write the following phrase as a variable
expression. Use x to represent "a number"
negative six subtracted from three times.
number
a

The area of the shaded region is equal to half the area of the circle.

What is the area of the circle?

The approximating parallelograms arbitrarily close and approximate the area of the circle by cutting it into ever-increasing slices.

The radius of the arc BC is |AB|=2rcosθ, and ∡AOB=π−2θ.

Dashed area= Area of sector BAC+ 2(Area of sector BOA−Area of triangleBOA)

= 1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)]

On the other hand, the area of the dashed surface is 1/2πr², then

1/2|AB|²(2θ)+2[1/2r²(π−2θ)−1/2r²sin(π−2θ)] = 1/2πr²

(2rcosθ)2(θ) + r²[π−2θ−sin(π−2θ)] = 1/2πr²

4θcos2θ+π−2θ−sin2θ = 1/2πr²

2θ(2cos2θ−1) = sin2θ−1/2π

2θcos2θ = (2sin2θ−π)/2

cos2θ = (2sin2θ−π)/4θ

Hence, the area of the shaded region is equal to half the area of the circle.

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The volume of the picture is given as 24000 ft square

The surface area of the shape is 5360 ft square

We would have to solve for the volume of a cuboid + the volume of a triangular prism

We are aware that the prism's volume is equal to its base area divided by its length. As a result, the formula Volume of triangular prism = (1/2) bh L is used to get the volume of the prism in this instance.

Such that we would have:  (1/2) bh L

where b = 30

h = 8

L = 50

when we put the values we would have

1 / 2 x 30 x 8 x 50

= 6000

The volume of a cuboid is l x b x h

= 30 x 50 x 12

= 18000

18000 + 6000 = 24000 cubic square

B. The surface area = 2(1/2 x 8 x 30) + 2(17 x 50) + 2(50 x 12) + 2(30 x12) + 950 x 30)

= 5360ft square

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The speed of the car will be 25.41 m/h

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path. In other words, velocity is a vector quantity, whereas speed is a scalar quantity

According to the given information

d = [tex]\frac{s^{2} }{10}[/tex] + s

We are given that

distance is 90 feet

So, the expression becomes

90 = [tex]\frac{s^{2} }{10}[/tex] + s

[tex]s^{2}[/tex] + 10s - 900 = 0

which is quadratic in s

So applying the discriminant formula

[tex]$$[/tex]s [tex]=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}[/tex]

[tex]$$[/tex]and then we input the values:

s [tex]=\frac{-10 \pm \sqrt{(10)^2-4(1)(900)}}{2(1)}$$[/tex]

and solve:

s [tex]=\frac{-10 \pm \sqrt{3700}}{2}$$[/tex]

It will have two answers

s = -35.41 m/h

s = 25.41m/h

Speed cannot be negative

So

The speed of the car will be 25.41 m/h

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The total time worked by Vernon in decimal hours is 19.50 hours.

Last week, Vernon worked the following days and times:

Therefore, the total time Vernon worked in decimal hours can be calculated as follows:

We have to sum the whole time Vernon worked in the 4 days.

Therefore, we have to convert all the minutes to hours.

total time worked = 5.25 + 6.5 + 3.75 + 4

total time worked = 19.50 hours

Therefore,

total time worked by Vernon = 19.50 hours

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The area of the shelf A is 30 square feet

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

Dimensions = 3 ft and 2 ft

The above parameters mean that

Length = 3 ft

Width = 2 ft

Number of shelves = 5

The area of the shelf A is then calculated as

Area = Number of shelves  * Length * Width

Substitute the known values in the above equation, so, we have the following representation

Area = 5 * 3 * 2

Evaluate the products

So, we have

Area = 5 * 6

Evaluate the products

So, we have

Area = 30

Hence, the area is 30 square feet

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Answer:

3/32

Step-by-step explanation:

When dividing fractions, we use keep change flip.

We keep the 1/4, change into multiplication, and flip 2 and 2/3.

First, we want to change 2 and 2/3 into improper fraction form, which is 8/3.

Our equation is now :

1/4 divided by 8/3

Now, we apply keep change flip.

1/4 * 3/8

Multiply numerator by numerator and denominator by denominator.

3/32

3/32 is your final answer. It cannot be simplified further.

From the properties of a complex number, it was found that the value for  [tex]i^{21}[/tex] is i.

A complex number is represented by the following form: a+bi, where a and b are real numbers.  The variables: a is the real part and bi imaginary part. See an example: 6 + 13i , then: 6 represents the real part and   14i represents the imaginary part.

Regarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 6i² = 6*(-1)= -6.

The question gives [tex]i^{21}[/tex], thus.

