Complete the equation. Answer as a fraction in its simplest form.

9xy * (2/3x)^3 = ( / )x^4 y

Answer:

A

Step-by-step explanation:

The formula for this type of interest is \(A=P(1+\frac{r}{n})^{nt}\), where A is the total amount, P is the initial investment, x is the interest rate, n is the amount of times that the investment is compounded a year, and t is the amount of years. Plugging in the numbers given, you get:

\(A=1800(1+\frac{0.025}{2})^{2\cdot 12}=\)

\(1800(1.0125)^{24}\approx 2425.23\)

Now, she invests this into a new account, and you can set up the following equation:

\(A=2425.23(1+\frac{0.04}{12})^{12\cdot 7}=\)

\(2425.23(1.0033333)^{84}\approx 3207.40\), or option A.

Hope this helps!

Answer:

10 √10

Step-by-step explanation:

Answer:

\(10\sqrt{10}\)

Step-by-step explanation:

The largest perfect square of the factors of 1000 is 100. We can therefore convert √1000 like this:

√100 × 10

Next, we separate the numbers inside the √ as such:

√100 × √10

√100 is a perfect square that equals 10. We can therefore put 10 outside the radical and get the final answer to square root of 1000 in simplest radical form as follows:

10√10

Answer:

so there will be 8 over 24 for the chocolate ice cream cones and since one cone was taken out, the denominator for the next fraction probability would be 23 and there are 10 vanilla ice cream cones so 10/23 so 8 over 24 * 10 over 23 So its not A and D the correct one is C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

quotient if 3 over 5 is 1.66666. (or) 1.7

The approximation for √16.2 using linear approximation (tangent line) is approximately 4.01249375.

To find the equation of the tangent line to f(x) = √x at x = 16, we need to determine the slope of the tangent line and the y-intercept. Taking the derivative of f(x) with respect to x, we get f'(x) = 1 / (2√x). Evaluating this at x = 16, we find f'(16) = 1 / (2√16) = 1/8.

The equation of a line can be written as y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values, we have y = (1/8)x + b. To find b, we substitute the coordinates of the point (16, f(16)) = (16, 4) into the equation and solve for b. This gives us 4 = (1/8)(16) + b, which simplifies to b = 2.

Therefore, the equation of the tangent line to f(x) at x = 16 is y = (1/8)x + 2. Plugging in x = 16.2 into this equation, we can approximate √16.2 as follows: L(16.2) ≈ (1/8)(16.2) + 2 ≈ 4.01249375.

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14 ) x + 37 + 37 = 180

or , x + 74 = 180

or , x = 180 - 74

or , x = 106

To complete the square for the equation x2 - 16x + 60 = -12, add 64 to each side of the equation. This will give us x2 - 16x + 124 = 52.

Then, factor out the coefficient of x2 (1) and the coefficient of x (16). This will give us (x - 8)2 = 52. Finally, subtract 52 from both sides to get (x - 8)2 = 0. Solving for x yields x = 8.

Equations are mathematical statements that express the equality of two expressions. They involve one or more unknowns that are represented by variables and involve numbers, constants, and operators. An equation states that the expressions on either side of the equal sign have the same value.

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The length of the QR is 16 cm when PQR ~MNO

In the given question, it is given that two similar triangles as PQR ~MNO

Then, the corresponding sides will be in equal proportion to each other as follows

PQ / MN = PR / MO = QR / NO

We need to find the length of the side QR

As above relations are given,

\(\frac{PQ}{MN}\) = \(\frac{PR}{MO}\) = \(\frac{QR}{NO}\)

\(\frac{30}{10}\) = \(\frac{5x + 7}{x+5}\) = \(\frac{4x}{\frac{16}{3} }\)

Equating all the fractions, equal to each we'll find

\(\frac{5x + 7}{x+5}\) = \(\frac{30}{10}\)

5x + 7 = 3(x +5)

5x + 7 = 3x + 15

2x = 8

x = 4

We know that, the length of the QR = 4x cm = 4 x 4 cm = 16 cm

Therefore, the length of the QR is 16 cm when PQR ~MNO

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The inequality that represents the number of songs and albums that Jorge could download is:

$2*s + $12*a ≤ $50

Here we have the variables:

s = number of songs.

a = number of albums.

