An input-output machine generates the information below
a- Find the values to fill in the table for variables a and b
b- write up a rule that describes the relationship between the input output.
c- what is the value of the output and input in 20?
d- what is the value of the input when the output is 77.
Answers
Using a linear function, we have that:
a) The values are: a = 11 and b = 5.
b) The rule is:
[tex]y = 3x + 2[/tex]
c) The value of the output is 62.
d) The value of the input is 25.
The equation of a linear function is given by:
[tex]y = mx + b[/tex]
In which
m is the slope, which is the rate of change.b is the y-intercept, which is the initial value.First, we are going to solve item b to find the rule, then we solve other items.
Item b:
In the table, we have two points: (1,5) and (2,8).
The slope is given by change in y divided by change in x, thus:
[tex]m = \frac{8 - 5}{2 - 1} = 3[/tex]
Then
[tex]y = 3x + b[/tex]
Point (1,5) means that when [tex]x = 1, y = 5[/tex], and this is used to find b.
[tex]5 = 3(1) + b[/tex]
[tex]b = 2[/tex]
Thus, the rule is:
[tex]y = 3x + 2[/tex]
Item a:
a is the value of y when x = 3, thus:
[tex]y = a = 3(3) + 2 = 11[/tex]
Thus, a = 11.
b is the value of x when y = 17, thus:
[tex]3b + 2 = 17[/tex]
[tex]3b = 15[/tex]
[tex]b = 5[/tex]
The values are: a = 11 and b = 5.
Item c:
The value of the output is y when x = 20, thus:
[tex]y = 3(20) + 2 = 60 + 2 = 62[/tex]
Thus, the value of the output is 62.
Item d:
The value of the input is x when y = 77, thus:
[tex]3x + 2 = 77[/tex]
[tex]3x = 75[/tex]
[tex]x = \frac{75}{3}[/tex]
[tex]x = 25[/tex]
The value of the input is 25.
A similar problem is given at https://brainly.com/question/25004958
Related Questions
1. What is the equation, in standard form, of a parabola that contains the following points? (1 point)
(-2, 18), (0.2). (4, 42)
Oy=-222 - 2x - 3
Oy=-3x2 + 2x - 2
Oy = 3x2 - 2x + 2
Oy=-2x2 + 3x + 2
Answers
Answer:
y=3x2−2x+2
Step-by-step explanation:
Standard form of equation of a parabola is [tex]y=ax^2+bx+c[/tex]
As it passes through points (−2,18), (0,2) and (4,42), each of these points satisfies the equation of parabola and hence
18=a⋅4+b⋅(−2)+c or 4a−2b+c=18 ........(A)
2=c ........(B)
and 42=a⋅16+b⋅4+c or 16a+4b+c=42 ........(C)
Now putting (B) in (A) and (C), we get
4a−2b=16 or 2a−b=8 and .........(1)
16a+4b=40 or 4a+b=10 .........(2)
Adding (1) and (2), we get 6a=18 or a=3
and hence b=2⋅3−8=−2
Hence equation of parabola is [tex]y=3x^2 -2x+2[/tex] and it appears as shown below
graph{3x^2-2x+2 [-10.21, 9.79, -1.28, 8.72]}
2²×2³×2⁸×2⁹+10+20²+10+10+10
Answers
___________
[tex] \: [/tex]
[tex]\boxed{ \rm{answer \: by \: { \boxed{ \rm{☆HayabusaBrainly}}}}}[/tex]
2² × 2³ × 2⁸ × 2⁹ + 10 + 20² + 10 + 10 + 10
= 2²² + (10 × 4) + 400
= 4.194.304 + 40 + 400
= 4.194.304 + 440
= 4.194.744✔
Answer:
(2²×2³×2⁸×2⁹)+10+20²+10+10+10=
=2²+³+⁸+⁹ + 10 + (20 x 20) +(10+10+10)
=2²² + 10 + 400 + 30
=4.194.304 + (410 + 30)
=4.194.304 + 440
=4.194.744
The basketball court in the park is rectangular two of the size of 84 feet long and the other two sides of 50 feet long what is the permit perimeter of the basketball
Answers
Answer:
8400
Step-by-step explanation:
84 x 50= 4200
84 x 50 = 4200
4200+4200= 8400
mathematics algebra sat
Answers
Answer:
D
Step-by-step explanation:
[tex]\frac{3}{5}[/tex] w = [tex]\frac{4}{3}[/tex] , that is
[tex]\frac{3w}{5}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )
9w = 20 ( divide both sides by 9 )
w = [tex]\frac{20}{9}[/tex] → D
the answer is w = 20/9
what is 26 divided by 9 as an improper fraction
Answers
Answer:
26/9
Step-by-step explanation:
26/9 is correct because it cannot be simplified so it is left as 26/9
What do I do when the output doesn't have a constant rate of change?
