Answer:
The answer is 0, 5.25
Step-by-step explanation:
Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse functions
Answer:
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Step-by-step explanation:
Given
[tex]a(d) = 5d - 3[/tex]
Solving (a): Write as inverse function
[tex]a(d) = 5d - 3[/tex]
Represent a(d) as y
[tex]y = 5d - 3[/tex]
Swap positions of d and y
[tex]d = 5y - 3[/tex]
Make y the subject
[tex]5y = d + 3[/tex]
[tex]y = \frac{d}{5} + \frac{3}{5}[/tex]
Replace y with a'(d)
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
Prove that a(d) and a'(d) are inverse functions
[tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex] and [tex]a(d) = 5d - 3[/tex]
To do this, we prove that:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
Solving for [tex]a(a'(d))[/tex]
[tex]a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})[/tex]
Substitute [tex]\frac{d}{5} + \frac{3}{5}[/tex] for d in [tex]a(d) = 5d - 3[/tex]
[tex]a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3[/tex]
[tex]a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3[/tex]
[tex]a(a'(d)) = d + 3 - 3[/tex]
[tex]a(a'(d)) = d[/tex]
Solving for: [tex]a'(a(d))[/tex]
[tex]a'(a(d)) = a'(5d - 3)[/tex]
Substitute 5d - 3 for d in [tex]a'(d) = \frac{d}{5} + \frac{3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}[/tex]
Add fractions
[tex]a'(a(d)) = \frac{5d - 3+3}{5}[/tex]
[tex]a'(a(d)) = \frac{5d}{5}[/tex]
[tex]a'(a(d)) = d[/tex]
Hence:
[tex]a(a'(d)) = a'(a(d)) = d[/tex]
A student has started a lawn care business. He charges $15 per hour to mow lawns and $20 per hour for gardening. Because he is still in school, he is only allowed to work for at most 20 hours per week. His goal is to make at least $300 per week. 1. Create a system of equations or inequalities that models the situation. Define the variables you use.
Answer:
15x=300, x=20
20x=300, x=15
Step-by-step explanation:
Answer:
:)
Step-by-step explanation:
15x=300
x will equal 20
20x=300
x will equal 15
Please hurry no clown answers and please do the whole thing
You are a member of your local movie theater’s club. Every time you see a movie at the theater, you earn 2 advantage points. When you earn 100 points, you get a free movie pass. Currently, you have 40 advantage points.
Write an equation to model the number of movies m you have to watch before you earn a free movie pass.
Solve the equation. Show your work.
100=40+2m
100-40=60
2m=60
60 divided by 2=30
30 movies
Answer:
2m+40=100, 30 movies
Step-by-step explanation:
1 movie = 2 points
1 pass= 100 points
curently have 40 points so
100points = 40points +2points *m
solve for m:
2m+40 =100 subtract 40 from both sides
2m = 100-40
2m=60 divide both sides by 2
m=60/2
m=30
What's 7 times 2 plus 5 to the 3rd power
Answer:
139
Step-by-step explanation:
7x2+5^3 = 139
2.332 divided by 2.2
Answer:
1.06
Step-by-step explanation:
2.332 divided by 2.2
= 1.06
Hope this helped!
Answer:
1.06
Step-by-step explanation:
What is 1+2+3+4+5+6+7+8+9+10=?
have a great day!! :)
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
Answer:
55
Step-by-step explanation:
9 + 1 = 10
8 + 2 = 10
7 + 3 = 10
6 + 4 = 10
5 + 10 = 15
10 + 10 + 10 + 10 + 15 = 55
2(4 + 7) − 8 ÷ 2 whats the answer
Answer:
your answer is 18 look below for an explanation!
Step-by-step explanation:
please just trust me i know for a fact its right plz leave a thx and may i please have brainliest?
because 2(4+7)= 8+14= 22. 8/2= 4. 22-4=18.
help me real quickhahahahaha
Answer:
19
Step-by-step explanation:
2d= 2 x 8= 16
16+3= 19
Answer:
Step-by-step explanation:
2d + 3 (d=8)
(2*8) + 3 =
16 + 3 =
19
How many solutions does 5 - 2x = 4 - 2x + 4 + x have?
