A cell phone tower is anchored by two cables on each side for support. The cables stretch from the top of the tower to the ground, with each being equidistant from the base of the tower. The angle of depression from the top of the tower to the point in which the cable reaches the ground is 23 degrees. If the tower is 140 feet tall, find the ground distance between the cables. Round to the nearest tenth.

The reasons and statements that completes the two-column table method used to prove that triangle ΔRVX is congruent to ΔTWU (ΔRVX ≅ ΔTWU) are as follows;

Statement                                   [tex]{}[/tex]         Reason

12. UW = VX                   [tex]{}[/tex]                   Transitive Property of Equality

13. ΔRVX ≅ ΔTWU [tex]{}[/tex]                           SSS

Two triangles are congruent if the lengths of the three sides of one triangle are the same as the lengths of the three sides of the other triangle.

The details and reasons for the statements used to prove the congruency of the ΔRVX and ΔTWU are as follows;

RV = RS + SV; Additive property of length

The additive property of length states that a point B can be located on a segment AC only if, we get; AC = AB + BC

RV = ST + SW Substitution

The substitution property states that if a = b then a can substitute b in equations and expressions, such that the values of the expressions and equations remain the same.

RV = TW Transitive Property of Equality

The transitive property of equality states that if a = b and b = c, then a = c

ΔRVX ≅ ΔTWU SSS

The SSS (Side-Side-Side) congruency postulate states that two triangles are congruent if the lengths of all three sides of one triangle are congruent to the lengths of the sides of the other triangle.

Learn more about the conditions for the congruency of triangles here:

https://brainly.com/question/3079413

#SPJ1

The ordered pair for Point N is (6,9).

What is the ordered pair?

An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.

Here, we have

Given the graph and we have to find the coordinates of all points.

N = (6,9)

M = (5,7)

R = (9,8)

D = (2,6)

C = (1,4)

B = (2,1)

A = (6,2)

Q = (7,5)

Hence, the ordered pair for Point N is (6,9).

To learn more about the ordered pair from the given link

https://brainly.com/question/1634684

#SPJ1

To manufacture a panels that are u = 48 in. wide and 2 in. thick with the profile of the roofing takes the shape of a sine wave with equation y = sin(pi x/12) from flat sheet, the width of the flat sheet would be 49.59in.

Therefore the answer is 49.59

To find the arc length of a continuous function, you need to first define the function and the interval over which you want to find the arc length. Then you can use the following formula:

Arc Length = ∫√(1+(f'(x))^2) dx

Here, f(x) is the function and the interval is [a, b].

The width, w of the flat metal sheet needed to make the panel is the arc length of the sine curve from x = 0 to x = 48in

In this case, f(x) = sin(pi x/12), so the derivative of f(x) is

f'(x) = (pi/12)cos(pi x/12)

Arc Length = ∫√(1+((pi/12)cos(pi x/12))^2) dx from x=0 to x=48

Arc Length ≈ 49.59 in

To know more on arc length

https://brainly.com/question/2005381

#SPJ4

Answer:

Step-by-step explanation:

hfhgfvbbkgb 56789+7567t+2345

y-mx+b

y=-3/2x+4

m- -3/2

b-4

y=-3/2x+4

The rule of reflection for the points (x, y) for the graph is (y, - x).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

The preimage of the given line has points(x, y), B(2, 3) and C(1, 6).

Now, The graph has been translated down 2 units and reflected 180° along the x-axis so the image of the graph has points(y, - x) B'(3, - 2) and C'(6, - 1).

learn more about transformations here :

https://brainly.com/question/11709244

#SPJ1

Step-by-step explanation:

A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.

Here the number is x557x55. The difference between the sum of alternate digits is,

[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]

[tex]\longrightarrow S=2x-7[/tex]

By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.

Let,

[tex]\longrightarrow 2x-7=11a[/tex]

[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]

We separate the RHS as the following.

[tex]\longrightarrow 2x=10a+a+6+1[/tex]

[tex]\longrightarrow 2x=10a+6+a+1[/tex]

[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]

In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.

Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,

[tex]\longrightarrow a+1=2k[/tex]

[tex]\longrightarrow a=2k-1[/tex]

Then (1) becomes,

[tex]\longrightarrow 2x=11(2k-1)+7[/tex]

[tex]\longrightarrow 2x=22k-4[/tex]

[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]

So this is expression for x, for any integer k.

As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,

[tex]\longrightarrow 1\leq x\leq 9[/tex]

From (2),

[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]

Adding 2,

[tex]\longrightarrow 3\leq 11k\leq 11[/tex]

Dividing by 11,

[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]

Since k is an integer, we get,

[tex]\longrightarrow k=1[/tex]

Then from (2),

[tex]\longrightarrow x=11(1)-2[/tex]

[tex]\longrightarrow\underline{\underline{x=9}}[/tex]

Hence the value of x is 9.

Yes, this equation is a quadratic equation.

What is a quadratic equation?

Quadratic equation are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx  + c = 0 where a, b, c ∈ R and a ≠ 0.

The given equation 3x² + 5x + 9x² + 7x + 3 = 0 can be written as 12x² + 12x +3 = 0, which is a general form of quadratic equation where a = 12, b = 12 and c =3.

Hence, the equation is a quadratic equation.

To learn more about quadratic equations click:

https://brainly.com/question/29011747

#SPJ4

No. of teeth on the pinion(TP)=17.

Diametral pitch(pd)=8 teeth/in.

Rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.

Rotational speed of the gear(NG)=544 rev/min or 544 rpm.

To calculate:

No. of teeth on gear(TG) & theoretical centre to centre distance(C).

Solution:

We know that;

Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear

For pinion,

pd=TP/DP  

Pittiong the values in above eq.

8 teeth/in =17/DP    =>DP=17/8 in.

or DP=2.125 in.

Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)

=>(NP/NG)=(TG/TP)

=>1120/544 =TG/17 =>TG=35

No. of teeth the gear(TG)=35 {Ans}

Also from gear ratio formula,

(NP/NG)=(DG/DP)

=>1120/544=DG/2.125

=>DG=4.375 in.

In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)

centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}

=>C=(DP+DG)/2

Diameter =2*radius}

=>C=(2.125+4.375)/2 in. =3.25 in.

Theoretical centre to centre distance (C)=3.25 in.

Learn more about Diametral pitch to visit this link

https://brainly.com/question/18521964

#SPJ4

We can find the domain and range of the function without the help of graphing calculator by the following steps mentioned below.

The domain of a function is the set of values that we are allowed to enter into our function.

This set consists of the x values for a function like f. (x).

The set of values that a function can accept as input is known as its range.

The function outputs this list of values once we enter an x value.

The domain of a function refers to the set of input values.

These numbers, which stand in for the independent variable, are corresponding to the x-axis value.

The range of a function refers to the set of output values.

These values, which indicate the dependent variable, are corresponding to the y-axis value.

Find a function's domain and range without graphing as follows:

(A) Place y = f(x)

(B) In terms of y, solve the equation y = f(x) for x. Let x = g (y)

(C) Discover the values of y and its domain of f for which the values of x, as determined by x = g(y), are real.

(D) The range of the supplied function is the collection of y values produced in step 3.

Therefore, we can find the domain and range of the function without the help of graphing calculator by the following steps mentioned above.

Know more about the domain and range here:

https://brainly.com/question/1942755

#SPJ4

The expression for area of a rectangle is A = 12x² + 55x + 50, the equation is second degree and the expression for perimeter is P = 14x + 30.

If a mathematical operation includes at least two words that are connected by an operator and either comprise numbers, variables, or both, it is referred to as an expression.

The operations with reflection coefficients include adding, subtracting, multiplying, and dividing. In order to include terms into an expression, a mathematical operation like reduction, addition, multiplication, or division is used.

As per the given information in the question,

Let the length of rectangle, l = (4x + 5) and,

The width of rectangle, w = (3x + 10)

a.

Use the formula of area of rectangle,

A = wl

A = (3x + 10)(4x +5)

So, the expression will be,

A = 12x² + 55x + 50

b.

The degree of the equation for area is second degree.

c.

