What to do: Complete each of the following problems involving ladders and walls by using trigonometric functions and inverse trigonometric functions to determine unknown lengths and angle measures.


Questions:

a) A ladder is placed against the wall of a building such that the bottom of the ladder is 3 ft from the bottom of the wall. If the ladder forms a 14 degree angle with the building, how high up the wall does the ladder reach?


b) A 15 foot ladder is leaned against a wall so that the bottom of the ladder forms a 75 degree angle with the ground. How far up the wall does the ladder reach?


c) You need to paint shutters on a window that is on the second floor of your house. You have a 20 foot ladder that you will use. There is a warning on the ladder that states the angle formed by the ladder and the ground must not be less than 70 degrees, or the ladder may slip and cause serious injury or death. You planned on placing the bottom of the ladder 3 feet from the base of the house.

Will the angle formed between the ground and the ladder be safe? What is the furthest possible distance the ladder can be placed to maintain a safe angle?


How you must answer:

- Sketch:

-We know:

-We want

-Rationale: Which ratio will you use and why?

-Solution


How do you answer:

= you must include an accurate sketch

= a statement identifying the known information - we know

= a statement that tells what you are solving for - we want

= the equation you used to solve the problem

Step-by-step explanation:

m<2: 65°( vertically opposite angle)

m<3: 180°-65°=115°(sum of straight line)

m<4: 180°- 65° = 115° (sum of straight line)

m<5: 180°- m<7=180-115=65

m<7 = m<4=115°(corresponding angle)

m<8 = m<5 =65°(vertically opposite angle)

m<6=m<7=115°( vertically opposite angle)

in this way 10,11,12 will be find.

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Step-by-step explanation:

correct this answer

mark a brain less

Answer:

kya- y= 100·(0.8)^t

chase= 100-18t

Step-by-step explanation:

I did the work on imagine math

The exponential function that fits the data is y= 100·(0.8)^t

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

We are given that Mrs. Evans gave her class a 100-page reading assignment.

Since 2 days, Kya and Chase each have 64 pages left to read.

Each student writes a function f(t) to model the pages left to read, where t is the number of days since the assignment was given.

Kya writes an exponential function that fits the data as;

y= 100·(0.8)^t

Chase writes a linear function that fits the data as;

chase= 100-18t

Learn more about function here:

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The 3 inside angles of a triangle need to equal 180.

X = 180 - 70 - 20 = 90

x = 90 degrees

Answer:

5/8 is smaller.

Step-by-step explanation:

A ratio is just a different type of fraction, a 5:8 ratio means 5/8 which is 0.625. A 7:9 ratio equals 7/9 which is 0.777777

Then to compare them you see which is smaller or bigger.

0.77777  is bigger than 0.625 so we know that 0.77777777 which was the 7:9 ratio is the bigger one.

Steps:-

[tex]\\ \rm\rightarrowtail 5:8::7;9[/tex]

[tex]\\ \rm\rightarrowtail 5/8:7/9[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{5(9)}{8(9)}:\dfrac{7(8)}{9(8)}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{45}{72}:\dfrac{56}{72}[/tex]

[tex]\\ \rm\rightarrowtail \dfrac{45}{56}[/tex]

Answer:

12 cm²

Step-by-step explanation:

Area of triangle: bh/2 = (2)(3)/2 = 3

Area of square: bh = (2)(3) = 6

Total area of the shape = 2 triangles + 1 square

Total area = 2(3) + 6 = 12 cm²

I hope this helps!

Answer:

12

Step-by-step explanation:

You can find the area of the shape 2 different ways.

I'll show you both ways.

First Way: find the area of each individual shape that makes it up then add them together

We can find the area by finding the area of the rectangle and then the two triangles and then adding the two multiples together

Area of a rectangle = length × width

Length = 3 and width = 2

So area = 3 × 2 = 6

Now to find the area of the triangles

Area of a triangle = 1/2bh

Where b = base length and h = height

The base length is 2 and the height is 3

So area = 1/2 × 2 × 3 = 3

There are two triangles and they both have the same dimensions

So the area of both triangles = 2 × 3 = 6

Finally we add the areas together to get the total area

Total Area = 6 + 6 = 12cm²

Second way : Use the area of a trapezoid formula:

The shape shown is a trapezoid so we could also use the area of a trapezoid formula.

