Select the correct answer.
Consider the graph and the equation of function f.
f(x)=2 sin (1/2x) + 1

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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The second pair of coordinates on the line parallel to q that passes through (0,1) is (1,-4/5) and that of (3,5) is (1,7).

The general form of the equation of a line is y=mx+c

where

m=slope

c is a constant

The equation of the line is

m= [tex]\frac{y-y_{1} }{x-x_{1} }[/tex]

M=[tex]\frac{5-4}{3+2}[/tex]

m=1/5

From the slope formula

m = -1/5

X₎=0

y₎=1

substitute these in the formula for slope

[tex]\frac{-1}{5} =\frac{y-1}{x-0}[/tex]

x=5y-5

x-5y=5

Now, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x-5y=5

1-5y=5

-5y=5-1

y=[tex]\frac{-4}{5}[/tex]

The other coordinate is (1,-4/5)

11.   In the second line (3,5)

Using the slope formula

m=[tex]\frac{Y_{2}-Y_{1} }{X_{2}-X_{1} }[/tex]

[tex]\frac{-1}{5} =\frac{y-5}{x-3}[/tex]

x-3=-y+2

x+y=5+3

x+y=8

Also, with the above-derived equation, we need to find the other co-ordinate as these coordinates will satisfy this equation.

when x=1,

x+y=8

1+y=8

y=8-1

y=7

Therefore the second coordinate is (1,7)

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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:

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 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:

a) 3-5*2=-7

b)3-5*-4=23

c)3-5*0=3

Step-by-step explanation:

you would plug each of them into the equation because they give you x so

a) 3-5*2=-7    x=2

b) 3-5*-4=23  x=-4

c) 3-5*0=3      x=0

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

Step-by-step explanation:

The equation has two solutions, on is extraneous and x = 7, and the real solution is x = -8.

Here we have the following equation:

x + 8x/(x - 7) = 56/(x - 7)

This is the original equation, notice that if x = 7, we will have a zero on the denominators, and we can't divide by zero, thus, x can't be equal to 7.

Now let's multiply all the equation by (x - 7)

(x - 7)*x + 8x = 56

Now we have a quadratic equation:

x^2 - 7x + 8x - 56 = 0

x^2 + x - 65 = 0

Using the quadratic formula we will get the two solutions:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*1*-56} }{2*1} \\\\x = \frac{-1 \pm15}{2*1}[/tex]

Then the two solutions are:

x = (-1 + 15)/2 = 7  (this one is an extraneous solution, we can discard this one)

x = (-1 - 15)/2 = -8

This is our solution.

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4 - 6x is linear equation .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

What makes an equation linear?

A linear equation's graph almost always takes the shape of a straight line.

                Definition of a Linear Equation: Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

let the number be =x

        4 - 6x

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The simplified form of the given expression, 4(3x^2y^4)3 / (2x^3y^5) ^4, is 27/x⁶y⁸

From the question, we are to simplify the given expression

From the given information,

The expression is

4(3x^2y^4)3 / (2x^3y^5) ^4

First, we will write the given expression properly

The given expression written properly is

4(3x²y⁴)³ / (2x³y⁵)⁴

Simplifying the expression

4(3x²y⁴)³ / (2x³y⁵)⁴

4 × (3x²y⁴)³ / (2x³y⁵)⁴

4 × (3)³(x²)³(y⁴)³ / (2)⁴(x³)⁴(y⁵)⁴

4 × (3)³ × (x²)³ × (y⁴)³ / (2)⁴ × (x³)⁴ × (y⁵)⁴

4 × 27 × x⁶ × y¹² / 16 × x¹² × y²⁰

108 × x⁶ × y¹² / 16 × x¹² × y²⁰

This can be further expressed as

108/16 × x⁶/x¹² × y¹²/y²⁰

27/4 × 1/x⁶ × 1/y⁸

= 27/x⁶y⁸
Hence, the simplified expression is 27/x⁶y⁸

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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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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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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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Mr. Dillon balance at the end of month is $809.

In a financial institution, a checking account is a deposit account that permits both deposits and withdrawals.

Money kept or held in any bank account is referred to as a deposit.

A withdrawal entails taking money out of a trust, pension, savings plan, or bank account.

As Mr. Dillon opened a checking account, so balance is $0 in starting.

When he deposits $1530, $896, $571, $472

Total deposit= $1530+$896+$571+$472

             = $ 3,469

Check is a kind of withdrawal.

He wrote check of $32 , $981 , $825 , $661 , $224

Total withdrawal= $32+$981,$825+$661+$224

                             = $2,660

Balance= Total deposit - Total withdrawal

             = $3,469 - $2,660

             = $809

Therefore, balance is $ 809.

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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 measure of the arc length of the sector will be 1.047 units. Then the correct option is A.

Let r is the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The radius of the sector is 1 unit and the central angle is π/3. Then the measure of the arc length of the sector will be given as,

Arc = [(π/3)/2π] 2π(1)

Simplify the equation, then we have

Arc = [(π/3)/2π] 2π(1)

Arc = (1/6) × 2π

Arc = π/3

Arc = 1.047 units

The proportion of the circular segment length of the area will be 1.047 units. Then, at that point, the right choice is A.

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Answer:

2.0 acres

Step-by-step explanation:

C(x) = 270 ln(x+1) + 1900 = 2200

270 ln(x+1) = 300

ln(x+1) = 10/9

x+1 = e^(10/9)

x = e^(10/9) - 1 = 2.0377

Answer:

For the problem with the horse: 10,000 grams

For the problem with the hiker labeled 11: 2 feet

I hope these answers are of use to you!

Step-by-step explanation:

Okay, for the horse problem I understood that it was a horse eating exactly 10 kg per day. If she does, then you just convert 10 kilograms to grams. To do this, you multiply the amount of kilograms by 1,000, since that is how it works.

10 x 1,000 = 10,000 grams.

For the problem labeled 11 with the hiker, you divide 120 ft by 60 since there are 60 seconds in a minute.

120 divided by 60 = 2 feet

Answer:

b

Step-by-step explanation:

4y = 2x

y = 2/4  x

y = 1/2 x               where y = kx    then k = 1/2

Z-tests are closely related to t-tests, but t-tests are best performed when the data consists of a small sample size, i.e., less than 30. The given statement is true.

Does critical value depend on sample size?

The sample size and the crucial value that the researcher employed must be connected. The variations in critical values between the t-distribution and the normal-shaped sampling distribution, however, are minimal for sample sizes bigger than 30.

Z-tests and t-tests are closely related, but t-tests work best with small sample sizes of data, or those with fewer than 30 participants. Additionally, whereas z-tests assume that the standard deviation is known, t-tests assume that it is unknown.

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.

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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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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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Answer:

5 percent

Step-by-step explanation:

100/40=2.5

2.5*2=5

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 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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Answer:

Step-by-step explanation:

I think its 40

The triangle is isosceles so the left and right side are equal in length.

you would equal 4x+4=6x-14 and solve, getting 18=2x the 9=x