Complete the steps to solve this linear equation: 2x 9(x – 1) = 8(2x 2) – 5 1.apply the distributive property: 2x 9x– 9 = 16x 16 – 5 2.combine like terms on each side: 11x – 9 = 16x 11 3.use the subtraction property of equality to isolate the variable term: –9 = 5x 11 use the subtraction property of equality to isolate the constant: –20 = 5x 4. use the division property of equality to solve: = x

Answer:

Step-by-step explanation:

Comment

The semicircle comes out towards we the viewer, then it goes upwards, and what one gets is 1/2 a sphere. If one keeps on rotating in the direction of the arrow eventually winding up where one started, the result is a full sphere.

Answer: Sphere

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]

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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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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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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Step-by-step explanation:

The volume of a cube is

[tex]a {}^{3} [/tex]

where a is the side length,

Note: If you want to remember this formula, know that a cube is basically a bunch of squares stacked on one another vertically and horizontally

The area of a square with side length a, is

[tex] {a}^{2} [/tex]

If we multiply that by the height of the cube, which is a.

[tex] {a}^{2} \times a = {a}^{3} [/tex]

That is the easy way to derive the formula of the volume of a cube.

Back on track, we know the volume so we must solve for a.

1.

[tex]125 = {a}^{3} [/tex]

Assuming you took algebra, to isolate the variable a, we must undo it being raised to the third power.

To do this, we take the cube root of both sides

[tex] \sqrt[3]{125} = \sqrt[3]{a {}^{3} } [/tex]

The cube root of 125 is 5 so

[tex]5 = a[/tex]

5 cm

2.

[tex]8 = {a}^{3} [/tex]

[tex] \sqrt[3]{8} = \sqrt[3]{ {a}^{3} } [/tex]

[tex]2 = a[/tex]

2 ft

3.

[tex]343 = {a}^{3} [/tex]

[tex]a = 7[/tex]

7 yd

4.

[tex]1000 = a {}^{3} [/tex]

[tex]10 = a[/tex]

10 mm

5.

[tex]1728 = {a}^{3} [/tex]

[tex]a = 12[/tex]

12 in. or 1 ft

6.

[tex]1 = {a}^{3} [/tex]

[tex]a = 1[/tex]

1 m

Answer:

A cube can be seen as a square that has been 'stretched'. We know that all four sides of a square are equal, thus, the sides of the faces of a cube are also equal.

In order to find the volume of a cube, the formula we apply is length x width x height (lwh).

Since all the sides are the same, another formula for the volume of the cube can be written as volume = x^3 in which x stands for the length of each side. When plugging in the formula:

1) V = 125 cm^3

   125 = x^3

   ∛125 = x

    5 = x

When finding the cube root, you can use a calculator or fingure out the answer yourself by multiplying any number by itself three times.

2) 8 = x^3

   ∛8 = x

      2 = x

3) 343 = x^3

 ∛343 = x

        7 = x

4) 1000 = x^3

 ∛1000 = x

         10 = x

5) 1728 = x^3

  ∛1728 = x

    12 = x

6) 1 = x^3

   ∛1 = x

      1 = x

Make sure to include the appropriate unit for each answer

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

Answer:

The first option

Kindly award branliest

 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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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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Answer:5

Step-by-step explanation:

321 123

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.

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:

  (d)  (4, -10)

Step-by-step explanation:

We are asked to identify the point that falls on a line defined by parametric equations.

The parametric equation can be written in a number of forms One of these is a vector form, in which some multiple of a vector is added to a known point.

  (x(t), y(t)) = (1/2t +4, 2t -10) = (4, -10) +(1/2t, 2t)

  (x, y) = (4, -10) +(t/2)(1, 4)

Clearly, when t=0, one point on the line will be (4, -10) — the last of the offered choices.

Another form of the equation can be had by solving the x(t) and y(t) equations for t, then equating those values.

  x = 1/2t +4   ⇒   2(x -4) = t

  y = 2t -10   ⇒   (y +10)/2 = t

Equating these gives ...