A. Infinitely many solutions
B. Two solutions
C. One solution
D. No solutions
Answer:
One solution, being x = -3
Step-by-step explanation:
For brainliest :)
Oml i need more characters
There :)
Answer:
Imfaooooooo
Step-by-step explanation:
Hope this helps or brightens your day! Please consider marking brainliest! Always remember, your smart and you got this! -Alycia :)
Answer:
characters for what?
anyways....I need brainiest! :P
If you flip a coin 6 times, what is the best prediction possible for the number of times it will
land on heads?
Answer:
3
Step-by-step explanation:
50/50
Answer:
3 times or a 50% chance
Step-by-step explanation:
we have two options so that means half of the options will be heads and half of the options will be tails.
i hope this helps :)
The least common denominator of[tex]\frac{1}{6} and \frac{5}{12}[/tex] is 12.
TrueFalse
Which values could be the values of x and y?
Answer:
1 3/4, 9 1/4
Step-by-step explanation:
continue the pattern
if the transformation was a rotation, tiffany..... be certain the trapezoids are congruent
A. can
B. cannot
The sum of two numbers is 8 and the diffrence is 6 what are the two numbers?
f(x) = -4x^2 + 5x
Find f(6)
Answer:
-114
Step-by-step explanation:
f(6) it means f(x=6) so substituting x=6 in your equation gives us
f(6)= -4*(6)²+5*(6)
= -4*36+30
= -144+30
= -114
Substitute 7 for xand evaluate the expression below.
9x-2x
Answer here
Answer:
The answer to this equation is 49
Step-by-step explanation:
9x-2x
9×7=63
2×7=14
63-14=49
Janka si vložila 3200 eur na termínovaný účet s 1,2 úrokovou mierov koľko bude mať po 1 roku
Answer:
the present value is 3,162 euros
Step-by-step explanation:
The computation of the present value is shown below:
As we know that
Future value = Present value × (1 + rate of interest)^number of years
3,200 euros = Present value × (1 + 0.012)^1
3,200 euros = Present value × 1.012^1
Present value is
= 3,200 euros ÷ 1.012
= 3,162 euros
Hence, the present value is 3,162 euros
I got 24 miles for each kind of gas in my car which one of the following is a equivalent radio of miles to gallons.
A. 48 to 2
B. 2 to 48
C. 1 to 24
D. 3 to 240
I believe that the answer is B
On a coordinate plane, a vector has an origin (0, 0) and terminal point (8, 7).
Which description of the vector shown is correct?
The magnitude is 15, and the direction angle is approximately 49°.
The magnitude is 15, and the direction angle is approximately 41°.
The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 49°.
The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.
Answer:
D. The magnitude is StartRoot 113 EndRoot, and the direction angle is approximately 41°.
Step-by-step explanation:
The correct description of the vector is that the magnitude is √(113) and therefore the direction angle is 41°.
What is the magnitude of the vector?The magnitude of the vector is the length of the vector which can be calculated from the coordinate of its endpoint.
Let (x1,y1) and (x2,y2) are the coordinate of the two endpoints of a vector V.
The magnitude of the vector= |V|= √(y2-y1)²+(x2-x1)²
We have,
Origin of vector = (0,0)
And,
Terminal point = (8, 7)
Here,
a = 8 and b = 7
Now,
To find the magnitude of the vector, we are going to use;
Formula, |v| = √(a² + b² )
|v| = √(8² + 7² )
|v| = √(64 + 49)
|v| = √113
So, the magnitude of the vector is √113.
Now,
Direction angle is find out using ;
Θ = tan ⁻¹ (b / a)
So, Here,
Θ = Angle Direction
Now,
Θ = tan ⁻¹ (7 / 8)
Θ = 41°
Therefore, the proper description of the vector is that the magnitude is √(113) and also the direction angle is 41°.
Learn more about the magnitude of the vector here:
https://brainly.com/question/27708309
#SPJ2
Please help! I’ll give brainliest to whoever gets it right!
Answer:
3.62
Step-by-step explanation:
I am big brain and very smort
Answer:
362/ 100 or 3 62/100
Step-by-step explanation:
A vector in standard position has its terminal point at (7, –4). What is the magnitude of the vector?
Answer:
Square root of 65
Step-by-step explanation:
Edge
The magnitude of the vector will be 8.0622 units.
What exactly is a vector?A vector is a quantity with a magnitude, and direction that follows the law of vector addition.
