Determining the Input Value to Produce the Same Output Value for Two Graphed Functions A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (negative 1, 2), (0, 2), and (2, 2). The second line is labeled y equals g(x) and passes through (negative 0.5, negative 2), points at (0, negative 1), and (1, 1). The lines intersect at (1.5, 2). Use the graph to determine the input value for which f(x) = g(x) is true. x = 0.5 x = 1 x = 1.5 x = 2
Answers
Y equals f(x) is written on the first line, The second line, marked y = g(x). When the input is for either of the two functions, the result is x=0 and return the output is same value.
Given that,
Y equals f(x) is written on the first line, which also passes through (-1, 2), (0, 2), and (2, 2). The second line, marked y = g(x), points at (0, -1), passes through (-0.5, -2), and (1, 1). The lines come together at (1.5, 2).
We have to find the input value for which f(x) = g(x) is true using the graph. x = 0.5, x = 1, x = 1.5, x = 2.
The final two actions:
f(x)=-2/3(x+1)
g(x)=1/3(x-2)
The output are equation
f(x)=g(x)
-2/3(x+1)=1/3(x-2)
-2(x+1)=1(x-2)
-2x-2=x-2
-2x-x=-2+2
-x=0
x=0
When x = 0 is used as an input, the first two functions always return the same results.
f(x) traverses (-1,2), (0,2), and (2,2)
The paths that g(x) takes are (-0.5,-2), (0,-1), (1,1)
Therefore, When the input is for either of the two functions, the result is x=0 and return the output is same value.
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make it simple its x=1.5
Related Questions
What is the slope of a line that passes through the ordered pairs (0,1) and (3,5)?
Answers
The slope of a line that passes through the ordered pairs (0,1) and (3,5) would be m = 4/3.
What is the slope of a line which passes through points ( p,q) and (x,y)?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal. Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.
Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
WE have been given line that passes through the ordered pairs (0,1) and (3,5).
Slope = m
Therefore,
[tex]m = \dfrac{y-q}{x-p}\\\\m = \dfrac{5 -1}{3-0}\\\\m = \dfrac{4}{3}[/tex]
Hence, the slope of a line that passes through the ordered pairs (0,1) and (3,5) would be [tex]m = \dfrac{4}{3}[/tex].
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Does anyone know where the a in front of the parentheses for the LCD : a(a+5)(a-6) came from?
Thank you!
Answers
Answer:
See below
Step-by-step explanation:
If you factor [tex]a^2-a-30[/tex] you get [tex]\left(a^2+5a\right)+\left(-6a-30\right)[/tex]
= [tex]a(a+5)-6(a+5)[/tex]
= [tex]a(a+5)(a-6)[/tex]
That's where the a comes in
Not sure if that answers your question
Solve −3 = x/4 + 5 using the replacement set {−32, 8, 32} .
A. −32
B. 8
C. 32
D. I don't know.
Answers
Answer:
A
Step-by-step explanation:
substitute the values from the replacement set into the right side of the equation to find which values of x make the equation true.
x = - 32
[tex]\frac{-32}{4}[/tex] + 5 = - 8 + 5 = - 3 ← True
x = 8
[tex]\frac{8}{4}[/tex] + 5 = 1 + 5 = 6 ≠ - 3 ← False
x = 32
[tex]\frac{32}{4}[/tex] + 5 = 8 + 5 = 13 ≠ - 3 ← False
the solution is therefore x = - 32
A survey of 541 adults aged 18-24 year olds was conducted in which they
were asked what they did last Friday night. It found:
181 watched TV
• 180 hung out with friends
• 150 ate pizza
• 46 watched TV and ate pizza, but did not hang out with friends
• 36 watched TV and hung out with friends, but did not eat pizza
• 29 hung out with friends and ate pizza, but did not watch TV
• 25 watched TV, hung out with friends, and ate pizza
How may 18-24 year olds did not do any of these three activities last Friday
Answers
Answer: 30
Step-by-step explanation:
181+180+150=
361+150=511
541-511=30 18-24 year olds
**46 of 181 students that watched TV ate pizza and the same 46 students of the 150 students that ate pizza watched TV.
PLEASE HELP!!!What is the effect on the graph of
f(x)=∣x∣when the function is changed to g(x)=∣3x∣+1?