Then the total cost can be written as:

$2*s + $12*a

And we know that Jorge has a maximum of $50 to spend, so the total cost can be equal to or smaller than $50, so the inequality is:

$2*s + $12*a ≤ $50

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Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -

1 - A

2 - C

3 - B

4 - D

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The y-intercept of the linear equation represented by the table is 8, so the correct option is C.

Here we have a function represented by the table:

x     y

-2    16

1      4

2      0

4      -8

7      -20

This seems to be a linear function, such that each time we increase the value of x by one unit, the value of y decreases by 4.

Then the equation is something like:

y = -4x + b

b is the y-intercept.

We can replace the values of a known point like (2, 0) to get:

0 = -4*2 + b

0 = -8 + b

8 = b

Then the line is:

y = -4x + 8

The y-intercept is 8, the correct option is C.

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Answer:12/5

Step-by-step explanation:

tan(x)=opposite/adjacent

tan(x)=12/5

Answer:

2.4

Step-by-step explanation:

This is a right-angled triangle:

where:
Side XY = hypotenuse

              = 13 units

With respect to Angle X:

Side YZ = opposite side

             = 12 units

Side XZ = adjacent side

              = 5 units

Trigonometric function:

Tan∅= \(\frac{opposite}{adjacent}\)

 ∴TanX = \(\frac{SideYZ}{SideXZ}\)

             = \(\frac{12}{5}\)

             = 2.4

Answer:

45m

Step-by-step explanation:

4m+19m+14m+8m=45m

Given expressions:

  Area of a rectangle  = L W

  Area of a triangle = \(\frac{1}{2} B H\)

Problem;

Create problems using the formula;

Solution:

Problem 1; Find the area of a rectangle whose length is 10cm and the width is half the size of the length?

    Given parameters:

    Length of rectangle  = 10cm

    Width of rectangle  = \(\frac{1}{2}\) x length  = \(\frac{1}{2}\) x 10  = 5cm

So, the area of the rectangle = 10cm x 5cm  = 50cm²

2. A triangle with a base length of 30cm and a height of 2cm will have an area of what?

    Given parameters:

         base length  = 30cm

         height  = 2cm

 Solution:

   Area of a triangle  = \(\frac{1}{2}\) x b x h

   Area of a triangle  = \(\frac{1}{2}\) x 30 x 2  = 30cm²

The area of the triangle will be 30cm²

To reparametrize the curve with respect to arc length, we need to find the arc length function s(t) and then solve for t in terms of s.

The arc length function is given by:

s(t) = ∫√[r'(t)·r'(t)] dt

where r'(t) is the derivative of r(t) with respect to t.

We can calculate r'(t) as:

r'(t) = (2e^(2t)cos(2t) - 4e^(2t)sin(2t))i + (12e^(2t)sin(2t))j + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))k

Now we can substitute this into the arc length formula and integrate:

s(t) = ∫√[(2e^(2t)cos(2t) - 4e^(2t)sin(2t))^2 + (12e^(2t)sin(2t))^2 + (2e^(2t)sin(2t) + 6e^(2t)cos(2t))^2] dt

This integral looks quite complicated, so we will use a numerical integration method to approximate s(t).

We can use the trapezoidal rule to numerically integrate s(t) between t = 0 and some value t = T:

s(T) ≈ ∑[s(iΔt) + s((i+1)Δt)]/2 * Δt

where Δt = T/n is the step size, and n is the number of intervals we use.

Once we have approximated s(t), we can solve for t in terms of s using numerical methods such as the bisection method or Newton's method.

For example, if we want to find the value of t that corresponds to s = 10, we can solve:

s(t) = 10

for t using numerical methods. Once we have t, we can plug it back into r(t) to get the reparametrized curve in terms of arc length s.

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Answer:

3.3lbs

Step-by-step explanation:

5 x 2/3 = 3.3

\(\frac{3}{14}\) is the straight section.

