Ashley compares the fees charged by two babysitting agencies.The fees are shown below. Determine which function is described in the table below.Drag-and-drop either agency A or agency B into each box to correctly identify which function is described.
Answers
Answer:
Agency A: y = 12x
So Agency A pays a rate of $12 per hour
Agency B: y = 10x + 20
So Agency B pays an initial fee of $20 plus a rate of $10 per hour.
Step-by-step explanation:
Agency A
To create a straight line equation for the data in table, use [tex]y = mx + b[/tex], where m is the slope and b is the y-intercept.
To find the slope m, take 2 points from the table and use the slope formula.
Let [tex](x_1,y_1)[/tex] = (3, 36)
Let [tex](x_2,y_2)[/tex] = (5, 60)
Slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{60-36}{5-3}=12[/tex]
Now use the point-slope formula to create the final equation:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-36=12(x-3)[/tex]
[tex]\implies y=12x[/tex]
Therefore, Agency A pays a rate of $12 per hour.
Agency B
From inspection, the function is a straight line.
Therefore we can use the straight line equation [tex]y = mx + b[/tex],
where m is the slope and b is the y-intercept.
From inspection, we can see that the line crosses the y-axis at (0,20). Therefore, the y-intercept is 20.
[tex]\implies y=mx+20[/tex]
Taking 2 points on the line and using the slope formula to find the slope m:
Let [tex](x_1,y_1)[/tex] = (0, 20)
Let [tex](x_2,y_2)[/tex] = (3, 50)
Slope formula: [tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{50-20}{3-0}=10[/tex]
Therefore, the final equation is: [tex]y=10x+20[/tex]
Therefore, Agency B pays an initial fee of $20 plus a rate of $10 per hour.
Related Questions
Find (f.g)(x) where f(x) = 3x + 1, g(x) = 2x + 7.
=
O (f•9)(x) = 6x2 + y 3x + 7
O (f.g)(x) = 6x2 + 7
O (fºg)(x) = 6x2 + 23x + 7
O(fºg)(x) = 5x + 8
Answers
Answer:
3rd option
Step-by-step explanation:
(f • g)(x)
= f(x) × g(x)
= (3x + 1)(2x + 7)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(2x + 7) + 1(2x + 7) ← distribute parenthesis
= 6x² + 21x + 2x + 7 ← collect like terms
= 6x² + 23x + 7
The slope, m, of a linear equation can be found using the formula m = y^2 - y^1, where the x-axis and y-values come from two ordered pairs, and (x^1, y^1) and (x^2, y^2). What is the equivalent equation solver for y^2?
Answers
This is the formula needed
Write the equation of the line in fully simplified slope-intercept form. 10 8 D 4 2 1 -12-11-10 -9 -8 -7 -6 -5 -4 -3 -2 6 - 8 9 10 11 12 12
Answers
Answer:
y = -5x - 5
Step-by-step explanation:
y = -5x - 5
Slope intercept form is y = mx + b where m is the slope and b is the y intercept.
-5 is the y intercept and -5/1 or -5 is the slope/
3-45 so just do it -
What is 6 (-2y+4) simplified
Answers
Answer:
-12y+24
Step-by-step explanation:
I used math---------way , so it is correct. brainliest please!
Answer:
Step-by-step explanation:
6 (-2y+4)
First, we use the distributive property to substitute the terms.
(-12y + 24)
Then we divide 24 by -12 to get -2.
24/-12 = -2.
y = -2
please help me !!! please The area, A, in square feet, of the base of a rectangular storage bin in a warehouse is given by the function A(x)=−2x^2+36x, where x is the width, in feet, of the storage bin. John said that factoring would be a more efficient way to solve for the maximum area compared to completing the square. Do you agree or disagree with John? I must Explain.
Answers
The area of the garden is the amount of space it occupies
John's claim is not true
How to determine if John's claim is trueThe function is given as:
[tex]A(x) = -2x^2 + 36x[/tex]
To determine the maximum area, we do not need to factorize the expression or apply completing the square.
Hence, John's claim is not true
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HELP THIS IS DUE SOON! PLEASE PROVIDE THE ANSWER ALONG WITH HOW YOU GOT THE ANSWER.
