1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Aneli [31]
3 years ago
6

The top of the ladder makes a 13° angle with the building. The base of the ladder is 6 feet from the base of the building. How f

ar up the building does the ladder reach
Mathematics
1 answer:
KonstantinChe [14]3 years ago
5 0

tan x = opp/hyp  

x is the side of the building and 6 is the distance from the bottom of the ladder to the building

tan 13 = 6/x

multiply both sides by x

x tan 13 =6

divide both sides by tan 13

x = 6/ tan 13

x = 26

The ladder goes 26 ft up the building

You might be interested in
If(x) = x + 2 and h(x) = x-1, what is f • h](-3)?
deff fn [24]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

4 0
3 years ago
Then each week thereafter, you add $5 to the account but no interest is earned. Suppose you receive $100 for a graduation presen
irga5000 [103]
100 + 5x = y

100 +5x = 310
x = 42 weeks

7 0
3 years ago
Read 2 more answers
Michael earns $8 an hour to baby sit the Jackson family. How many hours does he have to 1 point
notsponge [240]

Answer:

7 hours

Step-by-step explanation:

56/8=7

7 0
3 years ago
Karen got a bit confused in math class today when Mrs. Hudson was talking about the different subsets for classifying real numbe
VashaNatasha [74]
Let me give the significations following
natural numbers :ACA  counting numbers the numbers you naturally say when counting.
whole numbers: include all natural numbers zero
Integers: include all whole numbers and their opposites.
Rational: can be written ASA fraction or ratio of two integers also decimals that terminate or repeat 
Irrational: can not be written a fraction, decimals, do not terminate or repeat.




4 0
3 years ago
Read 2 more answers
At a particular restaurant, each chicken wing has 60 calories and each slider has 225 calories. A combination meal with chicken
Elden [556K]

x = number of chicken wings

y = number of sliders

60x + 225y = 1380

2y + y = 1380

7 0
3 years ago
Other questions:
  • Factor completely 9x^2-25
    9·1 answer
  • Solve the triangle below without using either the cosine or tangent ratios. Show your work.
    7·1 answer
  • I'm so stuck how do you do this??
    9·2 answers
  • I’m doing algebra homework and I’m really stumped on this problem I could use the help
    9·1 answer
  • Inverse function details
    12·1 answer
  • I don’t know this question what is 1/7 • 5/2=?
    10·1 answer
  • AB and BC are perpendicular lines.<br> А<br> 24<br> to<br> 24<br> B.<br> с<br> Find the value of x.
    7·1 answer
  • Paulie ordered 250 pens and 250 pencils to sell for a theatre club fundraiser. The pens cost 11 cents more than the pencils. If
    9·1 answer
  • A polygon is shown:
    10·2 answers
  • Please please help no scams please ​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!