Use the formula of perimeter of rectangle,

P = 2(l + w)

P = 2(4x +5 + 3x + 10)

P = 2(7x + 15)

Then, the expression of perimeter will be,

P = 14x + 30

To know more about Expression:

https://brainly.com/question/14083225

#SPJ1

Answer:

Step-by-step explanation:

If Z1 = (x1, y1) and Z2 = (x2, y2) are complex numbers, then their sum is given by:

Z1 + Z2 = (x1 + x2, y1 + y2)

For example, if Z1 = (3, 4) and Z2 = (-2, 5), then their sum is:

Z1 + Z2 = (3 + (-2), 4 + 5) = (1, 9)

In general, to add two complex numbers, we add their real parts and their imaginary parts separately.

The value of  [tex]z_1[/tex] +  [tex]z_2[/tex]  = ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Complex Numbers. Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a imaginary number called a "iota."

Given:

[tex]Z_1=(x_1,y_1)[/tex] and [tex]Z_2=(x_2,y_2)[/tex]

Also, we know by Complex number

[tex]z_1[/tex] = [tex]x_1[/tex] + i [tex]y_1[/tex]

and, [tex]z_2[/tex] = [tex]x_2[/tex] + i [tex]y_2[/tex]

Then, [tex]z_1[/tex] +  [tex]z_2[/tex]

= ( [tex]x_1[/tex] + i [tex]y_1[/tex]) + ( [tex]x_2[/tex] + i [tex]y_2[/tex])

= ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])

Hence, the addition gives  ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex]).

Learn more about Complex Number here:

https://brainly.com/question/20566728

#SPJ2

Yes, the given equation is quadratic equation.

Here it has been given that,

3x² - 5x + 9 = x² - 7x + 3

Now, after solving  above equation further we obtain,

2x² + 2x + 6 = 0

From the above equation the factor 2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0

The coefficients of the quadratic equation are compared  and if it meets the criteria then it is quadratic equation otherwise not.

Now as we can see, the above equation clearly represents a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 1 and c = 3.

Hence, the above given equation is a algebraic quadratic equation.

Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?

To learn more about the quadratic equation click here:

brainly.com/question/17177510

#SPJ4

Answer:

Step-by-step explanation:

you will need a 10ft tall ladder

i hope that helped

The measures of the angles are 72°, and 108°.

What is Angle Sum Property?

The sum of all angles of a triangle is equal to the angle of a straight line i.e. 180°. If we have a triangle ABC, then the Sum of angles A , B, and angle C will be 180 ° and the value of the exterior angle is equal to the sum of two interior opposite angles.

We have,

two angles form a linear pair. one angle measure is 36° more than the other.

If two angles form a linear pair, then the sum of the degree measure of the angles is 180°.

Let x be the measure of the smaller angle.

Then,

36° + x is the measure of the other angle.

So,

36° + x  + x = 180°

2x = 180° - 36°

2x = 144°

x = 144°/2

x = 72°

the measure of the smaller angle is  x = 72°,

the measure of the other angle is

36° +  72° = 108°

Hence, the measures of the angles are 72°, and 108°.

To know more about the Angle sum property visit,

brainly.com/question/21099419

#SPJ1

A checking account is used for daily basis transaction and a debt and is usually associated with it.Saving accounts is just used for saving money.It has a time limit then you can withdraw your money.It is not on daily basis.

A bank account that allow the user to withdraw the money ,pay bill,transfer money to other person or make a purchase anything by writing checks.Check accounts typically don't earn interest.By checking accounts we can easily deposit and withdraw money for daily transaction.

Saving accounts are intended for storing your money which you don't plan to use daily.saving accounts earns interest at your money.saving account is designed for the accumulation of money in a safe place for future use.saving accounts offer easy access to your money in any emergency.so keeping your money in a saving account means that your money is safe for your future use.

To learn more about check and saving accounts visit;

https://brainly.com/question/20984186

#SPJ4

Answer:

Step-by-step explanation:

D?

The correct answer to the expression is 10.