Answers
-2 gal/min
sry if it wrong
..........................................
Answers
Answer:
5678
Step-by-step explanation:
yeeeeeeeeeeeeeeeeeeeeeeee
leanna finds a buy two get one free sale at her favorite store. her purchases cannot exceed $100. A skit orginally sells $22. What is the greatest number of skirts that she can get.
Answers
6
her order can't exceed 100
and if she buys 2 she gets 1 free
each one costs 22
so she can get 6 skirts for 88 which is the highest it can go
Evaluate the expression −t/u+vw , where t = 2, u=−2/3 , v=−1 , and w=−1/3 .3 1/31 2/3−2 2/3
Answers
Answer:
The answer is 3 1/3
The value of the expression −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that,
The expression is:
= −t/u+vw
The values of t = 2, u=−2/3 , v=−1 , and w=−1/3
After pluggin the values of t, u, v, and w in the above expression we get:
= -2/(-2/3) + (-1)(-1/3)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
= 3 + 1/3
= 3 1/3 (in mixed fraction)
Thus, the value of the expression −t/u+vw is 3 1/3 after pluggin the values of t, u, v, and w in the expression.
Learn more about the expression here:
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3 1/3
what are the two integers
Answers
Answer:
3 and 4
Step-by-step explanation:
2^3 = 8
2^4=16
14 lies in between them
Rolling a six sidded die and getting a I or 5
Answers
Answer:
probability is the same
calculate log 1.125 please
Answers
Answer:
0.05115
Step-by-step explanation:
Plug it into your calculator and you'll get the same value
Find the equation of the line with slope m=−5/3 that contains the point (9,−15).
Answers
Answer:
y=-5/3x
Step-by-step explanation:
y = -5/3x+b
-15 = -5/3(9)+b
-15=-15+b - Add 15 to both sides
0 = b
What is the smallest distance between the origin and a point on the graph of:y=1/sqrt(2)*(x^2-8)
Answers
f
(
x
)
=
√
x
as
y
=
√
x
.
Now, what is this "distance?" How do we find it? Well, if you think back to Algebra I or Geometry, you'll remember that the distance between two points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is given by:
√
(
y
2
−
y
1
)
2
+
(
x
2
−
x
1
)
2
. For example, the distance between the points
(
4
,
0
)
and
(
0
,
3
)
would be:
√
(
3
−
0
)
2
+
(
4
−
0
)
2
=
√
9
+
16
=
√
25
=
5
Ok, so what is
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
in our example?
(
x
1
,
y
1
)
is simple - it's just the point given in the problem,
(
4
,
0
)
. Because we don't know what
x
2
is, we'll just call it
x
for now. As for
y
2
, we don't know that either; and since
y
=
√
x
, we'll call it
√
x
.
