 8x^(2). The coefficient of this term is 8, and the degree is 2.
- The second term is 6x. The coefficient of this term is 6, and the degree is 1.
- The third term is 8. The coefficient of this term is 8, and the degree is 0 (since there is no variable).

Therefore, the coefficients of the terms in the polynomial are 8, 6, and 8, and the degrees are 2, 1, and 0.

Learn more about Coefficient

brainly.com/question/28975079

#SPJ11

The given operation (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)  expressed in simplest form is x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

To express this operation in simplest form, we need to find the common denominator and combine the numerators.

Find the common denominator. The common denominator of (x-6) and (9x^(3)) is (9x^(3))(x-6).

Multiply each fraction by the common denominator to get the same denominator for both fractions.

(x²-11x+30)/(x-6) * (9x³)/(9x³) = (9x³)(x²-11x+30)/(9x³)(x-6)

(x²-12x+35)/(9x³) * (x-6)/(x-6) = (x-6)(x²-12x+35)/(9x³)(x-6)

Combine the numerators and keep the same denominator.

(9x³)(x²-11x+30) - (x-6)(x²-12x+35) / (9x³)(x-6)

Simplify the numerator by distributing and combining like terms.

(9x⁵-99x⁴+270x³) - (x³-18x₂+72x-35) / (9x³)(x-6)

9x⁵-99x⁴+269x³-18x²+72x-35 / (9x³)(x-6)

Simplify the denominator by multiplying.

9x⁵-99x⁴+269x³-18x²+72x-35 / 9x⁴-54x³

Simplify the fraction by dividing each term in the numerator by the term in the denominator with the highest power.

(9x⁵/9x⁴)-(99x⁴/9x⁴)+(269x³/9x⁴)-(18x²/9x⁴)+(72x/9x⁴)-(35/9x⁴)

Simplify each term.

x - 11 + (269/9)x⁻¹- (18/9)x⁻²+ (72/9)x⁻³ - (35/9)x⁻⁴

Combine like terms.

x - 11 + (29.89)x⁻¹ - (2)x⁻² + (8)x⁻³- (3.89)x⁻⁴

Therefore, the operation  (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³)   expressed in simplest form is  x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.

To learn more on Equation:

brainly.com/question/10413253

#SPJ11

Answer:

29+3374=32483 that is the solution for the question

hope this helps <3

Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:

State              Number     Total Cost

                  of Students    (After-tax)

Idaho                     10        $1,431.00

Mississippi             5          $722.25

Hawaii                  15        $2,106.00

Wisconsin             8          $1,134.00.

The total cost for each group of students from the four states can be determined by multiplication.

The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.

The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.

Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.

The price before state sales tax of each uniform = $135

Relevant Taxes and Number of Students:

State           Number of Students     Sales Tax Rate

Idaho                     10                                 6%

Mississippi             5                                  7%

Hawaii                  15                                  4%

Wisconsin             8                                  5%

State              Number      Total Cost     Total Cost

                  of Students    (Before tax)    (After-tax)

Idaho                     10        $1,350            $1,431.00 ($135 x 10 x 1.06)

Mississippi             5           $675             $722.25 ($135 x 5 x 1.07)

Hawaii                  15        $2,025          $2,106.00 ($135 x 15 x 1.04)

Wisconsin             8         $1,080            $1,134.00 ($135 x 8 x 1.05)

Learn more about the sales tax at https://brainly.com/question/30494127

#SPJ1

The maximum number of hours that you can park in the garage if you wish to pay no more than $14 is 5 hours.

Here's how to calculate it:

Therefore, the maximum number of hours you can park in the garage if you wish to pay no more than $14 is 5 hours.

For more information about divide, visit:

https://brainly.com/question/25289437

#SPJ11

Answer:

X=5

Step-by-step explanation:

instructions refer to the image

The  product of 3∛6 and 2∛6 is equals to 18.

What is underroot ?

In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.

To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.

D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:

3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6

So the sum of 3∛6 and 2∛6 is 5∛6.

E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:

4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6

So the difference between 4∛6 and 2∛6 is 2∛6.

