Answer:
a) - Compressing the P(new) function by a scale of 0.5 about the y axis.
- Moving the P(new) function down by 104 units.
b) The two simplified functions for P(original)
-0.08x² + 10.8x – 200.
-0.16x² + 21.6x – 504.
Step-by-step explanation:
Complete Question
An electronics manufacturer recently created a new version of a popular device. It also created this function to represent the profit, P(x), in tens of thousands of dollars, that the company will earn based on manufacturing x thousand devices: P(x) = -0.16x² + 21.6x – 400.
a. The profit function for the first version of the device was very similar to the profit function for the new version. As a matter of fact, the profit function for the first version is a transformation of the profit function for the new version. For the value x = 40, the original profit function is half the size of the new profit function. Write two function transformations in terms of P(x) that could represent the original profit function.
b. Write the two possible functions from part a in simplified form.
Solution
The equation for the new profit function is
P(x) = -0.16x² + 21.6x – 400
At x = 40, the original profit function is half the size of the new profit function
First, we find the value of the new profit function at x = 40
P(x) = -0.16(40)² + 21.6(40) – 400 = 208
Half of 208 = 0.5 × 208 = 104
P(original at x = 40) = P(new at x = 40) ÷ 2
Since we are told that P(original) is a simple transformation of the P(new)
P(original) = P(new)/2 = (-0.16x² + 21.6x – 400)/2 = -0.08x² + 10.8x – 200 ... (eqn 1)
Or, P(original) = 104
-0.16x² + 21.6x – 400 = 104
P(original) = -0.16x² + 21.6x – 400 - 104 = -0.16x² + 21.6x – 504.
So, the two functions that are simple transformations of P(new) to get P(original) are
-0.08x² + 10.8x – 200
Obtained by compressing the P(new) function by a scale of 0.5 about the y axis.
And
-0.16x² + 21.6x – 504.
Obtained by moving the P(new) function down by 104 units.
Hope this Helps!!!
How many centimeters are there in 75 meters?
Answer:
7500. There are 100 centimeters in a meter therefore 75 meters have 7500 centimeters.
Description:
Using the formula Multiply the length value by 100 . We multiply the length by the hundred. In this case length is 75. Meaning 75 times 100 = the answer. The answer for this question is 7500.
Metre 75 = Centimetre 7500
Formula: Multiply the length value by 100
Answer: 7500
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Hope this helps.
Use the unit circle to find the value of sin 3π/2 and cos 3π/2
Answer:
sin=-1
cos=0
Step-by-step explanation:
The sin of an angle on the unit circle is y value of that point. You can see that the y value of it is at -1. The cosine of the angle is the x coordinate, which you can see is 0. Hope this helps!
On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming
these flowers rapidly increases as the trees blossom. The locust population gains 87% of its size every 2.4
days, and can be modeled by a function, L, which depends on the amount of time, t (in days).
Before the first day of spring, there were 1100 locusts in the population.
Write a function that models the locust population t days since the first day of spring.
L(t) =
Answer:
[tex]L(t) = 1,100*(1+0.87)^{\frac{t}{2.4}}[/tex]
Step-by-step explanation:
The locust population grows according to an exponential model with the following general formula:
[tex]L(t) = L_0*(1+r)^{\frac{t}{T}}[/tex]
Where 'L0' is the initial locust population, 'r' is the increase rate after 'T' days, and 't' is the time passed, in days.
Applying the given data, the function that models the locust population t days since the first day of spring is:
[tex]L(t) = 1,100*(1+0.87)^{\frac{t}{2.4}}[/tex]
.
John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?
h c
0 485
3 510
8 535
12 560
h c
0 510
3 535
8 560
12 585
h c
0 485
3 560
8 685
12 785
h c
0 510
3 585
8 710
12 810
Answer:
Third
Step-by-step explanation:
h c
0 485
3 560
8 685
12 785
The table that shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project is third table.
What is multiplication?Multiplication is mathematical arithmetic operation. It is also a process of adding same types of expression to some number of times.
Example - 2 × 3 means 2 is added three times or 3 is added 2 times.
Given that John paid $485 to build a deck.
And he will pay $25 per hour to his brother for building the deck.
one hour of work costs John $25 + $485 .
Total cost of building deck = $25 × h number of hours + $485
3 hour of work costs $25 × 3 = $75 + $485 = $560
8 hour of work costs = $25 × 8 = $200 + $485 = $685
12 hour of work costs = $25 × 12 = $300 + $485 = $785
Therefore, the third table suggests the total cost of work.
