The first four terms of a sequence are shown below:
7,4, 1, -2
Which of the following functions best defines this sequence?
Of(1) = 7, f(n + 1) = f(n) + 3; for nx 1
O f(1) = 7, f(n + 1) = f(n) - 3; for nx 1
O f(1) = 7, f(n + 1) = f(n) – 4; for n 2 1
Of(1) = 7, f(n + 1) = f(n) + 4; for n > 1
Answer:
second option
Step-by-step explanation:
Given the sequence
7, 4, 1, - 2
There is a common difference d between consecutive terms, that is
d = 4 - 7 = 1 - 4 = - 2 - 1 = - 3
Thus to obtain any term in the sequence from the previous term, subtract 3
Thus
f(1) = 7 , f(n + 1) = f(n) - 3 for n ≥ 1
Find the length of the missing side.
Brainliest for whoever gets this right!
Make x the subject of the formula
a(x-b)=a^2+bx
Answer:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
Step-by-step explanation:
So we want to make x the subject of the formula:
[tex]a(x-b)=a^2+bx[/tex]
First, distribute the left side:
[tex]a(x)-a(b)=a^2+bx\\ax-ab=a^2+bx[/tex]
Combine all the terms with x with it on one side. To do this, first subtract bx from both sides. The right side cancels:
[tex](ax-ab)-bx=(a^2+bx)-bx\\ax-ab-bx=a^2[/tex]
Remove the -ab from the left. Add ab to both sides. The left side cancels:
[tex](ax-ab-bx)+ab=a^2+ab\\ax-bx=a^2+ab[/tex]
Now, distribute out the x from the left side:
[tex]ax-bx=a^2+ab\\x(a-b)=a^2+ab[/tex]
Divide both sides by (a-b). The left side cancels:
[tex]\frac{(x(a-b))}{a-b}=\frac{(a^2+ab)}{a-b} \\x=\frac{(a^2+ab)}{a-b}[/tex]
Therefore:
[tex]x=\frac{(a^2+ab)}{a-b}[/tex]
Answer:
Step-by-step explanation:
ax -ab = + bx
collect like terms
ax-bx= +ab
factorise
x(a-b)=a(a+b)
x=[tex]\frac{a(a+b)}{a-b}[/tex] or [tex]\frac{a^{2} + ab}{a -b}[/tex]
f(e+3) + 2(f+1) = 2(f-1)+5 , solve for e
Answer:
Step-by-step explanation:
fe+3f+2f+2=2f-2+5
fe+5f+2=2f+3
fe+2=-3f+3
e=2/-3+3f
Solve for 6x when x=6. I need your guys and girls' help.
Answer:
36
Step-by-step explanation:
if x=6 you are multiplying 6 by 6..
you substitute 6 in for x in the problem (6x) so it becomes 6 x 6
the you multiply and get 36
Answer: 36
Step-by-step explanation: 6x means the same thing as 6 · x.
In this case, we are given that x = 6.
So we have 6 · 6 which is 36.
Pls help answer....
Answer: 18
Step-by-step explanation: 4/3 times 6/5
Is 8/3, flip to 3/8. Use galgo technique: 18
Given the equation 3x+25 =7x-5 which order of operations completely solves for x?
Yesenia sells sports equipment and is a paid a commission of 5.55% her sales. What is the total commission for a week if she sells $8,880 in sports equipment
Answer:
Yesenia's total commission for the week is $492.84
Step-by-step explanation:
Yesenia sells sports equipment and is paid commission
Yesenia's commission=5.55%
Weekly sales=$8,880
Total commission = 5.55% of $8,880
= 5.55/100 × 8,880
=0.0555 × 8,880
=492.84
Total commission=$492.84
Yesenia's total commission for the week is $492.84
What is y = -3x+4 and y=-7x
Answer:
x=-1 , y=7
Step-by-step explanation:
y = -3x+4 and y=-7x
substitute y=-7x in the equation y = -3x+4
-7x=-3x+4 ( put variable(x) together)
-7x+3x=4
-4x=4
x=-4/4
x=-1
find y: y=-7x ⇒ y=-7(-1) ⇒ y=7
check :y = -3x+4
7=-3(-1)+4
7=7 ( correct)
determine whether the fractions 3/6 and 2/4 are equivalent
Answer:
They are equivalent
Step-by-step explanation:
3/6 is equal to 1/2
2/4 is equal to 1/2
Find the distance between the two points (-4, 6) and (3,-7) Your answer
Answer: 14.76 or the square root of 218
Step-by-step explanation:
To find the distance find the change in the x values and y values then square them and add them to find their square root.
