Write and solve the system of equations for each of the following problems. You have to write two equations for each problem PLEASE

1. A plane makes a 600 mile trip in 3 hours flying with the wind, but the return trip against the same wind takes 4 hours.
What is the rate of the plane in still air and the rate of the wind?
2. Two pizzas and four sandwiches cost $62. Four pizzas and 10 sandwiches cost $140. How much does each pizza
and sandwich cost?

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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The equation of line is y = -2/3x - 4, option C is correct.

A line's slope is defined as the ratio of the change in y coordinate to the change in x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

Given coordinates

(-6, 0) and (0, -4)

equation of line is y = mx + c

m = (y₂ - y₁)/(x₂ - x₁)

m = (-4 - 0)/(0 + 6)

m = -2/3

and c is y-intercept  = -4

equation is y = mx + c

y = -2/3x - 4

Hence option C is correct.

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Answer:

The equation of line is y = -2/3x - 4, option C is correct.

Step-by-step explanation:

By the property of parallelograms that diagonals are equal in length and they bisect each other we have determined the values of x and y.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

We know the diagonals of a parallelogram are equal and they bisect each other, From this property, we can write,

OA = OC.

x + 23 = 31.

x = 31 - 23.

x = 8 units.

XZ = 2(OX).

26 = 2(- 44 + x).

26 = - 88 + 2x.

2x = 114.

x = 57 units.

OL = OJ

8x - 56 = 24.

8x = 80.

x = 10.

OM = OK.

36 = 4y + 20.

4y = 16.

y = 4.

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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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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:

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

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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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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Answer:

6/8

Step-by-step explanation:

1/8+1/4+3/8

1/8+2/8+3/8

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:

Check the picture below.

Make sure your calculator is in Degree mode.

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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Answer:

-1

Step-by-step explanation:

Step-by-step explanation:

8 + (-9) is an expression that represents the mathematical operation of adding 8 and -9.

An equivalent expression for 8 + (-9) is 8-9 which is the same as 8 + (-9)

Both expressions are equivalent and have the same value, which is -1.

So, 8 + (-9) and 8-9 are equivalent expressions.

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:

There are four real roots for the quadratic-like equation x⁴ + 9 · x² - 10 = 0: x₁ = + √(- 9 / 2 + 11 / 2), x₂ = + √(- 9 / 2 - 11 / 2), x₃ = - √(- 9 / 2 + 11 / 2) and x₄ = - √(- 9 / 2 - 11 / 2)

In this problem we find a quadratic-like equation of the form a · x²ⁿ + b · xⁿ + c = 0, where a, b, c are real coefficients and whose roots must be found. This can be done by completing the square and clear variable x. First, write the polynomial:

x⁴ + 9 · x² - 10 = 0

Second, use the following substitution: u = x²

u² + 9 · u - 10 = 0

Third, complete the square:

u² + 9 · u + 81 / 4 = 10 + 81 / 4

u² + 9 · u + 81 / 4 = 121 / 4

Fourth, factor the expression and clear variable u:

(u + 9 / 2)² = 121 / 4

u + 9 / 2 = ± 11 / 2

u = - 9 / 2 ± 11 / 2

Fifth, reverse the substitution and clear variable x:

x² = - 9 / 2 ± 11 / 2

x = ±√(- 9 / 2 ± 11 / 2)

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x=8.

[tex]2log(x)=log(64)[/tex]

[tex]\frac{2log(x)}{2} =\frac{log(64)}{2}\\ \\log(x)=\frac{log(64)}{2}[/tex]

When a logarithm doesn't have it's base expressed (base is tipically written as a subscript) we can assume it'sbase is 10. Therefore, to solve this equation, take the following step:

[tex]10^{log(x)} =10^{\frac{log(64)}{2}} \\ \\x=10^{\frac{log(64)}{2}}\\ \\x=8[/tex]

If the result is correct, then the equation should return the same value of both sides of the equal symbol (=) when we substitute the variable "x" by it's calculated value, 8.

[tex]2log(8)=log(64)\\ \\1.806179974=1.806179974[/tex]

As you can tell, the same number appears on both sides of the equal symbol, this means that the result is correct!

Answer:

x = 8

Step-by-step explanation:

Given expression:

[tex]2\log x=\log 64[/tex]

[tex]\textsf{Apply the log power law}: \quad n\log x=\log x^n[/tex]

[tex]\implies \log x^2=\log 64[/tex]

Rewrite 64 as 8²:

[tex]\implies \log x^2=\log 8^2[/tex]

[tex]\textsf{Apply the log equality law}: \quad \textsf{If\;\;$\log x=\log y$\;\;then\;\;$x=y$}[/tex]

[tex]\implies x^2=8^2[/tex]

Square root both sides:

[tex]\implies x=8[/tex]

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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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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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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13students;it had already said it.

Answer:

Step-by-step explanation:

yooyyo

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:

Step-by-step explanation: true

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:

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 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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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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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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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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