Step-by-step explanation:
y=(3/2)x +8
that is the answer
The equation of the line is y = (3/2)x + 8 if the line that passes through ( - 8, - 4 ) and ( -6, - 1 ).
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
The line that passes through (-8, - 4 ) and ( -6, - 1)
The standard form of the line in slope-intercept form:
y = mx + c
Here m is the slope of the line
c is the y-intercept.
As we know, the ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{-1-(-4)}{-6-(-8)}[/tex]
m = 3/2
y = (3/2)x + c
Plug x = -8, y = -4
-4 = (3/2)(-8) + c
c = 8
y = (3/2)x + 8
Thus, the equation of the line is y = (3/2)x + 8 if the line that passes through ( - 8, - 4 ) and ( -6, - 1 ).
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Solve pls branliest!
Answer:
1 23 then 70 .2 corrected
solve pls brainliest
Answer:
Triangle A) acute
Triangle B) right
Triangle C) obtuse
Triangle D) obtuse
Step-by-step explanation:
Any triangle less than 90° is acute.
Triangles at exactly 90° are right triangles.
Any triangle more than 90° are called obtuse.
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).
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Need help with number 5 and number 6
Answer:
5 d) 9 1/3
6 d) 2
Step-by-step explanation:
Proportions:
5
7 ⇒ 4
BY ⇒3
BY = 7*4/3
BY = 28/3
28/3 = 27/3 + 1/3 = 9 1/3
BY = 9 1/3
6
12 ⇒ 3
8 ⇒ SX
SX = 3*8/12
SX = 2
To form the blue parallelogram, the red parallelogram is dilated using point A as the
center of dilation. Which statement is true?
Answer:
option b
Step-by-step explanation:
have a great day
pls mark as brainliest
Answer:
B
Step-by-step explanation:
The graph of y=3x+2x-2^2 is shown. A) what are the coordinates
Will mark BRAINELIST please answer both!!
Answer:
(
2
,
8
)
Explanation:
Two lines are parallel if they share the same slope.
Any line parallel to
y
=
10
x
will have the slope 10.
Now, we have:
y
=
3
x
2
−
2
x
We try to find
d
y
d
x
=>
d
d
x
(
y
)
=
d
d
x
(
3
x
2
−
2
x
)
Step-by-step explanation:
Why was cuneiform important?
Answer:
It is important because it provides information about ancient Sumerian history and the history of humanity as a whole.
Step-by-step explanation:
Hope this helps.
Choose the scientific notation for 800.
O 8 x 10
O 8 x 102
O 8 x 103
O 8 x 100
Answer:
O [tex]8 * 10^2[/tex]
Step-by-step explanation:
Hope it helps
Peace out
^^ ^-^ :) ;) ~-~
(10pts) Ivan bought three games and paid $65 for all three. The second game was 50% more expensive than the first one. The price of the third game was 50% of the price of the second game. Find the price of the first game.
PLSSSSSSSS HELPPPP NOWWWWWW!!!
Answer:
The price of the first game is $.
We are required to find the price of the first game
The price of the first game is $20
Given:
let
price of the first game = x
price of the second game = x + 50% of x
= x + 0.5x
= 1.5x
Price of the third game = 50% of 1.5x
= 0.5 × 1.5x
= 0.75x
Total cost of game = $65
Total cost of game = price of the first game + price of the second game + Price of the third game
65 = x + 1.5x + 0.75x
65 = 3.25x
divide both sides by 3.25
x = 65 ÷ 3.25
x = 20
Therefore, the price of the first game is $20
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what is the slope of the line? URGENT PLEASE
Answer:
when you have the two points of a line (-4,5) and (0,6) then you use the m = (y2-y1)/(x2-x1) and you get m = 1/4
6.71 x 10^6 divided by 3.6185 x 10^4
Answer:
185.436
Step-by-step explanation:
10^6=1000000
6.71×1000000=6710000
10^4=10000
3.6185×10000=36185
6710000÷36185=185.436
8/3 * (-2 1/2) the product is
Answer:
-28
Step-by-step explanation:
You have to do the parenthesis 1st, then the [tex]\frac{8}{3}[/tex], and multiply the result :D
simplify (3x³)⁴.......
Answer:
(3x)¹²
Step-by-step explanation:
(3x³)⁴ can be simplified into (3x)¹²
The simplified value of the given expression is 3x¹²
What is simplification?Simplification is the process of replacing a mathematical expression by an equivalent one, that is simpler, usually shorter.
Given that, an expression (3x³)⁴
Using the identity = (xᵃ)ᵇ = xᵃᵇ
(3x³)⁴ = (3x)³ˣ⁴ = 3x¹²
Hence, the simplified value of the given expression is 3x¹²
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Suppose there is a 1.2 drop in temperature for every thousand feet that an airplane climbs into the sky. If the temperature on the ground is 57.8, what will be the temperature when the plane reaches an altitude of 7000?
Answer:
ysgsvdbdbdjdnd dndjdnd
Gabe's bill at Colton's was $25. If he decided to leave his server a 20% tip, how muc
money did he spend in all?
Answer:
$31.25
Step-by-step explanation:
If I understood the question correctly, it should be $31.25. 25 x 0.25 (25 percent) = 6.25. 25 + 6.25 = 31.25.
