A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?

A)53.53 feetB)74.62 feetC)126.11 feetD)322.75 feet

Answer:

A. Steve

Step-by-step explanation:

We are given the expression, [tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex].

So, upon simplifying the expression, we get,

[tex]\frac{1}{x-1}-\frac{3}{x^{2}+2x-3}[/tex]

implies [tex]\frac{1}{x-1}-\frac{3}{(x-1)(x+3)}[/tex]

i.e. [tex]\frac{1(x+3)-3}{(x-1)(x+3)}[/tex]

i.e. [tex]\frac{x+3-3}{(x-1)(x+3)}[/tex]

i.e. [tex]\frac{x}{(x-1)(x+3)}[/tex]

So, from the options, we see that,

Steve has correctly subtracted the rational expressions.

Thus, option A is correct.

Answer: IT WAS B. -_-

Answer:

246 in^2

Step-by-step explanation:

just took the test

All linear function has a constant slope and degree as 1.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

Linear functions are lines in the coordinate and describe itself that the slope will be the same irrespective of the point.

A linear function is given by ;

y = mx  + x where m is slope.

As we can see the degree of x and y both are 1 so the linear function has a degree of 1.

Hence "All linear function has a constant slope and degree as 1".

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Final answer:

The probability that the five horses finish first through fifth in any order is 0.0004995 or 0.04995%.

Explanation:

The probability that the five horses owned by one person finish first through fifth, regardless of order, in a horse race with 14 entries can be calculated using combinatorics. First, we determine the number of ways to choose 5 horses out of 14 to finish in the top 5 positions, which is C(14,5). Then we calculate the number of favorable outcomes, which, since the order doesn't matter for the set of horses owned by the person, is just 1. To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes, resulting in 1/C(14,5). Using the formula for combinations C(n,r) = n! / (r! * (n-r)!), where n is the total number of entries and r is the number of horses owned by the person, we can calculate the exact probability.

The formula gives us C(14,5) = 14! / (5! * (14-5)!) = 14! / (5! * 9!) = 2002. Therefore, the probability is 1/2002, which simplifies to 0.0004995 or 0.04995%.

Answer:

6 lb 4 oz

Step-by-step explanation:

Since, 1 lb = 16 oz,

Here, the given phrase,

The sum of 36 ounces and 4 pounds,

[tex]= 36\text{ oz}+4\text{ lb}[/tex]

[tex]=36\text{ oz}+64\text{ lb}[/tex]

[tex]=100\text{ oz}[/tex]

Again,

1 oz = 1/16 lb,

[tex]100\text{ oz}=\frac{100}{16}=6.25\text{ lb} = 6\text{ lb}+0.25\text{ lb}=6\text{ lb }4\text{ oz}[/tex]

Hence, The sum of 36 ounces and 4 pounds is 6 lb 4 oz

Second option is correct.

Answer:

It is given that Suria has x apples and Oranges.

Which means ,total number of fruits which includes apple and Orange is equal to x.

Suppose, number of Oranges Suria has = A

And, Number of Apples  Possessed by Suria= B

→Number of Oranges +Number of Apple=x

→ A + B =x

So,total number of apples and Oranges does Suria have altogether = x

All expressions given, A, B, C, and D, are rational numbers. This is because they all result in a number that can be expressed as the quotient of two integers when the operations are performed according to the order of operations and squared.

A rational number is a number that can be expressed as the quotient or fraction  rac{p}{q} of two integers, a numerator p and a non-zero denominator q. To determine which expression represents a rational number, we look for an outcome that is expressible as such a fraction after carrying out any operations involved in the expression.

Let's evaluate whether the expressions given result in rational numbers when the operations are performed:

Therefore, all given expressions A, B, C, and D result in rational numbers when squared.

Option A, B, C, and D is a rational number.All given expressions result in rational numbers, as each step of their calculations simplifies to integers. Each integer can be expressed as the quotient of two integers, confirming they are rational.

To determine which expression results in a rational number, let's evaluate each option step by step. A rational number is any number that can be expressed as the quotient of two integers.

All the results are integers, which are rational numbers because any integer n can be expressed as n/1. Therefore, all given expressions result in rational numbers.

Answer:

C. $77

Step-by-step explanation:

Answer with explanation:

⇒ y=8.1 x

This is a Linear equation depicting linear relationship between y and x which is between the number of hours Alexander works, x, and the dollar amount he earns, y.

To determine a line you need two points.

→Put, x=0,in y=8.1 x, gives y=0 gives a Point (0,0).

→Put,x=1 gives , y=8.1 × 1→y=8.1 gives another point (1,8.1).

→So, Drawn a line passing through (0,0) and (1, 8.1),which is the required image of the equation given.

