Which of the following is the best first step in solving the quation below?
13+ Inx = 6
A. Inx¹3 = 6
OB. e¹3+nx = 6
OC. In x= -7
OD. In(x+13) = 6
SUBMIT

Answer:

  (d)  yes; -7

Step-by-step explanation:

The differences between terms are ...

  12 -19 = -7

  5 -12 = -7

  -2 -5 = -7

These are all the same, so this difference is "common". A sequence in which terms have a common difference is an arithmetic sequence.

This sequence is arithmetic, with a common difference of -7.

dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

The autonomous differential equation that satisfies all of the given properties is dy/dx = (y-3)(y+3). This equation has two equilibrium solutions at y = 0 and y = 3, and is positive for -inf < y < 0, and negative for 0 < y < 3, and positive for 3 < y < inf.

To demonstrate this, let's consider the equation at y=-3. Since y=-3 is less than 0, the equation can be simplified to dy/dx = 6. Since 6 is positive, y' is also positive, meaning that y is increasing. Similarly, if y=3, dy/dx = 0 which is neither positive nor negative, so y remains constant. Finally, for y>3, dy/dx = -6, which is negative, so y is decreasing.

Therefore, dy/dx = (y-3)(y+3) is the autonomous differential equation that satisfies all of the given properties.

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By the fundamental theorem of calculus,

\(\displaystyle y = \int_0^v \sqrt{3+4t^2} \, dt \implies \boxed{\frac{dy}{dv} = \sqrt{3+4v^2}}\)

In general,

\(\displaystyle \frac{d}{dx} \int_0^{g(x)} f(u) \, du = f(g(x)) \frac{dg}{dx}\)

Answer:

D. 240

Step-by-step explanation:

estimate means round off

59 becomes 60

3.7 becomes 4

60 x 4 is 240

Answer:

No.  The data in this study were not based on a random method.  This is a key requirement for an inference to be made from the two-sample t-test.

Step-by-step explanation:

1. Hayden can use the two-sample t-test (also known as the independent samples t-test)to find out if there was a difference in the time spent in the checkout time between two grocery stores and to conclude whether the difference in the average checkout time between the two stores is really significant or if the difference is due to a random chance.  There are three conditions to be met when using the two-sample t-test.

2. The first condition is that the sampling method must be random.  This requirement was not met in this study.  Each customer from each store should have an equal chance of being selected for the study.  This was not achieved.

3. The distributions of the sample data are approximately normal.  This is achieved with a large sample size of 30 customers selected for each study.

4. The last but not the least condition is the independence of the sample data.  Sample data here is independent for both samples.

Answer:

QS ≅ TR

Step-by-step explanation:

QS and TR are diagonals.

Diagonals are equal in both rectangle as well as parallelogram.

The value of the expression C(6,3) is 20

The expression is given as:

C(6, 3)

This means 6 combination 3.

And it can be written as:

\(^6C_3\)

Apply the combination formula

\(^6C_3 = \frac{6!}{3!3!}\)

Evaluate the expression

\(^6C_3 = 20\)

Hence, the value of the expression C(6,3) is 20

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Answer:

The answer should be A.) (0,2) and D.) (3,0)

Step-by-step explanation:

Hope i helped.

A brainliest is always appreciated.

Answer:

86.60254

Step-by-step explanation:

30-60-90 triangle, which means that the base is 10. 1/2(10)(10 rt 3). Simplify answer as needed :)

These two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

The correct system of equations to model this scenario is:

x + y = 414 (Equation 1)

9x + 12y = 3780 (Equation 2)

In this system, x represents the number of children and y represents the number of adults who played that day.

Equation 1 represents the total number of customers, which is 414. It states that the sum of the number of children (x) and the number of adults (y) is equal to 414.

Equation 2 represents the total cost of the games played. Since the cost for a child's game is $9 and the cost for an adult's game is $12, we multiply the number of children (x) by $9 and the number of adults (y) by $12. The equation states that the total cost, which is $3780, is equal to the sum of these individual costs.

Together, these two equations form a system that can be solved to find the values of x and y, representing the number of children and adults, respectively, who played on that day.

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The margin of error for the 90% confidence interval is 3.

To find the margin of error for a 90% confidence interval, we can use the formula:

Margin of Error = (Upper Limit - Lower Limit) / 2

Given the confidence interval (72, 78), where 72 is the lower limit and 78 is the upper limit, we can substitute these values into the formula to calculate the margin of error.

Margin of Error = (78 - 72) / 2

Margin of Error = 6 / 2

Margin of Error = 3

Consequently, the 90% confidence interval's margin of error is 3.