A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.

Given Data

Length = 5\(\frac{5}{6}\)

Length = \(\frac{35}{6}\)

Straight section = 1\(\frac{1}{4}\)

Straight section = \(\frac{5}{4}\)

Dividing them:

= \(\frac{35}{6}\) ÷ \(\frac{5}{4}\)

= \(\frac{35}{6}\) ×\(\frac{4}{5}\)

= \(\frac{6}{28}\)

= \(\frac{3}{14}\)

\(\frac{3}{14}\) is the straight section.

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The given expression is of the form y=mx+c. Comparing, we get the slope as 7.

The direction and steepness of a line are represented numerically by the slope or gradient of the line. It provides the ratio of how much y rises when x rises by a particular amount. The general form is therefore y=mx+c, where c represents the y-intercept and m represents the slope. This form gives the slope-intercept form.

Given the expression is  y=7x+3. Comparing this expression with the general form we get, slope or gradient as 7 and y-intercept as 3. Therefore, the required answer is 7.  

The complete question -

What is the gradient of the line y=7x+3?

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There are twο cοmpοnents that make up 10 and 15, namely 1 and 5. Hence, 5 is the biggest cοmmοn factοr between 10 and 15.

Numbers are present in every part οf οur everyday Iives, incIuding the number οf Iaps we cοmpIete οn the racetrack, the number οf hοurs we sIeep at night, and many οther things.

In math, a number can be even, οdd, prime, cοmpοsite, decimaI, fractiοnaI, ratiοnaI, irratiοnaI, naturaI, integer, reaI, whοIe, οr any cοmbinatiοn οf these.

Numbers are the basis οf mathematics.

We must Iearn abοut numbers if we are tο understand math.

There are many different kinds οf numbers.

There is a Iengthy Iist that incIudes whοIe numbers, οrdinaI numbers, οrdinaI numbers, naturaI numbers, οdd numbers, even numbers, cοnsecutive numbers, and sο οn.

Hence, There are twο cοmpοnents that make up 10 and 15, nameIy 1 and 5. Hence, 5 is the biggest cοmmοn factοr between 10 and 15.

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Answer:

1st answer choice

Step-by-step explanation:

The Power series representation of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.

An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.

The Maclaurin series will be used in this instance to expand the function:

\(tan^-^1x\) = \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}\)

and for    \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}\)

=>  \(tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)  -------(i)

and f(x) = \(x^8tan^-^1x^3\)

now we need to multiply \(x^8\) in the above equation to get the power series expansion of f(x)

\(x^8tan^-^1x^3\) = \(x^8\) \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}\)

=> \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}\)

=>  \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

so the expansion of f(x) = \(x^8tan^-^1x^3\) is \($$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}\)

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-2 is the minimum value of the given set.

Assume that x is the minimum value.

The difference between the largest value and the least value is therefore what we use to determine the range:

Range = Maximum value - Minimum value

6 = 4 - x

Solving for x, we can subtract 4 from both sides:

6 - 4 = 4 - x - 4

2 = -x

Finally, we can multiply both sides by -1 to get x by itself:

x = -2

Therefore, the minimum value is -2.

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Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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Answer:

sjobciducbqpfhivñqrjivbñkqjvbñqjirv

Answer:

162°

Step-by-step explanation:

To convert from radian to degree measure

degree measure = radian measure × \(\frac{180}{\pi }\) , then

degree = \(\frac{9\pi }{10}\) × \(\frac{180}{\pi }\) ( cancel π and 10/ 180 to simplify )

            = 9 × 18

           = 162°

Answer:

324.

Step-by-step explanation:

Answer:

Answer is actually 29

Step-by-step explanation:

To get the 3 consecutive numbers in the first place, you would do 90 = x + (x+1) + (x+2). This would basically be 90 = 3x +3 , which x = 29. If you wanted to find the 3 integers, which would be 29, 30, 31, you substitute x for 29

Answer:

40 US$

Step-by-step explanation:

hope this helps you! let me know if u have any questions