Ten times the smallest of three consecutive integers is 213 more than the sum of the other two integers. Find the integers.
Answer:
27,28 and 29
Step-by-step explanation:
10*a = a+1+a+2+213
10a - 2a = 216
8a = 216
a = 27
27, 28, and 29
write the first four terms of the sequence defined by the given rule f (1) = 3, f(n) = [ f(n - 1)] ^2
Answer:
3, 9, 81, 6561
Step-by-step explanation:
previous term × itself
[tex]\\ \sf\longmapsto f(n)=[f(n-1)]^2[/tex]
f(1)=3[tex]\\ \sf\longmapsto f(2)=(f(1))^2=3^2=9[/tex]
[tex]\\ \sf\longmapsto f(3)=(f(2))^2=(9)^2=81[/tex]
[tex]\\ \sf\longmapsto f(4)=(f(3))^2=(81)^2=6561[/tex]
Find an equation for the graph below
Answer:
y=4/5x-0.8
Step-by-step explanation:
Which values of a, b, and c represent the answer in simplest form?
7/9 * 4/9 = a b/c
Answer:
Option 2: A=1, B=3, C=4
Step-by-step explanation:
7/9÷4/9 = 7/9*9/4cancel 9 on each side=7/4= 1 3/4Can someone help me with letter b along with an explanation.
Step-by-step explanation:
Forced vital capacity: the maximum amount of air you can forcibly exhale from your lungs after fully inhaling. It is about 80 percent of total capacity, or 4.8 liters, because some air remains in your lungs after you exhale
9514 1404 393
Answer:
a) 1.70 L
b) 16 breaths per minute
Step-by-step explanation:
a) The maximum value of v(t) occurs when the sine function is at its maximum value of 1. In that case, the volume is ...
1.27 +0.43×1 = 1.70 . . . liters
__
b) One full breath cycle takes a period of time that makes the argument of the sine function be 2π. The that time period is ...
1.71t = 2π
t = 2π/1.71 ≈ 3.6744 . . . seconds
Then the number of breaths per minute is ...
(60 seconds/minute)/(3.6744 seconds/breath) ≈ 16.33 breaths/minute
The person takes about 16 breaths per minute while sleeping.
Box method sixty three
times thirty nine
Answer:
6237
Step-by step explanation
60 x 30 = 1800
30x3=90
9x60=540
9x3=27
1800+90+540+27=6237
simplify the expression
90 + 4B - 2B - 7B
Simplify the expression
90 + 4B - 2B - 7B
Already in like terms, therefore
90+2B-7B
90-5B
Please Mark BRAINLIEST.
list five rational numbers between -1 and 0
Answer:
-1 ,-1/2 , -3/4 , -1 /4, -5 / 8 , -7 / 8 , -13 / 16, 0.
Step-by-step explanation:
Find the distance between A(-4,4) and B(-2,2). Round your answer to the nearest tenth.
Answer:
6.3
Step-by-step explanation:
1) rule:
[tex]d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2)}[/tex]
2) according to the rule above:
[tex]d=\sqrt{36+4}=2\sqrt{10};[/tex]
d≈6.3
Answer:
6.3
Step-by-step explanation:
Hi hi! I'd appreciate the help, and I'll give Brainliest. I need this now please!
Answer:
Step-by-step explanation:
There are a few different ratios you can use:
2:1 = 12:6 = 24:12
3:1 = 12:4 = 36:12
4:1 = 12:3 = 48:12
5:1 = 15:3 = 60:12
These are just a few i could give
Which graph represents the function f(x)=0.5x+4?
Which graph represents the function f(x)=−2x−1?
Answer:
Step-by-step explanation:
1.)The 4th picture will be the correct one.
Step-by-step explanation:
The first picture shows the graph of f(x) and in the options there are pictures of graph of g(x) = f(x) -1
So, it is clear from the equation of the functions that the graph of f(x) and g(x) will be similar but the the y value in g(x) will be 1 less than the y value in f(x) corresponding to a certain x value.
So, the graph will translate down by 1 unit.
Therefore, the 4th picture will be the correct one.
2.)-(2^x) - 1 will have a y-intercept of -1-1 = -2, a horizontal asymptote of y=-1, and will be decreasing everywhere. The third selection is the graph that has these characteristics.
Answer:
graph 4
Step-by-step explanation: because I love you <3 ;)
The. Problem I in the picture
Answer:
can't see it clearly sorry about that
Question 5 of 10 What is the domain of the function in this table? х y 1 2 2 6 3 10 4 14 O A. (1,2,3,4) B. (1.2).(2.6), (3,10), (4,14) O C. (1.2) O D. (2,6,10,14)
1.35 - 0.829 SHOW YOUR WORK
Answer:
0.521
Step-by-step explanation:
It's just like subtracting
pls I need help, it's due tomorrow!!
Answer:
1)
Angle 1: 59
Angle 2: 88
Angle 3: 147
2)x =21
Step-by-step explanation:
1)
Angle on a straight line add up to 180 degrees and angles in a triangle add to 180 degrees
2)
Opposite angles are equal. (4x) and (2x+42) are opposite therefore equal, so
4x=2x+42
Minus 2x from both sides
2x = 42
Find 1x by dividing 42 by 2, therefore
X=21