A.
The graph is compressed vertically and shifted to the right 1 unit.
B.
The graph is stretched vertically and shifted to the left 1 unit.
C.
The graph is stretched horizontally and shifted up 1 unit.
D.
The graph is compressed horizontally and shifted up 1 unit.
Answers
Answer:
24
23fc
23
45jh4
66
35g
35
56
34
Does 7*10 to fifth power equal 7*100,000?
Answers
Step by step
7x 10^5 = 700,000
7 x 100,000 = 700,000
This is a positive power of 10 so you move the decimal point 5 places to the right
7.
Becomes
700,000
And 7 x 100,000
Becomes
700,000
Lucy paid $120 for an item at the store that was 20 percent off the original price. what was the original price?
Answers
Answer:
$150
Step-by-step explanation:
Given the following question:
Lucy paid 120 dollars for an item
The item was 20% off
What was the original price? To find the original price we will need to use the formula to calculate percentages.
20% of 150
[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{20\times150}{100}[/tex]
[tex]20\times150=3000[/tex]
[tex]3000\div100=30[/tex]
[tex]150-30=120[/tex]
[tex]=120[/tex]
Which means our original price is "$150."
Hope this helps.
A theater charges $8 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $5200. At one show, 25% of the main-floor seats and 50% of the balcony seats were
income was $1800 How many seats are on the main floor and how many are in the balcony?
Answers
By solving a system of equations we can see that there are 400 main-floor seats and 500 balcony seats.
How many seats are on the main floor and how many are in the balcony?Let's define the two variables:
x = number of seats on the main-floor.y = number of balcony seats.We know that if all the seats are sold, then the total income is $5,200, we can write the equation:
x*$8 + y*$4 = $5,200
And if 25% of the main-floor and 50% of the balcony seats are sold, then we get an income of $1800, then we can write:
0.25*x*$8 + 0.5*y*$4 = $1,800
x*$2 + y*$2 = $1,800
So we have a system of equations:
x*$8 + y*$4 = $5,200
x*$2 + y*$2 = $1,800
If we subtract twice the second equation for the first one we get:
(x*$8 + y*$4) - (x*$2 + y*$2) = $5,200 - 2*$1,800
x*$4 = $1,600
x = $1,600/$4 = 400
So there are 400 seats on the main-floor.
Using the first equation we can find:
x*$8 + y*$4 = $5,200
400*$8 + y*$4 = $5,200
$3,200 + y*$4 = $5,200
y*$4 = $5,200 - $3,200 = $2,000
y = $2,000/$4 = 500
So there are 500 balcony seats.
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Which measurement is closest to 270 cm: 9ft, 680in. or 270 in.?
Answers
The measurement 9 feet is closest to 270 centimeters.
What measure is equivalent to another measure?
In this problem we have a case of unit conversions, in which we must find what measure in a unit offers the best approximation to other represented in other unit. Please notice that a centimeter equals 25 / 762 feet and 50 / 127 inches. Now we proceed to calculate the equivalent quantities in feet and inches by simple rule of three:
x = 270 cm × (25 / 762 feet / cm)
x ≈ 8.858 feet
x = 270 cm × (50 / 127 inches / cm)
x ≈ 106.299 inches
The measurement 9 feet is closest to 270 centimeters.
