4.
3. On the first day of summer, Jackson landed in Japan
with $7440 in his account. He plans to spend an
average of $120 each day on his tour of Asia.
a) Write recursive and explicit functions m(t) to represent
the amount money left at t days.
Recursive:
Explicit:
R
Answer:
recursive: a[1] = 7440; a[n+1] = a[n] -120explicit: a[n] = 7440 -120(n -1)Step-by-step explanation:
The sequence of amounts in Jackson's account will be ...
7440, 7320, 7200, ...
with a first value (a1) of 7440 and a common difference (d) of -120.
The recursive formula for an arithmetic sequence is ...
a[1] = a1
a[n+1] = a[n] +d
For our sequence, the recursive formula is ...
a[1] = 7440
a[n+1] = a[n] -120
__
The explicit formula for an arithmetic sequence is ...
an = a1 +d(n -1)
For our sequence, the explicit formula is ...
a[n] = 7440 -120(n -1)
Which graph has a rate of change of zero?
Answer:
The line on the graph would be a flat line
Step-by-step explanation:
The line would not move up or down at all.
Answer:
A graph having a constant rate of change equal to zero means that the value of y is constant. A graph with slope zero is a horizontal line.
A snack mix recipe uses a ratio of 3/4 pound of dried apples to 1/2 pound of dried pears. What amount of dried apples would be needed per pound of dried pears?
Answer:
[tex]\frac{3}{8}[/tex]
Step-by-step explanation:
According to the question, data provided in the question is as follows
Given ratio
[tex]\frac{3}{4}[/tex] a pound of direct apples
[tex]\frac{1}{2}[/tex] a pound of dried pears
We can right
[tex]\frac{3}{4} : \frac{1}{2}[/tex]
Now we multiplied it to determine the amount of dried apples that required per pound of dried pears
[tex]\frac{3}{4} \times \frac{1}{2}[/tex]
[tex]\frac{3}{8}[/tex]
Hence the above is the answer and the same is to be considered by taking the pound of direct applies to pound of direct pears so that the correct amount could arrive
The amount of dried apple needed per pound of dried pear is 3/8
The question tells us that
3/4 pound of dried apples : 1/2 pound of dried pears
We are asked to find the amount of dried apples needed per pound of dried pears. To do this, we multiply both ratio together to get it in 1. This means that
3/4 * 1/2 = 3/8.
This then mean that for every pound of dried pear, 3/8 pound of dried apple was mixed.
see more here https://brainly.com/question/13419413
(-5.12)-(-4.7)+(7.021
Answer:
6.601
Step-by-step explanation:
We can remove the brackets, getting -5.12 + 4.7 + 7.021.
Then we can evaluate:
-5.12 + 4.7 + 7.021 = 6.601
Answer:
6.601
Step-by-step explanation:
(-5.12)-(-4.7)+(7.021) = -5.12 + 4.7+7.021 = 6.601
One airplane is located 200 km north and 50 km east of an airport. A second plane at the same altitude is located 30 km north and 100 km north and 100 km west.
The distance between the planes is closest to:
A. 150 km
B. 200 km
C. 300 km
D. 350 km
E. 400 km
Answer:
B. 200 km
Step-by-step explanation:
You can use the Pythagorean theorem for this question. First, you must find a and b. You can do this by finding the distance between North and South, and East and West. For this specific equation, you'd use 200 North - 30 North to get 170 miles on the y-axis. Then, you'd do 50 East + 100 West to get 150 kilometers distance on the x-axis. Now that you have 170 and 150, you can begin the equation
170^2 + 150^2 = c^2
28900 + 22500 = c^2
51400 = c^2
√51400 = √c^2
~226 = c
They are approximately 226 kilometers apart, and 226 is closest to 200, which is B.
While writing this, I felt like I wasn't explaining well. Please feel free to ask for clarification if you need.
The distance between the planes is closest to 200km
You can use the Pythagorean theorem for this question.
First, we need to find a and b. This is gotten by calculating the distance between North and South, and the East and West. From the question, we can say that, 200 North - 30 North gives 170 miles with respect to the y-axis. In the same vein, we know that 50 East + 100 West gives us 150 kilometers which is with respect to the x-axis.
Since we have found our a and b to be 170 and 150, we then use Pythagoras to find the answer to the equation.
170² + 150² = c²
28900 + 22500 = c²
c² = 51400
c =[tex]\sqrt{51400}[/tex]
c = ±226 km.
Since we can't have distance in negative, then our answer is 226 km. The answer asked us to find the closest distance, and thus, our answer is 200km.