By using BODMAS rule,

BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction in its entire form. Therefore, in BODMAS, the orders or exponents are given the second choice here (x n ) A method or sequence called the BODMAS rule is used in mathematics to simplify arithmetic expressions with many operators. When there are several operators in an equation, we must first determine the correct sequence in which to solve the equation. The BODMAS rule assists in the solution of this issue.

Given expression,

2+5*4-8/⅘

=2+20- 40/4    

= 22-10

= 10

Hence, the correct answer to the expression is 10.

To learn more about the BODMAS click here :

brainly.com/question/29795897

#SPJ4

The value of y obtained after solving the given equation will be equal to 11/3 or 3 2/3.

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

3/4y + 1/2 = 3 1/4

Firstly, write the equation in a simplified way,

3/4y + 1/2 = 13/4

3/4y = 13/4 - 1/2

3/4y = (13 - 2)/4

3/4y = 11/4

Now, solve the equation for y,

y = (11 × 4)/(4 × 3)

y = 11/3

In mixed fraction form, it can be written as 3 2/3.

To know more about equation:

https://brainly.com/question/29657983

#SPJ1

this was an accident how do I delete?

The equation that shows the number of plates that is remaining would be = Y = (Total salad plate/X) - 4.

A banquet hall is a building constructed is a way that various celebrations and functions can be held in such a place such as wedding receptions.

The total number of salad plates available = 144

The number of salad plate per every table set = 10

The number of salad plates remaining = y

The number of tables set by Duncan = x.

If 1 table = 10

X tables = 144

make X tables the subject of formula;

X tables = 144/10

X tables = 14 tables (approximately)

But 14 × 10 = 140 salad for the 14 tables

The remaining salad plates is 4 plates.

Y = (Total salad plate/X) - 4

Therefore, the number of salad plates remaining which is 4 depends on the number of tables Duncan sets which is 10.

Learn more about addition here:

https://brainly.com/question/25421984

#SPJ1

The zeros of the polynomial are 1/2√2 and -3/√2.

The zeros of a polynomial are all the x-values that make the polynomial equal to zero.

Given, the polynomial is 4x² + 5√2x - 3.

We have to find the zeros of the polynomial,

Let 4x² + 5√2x - 3 = 0

On factoring,

= 4x² + 6√2x - √2x - 3

= 2√2x(√2x + 3) - (√2x + 3)

= (2√2x - 1)(√2x + 3)

Now, 2√2x - 1 = 0

2√2x = 1

x = 1/2√2

Also, √2x + 3 = 0

√2x = -3

x = -3/√2

Therefore, the zeros of the polynomial are 1/2√2 and -3/√2.

For more references on zeros of the polynomial, click;

https://brainly.com/question/29775881

#SPJ4

Answer:

They are both irrational

Step-by-step explanation:

so the square root of 8 is 2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

the square root of 98 is also irrational for the same reason but the square root is 9.89949493661.

The product of two √8 and √98 irrational number is irrational.

A rational number is any number that can be expressed as a ratio (or fraction) of two integers.

Any real number that cannot be represented as the quotient of two integers is irrational.

Given:

The rational number are : √8 and √78

As, the √8=  2.82842712475 which is irrational because it is not a perfect square or repeated decimal pattern.

and, √98 = 9.89949493661 is also irrational.

Hence, the product of two irrational number is irrational.

Learn more about rational number here:

https://brainly.com/question/24398433

#SPJ2

The four fundamental translations or transformations in geometry are translation, reflection, rotation, dilation, and resizing.

For a function graph, four different transformations are feasible (and translation in math is one of them). When we translate, we move a figure in any direction. When we reflect, we turn a figure or a line over. The act of rotating a figure around a point is known as rotation.

In mathematics, a translation merely moves a shape up, down, left, or right without turning it. The image or the translated shapes seem to be the same size as the original shape, proving that they are congruent. Simply said, they have changed their path or directions.

Three types of translation are described in Jakobson's On Linguistic Aspects of Translation (1959, 2000): intralingual (inside one language, such as rewording or paraphrasing), interlingual (between two languages), and intersemiotic (between sign systems).

To learn more about translations refer to :

https://brainly.com/question/1046778

#SPJ4

Yes , SAS (Side-Angle-Side) is a second Congruence postulate to prove triangle congruence by showing that two sides and their included angles are congruent.

