Lin bought 4 bags of apples. Each bag had the same number of apples. After eating 1 apple from each, she had 28 apples left.
Write an equation that represents the story.

Answer: To differentiate a function using the first principle, we first need to know the function and it's original value. Given that the function is f(x) = 5√x .

The first principle of differentiation states that the derivative of a function f(x) at a point x is approximately equal to the change in f(x) for an infinitesimal change in x. We can use this principle to find the derivative of a function f(x) at a point x by calculating the limit of the ratio (f(x+dx)-f(x))/dx as dx approaches zero.

To differentiate f(x) = 5√x with respect to x using the first principle, we take the following steps:

Find the change in f(x) as x changes by dx, which is f(x + dx) - f(x)

Divide that change by dx to find the slope of the function at that point

Take the limit of that slope as dx approaches zero

So:

f(x + dx) = 5√(x + dx)

f(x) = 5√x

change in f(x) = f(x + dx) - f(x) = 5√(x + dx) - 5√x

slope = change in f(x) / dx

= (5√(x + dx) - 5√x) / dx

The limit as dx approaches zero is the derivative of the function,

lim (dx->0) [(5√(x + dx) - 5√x) / dx]

= lim (dx->0) [(5(x+dx)^1/2 - 5x^1/2) / dx]

= 5 * lim (dx->0) [(x+dx)^1/2 - x^1/2] / dx

= 5 * (1/2)x^(-1/2)

So the derivative of the function f(x) = 5√x is (5/2)x^(-1/2)

This is the slope of the function at a point x, which is the rate of change of the function at that point x.

Step-by-step explanation:

The algebraic equation that expresses the cost, C, of running the Ad Ramon  plans to place in the newspaper where the cost of the first g Ad is y dollars and the cost per extra line is p dollars is; C = y + (x - g)×p

An algebraic equation contains two algebraic expressions, indicated to be of the same quality or quantity by joining them with a '='. It is a statement that the two expressions on either side of the '=' are equal or equivalent.

The number of lines in the Ad Ramon plans to place in the newspaper  = x lines

The amount the newspaper charges for the first g lines = y dollars per week

The amount the newspaper charges for the extra lines = p dollars per week

The possible number of lines in Ramon's Ad = x > g

The cost of running the Ad per week, where x > g is therefore;

The cost for the first g lines added to the cost of the extra lines

The cost of the first g lines = y

The number of extra lines = x - p

The cost of the extra lines is therefore;

Cost of extra lines = (x - g) × p

The cost of running the Ad Ramon plans to place in the newspaper for a week is therefore;

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The solution is Option C , Option E.

The total volume of the toy is the sum of volumes of cone and cylinder

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πrl

where l = √ ( b² + r² )

Given data ,

Let the total volume of the child's toy be represented as V

Now , the value of V is

Let the cone be represented as C

The volume of Cone C = ( 1/3 ) πr²h

The radius of the cone r = 5 cm

The height of the cone h = 13 cm

So , the volume of Cone = ( 1/3 ) π ( 5 )² x 13

The volume of Cone = ( 325/3 )π cm³

Now , the volume of cylinder = πr²h

The height of cylinder = 2 cm

The volume of cylinder = π ( 5 )² x 2

The volume of cylinder = 50π cm³

So , the volume of toy = volume of cylinder + the volume of Cone

The volume of toy = ( 325/3 )π cm³ + 50π cm³

The volume of toy = ( 475/3 )π cm³

Hence , the volume of toy is ( 475/3 )π cm³

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Check the picture below.

Make sure your calculator is in Degree mode.

Answer: The probability of an event happening is the number of successful outcomes (also known as favorable outcomes) divided by the total number of possible outcomes.

In this case, the spinner has 16 equal regions numbered from 1 to 16, so the total number of possible outcomes is 16.

The spinner will stop on an even number or a multiple of 3 when it stops on one of these numbers: {2, 4, 6, 8, 10, 12, 14, 16, 3, 9, 15}. So the number of successful outcomes is 11.

Therefore, the probability that the spinner will stop on an even number or a multiple of 3 is:

11 / 16

This can be simplified to 11/16, which is equivalent to 0.6875 as a decimal. Rounded to four decimal places, it is 0.6875.

Alternatively, you could divide the 11 favorable outcomes by the 16 possible outcomes and also multiply by 100 to convert it to percentage point probability.

Step-by-step explanation:

The sequence that lists the sides of the given triangle STU in order from shortest to longest is, US<ST<UT.

The three types of triangles based on their sides are: equilateral, isosceles and scalene.

The three types of triangles based on their angles are: acute, right and obtuse.

