let H be the altitude from vertex C. Which proves the first equality in the law of sines
The sine law of triangles can be proved by dividing the triangle into right-triangles.
Option (c) proves the first equality in the law of sines
From the question, we have:
h equals to the distance from point C to segment AB
The sine of angle is:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
For angle at A, we have:
[tex]\mathbe{\theta = A}[/tex]
[tex]\mathbf{Hypotenuse = b}\\\mathbf{Opposite = h}[/tex]
So, we have:
[tex]\mathbf{sin(\theta) = \frac{Opposite}{Hypotenuse}}[/tex]
Substitute values for Opposite, Hypotenuse and theta
[tex]\mathbf{sin A = \frac{h}{b}}[/tex]
Similarly
[tex]\mathbf{sin B = \frac{h}{a}}[/tex]
Make h the subject
[tex]\mathbf{h = a\ sinB}[/tex]
Substitute [tex]\mathbf{h = a\ sinB}[/tex] in [tex]\mathbf{sin A = \frac{h}{b}}[/tex]
[tex]\mathbf{sin A = \frac{a\ sinB}{b}}[/tex]
Divide both sides by a
[tex]\mathbf{\frac{sin A}{a} = \frac{sinB}{b}}[/tex]
Hence, the correct option is (c).
Read more about proof of sine law at:
https://brainly.com/question/4637169
The carpet costs $2.59 per square foot, and sales tax is 7.5%. What is the total cost of the carpet? (Round to two decimal places as usual.)
what is the answer to 12 divided by 51.6??? can i have an explanation to please if you guys don't mind??
Answer:
will u give the brainliest?
What is the missing measure?
Answer:
Step-by-step explanation:
This is a problem of ratios:
Set the problem up with matching similar side lengths equal:
50/10 = x/12
First simplify the left side:
50/10 = 5
Next, multiply both sides by 12.
We are left with:
x = 12(5)
x = 60
Si el punto (5,0) está en una gráfica, żes (5,0)
la intersección con el eje y de la gráfica? Explica
Answer:
Can you put it in English pls..
Step-by-step explanation:
Now when the spending multiplier is same as the one calculated in Q 4c and if there is a decrease in government purchases by $50,000. Calculate the change in AD. (Show your work)
Will AD increase or decrease?
Answer:
a. The real GDP increases by $200,000.
a. The real GDP increases by $150,000.
Step-by-step explanation:
a. What is the eventual effect on real GDP if the government increases its purchases of goods and services by $50,000?
Eventual effect on real GDP = Amount of increase in government spending * (1 /(1 - MPC)) = $50,000 * (1 / (1 – 0.75)) = $200,000
Therefore, the real GDP increases by $200,000.
a. What is the eventual effect on real GDP if the government, instead of changing its spending, increases transfers by $50,000?
Eventual effect on real GDP = (Amount of increase in government transfers * (1 /(1 - MPC))) - Amount of increase in government transfers = ($50,000 * (1 / (1 – 0.75))) - $50,000 = $150,000
Therefore, the real GDP increases by $150,000.
0.28÷0.007please answer me
Answer:
40
Step-by-step explanation:
0.28÷0.007
=280÷7
=40
_________
[tex] \: [/tex]
0,28 ÷ 0,007 = ...
[tex] = \frac{28}{100} \div \frac{7}{1.000} [/tex]
[tex] = \frac{28}{100} \times \frac{1.000}{7} [/tex]
[tex] = \frac{28.0 \cancel{00}}{7 \cancel{00}} [/tex]
[tex] = \frac{280}{7} [/tex]
[tex] \longmapsto \boxed{ \bold{ \red{40}}}[/tex]
Which of the following functions has an inverse that is NOT a function?
A) f(x) = (1/2)x - 1/2
B) f(x) = (x - 1)^3 + 2
C) f(x) = 2^x
D) f(x) = x(x - 1)
Step-by-step explanation:
Content
Functions and their inverses
We begin with a simple example.
Example
Let f(x)=2x and g(x)=x2.
Apply the function g to the number 3, and then apply f to the result:
g(3)=32andf(32)=3.
A similar thing happens if we first apply f and then apply g:
f(3)=6andg(6)=3.
It is clear that this will happen with any starting number. This is expressed as
f(g(x))g(f(x))=x,for all x=x,for all x.
The function f reverses the effect of g, and the function g reverses the effect of f. We say that f and g are inverses of each other.
As another example, we have
(x−−√3)3=xandx3−−√3=x,
for all real x. So the functions f(x)=x3 and g(x)=x−−√3 are inverses of each other.
If x≥0, then (x−−√)2=x and x2−−√=x. If x<0, then x−−√ is not defined. So the functions f(x)=x2 and g(x)=x−−√ are inverses of each other, but we need to be careful about domains. We will look at this more carefully later in this section.