Torrance is buying presents for members of his family. He wants to spend $10 less on his brother than he spends on his sister, and six dollars more than twice the amount he spends on his sister on his mother. If Torrance has $100 to spend, how much does he intend to spend on his brother?
Let x = the $ Torrance spends on his sister
Answers
Answer:
Torrance spends 16$ on his brother
Step-by-step explanation:
You have 100$
So, we have
x (brother) + x (sister) + x (mother) = 100
But, since 10$ less will be spent on the sister than the brother, it becomes (x - 10) and twice + 6$ is spent on the mom, it also becomes (2x + 6)
Our equation then becomes
(x - 10) + x + (2x + 6) = 100
X will end up equaling 26. This is how much is spent on the sister.
(x - 10) will be substituted for (26 - 10), which equals 16.
I'm not sure if this is right so you might want to check with somebody (since I may be wrong) I hope this helps you understand how to basically do it though. <3
Which of the following has the solution set
{}?
o |x| > 5
o |x| < -5
o |x|< 10
o |x|> -10
Answers
Answer:
why?
Step-by-step explanation:
In a data set, the number of items that are in a particular category is called the.
Answers
In a data set, the number of items that are in a particular category is called the frequency
What is frequency?Frequency can be defined as the number of items that are in a particular category in a data set.
It is also described as the number of times the value \appears in the data set.
The distribution of a variable is defined by the pattern of frequencies, this means that, the set of all possible values and the frequencies associated with these values
Frequency distributions are also portrayed as frequency in tables or charts,
It is also important to note that relative frequency is the proportion of items in a particular category in a data set.
Hence, it is the frequency
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What is the range?
-2 -4 -4 -2 3 5
Answers
Answer:
9
Step-by-step explanation:
you do the max- min. so 5-(-4) which is really 5+4=9
Answer:1. range(1,10,2) - 1 to 9 with a gap of 2 numbers each so it yields - 1,3,5,7,9 2. [-2,-4,-6,-8,-10] - range(-2,-11,-2) 3. (i) range(4,20)[2:5] - Generates the list of number…
example: 1.What sequence of numbers is equivalent to the given ranges?
range(1,10,2)
2.Express the following as a range.
[-2,-4,-6,-8,-10]
3.What do each of these expressions yield?
(1) range(4,20)[2:5] (2) list(range(10,60,4)[-2:1:-4] (3) range(3,12,4)[2]
(4) range(0,9,2)[:] (5) range(2,20)[-2:-10:-1] (6) range(3,18,2)[::2]
(7) range(1,33,6)[1::2] (8)range(-5,20,3)[-8:5:2]
Evaluate:
–7.68 (–1.6)
A. –48
B. –4.8
C. 4.8
D. 48
Answers
In conclusion answer is D for anyone who did not read explanation above
Your Answer Should Be C.
graph the basic exponential function helpp pleasereeeeee
Answers
Answer:
Step-by-step explanation:
The red one is g(x)=2^x+4
The blue one is f(x)=2^x-1 exponential function
How do you find the probability of getting one correct?
Answers
Answer: The probability she gets at least one right is 1 minus this, or 0.988470785. In other words, she has an approximately 99% chance of getting at least one right.
Step-by-step explanation: IF CORRECT MARK ME BRAINLIEST
Please answer this (who ever answers correctly gets brainlest)
Answers
Answer:
5 and 1/3 yards = 16 ft
So 16 ft + 2 extra ft
The total is 18 ft (C.)
Find the common ratio of the geometric sequence 11, -55, 275,...11,−55,275,...
Answers
Answer:
r = -5
Step-by-step explanation:
common ratio (r) is found be dividing one term by its preceding term:
r = 275 ÷ -55 = -5
or, r = -55 ÷ 11 = -5
Therefore, r = -5
A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t2+120t +6, where h(t) represents the height, in feet, and t is the time, in seconds. Find the average rate of change from the initial launch to the maximum height.
