Answer:
Two functions f(x) and g(x) are inverses if and only if:
f( g(x) ) = x
and
g( f(x) ) = x
In this case, we have:
f(x) = 1*x - 6
g(x) = 6*x + 1
Let's check if the functions are inverses.
f( g(x) ) = 1*g(x) - 6 = 1*(6x + 1) - 6 = 6x + 1 - 6 = 6x - 5
and
g( f(x) ) = 6*f(x) + 1 = 6*(1x - 6) + 1 = 6x - 36 + 1 = 6x - 35
So we can see that:
f( g(x) ) ≠ x
g( f(x) ) ≠ x
Thus, f(x) and g(x) are not inverses.
Particularly, the two compositions are:
f( g(x) ) = 6x - 5
g( f(x) ) = 6x - 35
Both of these are linear functions, thus the domain in both cases is the set of all real numbers, that can be written as:
domain = (-∞, ∞)
what is the answer to this? help, please
This is because angles 1 and 4 are vertical angles. Such angles form whenever we have an X shape like this. Vertical angles are always opposite one another and they are always the same measure. The fact that lines k and l are parallel has no relevance (so they could easily be not parallel and the two angles mentioned are still congruent).
Titus works at a hotel. Part of his job is to keep the complimentary pitcher of water at least half full and always with ice. When he starts his shift, the water level shows 8 gallons, or 128 cups of water. As the shift progresses, he records the level of the water every 10 minutes. After 2 hours, he uses a regression calculator to compute an equation for the decrease in water. His equation is W –0.414t + 129.549, where t is the number of minutes and W is the level of water. According to the equation, after about how many minutes would the water level be less than or equal to 64 cups?
Answer:
Step-by-step explanation:
If we are looking for how long it will take the level to be less than or equal to 64 cups, we are solving an inequality as opposed to an equation. It would look like this:
-.414t + 129.549 ≤ 64 We subtract 129.549 from both sides to get
-.414t ≤ -65.549 and then divide by -.414. But because we are dividing by a negative number we need to change the way the inequality is pointing:
t ≥ 158.3 minutes which is about 2.6 hours
Answer:
t ≥ 158.33, or rounded, t ≥ 160.
Explanation:
The equation we're given is
W = -0.414t + 129.549, which an be written as
-0.414t + 129.549 = W.
We are asked to find the amount of time it would take for the water level to be less than or equal to 64 cups. Plugging this information in, we have:
-0.414t + 129.549 ≤ 64
To solve this, we first cancel 129.549 by subtracting from both sides:
-0.414t + 129.549 - 129.549 ≤ 64 - 129.549
-0.414t ≤ -65.549
Now divide both sides by -0.414:
-0.414t/-0.414 ≤ -65.549/-0.414
t ≥ 158.33
(When we multiply or divide both sides of an inequality by a negative number, we must flip the inequality symbol)
pls help and pls provide workings
(x-h)²+(y-k)²=r²
(3-h)²+(3-0)²=5²
h²-6h+9+9=25
h²-6h-7=0 —> (h-7)(h+1)=0
h=7 , h=-1
h=7 —> (x-h)²+y²=r² —> (x-7)²+y²=25 —>
x²-14x+49+y²=25 —> x²+y²-14x+24=0
h=–1 —> (x-h)²+y²=r² —> (x+1)²+y²=25 —>
x²+2x+1+y²=25 —> x²+y²+2x–24=0
I hope it helped you ^_^
which set of ordered pairs represent a function
Answer:
A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can't have two ordered pairs with the same x -value but different y -values.
Step-by-step explanation:
Find the 57th term of the following arithmetic sequence. 13, 20, 27, 34
Answer:
[tex]{ \tt{n _{th} = a + (n - 1)d}} \\ { \tt{n _{57} = 13 + (57 - 1) \times 7}} \\ { \tt{n _{57} = 405}}[/tex]
a plane traveled 510 miles in 1.5 hours. What was the average rate of speed of plane?
Answer:
340 miles per hour
Step-by-step explanation:
To find the speed, take the distance and divide by the time
510 miles / 1.5 hours
340 miles per hour
Answer:
340 miles
Step-by-step explanation:
Speed= Distance/ Time=
510/ 1.5= 340 miles
Determine which quadratic equations have
2 real solutions. Select two that apply.
Answer:
A & D
First and last
Step-by-step explanation:
Let 0 be an acute angle of a right triangle. Evaluate the other five trigonometric functions of 0.