-4 -3 = -7
6 - (-7) = 13
7^2 + 13^2 = c^2
49 + 169 = c^2
218 = c ^2
c= 14.76
Which of the following is not an integer? 36 0 -22 0.75
Answer:
[tex]\Huge \boxed{\mathrm{0.75}}[/tex]
Step-by-step explanation:
Integers are whole numbers.
Integers include all negative and positive whole numbers. Zero is also included as an integer.
36 is a positive whole number. 36 is an integer.
0 is a whole number. 0 is an integer.
-22 is a negative whole number. -22 is an integer.
0.75 is not a whole number. 0.75 is not an integer.
Jennifer earns $8.50 per hour for regular work time and $10.50 per hour for overtime. Last week, Jennifer worked 43 hours of regular time and 612 hours of overtime. What amount, in dollars, did Jennifer earn last week? Enter your answer in the box below.
Answer:
$6791.50
Step-by-step explanation:
To answer this question create variables x & y
x = regular work time hours
y = overtime hours
Now make an expression
8.50x + 10.50y
After that substitute 43 for x and 612 for overtime
This means the expression will be 365.5 + 6426
Lastly, add the 2 numbers to find out how much money Jennifer made
6791.50
What is the equation for the axis of symmetry of a parabola?
Hey there! I'm happy to help!
The equation for the axis of symmetry of a parabola is x=a, where a is the x-value of the vertex. It is a vertical line that cuts the parabola in half.
I hope that this helps! Have a wonderful day! :D
A bucket has 16 inches of water in it but there is a hole in the bottom. Use interval notation to write the domain and range of the function H(x) = 16 - 1.25x, where x is the time the water has been leaking for (in minutes) and is the height of the water (in inches). *
Answer: range: {0in, 16in}
domain {0min, 12.8 min}
Step-by-step explanation:
When we have a function:
f(x) = y.
The range is the set of possible values of y and the domain is the set of all the possible values of x.
In this case, our function is:
H(x) = 16 - 1.25*x
which is a linear equation, and we know that the linear equations are defined (for range and domain) in the set of all the real numbers, but this is a physical situation, so we must see at the real problem.
The bucket can not have more water than the initial amount, 16 inches, so this is the maximum in the range.
The minimum height of water that we can find in the bucket is 0 inches (so the bucket is empty) then this is the minimum of the range.
Then we can write the range as:
R: 0in ≤ y ≤ 16in. = {0in, 16in}
Now we can find the extremes of the domain by using the extremes of the range:
y = 16 = 16 - 1.25*x
0 = -1.25*x
then we have x = 0min, this will be the minimum of the domain.
Now using the minimum of the range y = 0 we have:
y = 0 = 16 - 1.25*x
1.25*x = 16
x = 16/1.25 = 12.8 mins
This is the maximum time in the domain (because after this time, there is no water in the bucket)
Then the domain is:
D: 0min ≤ x ≤ 12.8 min
0
The commission rate at Toys R Us
is 4%. If the salesman sold $450
in toys how much did he make in
commission?
Answer:
$18
Step-by-step explanation:
To find a percent of a number, change the percent to a decimal by dividing it by 100, and multiply the decimal by the number.
4% of $450 = 4% * $450 = 0.04 * $450 = $18
How the exponent can be multiplied?
Answer:
D
Step-by-step explanation:
The answer is D, because it is saying for you to do,
2⁶ multiplied 5 times in a row,
2⁶×2⁶×2⁶×2⁶×2⁶ and this is equal to 2³⁰.
Answer:
Option D
Step-by-step explanation:
Whenever we multiply the same numbers with different exponents, we write the same number and add the exponents.
Example: (1/5)^2 x (1/5)^6
=> (1/5)^2 + 6
=> (1/5)^8
Example: 7^3 x 7^8
=> 7^3+8
=>7^11
Whenever we divide the same number with different exponents, we write the same number and subtract the exponents.
Example: 9^3 / 9^4
=> 9^3-4
=> 9^-1
Whenever there is an number with the exponent, and there is an exponent outside the bracket, then we multiply.