Formula : [tex]A=\frac{a+b}{2} h[/tex]

where a and b = base lengths and h = height

The base lengths appear to be 2 and 6 and the height is 3

So a = 2 , b = 6 and h = 3

Which means [tex]A=\frac{2+6}{2} 3[/tex]

Simplify addition

[tex]A=\frac{8}{2} 3[/tex]

simplify division

A = (4)3

Then multiply
A = 12cm²

Answer:

Step-by-step explanation:

The quadratic expression can be factored into two binomials if it has two real roots.

Two real roots possible with non-negative discriminant:

As D = b² - 4ac, we get the following inequality

This is true for any value of k

Answer:

(-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]

Step-by-step explanation:

Binomial:  two terms connected by a plus or minus sign.

Discriminant

[tex]b^2-4ac\quad\textsf{when}\:ax^2+bx+c=0[/tex]

[tex]\textsf{when }\:b^2-4ac > 0 \implies \textsf{two real roots}[/tex]

[tex]\textsf{when }\:b^2-4ac=0 \implies \textsf{one real root}[/tex]

[tex]\textsf{when }\:b^2-4ac < 0 \implies \textsf{no real roots}[/tex]

If a quadratic expression factors into two binomials, it will have two real roots.  Therefore, the discriminant will be greater than zero.

Given quadratic expression:

  [tex]3x^2+kx-8[/tex]

[tex]\implies a=3, \quad b=k, \quad c=-8[/tex]

Substitute the values of a, b and c into the discriminant, set it to > 0:

[tex]\implies k^2-4(3)(-8) > 0[/tex]

[tex]\implies k^2+96 > 0[/tex]

As k² ≥ 0 for all real numbers,

[tex]\implies k^2+96 \geq 96[/tex]

Therefore, the values of k are (-∞, ∞)  or  [tex]k \in \mathbb{R}[/tex]

Answer:

x ≈ 59.0°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanx = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{30}{18}[/tex] , then

x = [tex]tan^{-1}[/tex] ( [tex]\frac{30}{18}[/tex] ) ≈ 59.0° ( to the nearest tenth )

Answer: 77 is right.

Step-by-step explanation:

In the given box-and-whisker plot, the value of first quartile is 85.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median.

From the given box and whisker plot,

Minimum=77

Maximum=92

First Quartile=85

Median=87

Third Quartile=89

Therefore, in the given box-and-whisker plot, the value of first quartile is 85.

Learn more about the box plot here:

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Answer:

S= -15/5

the slashes are supposed to be fractions.

Step-by-step explanation:

Answer:63.75

Step-by-step explanation: 1500x0.085x0.5=63.75

Answer:

2/10 = 1/5

Step-by-step explanation:

It landed five 2 times and you rolled it 10 times

Answer:

41,636

Step-by-step explanation:

Easy, on each row, there are 28 seats, and we know there's 1487 rows in total.

Hence, number of rows multiplied by number of seats counted

   1487 × 28

   =41,636

(Dang, that's alot of seats then)

The total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.

Percentage of a number is the part of the number expressed in the in every hundred. Percentage of a number is expressed with the symbol '%'.

To calculate the percentage part of number, multiply it with the original number and divide with 100.

Tom is exchanging money for his trip to india. The exchange rate of us dollars to indian rupees is,

[tex]r=\dfrac{1}{45.897}[/tex]

Tom needs 11,550 rupees. The dollars need for 11550 Indian rupees are,

[tex]n=\dfrac{11550}{45.897}\\n=251.65[/tex]

The currency exchange service he is using charges a fee of 7.25% after the exchange is made. Thus the total dollar requied after the service charge is,

[tex]n=251.65+\dfrac{7.25}{100}\times251.65\\n=251.65+18.245\\n=269.895\\n\approx270[/tex]

Thus, the total US dollars it cost to Tom to get the rupees he wants for the trip of India is $270 round to the nearest dollar.

Learn more about the percentage here;

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Answer:

Step-by-step explanation:

Total number of Hamburgers and Cheeseburgers = 394

Let the number of hamburgers = x

x + x - 56 = 394                           Combine the left

2x - 56 = 394                               Add 56 to both sides

2x - 56 + 56 = 394 + 56              Combine

2x = 450                                       Divide both sides by 2

2x/2 = 450/2

x = 225

Answer

Answer:

B. 12

Step-by-step explanation:

Edges are the straight lines

Answer:

x = 9 m

y = 1 m

Step-by-step explanation:

6/1 = x/1.5

x = 1.5 × 6

x = 9

6/1 = 6/y

6y = 6

y = 1

Answer:

19 is B

Step-by-step explanation:

7/8 x 8x = 7x

7/8 x 16 = 14

Answer:

D.