[tex]i^{21}=i^{20}*i[/tex]

[tex]i^{21}=(i^{2})^{10}*i\\ \\ i^{21}=(-1)^{10}*i\\ \\ i^{21}=1*i=i[/tex]

Therefore, the result for the question is i.

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Answer:

8

Step-by-step explanation:

the answer is 8

Answer:

8

Step-by-step explanation:

total students=20

boys=2/5×20

=8

Answer: 51.85

Step-by-step explanation: you use the formula given and plug is 25 for t because it is the number of years. So you get 200*e^(-0.054*25) = 51.85

The number of different routes she can take from City Upper C to City Upper G​ is 18

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

Routes from City Upper C to City Upper D = 3 routes

Routes from City Upper D to City Upper G = 6 routes

The number of different routes she can take is calculated as

Routes = Routes from City Upper C to City Upper D x Routes from City Upper D to City Upper G

Substitute the known values in the above equation, so, we have the following representation

Routes = 3 * 6

Evaluate

Routes = 18

Hence, the number of routes is 18

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Answer:

D

Step-by-step explanation:

The taxi charges $2.00 for any distance less than or up to 1 mile.

Then for every mile after the taxi will charge you a fee of $1.60 dependent upon how many miles you go.

This can be modeled as:

y = 2.00 +1.60(x)

where x is the number of miles after the first mile.

The distance left after x minutes is modeled by the linear equation:

f(x)= 10 - (1/4)*x

The correct option is the last one.

We know that the total distance of the race is 10 kilometers, and the student runs 1 kilometer every 4 minutes, so the student's speed is:

S = 1km/4min = 0.25 km/min

The distance to the finish line is modeled by an equation of the form:

f(x) = total distance - speed*time

Here we know that:

Then the equation is:

f(x)= 10 - (0.25)*x

We can rewrite the decimal as a fraction:

f(x)= 10 - (1/4)*x

The correct option is the last one.

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The inequality is [tex]|x|\geq4[/tex].

What are the inequalities of a graph?

We can see the areas that satisfy one or more inequalities by visualizing them as inequalities on a graph. These inequalities can be represented using straight-line graphs in GCSE maths because they are frequently linear. You might need to draw lines and designate a region that fulfills the system of inequalities to find solutions to the inequalities, or you might need to use the graphs that have already been provided.

Here, in the graph given, we see that the points on and from 4 / -4 are highlighted. Since the interval has 0 in between, we write the variable as [tex]|x-0|[/tex]. Now, the graph excludes points from -4 to 4.

Therefore, we conclude that the absolute value inequality for the given graph is [tex]|x|\geq4[/tex].

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Absolute value is 7 or greater.

What is inequality?

In mathematics, an inequality is a statement that compares two values or expressions using one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). For example:

2 < 3 (2 is less than 3)

5 > 3 (5 is greater than 3)

2 ≤ 3 (2 is less than or equal to 3)

5 ≥ 3 (5 is greater than or equal to 3)

Inequalities can be used to describe a range of values that a variable can take on. For example, the inequality x > 0 describes all values of x that are greater than 0.

Inequalities can be solved by finding the values of the variable that make the inequality true. For example, the solution to the inequality x > 0 is all values of x that are greater than 0, such as 1, 2, 3, etc.

Inequalities can also be combined using the logical operators "and" (represented by the symbol ∧) and "or" (represented by the symbol ∨). For example, the inequality x > 0 ∧ x < 10 describes all values of x that are greater than 0 and less than 10, such as 1, 2, 3, etc. The inequality x > 0 ∨ x < 10 describes all values of x that are either greater than 0 or less than 10, which includes all values of x.

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Answer:

y=2(x-4)^2+9

Step-by-step explanation:

Vertex form: y=a(x-h)^2+k

The vertex represents the h and k variables.

For given 30-60-90 triangle, the measure of the shorter leg = 5.78 units and hypotenuse = 11.55 units

In this question we have been given 30-60-90 triangle with a measure of 10 (longer leg)

We need to find the hypotenuse and shorter leg.

We know that longer leg of 30-60-90 triangle is opposite to angle 60

Consider the sine of angle 60

sin(60) = 10/hypotenuse

(√3)/2 = 10/hypotenuse

hypotenuse = 10 * (2/√3)

hypotenuse = 11.55 units

By Pythagoras theorem,

hypotenuse² = (longer leg)² + (shorter leg)²

11.55² = 10² + (shorter leg)²

(shorter leg)² = 11.55² - 10²

shorter leg = √(33.4025)

shorter leg = 5.78 units

Therefore, shorter leg = 5.78 units and hypotenuse = 11.55 units

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Answer:

5 percent

Step-by-step explanation:

100/40=2.5

2.5*2=5

The distance of the foot of the ladder from the wall is 10.58m, the distance can find using pythagoras theorem states that in a right-angled triangle.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula. The Pythagorean theorem can be rewritten as d=√((x_2-x_1)²+(y_2-y_1)²) to calculate the separation between any two points.