Basics
In an earlier section of this module, we defined the composite of two functions h and g by (g∘h)(x)=g(h(x)).
Definitions
The zero function 0–:R→R is defined by 0–(x)=0, for all x.
The identity function id:R→R is defined by id(x)=x, for all x.
Example
Consider a function f:R→R.
Prove that
0–∘f=0–
f∘id=f
id∘f=f.
Show that f∘0– does not necessarily equal 0–.
Solution
We have (0–∘f)(x)=0–(f(x))=0, for all x, and so 0–∘f=0–.
We have (f∘id)(x)=f(id(x))=f(x), for all x, and so f∘id=f.
We have (id∘f)(x)=id(f(x))=f(x), for all x, and so id∘f=f.
Consider the function given by f(x)=2, for all x. Then f∘0–(x)=f(0–(x))=f(0)=2, and so f∘0–≠0–.
Definition
Let f be a function with both domain and range all real numbers. Then the function g is the inverse of f if
f(g(x))g(f(x))=x,for all x,and=x,for all x.
That is, f∘g=id and g∘f=id.
Notes.
Clearly, if g is the inverse of f, then f is the inverse of g.
We denote the inverse of f by f−1. We read f−1 as 'f inverse'. Note that f inverse has nothing to do with the function 1f.
Example
Let f(x)=x+2 and let g(x)=x−2. Show that f and g are inverses of each other.
Solution
We have
f(g(x))=f(x−2)=x−2+2=x,for all x(f∘g=id)
and
g(f(x))=g(x+2)=x+2−2=x,for all x(g∘f=id).
Hence, the functions f and g are inverses of each other.
Exercise 5
Find the inverse of
f(x)=x+7
f(x)=4x+5.
Example
Let f(x)=ax+b with a≠0. Find the inverse of f.
Solution
We have x=f(x)−ba, for all x. So let g(x)=x−ba. Then
f(g(x))g(f(x))=f(x−ba)=a(x−ba)+b=x=g(ax+b)=(ax+b)−ba=x,
for all x. Hence, g is the inverse of f.
Exercise 6
Show that f(x)=x5 and g(x)=x15 are inverses of each other.
Find the inverse of f(x)=x3+2.
We do not yet have a general enough concept of inverses, since x2 and x−−√ do not fit into this framework, nor do ex and logex. We will give a definition that covers these functions later in this section.
The horizontal-line test
Consider the function f(x)=x2, which has domain the reals and range A={x:x≥0}. Does f have an inverse?
The following graph shows that it does not. We have f(−2)=f(2)=4, and so f−1(4) would have to take two values, −2 and 2! Hence, f does not have an inverse.
Graph of y = x squared and the line y = 4 on the one set of axes.
This idea can be formulated as a test.
Horizontal-line test
Let f be a function. If there is a horizontal line y=c that meets the graph y=f(x) at more than one point, then f does not have an inverse.
Notes. Remember that the vertical-line test determines whether a relation is a function.
Example
Consider the function
f(x)=x3−x=(x+1)x(x−1).
Its graph is shown in the following diagram.
Graph of y = x cubed minus x.
Does f have an inverse?
Solution
The line y=0 meets the graph at three points. By the horizontal-line test, the function f does not have an inverse.
The function whose inverse does not exist is f(x) = x(x - 1)
The correct option is (D) f(x) = x(x - 1)
What is inverse of a function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
First, f(x)= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
let y= [tex]\frac{1}{2} x -\frac{1}{2}[/tex]
On solving for x we get a unique value
Then replace x and y.
It shows that the function have a unique value, which satisfies the condition of inverse.
Now, f(x) =[tex](x - 1)^3 + 2[/tex]
Again, solving for y we can get a cube root function which is a inverse of cube.
Hence, the inverse of [tex](x - 1)^3 + 2[/tex] exists.
Next, f(x) =[tex]2^x[/tex]
Solving for above we get logarithmic value. Log function are inverse of exponential function.
Hence, the inverse of [tex]2^x[/tex] exists.
Last, f(x)= x(x-1)
Solving for above create a square value.
The inverse of square never exist because having square root gives two value one is positive and other is negative.
Hence, the inverse of x(x-1) not exists.
Hence the function whose inverse does not exist is x(x-1).
Learn more about inverse of function here:
https://brainly.com/question/2541698
#SPJ2
What is 6 tens = ? Ones
Students were asked to find an equivalent value of the expression 13 divided by 19/100 which could a student use?
Answer:
68.4210526316
you first divide 19/100 and then you divide the out put 13/ 0.19
Step-by-step explanation:
The price of an item has dropped to $81 today. Yesterday it was $135. Find the percentage decrease.
