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Dwayne is trying to find the fraction represented by the repeating decimal 0.5. He completes the three
steps shown:
1) Let x = 0.5
2) 10x = 5.5
3)
10x =
5.5
-X =
9x = 5
0.5
What is the purpose of Step 3?
It removes the repeating part of the decimal from the equation.
o It shows that 0.5 is an irrational number.
It puts the fraction in lowest terms.
It shows that 0.5 is a terminating decimal.​

Answer:

i think A

Step-by-step explanation:

correct me if I wrong k

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.

we have a line passing through (-6,0) and (0,8), side one

we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two

we have a line passing through (0,-4) and (6,4), side three

now, side four is simply the line connecting one and three.

the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?

well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)

\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)

now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to  (-3 , 4).  Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.

now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)

Answer: all of dem except for 6

Step-by-step explanation:

Answer:

b = 4

Step-by-step explanation:

4/6 is equivalent to 2/3, so with the slopes and y-intercepts being the same, there will be infinitely many solutions

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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Answer:

Step-by-step explanation:

I'm ASSUMING that T means to translate by the ordered pair in (x, y) coordinates, and r means to rotate by the ordered pair (degrees, center of rotation) or mirrored about the given axis

2. T(-1,2) Rx-axis (QRST)

Q (1, 4) translates to (1 - 1, 4 + 2) = (0, 6) then mirrors to (0, -6)

R (3, -1) translates to (3 - 1, -1 + 2) = (2, 1) then mirrors to (2, -1)

S (0, 0) translates to (0 - 1, 0 + 2) = (-1, 2) then mirrors to (-1, -2)

T (-2, 2) translates to (-2 - 1, 2 + 2) = (-3, 4) then mirrors to (-3,-4)

3.Ry-Axis r(180,O) (QRST)

Q (1, 4) mirrors to (-1, 4) rotates to (1, -4)

R (3, -1) mirrors to (-3, -1) rotates to (3, 1)

S (0, 0) mirrors to (0, 0) rotates to (0, 0)

T (-2, 2) mirrors to (2, 2) rotates to (-2, -2)

4.r(90,O) T(-2,-3) (QRST)

Q (1, 4) rotates to (-4, 1) translates to (-6, -2)

R (3, -1)  rotates to (1, 3) translates to (-1, 0)

S (0, 0)  rotates to (0, 0) translates to (-2, -3)

T (-2, 2) rotates to (-2, -2) translates to (-4, -5)

5. (Ry-axis T(3,0)(QRST)

Q (1, 4) mirrors to (-1, 4) translates to (2, 4)

R (3, -1) mirrors to (-3, -1) translates to (0, -1)

S (0, 0) mirrors to (0, 0) translates to (3, 0)

T (-2, 2) mirrors to (2, 2) translates to (5, 2)

Answer:

There correct

Step-by-step explanation:

The solution of the triangle have been shown below.

To solve a triangle means to find the values of all its angles and sides. The method for solving a triangle depends on the given information.

Given that;

a/Sin A = b/SinB

Sin B = bSin A/a

B = Sin-1(bSin A/a)

B = Sin-1 (23Sin 40/17)

B = 60.4 degrees

Then we have that

C = 180 - (40 + 60.4)

= 79.4 degrees

Then;

a/sinA = c/Sin C

c= aSin C/Sin A

c = 17 * Sin 79.4/Sin 40

c =   16.71/0.643

c = 25.9

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Answer:

5,004,300

Step-by-step explanation:

Assuming the -5 is with the x

You have 3^(x-5) =9

Convert the 9 to base 3: 3^2 = 9

Now you have:

3 ^(x-5) = 3^2

Now solve for exponents:

X-5= 2

Add 5 to both sides:

X = 7

Add five on both sides. Divide both sides by three

Answer: x = 4.66666666667

Answer:

x=9

Step-by-step explanation:

f(x) = −(x − 7)2 + 4

(substitute f(x) = 0)

0= −(x − 7)2 + 4

(distribute 2 into brackets)

0= −(2x - 14) + 4

(remove brackets and change the sign of each expression inside the brackets)

0= - 2x + 14 + 4

(add the numbers)

0= - 2x + 18

(move variable to the other side and change its sign)

2x = 18

(divide both sides by 2)

x = 9

The given expression is quadratic, parabolic graph, relative maxima and real zeros. The correct options are (a), (c) and (f).

The general form of a quadratic equation is given as ax^2 + bx + c = 0.

Here, a ≠ 0 and b and c are integers.

The degree of a quadratic equation is 2.

The given expression is f(x) = -(x - 7)² + 4

Since the degree of the expression is 2, it is quadratic.

The graph of the given equation will be parabolic.

By comparing from the general vertex form (x - h)² + k, its vertex can be found as (7, 4).

Axis of symmetry is x = 7.

y-intercept can be obtained by plugging x = 0 as,

-(0 - 7)² + 4 = 53.

Maxima or minima can be found as below,

f'(x) = 0

⇒ -2(x - 7) = 0

⇒ x = 7

In order to find the solution write the expression as follows,

-(x - 7)² + 4 = 0

⇒ -x² + 14x - 49 + 4 = 0

⇒ x² - 14x + 45 = 0

⇒ x = 5,9

Thus, the equation has real solutions.

Hence, the properties of the given equation are derived as quadratic, parabolic graph, relative maxima and real zeros.

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Answer:

Adam's thinking is not correct.

When subtracting 10 from 708, we need to borrow 1 from the hundreds digit and add it to the tens digit. This will result in a new hundreds digit of 6 and a new tens digit of 9. The ones digit remains the same. Therefore, the correct answer would be 698.