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The length of a spring varies directly with the mass of an object that is aftached to it. When a 30-gram object is attached, the
spring stretches 9 centimeters. Which equation relates the mass of the object, m, and the length of the spring, s?
vx
3
S =
10
3
3
M =
S
10
m =
1
30
S
Answer:
s = [tex]\frac{3}{10}[/tex] m
Step-by-step explanation:
Given s varies directly with m then the equation relating them is
s = km ← k is the constant of variation
To find k use the condition s = 9 when m = 30 , thus
9 = 30k ( divide both sides by 30 )
k = [tex]\frac{9}{30}[/tex] = [tex]\frac{3}{10}[/tex]
s = [tex]\frac{3}{10}[/tex] m ← equation of variation
HELP!!! WILL MARK BRAINLIEST!!!
The following graph describes function 1, and the equation below it describes function 2. Determine which function has
a greater maximum value, and provide the ordered pair.
Function 1
Function 2
f(x) = -x2 + 2x - 3
Function 1 has the larger maximum at (1,4).
Function 1 has the larger maximum at (4,1).
Function 2 has the larger maximum at (1, -2).
Function 2 has the larger maximum at (-2, 1).
Answer:
the answer is function 1 has the larger max. at (4,1)
Step-by-step explanation:
draw function 2 : the vertex is (1,-2)
the vertex of function 1 is (4,1)
The function 1 has a greater maximum value than function 2, and the ordered pair is (1,4).
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.
Linear function is a function whose graph is a straight line
We are given that;
f(x) = -x2 + 2x - 3
Now,
To find the maximum value of a function, we can use the vertex form of a quadratic equation, which is y=a(x−h)2+k
, where (h,k) is the vertex of the parabola. The maximum value of the function is the y-coordinate of the vertex.
For function 1, we can rewrite it as [tex]$$f(x) = -(x-1)^2 + 4$$[/tex]
by completing the square. This means that the vertex of function 1 is (1,4) and the maximum value is 4.
For function 2, we can rewrite it as
[tex]$$f(x) = -\frac{1}{4}(x+2)^2 - 2$$[/tex]
by completing the square. This means that the vertex of function 2 is (−2,−2) and the maximum value is -2.
Therefore, by the given function answer will be (1,4).
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Use the method of combining like terms to find the equivalent expression to 6u+2v+3u−7v−2.
Step-by-step explanation:
The like terms are 6u and 7u and also 2v and -7v so the answer is 9u - 5v - 2.
Solve the equation: √(y−1)^2 =15 Please help ASAP!! Thank you!!!
Answer:
Remove the radical by raising each side to the index of the radical.
y = 226
Step-by-step explanation:
3 facts about quadrilaterals
Answer:
A 4 sided shape with. A 4 sided shape with 2 parallel sides.
all right angles are. all right angles are 90 degress.
All the angles add up to 360 degrees. All the angles add up to 360 degrees.
Step-by-step explanation:
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James went shopping for a new watch. The original price was $150. It was marked down to $110. What is the percent of decrease?
Answer:
26.7% is the percent of decrease
Step-by-step explanation:
$150=100% price (starting og price)
110 =? or x (discounted price)
We need to find what is the decrease from 150 to 110 in percentage
Use ratios to solve:
$150:100%
$110:x (unknown)
Cross multiply to find x
150 times x= 150x, and 100x110 = 11000
= 150x=11000
Lets get x all by itself to fully solve. We have to divide to get x by itself:
= 150x/150=11000/150 (divide 150 both sides always)
= 73.3,
Now we subtract 73.3 from 100 to get the decrease percentage
100-73.3=26.7 which is the percent of decrease
An expression that equivalent to 12x + 8
Answer:
4(3x+2)
Step-by-step explanation:
Just factor the expression.
An equivalent expression is, 4 (3x + 2)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 12x + 8
Now, We can find an equivalent expression as;
⇒ 12x + 8
⇒ 4 × 3x + 4 × 2
⇒ 4 (3x + 2)
Thus, An equivalent expression is,
⇒ 4 (3x + 2)
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Solve for a.
ab + c = d.
Answer:
a = (d-c)/b
Step-by-step explanation:
ab + c = d
ab = d -c
a = (d-c)/b
Answer: a = d - c/b
Explanation: To get a by itself, we first subtract c from both sides.
So we have ab = d - c.
Now divide both sides by b to get a = d - c/b.
HELP ASAP I WILL GIVE YOU THE POINTS !!!
What is the value of x?
