Answers
Answer: X=4/2x+3
Step-by-step explanation:
I just know
y-4 = (1/2)(x -2).
The equation for point slope form is
y - y1 = m(x - x1)
The point on the graph is given as (2,4) so you can substitute that into the equation as
y - 4 = m(x - 2)
M represents the slope.
By looking at the graph, you can see that the y-intercept is (0,3). The slope is change in y / change in x or the rise/run. From (0,3) to (2,4).
Change in y = 4 - 3 = 1
Change in x = 2 - 0 = 2
Therefore the slope = 1/2 = m.
Substitute m in for the slope and the final equation in point slope form would be y-4 = (1/2)(x -2).
Related Questions
g An employee joined a company in 2017 with a starting salary of $50,000. Every year, the employee receives a raise of $1,000 plus 5% of the salary of the previous year. (a). Set up a recurrence relation for the salary of the emplyee n years after 2017. A recurrence relation of a sequence is an equation that express a subscript n using one or more of previous terms. (b). What will be the salary of the employee in 2025
Answers
Answer:
a) s[n] = 1.05s[n-1] +1000; s[0] = 50,000
b) $83,421.88
c) s[n] = 70000·1.05^n -20000
Step-by-step explanation:
a) Let s[n] represents the employee's salary in dollars n years after 2017. The salary in 2017 is given as $50,000, so ...
s[0] = 50000 . . . . the recursion relation initial condition
The next year, the salary is multiplied by 1.05 and 1000 is added:
s[1] = 1.05·s[0] +1000
This pattern repeats, so the recursion relation is ...
s[n] = 1.05·s[n-1] +1000
__
c) It is convenient to find a formula for the salary before trying to compute the salary 8 years on. So, we work part (c) before part (b).
The base salary gets multiplied by 1.05 each year, so can be described by the exponential function ...
base salary after n years = 50,000·1.05^n
The add-on to the raise becomes a geometric sequence whose common ratio is 1.05. The sum can be described by the formula for the sum of such a sequence:
sum = a1(r^n -1)/(r -1) . . . . . (see note below)
sum of add-ons = 1000(1.05^n -1)/(1.05 -1) = 20000(1.05^n -1)
So, the total salary after n years is ...
s[n] = 50000·1.05^n + 20000(1.05^n -1)
The exponential terms can be combined, so we have the explicit formula ...
s[n] = 70000·1.05^n -20000
__
b) The year 2025 is 8 years after 2017, so we want to find s[8].
s[8] = 70000·1.05^8 -20000 = 70000·1.4774554 -20000
= 103,421.88 -20000 = 83,421.88
In 2025, the employee's salary will be $83,421.88.
_____
Note on the sum of the add-ons
A geometric sequence starts with term a1 and gets multiplied by a ratio r to make the next term: a2=r·a1; a3=r²·a1, ....
The sum of such a geometric sequence has the formula
Sn = a1·(r^n -1)/(r -1)
Here, the sequence starts in year 1 with a1=1000 and has a common ratio r=1.05. The denominator of the sum is r-1 = 0.05 = 1/20, so the sum can be written as
Sn = 20000·(1.05^n -1).
50,000 is 20% of what?
Answers
Answer:
250000
Step-by-step explanation:
20% of x is 50000
----------------------------
50000=20x/100
50000= x/5
5(50000) = x
250000 = x
What is the domain of the function?
Negative infinity less-than x less-than infinity
Negative 1 less-than x less-than infinity
0 less-than-or-equal-to x less-than infinity
1 less-than-or-equal-to x less-than infinity
Answers
Answer:
(-∞,∞)
Step-by-step explanation:
Answer:
first one
Step-by-step explanation:
[tex] \sqrt[3]{x} [/tex]
has the domain all of the real numbers
The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting.
A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.
Which statement describes the distribution?
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of –1.2 ounces.
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
The distribution is approximately Normal, with a mean of 1.2 ounces and a standard deviation of 8 ounces.
The distribution is uniform, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
Answers
Using concepts of the normal and of the uniform distribution, it is found that the correct option is:
The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
In an uniform distribution, all outcomes are equally as likely, thus they have the same height.In the normal distribution, the outcomes with the highest likelihood are those closest to the mean, thus they have the highest height. This means that the mean of this distribution is 8.The standard deviation cannot be a negative value, so in this problem, it is 1.2, which means that the correct option is:The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.
A similar problem is given at https://brainly.com/question/25128186
square root of 31 is between which two integers?
Answers
Answer:
5 and 6
Step-by-step explanation:
The formula E =1/2 kx^2gives the potential energy E of a spring with spring constant k that has
been stretched by length x. Solve the formula fork to find the constant of a spring with a iven
potential energy and stretch.
