Which of the following is a radical equation?
X3 - 13
X+ 15 - 13
√x+3-13
x+3 - 13

To turn the specified limit, which is a Riemann sum, within the known interval, [2, 6], and variable, \(x_i\), to a definite integral, the value, Δx is dx as n approaches infinity, to get;

\(\displaystyle \lim\limits_{n\to \infty}\sum\limits^n_{i=1}x_i\cdot \ln \left(1+x_i^2 \right) \Delta x, [2, \,6] = \int\limits^6_2 {x\cdot \ln \left(1+x_i^2 \right)} \, dx\)

A Riemann sum is an approximation of an integral, which is the area of a region, by making use of the sum of simplified slices that make up the region.

A definite integral is a calculation used to find the area under a graph of a function by making use of very small or infinitesimal stripes of the region under the graph of the function.

The expression in the question is a Riemann sum

\(\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot ln \left(1 + x_i^2 \right) \Delta x, [2, 6]\)

The Riemann sum can be converted into a definite integral, using the equation, \(\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n f(x_i)\Delta x = \int\limits^b_a {f(x)} \, dx }\)as follows;

The value of Δx is the value which values in the parenthesis are multiplying on the left, therefore; Δx is replaced with dx, as n → ∞

The limits of the Riemann sum in the question = [2, 6]

\(f(x_i) = x_i \cdot \ln\left(1 + x_i^2 \right)\), therefore, \(f(x) = x \cdot \ln\left(1 + x^2 \right)\)

Plugging in the the above values into the expression for the Riemann sum, we get the following definite integral;

\(\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot \ln \left(1 + x_i^2 \right) \Delta x, [2, 6] = \int\limits^6_2 {x\cdot \ln\left(1 + x^2\right)} \, dx\)

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Answer:

\(a_n=3(-3)^{n-1}\)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: \(a_n=ar^{n-1}\)

where:

Given:

To find the common ratio r, divide consecutive terms:

\(\implies r=\dfrac{a_2}{a_1}=\dfrac{-9}{3}=-3\)

Therefore, the equation is:

\(a_n=3(-3)^{n-1}\)

Steps to solve:

4(w + 3) - 2

~Disribute

4w + 12 - 2

~Combine like terms

4w + 10

Best of Luck!

The length of the arc of the circle subtended by the angle is option (b) 5π/3 meters.

Arc length is the length of a portion of the circumference of a circle. It is the distance along the curved line that makes up the circle's boundary, measured in linear units

The length of the arc of a circle subtended by a central angle can be found using the formula

arc length = (central angle / 360°) × 2πr

where r is the radius of the circle.

Substituting the given values, we get

arc length = (150° / 360°) × 2π(2 meters)

arc length = (5/12) × 2π(2 meters)

arc length = (5/3)π meters

Therefore, the correct option is (b) (5/3)π meters

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The area of a rectangle can be calculated with the following expression:

In this case, we have the width and height given in scientific notation, which means they have a power of 10. In order to multiply two numbers represented in this manner, we need to make both powers have the same exponent, this is done by adding one zero on the first notation.

Answer:

Step-by-step explanation:

Using A=P(1+r/n)^nt

Where,

P = principal amount (the initial amount you borrow or deposit), in this case $3000

r = annual rate of interest (as a decimal), in this case 0.06

t = number of years the amount is deposited or borrowed for, in this case we don't know it

A = amount of money accumulated after n years, including interest, in this case $21000

n = number of times the interest is compounded per year, in this case 12

     This gives us 21,000=3,000(1+0.06/12)^12t

    After simplification, 7=(1.005)^12t

By taking the logarithm of both sides,

                            Log7=Log1.005^12t

                               12t = Log 7/Log 1.005

                               12t =390.1545

          This gives us 32.5months

The inequality that represents the value of x is (b)  x > 80

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

The figure

The general rule is that

The larger the side length, the larger the angle opposite it

using the above as a guide, we have the following:

1/8x > 10

So, we have

x > 80

Hence, the inequality is x > 80

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The rule of (x, y) → (-x, y), which is reflection over y-axis.