Given data;
u = (7, –4)
The magnitude of the vector is, R found as;
[tex]\rm R = \sqrt{7^2+(-4^2)} \\\\ R = \sqrt {65} \\\\ R = 8.0622 \ units[/tex]
Hence the magnitude of the vector will be 8.0622 units.
To learn more about vectors, refer;
https://brainly.com/question/13322477
#SPJ2
2. Solve (x – 4)(x + 7). (2 points) O x = 4, X= 7 X = =4, x = -7 x = 4, X = -7 X = -4, X = 7
Answer:
X = 4, x = -7
Step-by-step explanation:
You can set each equation in the parenthesis Equal to 0.
x - 4 = 0 and x + 7 = 0
start with x - 4 =0
add 4 to both sides
x = 4.
then do x +7 =0. subtract 7 from both sides.
x = -7
so x =4, and x = -7
1. In a class there are 2 boys to every 3 girls. How many girls would be in the class if there are 12 boys? (set up a proportion and solve, think about what two things you have and put them one over the other)
2. A boat traveled 27 miles in 2 hours. At this rate how many miles would the boat travel in 0.5 hour? (set up a proportion and solve)
3. Joe uses 6 grams of coffee beans to make 24 ounces of coffee. How many grams of coffee beans would be used for 288 ounces of coffee? (this problem has ounces but it also gives you three numbers already)
4. A recipe says to use 3 cups of flour for 48 cookies. How many cups of flour would be used to make 72 cookies?
5. A man walks 4 miles in 1.5 hours. How many hours would it take the man to walk 10 miles?
6. It costs $22.50 for 5 pounds of salmon. How much would it cost for 8 pounds of salmon?
Answer:
1. 12 boys,
5. 15 hours
6. 36
Im not so sure on the others, Gl!
A store had a sale where you could get 5 bags of cashews for $4. If you
wanted to buy 50 bags, how much would it cost?
Answer:
$40
Step-by-step explanation:
50/5=10, 10•4=40
what is 3 tenths plus 8 tenths?
Answer:
1.1
Step-by-step explanation:
Dont answer this PLEAS
Answer:
why? also the answer is 1.6y+y-4/15y+7/6y=21/3
We move all terms to the left:
1.6y+y-4/15y+7/6y-(21/3)=0
Domain of the equation: 15y!=0
y!=0/15
y!=0
y∈R
Domain of the equation: 6y!=0
y!=0/6
y!=0
y∈R
We add all the numbers together, and all the variables
1.6y+y-4/15y+7/6y-7=0
We add all the numbers together, and all the variables
2.6y-4/15y+7/6y-7=0
We calculate fractions
2.6y+(-24y)/90y^2+105y/90y^2-7=0
We multiply all the terms by the denominator
(2.6y)*90y^2+(-24y)+105y-7*90y^2=0
We add all the numbers together, and all the variables
(+2.6y)*90y^2+(-24y)+105y-7*90y^2=0
We add all the numbers together, and all the variables
105y+(+2.6y)*90y^2+(-24y)-7*90y^2=0
Wy multiply elements
-630y^2+105y+(+2.6y)*90y^2+(-24y)=0
We get rid of parentheses
-630y^2+105y+(+2.6y)*90y^2-24y=0
We add all the numbers together, and all the variables
-630y^2+81y+(+2.6y)*90y^2=0
Step-by-step explanation:
Two triangular tiles each have two sides measuring four inches. Which is a true statement?
A) Their corresponding angles are congruent.
B) The triangles are congruent.
C) The triangles may be congruent.
D) The triangles cannot be congruent.
Answer:
C; The triangles may be congruent
Step-by-step explanation:
Here, we have two sides of the each of the triangles equal already
By congruency, we might have SSS or SAS
if SSS, this mean that all the sides are equal
Since we do not know the measure of the third side, we cannot say that they are not congruent or they are congruent
Also, we do not know the measure of the angles of the triangles
If we have an angle that is equal in the two triangles, then we can have congruency through SAS
But since we do not know how these measures, we use the word ‘may’
-5+12+6x=7x-10+53+3x
Answer:
x=-9
Step-by-step explanation:
Jorge's family arrived home at 8:00 at night after traveling in the car for 5 hours and 15 minutes. What time did Jorge's family leave?
Answer:
2:45 P.M
Step-by-step explanation:
Answer:
3:45
Step-by-step explanation:
8:00-5 hours and 15 min=3:45