An 18-ounce bottle of milk costs $3.60. A 12-ounce bottle of milk costs $3.00. Which bottle of
milk costs less per ounce and by how much?

The vertex of the given function g(x) = -3x² + 18x + 2 is (3, 29)

Function in math is defined as  a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given the function called g(x)  has the expression -3x² + 18x + 2.

And here we need to find the vertex for the function that can be calculated as,

As we all know that vertex form of a parabola is written as,

=> y = a (x - h)² + k

Here we know that (h, k) is the vertex

Then the given expression is written as,

=> g(x) = -3x²  + 18x + 2

When we can be written by completing the square as follows,

=> y = -3x²  + 18x + 2

Here we have to take 3 as common term, then we get

=> -3(x²  + 6x)+ 2

now, we have to expand the expression within the brackets, then we get,

=> -3(x²  + 6x+ 9)+ 2 + 27

Then the resulting vertex form o the equation is written as

=> y = - 3(x - 3)2 + 29

While we comparing this with the standard form then we get the value of vertex is (3, 29).

Complete Question:

What is the vertex of the function g(x) = -3x² + 18x + 2?

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The area of the triangle xyz is 33.941...

To calculate area of triangle, we need to take the base and height's measurement.

Formula- 1/2 x Base x Height

However, Area may also be calculated when we know the 3 sides of the triangle.

It is known as "Heron's Formula"

Simply use this 2 step process :

Step 1-

Calculate "S" (which is half of the triangle's perimeter)

S = (side1 + side2 + side3) / 2

Naming the sides as a b and c respectively.

4 inches = a

5 inches = b

7 inches = c

 S = ( a + b + c ) / 2

S = ( 4 + 5 + 7 ) / 2

S = 16/2

S = 8

Step 2: Calculating the area of the triangle XYZ

Formula:

Area ( A ) = √S(S−a)(S−b)(S−c)

put the values and you will get the answer.

A = √8(8−4)(8−5)(8−7)

A = 33.941..

The area of the triangle xyz is 33.941...

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Answer:

14 square inches

Step-by-step explanation:

Area of triangle = (h.b)/2

The height and base aren't specified, and no pic is provided

So I'll assume that the height is 4 and base is 7 ( or the opposite)

Area = (4.7)/2

= 14 square inches

If the height is 5 and base 7 ( or the opposite)

Area = (5.7)/2

= 17.5 square inches

If the height is 4 and base is 5 ( or the opposite)

Area= (4.5)/2

= 10 square inches

Answer:

20 times

Step-by-step explanation:

40 / 2 = 20?? sorry if im wrong

The Cartesian Product of sets A and B is defined as the set of all ordered pairs (x, y) such that x belongs to A and y belongs to B.

Now, According to the question:

Cartesian Product of Vector Spaces:

The Cartesian product U × V of two finite-dimensional vector spaces U and V consists of all pairs {u, v} of vectors u in U and v in V. The vector space operations are defined component wise: (1) (2).

The Cartesian product of two vectors is :

The Cartesian Product of sets A and B is defined as the set of all ordered pairs (x, y) such that x belongs to A and y belongs to B. For example, if A = {1, 2} and B = {3, 4, 5}, then the Cartesian Product of A and B is {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}.

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Latitude is always presented before longitude when giving a coordinate. Degrees, minutes, and seconds are used to divide latitude and longitude. While a degree is made up of 60 minutes, a minute is made up of 60 seconds.

Latitude lines run parallel with each other from east to west. The more north you travel, the higher the latitude values. Last but not least, latitude values vary from -90 to +90. However, longitude lines run from north to south. Latitudes are lines that are horizontal and indicate how far away from the equator a location is. East and west directions with reference to the Greenwich, England, meridian are shown using longitudes, which are vertical lines. Cartographers and geographers. The grid system that enables us to locate precise or absolute locations on the surface of the globe is made up of latitude and longitude meridian. Drawing imaginary lines that circle the globe vertically (up and down) and connect at the North and South Poles is one step in the longitude calculation.

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If O is the center of the circle in the figure, the value of x. is 80°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry.

Given: ∠ BAC = 35°, ∠ DBC = 65°,

∠BDC = ∠BAC = 35° (Angle in same section).

∠BDC + ∠BCD + ∠DBC = 180° in ABCD.

35° + x + 65° = 180°

⇒ 100° + x = 180°

. '. x = 80°

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Complete question -

The value of x from the given  linear equation is -1 and y = 1

A linear polynomial over a field, from which the coefficients are taken, can be equalized to zero to produce a linear equation.

A line in the Euclidean plane is formed by a linear equation's solutions, and every line may be thought of as the collection of all solutions to a linear equation with two variables. This is where the term "linear" for this class of equations came from

It is given that y = 3x+4 (i) and y = x+2 (ii)

Put equation i) = ii)

Then, we get 3x+4 = x+2

2x = -2

x = -1.

Put the value of x in equation ii)

y = -1+2

y = 1

Hence, the value of x from the given  linear equation is -1 and y = 1

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The correct way to write greater than B is A > B where it tells that B having greater value than A.