Learn more about Pythagoras theorem here https://brainly.com/question/15138986
I really need help I’m very confused
Answer:
10: -11n^5
12: 6k^2 -6k+7
Step-by-step explanation:
Ok so what your gonna do is add or subtract the ones with the same exponent.
so -15+4= -11 since they are both n^5 you can add them so your answer is:
-11n^2
now you have 8k^2-k-5k+7-2k. so you are gonna rearrange them so the same exponents are together.(keep the sign in front in front, if no sign it is positive)
8k^2-2k^2-5k-k+7
add like exponents
6k^2-6k+7
please help me out guys.
Answer:
| 5x| = 0
Step-by-step explanation:
Absolute values have two solutions, one positive and one negative
The exception to this rule is when it is equal to zero
+0 = -0 = 0
5x = 0
x =0
Find the DISTANCES of AB and CD to determine if AB is congruent to CD. A(-7,1) B(-4,-3) C(3,-5) D(7,-2)
Answer:
Step-by-step explanation:
The formula for calculating the distance between 2 points is expressd as;
D = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinates A(-7,1) B(-4,-3) C(3,-5) D(7,-2)
The disyance AB will be expressed as
AB = √(x₂-x₁)²+(y₂-y₁)²
Given the coordinates A(-7,1) B(-4,-3)
AB = √(-4-(-7))²+(-3-1)²
AB = √(-4+7)²+(-4)²
AB = √3²+4²
AB = √25
AB = 5
For CD with coordinates C(3,-5) D(7,-2)
CD = √(7-3)²+(-2-(-5))²
CD = √(4)²+3²
CD = √16+9
CD = √25
CD = 5
Congruent sides are sides that are equal. Hence since AB is equal to CD, this means that the distances AB and CD are congruent
During a recent season, Miguel Cabrera and mike Jacobs hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs. How many home runs did each player hit ? Define a variable, write an equation, and solve the problem
Answer:
Jacobs: 20Cabrera: 26Step-by-step explanation:
Let j represent the number of home runs Jacobs hit. The Cabrera hit j+6, and their total is ...
j +(j+6) = 46
2j = 40 . . . . . . subtract 6
j = 20 . . . . . . . divide by 2
j+6 = 26
Jacobs hit 20 home runs; Cabrera hit 26.
(5x-2)+(4x-4)+(6x-8)
Answer:
15x -14
Step-by-step explanation:
(5x-2)+(4x-4)+(6x-8)
Combine like terms
(5x+4x+6x-2+-4-8)
15x -14
Answer:
15x - 14Step-by-step explanation:
[tex](5x - 2) + (4x - 4) + (6x - 8) \\ 5x - 2 + 4x - 4 + 6x - 8 \\ 5x + 4x + 6x - 2 - 4 - 8 \\ 15x - 14[/tex]
In the last school election, 88% of the student body voted. If the school has an enrollment of 350 students, how many students voted in the last election?
A. 42
B. 88
C. 220
D. 308
Answer:
Its D
Step-by-step explanation:
Draw two lines and a transversal...
picture:
=================================================
Explanation:
It might help to move either line m or line n to make them parallel to one another. This isn't required but it might help to see the answer better.
Angles 1 and 2 are between lines m and n, so they are interior angles. They are alternate interior angles as they are on alternate sides of the transversal line.
Angles 2 and 3 are on the same side of the transversal, and both are above their adjacent parallel line counterpart, so they are corresponding angles.
Angles 3 and 4 are outside the interior region, and they alternate on either side of the transversal. They are alternate exterior angles.
Angles 1 and 4 are corresponding for similar reasons as angles 2 and 3 are.
-------------
Notes:
Drawing A has angles 1 and 2 be alternate interior, but angles 2 and 3 are not corresponding (they're vertical angles)Drawing C is a similar story as drawing A, just things have been rearranged.Drawing D has angle 1 as an exterior angle, so it cannot be an alternate interior angle.
16) Find the width of a rectangle whose area is (x^2 +16x+48) ft^2 and whose
length is (x+4) ft.
Answer: x+12
We know that the area is length * width. Since length is x+4, we know
(x+4) * something = x^2+16x+48.
To find that something, note that 48 (from the right side) = 4 (from the left side) * 12. Why is this important? Well, then we know that the something is x+12.
This is because (x+4) * (x+12) = x^2 + 16x + 48. But just focus on this part: 48. Even if we put like 3x+12 or something, that would work out to 3x^2+28x+48. It's 48 every time.
Hope that helped,
-sirswagger21
Go Tennis is a tennis club for kids to come and learn more about the fundamentals of tennis. The first year it was open, it had 20 kids join. If 15 kids join each year, write an equation that represents how many kids will be enrolled in x years.
Answer:
20+15x
Step-by-step explanation:
because we start with 20 and every year 15 kids join we multiply 15 by x years with 20 kids so we get 20+15x
Is -8/5 a rational number
Answer:
yes
Step-by-step explanation:
i think
Lea left home and drove toward the ferry office at an average speed of 22 km.H. Trevon left at the same time and drove in the opposite direction with an average speed of 43 km/h. How long does Trevon need to drive before they are 65 km apart?