Answers
Answer:
60
Step-by-step explanation:
The given function is:
The average rate of change of h(t) from t=a to t=b is given by:
We can rewrite this function as:
The maximum height of the rocket is 231 and it occurs at t=3.75
The initial launch occurs at: t=0
and
The average rate of change from the initial launch to the maximum height is
The average rate of change from the initial launch to the maximum height is 59.21 ft/s.
We have a equation that represents the Rocket path.
We have to find the average rate of change from the initial launch to the maximum height.
What do you mean by a Time - varying quantity ?A time varying quantity is the quantity whose absolute value change with time. For example - y = f(t) = 2t - 1 , where y is the displacement and it varies as y = 2t - 1 with time.
According to the question, we have -
Equation → [tex]h(t) = -16t^{2} +120t+6[/tex]
Height of podium → 6 feet.
Initial velocity (u) = 0
Now -
[tex]h(t) = - 16t^{2} +120t+6[/tex]
Differentiating w.r.t time, we get →
[tex]$\frac{dh}{dt} = - 32t + 120[/tex]
For maximum height → [tex]$\frac{dh}{dt} = 0[/tex]
-32t + 120 = 0
32t = 120
t = 3.8 seconds
This means that at t = 3.8 seconds the rocket will reach its maximum height. Therefore, the maximum height will be -
h(t) = - 16 x 3.8 x 3.8 + 120 x 3.8 + 6
h(t) = - 231.04 + 456 + 6
h(t) = 224.96 + 6
h(t) = 230.96 = 231
The maximum height reached by the rocket is 231 feet's.
Now -
Initial height = 6 feet
Initial time = 0 s
Final height (max) = 231
Time at maximum height = 3.8
Therefore, the average rate of change from the initial launch to the maximum height will be -
[tex]$v_{avg} = \frac{231-6}{3.8-0}=59.21[/tex]
v (avg) = 59.21 ft/s
Hence, the average rate of change from the initial launch to the maximum height is 59.21 ft/s
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Calculate the area of the right triangle that has vertices at A(626, 200), B(726, 200), and (025,10)
Answers
Answer:
Calculate the area of the right triangle that has vertices at A(626, 200), B(726, 200), and (025,10)
I need some help with this one.
Answers
Answer:
B
Step-by-step explanation:
In the middle of the kite, there are 4 angles that are the same (90*)
So using the given angle 54 and the 90* we can find the last angle
54 + 90 = 144
180 - 144 = 36
The left-over angle is 36*
Given that 10 cm is approximately equal to 4 inches, which of the following expressions models a way to find out approximately how many inches are equivalent to 350 cm?
A
350×(104)
B
350×(410)
C
(10−4)×350
D
(350−10)×4
Answers
Answer: I don't Know
Step-by-step explanation: Thanks for the point tho :)
7(4g) + 3(5h) + 2(-3g); for g=1/2 ;.h =1/3
Helpppp
Answers
Answer:
16
Step-by-step explanation:
7(4g) + 3(5h) + 2(-3g); for g=1/2 ;.h =1/3
28g + 15h - 6g =
= 22g + 15h
= 22(1/2) + 15(1/3)
= 11 + 5
= 16
Explanation:
7(4•1/2)+3•(5•1/3)+2(-3•1/2) =
7•2+3•5/3+2(-3/2) =
14+5-3=
=16
I need help please
Answers
Answer:
1+1=2
Step-by-step explanation:
Line m passes through point (-2,-1) and is perpendicular to the graph of y=-2/3x+6. Line n is parallel to line m and passes through the point (4,-3). What is the equation in slope-intercept form of line n?
Answers
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{2}{3}} x+6\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
well, we know that "m" is perpendicular to the line above, so that means that line "m" has a slope of
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{-\cfrac{2}{3}} ~\hfill \stackrel{reciprocal}{-\cfrac{3}{2}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{3}{-2}\implies \cfrac{3}{2}}}[/tex]
keeping in mind that parallel lines have exactly the same slope, and since we know that "n" is parallel with "m", that means that if "m" has a slope of 3/2 than "n" must have the same slope.
so we're really looking for the equation of a line whose slope is 3/2 and passes through (4 , -3)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad \qquad \stackrel{slope}{m}\implies \cfrac{3}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{3}{2}}(x-\stackrel{x_1}{4}) \\\\\\ y+3=\cfrac{3}{2}x-6\implies y=\cfrac{3}{2}x-9[/tex]
What is the y‐intercept of the graph of y=5x ?