Let AC be the ladder and A be the window.

Given: AC=15m, AB=12m, CB=am

In right angled triangle ACB,

(Hypotenuse) ²  =(Base)² +[Perpendicular)²   [By Pythagoras theorem]

⇒(AC)²   =(CB)² +(AB)²

⇒(16)²   =(a)²  +(12)²

⇒256 = a²  + 144

⇒ a = √112 = 10.58cm.

The distance of the foot of the ladder from the wall is 9m.

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Answer: normal formula define the cup full of is Q -2+ you and me 32,000 you’re welcome

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to write exponential functions through the given points.

The exponential function ...

  f(x) = a·b^x

will have the values ...

Using these relations we can write the function from the table values:

  f(x) = 10400·(2600/10400)^x

  f(x) = 10400·(1/4)^x

Then your table is ...

  [tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7}\vphantom{\dfrac{b}{g}}x&-1&0&1&3&4&6\\\cline{1-7}\vphantom{\dfrac{b}{g}}f(x)&41600&10400&2600&162.5&40.625&2.5390625\\\cline{1-7}\end{array}[/tex]

Using the given points in the exponential function form, we have ...

   4.32 = a·b^1

   59.71968 = a·b^4

Dividing the second equation by the first, we find ...

  59.71968/4.32 = b^3   ⇒   b = 2.4

Using this in the first equation, we get ...

  4.32 = a·2.4   ⇒   a = 1.8

The equation of the function is ...

  g(x) = 1.8·2.4^x

The exponential function ...

  y = a·b^x . . . . . . a > 0, b > 0

will be increasing when the growth factor (b) is greater than 1. When 'b' is less than 1, the function will be decreasing.

Sarah's belief is incorrect.

Answer:

[tex]\textsf{1.} \quad f(x)=10400(0.25)^x[/tex]

     (-1, 41600)  and  (3, 162.5)

[tex]\textsf{2.} \quad g(x)=1.8(2.4)^x[/tex]

3.   Sarah is incorrect.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$f(x)=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

The y-intercept is when x = 0.  

Therefore, from inspection of the given table, the y-intercept is 10400:

[tex]\implies a=10400[/tex]

Substitute point (1, 2600) and a = 10400 into the exponential function and solve for b:

[tex]\implies 2600=10400b^1[/tex]

[tex]\implies 2600=10400b[/tex]

[tex]\implies b=\dfrac{2600}{10400}[/tex]

[tex]\implies b=0.25[/tex]

Therefore, the equation of the function is:

[tex]\boxed{f(x)=10400(0.25)^x}[/tex]

Find the value of x when f(x) = 41600:

[tex]\begin{aligned} f(x)&=41600\\\implies 10400(0.25)^x&=41600\\(0.25)^x &=\dfrac{41600}{10400}\\(0.25)^x &=4\\\ln (0.25)^x &=\ln 4\\x \ln (0.25)&=\ln 4\\x&=\dfrac{\ln 4}{\ln (0.25)}\\x&=-1\end{aligned}[/tex]

Find the value of f(x) when x = 3:

[tex]\begin{aligned}x=3 \implies f(3) & =10400(0.25)^3\\& =10400(0.015625)\\& = 162.5\end{aligned}[/tex]

Therefore, the completed table is:

[tex]\begin{array}{|c|c|c|c|c|c|c|}\cline{1-7} \vphantom{\dfrac12}x & -1 & 0 & 1 & 3 & 4 & 6\\\cline{1-7} \vphantom{\dfrac12}f(x) &41600 &10400 &2600 &162.5 &40.625 & 2.5390625\\\cline{1-7} \end{array}[/tex]

Given points:

Substitute the given points into the exponential formula g(x) = abˣ

[tex]\implies ab=4.32[/tex]

[tex]\implies ab^4=59.71968[/tex]

To find b, divide the equations:

[tex]\implies \dfrac{ab^4}{ab}=\dfrac{59.71968}{4.32}[/tex]

[tex]\implies b^3=13.824[/tex]

[tex]\implies b=\sqrt[3]{13.824}[/tex]

[tex]\implies b=2.4[/tex]

Substitute one of the points and the found value of b into the equation and solve for a:

[tex]\implies 2.4a=4.32[/tex]

[tex]\implies a=\dfrac{4.32}{2.4}[/tex]

[tex]\implies a=1.8[/tex]

Therefore, the equation of the function is:

[tex]\boxed{g(x)=1.8(2.4)^x}[/tex]

Sarah is incorrect.  For an exponential function in the form a · bˣ:

Answer:

No solution

Step-by-step explanation:

The square root of a negative number is not a real number

On solving the linear equations we get the result  as

x1   + x2   − 2x3 + 3x4 + 2x5 = 6

3x1 + 3x2 − x3   + x4   + x5   = 12

2x1 + 2x2 − x3   + x4   − 2x5 = 5

4x1 + 4x2 + x3    +0x4 − 3x5 = 16

8x1 + 5x2 − 2x3 − x4   + 2x5 = 29

where ,

x1 =  5,x2 = -1, x3 =  3 ,x4 =  2 , x5 =  1

Finding the value of an equation's unknown variable can be done by solving the equation. If an equation contains a "equal to" sign, it is considered to be balanced. This equation so shows that the two quantities on both sides of it are equal. Left hand side and right hand side are the two sides of the equation (Right hand side).

One equation is x - 4 = 5, for instance. It illustrates that x - 4 (LHS) = 5. (RHS). Here, x is an unknowable quality or variable. Therefore, in order to determine the value of x, we must solve this equation.

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The solutions for the given questions are given below:

Earnings from employment, investments, or company operations. Sam, for instance, had a weekly income of $770 after receiving $30 in bank interest, $700 from his employment, and an additional $40 from buying and selling veggies.

Wages is the amount of money obtained through employment; income is the entire amount of money obtained, which includes earnings, benefits, pensions, and other types of payments.

1.a 500000 shares have been authorized.

1/(210000) = 210000 shares issued Number of shares issued [Common stock account balance / par value of each share]

1-c) The number of shares outstanding is 210000 - 3100, or 206900 shares.

2) The APC Account Balance is $4620000, which is calculated as 210000 * (23 - 1).

3) Net income divided by the number of outstanding shares equals 165520 divided by 206900, or 0.8 per share.

4) The dividend per common share was paid at 53794/206900, or 0.26 per share.

5) 3100 * 21 = $65,100 should be stated for Treasury Stock in the Stockholders' Equity part of the Balance Sheet.

6) Following the stock split, the par value of each share is equal to 1 / 2 ($0.50 per share).

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The perimeter of the scale floor is 56 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape.

To solve, we can set up fractions:

34/17 = 22/x

Cross multiply and you get:

34x = 374

Divide each side by 34:

x = 11

Since we are trying to find the perimeter of the floor, you can use this equation:

2w + 2l = p

Substitute to solve:

2 ( width = 11 )

2 ( length = 17 )

2 ( 17 ) + 2 ( 11 ) = p

34 + 22 = p

p = 56

Hence, the perimeter is 56inches

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The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The name of the point located at (4, 3) is X.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates of a point = (4, 3)

Point (4, 3) is located on the graph at point X.

(4, 3) means 4 is on the x-axis and 3 is on the y-axis.

The meeting point is point X.

Thus,

The name of the point located at (4, 3) is X.

Option D is the correct answer.

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tan(x + kπ) = 0.4 where  k∈Z

What do you mean by trignometry?

Trigonometry is one of the important branches in the history of mathematics that studies the relationship between the sides and angles of right triangles.

Trigonometric ratios of triangles are also called trigonometric functions. Sine, cosine, and tangent are three important trigonometric functions, abbreviated sin, cos, and tan

It is given that tan(x) = 0.4

Also, tan(x + kπ) = tanx where  k∈Z

Therefore,  tan(x + kπ) = 0.4 where  k∈Z

Hence, option D is correct.

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he is supposed to lose an average of 1.36$ per roll

Answer:

Sammy loses $3.47 on average

Step-by-step explanation:

When you roll two number cubes, the number of possible combinations is 36 ( 6 * 6 ).

The only way to get a sum of two is rolling snake eyes (two ones), which means there's only one combination that gets this sum.

The chances of winning is 1/36 whilst the chance of losing is 35/36

$50*(1/36) - $5(35/36) = $1.39 - $4.86 = -$3.47

which means Sammy loses $3.47 on average

The equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.

What is the system of linear equations?

A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).

To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).

To find the slope of the line, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

The equation y = -x - 2 is in slope-intercept form, so the slope of the line is -1.

The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.

Since the given line passes through the point (2, -2), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:

-2 = -1 * 2 + b

Solving for b gives us:

b = -4

Therefore, the equation of the line that passes through the point (2, -2) and is parallel to the graph of y = -x - 2 is y = -x - 4.

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Answer:

y=5/2x-4

Step-by-step explanation:

y=mx+b

5/2 is the slope

-4 is the y intercept