Answer:
1 hour
Step-by-step explanation:
Lea's speed = 22km/hr
Trevon's speed = 43km/hr in a direction opposite Lea's
How long does Trevon needs to drive before they are 65km apart.
Note : both took at the same time and in opposite direction.
Recall : speed = distance / time
Distance = speed * time
Distance between them = 65km
Let Trevon's distance = D2 = 43 * t
Lea's distance = D1 = 22 * t
t is the same since they both left at the same time.
D2 + D1 = 65
43t + 22t = 65
65t = 65
t = 65/65
t = 1 hour
You are a caterer specializing in children's birthday parties. You have 12 birthdays to cater next week. You must bake 2 cakes for each party. Each cake will have 6 candles on it. How many birthday candles do you need for the 12 parties.
Answer:
We need 144 birthday candles do you need for the 12 parties.
Step-by-step explanation:
We are given that you are a caterer specializing in children's birthday parties. You have 12 birthdays to cater to next week. You must bake 2 cakes for each party. Each cake will have 6 candles on it.
And we have to find the birthday candles we need for the 12 parties.
AS it is stated that next week you have 12 birthday parties and for each birthday party you must bake 2 cakes.
This means that for 12 birthday parties you have to make = [tex]12 \times 2[/tex] = 24 cakes.
Also, each cake has 6 candles on it. This means that the total number of candles for 24 cakes = [tex]24 \times 6[/tex] = 144 candles.
Hence, we need 144 birthday candles for the 12 parties.
Line l contains the points A(2, 2) and B(3,6). Line k contains the points C(0,5) and D(1,9).
Are lines land k parallel? Justify your response.
Answer:
Yes, line L and line K are parallel because the slopes are equal.
Step-by-step explanation:
From the question given:
Line L contains point A(2, 2) and B(3, 6)
Line K contains point C(0, 5) and D(1, 9)
To know if the lines are parallel, we need to determine the slope of each line.
The slope of each line can be obtained as follow:
1. Determination of the slope of line L.
Line L contains point A(2, 2) and B(3, 6)
x1 coordinate = 2
x2 coordinate = 3
y1 coordinate = 2
y2 coordinate = 6
Slope = Chang in y coordinate / change in x coordinate
Slope = y2 - y1 / x2 - x1
Slope = 6 - 2 / 3 - 2
Slope = 4/1
Slope = 4
Therefore, the slope of line L is 4.
2. Determination of the slope of line K.
Line K contains point C(0, 5) and D(1, 9)
x1 coordinate = 0
x2 coordinate = 1
y1 coordinate = 5
y2 coordinate = 9
Slope = Chang in y coordinate / change in x coordinate
Slope = y2 - y1 / x2 - x1
Slope = 9 - 5 / 1 - 0
Slope = 4/1
Slope = 4
Therefore, the slope of line K is 4.
Summary
Line >>>>>>>>>>> Slope
L >>>>>>>>>>>>> 4
K >>>>>>>>>>>>> 4
From the above calculations, we can see that line L and line K has the same slope.
Therefore, line L and line K are parallel.
4 times the difference of a number and 12 is 120
Answer:
the answer is 42
Step-by-step explanation:
let the number be ''x''
the difference between ''x'' and 12 can be written as
x - 12
4 times means multiplied by 4, so
4 (x - 12) = 120
4x - 48 = 120
4x = 120 + 48
4x = 168
x = 168/4
x = 42
find x such that 2x^2 +2x=12
Answer:
2 and -3
Step-by-step explanation:
2x^2=4x
4x+2x=12
6x=12
how many times does 6 go into 12?
right, 2 times!
x=2
---
2x^2+2x-12=0
x^2+x-6=0
(x+3)(x-2)=0
X=-3 and 2
Michael wrote a novel that sells for $20 dollars each. He received a bonus of $50,000 to sign the contract to write the book, and he receives 9% commission on each book sale. If he sells 10,000
books how much will he make? Clearly show your work
Simplify to create an equivalent expression. 8k−5(−5k+3) Choose 1 answer: A 33k+15 B 33k-15 C 3k+3 D 3k-3
Answer:
B 33k-15
Step-by-step explanation:
[tex]8k-5(-5k+3)\\\mathrm{Expand}\:-5\left(-5k+3\right):\quad 25k-15\\=8k+25k-15\\= 33k-15[/tex]
The cube of the difference of a number and 9.
Answer:
Hey there!
Let x be the number.
Thus, we have [tex](x-9)^3[/tex]
Hope this helps :)
Which of the following is not something you should consider when evaluating an investment advisor? a. Their experience b. Whether or not they are registered with FINRA c. Whether or not they are registered with the SEC d. Their educational background
Answer: Whether or not they are registered with FINRA.