To find the sequence of length from shortest to longest we first need to find the missing angle S,

we're given,  

angle U = 65

angle T = 45

Using the property of sum of interior angles of a traingle,

U + T + S = 180 degrees

or, 65 + 45+ S =180

therefore, S = 70

As we know the side opposite to the largest angle is the longest, hence the sequence becomes, US<ST<UT.

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The distance in miles he biked up to the point of both stops is 10 1/2 miles

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

Total distance = 24 3/4 miles

When he stops a third of the way, we have the expression to be (24 3/4)/3

So, we have the following equation

Required distance = 24 3/4 - ((24 3/4)/3 + 5 3/3)

Evaluate

Required distance = 10 1/2

Hence, the distance is 10 1/2 miles

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The length of the line segment JN in the triangle JLQ, found by making applying the Pythagorean Theorem is about 6.7 units long

The Pythagorean Theorem states that the square of the length of the hypotenuse side is equal to the sum of the squares of the legs of the a right triangle.

The specified information are;

MN = 5.6, MQ = 8.7

Part of the question includes;

The circumcenter of triangle JLQ = M

The circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle, therefore;

The line segment MN is the perpendicular bisector of the side JQ

The point N is the point the segment MN intersects the side JQ, therefore, N is the midpoint of JQ

NQ = JN by the definition of midpoint of the bisected side JQ

Triangle MNQ is a right triangle, with MQ = 8.7, as the hypotenuse side, and MN and NQ are the legs.

MN = 5.6, therefore, according to the Pythagorean Theorem, we get;

NQ = √(8.7² - 5.6²) ≈ 6.7

JN = NQ ≈ 6.7

The approximate length of the side JN is about 6.7 units long

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The number of mini cherry pie and mini peach pie that she sold each would be = 12

The price for each cherry pie = $4

The price for each peach pie = $3

The total price for the whole pies sold = $84

The quantity of each pie sold. is calculated as thus;

= 4+3 = 7

For cherry pie;

= 4/7 × 84

= 336/7

= $48

The number of cherry pie sold = 48/4 = 12

For peach pie;

= 3/7× 84

= 252/7

= $36

The number of peach pie sold = 36/3 = 12

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So on solving the provided question given scatter plot shows a negative correlation so correct option is (b).

The values for two different numerical variables are represented by dots in a scatter plot. Each dot's location on the horizontal and vertical axes represents a data point's values. To view relationships between variables, employ scatter plots.

The options given are the following:

A)There is a positive correlation in the data set.

B)There is a negative correlation in the data set.

C)There is no correlation in the data set.

D)More points are needed to determine the correlation.

Positive correlation

We say there is a positive correlation between the variables when the y variable tends to rise when the x variable rises.

Negative correlation

We say there is a negative correlation between the variables when the y variable tends to decrease as the x variable increases.

No correlation

We claim there is no correlation between the two variables when there is no obvious connection between them.

From observing the given graph, we can see that as x value increases, the y value decreases.

So the correlation shown in the scatter plot is a negative correlation.

Therefore the correct option is option(B).

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The perimeter of the rectangular mural is 18feets

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. l is in this case the length of the rectangle while w is the width of the rectangle. The perimeter, P, is: P=l+l+w+w

P = 2l + 2w = 2(l+w)

The length of the rectangular mural = 3.5 feet

the width = 5.5 width

Therefore the perimeter = 2( 3.5+5.5)

= 2×9 = 18feets

therefore the perimeter of the mural is 18feets

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13students;it had already said it.

Answer:

Below

Step-by-step explanation:

30 hens   x 40 days   = 120 hen days of food

120 hen days / 40 hens =    30 days   of food for 40 hens

Yes, Helen is correct. Pressure is directly proportional to force applied. Pressure is inversely proportional to the area.

Forces can act over a large or small area and can be strong or weak. A way to gauge the amount of force acting on a region is through pressure. High pressure is produced by a strong push on a small area, whereas low pressure is produced by a weak push distributed over a large area. Force per area is known as pressure.

Here,

Thus, when the area over which it acts is constant, we can state that pressure is directly proportional to force.

As a result, pressure increases as the force acting on a given area increases.

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The factorized form of the given expression is [tex]\frac{ \textbf5}{( \textbf{x + 2})}[/tex].

In mathematics, factorisation or factoring is defined as the breaking or decomposition of an entity (for example, a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or matrix, etc. This concept will be emphasised heavily in your lower secondary classes from grades 6 to 8.

It is simply the division of an integer or polynomial into factors that, when multiplied together, result in the original or initial integer or polynomial. The factorisation method simplifies any algebraic or quadratic equation by representing it as the product of factors rather than expanding the brackets.

