Choose all of the statements that correctly compare the two functions shown.
Alec's rate of savings is greater than Beth's.
entific
Alec and Beth are saving at the same rate.
Alec started with more money than Beth
mulas
Time
maining
:19:23
Beth started with more money than Alec,
de les
At 10 days, Alec will have $1 more than Beth in savings,
Answers
Answer:
b, c and e
Step-by-step explanation:
Given
See attachment for functions
Required
Select all statements that contain both functions
First, calculate the rate (slope) of both functions.
This is calculated as:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Alec's
[tex](x_1,y_1) = (0,3)[/tex]
[tex](x_2,y_2) = (2,9)[/tex]
So, the slope is:
[tex]m = \frac{9 - 3}{2 - 0}[/tex]
[tex]m = \frac{6}{2}[/tex]
[tex]m =3[/tex]
For Beth's
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (12,38)[/tex]
So, the slope is:
[tex]m = \frac{38 - 17}{12 - 5}[/tex]
[tex]m = \frac{21}{7}[/tex]
[tex]m =3[/tex]
Beth and Rec have the same slope. Hence, they save at the same rate.
Next, determine the amount they started with.
This implies that we calculate y when x = 0
From Alec's graph.
[tex](x,y) = (0,3)[/tex]
Alec's initial savings is 3
For Beth's savings, we make use of slope formula.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex](x_1,y_1) = (5,17)[/tex]
[tex](x_2,y_2) = (0,y)[/tex]
So, we have:
[tex]3 =\frac{y - 17}{0 - 5}[/tex]
[tex]3 =\frac{y - 17}{ - 5}[/tex]
[tex]y - 17 = -15[/tex]
[tex]y = 17 -15[/tex]
[tex]y = 2[/tex]
Beth's initial savings is 2
Hence, Alec started with more money
Next, is to determine who has more money after 10 days.
Since they save at the same rate, the difference in their savings after any number of days will be the difference in their initial savings.
The difference (d) is calculated as:
[tex]d = 3 - 2[/tex]
[tex]d = 1[/tex]
Hence, Alec will have $1 more than Beth after 10 days
Answer:
its bc and e or Alec and Beth are saving at the same rate. Alec started with more money than Beth. and At 10 days, Alec will have $1 more than Beth in savings.
Step-by-step explanation:
Related Questions
NASA launches a test rocket with an initial velocity of 235 meters per second from an initial height of 15 meters above sea-level. Find a quadratic function that models the height of the rocket, in meters above sea-level, as a function of time t , in seconds after the launch. (HINT: 4.9 meters = 16 feet) Use your model to answer the following questions. Assuming that the rocket will splash down into the ocean, how many seconds after launch does splashdown occur? (round to the nearest tenth of one second) The rocket splashes down after seconds. What is the maximum height above sea-level attained by the rocket? (round to the nearest meter) The maximum height is meters above sea-level.
Answers
9514 1404 393
Answer:
48.0 seconds2833 metersStep-by-step explanation:
A graphing calculator shows the points of interest nicely.
The rocket splashes down after 48.0 seconds.
The maximum height is 2833 meters above sea level.
__
The equation for the motion is ...
h(t) = -4.9t^2 +235t +15 . . . . launch at 235 m/s from height of 15 m
The vertex (maximum height) is found at ...
t = -(235)/(2(-4.9)) = 235/9.8 ≈ 23.980 . . . seconds
Then the maximum height is ...
h(23.980) = (-4.9(23.980) +235)(23.980) +15 ≈ 2833 . . . meters
The value of t when h(t) = 0 can be found using the quadratic formula.
t = (-235 -√(235² -4(-4.9)(15)))/(2(-4.9)) = (-235 -√55519)/-9.8
t ≈ 48.023 ≈ 48.0 . . . seconds
write an equivalent expression 8(y-7z+1)
Answers
Answer:
8y−56z+8
Step-by-step explanation:
how many 5/8 pound bags does it take to get 16 pounds of soil?
Answers
Answer:
10
Step-by-step explanation:
Given f (x) = x + 1 and g(x) = x2, what is (gof)(x)?
Answers
Answer:
(gof)(x) = x² + 2x + 1
Step-by-step explanation:
You can solve this by plugging f into g and finding the result:
(gof)(x) = f(x)²
= (x + 1)²
= x² + 2x + 1
PLEASE HURRYYYYYYYYY
Answers
Answer:
12r ft
Step-by-step explanation:
you're welcome have a nice day
find the diagonal that goes through the 3D shape.
