Express 324000000 in scientific natation​

Eliminate [tex]y[/tex].

[tex]u + v = (3x - 4y) + (x + 4y) = 4x \implies x = \dfrac{u+v}4[/tex]

Eliminate [tex]x[/tex].

[tex]u - 3v = (3x - 4y) - 3 (x + 4y) = -16y \implies y = \dfrac{3v-u}{16}[/tex]

The Jacobian for this change of coordinates is

[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} \dfrac14 & \dfrac14 \\\\ -\dfrac1{16} & \dfrac3{16} \end{bmatrix}[/tex]

with determinant

[tex]\det(J) = \dfrac14\cdot\dfrac3{16} - \dfrac14\cdot\left(-\dfrac1{16}\right) = \dfrac1{16}[/tex]

 45° only the possible values for x.

What is the meaning of trigonometric ratio?

The given equation can be presented as follows;

[tex]\frac{cos (2 . x )}{cosine(x) + sin(x)} = 0[/tex]

We have that cos(2·x) = cos²(x) - sin²(x)

Also, we have, by the difference of two squares, the following relation;

cos²(x) - sin²(x) = (cos(x) - sin(x))(cos(x) + sin(x))

Therefore, the given equation can be written as follows;

[tex]\frac{cos (2 . x )}{cosine (x) + sin(x) } = \frac{(cos(x) - sin(x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = 0[/tex]

Crossing the common term, (cos(x) + sin(x)), in the numerator and the denominator, we have-

[tex]\frac{(cos(x) - sin (x) * (cos(x) + sin(x)}{(cos(x) + sin(x))} = cos (x) - sin(x) = 0[/tex]

From cos(x) - sin(x) = 0, we have;

Adding sin(x) to both sides of the equation

cos(x) - sin(x) + sin(x) = 0 + sin(x)

cos(x) = sin(x)

Therefore, the opposite leg and the adjacent leg of the right triangle formed with reference to the angle x are equal

∴ x = 90/2 = 45° only for 0° ≤ x ≤ 180°

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[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{10})[/tex]

Answer:

x = 1; y = 2

Step-by-step explanation:

y = 3x − 1

y = -4x + 6

In the first equation, y = 3x - 1.

Substitute 3x - 1 for y in the second equation.

3x - 1 = -4x + 6

7x = 7

x = 1

Substitute 1 for x in the first original equation.

y = 3x - 1

y = 3(1) - 1

y = 3 - 1

y = 2

Solution: x = 1; y = 2

Using compound interest and a graphing calculator, it is found that it will take about 15 years for the loan to be paid off.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For this problem, the parameters are given as follows:

A(0) = 95000, r = 0.06, n = 12.

Hence the value of the loan after t years is:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 95000\left(1 + \frac{0.06}{12}\right)^{12t}[/tex]

[tex]A(t) = 95000(1.005)^{12t}[/tex]

You have monthly payments of $1,200, hence the amount paid after t years is:

P(t) = 12 x 1,200t = 14400t

Then we have to solve for:

A(t) = P(t)

[tex]14400t = 95000(1.005)^{12t}[/tex]

Which is solved in the graph below, meaning that it will take about 15 years for the loan to be paid off.

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The star system is pictured is  open cluster

A type of star cluster known as an open cluster is composed of up to a few thousand stars that are around the same age and originated from the same massive molecular cloud. Within the Milky Way galaxy, more than 1,100 open clusters have been found, and it is believed that there are many more.

The Sun and the things that circle it make up the gravitationally bound solar system. It was created 4.6 billion years ago when a massive interstellar molecular cloud collapsed because to gravity. The Sun is the system's primary mass source, while Jupiter is home to the majority of the system's leftover mass.

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I understand that the question you are looking for is :

| Will mark brainliest | Which type of star system is pictured? |

A. globular cluster

B. open cluster

C. binary

Answer:

B

Step-by-step explanation:

open cluster

The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.