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Answer:

1586.91 m³

Step-by-step explanation:

From the diagram attached,

Applying,

A = πrl.................. Equation 1

Where A = surface area of the cone, l = slight heigth of the cone, π = pie.

make l the subject of the equation,

l = A/πr.............. Equation 2

From the question,

Given: A = 628.32 m², π = 3.14, r = 8 m

Substitite these values into equation 2

l = 628.32/(3.14×8)

l = 25 m

But,

l² = h²+r².................... Equation 3

Where h = height of the cone.

h = √(l²-r²)

h = √(25²-8²)

h = √(625-64)

h = √(561)

h = 23.69 m

Also Applying,

V = 1/3πr²h

Where V = volume of the cone.

Therefore,

V = (3.14×8²×23.69)/3

V = 1586.91 m³

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

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Answer:

D. 8x²y² - 15x²y + xy² + 5y

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define Expression

(8x²y² - 9x²y + 9y) - (6x²y - xy² + 4y)

Step 2: Simplify

Answer:

451 feet tall

Step-by-step explanation:

3*12=36

36+5=41

41*11= 451

Answer:

\(12\sqrt{3}\)

Step-by-step explanation:

I do not know if this is completely correct

Answer:

C

Step-by-step explanation:

Because it would then all equal a 180 degree triangle.

Answer:

C

Step-by-step explanation:

180-29-90=61

Answer:

-8

Step-by-step explanation:

The term-to-term rule is -8.

16 - 24= -8

8 - 16 = -8

0 - 8 = -8

The arithmetic sequence is a concept of algebra and in given sequence 24, 16, 8, 0 the next term is, -8

In the arithmetic sequence  the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).

Formula for any \(n^{th}\) term in AP,

T = a + (n-1)d

d = T₂-T₁

Where, a is first term , n is \(n^{th}\)  term and d is common difference

Given sequence,

24, 16, 8, 0

a = 24

n = 5

d = 16-24 = -8

T₅ = 24 +( (5-1)×(-8))

T₅ = -8

Hence,  \(5^{th}\) term of sequence is -8

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The graphing form of the function g(x) is: C) none of the answer choices.

The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.

Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:

a = 1 (coefficient of x^2)

b = 4 (coefficient of x)

c = -7 (constant term)

Therefore, the graphing form of the function g(x) is:

C) none of the answer choices

None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.

In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.

The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C

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A circle with Centre \((a,b)\)  has the general equation:

\((x-a)^2 + (y-b)^2 = r^2\)

where \(r\) is the radius and \((a,b)\) is the Centre.

Given that the Centre is at \((0,9)\), the equation is as follows:

\((x-0)^2 + (y-9)^2 = r^2\)

If we simplify, we get:

\(x^2 + (y-9)^2 = r^2\)

The fact that the circle comprises the coordinates  \((65,12)\)  is also provided. Therefore, we may change these values into the equation and find \(r\):

\(65^2 + (12-9)^2 = r^2\)

\(4225 + 9 = r^2\)

\(r^2 = 4234\)

When we square the two sides, we obtain:

\(r = \sqrt{4234}\)

The circle's equation is as follows:

\(x^2 + (y-9)^2 = 4234\)

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Answer:

15/8 minutes

Step-by-step explanation:

The inverse relationship implies the following equation.

\(t=\frac{k}{T}\)

where k is a constant.

You are given a t and T that go together, so

\(2=\frac{k}{75}\)

This implies that k=150.  Now you know that the relationship is

\(t=\frac{150}{T}\)

Now substitute 80 for T to get the answer.

\(t=\frac{150}{80}=\frac{15}{8}\)\(t=\frac{150}{80}=\frac{15}{8}\)

minutes.

It takes an ice cube of the same size to melt in 80f water 15/8 minutes.

We have given,

The time t  for am ice cube to melt. is inversely proportional to the

temperature T of the water in the ice cube is placed.

The inverse relationship implies the following equation.

\(t=\frac{k}{T}\)

Where k is a constant.

You have given a  t and T that go together, so

\(2=\frac{k}{75}\)

This implies that k=150.

Now you know that the relationship is

\(t=\frac{150}{T}\)

Now substitute 80 for T to get the answer.

\(t=\frac{150}{80} =\frac{15}{8}\)

It takes an ice cube of the same size to melt in 80f water 15/8 minutes.

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The proportional relationship used to determine the total number of chairs in x rows is given as follows:

y = 38x.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

There are 304 chairs in 8 rows, hence the constant is given as follows:

k = 304/8

k = 38.

Meaning that the equation is given as follows:

y = 38x.

And that the fourth option is correct.

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Given:

ABCD is the parallelogram.

vertices are A(8,2), B(6,-4), and C(-5,-4)

We know the diagonals of the parallelogram bisect each other.

