Determine whether each of the equations in Problems 1 through 8 is exact. If it is exact, find the solution. 1. (2x + 3) + (2y - 2)y' = 0 2. (2x + 4y) + (2x - 2y)y' = 0 3. (3x2 - 2xy + 2) + (6y2 - x2 + 3) y' = 0 dy ax + by 4. dx bx + cy dy ax - by 5. dx 6. (ye"y cos(2x) -2e* sin(2x)+2x)+(xey cos(2x) -3) y'=0 7. (y/x+6x) +(In x - 2)y' = 0, > 0 8. у dy + 0 (x2 + y2)3/2 (x2 + y2)3/2 dx bx - cy x

Answer:

s = 150 (Please brainlist)

Step-by-step explanation:

s = ut+ 16t^2

s= (2*3)+16*3^2
s= 6+ 144
s= 150

Answer:

B) \(-4\sqrt{10}+13\)

Step-by-step explanation:

\(\sqrt{100}+4\sqrt{10}+3-8\sqrt{10}\)

\(10-4\sqrt{10}+3\)

\(13-4\sqrt{10}\)

\(-4\sqrt{10}+13\)

Answer:

Step-by-step explanation:

MODE

3,4,4,5,5,5,5,5,7,7,8,8,10,10,14

MEAN

10-6=4

MEDIAN

3,4,4,5,5,5,5,5,5,7,7,8,8,10,10,14 CROSS OUT THE FIRST AND THE END THE DO IT AGAIN UNTIL YOU GET TO THE middle.

MEDIAN =5

RANGE IS BIGGEST- SMALLEST

10-3=7  

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

A cylinder is three-dimensional. It's not a flat thing. There are parallel circular bases in this shape. These bases have a curved face affixed to them. A cylinder in this instance has three faces. Along both end of a curved face, which rounds back to the face's origin, are two spherical bases.

Given that-

Volume of cylinder = πr²h

Volume of cylinder = 3.14 *5²*18

Volume of cylinder = 3.14*25*18

Volume of cylinder = 1413 ft³

Thus, the volume of cylinder with the given height and diameter is found as 1413 ft³.

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The value of x obtained using the inverse trigonometric ratios for tangent  is x ≈ 51.1°

The tangent of an angle, θ, tan(θ) in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the side opposite to the angle.

Mathematically; tan(θ) = Opposite/Adjacent

The details in the question includes;

The shape of the figure = A right triangle

The length of the side adjacent to the angle, ON x = 7.5

Length of the side opposite to the angle, NM x = 9.3

The measure of the angle x° can be found using the trigonometric ratio for tangent as follows;

tan(x) = NM/ON

Therefore;

tan(x) = 9.3/7.5

x° = arctan(9.3/7.5) ≈ 51.1°

x ≈ 51.1°

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Answer:

1,800 lbs of sand

900 lbs of gravel

600 lbs of cement

Step-by-step explanation: 11*300=3,300. 300*6=1,800, 300*3=900, and 300*2=600. This is correct because if you add 1,800+900+600 you get 3,300.

An equation which is true include the following: A. 4 × n × n × n × n = 4n⁴.

In Mathematics, an exponent is a mathematical operation that is typically used in conjunction with an algebraic expression in order to raise a quantity to the power of another.

This ultimately implies that, an exponent is represented by the following mathematical expression;

bⁿ

Where:

By applying the multiplication law of exponents for powers to each of the expressions, we have the following:

4 × n × n × n × n = 4n⁴

4 × n⁴ = 4n⁴

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Answer:

22 1/2

Step-by-step explanation:

1/4×6=1 1/2

3×7=21

21+1 1/2=22 1/2

Answer as a decimal = 22.5

Answer as a fraction = 45/2

===========================================================

Explanation:

Replace c with 6, and replace d with 7.

Then use the order of operations (PEMDAS) to simplify until you get a single number.

\(\frac{1}{4}c + 3d\\\\\frac{1}{4}(6) + 3(7)\\\\\frac{6}{4} + 21\\\\1.5 + 21\\\\22.5\\\\\)

If you want to convert this to an improper fraction, then,

\(22.5 = 22 + 0.5\\\\22.5 = 22 + \frac{1}{2}\\\\22.5 = 22*\frac{2}{2} + \frac{1}{2}\\\\22.5 = \frac{44}{2} + \frac{1}{2}\\\\22.5 = \frac{44+1}{2}\\\\22.5 = \frac{45}{2}\\\\\)

Answer:

17.