Step-by-step explanation:

It will move but stay the same size. You are translating the shape to a different spot, not adding onto its size.

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I hope this helps!

-No one

Answer:

Step-by-step explanation:

cos(π+θ)=-cos θ=-(0.83)/1=-0.83

cos (2π-θ)=cos θ=0.83/1=0.83

Answer:

5/4

Step-by-step explanation:

Answer:

gradient:  1/4; y-intercept:  3

Step-by-step explanation:

In math, 'gradient' is another word for slope.

Here we have y = (1/4)x + 3.  The coefficient of x is the slope or gradient:  1/4.  The y - intercept is 3:  (0, 3).

Answer:

Step-by-step explanation:

The equation is in y = mx + b form.

Here, m is the slope or gradient and b is the y-intercept.

[tex]y =\dfrac{1}{4}x+3\\\\\\Gradient =\dfrac{1}{4}[/tex]

y-intercept = 3

Answer:

I believe the answer is C, the area of a circle, because pi is irrational, and anything multiplied by it will always result in an irrational number.

Step-by-step explanation:

I hope this helps and please mark me as brainliest!

Answer:

3w, 4x, 4w, 7y, 7x, 3y,  5w,

Step-by-step explanation:

Answer:

Hope the picture will help you

Answer:

if youre doing this on paper use a protractor

Step-by-step explanation:

place the straight line ontop of the side you're trying to read the angle from and go in a clockwise direction when using the compass until you find the angle degree.  hope that helps:-)

Answer:

[tex]\tt x=-2[/tex]

Step-by-step explanation:

[tex]\tt -3(x + 5) = -9[/tex]

Step (1) :- Distribute

[tex]\tt -3x-15=-9[/tex]

Step (2) :- Add 15 to both sides

[tex]\tt -3x-15+15=-9+15[/tex]

Step (3) :- Simplify

[tex]\tt -3x=6[/tex]

Step (4) :- Divide both sides by -3:-

[tex]\tt \cfrac{-3x}{-3}=\cfrac{6}{-3}[/tex]

[tex]\tt x=-2\;\; \bf Answer[/tex]

____

[tex] \sf:\implies \quad {\pmb{\sf x = -2}} [/tex]

Let's solve the given problem step by step :

[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]

First, distribute the given problem :

[tex]:\implies \quad \sf - 3(x + 5) = - 9[/tex]

[tex] \sf:\implies \quad - (3 \times x) - (3 \times 5) = - 9[/tex]

Add 15 to both sides :

[tex] \sf:\implies \quad - 3x - 15 = - 9[/tex]

[tex] \sf:\implies \quad - 3x - 15 + 15 = - 9 + 15[/tex]

On simplifying :

[tex] \sf:\implies \quad -3x-15+15 = -9+15[/tex]

[tex] \sf:\implies \quad - 3x = 6[/tex]

Dividing both sides with same factor :

[tex] \sf:\implies \quad - 3x = 6[/tex]

[tex] \sf:\implies \quad \dfrac{ - 3x}{ - 3} = \dfrac{6}{ - 3} [/tex]

[tex] \sf:\implies \boxed{ \pmb{ \sf\quad x = - 2}}[/tex]

Answer:

preference ballot

Step-by-step explanation:

A preference ballot is a ballot in which the voter ranks the choices in order of preference.

Answer:

Traditional ballots

Step-by-step explanation:

i took the test

Answer:

length: 40, width: 20

Step-by-step explanation:

length = 1/2×80/1 = 40

width = 1/4 × 80/1 = 20

hope this helps =)

Alright let's solve this problem step by step:

   The figure is made up triangles

      ⇒ however, we do not know the slanted line that goes from the tip to

           the edge of the base.

           ⇒ we can use the Pythagorean Theorem to help us

                 [tex]2^2 + (5.7)^2 = slanted-line^2\\slanted-line = 6.04[/tex]

   Perimeter = 6.04 + 6.04 + 6.04 + 6.04 + 6.04 + 4 + 4 + 4 + 4 + 4

                      = 50.2 inches

         *look at image attached to better understand this definition

           ⇒ Slant height = 5.7inches

   Lateral Area = 5 * (Area of Triangle Faces)    

                         = [tex]5 *(\frac{1}{2} *5.7 * 4) = 5*2*5.7 = 5 * 11.4[/tex]

                         = 57 in^2

Hope that helps!