The given values exist

x,      f(x)

6,      -2

7,       4

8,       6

9,       4

10,      -2

The equation of the function in vertex form exists

f(x) = a(x - h)² + k

To estimate the values of a, h, and k,

When x = 6, f(x) = -2 then

-2 = a(6 - h)² + k

= (h²-12·h+36)·a + k.............(1)

When x = 7, f(x) = 4 then

4 = a( 7- h)² + k

= (h²-14·h+49)·a + k...........(2)

When x = 8, f(x) = 6

6 = a( 8- h)² + k ...........(3)

When x = 9, f(x) = 4.

4 = a( 9- h)² + k ..........(4)

When x = 10, f(x) = -2

-2 = a(10- h)² + k ...........(5)

Subtract equation (1) from (2)

4 - 2 = a( 7- h)² + k - (a(6 - h)² + k )

= 13·a - 2·a·h........(6)

Subtract equation (4) from (2)

a (9 - h)² + k - a( 7- h)² + k

32a -4ah = 0

Simplifying the equation, we get

4h = 32

h = 32/4 = 8

From equation (6) we have;

13·a - 2·a·8 = 6

-3a = 6

a = -2

From equation (1), we have;

-2 = -2 × ( 10- 8)² + k

-2 = -8 + k

k = 6

The value of k = 6.

The equation of the function in vertex form exists f(x) = -2·(x - 8)² + 6.

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Answer:

That's a reflection in the x axis.

Step-by-step explanation:

Triangle C is the mirror image  of B with the x axis acting as a mirror.

Answers

The ratio x:y:z is 10:5:3  

Ali got 20,000

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

Explanation:

Let

Those amounts add to 36,000

x+y+z = 36,000

We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps

x+y+z = 36,000

2y+y+z = 36,000

3y+z = 36,000

We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.

3y+z = 36,000

5z+z = 36,000

6z = 36,000

z = (36,000)/6

z = 6,000

This tells us that Chris got 6,000

Use this to find y

3y = 5z

3y = 5*6,000

3y = 30,000

y = (30,000)/3

y = 10,000

Ben received 10,000

Lastly, determine x.

x = 2y

x = 2*10,000

x = 20,000 which is the amount Ali got.

The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.

-------------------------

Check:

Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000

which helps confirm the answer.

The expression that represents the height of the oblique prism is: 1/2x.

What is the Volume of a Prism?

Prism Volume = base area × height of the prism

Given that the oblique prism has:

Volume = 1/2x³ cubic units

edge length = x units

Therefore,

base area = x²

Thus:

1/2x³ = (x²)(height)

Divide both sides by x²

1/2x³ ÷ x² = height

1/2x³ × 1/x² = height

x³/2 × 1/x² = height

height = x³/2x²

height = x/2

Therefore, the expression that represents the height of the oblique prism is: 1/2x.

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The complete question is -

An oblique prism with a square base of edge length x units has a volume of x3 cubic units. Which expression represents the height of the prism?

Answer:3 - x/4

Step-by-step explanation: quotient of x and 4 = x/4. 3 minus x/4 = 3 - x/4.

The expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

We have a sentence - "3 minus the quotient of x and 4".

We have to determine the expression that represents the sentence.

The expression representing the above statement is -

x - y = π.

According to the question, we have -

3 minus the quotient of x and 4.

Using the Division Algorithm -

x = 4q + r

Substituting r = 0 by introducing decimals in the quotient, we get -

q = [tex]$\frac{x}{4}[/tex]

Therefore -

[tex]$3 -\frac{x}{4}[/tex]

Hence, the expression representing the sentence is [tex]$3 -\frac{x}{4}[/tex].