Answer: 60%
Step-by-step explanation:
81/135= 60/100
Solve for a side in right angles picture added
Answer:
AC=5
in a basic right triangle the small side is always one shorter than the big side which is always one smaller than the hypotenuse.
determine the value of x which r || s. then find m<1 and m<2.
m<1 = 60-4x
m<2= 80-12x
Answer:
Step-by-step explanation:
Answer:
say what now-
Step-by-step explanation:
15. In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total $4.60. How
many of each coin does he have?
10 quarters 6 nickels 18 dimes
What is the coefficient in the expression - X + 21?
Answer:
there are no like terms
Step-by-step explanation:
-x + 21 = -x + 21
Does anyone know how to do multiple in fractions like for a example 1/12•1/3? Please explain step by step
[tex] \frac{1}{12} \times \frac{1}{3} \\ = \frac{1 \times 1}{12 \times 3} \\ = \frac{1}{36} [/tex]
When you want to multiply 2 fractions, merge the fractions together & then multiply the numerator first & then the denominator. After that, simplify to the lowest form if possible.rounding 615×38 to 1 significant figure estimate
Answer:
24,000
Step-by-step explanation:
615 ≈ 600
38 ≈ 40
600 × 40 = 24,000
Therefore, 615 × 38 ≈ 24,000
10 cm 10 cm 30 cm. 14.1 cm
answer; you
Step-by-step explanation:
I dont know
sssooooooorrrrrrrrrryyyyyyyyyyyy
Write < , >, or = to make the statement true 0.333 1.03
Answer:
0.333 < 1.03
Step-by-step explanation:
1.03 is greater than 0.333.
In fraction form, 1.03 is [tex]1\frac{3}{100}[/tex].
While 0.333 is [tex]\frac{33}{100}[/tex], which is a third of 1.
Therefore, 0.333 < 1.03.
The area of a square equals the square of a length of the side of the square. The perimeter equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65 while the difference in their areas is 33. Find the sum of their perimeters.
The sum of the perimeters is [x]
Answer:Each side of x would be 7 and each side of y would be 4.
Step-by-step explanation:
-2/3,0.6,3/4,-7/4,0,3 from least to greatest
Answer:
-7/4 < -2/3 < 0 < 0.6 < 3/4 < 3
Step-by-step explanation:
4x-9=-3 2/3 can someone evaluate x for me
Answer:
x=1 1/3
Step-by-step explanation:
what is the purpose of using measures of variability?
0.25555555 as a fraction
Answer:
23/90
Step-by-step explanation:Sorry if it's wrong!!!
The table below represents an exponential function of the form y = a . b^x
Complete the table and find the equation. Write all your numerical answers in
Fraction form.
What is the value of a?
What is the value of b?
Answer:
Step-by-step explanation:
If one of the data points has the form (0,a)
, then a is the initial value. Using a, substitute the second point into the equatio f(x)=a(b)x, and solve for b.If neither of the data points have the form (0,a)
, substitute both points into two equations with the form f(x)=a(b)x Solve the resulting system of two equations in two unknowns to find a and b.Using the a and b found in the steps above, write the exponential function in the form f(x)=a(b)x.
PLEASE HELP ITS MATH THANK YOUUUU
Answer:
8 millimeters 4x where x is 2 millimeters
solve for w
6w+2=9w+14
Answer:
w = 4
Step-by-step explanation:
6w+2=9w+14
9w-6w=14-2
3w=12
w=12/3
w=4
Find the least common denominator of the two fractions 3/4 over 1/6?
Answer:
(2/12 & 9/12)
Step-by-step explanation:
12 is the least common denominator for the fractions, so they must be rewritten to have the same denominator, but hold the same value.
( not written by me )
Can someone please help as I'm not sure how to tackle this step by step? Especially question b, d, g, j, k, l. Not how sure to do it if contains a surd just on its own.
Step-by-step explanation:
√a = 1√a so we can solve them easily:
b) 3√7 -√7= 3√7 - 1√7 =( 3-1)√7= 2√7
d) 5√6 - 2√6+√6= (5-2+1)√6 = 4√6
g) √2+2√2= 3√2
j) √5+5√5 - 3√5 = 3√5
k) 2√3 + √3 - 5√3= -2√3
I) 5√11 + 7√11 - √11 = 11√11
evaluate f(m-5) and simplify if f(x)=5x-9
Answer:
f(m-5) = 5m-34
Step-by-step explanation:
f(x)=5x-9
Replace x with m-5
f(m-5) = 5(m-5) -9
Distribute
= 5m-25 -9
= 5m-34
Answer:
answer is 5m - 34
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!