Answers
Answer:
Diagonal = 13 yd
Step-by-step explanation:
The diagonal of the 3D shape can be solved using the extension of the pythagorean theorem, which is given as: d² = a² + b² + c²
Where,
a = 12 yd
b = 3 yd
c = 4 yd
d = diagonal
Plug in the values
d² = 12² + 3² + 4²
d² = 169
d = √169
d = 13 yd
Someone answer this Please
Answers
Answer:
15 miles
Step-by-step explanation:
The Pythagorean theorem states that [tex]a^2+b^2=c^2[/tex] where a and b are the two legs (the sides of the triangle that are adjacent to the right angle) and c is the hypotenuse (the longest side). This only applies to right triangles.
Plug 12 mi and 9 mi into [tex]a^2+b^2=c^2[/tex] as a and b.
[tex]a^2+b^2=c^2\\12^2+9^2=c^2\\144+81=c^2\\225=c^2[/tex]
Take the square root of both sides
[tex]15=c[/tex]
Therefore, the length of the hypotenuse is 15 miles.
I hope this helps!
What is 2/3x2/5pls I need an answer fast sorry I suck at math
Answers
Answer:
4 /1 5 also 0.26666666666
Please mark as brainliest
Have a great day, be safe and healthy
Thank u
XD
Find the value of f(4) for the function
Answers
Answer:
f(4) = 7
Step-by-step explanation:
The notation for these type of problems is very confusing. Just remember that f(x) is the same thing as y (or some variable). Even if there is a number or something on the inside of the parentheses, it's still just a variable.
In our case
f(a) = 2(a + 4) -9
could be rewritten as
y = 2(a + 4) - 9
the thing on the inside of the parentheses signifies what the equation is dependent on.
so when is says f(4), it just want's you to trade out a for a 4, but the equation is still the same.
f(4) = 2((4) + 4) - 9
Now, just follow the order of operations
f(4) = 2(8) - 9
f(4) = 16 - 9
f(4) = 7
help please triangles and trig
Answers
Answer:
[tex]\sin L = \frac{3}{5}[/tex]
[tex]\tan N = \frac{4}{3}[/tex]
[tex]\cos L = \frac{4}{5}[/tex]
[tex]\sin N = \frac{4}{5}[/tex]
Step-by-step explanation:
Given
The above triangle
First, we calculate the length LM using Pythagoras theorem.
[tex]LN^2 = LM^2 + MN^2[/tex]
[tex]10^2 = LM^2 + 6^2[/tex]
[tex]100 = LM^2 + 36[/tex]
Collect like terms
[tex]LM^2 = 100 - 36[/tex]
[tex]LM^2 = 64[/tex]
Take positive square root
[tex]LM=8[/tex]
Solving (a): Sin L
[tex]\sin L = \frac{Opposite}{Hypotenuse}[/tex]
[tex]\sin L = \frac{MN}{LN}[/tex]
[tex]\sin L = \frac{6}{10}[/tex]
Simplify
[tex]\sin L = \frac{3}{5}[/tex]
Solving (b): tan N
[tex]\tan N = \frac{Opposite}{Adjacent}[/tex]
[tex]\tan N = \frac{LM}{MN}[/tex]
[tex]\tan N = \frac{8}{6}[/tex]
Simplify
[tex]\tan N = \frac{4}{3}[/tex]
Solving (c): cos L
This calculated as:
[tex]\cos L = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]\cos L = \frac{LM}{LN}[/tex]
[tex]\cos L = \frac{8}{10}[/tex]
Simplify
[tex]\cos L = \frac{4}{5}[/tex]
Solving (d): sin N
This is calculated using:
If [tex]a + b = 90[/tex]
Then: [tex]\sin a = \cos b[/tex]
So:
[tex]\sin N = \cos L[/tex]
[tex]\sin N = \frac{4}{5}[/tex]
Help. Please and a few others are
Answers
Answer:
YES ITS MEDIAN!!!
Step-by-step explanation:
Answer:
yes you are correct it is the median.
Step-by-step explanation:
Nicholas has a salt shaker in the shape of a cylinder. It has a radius of 8 mm and a height of 30 mm. What is the lateral surface area of the shaker?