Given that, ΔABC maps to triangle ΔA'B'C'.

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

The coordinate points of ΔABC are A(-4, 3), B(-3, -3) and C(1, 2) and the coordinate points of ΔA'B'C' are A'(4, 3), B'(3, -3) and C'(-1, 2).

Here, A(-4, 3) → A'(4, 3), x-coordinate is negated and y-coordinate remains same.

Similarly, B(-3, -3) → B'(3, -3) and C(1, 2) → C'(-1, 2) follows the same pattern.

From this, it is clear that the coordinates of triangle ABC is reflected on y-axis.

Therefore, the rule of (x, y) → (-x, y), which is reflection over y-axis.

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✏️VOLUME

Solution:

Figure #1.

Since the given is a rectangular prism, use the formula:

Where:

Given:

» Substitute the givens on the formula.

Therefore, the volume of the rectangular prism is 1 620 in.³

Figure #2

Since the given a cube, use the formula:

Where:

Given:

» Substitute the given on the formula.

Therefore, the volume of the cube is 729 in.³

Figure #3

Since the given is a cylinder, use the formula:

Where:

Given:

» Substitute the givens on the formula.

Therefore, the volume of the cylinder is 351.68 in.³

Answer:

Number #1

Number #2

Number #3

•••••••••••••••••••••••••••••••••••••••••••••••••

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The probability of 5 or fewer Mexican Americans among 12 jurors is 0.0089.

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true.

Consider the probabilities,

x               P(x)

0                0+          

1                0+

2                0+

3             0.0002

4             0.0014

5             0.0073

6             0.0285

7             0.0818

8             0.1712

9             0.2547

10           0.2558

11           0.1557

12           0.0434

So, the probability of 5 or fewer Mexican Americans among 12 jurors is:

P( x ≤ 5 ) = P( x = 0 ) + P( x = 1 ) + P( x = 2 ) + P( x = 3 ) + P( x = 4 ) + P( x = 5 )

P( x ≤ 5 ) = 0 + 0 + 0 + 0.0002 + 0.0014 + 0.0073

P( x ≤ 5 ) = 0.0089

Therefore, 0.0089 is the probability that 5 or fewer Mexican Americans among 12 jurors.

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Step-by-step explanation:

Log(x²+8)=log 10+ log x

Log(x²+8)=log(10×x)

x²+8=10x

x² - 10x + 8=0

x is approximately to - 1 and - 8✅

The solutions to the given equation are x = -1 and x = 8.

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

Using logarithmic properties, we can simplify the given equation:

logs(x² + 8) = 1 + log g(x)

logs(x² + 8) - log g(x) = 1

log[(x² + 8)/g(x)] = 1

(x² + 8)/g(x) = 10

x² + 8 = 10g(x)

Now we can solve for x by substituting the given answer options and solving for g(x):

For x = -2 and x = -4:

x = -2:

(-2)² + 8 = 12, which is not equal to 10 g(x) for any value of g(x).

So x = -2 is not a solution.

x = -4:

(-4)² + 8 = 24, which is also not equal to 10g(x) for any value of g(x).

So x = -4 is not a solution.

For x = -1 and x = 8:

x = -1:

(-1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = -1 is a solution.

x = 8:

(8)² + 8 = 72, which is equal to 10g(x) when g(x) = 7.2.

So x = 8 is a solution.

For x = 1 and x = -8:

x = 1:

(1)² + 8 = 9, which is equal to 10g(x) when g(x) = 0.9.

So x = 1 is a solution.

x = -8:

(-8)² + 8 = 56, which is not equal to 10g(x) for any value of g(x).

So x = -8 is not a solution.

Therefore,

The solutions to the given equation are x = -1 and x = 8.

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The annual interest rate is 7.5%.

What is Simple interest?

Simple interest is a type of interest that is calculated on the principal amount (or the initial amount) of a loan or investment, without taking into account any accumulated interest from previous periods.