Find the midpoint of AC.

Now, the midpoint of BD is given as,

The coordinate of D is (-3,2).

The simplified expression is -16∛3.

We have,

-2∛24 - 4∛81

Now,

\(3^4\) = 81

So,

∛81 = ∛(3³ x 3) = 3∛3

And,

2³ = 8

∛24 = ∛(8 x 3) = ∛8 x ∛3 = 2∛3

Now,

-2∛24 - 4∛81

-2 x 2∛3 - 4 x 3∛3

= -4∛3 - 12∛3

= -16∛3

Thus,

The simplified expression is -16∛3.

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Therefore, the correct statement is:" D corresponds to E." that is option B.

A rectangle is a four-sided flat shape with four right angles (90-degree angles) between its sides. It is a type of parallelogram that has two pairs of opposite sides that are parallel and congruent (equal in length), and all four angles are right angles. In a rectangle, the opposite sides are equal in length, which means that the width (or height) of the rectangle is the same throughout. The length of a rectangle is the longer side, while the width (or height) is the shorter side. The perimeter of a rectangle is the sum of the lengths of all its sides, while the area is the product of its length and width. These formulas are often used to calculate the dimensions of a rectangle or to solve problems related to its area or perimeter. Rectangles are used in many applications such as architecture, engineering, mathematics, and art, and they are commonly found in everyday objects such as books, windows, doors, and computer screens.

Here,

In a translation, every point on the preimage (the original figure) moves the same distance and in the same direction to become a point on the image (the translated figure).

To determine which statement is true, we can look at the corresponding vertices of the rectangle ABCD and its image EFGH.

A corresponds to E, B corresponds to F, C corresponds to G, and D corresponds to H.

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The option that can be used to verify the trigonometric identity, \(tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)\) is option C;

C. \(tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)\)

A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions

The specified identity is presented as follows;

\(tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)\)

The half angle formula for tangent indicates that we get;

\(tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}\)

\(\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}\)

When η = 0, we get;

\(-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}\)

\(cot\left(x \right) = \dfrac{cos(x)}{sin(x)}\)

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}\)

\(\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)\)

Therefore;

\(tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)\)

The correct option that can be used to verify the identity is option C

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Answer: Mrs Tan paid $9 for each bowl.

Step-by-step explanation:

Let's first assume the cost of each cup is x, then the cost of each bowl is 3x (since each bowl costs 3 times as much as each cup). According to the problem, Mrs Tan paid $39 for 4 cups and 3 bowls. So we can set up the following equation:

4x + 3(3x) = 39

This simplifies to:

4x + 9x = 39

13x = 39

x = 3

So one cup costs $3.To find out how much each bowl costs, we can simply substitute x = 3 into the expression 3x:

3(3) = 9

So each bowl costs $9.Therefore, Mrs Tan paid $9 for each bowl.

She Paid $9 For Each Bowl

━━━━━━━━━━━━━━━━━━━━━━

ㅤㅤ [ LET :: ]

ㅤ

➔ Cost Of 1 Cup = $x

➔ Cost Of 1 Bowl = $3x

ㅤ

ㅤㅤ [ THEN :: ]

ㅤ

➔ Cost Of 4 Cups = $4x

➔ Cost Of 3 Bowls = $(3×3) = $9x

ㅤ

ㅤㅤ [ ATQ :: ]

ㅤ

\(\begin{gathered} \; \; \sf{:\longmapsto{4x + 9x = 39}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{13x = 39}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{x = \cancel{\dfrac{39}{13}}}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; :\longmapsto{\underline{\boxed{\orange{\frak{x = 3}}}}} \; \pmb{\bigstar} \\ \\ \end{gathered}\)

ㅤ

\(\begin{gathered} \\ \; \; \dag \; {\underline{\underline{\sf{Cost \; Of \; Each \; Bowl:-}}}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; \sf{:\longmapsto{\${(3 \times 3)}}} \\ \\ \end{gathered}\)

\(\begin{gathered} \\ \; \; :\longmapsto{\underline{\boxed{\frak{ \: \: \: \$ \: {9} \: \: \: }}}} \; \pmb{\red{\bigstar}} \\ \\ \end{gathered}\)

\(\bf{\pmb{\underline{\rule{170pt}{5pt}}}}\)

The possible values of x are 3 and 7

Given the rational expression below;

√60-8x = x - 9

Square both sides to have:

(60-8x)² = (x-9)²

60-8x = x²-18x+81

Equate to zero to have;

x²-18x+81 - 60 + 8x = 0

x² - 10x + 21 = 0

x² -3x-7x +21 = 0

x(x-3)-7(x-3) = 0

x = 3 and 7

Hence the possible values of x are 3 and 7

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