Side-Angle-Side is the rule used to prove whether a given set of triangles are congruent. The SAS rule states: Triangles are congruent if two sides and an included angle of a triangle are equal to two sides and an included angle of another triangle. An included angle is the angle formed by two given sides.. For example : let's us consider two triangles ∆SQR and ∆TSR ,

In above given figure, sides

RS = RS ( common side)

QS = ST ( S divides QT in two equal parts) and angle between QS and SR equal to angle between SR and ST i.e. ∠QSR = ∠RST = 90° (right angle ) and it is included angle . So, by SAS Congruence rule, both of triangles are congruent. Hence, Δ ABC ≅ Δ PQR.

To learn more about SAS Congruence rule, refer:

https://brainly.com/question/26157404

#SPJ4

Answer:

y = - 5/4x -12

Step-by-step explanation:

Original slope= (0- -4)/(5-0)=4/5

slope of perpendicular line of original = -5/4

so the line passes through the point (-8,-2)

(y - -2) = -5/4 (x - -8)

y + 2 = -5/4x - 10

y = - 5/4x -12

The equation of line u passing through the point (-8, -2) and which is perpendicular to the line y that cut the x-axis at x = 5 and y-axis at y = -4 is 5x + 4y + 18 = 0

Given that line, u passes through (-8,-2) and is perpendicular to line y

line y cut x-axis at x=5 and y-axis at y=-4

that is the point of intercept are : (x1, y1) = (5,0) and (x2, y2) = (0, -4)

Now, the equation of line = (y - y1) = m1*(x - x1)

Here m is the slope of line y

m1 = (y1 - y2)/(x1 - x2)

On solving,

m1 = (0 - (-4))/(5 - 0) = 4/5

We know that when two equations are perpendicular then the multiplication of their slopes = -1

m1 * m2 = -1

Now, m2 = -1/m1 = -5/4

Equation of line u passing through the point (-8, -2) and perpendicular to the line = (y - y1) = m2*(x - x1) =>  (y - (-2)) = -5/4*(x - (-8)

5x + 4y + 18 = 0

To know more about circle follow the given link :

https://brainly.in/question/2178053

The solution to both inequality is 2 ≥  -x and -x≥ 14

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.

We have the equation 1≥-x-1 and -x-1≥ −13

Let us solve the inequality

1 ≥ - x - 1

1 + 1 ≥ -x

2 ≥  -x

Now, let us solve the inequality

-x-1≥ −13

-x+13 ≥ -1

-x≥ 14

Therefore the solution to both inequality is 2 ≥  -x and -x≥ 14

To learn more about inequality refer to :

https://brainly.com/question/24372553

#SPJ1

Answer:

y=1/2x+-2

Step-by-step explanation:

10 more than 37 will be Addition of 10 and 37 which is supposed to be 10 plus 37 = 47.

Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.

We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 37 to add 10 to 37. Therefore, the answer is 47 once more.

Learn more about Addition:

brainly.com/question/29464370

#SPJ4

a sampling plan in which an initial sample is selected and the audit team either draws a final conclusion or selects additional items before drawing a final conclusion is known as Sequential sampling

Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary. This sampling strategy offers the researcher limitless opportunities to adjust his research procedures and obtain a keen understanding of the study he is currently conducting.

Sequential sampling has a number of benefits, including limitless options for sample size selection and sampling schedule, little cost and labor requirements, and the ability to make minor alterations and modifications to the primary research even during the early stages of the project.

Learn more about Sequential sampling here:https://brainly.com/question/13219833

#SPJ4

The mean of the given observation is 9.

What are the mean, median, and example?

The ratio between the total number of observations in a data set and the sum of all observations is known as the mean in statistics. The most frequent number, or the one that happens the most frequently, is known as the mode.

                   Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

Mean = Sum of all the observations/Number of observations

Mean = 4+6+8+10+12+14/6

Mean = 54/6

Mean = 9

Hence, the mean of the given observation is 9.

Learn more about mean in mode

brainly.com/question/6813742

#SPJ4