You place a ladder up against a building. The bottom of the ladder is 6.5 feet from the base of the building. The ladder reaches 20 feet up onto the building. To the nearest foot, how long is the ladder?

Answer:

Your answer is C.

Step-by-step explanation:

I answered it on paper. When it comes to explaining I have to be person to person. But I hope this helps. :)

Recall that sine is the ratio of opposite over hypotenuse, so we say

sin(theta) = opposite/hypotenuse

If we have a triangle labeled as such in the diagram below, then we can use symbols to write sin(theta) = A/C

Similarly, cos(theta) = B/C since cosine is the ratio of adjacent over hypotenuse.

Then from here we use a bit of algebra to compute the left hand side of the given equation. The goal is to see if we can simplify it to 1.

[tex]\sin^2\left(\theta\right)+\cos^2\left(\theta\right)\\\\\left(\sin\left(\theta\right)\right)^2+\left(\cos\left(\theta\right)\right)^2\\\\\left(\frac{A}{C}\right)^2+\left(\frac{B}{C}\right)^2\\\\\frac{A^2}{C^2}+\frac{B^2}{C^2}\\\\\frac{A^2+B^2}{C^2}\\\\\frac{C^2}{C^2}\\\\1[/tex]

So this shows that the left hand side is identically the same as the right hand side (both sides are 1), and it doesn't matter what you replace theta with. Theta can be any real number and the equation will always be true.

Note: if you're wondering how A^2+B^2 became C^2, it's because of the pythagorean theorem. So that's why this trig identity is often referred to as the pythagorean trig identity.

Answer:

Step-by-step explanation:

given=  -3(2n-3)=25-8n

distributive property=-6n+9=25-8n

subtraction property= 2n+9=25

division property =2n=16

n=8  

Answer:

Your loan was for $16,000.  

Step-by-step explanation:

The formula for simple interest is i = prt, where p is the principal, r is the interest rate as a decimal fraction, and t is the time in years.

If i = prt, then p = i / (rt)

Here, p = ($1200) / 0.075 = $16,000

Your loan was for $16,000.  

Answer:

50 people

Step-by-step explanation:

If you are to calculate the number of people that will come to the concert that will ensure option 1 and option 2 to yield equal amount

Let

x = number of people

Option 1:

Malcolm's Music Hall = 100 + 15x

Option 2:

Reggie's Reggae Room = 350 + 10x

Equate both options

100 + 15x = 350 + 10x

Collect like terms

100 - 350 = 10x - 15x

-250 = - 5x

x = -250/-5

x = 50 people

Answer:

c = 50

Step-by-step explanation:

Using the Pythagorean Theorem:

Plug in the values of a = 14, and b = 48

[tex]a^{2} +b^{2} =c^{2}\\14^{2} +48^{2} =c^{2} \\c^{2} = 2500\\c = \sqrt{2500} \\c = 50[/tex]

Answer:

Step-by-step explanation:

As we move from (0, 3) to (9, 0), we see x increasing by 9.  This is the 'run.'

At the same time, we see y decreasing by 3.  This is the 'rise.'

The slope of this line (graph) is m = rise / run = -3/9, or m = -1/3

Since we witness a decrease in y as we move from the first point to the second, we immediately suspect that the slope is negative.

Answer:

yes it is greater:)

[tex]\huge\textsf{Hey there!}[/tex]

“[tex]\rm{Is \ \dfrac{25}{4} \ greater \ than \ \dfrac{40}{5}?}[/tex]”

[tex]\rm{In \order\ to \ find\ out \ which \ one \ is \ bigger, you \ can \ divide \ both \ fractions\ and\ you}\\\rm{can\ turn \ them \ into \ a \ decimal }[/tex]

[tex]\rm{\dfrac{25}{4}=\boxed{\rm{\bf 6.25}}}\large\checkmark[/tex]

[tex]\rm{\dfrac{40}{5}=\boxed{\rm{\bf 5}}}[/tex]

[tex]\rm{Usually, \ decimals\ and \ negative \ numbers \ are \ BELOW \ zero \ as\ positive \ numbers}\\\rm{and \ regular/real \ numbers\ are \ ABOVE \ zero }[/tex]