Our formula then becomes:
√
(
√
x
−
0
)
2
+
(
x
−
4
)
2
=
√
(
√
x
2
)
+
x
2
−
8
x
+
16
=
√
x
+
x
2
−
8
x
+
16
=
√
x
2
−
7
x
+
16
We are being asked to minimize this distance, which we'll call
s
to make the following calculations easier. To minimize something, we have to take its derivative, so let's start there:
s
=
√
x
2
−
7
x
+
16
=
(
x
2
−
7
x
+
16
)
1
2
d
s
d
x
=
(
2
x
−
7
)
⋅
1
2
(
x
2
−
7
x
+
16
)
1
2
→
Using power rule and chain rule
d
s
d
x
=
2
x
−
7
2
√
x
2
−
7
x
+
16
Now we set this equal to
0
and solve for
x
:
0
=
2
x
−
7
2
√
x
2
−
7
x
+
16
0
=
2
x
−
7
x
=
7
2
This is known as the critical value, and it represents the
x
-value for which the function is minimized. All we need to do now is find the corresponding
y
-value, using the definition of
y
:
y
=
√
x
. Substituing
7
2
for
x
:
y
=
√
7
2
y
≈
1.87
And voila, the
y
-value. We can now say that the minimum distance between
f
(
x
)
=
√
x
and the point
(
4
,
0
)
(the place where these two are closest) occurs at
(
7
2
,
1.87
)
. For a little extra fun, we can use the distance formula to see what the actual distance between the points is:
s
=
√
(
1.87
−
0
)
2
+
(
7
2
−
4
)
2
≈
1.8
units
From the fig. find the angle which is equal to 110˚. *
1 point
∠A
∠C
∠D
none of the above
Answers
Answer:
∠C is equal to 110⁰ (alternate interior angles)
Step-by-step explanation:
Pls mark as brainliest
literally the only question I'm struggling to understand rn...i hate puzzles :C.
Answers
Answer:
It's 2 4 7
Step-by-step explanation:
The first column says "one number is correct and well placed," so it's number two, because the third column says "One number is correct but incorrectly placed," which means number 2 is in the same place, and number 4 is in the last, but the fourth column says "Two numbers are correct but incorrectly placed," means 4 and 7 are in the first and second columns, but supposed to be in the 2nd and 3rd place, respectively. As a result, it's 2, 4, 7, and I hope you understand because I'm terrible at explaining things.
If maya had 1/5 of a cup of butter and she used that cup to make 2/3 of butter cake how much butter was left in her cup?
Answers
Answer:
7/15 was left in her cup or 0.46
Step-by-step explanation:
Maya used 1/5 to make a 2/3 butter cake, so you would subtract 1/5 from 2/3
2/3-1/5=7/15
Solve for x in terms of h and k:
2(2x - h) - k = 6
Answers
Answer:
Well what i got was x= 3/2 + h/2 + k/4= 6+ 2h+k=4
I'm not sure if that exactly helps but it's what i got
Step-by-step explanation:
9.6 + 7.9u − 0.16 = –9.31 − 4.6u?
Answers
Answer:
u = -1.5
9.6 + 7.9(-1.5) − 0.16 = –9.31 − 4.6(-1.5)
-2.41 = -2.41
Step-by-step explanation:
I used a calculator, pls let me know if im incorrect
Can someone help me I’m doing a khan academy and need help ASAP marking brainliest
Answers
Answer:
x = 180 - 89 = 91
Step-by-step explanation:
A- 63
B- 125
C-44
D-45
Answers
Answer:
So, the sum of the 3 angles in a triangle is 180.
What you would do is:
180= 73+6x-4+7x+7.
Then, you add the common coefficients:
180=76+13x
Then you subtract:
104=13x
Then you divide:
x=8.
Then substitute the x value into the A value to get 44, meaning that C is the correct answer.
Wrong and silly answer will be reported .
Answers
I HOPE IT WILL HELP YOU.
Thank you.
B is the midpoint of AC. C is the midpoint of AD. Find the coordinates of B and D given the coordinates of A (-2,5) and the coordinates of C (8,7).
Answers
B= (3,6) and D= (18,9)
Step-by-step explanation:
To find the midpoint of two given points add X1 and X2 together, then divide by 2 to get the X value of the midpoint and do the same thing for the Y value. That will get you B. From there you can see to get from point A to point C you add 10 to the x value and add 2 to the y value. Because C is the midpoint just double what you had to add to get point D (add 20 to x and add 4 to y)
Homework Progress
579 Marks
Aplo of sand has a weight of 90 kg.
The sand is put into a small bag, a medium bag and a large bag
in the ratio 2:3:7.
Work out the weight of sand in each bag.
Answers
Answer:
77
Step-by-step explanation:
2:3:7.
Given: PQ = RS; PQ|| RS
Prove: PQRS is a parallelogram
Answers
Answer:
If PQRS is a parallelogram, then — PQ ≅ — RS and — QR ≅— SP . If a quadrilateral is a parallelogram, then its opposite angles are congruent. If PQRS is a parallelogram, then ∠P ≅ ∠R and ∠Q ≅ ∠S.