In mathematics,

→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.

→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.

→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.

→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.

These symbols are commonly used in mathematical expressions, equations, and inequalities.

To write "greater than B" in mathematical notation, you would use the greater than symbol (>) followed by the letter B. For example:

A > B

This means that A is greater than B.

Therefore, the correct way to write greater than B is A > B where it tells that B having greater value than A.

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Heather would have to work 4.6 hours to make $65.

Time and work is a branch of mathematics that deals with the relationship between the time required to complete a task and the amount of work done. The basic formula used in time and work is:

Work = Time x Rate

Where,

Work = amount of work done

Time = time taken to complete the work

Rate = the rate at which the work is done

We can calculate this by using the formula:

Hours = (Money earned / Hourly rate)

In this case, you can use the proportion:

(x hours) / (65) = (12 hours) / (156)

Solving for x you get:

x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)

Therefore, Heather would have to work 4.6 hours to make $65.

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In this case, you can use the proportion:

(x hours) / (65) = (12 hours) / (156)

Solving for x you get:

x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)

No, thirty-two is not a prime number i.e., it is a composite number.

A prime number is a number that has only two divisors that is 1 and the number itself. Consider the number 7, which has only two factors, 1 and 7 so it is a prime number. As another example, let's take the example of 8, which has two or more divisors of 1, 2, 4, and 8. This means that 8 is not prime i.e., it is a composite number. I have a number 32 and I need to check if it is prime. To do this, we need to determine 32 factors. The factors of 32 are 1,2,4,8,32, so 32

= 1×2×2×2×2. Here we see that 2, 4, and 8 are factors of 32 that are different from 1 and 32. So there are more than two factors. Therefore it is not prime.

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Complete question:

Is 32 a prime number?

The hypotenuse is the longest side of a triangle which is opposite to the right angle.

A right triangle's hypotenuse is always the side that faces the right angle. This side is longest in a right triangle. The other two sides are those that are opposed and close by. The labels on these sides relate to an angle.

The word "hypotenuse," which refers to the longest side, is derived from two Greek roots that mean "to stretch." One side is across from another at a particular angle. The non-hypotenuse side that lies next to a particular angle is known as the neighboring side.

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8 gigabytes would have to be used for the plans to cost the same. The cost will be $100.

Given is that Smart One smartphone plan cost $20 per month for talk and messaging and $10 per gigabyte of data used each month. A second smartphone plan cost $60 per month for talk and messaging and $5 per gigabyte of data used each month.

Let {C} represent the total cost in dollars and {D} represent the amount of data used in gigabytes. The system of equation can be used to represent this situation are -

C = 20 + 10d

C = 60 + 5d

For same cost -

20 + 10d = 60 + 5d

5d = 40

d = 8

The cost would be -

C = 20 + 10d

C = 20 + 10 x 8

C = 100

Therefore, 8 gigabytes would have to be used for the plans to cost the same. The cost will be $100.

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There were 192 birds in the aviary in total.

There were 16 habitats in the aviary at the zoo, and each habitat had 12 birds. To find out how many birds were in the aviary in total, we need to multiply the number of habitats by the number of birds in each habitat.

16 habitats * 12 birds/habitat = 192 birds

So there were 192 birds in the aviary in total.

This is done by using the distributive property of multiplication. Basically, if you have a certain number of groups, each containing a certain number of items, and you want to find the total number of items, you can multiply the number of groups by the number of items in each group. In this case, the number of groups is the number of habitats (16) and the number of items in each group is the number of birds (12). So by multiplying those two numbers together, we get the total number of birds in the aviary.

Therefore, There were 192 birds in the aviary in total.

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16 areas with 12 birds each equals 192 birds.

Thus, there were 192 animals in all in the aviary.

Utilizing multiplication's distributive principle, this is accomplished. Basically, you can increase the total number of groups by the total number of items in each group if you have a certain number of groups, each of which contains a specific number of items. In this instance, the number of objects in each group equals the number of birds, and the number of groups equals the number of habitats (16). (12). We can calculate the overall number of birds in the aviary by multiplying those two numbers.

Consequently, there were 192 animals in all in the aviary.

The area of ​​the RMC triangle is 43.4.

3 sides, 3 corners, 3 corners form a closed triangle. The mathematical sign of a three-sided triangle is RMC. Triangle-shaped sandwiches and signs are the most common triangles.

Three sides and three interior angles together define a triangle (a rectilinear polygon). This symbol is used to represent one of the basic geometric shapes with three connected vertices.

Triangles are classified in different shapes depending on their sides and angles. Different parts form a triangle. It consists of 3 corners, and 3 sides.

If we round the area to the nearest 10th digit then it will be 116.

Use the Law of Cosines to find the length of the third side RC: RC = [tex]sqrt(19^2 + 27^2 - 2(19)(27)cos(27))[/tex]

Compute the semi-perimeter s = (19+27+RC)/2

Compute the area of the triangle with Heron's formula

A = [tex]sqrt(s(s-a)(s-b)(s-c))[/tex]

After the calculation, we can get the area is approximately 43.4

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Answer:

(-2, 3)

Step-by-step explanation:

the angle between 0 and 2pi in radians that is coterminal to 44pi/9 then terminal angle for 43pi/10 is 3pi/10.