Answer:
sin θ = (√119)/12
tan θ = (√119)/5
csc θ = 12/(√119)
cot θ = 5/(√119)
Five trigonometric functions of θ are
sinθ = [tex]\frac{\sqrt{119} }{12}[/tex]cosθ = [tex]\frac{5}{12}[/tex]tanθ = [tex]\frac{\sqrt{119} }{5}[/tex]cosecθ = [tex]\frac{12}{\sqrt{119} }[/tex]secθ = [tex]\frac{12}{5}[/tex]cotθ = [tex]\frac{5}{\sqrt{119} }[/tex]
What is trigonometric functions?"The trigonometric functions of θ are functions of an angle. sine, cosine, and tangent are familiar trigonometric functions. The trigonometric functions relates the angles of a triangle to the length of its side."
Let θ be an acute angle of a right angle triangle
What is acute angle?"An acute angle ("acute" meaning "small") is an angle smaller than a right angle. The range of an acute angle is between 0 and 90 degrees."
What is right angled triangle?"A right angled triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle).
What is hypotenuse?"The side opposite the right angle is called the 'hypotenuse'. The hypotenuse is always the longest side. The sum of the other two interior angles is equal to 90°."
What is opposite side?"An 'opposite' side is the one across from a given angle."
What is adjacent side?"An 'adjacent' side is next to a given angle. We use special words to describe the sides of right triangles."
we have,
cosθ = [tex]\frac{5}{12}[/tex]
secθ = [tex]\frac{12}{5}[/tex]
Hypotenuse side = 12
Adjacent side = 5
∴ Opposite side = [tex]\sqrt{hyp^{2}-adj^{2} }[/tex]= [tex]\sqrt{12^{2}-5^{2} }[/tex] = [tex]\sqrt{119}[/tex]
sinθ = [tex]\frac{opp}{hyp}[/tex] = [tex]\frac{\sqrt{119} }{12}[/tex]
tanθ = [tex]\frac{opp}{adj}[/tex] = [tex]\frac{\sqrt{119} }{5}[/tex]
cosecθ = [tex]\frac{hyp}{opp}[/tex] = [tex]\frac{12}{\sqrt{119} }[/tex]
cotθ = [tex]\frac{adj}{opp}[/tex] = [tex]\frac{5}{\sqrt{119} }[/tex]
Learn more about trigonometric functions, acute angle and right angle triangle here
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6a²+11x-10= answer.
6a²+11x-10= (3a+5)(3a-2)
Answer:
Solution given:
6a²+11x-10
doing middle term factorisation
6a²+(15-4)x-10
6a²+15x-4x-10
3a(3a+5)-2(3a+5)
(3a+5)(3a-2)
Step-by-step explanation:
if
6a²+11x-10=0
(3a+5)(3a-2)=0
either
a=-5/3
it
a=⅔
i need help plz!!!!!!!!!!!!
Answer:
54 and 36
Step-by-step explanation:
84
45% of 120 students chose the amusement park , then
45% of 120 = 0.45 × 120 = 54
54 students chose the amusement park
85
45% of 180 = 0.45 × 180 = 81
25% of 180 = 0.25 × 180 = 45
81 - 45 = 36
36 more students chose the amusement park than the water park
Answer:
54, 36
Step-by-step explanation:
84
45% of 120 students chose the amusement park
45% of 120 = 0.45×120=54
54 students chose the amusement park
85
45% of 180 = 0.45 × 180 = 81
25% of 180 = 0.25 × 180 = 45
81 - 45 = 36
36 students chose the amusement park than the water park
if the price of an article is without tax is ₹ 800, and the price with tax is ₹ 860 the sales tax rate is_____________
9514 1404 393
Answer:
7.5%
Step-by-step explanation:
The tax as a proportion of the selling price is ...
₹(860 -800)/₹800 = 60/800 = 0.075 = 7.5%
plzzz helpppp333332222222222
Answer: The answer is C or 13 units
How?: by a method called rise over run
the rise is at the y axis and the run is at x axis
*COUNT VERY CAREFULLY*
if you count right you should get 6 as a rise and 7 for run
6+7= 13
Answer:
B. 10 units
Step-by-step explanation:
Use the pythagorean theorem. (a^2 + b^2 = c^2)
Pretend that PQ is the hypotenuse of a right triangle.
Count the number of units for the supposed legs of the triangle.