PQ=RS and PQ||RS implies PQRS is a parallelogram by showing that the diagonals bisect each other at O.
What is a parallelogram?
A quadrilateral with opposite sides equal and parallel but the angles are not right angle is called parallelogram.
Given that PQ=RS and PQ||RS .
Draw the parallelogram PQRS as in figure
To prove: PQRS is a parallelogram.
Construction: Join PS and QS as diagonals.
From the ΔORS and ΔOPQ,
PQ=RS (Given)
∠SOR=∠POQ (opposite angles)
∠PQO=∠OSR (since PQ=RS and PR is a traversal)
∴ΔOQS≅ΔOPQ
Hence, Op=OR and OQ=OS
Therefore , the diagonal of quadrilateral PQRS bisects each other.
Hence the given quadrilateral PQRS is a parallelogram.
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Marie is reading a 271-page book. She has already read 119 pages. If she reads
at about 8 pages per hour, how long will it take her to finish the book?
Which equation helps to solve this problem?
Answers
Answer:
119+8h=271
Step-by-step explanation:
We already know she has read 119 pages out of 271. And we know the constant proportionality in this is 8 pages every hour. If we were able to find out how long it took for her, then we would add that with 119, because that, in total, will be 271/the whole book, with 152 pages of it in hours.
sorry if this doesn't make sense, if you want me to explain more on it go ahead and ask!
HELP ASAP I NEED THIS IN ONE HOUR WILL REPORT WRONG ANSWERS
A new drill is used to dig a hole in the ground. At noon, the hole is 13.2 feet deep when the new drill is turned
on for the first time that day. At 2 p.m., the drill has dug the hole to be 42 1/4 feet deep. The new drill dug
1.5 times as much of the hole as the old drill would have in the same length of time.
(a) What expression represents the number of feet the new drill dug?
(b) How many feet would the old drill have dug in the same length of time? Show your work. Answer the
question in a complete sentence.
Answers
Answer:
(a) 42.25 - 13.2
(b) The old drill would have dug 19.367 ft in the same length of time (2 hours).
Step-by-step explanation:
(a) In the two hours, 12 Noon to 2 p.m., the new drill dug
42.25 - 13.2 =
29.05 feet.
(b) Let r = the old drill dig rate in units of ft/hour
Then, 1.5r = the new drill dig rate.
So, 1.5r (2 hours) = 29.05, so that
r = (29.05)/(1.5 * 2) = 9.6833333 ... ft/hour.
So, the answer is: 9.683333 ... * 2 = 19.367 ft, rounded to the nearest 1000th. Thus, the old drill would have dug 19.367 ft in the same length of time (2 hours).
The required expression and the length of hole are 1.5( 42(¹/₄) - 13.2) and 43.57 feet respectively.
What is Unitary method?In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.
The given problem can be solved by unitary method as follows,
(a) The expression that represents the length of hole dug by new drill is given as,
The length of hole dug by old drill in 2 hours is given as,
42(¹/₄) - 13.2
For new drill it is 1.5( 42(¹/₄) - 13.2) feet.
(b) The length of drill dug by old drill is,
42(¹/₄) - 13.2
= 42.25 - 13.2
= 43.57 feet.
Hence, the expression for hole length by the new drill and the length of hole dug by old drill are given as 1.5( 42(¹/₄) - 13.2) and 43.57 feet respectively.
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Pls help will mark brainliest, no fake answers
Answers
Step-by-step explanation:
b = what Bernie earns per day = Php 1000
m = what Mitch earns on a given day
e = what Eugene earns on a given day
r = what Rowan earns on a given day
a.
t = the total earnings of Bernie and Mitch on a given day
t = m + 1000 (or m + b)
b.
e = m/2
c.
r = 2×(m + 1000) or 2×t
Please help me with this. Please dont just type in the wrong answer to get points. I will give 30 points to anyone who answers correctly and i will mark you as the brainliest so you will get rewarded.
Answers
it is 53cm because it says beside the d 53cm and it the length
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please need help asap
Answers
Answer:
30 = 6 x 5
g = 5
I think that might be the answer
Step-by-step explanation:
Answer: g x 6 = 30
5 times 6 is 30, so g is 5.