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Homework 4.3 Partial Derivatives
Answers
If Partial Derivatives f(x,y) -8e^4x sin(7y) is 32 e^(4 x) sin(7 y) and
56 e^(4 x) cos(7 y)
Partial Derivatives
d/dx(8 e^(4 x) sin(7 y))
Factor out constants:
= 8 (d/dx(e^(4 x))) sin(7 y)
Using the chain rule, d/dx(e^(4 x)) = (d e^u)/(du) (du)/(dx), where u = 4 x and d/(du) (e^u) = e^u:
= e^(4 x) (d/dx(4 x)) 8 sin(7 y)
Factor out constants:
= 4 (d/dx(x)) 8 e^(4 x) sin(7 y)
Simplify the expression:
= 32 e^(4 x) (d/dx(x)) sin(7 y)
The derivative of x is 1:
= 32 e^(4 x) sin(7 y)
Simplify the expression:
32 e^(4 x) sin(7 y)
Part 2:
Partial Derivatives
d/dy(8 e^(4 x) sin(7 y))
Factor out constants:
= 8 e^(4 x) (d/dy(sin(7 y)))
Using the chain rule, d/dy(sin(7 y)) = (dsin(u))/(du). (du)/(dy), where u = 7 y and d/(du) (sin(u)) = cos(u):
= cos(7 y) (d/dy(7 y)) 8 e^(4 x)
Factor out constants:
= 7 (d/dy(y)) 8 e^(4 x) cos(7 y)
Simplify the expression:
= 56 e^(4 x) cos(7 y) (d/dy(y))
The derivative of y is 1:
= 56 e^(4 x) cos(7 y)
Simplify the expression:
56 e^(4 x) cos(7 y)
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Your cell phone plan costs $24.99 per month plus $0.19 for each text message you send or receive. You have at most $34 to spend on your cell phone bill. What is the maximum number of text
messages that you can send or receive next month?
The maximum number of text messages is
Answers
Answer:
33
messages
Step-by-step explanation:
Draw AABC with vertices at A(1,6), B(1, 1) and C(5, 1). In this triangle, AB²+ BC² = AC².
Next, use the GeoGebra tools to draw ADEF such that AB = DE, m/E = 90°, and
EF = BC.
Paste a picture of your drawing in the answer box.
Answers
The picture of the triangle ΔDEF is attached below.
A triangle can be defined as a basic polygon which has 3 sides.
The sum of all the interior angles of a triangle is given by 180°.The area of any triangle is calculated by [tex]\frac{1}{2}[/tex] × base × height.In a right-angled triangle the side opposite the largest angle which is 90° is called the hypotenuse.Pythagoras' theorem states that the sum of the squares of the legs of aright-angles triangle is equal to the square of the hypotenuse of the triangle.In the given ΔABC we see that AC is the hypotenuse and the two sides AB and AC are the legs of the triangle.
m∠B=90°
The ΔDEF is drawn such that m∠E=90° and AB=DE and EF=BC .
Therefore we can say that the two triangles are congruent by SAS axiom of congruency.
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Write a function g whose graph represents the indicated transformation of the graph of f.
f(x) = 3x ; translation 5 units up
the translated function is g(x) =
Answers
Answer:
g(x) = 3x +5
Step-by-step explanation:
You want the function that results from translating f(x) = 3x upward by 5 units.
TranslationThe y-coordinate of a point tells how far above the x-axis it is. Adding 5 to the y-coordinate will move that point 5 units farther above the x-axis, which is to say 5 units upward.
The y-coordinate of a point on a graph is the value of the function of the x-coordinate of that point. That is, each point is (x, f(x)). If we want to translate that point 5 units upward, we add 5 to the function value:
(x, f(x) +5) . . . . . graph translated 5 units up
Using the given definition of f(x), this becomes ...
(x, 3x +5)
The translated function is defined as g(x), so we have ...
(x, g(x)) = (x, 3x +5)
or ...
g(x) = 3x +5
if angle 2=6x+8 and angle 4=4x+11 what is the value of angle 2?
Answers
Answer:
17
Step-by-step explanation:
Angle 2 and angle 4 are alternate exterior angles so they congruent angles which means they have same angle measurement.
To find the measure of angle 2 we first need to find the value of x.
And to do that we can write the following equation based on the information we have in hand:
6x + 8 = 4x + 11 transfer like terms to the same side of the equation
6x - 4x = 11 - 8 add/subtract like terms
2x = 3 divide both sides by 2
x = 1.5 now to find the measure of angle 2 replace x with 1.5
6×(1.5)+8 = 17
add 1/2 + 1/4 + 1 1/4
Answers
Answer:
Final answer is 2
Step-by-step explanation:
1/4 = 0.25
1 1/4 = 1.25
1.25 + 0.25 = 1.5 + 0.5 = 2
Amy paid $66.94 for a pair of running shoes during a 15%-off sale. What was the regular price?