Answers
Answer:
[tex]k = 2E/x^2[/tex]Step-by-step explanation:
Given formula:
[tex]E = 1/2kx^2[/tex]To solve for k, multiply both sides by 2 and divide by x²:
[tex]2E=kx^2[/tex][tex]k = 2E/x^2[/tex]Answer:
[tex]\sf\longmapsto \: k = \frac{2E}{x {}^{2} } [/tex]
Step-by-step explanation:
The formula given is :
[tex]\sf\longmapsto \: E = \frac{1}{2} kx²[/tex]
Now, multiply (×) both sides by 2 and divide (÷) by x^2
[tex]\sf\longmapsto \: 2E = kx²[/tex]
[tex]\sf\longmapsto \: k = \frac{2E}{x {}^{2} } [/tex]
Find the value of 15625 × (-2) + (-15625) × 98
Answers
Answer:
-1562500
Step-by-step explanation:
15625 × (-2) + (-15625) × 98 = -31250 + (-1531250)
= -31250 - 1531250
= -1562500
Answer:
[tex]-1562500[/tex]
Step-by-step explanation:
[tex]5625\left(-2\right)+\left(-15625\right)\times \:98[/tex]
[tex]15625\left(-2\right)[/tex]
[tex]=-31250[/tex]
[tex]15625\times \:98[/tex]
[tex]=1531250[/tex]
[tex]-31250-1531250[/tex]
[tex]-1562500[/tex]
Milena is trying to determine an algebraic expression to represent the amount of punch she needs to make for her party. She does not know the exact number of guests, but she wants to have 3 cups of punch per guest, plus an additional 20 cups of punch.
Which expression represents the amount of punch Milena will need for her party?
g + 20
3g
3g + 20
3(20)
Answers
Answer:
let g = number of guests. if each guest is to have 3 cups we represent this as
3g
for the additional 20 cups, we add 20
3g + 20
Answer: 3g + 20
Step-by-step explanation:
hope this helps
A meter is a unit of length approximately equal to 39.37 inches. If someone is 77 meters tall, what is his or her approximate height in inches?
Answers
Answer:
It is 3031.49 Inches.
Step-by-step explanation:
77 times 39.37
= 3031.49
The table represents the ratio of tulips todaffodils in a garden how many tulips will there be if the garden has 60 daffodils
Answers
There would be 85 Tulips in the garden if the garden has 60 daffodils
Two variables are said to be proportional if an increase in one variable leads to an increase in another variable and vice versa.
From the table, 12 daffodils corresponds with 17 Tulips.
Hence the ratio of tulips to daffodils = 17 tulips / 12 daffodils
Therefore for 60 daffodils:
Number of Tulips = (17 tulips / 12 daffodils) * 60 daffodils
Number of Tulips = 85 Tulips
There would be 85 Tulips in the garden if the garden has 60 daffodils
Find out more at: https://brainly.com/question/17741678
If a small boy in 30 days saved 1.00 to spend how much did he save each day
Answers
Answer:5 Penny's everyday for thirdy days
Step-by-step explanation:
Find all triples of natural numbers (a, b, c) satisfying the system of equations
Answers
9514 1404 393
Answer:
(±7, ±1, ±4)(±13, ±11, ±16)Step-by-step explanation:
Solution of the system by the usual means yields the parametric equations ...
(a², b², c²) = (41 +t, t -7, 2t)
Since we want t-7 to be a perfect square, we can let ...
t -7 = n²
t = n² +7
Then the solutions are ...
(a, b, c) = (±√(n²+48), n, ±√(2(n² +7)))
The only integer solutions are for n=±1 and n=±11. Then the 16 possible triples are ...
(±7, ±1, ±4) and (±13, ±11, ±16) . . . where the signs can have any combination
solve the following inequality using the algebraic approach: 3x>-6
Answers
Answer:
x > -2
Step-by-step explanation:
3x>-6
Divide each side by 3
3x/3 > -6/3
x > -2
what is the greatest common factor of 42, 12, and 6?
Answers
Answer:
The greatest common factor is surprisingly 6.
All three numbers can be divided by 6 and it is the highest value that can be taken from all three numbers.
Step-by-step explanation:
Hope this helps.
<3
Answer:
the GCF of those numbers is 6.
Step-by-step explanation:
One way to solve this is to list the factors of them, then find the greatest one that they share.
42: 1, 2, 3, 6, 7, 14, 21, 42
12: 1, 2, 3, 4, 6, 12
6: 1, 2, 3, 6
If we look at them, notice that six is in all of them. All of them have factors of six. Can we go any higher than that? No because six is the greatest factor of six, so we can't go any higher and still have all of them share a GCF. So your answer is 6.
Find the equation of the linear function represented by the table y 6 9 12 15 x 1 2 3 4
Answers
Answer:
y = 3x + 3
Step-by-step explanation
Values on the y-axis are increasing by 3, while values on the x axis are increasing by 1, so the slope is 3/1 or just 3
To find b, you the slope, 3, from the 6. You also subtract 1 from 1 in the x-collum. You do this to find the y-intercept, or when x=0.
t
Given the two points, write the
I equation in slope-intercept form.
(-5, 2) and (10, 8)
Answers
Answer:
y = 2/5x + 4
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope:
( y1 - y2 ) / ( x1 - x2 )
( 2 - 8 ) / ( -5 - 10 )
( -6 ) / ( -15 )
2 / 5
Y-Intercept:
8 = 2/5(10) + b
8 = 4 + b
4 = b
Hopefully this helps!