The height would be 6 while the base is 8.
6^2 + 8^2 = PQ^2
36 + 64 = PQ^2
100 = PQ^2
PQ = 10
So, the answer is B.
Solve for x. 4/3 = 24/x
Help me please!!
The iPod costs $200.00. If Alex did his jobs every week, then how long would it take him to earn $200.00??
Plz help I’m confused
Answer:
It would take him 5.9 weeks (rounded). basically almost 6 weeks
Step-by-step explanation:
he makes 6 dollars a week by walking the dog out. he earns 2$ every time he walks the dog out, and he does it 3 times, so 2 x 3 = 6
he makes another 10 dollars a week by babysitting. he earns 2.50$ per hour of babysitting, and he does it for 4 hours per week, so 2.50 x 4 = 10
he makes another 18$ dollars a week by mowing the lawn. he does this once a week. he gets 15$ dollars if he mows, and another 3$ if he pulls weeds. if he does both, he would get 15+3 = 18$ per week by mowing
so add the numbers 6, 10, and 18, and you get 34.
he makes 34 dollars a week
divide the number he wants to make by what he earns in a week to figure out how many weeks it would take.
he wants to get 200$, so the equation is
200 / 34 = 5.88
Its 5.9 rounded or 5.88 weeks exact.
Answer:
6 weeks
Step-by-step explanation:
Job 1:
2 x 3 = 6
$6 per week
Job 2:
2.50 x 4 = 10
$10 per week
Job 3:
15 + 3 = 18
$18 per week
6 + 10 + 18 = 34
$34 per week
200/34 = 5.88
Please help me I have been stuck on this question forever
19 Step-by-step explanation:
Answer:
3.45 sqft
Step-by-step explanation:
Calculate all the areas individually, the 3 lateral sides are the same and using the formula for area we have 1/2 base times height. The height is 2 ft and the base is 1 ft so the area of one of the lateral sides is 1 ft.
There are three lateral sides so you multiply 1 by 3 to get 3.
The base is done the same way. It's base is 1 ft and it's height is 0.9ft so the area is 0.45.
3 + 0.45 = 3.45
The surface area is 3.45 sqft.
I could be wrong but the formula and process is the same, calculate the sides individually using the base height formula for area.
зх:
90
Х
2х:
What is the value of x?
Answer:
60
Step-by-step explanation:
To get the value of x;
3x:90
(90/3) = 30
x = 30
To get the value of 2x;
(2×X);
2 × 30
=60
What is the class width for the class (65-72)kg?
Answer: Super Lightweight to Middleweight
Step-by-step explanation: I'm assuming you're talking about boxing weight class. If not, please let me know.
1045.521984 to the nearest pound
Answer:
Step-by-step explanation:
1046 pound
Answer:
1,046
Step-by-step explanation:
because 5 rounds up we raise it to the next whole number
Which are the solutions of x2 = -7x – 8?
Ž
17 7
4
+
17
4
-
글
그를
+
ZIA
+
V 17
4
4
7 - 17 7 + /17
-
-7 - V 17 -7 + v17 .
2
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
SOMEONE PLEASE HELP ME ASAP !!!
Mrs. Pregnals's biology classes are going on a field trip. She has them break into groups of three or four students in order to do labs. She has a total of 120 students and 32 total groups are formed.
If t represents the number of three person groups and frepresents the number of four person groups, then write a system of equations that models this situation.
How many four person groups are there? Only an algebraic solution will receive full credit.
PLEASE HELP !!!!
x + y = 32 (1)
3x + 4y = 120 (2)
x = 8; y = 24
Step-by-step explanation:
Total students = 120
Number of groups = 32
If the number of three person groups = x
Number of four person groups = y
write a system of equations that models this situation
x + y = 32 (1)
3x + 4y = 120 (2)
From (1)
x = 32 - y
Substitute x = 32 - y into (2)
3(32 - y) + 4y = 120
96 - 3y + 4y = 120
- 3y + 4y = 120 - 96
y = 24
Substitute y = 24 into (1)
x + y = 32
x + 24 = 32
x = 32 - 24
x = 8
x = 8; y = 24
Help please
Find the volume of this cone.
Use 3 for T.
V
Tr²h
3
V =
V ~ [?]cm3
112cm
8cm
Answer:
192
Step-by-step explanation:
3(pi) x 4^2 x 12 ÷ 3 = 192
Find the center and radius of the circle with the equation x^2 + y^2 = 9. Then graph the circle.