...
Answers
$66.94/85 = $0.78752941 x 100 = $78.75
4(xy)² – 2x + 5y for x = 6 and y
=2
Answers
Answer:
574
Step-by-step explanation:
4[12]²-12+10
4(144)-2
576-2
574
Hope this helps!
Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
E (-8,9)
F(-4,9)
G(-4,2)
D(2,-8)
Answers
The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).
A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.
Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:
E'( - 9, - 8 )
When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:
F'( - 9, - 4 )
When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:
G'( - 2, - 4 )
When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:
D'( 8, 2 )
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7. An aircraft flies 400 km from a point O on a bearing of 025°
and then 700 km on a bearing of 080° to arrive at B.
a) How far north of O is B?
b) How far east of O is B?
Answers
Answer:
484 km north858 km eastStep-by-step explanation:
You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.
Coordinate transformationFor some distance r and bearing angle θ, the (north, east) coordinates will be ...
(north, east) = (r·cos(θ), r·sin(θ))
ApplicationFor the trip at hand, the final coordinates of the plane are ...
a)Distance north = (400 km)cos(25°) +(700 km)cos(80°)
= 362.52 km +121.55 km = 484.07 km
B is about 484 km north of O.
b)Distance east = (400 km)sin(25°) +(700 km)sin(80°)
= 169.05 km +689.37 km = 858.41 km
B is about 858 km east of O.
__
Additional comment
Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...
(x, y) = (r·cos(θ), r·sin(θ))
You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.
Write a polynomial equation with integer coefficients that has the given roots.
x = -1 x=-6
Answers
Polynomial equation with integer coefficients that has roots x= -1 and
x = -6 is equal to x² +7x +6=0.
As given in the question,
Given roots for the polynomial equation with integer coefficient are
x = -1 ⇒ x + 1=0
x = -6 ⇒ x + 6 =0
Polynomial equation is
( x + 1) ( x + 6) =0
⇒ x² + 1x + 6x + 6 =0
⇒ x² + 7x + 6 =0
Therefore, polynomial equation with integer coefficients that has roots x= -1 and x = -6 is equal to x² +7x +6=0.
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Can you please help with this
Answers
The fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
How to simplify the given fraction?Here we want to simplify the fraction 24/56. To do so, we need to find the greatest common factor between 24 and 56, to find that, we need to write both of these numbers as a product of their prime factors.
We will get:
24 = 2*2*2*3
56 = 2*2*2*7
We can identify the greatest common factor between parenthesis:
24 = (2*2*2)*3
56 = (2*2*2)*7
So the greatest common factor is 2*2*2 = 8, then we can divide both numerator and denominator by 8, we will get:
24/8 = 3
56/8 = 7
Then the fraction 24/56 can be simplified to 3/7, and we can't keep simplifying this.
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PLEASE HELP!
The data show what an apartment resident paid per month for her electric bill during a calendar year.
$56, $72, $120, $120, $122, $124, $128, $135, $152, $168, $183, $200
Use the data to answer the questions.
What is 1.5 ∙ IQR?
A: 40
B: 60
C: 80
What is the lower boundary?
A: 60
B: 66
C: 120
What is the upper boundary?
A: 160
B: 220
C: 251.5
Which sentence describes the outliers?
A: There are no outliers.
B: The outlier is less than the lower boundary.
C: The outlier is greater than the upper boundary.
Answers
Using the median concept and the quartiles, we have that:
1.5 IQR is: B. 60.The lower boundary is: A. 60.The upper boundary is: B. 220.The sentence that describes the outliers is: B: The outlier is less than the lower boundary.What are the median and the quartiles of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.The first quartile is the median of the first half of the data-set.The third quartile is the median of the second half of the data-set.The interquartile range is the difference between the third quartile and the first quartile.Values that are more than 1.5 IQR from either quartile are considered outliers.In this problem, there are 12 elements, hence:
Q1 is the 0.25 x 12 = 3rd element.Q3 is the 0.75 x 12 = 9th element.Thus, Q1 = 120, Q3 = 160 and the IQR is:
IQR = 160 - 120 = 40.