5
1
25
0
Answers
Answer:
0 is your y intercept and 5 is the x intercept
Research done in the mid 1980s indicated that 80% of grizzly bears in the greater ecosystem of Yellowstone National Park entered their den for hibernation by the last day of November. This has come into question as of late. Researchers have hypothesized that climate change has postponed bears entering hibernation until later in the season; that is, researchers believe that a smaller percentage of bears are entering their den for hibernation by the last day of November. Sixty-two Yellowstone grizzly bears were tracked via radio monitors, which allow scientists to pinpoint when the bears enter their dens with a high degree of accuracy. Of the sixty-two Yellowstone grizzly bears being tracked, forty-two entered their den for hibernation by the last day of November.
What values would you enter for each of the following in the One Proportion applet to conduct a simulation-based hypothesis test with these data?
Answers
The sample size that's given is 62 and the probability of success will be 0.68.
How to calculate probabilityFrom the complete question, it can be noted that the sample size that's given is 62 while the number of samples is 42.
In this case, the probability of success will be:
= Number of samples / Sample size
= 42/62 = 0.68
In conclusion, the probability of success is 0.68.
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If $5000 is invested at a rate of 3% interest compounded
quarterly, what is the value of the investment in 5 years?
(Use the formula A = P (1 + )", where A is the amount
accrued, P is the principal, r is the interest rate, n is the
number of times per year the money is compounded, and t
is the length of time, in years.)
Answers
Answer:
$5805.92
Step-by-step explanation:
A= P(1+i)^n
= 5000(1+3%/4)^5×4
=$5805.92
Under her cell phone plan, Leah pays a flat cost of $42 per month and $4 per
gigabyte. She wants to keep her bill at $48.80 per month. Write and solve an
equation which can be used to determine g, the number of gigabytes of data Leah can
use while staying within her budget.
Answers
Our goal is to isolate g. We can do that by subtracting 42 from both sides. This gives us 4g = 6.8. Then, we need to divide both sides by 4. This gives us g = 1.7.
The equation we can use to represent this situation is 4g + 42 = 48.80, and she can only spend 1.7 gigabytes or less to stay within her budget. (I am not sure if 1.7 should be rounded, but if so, it should be rounded down to 1.)
Prem has $45000 to invest for 1 year. The bank tells him the interest rate is 6%. Calculate how much the investment is worth at the end of the year…
1) If the interest is paid every 6 months
2) If interest is paid quarterly
Answers
Answer:
1) $47,740.50
2) $47,761.36
Step-by-step explanation:
hope this helps :)
Find the magnitude of the vector (2,-5).
Write your answer in simplified radical form.
Answers
[tex] \rm \hookrightarrow \: \sqrt{ {2}^{2} + { - 5}^{2} } [/tex]
[tex] \rm \hookrightarrow \: \sqrt{4 \: \: \: \: + \sqrt{ 25 }}[/tex]
[tex] \rm \hookrightarrow \: \sqrt{29 }[/tex]
[tex] \rm \hookrightarrow \: 5.38 [/tex]
What is the slope of the line that passes through the points (4,7) and (7, 16)? Write
your answer in simplest form.
Answers
Your answer would be either:
[tex]\frac{3}{1}[/tex] or just 3
Step-by-step explanation:
To solve, we used Rise over run [tex]\frac{rise}{run}[/tex]
m = [tex]\frac{16-7}{7-4}[/tex] we get 9/3 and simplify it to 3/1 or 3
3(x-2)
I don’t know how to do this
Answers
Answer:
3x - 6 should be it
3(x-2) ;expand the linear equation
=3x-6
Which equation is equivalent to 16x−8+2x=100?
Answers
Answer: X=6.
Step-by-step explanation:
16x-8+2x=100
18x-8=100
18x=100+8
18x=108
x=108/18
x=6
Answer:
14x-8
Step-by-step explanation:
another equation is 14x-8=100
combine like terms