[tex]\boxed{\boxed{\large\textsf{So, therefore your ANSWER is: }\mathsf{\dfrac{25}{4}>\dfrac{40}{5}}}}\huge\checkmark[/tex]

[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

tanM = [tex]\frac{15}{8}[/tex]

Step-by-step explanation:

tanM = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{KL}{LM}[/tex] = [tex]\frac{45}{24}[/tex] = [tex]\frac{15}{8}[/tex]

Answer:

Step-by-step explanation:

a) pencil = x +25

b) bob = x - 6

c) x +2

Answer:

3.897 [tex]in^{2}[/tex]

Step-by-step explanation:

equilateral triangles are also equiangular, meaning the have equal angles.

Triangle sum theory says that angles of a triangle add up to 180.

That means each angle is 60.

A = bh/2

You need the (h). The base of is 3.  Perimeter = 9, so each side is 3

Draw a perpendicular line for the height. The line cuts the base in half (1.5)

Using trigonometry you can find the height.

tan 60° = h/1.5

h = height, 1.5 is half of 3, 60° is the base angle.

multiply each side by 1.5

1.5(tan 60°) = h

h=2.598

then substitute h into formula

A= (2.598)(3)

           2

A = 3.897 rounded

Answer:

729 x [tex]\frac{1}{3}[/tex]^x

Step-by-step explanation:

the third option

- trial and error

Answer:

Step-by-step explanation:

4x + 2y = −2

Divide by two on both sides

2x+y = -1

subtract 2x from both sides

y = -1 -2x = -2x -1

Answer:

y = -2x - 1

Step-by-step explanation:

4x + 2y = -2

→ Minus 4x from both sides

2y = -4x - 2

→ Divide both sides by 2

y = -2x - 1

Answer:

4-3

Step-by-step explanation:

solve for x

Value of function f(x) = 4(1/3)ˣ when x = 3, f(3) = 4/27

Correct option is C.

As the name suggests, the exponential function contains an exponent. Note, however, that the exponential function has a constant as its base and a variable as its exponent, not vice versa (if a function has a variable as its base and a constant as its exponent, it is a power function). The exponential function can be in one of the following forms:

Definition of exponential function

In mathematics, an exponential function is a function of the form f(x) = aˣ. where "x" is a variable and "a" is a constant  called the base of the function, which must be greater than 0.

Given, exponential function

f(x) = 4(1/3)ˣ

exponential function is defined for x∈R

Putting x = 3

f(3) = 4(1/3)³

f(3) = 4/27

Hence, 4/27 is value of function f(x) = 4(1/3)ˣ when x = 3

Learn more about exponential function here:

https://brainly.com/question/14355665

#SPJ7

Answer:

y = -3x + 21

Step-by-step explanation:

(5,6)

y = mx + b

6 = -3 × 5 + b

solving for b

b = 6 - (-3)(5)

b = 21

Therefore,

y = -3x + 21

Answer:

We are losing Earth's greatest biological treasures just as we are beginning to appreciate their true value. Rainforests once covered 14% of the earth's land surface; now they cover a mere 6% and experts estimate that the last remaining rainforests could be consumed in less than 40 years.

One and one-half acres of rainforest are lost every second with tragic consequences for both developing and industrial countries.

Rainforests are being destroyed because the value of rainforest land is perceived as only the value of its timber by short-sighted governments, multi-national logging companies, and land owners.

Nearly half of the world's species of plants, animals and microorganisms will be destroyed or severely threatened over the next quarter century due to rainforest deforestation.

Experts estimates that we are losing 137 plant, animal and insect species every single day due to rainforest deforestation. That equates to 50,000 species a year. As the rainforest species disappear, so do many possible cures for life-threatening diseases. Currently, 121 prescription drugs sold worldwide come from plant-derived sources. While 25% of Western pharmaceuticals are derived from rainforest ingredients, less that 1% of these tropical trees and plants have been tested by scientists.

Most rainforests are cleared by chainsaws, bulldozers and fires for its timber value and then are followed by farming and ranching operations, even by world giants like Mitsubishi Corporation, Georgia Pacific, Texaco and Unocal.

There were an estimated ten million Indians living in the Amazonian Rainforest five centuries ago. Today there are less than 200,000.