Answer:
80
Step-by-step explanation:
70 + 30 = 100
180 - 100 = 80
Answer:
[tex]x = 80 \: \: degrees[/tex]
Step-by-step explanation:
[tex]70 + 30 + x = 180 \\ 100 + x = 180 \\ x = 180 - 100 \\ x = 80 \: \: degrees[/tex]
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Which two numbers add to -22 and multiply to 121?
-11 and -11 are the two numbers that adds to -22 and multiply to 121
If we add 11 and 11 then it equals to -22.
if we multiply 11 and 11 then,it equals to 121
hope it helps...
Good luck on your assignment
Answer: Both numbers are -11.
Step-by-step explanation:
You can represent this using two equations, where the variables are x and y:
[tex]x + y = -22\\x * y = 121[/tex]
Then, solve the system using substitution by substituting y in the first equation into the second equation:
[tex]y = -22 - x\\ x * (-22 - x) = 121\\\\-x^2 - 22x - 121 = 0\\x^2 + 22x + 121 = 0\\[/tex]
Then, solve the quadratic equation by factoring it:
[tex](x+11)^2 = 0[/tex]
The only solution (or zero) to the equation is -11.
This means that both numbers are equal to -11.
-11 - 11 = -22
-11 * -11 = 121
PLEASE HELP! I HAVE A TIME CRUNCH! WILL MARK BRAINLIEST!! LOVE Y'ALL Fill in each * so that the statement is true.
a.) (x^2)^3=x^2·x*
b.) (x^3)*=x^5·x^7
c.) (x^2)*=x^4·x^22
d.) (x^2)^8=x^2·x*
e.) x^10/x^3 = x^20 · x*
f.) x^−3=x^4·x*
g.) 1/x^−3 =x^4·x*
Thank You!
Answer:
a, (x^2)^3 = x^6 = x^2.x^4
b, x^5·x^7 = x^12 = (x^3)^4
c, x^4·x^22 = x^26 = (x^2)^13
d, (x^2)^8 = x^16 = x^2.x^14
e, x^10/x^3 = x^7 = x^20.x^(-13)
f, x^(-3) = x^4.x^(-7)
g, 1/x^(-3) = x^3 = x^4.x^(-1)
Hope this helps!
:)
Find the equation of the line that is perpendicular to y = 1/4x – 2 and passes though the point (5, –2). A) y = –1/4x + 18 B) y = –1/4x – 22 C) y = –4x + 18 D) y = –4x – 22
Since our line is perpendicular to this line, the slope of
our line is the negative reciprocal of 1/4, which is -4/1.
Remember, negative reciprocal is just a fancy way
of saying flip the fraction and change the sign.
So the slope of our line is -4/1 and we use this slope along
with our given point to write the equation of our line.
Start with the point-slope formula.
Y - y1 = m(x - x1).
~Substitute
Y - -2 = -4/1(x - 5).
Minus a negative is plus a positive.
Y + 2 = -4/1x + 20.
Subtract 2 from both sides.
Y = -4/1x + 18
So, our answer is C.
Unit Test
Active
1
2
TIME REMAINING
01:21:05
Tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. The total cost in
dollars for ordering 5 tickets is $108.00. Which linear function represents c, the total cost, when x tickets are ordered?
O c(x) = 5.50 + 20.50x
O c(x) = 5.50x + 20.50
Oc(x) = 5.50 +21.60x
O c(x) = 5.50x + 21.60
Answer: c the third option
Step-by-step explanation:
Answer:
Hope this helps!
Step-by-step explanation:
cost=flat fee+changing fee
flat fee=5.50
changing fee=cost per ticket times number of tickets
we know that 5 times cost per ticket=108
divide by 5
cost per ticket=21.6
c=number of tickets
total cost=5.5+21.6c
TC=21.6c+5.5
Jason enjoys watching the squirrels in his neighborhood park. They eat the red oak acorns. After the city removed 4 diseased red oak trees, the population of squirrels decreased from 105 to 98 in one year. If the population continues to decline at the same rate, how many squirrels will live in the park in 15 years? First, calculate the rate of decay by subtracting the two populations and dividing the difference by the initial population. Then, use the formula A=a0ekt
a. 0 squirrels
b. 95 squirrels
c 81 squirrels
d 34 squirrels
Answer:
0 squirrels
Step-by-step explanation:
If you subtract 98 from 105 then you get 7. That means that 7 squirrels will be lost per year. If you then multiply 7 by 15 (15 is the amount of years) then you get 105 and since there were 105 to start off with, there will be no squirrels left after 15 years.