Adam's answer is also 698, but his reasoning is incorrect. He thinks that both the tens and hundreds digits change, which is not the case. In reality, only the tens digit changes while the hundreds digit decreases by 1 due to the borrowing process.

thank me by marking my answer as brainliest!

Answer:

Hi yes ik I'm not that good at math but wouldn't it be

a n=1∗1 n =1

Answer:

The model represents the equation "0 + x² = 1/2", which is not directly related to multiplying with fractions.

Answer:

Z

Step-by-step explanation:

The areas of the systems formed by rectangles are listed below:

Case T: A = 88 cm²

Case M: A = 72 cm² + 6 · x cm², where x is a non-negative real number.

Case 1: A = 132 cm² (Correct choice: B)

Case 2: A = 250 m² (Correct choice: C)

Case 3: A = 36 m² (Correct choice: A)

In this problem we need to determine the area of rectangles and combinations of rectangles, whose formula is shown below:

A = ∑ (b · h)

Where:

Now we proceed on each case:

Case T

A = (4 cm)² + (12 cm) · (6 cm)

A = 16 cm² + 72 cm²

A = 88 cm²

Case M

A = (18 cm) · (4 cm) + (6 cm) · (x cm)

A = 72 cm² + 6 · x cm²

Case 1

A = (6 cm)² + (12 cm) · (8 cm)

A = 36 cm² + 96 cm²

A = 132 cm² (Correct choice: B)

Case 2

A = (15 m)² + (5 m)²

A = 250 m² (Correct choice: C)

Case 3

A = (3 m) · (12 m)

A = 36 m² (Correct choice: A)

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Answer: Simplified expression- \(18y^{5} - 27y^{4} + 18y^{3}\)

Step-by-step explanation: You get the product by simplifying it.

I tried my best, I hope this it what you were looking for:)

Answer:

170, 171, 172

Step-by-step explanation:

x + x + 1 + x + 2 = 513

3x + 3 = 513

3x = 510

x = 170

x + 1 = 171

x + 2 = 172

The Fill ups for the Volume Concept is matched below.

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

given:

Cone:

R= r

h= 3r

So, Volume of Cone = 1/3πr²h

                                  = 1/3 π r² (3r)

                                  = 1/3 π 3r³

                                  = πr³

As, Volume of Cone = 25n

Cylinder:

R= r

h= 3r

So, Volume of Cylinder = πr²h

                                  = π r² (3r)

                                  = π 3r³

                                  = 3πr³

So, Volume of Cylinder = 3(25n) = 75n

Sphere:

R= r

So, Volume of Sphere = 4/3πr³

 Volume of Sphere = 4/3(25n)= 100/3 n

Now, Volume of sphere + Volume of Cone= Volume of Cylinder

4/3πr³ + 1/3πr²h = πr²h

4/3πr³ = πr²h- 1/3πr²h

4/3πr³ = πr²h(1 - 1/3)

4/3πr³ = πr²h(2/3)

4/3r = 2h/3

h= 4r/3 x 3/2

h= 2r

So, for Volume of sphere + Volume of Cone= Volume of Cylinder the height should be 2r not 3r.

Now, The Volume of Cylinder is 3 times larger than Volume of Cone.

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Answer:

B

Step-by-step explanation:

3p+6p+6p=180°

15p=180

p=12

3p=12×3=36°

6p=12×6=72°

This function written in vertex form include the following: A. f(x) = (x –1)² – 7.

In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical equation:

Axis of symmetry = -b/2a

Where:

a and b represents the coefficients of the first and second term in the quadratic function.

For the given quadratic function f(x) = x² – 2x – 6, we have:

a = 1, b = -2, and c = -6

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(-2)/2(1)

Axis of symmetry, Xmax = 2/2

Axis of symmetry, Xmax = 1.

Next, we would determine vertex as follows;

f(x) = x² – 2x – 6

f(x) = 1² – 2(1) – 6

f(x) = -7.

Now, we can write quadratic function in vertex form;

f(x) = a(x - h)² + k

f(x) = (x - 1)² - 7

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Complete Question:

The image shows a geometric representation of the function f(x) = x² – 2x – 6 written in standard form.

What is this function written in vertex form?

f(x) = (x –1)² – 7

f(x) = (x +1)² – 7

f(x) = (x –1)² – 5

f(x) = (x +1)² – 5

Answer:

8

Step-by-step explanation:

the answer is 8

Answer:

8

Step-by-step explanation:

total students=20

boys=2/5×20

=8

He makes $9571 in commission

The nearest whole number, we get x = 12. We can find the value of x by using the law of sines. The law of sines states that the ratio of the sine of an angle of a triangle to the length of the side opposite that angle is the same for all three angles of the triangle.

In this case, the angle opposite x is 24 degrees, and the side opposite x is 24 units. Therefore, we have:

sin(24°)/x = sin(C)/24

Solving for x, we get:

x = 24 x sin(24°) / sin(C)

Plugging in the values of the angles, we get:

x = 24 x sin(24°) / sin(120°) = 12.02

The nearest whole number, we get x = 12.

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Answer: 23 7/10

Step-by-step explanation:

Answer: x = 2

Step-by-step explanation:

Let x represent the unknown number:

2x + 5 = 9

Subtract 5 from both sides

2x = 4

Divide both sides by 2

x = 2

Answer: 3^3 Square root 3

Step-by-step explanation:

Answer:

792

Step-by-step explanation:

The first three composite numbers are 4,  6 ,8

so 4^3+6^3+8^3=64+216+512=792