Example: (2^6)^-5
=> 2^6 x -5
=> 2^-30
So, the Answer is D.
Solve for 30 points 1 Thanks and 5 stars and maybe brainiest
Answer:
Step-by-step explanation:
Median: 45.5
Least value of second group: 34.7
Greatest value of third group: 63.6
The median is the middle number. This is pretty obvious to see that the middle number is 45.5.
Next, we need to see what the second group is in the first place. Do you see under the number line, those two boxes? Those are the 2nd and 3rd groups. The first box is the 2nd group. You can see that there are two numbers on the 2nd group (right above the box, on the number line). They are 34.7 and 45.5. The least value of these two is 34.7.
Similarly, the 3rd group is the other box. It has 45.5 and 63.6 on it. So the greatest value of these two is 63.6.
Hope that helped,
-sirswagger21
Which of the following best describes the term constructions in geometry?
The options in this question are missing; here is the complete question:
Which of the following best describes the term constructions in geometry?
A. Combining two or more figures together to create a new figure or shape.
B. A way to draw precise figures using a compass and a straightedge.
C. Creating a figure or shape by hand.
D. Places where things are being built that often slow down traffic.
The answer to this question is B. A way to draw precise figures using a compass and a straightedge.
Explanation:
Geometry is a sub-field of mathematics that studies figures, lines, angles, and related features. In this, the term "construction" describes the creation of figures by using a straight edge such as a ruler, a compass (object to draw circles or arcs and measure distances), and a pen, pencil, or similar instrument to draw. For example to draw or construct a circle a compass is mainly used while the construction of a hexagon requires a straight edge and compass. According to these ideas, the correct answer is B.
1. Simplify: 8x ÷ (-1/4)
Answer:
-32x
Step-by-step explanation:
Dividing a fraction is the same as multiplying its reciprocal, so we can rewrite the expression as 8x (-4).
We then solve, getting -32x.
Answer:
-32x
Step-by-step explanation:
Hello!
when you divide by a fraction you multiply the denominator to the dividend
8x * -4 = -32x
The answer is -32x
Hope this helps!
On each bonce, a ball rises to 4/5 of its previous height. To what height will it rise after the third bounce, if dropped from height of 250 cm?
Answer:
128 cm
Step-by-step explanation:
After the first bounce
height = [tex]\frac{4}{5}[/tex] × 250 = 4 × 50 = 200 cm
After the second bounce
height = [tex]\frac{4}{5}[/tex] × 200 = 4 × 40 = 160 cm
After the third bounce
height = [tex]\frac{4}{5}[/tex] × 160 = 4 × 32 = 128 cm
The ball will rise to 128 cm after the third bounce, if dropped from a height of 250 cm.
What is Multiplication?Multiplication is the process of operating a number by adding the number repeatedly to itself up to the times of the other number which is multiplied to the given number.
Mathematically, we can define this as for two numbers p and q, p × q implies that p is added to itself q times or q is added to itself p times.
Initial height = 250 cm
On each bounce, a ball rises to 4/5 of its previous height.
On first bounce,
Height = (4/5) × 250 = 4 × 50 = 200 cm
On second bounce,
Height = (4/5) × 200 = 4 × 40 = 160 cm
On third bounce,
Height = (4/5) × 160 = 4 × 32 = 128 cm
This problem can also be solved using geometric progression with the formula for nth term as (a rⁿ⁻¹) where a is the first term 250, r is the common ratio 4/5 and n is 4, implies the 4th term.
Hence the height ball rise after the third bounce is 128 cm.
Learn more about Geometric Progression here :
https://brainly.com/question/4853032
#SPJ3
Given__________
there is one,
and only one, line perpendicular to the plane through that point.
Answer:
plane containing a line
Step-by-step explanation:
In accordance with a plane postulate corollary, it is concluded that, for a given PLANE CONTAINING A LINE, there is one and only one perpendicular line through a given point on the line.
Hence, in this case, the correct complete statement is written as: Given PLANE CONTAINING A LINE there is one, and only one, a line perpendicular to the plane through that point.
Clyde’s truck travels an average distance of 12 miles per gallon of gas. When full, his truck’s tank holds 40 gallons of gas. If the tank is 8 7 empty, about how many more miles can the truck travel before the tank is completely empty?