Step-by-step explanation:

Divide 2225 by 24 and round down. (92) Multiply 92 by 24 and subtract that (2208) from the total number (2225). you get 17

Answer:

x=5

Step-by-step explanation:

2^x= 32

2^x=2^5

(comparing, common denominator)

therefore x=5.

Answer:

  72

Step-by-step explanation:

If the rates d and c are flowers per day, we have ...

  150/d = 120/c

  d -c = 18

__

Multiplying the first equation by cd/30, we have ...

  5c = 4d

Multiplying the second equation by 4 gives ...

  4d -4c = 72

Adding these equations together, we get ...

  5c +4d -4c = 4d +72

Simplifying and subtracting 4d leaves ...

  c = 72

Charlie can plant 72 flowers per day.

Answer:

y = -4x + 6

Step-by-step explanation:

The graph for the given equation of a line with the coordinates (0, 6), (1, 2), (2, -2), (3, -6) and so on are plotted.

The equation of a line is 4x+y=6.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Here, y=6-4x

Substitute x=0, 1, 2, 3, 4, 5,..... in the given equation, we get

When x=0

y=6

When x=1

y=2

When x=2

y=-2

When x=3

y=-6

So, the coordinates are (0, 6), (1, 2), (2, -2), (3, -6) and so on.

Therefore, the graph for the given equation of a line with the coordinates (0, 6), (1, 2), (2, -2), (3, -6) and so on are plotted.

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Answer:

100, 162, 262

Step-by-step explanation:

to find each number you add the previous number

4+10=14

10+14=24

14+24=38

24+38=62

38+62=100

62+100=162

100+162=262

The angle measure that belongs in the green box is given as follows:

70.67º.

We consider a triangle with side lengths and angles related as follows, as is the case for this problem:

Then the lengths and the sines of the angles are related as follows:

sin(A)/a = sin(B)/b = sin(C)/c.

The relation for this problem is given as follows:

sin(x)/12  = sin(76º)/12.34

Applying cross multiplication, the missing angle measure is given as follows:

sin(x) = 12 x sine of 76 degrees/12.34

sin(x) = 0.9436.

x = arcsin(0.9436)

x = 70.67º.

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Answer:

15.  125

16.   160

17. 110

18. 150

19. 35

20. 80

Step-by-step explanation:

This should work, if not, well sorry

The length of segment GH is approximately 2.2

We have,

To find the length of segment GH, we need to calculate the distance between points G(-1, -4) and H(-3, -3).

The distance formula between two points \((x_1, y_1) ~and ~(x_2, y_2)\) in a coordinate plane is given by:

\(d = \sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)}\)

Applying the formula to the coordinates of points G and H, we have:

d = √((-3 - (-1))² + (-3 - (-4))²)

d = √((-3 + 1)² + (-3 + 4)²)

d = √((-2)² + (1)²)

d = √(4 + 1)

d = √(5)

The length of segment GH is the square root of 5, which is approximately 2.24 when rounded to the nearest tenth.

Therefore,

The length of segment GH is approximately 2.2

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Step 1: What is a trinomial expression?

A trinomial is an algebraic expression composed of three terms and is normally of the form

Where c is the constant term

A constant term is a term without x

Step 2:

From the options, it only options A and B that are trinomial.

Step 3:

Final answer

Let's say there are $v$ varsity players and $j$ JV players.

The problem tells us that 2/3 of the varsity players are partnered with 3/5 of the JV players. So the number of varsity players partnered with a JV player is:

$\sf\implies\:(2/3)v$

And the number of JV players partnered with a varsity player is:

$\sf\implies\:(3/5)j$

Since these two numbers represent the same group of paired players, they must be equal:

$\sf\implies\:(2/3)v = (3/5)j$

To find the fraction of players who are partnered, we can divide the total number of paired players by the total number of players:

$\implies\:\frac{(2/3)v}{v} = \frac{2}{3}$ of the varsity players are paired

$\implies\:{\sf{\frac{(3/5)j}{j}} = \frac{3}{5}}$ of the JV players are paired

So the total fraction of players who are paired is:

$\sf\implies\:\frac{2}{3} + \frac{3}{5} - \frac{2}{15}$ (since some players will be counted in both fractions)

Simplifying:

$\sf\implies\:\frac{10}{15} + \frac{9}{15} - \frac{2}{15} = \frac{17}{15}$

Therefore, the fraction of players who are partnered for training is $\frac{17}{15}$, which is greater than 1. This means that the problem may have been set up incorrectly, or there may be additional information missing.

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The reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).

First, let us understand the reflection of a point:

The reflection of a point or set of points across the line y = x results in a point or set of points whose coordinates are the interchange of the x-value and the y-value of the original point or set of points.