Given to simply the expression

⇒ [tex]$ \frac{5}{x} - \frac{10}{x^2 + 2x}[/tex]

[tex]$ \Rightarrow \frac{5}{x} - \frac{10}{x(x + 2)}[/tex]

[tex]$ \Rightarrow \frac{5(x + 2)}{x(x + 2)} - \frac{10}{x(x + 2)}[/tex]

[tex]$ \Rightarrow \frac{5(x + 2) - 10}{x(x + 2)}[/tex]

[tex]$ \Rightarrow \frac{5x + 10 - 10}{x(x + 2)}[/tex]

[tex]$ \Rightarrow \frac{5x}{ x(x + 2)}[/tex]

[tex]$ \Rightarrow \frac{ \textbf5}{( \textbf{x + 2})}[/tex]

Thus, the factorized form of the given expression is [tex]\frac{ \textbf5}{( \textbf{x + 2})}[/tex].

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Using the absolute value function, we have that:

The minimum time is of 1.833 hours.

The maximum time is of 2.833 hours.

The absolute function is defined by:

|x| = x, x ≥ 0.

|x| = -x, x < 0.

It measures the distance of a point x to the origin, hence |2| = |-2| = 2.

here, we have,

In this problem, the minimum and maximum distances are within 30 miles of 140, hence:

|d - 140| = 30.

The minimum distance is of:

d - 140 = -30

d = 110.

Hence the minimum time(distance divided by velocity) is:

110/60 = 1.833 hours.

The maximum distance is of:

d - 140 = 30

d = 170.

Hence the maximum time(distance divided by velocity) is:

170/60 = 2.833 hours.

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Answer:

Square root of 42.25 is 6.5

The square root of 42.25 is 6.5.

To find the square root of 42.25, we need to determine the number that, when multiplied by itself, equals 42.25. In this case, the square root of 42.25 is 6.5 because 6.5 multiplied by itself (6.5 x 6.5) equals 42.25.

Mathematically, it can be represented as:

√42.25

= 6.5

The square root (√) is the inverse operation of squaring a number.

When we square a number, we multiply it by itself.

In this case, squaring 6.5 (6.5 x 6.5) gives us the original value of 42.25.

Therefore, the square root of 42.25 is 6.5.

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Answer:
24 studens

3 students and 1 adult - [tex] \frac{3}{1}

24 students and x adults - [tex]\frac{24}{x}

After solving the answer is 8 adults to 24 kids

Step-by-step explanation:

After these reflections, the coordinates of P′ will be ( __4__ , __-4__ ).

What are coordinates?

Coordinates are a pair of numbers that identify a specific point on a coordinate plane, which is a grid of integers. Any point's location on a plane can be described by an ordered pair of values (x, y), which are referred to as coordinates.

Step by step Explaination:

* Let's update a few changes.

If x-axis reflection at position (x, y)

∴ Seeing it is (x , -y)

If the y-axis at position (x, y) was reflected

∴ Seeing it is (-x , y)

* Let's deal with the issue.

The triangle PQR, which is defined by the points P(-4, -4), Q(-1, -3), and R. (-3, -1)

Across the x-axis, the triangle is reflected.

PQR is visible along the x-axis.

All y-coordinates of the vertices P, Q, and R have their signs reversed.

∴ The new points are going to be (-4, 4), (-1, 3), and (-3 , 1)

A reflection of the new vertices along the y-axis will occur.

All of the new vertices' x-coordinates had their signs reversed.

The new points are (4, 4), (1, 3), and (3 , 1).

The updated vertex positions will reflect along the x-axis to produce the letters P'Q'R.

∴ The new vertices' y-coordinates all had their signs flipped.

∴ P' = (4 , -4) , Q' = (1 , -3) , R' = (3 , -1) (3 , -1)

The coordinates of P′ following these reflections will be (4 , -4).

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Answer:  B has only one unique intercept.

Step-by-step explanation:  line has only one unique intercept when it is not a vertical or horizontal line, which means it has a slope.

In this case, line A has the equation x = 8, which is a vertical line and does not have a slope, thus it does not have a unique intercept.

Line B has the equation -8x - 7y = -7, which has a slope of -8/7. Since it has a slope, it has one unique intercept.

Line C has the equation 9y = 5, which is a horizontal line and does not have a slope, thus it does not have a unique intercept.

Line D has the equation -3x - 3y = 0, which has a slope of -3/-3 = 1. Since it has a slope, it has one unique intercept.

Thus, only line B has only one unique intercept.

A composite number is any positive integer that can be formed by multiplying two other positive integers.

Any positive integer that may be created by multiplying two other positive integers is referred to as a composite number.

A prime number is a natural number greater than one that cannot be calculated as the product of two smaller natural numbers. A composite number is a natural number greater than one that is not prime.

It is, in other words, a positive integer that has at least one divisor besides itself and the number 1.

Solving an example to explain the composite number.

The first five composite numbers are 4, 6, 8, 9, 10, 12, 14, and 15.

They are often referred to as "composites" for short.