Answers
Answer:
1507.96
Step-by-step explanation:
Each small square in the figure below measures 1 foot on each side what is the area of the triangle
Answers
Answer:
It should be 0.5 if I’m wrong let me know
Step-by-step explanation:
A=HbB/ 2 = 1x1/2=0.5
how many degrees is a acute angle
Answers
Any angle that measures less than 90 degrees
Question 5 (2 points)
Given the function rule y = 3x + 11, what is the value of y if x = 27
Answers
Answer: Y=83
Step-by-step explanation:
Answer:
y = 92
Step-by-step explanation:
plug in x = 27 into the equation y = 3x + 11,
y = 3(27) + 11
=> y = 81 + 11
=> y = 92
if $1000 is divided among the three people In the ratio 2:3:5,find the share of each
Answers
Answer:
$200, $300, $500
Step-by-step explanation:
Given data
Total Amount= $1000
Ratio= 2:3:5
The combined ratio is = 10
Let us apply the part to all method to find the individual amount
The first person will take
10/1000= 2/x
1/100=2/x
cross multiply
x= 200
The second person will take
10/1000= 3/x
1/100=3/x
cross multiply
x= 300
The third person will take
10/1000= 5/x
1/100=5/x
cross multiply
x= 500
Simplify fully
4x2 + 4x
2x² – 2
Answers
Answer:
4 × 2 = 8 + 4 = 12 × 2 = 24 - 2 = 22
22 is the FINAL answer
#carryonlearning
A coat cost $37.88 at Walmart. The sales tax is 5.5%. What is the total amount of the coat including the sales tax?
Answers
HELP ILL GIVE BRAINLIEST AND NO LINKS
Answers
Answer:
x<9
Step-by-step explanation:
Which of the following is true about the figure?
a. m MUC - m MUP = m PUC
b. m DUC + m VUA = m DUV
C. m MUC = m MUV = m VUA = m AUD
d. m CUA + m DUP = m PUM
Answers
Answer:
a. m<MUC - m<MUP = m<PUC
Step-by-step explanation:
From the options given, the only statement that is true of the figure shown is:
a. m<MUC - m<MUP = m<PUC
Rationale:
m<MUC = m<MUP + m<PUC (Angle Addition Postulate)
Subtract m<MUP from each side
m<MUC - m<MUP = m<PUC
Write an expression for " x divided by nine".
Please help!!
10 POINTS
Answers
Answer:
x/9
Step-by-step explanation:
x divided by 9
=> x ÷ 9
Take that and turn it into a fraction
=> x/9
hope this helps and is right. p.s. i really need brainliest :)
Answer:
45
Step-by-step explanation:
luego le digo 4yo1 xkw k
Answers
Answer:
okay luego le digo 4yo1 xkw k
Step-by-step explanation:
A rectangular prism and its dimensions are shown in the diagram.
Dimensions:length 7.5 width 5 height 6.5
what is the total surface area
Answers
Answer:
237.5
Step-by-step explanation:
2·(5·7.5+6.5·7.5+6.5·5)=237.5
help pleaseeeeeee :(
Answers
Answer:
Do 16 times pi.
Step-by-step explanation:
The closest answer is D.
Answer:
8 (option 1)
Step-by-step explanation:
Mark it as option 1 => 8 is the crt answer
2pi r = 16
r = 8
Please answer number 9 I’ll give brainliest thank you!
Answers
Answer:
C (95 people)
Step-by-step explanation:
380 is basically like 100% so 380÷100= 3.8 (which is equal to 1%), then use a calculator to do 3.8x25=95 (this makes 25%)
Answer:
C.95
Step-by-step explanation:
25/100=0.25
380*0.25=95
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-15x^2+801x-5900
Answers
Answer:
In order to maximize profit, each widget should sell for $26.70.
Step-by-step explanation:
The total amount of profit y given by the selling price of each widget x is given by:
[tex]y=-15x^2+801x-5900[/tex]
And we want to determine the price of each widget such that is yields the maximum profit.
Since the equation is a quadratic, the maximum profit will occur at the vertex of our parabola.
The vertex of a quadratic is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]
So, let's find the vertex. In our equation, a = -15, b = 801, and c = -5900.
Therefore, the price that maximizes profit is:
[tex]\displaystyle x=-\frac{801}{2(-15)}=\$26.70[/tex]
Therefore, in order to maximize profit, each widget should sell for $26.70.
Notes:
Then substituting this back into the equation, the maximum profit is:
[tex]y_{\text{max}}=-15(26.7)^2+801(26.7)-5900=\$ 4793.35[/tex]
What is the mean absolute deviation of each swim club?
A:5
B:50
C:0
D:10
Answers
Answer:
c
Step-by-step explanation:
. Three employees each clocked a different number of hours worked this week.
Employee Hours Worked Total Earned (in dollars)
A 35 $420
B 22 $242
C 16 $216
Which employee has the highest earnings per hour?
A) Employee A
B) Employee B
C) Employee C
Answers
Answer:
C IS THE ANSWER
3x2 - 4x + 2
a) cubic binomial
b) quartic trinomial
c) quadratic trinomial
d) quadratic binomial
Answers
Answer:
c
Step-by-step explanation:
A quadratic trinomial has the form of ax² + bx + c
e.g. 3x² + 4x + 2
A quadratic binomial has the form of ax² + bx
e.g. 3x² + 4x
A cubic binomial has the form : ax³ + bx
3x³ + 4x
a family wants to have two children determine the probability of a family having two girls