How do you find Coterminal angles?

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.

The coterminal angle lie in between [0, 2pi].

Simplify the coterminal angle 43pi/10 to obtain in [0, 2pi].

43pi/10= 4pi+3pi/10

So coterminal angle for 43pi/10 is 3pi/10.

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Answer:

5x – 30 = 176

Step-by-step explanation:

The equation which represents the same line as the points in the table is y = -3/4 x + 2. (Option C)

The equation of the points given in the table can be determined by using the slope-intercept form which is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept.

The slope of the line can be determined by:

m = rise/run = Δy/ Δx = (y2 – y1)/(x2 – x1)

Hence, taking two points from the table say (-4, 5) and (0, 2)

m = (2 – 5)/(0 – (-4)) = -3/4

y intercept is the value of y when x = 0

From the table, y-intercept b = 2

Hence, the equation of the line is: y = -3/4 x + 2

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Answer: d

Step-by-step explanation:

-2/5 is the absolute value of - |- 2/5|

An expression is combination of variables, numbers and operators.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

Given that negative absolute value of negative two fifths.

- |- 2/5|

Solving the modulus we get;

|- 2/5| = 2/5

Then negative,

- 2/5

Hence - 2/5 is the absolute value

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Answer: x - 15

Step-by-step explanation:

The answer is x - 15

Answer:

x-15

Step-by-step explanation:

When each number is rounded to the nearest hundred, the difference I 100 the number could be 14,499 less 13,500 or 999

To the closest hundred, the biggest number that can be named 14,000 is 14,050. To the closest hundred, the least number that can be named 14,000 is 13,950. There is a 100 difference between the two.

This claim may be generalized as follows.

The difference between the upper and lower limits is m for any integer N that has been rounded to the nearest m.

The maximum is N+m/2.

N-m/2 is the lower limit.

(N+m/2) is the difference between the two. (N-m/2) = (N-N) +m/2 - (N-N) -m/2

= 0 + m/2 + m/2

= 2(m/2)

= m.

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Answer:

----------------------------------

Let the air speed of the planes be s and the speed of the wind be w.

The two equations are:

Add up the two equations, it will eliminate w and we'll solve it for s:

The air speed of planes is 522.5 mi/hr.

Find the wind speed:

The wind speed is 27.5 mi/hr.

The original price of the TV is $4691.5

percentage, a relative value indicating hundredth parts of any quantity.

Given that You walk into a store and see a sign that says "Tv: 47% off, only pay $1,500 today!"

We have to find the original price of the TV.

Convert 47% to decimal value.

47/100=0.47

Now multiply 0.47 with x which gives 1500

0.47x=1500

Divide both sides by 0.47

x=1500/0.47

x=$3191.48

Now add $1500 and $3191.5 to find the original price.

1500+3191.5

$4691.5

Hence, the original price of the TV is $4691.5

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Answer:

In a right rectangular prism, a cross section can be cut on a slant to produce a variety of additional shapes. Depending on the angle of the cut, the cross section can be a triangle, quadrilateral, pentagon, or hexagon. The maximum number of "sides" of a cross section (plane section) equals the number of faces (surfaces) of the solid

Answer:

a rectangle

Step-by-step explanation:

When a geometric plane slices a prism so that the cut is parallel to the plane of the base, the cross section will have the shape of the base. So, in the case of a right rectangular prism, the cross section is a rectangle.

s = 990 / (-22)

s = -45

The answer is -45

Answer:

s = -45

Step-by-step explanation:

Now we have to,

→ find the required value of s.

The equation is,

→ -22s = 990

Then the value of s will be,

→ -22s = 990

→ s = 990/-22

→ s = -(990/22)

→ [ s = -45 ]

Hence, the value of s is -45.

Yes. There is the square root of 1. The square root of 1 is 1. The square root of 1 is always taken with positive sign. Square root of 1 is a rational number.

The square root of any number is an inverse mathematical operation of a square. square root is the the value which gives the number when it is multiplied by itself. The symbol √ is used to indicate the square root. A number is said to be a rational number that can be made by dividing an integer by an integer. It can be written as a fraction. There are so many ways to find square roots. whose square and the square root are equal is 1. It is neither prime nor composite. Square root of 1 is never be a negative number. It always taken as positive. From the natural numbers only perfect squares have square roots and negative numbers aren’t members of the set.

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This indicates that Rio has advanced 3 steps from his starting position.

Rio has now advanced five steps from his starting position.

8 backward steps.

Rio has moved 5 - 8 = - 3 steps from his starting place, according to this calculation.

Rio has now advanced (-3 + 9) = 6 steps from his starting place.

3 backward steps.

This indicates that Rio has advanced 6 – 3 = 3 steps from his starting position.

Note: Include the stages as you proceed.

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