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Answer:

[tex]\displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=-4 \ln |x|+5 \ln|x-1|+\dfrac{3}{x-1}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x[/tex]

Factor the denominator:

[tex]\begin{aligned}\implies x^3-2x^2+x & = x(x^2-2x+1)\\& = x(x^2-x-x+1)\\& = x(x(x-1)-1(x-1))\\ & = x((x-1)(x-1))\\& = x(x-1)^2\end{aligned}[/tex]

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int \dfrac{x^2-4}{x(x-1)^2}\:\:\text{d}x[/tex]

Take partial fractions of the given fraction by writing out the fraction as an identity:

[tex]\begin{aligned}\dfrac{x^2-4}{x(x-1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x-1)}+\dfrac{C}{(x-1)^2}\\\\ \implies \dfrac{x^2-4}{x(x-1)^2} & \equiv \dfrac{A(x-1)^2}{x(x-1)^2}+\dfrac{Bx(x-1)}{x(x-1)^2}+\dfrac{Cx}{x(x-1)^2}\\\\ \implies x^2-4 & \equiv A(x-1)^2+Bx(x-1)+Cx \end{aligned}[/tex]

Calculate the values of A and C using substitution:

[tex]\textsf{when }x=0 \implies -4=A(1)+B(0)+C(0) \implies A=-4[/tex]

[tex]\textsf{when }x=1 \implies -3=A(0)+B(0)+C(1) \implies C=-3[/tex]

Therefore:

[tex]\begin{aligned}\implies x^2-4 & \equiv -4(x-1)^2+Bx(x-1)-3x\\& \equiv -4(x^2-2x+1)+B(x^2-x)-3x\\& \equiv -4x^2+8x-4+Bx^2-Bx-3x\\& \equiv (B-4)x^2+(5-B)x-4\\\end{aligned}[/tex]

Compare constants to find B:

[tex]\implies 1=B-4 \implies B=5[/tex]

Substitute the found values of A, B and C:

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-\dfrac{3}{(x-1)^2}\:\:\text{d}x[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]

[tex]\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x=\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-3(x-1)^{-2}}\:\:\text{d}x[/tex]

[tex]\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int ax^n\:\text{d}x=a \int x^n \:\text{d}x$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating} $\dfrac{1}{x}$\\\\$\displaystyle \int \dfrac{1}{x}\:\text{d}x=\ln |x|+\text{C}$\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]

[tex]\begin{aligned}\implies \displaystyle \int \dfrac{x^2-4}{x^3-2x^2+x}\:\:\text{d}x & =\displaystyle \int -\dfrac{4}{x}+\dfrac{5}{(x-1)}-3(x-1)^{-2}}\:\:\text{d}x\\\\& = \displaystyle -4\int \dfrac{1}{x}\:\:\text{d}x+5\int \dfrac{1}{(x-1)}\:\:\text{d}x-3 \int (x-1)^{-2}}\:\:\text{d}x\\\\& = \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int (x-1)^{-2}}\:\:\text{d}x\end{aligned}[/tex]

Use Integration by Substitution:

[tex]\textsf{Let }u=(x-1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]

Therefore:

[tex]\implies \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int (x-1)^{-2}}\:\:\text{d}x[/tex]

[tex]\implies \displaystyle -4 \ln |x|+5 \ln|x-1|-3 \int u^{-2}}\:\:\text{d}u[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|-\dfrac{3}{-1}u^{-2+1}+\text{C}[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|+3u^{-1}+\text{C}[/tex]

[tex]\implies -4 \ln |x|+5 \ln|x-1|+\dfrac{3}{u}+\text{C}[/tex]

Substitute back in u = (x - 1):

[tex]\implies -4 \ln |x|+5 \ln|x-1|+\dfrac{3}{x-1}+\text{C}[/tex]

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Answer:5

Step-by-step explanation:

321 123

The total amount Aisha would pay to paint her room is $54.

The first step is to determine the area of the walls. The walls have the shape of a rectangle. Thus, the formula for the area of a rectangle would be used to determine the area of the wall.

Area of the three walls without a door : 3 x (length x width)

3 x (2.4 x 5.2) = 37.44 m²

Area of the fourth wall with a door : area of the wall - area of the door

(2.4 x 5.2) - (2 x 0.8) = 10.88m²

Total area of the walls : area of the three walls + area of the wall with the door

10.88m² + 37.44 m² = 48.32 m²

The next step is to determine the number of tins that would be needed:

48.32 /12 = 4.03

5 tins would needed

Cost of the 5 tins: (4 x 12) + (0.5 x 12) = $54

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Answer:

The first option

Kindly award branliest

Given the:

ln(x + 6) - ln(2x - 1) = 1

Using the logarithm rule:

We know,

Simplifying we get,

By cross multiplication we get,

Therefore, the value of x is 1.97.