The formula for simple interest is:

I = P × r × t

where I is the interest earned, P is the principal (initial amount), r is the annual interest rate as a decimal, and t is the time in years.

In this case, we know I = $562.50, P = $1500, and t = 5 years.

we ca substitute values into the formula,

562.50 = 1500× r ×5

Simplifying, we get:

r = 562.50 / (1500 ×5)

r = 0.075

r = 7.5%

Therefore, the annual interest rate is 7.5%.

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Answer:

I'm pretty sure the answer is 90

Step-by-step explanation:

27.7 rounded up is 28 and 2.8 rounded up is 3, and the product of those 2 numbers is 84 and 90 is the closest number so that should be the answer :)

Answer:

The answer is 90

Step-by-step explanation:

27.7 rounded up is 28 and 2.8 rounded up is 3 so 28 times 3 is 84 and the closest number to 84 is 90

The location of the point B on the line with the endpoints is 63

On the segment, we have the following endpoints

A = -3

C = 8

Rewrite the endpoints of the line segment as

A = (-3,0) and C = (8,0)

The ratio of the line is given as

Ratio, A : B = 1 :5

This means that

Point C = A/A + B

So, we have

C = 1/1 + 5

Evaluate

C = 1/6

The coordinate of point C on the line segment is calculated using

Point C = C * (B - A) + A

So, we have

8 = 1/6 * (B + 3) - 3

This gives

1/6 * (B + 3) = 11

So, we have

B + 3 = 66

Subtract 3

B = 63

Hence, the coordinate of the point B on the line segment is  63

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Possible question

if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?

A = -3  and C = 8

The maximum temperature during summer in that year was 34°C.

It's not possible for the maximum temperature in Gulmarg, Kashmir to rise by 44°C during the summer.

A temperature rise of that magnitude would be extremely unusual and potentially dangerous.

However, assuming that the question meant to ask about the difference between the minimum temperature in January and the maximum temperature in summer, we can proceed with the calculation.

The minimum temperature in January was -10°C, and if we add 44°C to it, we get:

-10°C + 44°C = 34°C

Therefore, the maximum temperature during summer in that year was 34°C.

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Answer:

Int 2520, Ext 360

Int 3960, Ext 360

Int 5040, Ext 360

Int 2160, Ext 360

Int 3600, Ext 360

Int 6840, Ext 360

Step-by-step explanation:

Interior angles of a polygon = (sides - 2) × 180

Exterior angles are always 360

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The measures of an exterior angle are 2520°, and an interior angle is 360° in the given regular polygon with 16 sides.

An interior angle is defined as an angle produced on the inside of a polygon by extending the sides of the polygon.

Interior angles of a polygon = (sides - 2) × 180°

To determine the measures of an exterior angle and an interior angle given a regular polygon with 16 sides.

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 16

Interior angles of a polygon = (16 - 2) × 180

Interior angles of a polygon = (14) × 180

Interior angles of a polygon = 2520

And, Exterior angles are always 360° in the regular polygon.

Similarly, the other regular polygons :

A regular polygon with 24 sides: Int 3960, Ext 360

A regular polygon with 30 sides: Int 5040, Ext 360

A regular polygon with 14 sides: Int 2160, Ext 360

A regular polygon with 22 sides: Int 3600, Ext 360

A regular polygon with 40 sides: Int 6840, Ext 360

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Answer:

area of trapezium in terms of x=1/2*x(x+3+x+1)

Step-by-step explanation:

Answer:

(x^2 + 2x) cm^2

Step-by-step explanation:

Area of trapezium = 1/2 (a+b)h

= 1/2 [(x+3)+(x+1)] (x)

=1/2 (2x+4)(x)

= 1/2 (2x^2 + 4x)

= x^2 + 2x

Answer:

1/2? I believe it is 1/2 you go up one and over 2

Answer:

You forgot something

Step-by-step explanation:

"which of the following points "

no points follow?????