Answer:

B,E

Step-by-step explanation:

B,E

Answer:

the answer is 192in

Step-by-step explanation:

Answer:

The answer is true

Step-by-step explanation:

we know that

A polyhedron is  is a solid with flat faces and a cone is a solid with a curved side

therefore

A cone is not a polyhedron  ( Is true)

1) The angle the shelf makes with the floor is approximately 77.905°. (Choice A)

2) The approximate angle of inclination of the sun is approximately 51.340°. (Choice A)

1) In this case we know that shelf has a vertical height ([tex]h[/tex]) of 7 feet and a horizontal distance between the floor from the wall to the front of the shelf ([tex]l[/tex]) is 1.5 feet. The angle ([tex]\theta[/tex]), in degrees, is determined by tangent function:

[tex]\theta = \tan^{-1} \frac{7\,ft}{1.5\,ft}[/tex]

[tex]\theta \approx 77.905^{\circ}[/tex]

The angle the shelf makes with the floor is approximately 77.905°. (Choice A) [tex]\blacksquare[/tex]

2) The length of the shadow ([tex]l[/tex]) is 12 feet and the height of the building ([tex]h[/tex]) is 15 feet. The angle of inclination of the sun is determined by tangent function:

[tex]\theta = \tan^{-1} \frac{15\,ft}{12\,ft}[/tex]

[tex]\theta \approx 51.340^{\circ}[/tex]

The approximate angle of inclination of the sun is approximately 51.340°. (Choice A) [tex]\blacksquare[/tex]

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Answer: b. -3 or 2

Step-by-step explanation:

Answer:

I got 79 degrees in my pocket, gonna solve this math problem, its just like a pick on a locket, no wonder your grades are gonna skyrocket.

Step-by-step explanation:

The number of degrees ahead of the hour hand will be 128 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

If the minute hand of a clock is 20 degrees behind the hour hand at this moment.

We know that the rotation of the minute hand in each minute is 6°.

The angle when minutes shows 18 minutes is given as,

⇒ 18 x 6°

⇒ 108°

The number of degrees ahead of the hour hand will be given as,

⇒ 108° + 20°

⇒ 128°

The number of degrees ahead of the hour hand will be 128 degrees.

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 1.1      Factoring:  x2-15 

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =
         A2 - AB + BA - B2 =
         A2 - AB + AB - B2 = 
         A2 - B2

Note :  AB = BA is the commutative property of multiplication. 

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 15 is not a square !! 

Ruling : Binomial can not be factored as the difference of two perfect squares.

 2.1      Solve  :    x2-15 = 0 

 Add  15  to both sides of the equation : 
                      x2 = 15 
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ 15  

 The equation has two real solutions  
 These solutions are  x = ± √15 = ± 3.8730  
 

Final answer:

Explaining the number of real number solutions for the given quadratic equation x²-15=0.

Explanation:

x²-15=0

To find the number of real number solutions for the equation, we start by setting the expression to zero:

x² - 15 = 0

x² = 15

x = ±√15

Therefore, the equation has two real number solutions, which are ±√15.

We are given this equation

[tex] y=-2x^{2} +2x+2 [/tex]

The vertex form is given by:

[tex] y=a(x-h)^{2} +k [/tex]

Now let us try to convert our equation into vertex form:

[tex] y=-2x^{2} +2x+2 [/tex]

Vertex form is given by:

[tex] y=-2(x-0.5)^{2} +2.5 [/tex]

comparing our equation with vertex form ,

The vertex (h,k) is (0.5, 2.5)

Next we have to find y when x=6, plugging x as 6 in the given equation,

[tex] y=-2(6)^{2} +2(6)+2 [/tex]

y=-58

So at x=6, y=-58.

Answer:

[tex]3^{\circ}[/tex]

Step-by-step explanation:

Let x represent the angle of elevation.

We have been given that Jamison takes a 20 foot board and props it up with a one foot block at the far end to make a daredevil jump ramp for his bike.

Upon looking at our attached file, we can see that 20 feet board and 1 foot board forms a right triangle with respect to ground, where side of 1 foot is opposite side and 20 feet side is hypotenuse.

We know that sine relates the opposite side of right triangle to its hypotenuse, so we can set an equation as:

[tex]\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

[tex]\text{sin}(x)=\frac{1}{20}[/tex]

Using arcsin we will get,

[tex]x=\text{sin}^{-1}(\frac{1}{20})[/tex]

[tex]x=2.865983982599^{\circ}[/tex]

Upon rounding our answer to nearest degree we will get,

[tex]x\approx 3^{\circ}[/tex]

Therefore, the measure of the angle of elevation of the ramp is 3 degrees.