So, 33 is a composite number.

Because 33 can be made by multiplying 2 smaller numbers.

The factors of 33 are: 1, 3, 11, 33

So the correct option is (C).

Therefore, 33 is a composite number with factors (C) 1, 3, 11, and 33.

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The inequality expression is 17 + 6x >= 59

We can represent the inequality using the variables x for the number of minutes Lashonda adds water to the tank and y for the total amount of water in the tank.

The inequality will be:

y >= 59

Where y is the total amount of water in the tank after adding x minutes of water

We know that the initial amount of water in the tank is 17 liters and she plans to add 6 liters per minute

y = 17 + 6x

We can substitute this expression of y in the inequality y >= 59:

17 + 6x >= 59

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Complete question

Represent as an inequality. Lashonda's fish tank has 17 liters of water in it. She plans to add 6 liters per minute until the tank has at least 59 liters.

The pair of corresponding angles in the diagram will be 1 and 5.

When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal (i.e. the transversal).

The angles created when a transversal intersects two parallel lines are known as corresponding angles. The sides in any two-dimensional shape that are in the same position are said to be corresponding sides. Any two polygons must be precisely the same size and shape in order for them to be considered congruent. As a result, each of their interior angles and corresponding sides must have the same measurement.

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Relation between these given lines are given as follows:

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given a graph, there are a few lines in the graph we need to find the relation between them.

Since there is no mathematical data we need to observe the lines as per the graph

Since we already know about parallel and perpendicular.

So, Horizontal and verticle lines are:

A vertical line is a line, parallel to the y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to the x-axis and goes straight, left, and right.

Therefore, Relation between these given lines are given as follows:

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The first equation that represents 42 - p -p= 21 is correct.

An equation is a mathematical statement that express the equality between two or more number of expressions. An equal sign is mandatory for equation. An equation is used to determine unknown values in terms of variables. In our everyday life equation is used by many professionals necessarily. By using equation many complicated problems can be easily solved within a limited time.

Isaac has $42 cash in hand when arrived Saturday market.

He buys two posters that each cost selling price or SP.

when he leaved the market had $21 cash in hand.

assume, each poster has a price = p

The situation is represented by the following.

initial amount - cost for two posters = final amount

42 - p - p = 21

hence, the first equation that given in the question is correct.

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According to the problem the solution to the equation is x -8.

A solution is a means of solving a problem or addressing a challenge. It is a set of actions, processes, or strategies that are put in place to achieve a specific result.

To solve this equation, we need to move the 4 to the other side of the equation which will make the left side equal 0. We can do this by subtracting 4 from both sides of the equation:
4√x-4 = 3
4√x - 4 - 4 = 3 - 4
4√x - 8 = -1
Next, we need to isolate the radical on the left side of the equation. To do this, divide both sides of the equation by 4:
4√x - 8 = -1
(4√x - 8) ÷ 4 = (-1) ÷ 4
√x - 2 = -1/4
Finally, to isolate the radical, we can add 2 to both sides of the equation:
√x - 2 = -1/4
√x - 2 + 2 = -1/4 + 2
√x = -8
Therefore, the solution to the equation is x = -8.

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Dimension is a term used to describe the length, width, and height of an item, such as a box, in common usage.

In mathematics, a dimension is a way of describing the length or width of an area, a space, or an object as viewed from one particular angle. The measurement of anything's length, width, and height can be put more simply. Typical ways to express dimensions include: Length.

There are three dimensions in everything around us, including the buildings we live in and the items we use on a daily basis.

something's height, length, or width measured in a specific direction: 26 feet by 15 feet is the room's size.

In everyday speech, a dimension is the sum of an object's length, width, and height that describes the size of an object, like a box. A line is one dimension, a plane is two dimensions, and space is three dimensions. In mathematics, the concept of dimension is an extension of these ideas.

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Answer:

Step-by-step explanation:

yooyyo

Brian's gross income last month will be $3319.

The percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

From the information, Brian is a salesman for a wholesome computer parts company. He earn straight commission at a rate of 4% last month is total sales were 82,968.

Brian's gross income last month will be:

= 4% × 82968

= $3319

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Both planes have a speed of 340 miles per hour and 510 miles per hour, respectively.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation.

Here,

Let tc be the time of commercial jet and tp be the time of private airplane.

Let vc be the speed of commercial jet and vp be the speed of private airplane.

Let dc be the distance of commercial jet and dp be the distance of private airplane.

now,

dc=dp

vc=vp+170

vc*tc=vp*tp

(vp+170)*1.2=vp*1.8

(vp+170)*2=vp*3

2vp+340=3vp

vp=340 miles/hour

vc=340+170

vc=510 miles/ hour

The speed, in miles per hour, of both airplanes is 340 miles per hour and 510 miles per hour.

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