Answer:
34 Squirrels
Step-by-step explanation:
7\ 105 ~0.07
A=Aoe^kt
A=98e^(-0.07•15)
A=98e^-.05
A=34.3~ 34 Squirrels
2. Solve the following equation for c. (5 points)
-8(1 + 4c) + 7c = -25 - 80
C=
Answer:
c=1
Step-by-step explanation:
Simplify both sides of the equation first.
−8(1+4c)+7c=−25−8c
(−8)(1)+(−8)(4c)+7c=−25+−8c
−8+−32c+7c=−25+−8c
(−32c+7c)+(−8)=−8c−25
−25c+−8=−8c−25
−25c−8=−8c−25
Add 8 to both sides.
−17c−8+8=−25+8
−17c=−17
Divide both sides by -17.
-17c/-17 = -17/-17
c=1
PLS HELP ASAP NEED FAST
Answer:
there is no mistake.
Step-by-step explanation:
the steps are all correct.
it cant be 'they should be divided' since that's not how it works.
it cant be 'tan 68 should be cos 68' since for cos we need [tex]\frac{adjacent}{hypotenuses}[/tex]
and since for tan it is [tex]\frac{opposite}{adjacent}[/tex] it cant be[tex]\frac{14}{x}[/tex]
I need a lil help, ANSWER QUICKLY!
Answer:
yes
Step-by-step explanation:
Counterclockwise is going left, so if you start at the top, 270 degrees left of a clock will result in the same as 90 degrees clockwise.
Answer:
Yes it will.
Step-by-step explanation:
Imagine a circle. A full rotation is 360 degrees. So, that means you're going to be 90 degrees froma full rotation. That means that if you back track 90 degrees you're going to get to the same spot as when you go clockwise 270 degrees. The best way to think of it is having the hands of a clock start at 12.
Melanie had two $10 bills one$5 bill,four dimes, and six pennies. Then she bought a fruit cup for $2.19
Answer:
$23.27
Step-by-step explanation:
yes
40 points. Can someone do this real quick and show work? I'm sorry I justcan't process it
Answer:
x = 6
Step-by-step explanation:
(3x-2)/4 +1 =5
subtract 1 from each side
(3x-2)/4 +1 -1 =5-1
(3x-2)/4 =4
Multiply each side by 4
(3x-2)/4 *4 = 4*4
3x-2 = 16
Add 2 to each side
3x-2+2 = 16+2
3x = 18
Divide each side by 3
3x/3= 18/3
x = 6
Answer:
[tex]x = 6[/tex]
Step-by-step explanation:
[tex] \frac{3x - 2}{4} + 1 = 5 \\ \frac{3x - 2}{4} = 5 - 1 \\ \frac{3x - 2}{4} = 4 \\ 4 \times \frac{3x - 2}{4} = 4 \times 4 \\ 3x - 2 = 16 \\ 3x = 16 + 2 \\ 3x = 18 \\ \frac{3x}{3} = \frac{18}{3} \\ x = 6[/tex]
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Find the value of c so that (x – 2) is a factor of the polynomial p(x).
p(x) = x3 – 4x² + 3x + c
Answer:2
Step-by-step explanation:
a dosage is changed from 15 mg per day to 12 mh per day. what is a percentage decrease
Answer:
20%
Step-by-step explanation:
dosage change from 15 mg/d to 12 mg/d
change= 15-12= 3
change %= 3/15*100%= 20% decrease
raming Which best describes the relationship between the
125° angle and angle A?
They are same side interior angles. Angle A
measures 55°.
They are alternate interior angles. Angle A
measures 125°.
They are vertical angles. Angle A measures 125°
They are corresponding angles. Angle A measures
55°
Answer:
Step-by-step explanation:
If Maria is trying to find 42% of 350 which of the following calculations will give her the correct answer?
Answer:
42% * 320
Step-by-step explanation:
it's 147
Step-by-step explanation:
42/100 ×350/1=147
Slove the equation y+3=-y+9 on edge
A)y=1
B)y=3
C)y=6
D)y=9
Answer:
y + 3 = -y + 9
-y -y
3 = -2y + 9
+2y +2y
2y + 3 = 9
-3 -3
2y = 6
y = 3
Which of the following pairs of functions are inverses of each other?
you need an pic for an Answer:
Step-by-step explanation:
-5/12-3/4=
????
please answer
Answer:
-7/6
Step-by-step explanation:
You first have to find the common denominator, which in this case is 12. 3/4ths can be converted to 9/12ths. Then you subtract 9/12ths from -5/12, and get -14/12. Finally you simplify it and get -7/6.:)