InIIIIII AMMMM ABBBOOuUUTT TOO PI$$$$$$ MINE SELLFF Brazil alone, European colonists have destrotheir homelands continue to be destroyed by deforestation, rainforest peoples are also disappearing.

, it is as if a library has burned down.

When a medicine man dies without passing his arts on to the next generation, the tribe and the world loses thousands of years of irreplaceable knowledge about medicinal plants.

Step-by-step explanation:

Answer:

a). -65

b). -61

c). -20ab + 3bc +3ac

Step-by-step explanation:

According To the Question,

a). the sum of 72 − 104 + 5 and -32 + 4 - 10 .

b). What should be added to 32 + 32 + 3 to get 3 + 3 , Let X be Added .

c). Subtract  the sum of 12ab –10bc –18ac and 9ab + 12bc + 14ac from the sum of ab + 2bc and 3bc – ac.

Answer:

2/5 =w

Step-by-step explanation:

4/w = 10

Multiply each side by w

4/w *w = 10*w

4 = 10w

Divide by 10

4/10 = 10w/10

2/5 =w

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]w=\frac{2}{5}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\frac{4}{w}=10\\-----------\\\rightarrow (\frac{4}{w})w =10*w\\\\\rightarrow 4 = 10w\\\\\rightarrow 10w=4\\\\\rightarrow\frac{10w=4}{10}\\\\\rightarrow w=\frac{4}{10}\\\\-----------------\\\frac{4}{10}\text{ can be simplified.} \\\\\rightarrow\frac{4}{10}=\frac{4/2}{10/2}=\frac{2}{5}\\-----------------\\\\\rightarrow\boxed{w=\frac{2}{5}}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

i believe the answer is B

Step-by-step explanation:

hope this helps

Answer:

Step-by-step explanation:

1. 8x + 6

2(4x+3)

2.4x+2

2(2x +1)

Answer:

[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]

1. [tex]\boxed{Factorise \ = \ 8x + 6}[/tex]

⎆To factorise this, you have to take the common factor out. In this case, it's 2.

[tex]8x + 6 \\ = 2(4x + 3)[/tex]

[tex]\boxed{Answer \ = \ 2(4x + 3)}[/tex]

2) [tex]\boxed{Factorise \ = \ 4x + 2}[/tex]

⎆To factorise this, you have to take the common factor out. In this case also, it's 2.

[tex]4x + 2 \\ = 2(2x + 1)[/tex]

[tex]\boxed{Answer \ = \ 2(2x + 1)}[/tex]

____________________

ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ

ღ [tex]RainbowSalt2^{2}2^{2} [/tex]

Answer:

[tex]\text{B. }\frac{1}{3}x-3=-x+1[/tex]

Step-by-step explanation:

Let's start by taking a look at the blue line. The slope of any line that passes through two points is equal to the change in y-values over the change in x-values. We can see that the line passes through points (0, 1) and (1, 0). Assign these points to [tex](x_1,y_1)[/tex] and [tex](x_2, y_2)[/tex] (doesn't matter which you assign) and use the slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Let:

[tex](x_1,y_1)\implies (0,1)\\(x_2,y_2)\implies (1, 0)[/tex]

The slope is equal to:

[tex]m=\frac{0-1}{1-0}=\frac{-1}{1}=-1[/tex]

Therefore, the slope of this line is -1. In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents slope, so one of the lines must have a term with [tex]-x[/tex] in it, which eliminates answer choices A and D.

For the second line, do the same thing. The red line clearly passes through (0, -3) and (3, -2). Therefore, let:

[tex](x_1,y_1)\implies (0,-3)\\(x_2,y_2)\implies (3, -2)[/tex]

Using the slope formula:

[tex]m=\frac{-2-(-3)}{3-0}=\frac{1}{3}[/tex]

Thus, the slope of the line is 1/3 and the other line must have a term with [tex]\frac{1}{3}x[/tex] in it, eliminating answer choice C and leaving the answer [tex]\boxed{\text{B. }\frac{1}{3}x-3=-x+1}[/tex]

*You can find the exact equation of each line by using the slope formula as shown and plugging in any point the line passes through into [tex]y=mx+b[/tex]

Answer:

B

Step-by-step explanation:

Add both sides of the equation by 7, which satisfies the definition of the addition property of equality.