We are given:

The vertices of a triangle are P(-1, 4), Q(8, -3) and R(2, -6).

We need to find the reflection of the points across the line y = x.

So,

P(-1, 4) = P'(1, -4)

Q(8, -3) = Q'(-8, 3)

R(2, -6) = R'(-2, 6)

Thus, the reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).

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To purchase the Apple iPad Pro, based on an equation, Sandra contributed $257 while her parents contributed $643.

An equation is a mathematical statement that states that two or more mathematical expressions are equal or equivalent.

Mathematical expressions are depicted as equations using variables, constants, numbers, and values and the equation symbol (=).

The total cost of the Apple iPad Pro = $900

The contribution of Sandra's parents per $2 = $5

The contribution of Sandra = $2

Let x = the variable contributed by each party

2x + 5x = 900

7x = 900

x = 128.57

Sandra's contribution = $257 (2 x 128.57)

Parents contribution = $643 (5 x 128.57)

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The types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

A. To find f(x) + g(x), we add the two functions together:

f(x) + g(x) = (x + 2)/(x^2 - 9) + 11/(x^2 + 3x)

To add these fractions, we need a common denominator. The common denominator in this case is (x^2 - 9)(x^2 + 3x). So, we rewrite the fractions with the common denominator:

f(x) + g(x) = [(x + 2)(x^2 + 3x) + 11(x^2 - 9)] / [(x^2 - 9)(x^2 + 3x)]

Simplifying the numerator:

f(x) + g(x) = (x^3 + 3x^2 + 2x^2 + 6x + 11x^2 - 99) / [(x^2 - 9)(x^2 + 3x)]

Combining like terms:

f(x) + g(x) = (x^3 + 16x^2 + 6x - 99) / [(x^2 - 9)(x^2 + 3x)]

B. To find the excluded values, we look for values of x that would make the denominators zero, as division by zero is undefined. In this case, the excluded values occur when:

(x^2 - 9) = 0  --> x = -3, 3

(x^2 + 3x) = 0 --> x = 0, -3

So, the excluded values are x = -3, 0, and 3.

C. To classify each type of discontinuity, we examine the excluded values and the behavior of the function around these points.

At x = -3, we have a removable discontinuity or hole since the denominator approaches zero but the numerator doesn't. The function can be simplified and defined at this point.

At x = 0 and x = 3, we have vertical asymptotes. The function approaches positive or negative infinity as x approaches these points, indicating a vertical asymptote.

Therefore, the types of discontinuities are: removable discontinuity at x = -3 and vertical asymptotes at x = 0 and x = 3.

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9514 1404 393

Answer:

  24

Step-by-step explanation:

Jermey sold 2/3 of 36 = ...

  (2/3)×36 = (2×36)/3 = 2×(36/3) = 2×12 = 24

Jermey sold 24 tickets.

Answer: 69

Step-by-step explanation:

duhhhhhhhhhhhh

Answer:

24000

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

if a line is parallel to a side of a triangle and it intersects the other two sides then id divides those sides proportionally.

DE is such a line , then

\(\frac{BD}{AD}\) = \(\frac{BE}{EC}\)  ( substitute values )

\(\frac{x+2}{x}\) = \(\frac{3}{2}\) ( cross- multiply )

3x = 2(x + 2)

3x = 2x + 4 ( subtract 2x from both sides )

x = 4

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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The equation in terms of x that represents the given relationship is 114 = (1 + 3x) * (Width)

Let's break down the information given:

Height of the rectangular box = 7 ft

Length of the rectangular box = 1 ft longer than thrice the width (x)

Volume of the rectangular box = 798 ft³

To write an equation that represents the given relationship, we need to relate the length, width, and height to the volume.

The volume of a rectangular box is given by the formula: Volume = Length * Width * Height.

Given that the height is 7 ft, we can substitute this value into the equation.

Volume = (Length) * (Width) * (7)

Now, let's focus on the length. It is described as 1 ft longer than thrice the width.

Length = 1 + (3x)

Substituting this value into the equation, we have:

Volume = (1 + (3x)) * (Width) * (7)

Since the volume is given as 798 ft³, we can set up the equation as follows:

798 = (1 + (3x)) * (Width) * 7

Simplifying further, we get:

798 = 7 * (1 + 3x) * (Width)

Dividing both sides of the equation by 7, we have:

114 = (1 + 3x) * (Width)

Therefore, the equation in terms of x that represents the given relationship is:

114 = (1 + 3x) * (Width)

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Answer: 13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

There are 12 1/4s in 3

Add the extra 1/4 + 13 1/4s