  2(x -4) = (y +10)/2 . . . . t = t

  4x -16 = y +10 . . . . . . . multiply by 2

  4x -y = 26 . . . . . . . . . add 16-y to put in standard form

Dividing by 26 gives intercept form:

  x/6.5 +y/(-26) = 1 . . . . . x-intercept: 6.5, y-intercept: -26.

This tells you the value of y will be negative for all x-values less than 6.5. All of the offered points have x-values less than that, so the only viable answer choice is (4, -10).

Answer:

(4.-10)

Step-by-step explanation:

When t = 0:

x(t)=1/2t+4

x(0)=1/2(0)+4

x(0) = 4

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

y(t)=2t−10

y(0)=2(0)−10

y(0) = -10

(x,y) at t = 0 is (4, -10)

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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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".

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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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

The probability of Maria selecting 2 questions on Science is 1/ 5

From the information given, we have that there are;

The total questions = 2 + 4 + 4 = 10 questions

We have that Maria picks two questions at random

The probability of her selecting two questions on Science is given as

P(2 science) = number of Science questions/ total number of questions

P(2 science) = 2/ 10

P(2 science) = 1/ 5

The probability of picking two questions on Science is 1/5

Thus, the probability of Maria selecting 2 questions on Science is 1/ 5

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Answer:

1/45

Step-by-step explanation:

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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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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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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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:

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.

Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. A function's range is its potential output, whereas its domain is the set of all possible input data.

The function can be written as :

[tex]f(x)=\sqrt[\frac{2}{3} ]{108^{2x} } \\f(x)=108^{\frac{3}{2}^{2x} }[/tex]

Now that x is an exponent, all real values are possible for it. Therefore, all real numbers make up its domain for f(x). But value of f(x) cannot be less than 1 because for x = 0 the value of f(x) is 1 and also for any values of x, the value of f(x) can never be less than 1

So, Range of f(x) is all real numbers greater than 0

Hence, Domain and Range of f(x) is given by:

Domain: {x | all real numbers} ;

Range: {y | y > 0}

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See attachment for the graph of the functions y = x + 2, y = 2x and y = -x

Equation 14

The equation is given as:

y = x + 2

When x = 0, we  have

y = 0 + 2 = 2

When x = 1, we  have

y = 1 + 2 = 3

When x = 2, we  have

y = 2 + 2 = 4

So, the complete table is

x    y

0     2

1      3

2     4

See attachment for the graph of the function y = x + 2

Equation 15

The equation is given as:

y = 2x

When x = 0, we  have

y = 2 * 0 = 0

When x = 1, we  have

y = 2 * 1 = 2

When x = 2, we  have

y = 2 * 2 = 4

When x = 3, we  have

y = 2 * 3 = 6

So, the complete table is

x    y

0    0

1     2

2    4

3    6

See attachment for the graph of the function y = 2x

Equation 16

The equation is given as:

y = -x

When x = -3, we  have

y = 3

When x = -1, we  have

y = 1

When x = 1, we  have

y = -1

When x = 3, we  have

y = -3

So, the complete table is

x    y

-3    3

-1     1

1     -1

3    -3

See attachment for the graph of the function y = -x

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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

[tex]\boldsymbol{\sf{\dfrac{19}{23}\times50 }}[/tex]

We express 19/25 x 53, as a single fraction as follows:

[tex]\boldsymbol{\sf{\dfrac{19\times50}{23} \ \ \longmapsto \ \ \ [Multiply] }}[/tex]

[tex]\boldsymbol{\sf{\dfrac{950}{23} }}[/tex]

Like the fraction 950/23, it cannot be further simplified, so it remains that way, therefore

                  [tex]\red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ \frac{950}{23} }}}}[/tex]

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]

The percentage of the whole school that plays soccer is 35.5%

The percentage of the boys is given as

Percentage boys = 45%

This means that the percentage of the girls is given as

Percentage girls = 55%

Also, from the question, we have:

30% of the boys and 40% of the girls play soccer

So, the percentage of the whole school that plays soccer is

P = Boys * Percentage Boys + Girls * Percentage Girls

This gives

P = 45% * 30% + 55% * 40%

Evaluate the product

P = 13.5% + 22%

Evaluate the sum

P = 35.5%

Hence, the percentage of the whole school that plays soccer is 35.5%

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