Answer:
center = origin (0,0)
radius = 3
to graph it, draw a circle that goes through the points (3,0), (0,3), (-3,0), (0,-3)
Step-by-step explanation:
The perimeter of a rectangle is 25 2/5 ft. The length is
width. Find the length and width of the rectangle.
A. = 9.375 ft and w = 3.125 ft
B. = 9.525 ft and w = 3.175 ft
C. = 19.05 ft and w = 6.35 ft
D. = 7.85 ft and w = 4.85 ft
Answer:
Width = 4.85 feet
Length = 7.85 feet
Step-by-step explanation:
Given:
Perimeter of a rectangle = 25 2/5 ft = 25.4 feet
Length = 3 + Width
Computation:
Assume;
Width = a
So,
Length = 3 + a
Perimeter of a rectangle = 2(l + b)
25.4 = 2[(3 + a) + a]
25.4 = 2[3 + 2a]
25.4 = 6 + 4a
4a = 19.4
a = 4.85
Width = 4.85 feet
Length = 3 + 4.85
Length = 7.85 feet
help me plsss thankyouuuu
Answer:
a) 231
b) 52.8
Step-by-step explanation:
210*.10 = 21. 21+210 = 231
48*.10=4.8 4.8+48 =52.8
Answer:
a) 231
b) 52.8
Step-by-step explanation:
a)210x.1=21
210+21=231
b)48x.1=4.8
48+4.8= 52.8
please help me with this fast please
Answer:
the last one
Step-by-step explanation:
answer is needed however explanation is needed more..
no. of even factora of 120 which are greater than 20 and less than 120 are = 6
Maxine is taking 5 gallons of drinking water on a camping trip. How many quarts of drinking water is Maxine taking on the camping trip?
Answer:
20 quarts
Step-by-step explanation:
There are 4 quarts in a gallon
5 gallons * 4 quarts / 1 gallon = 20 quarts
Answer:
20 US quarts
Step-by-step explanation:
there are 4 quarts in a gallon so you have to multiply 5 x 4 to get the total amount of quarts in a gallon.
Hope it helps c:
find the equation of the lines: with a y-intercept of 4 and passes through the point (-1,3)
Answer:
equation is 4x-4y= -16
Step-by-step explanation:
b = 4
x = -1
y = 3
so
x/a + y/b = 1
or, -1/a + 3/4 = 1
or, (-4 + 3a) = 4a
or, -4 = 4a - 3a
so, a = -4
now
x/a + y/b = 1
or, x/-4 + y/4 = 1
or, 4x-4y = -16
so
equation : 4x-4y = -16
Answer:
Answer is y=x+4
Step-by-step explanation:
Find the value of x in the isosceles triangle shown below.
2
2
5
8
Answer:
[tex]\sqrt{41}[/tex]
Step-by-step explanation:
think of this triangle being made up of 2 triangles with the lengths of 5, 4, and x.
x being the hypotenuse, 5 being one of the legs, and 4 being one of the legs. (8/2).
pythagorean theorem:
a^2 + b^2 = c^2
5^2 + 4^2 = x^2
25 + 16 = x^2
41 = x^2
x = sqrt 41
Can you answer this math homework? Please!
Answers:
airspeed = 42 mphwind speed = 12 mph============================================================
Explanation:
Let's solve the first equation for y
[tex]18 = (x+y)\frac{1}{3}\\\\18*3 = x+y\\\\54 = x+y\\\\x+y = 54\\\\y = 54-x\\\\[/tex]
Then we'll plug this into the second equation and solve for x
[tex]18 = (x-y)*\frac{3}{5}\\\\18 = (x-(y))*\frac{3}{5}\\\\18 = (x-(54-x))*\frac{3}{5}\\\\18 = (x-54+x)*\frac{3}{5}\\\\18 = (2x-54)*\frac{3}{5}\\\\18*5 = 3(2x-54)\\\\90 = 6x-162\\\\6x-162 = 90\\\\6x = 90+162\\\\6x = 252\\\\x = 252/6\\\\x = 42\\\\[/tex]
This is the average airspeed of the plane, in miles per hour (mph). It's the speed without accounting for the wind. If there's no wind at all, then this would be the ground speed of the plane.
Use this value of x to find y
y = 54-x
y = 54-42
y = 12
The average speed of the wind is 12 mph.