F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:

3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36

Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:

6∛36 = 6 x 3 = 18

Therefore, the product of 3∛6 and 2∛6 is equals to 18.

To learn more about Underroot from given link.

https://brainly.com/question/21492333

#SPJ1

The expression to represent the total cost of hiring a plumber is y = 50 + 40x

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

Charges = $50 for visiting

Rate = $40 every hours

Represent the number of hour with x and the total charge with y

Using the above as a guide, we have the following:

y = Charges + Rate * x

Substitute the known values in the above equation, so, we have the following representation

y = 50 + 40x

Hence, the equation is y = 50 + 40x

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

The simplest form of the given expression x will be 42.

Using variables and coefficients, polynomials are algebraic expressions. The term "indeterminates" is sometimes used to describe variables. The terms Poly and Nominal, which together signify "many" and "terms," make up the word polynomial.

When exponents, constants, and variables are combined using mathematical operations like addition, subtraction, multiplication, and division, the result is a polynomial (No division operation by a variable). The expression is categorized as a monomial, binomial, or trinomial based on the number of terms it contains.

Here we assume that no of suitcases be x

So, 7/24 = x/144

24x = 1008

x = 42.

Hence the simplest form of the given expression x will be 42.

Learn more about polynomials, by the following link.

https://brainly.com/question/2833285

#SPJ1

Answer:

51.2

Step-by-step explanation:

By dividing :0

The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.

Remember that the recursive formula for a geometric sequence is:

f(n) = r*f(n - 1)

Where r is the common ratio.

Here we have the terms:

5, 11, 29, 83

To get the value of r, take the quotient between consecutive terms:

r = 11/5 = 2.2

r = 29/11 = 2.63

r = 83/29 = 2.86

We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.

Learn more about geometric sequences at:

https://brainly.com/question/24643676

#SPJ1

By forming and solving the equations we know that the speed of the plane was 220 mph.

In mathematical formulas, the equals sign is used to indicate that two expressions are equal.

A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.

like 3x + 5 = 15, for instance.

Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.

So, d = rt.

t = d/r

The distances are equal.

140/r = 440/(r + 150)

Cross multiply:

140(r + 150) = 440r

140r + 21,000 = 440r

300r = 21,000

r = 70

70 + 150 = 220 mph

Therefore, by forming and solving the equations we know that the speed of the plane was 220 mph.

Know more about equations here:

brainly.com/question/22688504

#SPJ1

37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1

Learn more about Trigonometric functions:

brainly.com/question/6904750

#SPJ11

a) 0.33143; b) 17586.76

a) 33.143 / 100

   33.143 ÷ 100

       = 0.33143

b) 175.876 / 0.01

   175.876 ÷ 0.01

       = 17586.76

Learn more about long division

brainly.com/question/28824872

#SPJ11

The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.

The number of bottles that need to be sold to earn back the amount spent on water is :

= Total spent / profit per bottle

= 50 / 2

= 25 bottles

Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.

Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.

Find out more on graphs at https://brainly.com/question/3889458

#SPJ1

The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System.  3. Expressions and Equations.  4. Geometry.  5. Statistics and Probability.

1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.

2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.

3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.

4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.

5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.

These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.

Know more about Focal Points here:

https://brainly.com/question/30761313

#SPJ11

Answer:

[tex]\boxed{The \ height \ of \ the \ tabletop \ is \ 63.5 \ centimeters}[/tex]

Step-by-step explanation:

We are given that,

Length of the base = 127 centimeters

Width of the base = 85 centimeters

Area of the trapezoid shaped base = 6,731 square centimeters.

Since, we know,

[tex]\bold{Area \ of \ a\ trapezoid}=\frac{Length +Width}{2}\times Height[/tex]  

So, we get,

[tex]6731=\frac{127+85}{2}\times Height[/tex]

i.e. [tex]6731=\frac{212}{2}\times Height[/tex]

i.e. [tex]6731=106\times Height[/tex]

i.e. [tex]Height=\frac{6731}{106}[/tex]

i.e. Height = 63.5 centimeters

Hence, the height of the tabletop is 63.5 centimeters.