Brainliest please?
Q1) Gary has 40 oranges. Gary gives Maya 1/4 of his oranges. Gary also loses 2/5 of the rest of them. How many does Gary have left?
Answers
Answer: 3
Step-by-step explanation:
40/4 = 10
So, if he gave away 1/4 of his oranges he now has 30 oranges left
Next, to find 2/5 of 30, divide 30 by 5 and multiply by 2
30/5=6
6•2=12
So, he lost 12 oranges which leaves him with 18.
40-10=30
30-12=18
Gary has 18 oranges left
i need help with this question
Answers
Answer:
below
Step-by-step explanation:
I'm not absolutely know what are you asking for the answer, but this graph shows ...
The first 20 minutes he has a constant speed of 1.8/20=0.09 km/min progress to 1.8 km away from home, then has 10 minutes (from 20-30) stop at the spot.
Then he drive home with speed of 0.045 km/min (1.8/40=0.045) for 40 minutes to return to the start point.
need help with homework plz and thank u :)
Answers
Answer:
B
Step-by-step explanation:
The zeros are where the function crosses the x-axis. In this case, it is 5/2 and -3, which eliminates options C and D. Next, the y-intercept is the point as to where the function crosses the y-axis. Here, it is (0,15), but does not help us to narrow down our options. Finally, the maximum is the highest y-value that the function touches. If you observe the graph at its highest point, it can be inferred that it's y-value is slightly above 15, and so it is at 15.1 (x-value has no importance in this context).
7 and a number equals 21
Answers
Answer:
7x3=21
Step-by-step explanation:
7+7+7=21, 7x3=21
(-8r^2s^-8)(-3r^-7s^8)
Answers
24r^−5s^0 would be your answer
Divide:
27.68) 2363.872
Answers
Answer:
85.4
Step-by-step explanation:
whats nine plus 10 ;)
Answers
Answer:
19
Step-by-step explanation:
9+10=19
please mark me brainliest
Answer:
21 ^^
jk jk lol 19 >->
but reality... i believe it's 2356486513
8×5 implies that 40 is a multiple of......................... And........................
Answers
5.10.15.20.35.40
8.16.24.32.40
solve pls brainliest
tell me where the dot go!
Answers
Answer:
The first dot is on -9 and the second dot is on -7.
(a) -9 is to the left of -7.
(b) -9<-7
Step-by-step explanation:
What are the measurements of angles x,y,z & w?
Thank you<3
Answers
Step-by-step explanation:
z°=180°-25°
z°= 155°
z°=x°=155° (vertically opposite angle).
w°=25°(alternate angle).
y°=z°=155°(alternate angle).
hope this helps you.
Answer:
See belowStep-by-step explanation:
As AB and CD are parallel lines cut by a transversal, we have:
∠x and ∠z are congruent as vertical angles∠x and y are congruent as corresponding angles∠w is congruent with 25° as alternate interior anglesSo the measures are:
m∠x = m∠y = m∠y = 180° - 25° = 155° (supplementary angles sum to 180°)m∠w = 25°The graph shows a proportional relationship between the number of cans of tennis balls and the total number of tennis balls.
What does the point (2, 6) represent in this situation?
Tennis Balls graph showing number of tennis balls on the y axis and number of cans on the x axis. A line begins at the origin and passes through the points 1 comma 3 and 2 comma 6.
Answers
Answer:
There are 6 tennis balls in 2 cans.
Answer: c and e
Step-by-step explanation:
because im smart like that
What is the relationship for angle 1 and angle 8
Answers
Answer:
Step-by-step explanation:
In this cofiguration, there are 8 angles. 4 equal one value and 4 are their supplements of the first 4.
6 and 80 and 2 and 3 are all equal to 80 degrees.
1 4 5 and 8 are the supplements. So whatever their value, they are all equal to the same thing. <1 = <8
They are supplementary to the 80 degree angle
<1 + 80 = 180 Subtract 80 from both sides
<1 = 180 - 80
<1 = 100
So angle 1 and <8 both equal 100 degrees.
Answer:
Alternate exterior angles.
Step-by-step explanation:
Alternate exterior angles are angles on opposing sides of the transversal and the outside of the parallel lines. Moreover, they are congruent. Therefore, ∠1 ≅ ∠8.
Jake needs to buy 120beverages for a party. What equation, in standard form, determines the number x of 8-packs of juice and the number y of 12-packs of water Jake can buy?
Answers
8x+12y=120
8 packs -> x value
12 packs -> y value
-------------------------------
total amt. of beverages is 120
Pleas answer this question!
Answers
a) x = -2 y = -1 so (-2,-1)
Answer:
(- 2, - 1 ) and (- 3, 0 ) , (- 1, 0 )
Step-by-step explanation:
(a)
The coordinates of the turning point ( vertex ) = (- 2, - 1 )
(b)
The roots are where the graph crosses the x- axis , that is
(- 3, 0 ) and (- 1, 0 )