Step-by-step explanation: When evaluating an investment advisor, it is important to evaluate their level of experience, educational background as it goes a long way in giving clients a clue of the advisors possible offering, knowledge and expertise. Additionally, an Investment advisor should be registered with the Security and Exchange Commission (SEC), which is a federal regulatory agency charged with making regulatory policies that aid investor protection and proper market functioning. Being registered with FINRA, Financial Industry Regulatory Authority is not really to be considered as it is a self regulatory body (that is non governmental) and the main rules and policies guiding the market are made by SEC.
Answer:
B
Step-by-step explanation:
ED2020
this is a very dumb question but what is -1^2? my calculator says its -1 but isnt -1*-1 = 1???? im very confused plzz help
Answer:
yes; -1² is 1.
if you put -1 in parentheses, like this (-1)², then it comes out as 1
Answer:
it is 1
Step-by-step explanation:
you have to put the number between parenthesis to give you the right answer. the calculator actually taking the minus sign separate from 1 because no brackets . Try (-1)²
How do you do question 12? Options:
A 4
B 1/4
C -1/4
D -4
Answer:
it is D
Step-by-step explanation:
Draw a conclusion from the given information. look at picture...
Thanks! Please help soon! :)
Hey there! I'm happy to help!
When looking for a conclusion, we have to find something that we can figure out from the information but they don't directly tell us.
Answer B says that a conclusion is that the lines meet at a 90 degree angle, but they already told us that, so this is wrong.
Answer C does the same thing, so it is wrong as well.
A 90 degree angle is a right angle. They already told us that the lines intersect at a right angle, so this is not a conclusion.
Answer A says that the lines are perpendicular. They don't directly tell us that these specific lines are perpendicular, but from the information they gave us we can figure it out. Therefore, the correct answer is A. The lines are perpendicular.
Have a wonderful day! :D
HELP PLEASE... Find the length of the side x in this Right triangle
A. 5 tan 50.1
B. (tan 50.1)/5
C. tan^-1(5/50.1)
Answer:
C
Step-by-step explanation:
pls help
will give the brainliest!
Urgent!!
need explanation.
a)
The rotation transformations are:
[tex] x=x' \cos \theta - y' \sin \theta\\
y= x' \sin \theta + y' \cos \theta[/tex]
where $(x', y')$ are new coordinates.
Since we want an anti-clockwise rotation of the axes, put $\theta= 90$° to get the required coordinates as $(4,-1)$
b)
The equation of the given line is $x-y=0$
Use the mirror formula:
[tex] x'= x_o - \frac{2 a}{a^2+ b^2}(a x_o + by_o +c)[/tex]
Replace $x$ by $y$ above to get the corresponding formula for the y-coordinate.
Here we have
$a=1$
$b=-1$
$c=0$
$x_o= 1$
$y_o =4$
Substitute these values to get the required coordinates as $(4,1)$
c)
$(5,3)$ maps onto $(1,1)$
Let's keep it simple here: To get the new coordinates you subtract 4 from the x coordinate and 2 from the y coordinate.
Thus for our point $(1,4)$ our image is $(1-4, 4-2)$ which is $(-3,2)$
Juan is interested in the chance of rain for the upcoming week based on studying prior weather data for this time of year. Juan wants to know about what?
Answer:
time and weather data is dis right
Step-by-step explanation:
Step-by-step explanation:
Weather forecasting is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for millennia and formally since the 19th century. Weather forecasts are made by collecting quantitative data about the current state of the atmosphere at a given place and using meteorology to project how the atmosphere will change.
Once calculated by hand based mainly upon changes in barometric pressure, current weather conditions, and sky condition or cloud cover, weather forecasting now relies on computer-based models that take many atmospheric factors into account.[1] Human input is still required to pick the best possible forecast model to base the forecast upon, which involves pattern recognition skills, teleconnections, knowledge of model performance, and knowledge of model biases. The inaccuracy of forecasting is due to the chaotic nature of the atmosphere, the massive computational power required to solve the equations that describe the atmosphere, the error involved in measuring the initial conditions, and an incomplete understanding of atmospheric processes. Hence, forecasts become less accurate as the difference between current time and the time for which the forecast is being made (the range of the forecast) increases. The use of ensembles and model consensus help narrow the error and pick the most likely outcome.
There is a vast variety of end uses to weather forecasts. Weather warnings are important forecasts because they are used to protect life and property. Forecasts based on temperature and precipitation are important to agriculture, and therefore to traders within commodity markets. Temperature forecasts are used by utility companies to estimate demand over coming days. On an everyday basis, many use weather forecasts to determine what to wear on a given day. Since outdoor activities are severely curtailed by heavy rain, snow and wind chill, forecasts can be used to plan activities around these events, and to plan ahead and survive them. In 2009, the US spent approximately $5.1 billion on weather forecasting.[2]
History