\(\huge\text{Hey there!}\)

\(\huge\textbf{Original equation/problem:}\)

\(\mathbf{687\times391}\)

\(\mathbf{= 391\times687}\)

\(\mathbf{= 268,617}\)

\(\huge\textbf{Now, we're going to solve for your}\\\huge\textbf{question:}\)

\(\huge\text{Assuming you want us to estimate to the}\\\huge\text{nearest hundred. So we will do so, because}\\\huge\text{it is easier to understand it like that.}\)

\(\mathbf{687 \rightarrow 700}\\\mathbf{391\rightarrow 400}\)

\(\huge\textbf{New equation:}\)

\(\mathbf{700 \times 400}\)

\(\mathbf{= 400\times700}\)

\(\mathbf{= 280,000}\)

\(\huge\text{Therefore, your answer is: \boxed{\mathsf{Option\ A.\ 280,000}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

23.33

Step-by-step explanation:

The whole number that can be substituted for z is 1.

To order these numbers from least to greatest, we need to first find a value for x that makes the expressions comparable.

1/x can be rewritten as 0.01/x

80% can be written as 0.8

So, the list becomes:

0.01/x, x/3, 0.8

To compare 0.01/x and x/3, we can cross-multiply and simplify:

0.01/x < x/3

0.01*3 < x^2

0.03 < x^2

x > sqrt(0.03)

Since x has to be a whole number, the smallest possible value for x is 1.

So, substituting x = 1, the list becomes:

0.01, 1/3, 0.8

Ordering these from least to greatest, we get:

0.01, 0.8, 1/3

Therefore, the whole number that can be substituted for z is 1.

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Answer:

3240 sq meters

Step-by-step explanation:

Area of garden = 90*60= 5400 square meters.

Flowers grown on = 40%

So, grass grown on = (100 -40)% = 60%

60% of 5400 = 0.6*5400 = 3,240.

So, the area of the garden that is grass = 3,240 square meters

Answer:

c) (6,5)

Step-by-step explanation:

The horizontal axis represents x values

The vertical axis represents y values

Answer:

The answer is D. infinite.

Answer:

infinte

Step-by-step explanation:

→ For any value of x which is substituted you will get that value

\(14^{-x+10}~~ = ~~13^{3x} \\\\[-0.35em] ~\dotfill\\\\ \log(14^{10-x})=\log(13^{3x})\implies (10-x)\log(14)=x\log(13^3) \\\\\\ 10-x=\cfrac{x\log(13^3)}{\log(14)}\implies \cfrac{10-x}{x}=\cfrac{\log(13^3)}{\log(14)}\implies \cfrac{10}{x}-\cfrac{x}{x}=\cfrac{\log(13^3)}{\log(14)}\)

\(\cfrac{10}{x}-1=\cfrac{\log(13^3)}{\log(14)}\implies \cfrac{10}{x}=\cfrac{\log(13^3)}{\log(14)}+1\implies \cfrac{10}{~~\frac{\log(13^3)}{\log(14)}+1~~}=x \\\\\\ \cfrac{10}{~~\frac{\log(13^3)+\log(14)}{\log(14)}~~}=x\implies \cfrac{10\log(14)}{\log(13^3)+\log(14)}=x\)

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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The coordinates of point G are (1.5, -4). The reflection of point G across x-axis and y-axis lies in quadrant II, and the coordinates of that point are (-1.5, 4). ​

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

Based on the, the coordinates of point G are located at (1.5, -4) in quadrant IV.

By applying a reflection over the x-axis to the coordinates of point G, we have the following coordinates of the image G';

(x, y)                              →      (x, -y)

Point G (1.5, -4)             →      G' (1.5, -(-4)) = G' (1.5, 4)

By applying a reflection over the y-axis to the coordinates of point G', we have the following coordinates of the image G";

(x, y)                            →      (-x, y)

Point G' (1.5, 4)           →      G" (-1.5, 4), which is located in quadrant II.

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