The correct option in the exercise ln (x + 6) - ln (2x - 1) = 1 is alternative "D".

Answer:

MO = 12

PR = 3

Step-by-step explanation:

The perimeter of a triangle is calculated by adding all side lengths up:

The perimeter of triangle MNO is given as 48

The perimeter of triangle PQR is given as 12

The ratio is 1/4 (simplified ratio of 12/48)

we can write the following equation using this information:

[tex]\frac{x+2}{12x} = \frac{1}{4}[/tex]

cross multiply fractions

12x = 4x + 8

subtract 4x from both sides

8x = 8

divide both sides by 8

x = 1

Now to find the measure of side lengths in question we replace x with 1

for MO = 12x

12*1 = 12

for PR = x + 2

1 + 2 = 3

By using properties of right triangles and trigonometric functions, we conclude that the length of the side BC is 19 units.

In this problem we can use trigonometric functions to determine the length of the side BC in three steps:

Step 1

BE = AB/tan 60°

BE = 19√2 /4

Step 2

BD = BE/cos 45°

BD = 19/2

Step 3

BC = BD/sin 30°

BC = 19

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The given series is diverges according to the P Test.

According to the statement

we have given that the a series and we have to find that the those series is a converges or diverges.

So, For this purpose, we know that the

P-series test to say whether or not the series converges.

So, The given series is

[tex]1 + 1/\sqrt{32} + 1/\sqrt[3]{243 } + 1/\sqrt[4]{1024} + 1/\sqrt[5]{3125}[/tex]

And then

The value of  P becomes P = 5/6 < 1  when we find it using the p series test.

Hence, the p-series diverges

Because according to the p series test, The series converges if, and only if, the power satisfies p>1.

And diverges if, and only if, the power satisfies p<1.

So, The given series is diverges according to the P Test.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use Theorem 9.11 to determine the convergence or divergence of the p-series. 1 + 1/32 squareroot + 1/243 squareroot 3 + 1/1024 squareroot 4 + 1/3125 squareroot 5.

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Answer:

Step-by-step explanation:

6:1 i think

The bags of candy that was sold is 6

The bags of cookies that was sold is 10.

$8.50c + $4.50o = 79 equation 1

o - c = 6

o = 6 + c  equation 2

Where:

Substitute for o in equation 1 using equation 2

$8.50c + $4.50(6 + c) = 79

$8.50c + 27 + 4.50c = 79

$8.50c + 4.50c = 79 - 27

$13c = 52

c = 52 / 13

c = 4

Substitute for c in equation 2

0 = 6 + 4 = 10

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Answer + Step-by-step explanation:

(a)

[tex]\overrightarrow{PQ} =a+\frac{3}{5} b[/tex]

(b)

we are given:

[tex]\left\vert \overrightarrow{RQ} \right\vert =\frac{3}{5} \left\vert \overrightarrow{OP} \right\vert[/tex]

Then

[tex]\left\vert \overrightarrow{WR} \right\vert =\frac{3}{5} \left\vert \overrightarrow{WO} \right\vert[/tex]

and we know that :

[tex]\overrightarrow{OW} = \overrightarrow{OR} + \overrightarrow{RW}[/tex]

Then

[tex]\overrightarrow{OW} = a +\frac{3}{5} \overrightarrow{OW}[/tex]

Then

[tex]\frac{2}{5} \overrightarrow{OW} = a[/tex]

Then

[tex]\overrightarrow{OW} = \frac{5}{2} a[/tex]

since we know that M is the midpoint of the AB segment, that simply means that the two halves it makes are congruent, namely AM = BM.

[tex]\stackrel{AM}{4x+13}~~ = ~~\stackrel{BM}{3x+17}\implies x+13=17\implies x=4~\hfill \stackrel{3(4)~~ + ~~17}{BM=29}[/tex]

The required length of the side BM is 29.

Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.

In the given question,

Point M is the midpoint of line AB.

AM = 4x + 13,

and BM = 3x + 17

To find the length of MB, use midpoint property.

Since, Point M is the midpoint of AB,

Therefore, AM = MB

4x + 13 = 3x + 17

4x - 3x = 17 - 13

x = 4

The length of MB = 3x + 17 = 3 × 4 + 17 = 12 + 17 = 29.

The length of MB, where M is midpoint of AB, is 29.

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The athlete that has the shortest training ride is athlete A.

The athlete that has the shorter range is Athlete B.

The athlete that has the greater median is Athlete B.

The athlete that has the greater IQR is  athlete A.

A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers. The first whisker represents the minimum number and the second whisker represents the maximum number. The difference between the whiskers is known as range.

Range of Athlete A = 36 - 13 = 13

Range of Athlete B = 30 - 19 = 11

Training ride of  Athlete A = 16

Training ride of  Athlete B = 21

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

Median of  Athlete A = 20

Median of  Athlete B = 25

IQR of  Athlete A = 30 - 16 = 14

IQR of  Athlete B = 28 - 21 = 7

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The explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

The given parameters are:

The explicit form is for an arithmetic function.

An arithmetic function has an explicit form represented as:

f(n) = a + (n -1) * d

Substitute the values of n and a in the above equation

f(n) = 3 + (n -1) * -4

Evaluate the product i.e. multiply -4 by (n - 1)

f(n) = 3 -4(n - 1)

Rewrite the equation as

f(n) = -4(n - 1) + 3

The seventh term is then calculated as:

f(n) = -4(n - 1) + 3

Substitute 7 for n in the above equation

f(7) = -4(7 - 1) + 3

Evaluate

f(7) = -21

Hence, the explicit function is (b) f(n) = -4(n - 1) + 3; the seventh term is -21

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The inequality of the graph is expressed as: y > 1/2x + 2.

The graph given has a broken line and the shaded part is above the boundary line, therefore, we would use the sign, ">" in our inequality. The inequality would be expressed as y > mx + b.

Find the slope (m):

Slope (m) = rise/run = 1 units/2 units

m = 1/2

b = 2 (y-intercepts)

Substitute m = 1/2 and b = 2 into y > mx + b

y > 1/2x + 2.

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The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:

Semicircle

A = 0.5π · x²     (1)

Half Semicircle

A = 0.25π · (x + 2)²      (2)

By equalizing (1) and (2):

0.5π · x² = 0.25π · (x + 2)²  

2 · x² = (x + 2)²  

2 · x² = x² + 4 · x + 4

x² - 4 · x - 4 = 0

x² - 4 · x + 4 = 8

(x - 2)² = 8

x - 2 = ±√8

x = 2 ± √8

x = 2 ± 2√2

x = 2 · (1 ± √2)

x = 2 · (1 ± 1.41)

x₁ = 2 · 2.41   ∨   x₂ = 2 · (- 0.41)

x₁ = 4.82   ∨   x₂ = - 0.82

The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.

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Answer:

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

The distance traveled by two planes in an hour is:

Let the rate of one plane be x, then the other plane's rate is x - 66.

The sum of two rates is the distance traveled in one hour:

So the rate of one plane is 926 km/h and of the other plane is:

Answer:

The answer would be (7, 18)

Step-by-step explanation:

The answers simple,

in the equation y=|-3x+3|

x and y would be said like this (x,y). just like the answer choices

now in the first option, x is R, so i couldn't understand that. so I'm gonna skip that.

in the second one, (7,0) would no work as

0=|-3(7) + 3|

0=|-21+3|

0=|-18|

and since "|" is absolute value, meaning that instead of the number being negative or positive the number will just be translated into how much distance is from the number and 0, or just make the number positive.

lets continue,

0=18, so (7,0)

the second one, (7,-18)

-18=|-3(7)+3|

-18=|-18|

again, its absolute value so

-18=18, so it still doesn't work

the last one, (7,18)

18=|-3(7)+3|

18=|18|

18=18

so (7,18) would work.