The truck can travel 60 miles before the tank is completely empty
How to determine the number of miles?The capacity of the truck is;
Capacity = 40 gallons
When it is 7/8 empty, the amount of gas in the truck is:
Amount = (1 - 7/8) * 40 gallons
Amount = 5 gallons
The rate is given as:
Rate = 12 miles per gallon
So, the number of miles it can travel from this point is:
Miles = Amount * Rate
Miles = 5 * 12
Miles = 60
Hence, the truck can travel 60 miles before the tank is completely empty
Read more about rate at:
https://brainly.com/question/14335655
#SPJ9
can someone help me in kinda dumb
Answer:
[tex]\Huge \boxed{\mathrm{d}}[/tex]
Step-by-step explanation:
y is equal to $1.67 per pounds of peanuts
pounds of peanuts = x
y is equal to $1.67 per x
per is for each
y = $1.67 × x
The equation that correctly describes this relation is option d.
A skydiver weighing 160 lb (including equipment) falls vertically downward from an altitude of 20,000 ft and opens the parachute after 18 s of free fall. Assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.7|v| when the parachute is closed and is of magnitude 14|v| when the parachute is open, where the velocity vis measured in ft/s. Assume that acceleration due to gravity has magnitude 32 ft/s; remember that weight is the product of mass and gravitational acceleration.
Required:
a. Find the speed of the skydiver when the parachute opens.
b. Find the distance fallen before the parachute opens.
c. What is the limiting velocity vL after the parachute opens?
d. Determine how long the sky diver is in the air after the parachute opens.
e. Plot the graph of velocity versus time from the beginning of the fall until the sky diver reaches the ground.
If 5 becomes 11 and 12 becomes 25, what does 15 become?
Answer:
31
Step-by-step explanation:
5---11
12---25
hmmm
isn't that jsut x * 2 + 1?
soooo
15 would be
15*2+1
which is 31
Answer:
31.
Step-by-step explanation:
5+5 = 10 + 1 = 11
12 + 12 = 24 +1 = 25
15 + 15 = 30 + 1 = 31
I don't know I tried to see if that was the pattern. It checks out math wise.
Amber would like to go on the field trip this Saturday. However, she was scheduled to work 10 hours and she makes $8.50 an hour. Additionally, the field trip activity fee was $30. What is her opportunity cost to go on the field trip?
Answer:
The opportunity cost is $85.
Step-by-step explanation:
The scheduled for work = 10 hours.
Money that Amber makes by earning = $8.50 per hour.
Total money earned by Amber = 10 ×8.50 = $85
The fee of the filed trip = $30
Now we have to find the filed trip’s opportunity cost. Since we know that the opportunity cost is the amount that is left in order to get the best alternative. Therefore, if Amber goes on a field trip then he has to forgive the earning. So, the total earning $85 is the opportunity cost.
A business man bought a car at rs 550000 and sold it rs 533500 find his loss percentage
Answer:
Cost price (c.p) = Rs. 550000
selling price (s.p) = Rs. 533500
Loss (l) = c.p - s.p
= Rs. 550000 - Rs. 533500
= Rs. 16500
Now,
Loss percentage = Actual loss * 100%
c.p
= Rs. 16500 * 100%
Rs. 550000
= 3%
Answer:
loss%=3.09%
Step-by-step explanation:
given,s.p=550000
c.p=533500
Now,loss percent= Actual loss /c.p×100%
=16500/53500×100%
=3.09%
what is 40 x 90 in multiplacation
Answer:
3600
Step-by-step explanation:
We multiple 40 x 90 which is equal to 4 x 10 x 9 x 10.
4 x 9 = 36 and 10 x 10 = 100, so 40 x 90 = 36 x 100 = 3600.
Answer:
The answer is 3,600
Step-by-step explanation:
40x90=3,600
Look at picture for step by step!
Hope this helps!
By: BrainlyAnime
Brainliest would be appreciated!
A turtle moves an an average speed of 12 inches/hour. How long does it take the turtle to travel 8 inches?
Answer:
40 minutes
Step-by-step explanation:
We can solve this problem through finding the proportion...
Let the time taken to travel 8 inches at the speed be x
Hence, 12:60 :: 8:x
We must multiply the extremes and the nears..
Hence,
12x=60×8
x=60×8/12
x=40 minutes