1.5 IQR is: 1.5 x 40 = 60.
The boundaries are:
120 - 60 = 60. (lower).160 + 60 = 220(upper).There is a value less than 60 in the data set, hence the sentence that describes the outliers is: B: The outlier is less than the lower boundary.
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Answer:
Use the data to answer the questions.
What is 1.5 ∙ IQR? ✔ 60
What is the lower boundary? ✔ 60
What is the upper boundary? ✔ 220
Which sentence describes the outliers? ✔ The outlier is less than the lower boundary.
Step-by-step explanation:
edge 2023
3. Write the number: three hundred
seven thousand, fifty-nine and six
tenths
S
Answers
84x7 complete the equation
Answers
Answer:
The answer to your question is 588
Answer:
588
Hope this helps
At a certain company, the average starting salary s for a new worker is $25,000. The actual salary has an absolute deviation of at most $1800. Write and solve an inequality to find the range of the starting salaries.
Answers
The range of the salary will be the closed interval [23,200, 26,800].
What is an absolute function?The absolute function is also known as the mode function. The value of the absolute function is always positive.
The absolute function is given as
f(x) = | x |
A new hire at one organization may expect to get an average beginning pay of $25,000 per year. The absolute divergence from the real compensation is no more than $1800.
Let 'x' represent the actual salary. Then the inequality is given as,
|x - 25,000| ≤ 1800
- 1,800 ≤ x - 25,000 ≤ 1,800
25,000 - 1,800 ≤ x ≤ 25,000 + 1,800
23,200 ≤ x ≤ 26,800
The range of the salary will be the closed interval [23,200, 26,800].
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Question 5
A swimming pool has a length of 30 ft, a width of 12 ft, and a uniform depth of 8 ft. How many gallons of water does it hold?
(Hint: Find the volume in cubic ft and then use dimensional analysis to convert to gallons. 7.5 gal - 1 cubic ft.)
Round your answer to the nearest whole gallon, but do not include a unit of measure with your response.
Answers
1,718 gallons
Because 12-Feet by 30-Inches and able to hold up to 1,718 gallons of water!
V = 4 + at, solve for a.
Answers
Answer: a=(V-4)/t
Step-by-step explanation:
V = 4 + at
V-4=at
a=(V-4)/t
After a person gets a 2% raise in salary, the new salary is $11874. What was the original salary?
Answers
Answer:
Original salary was $11641.17Step-by-step explanation:
Let the initial salary be x.
Set equation and solve for x:
x + 2% of x = 11874x + x*2/100 = 11874x + 0.02x = 118741.02x = 11874x = 11874/1.02x = 11641.17 (rounded to the nearest cent)
Answer:
The original salary is $11641.18.
Step-by-step explanation:
The equation will be,
→ x + (x × 2)/100 = 11874
Now the original salary will be,
→ x + (x × 2)/100 = 11874
→ x + 0.02x = 11874
→ 1.02x = 11874
→ x = 11874/1.02
→ x = 11641.1764706
→ [ x = 11641.18 ]
Hence, original salary is $11641.18.
help i need help i this please
Answers
Answer:
-∞ and -∞ both answers
Step-by-step explanation:
From the graph it is clear that as x becomes smaller and smaller, y gets smaller and smaller. So as x → -∞, y → -∞
On the positive x side, as x gets bigger and bigger, y gets smaller and smaller so
as x → +∞, y → -∞
Hey y’all, 10 pm now :( got one more question and then I’ll be gone so pls help
Answers
Answer:
x=27 or x= -8
Step-by-step explanation:
rearrange the terms
convert the expression
simplify the expression
rewrite the equation
solve the equation
formulate new equations
I can't show the full steps since there's no image
Answer:
this is answers
scan and see