PLEASE HELP IM BEING TIMED!!! WILL MARK BRAINLIEST FOR CORRECT ANSWER!!! 100PTS!!!
Adding two functions results in h(x) = –x + 9, while multiplying the same functions results in j(x) = –9x.
Which statements describe f(x) and g(x), the original functions? Select two options.
A. Both functions must be quadratic.
B. Both functions must have a constant rate of change.
C. Both functions must have a y-intercept of 0.
D. The rate of change of either f(x) or g(x) must be 0.
E. The y-intercepts of f(x) and g(x) must be opposites.
Answers
Answer:
Both functions must have a constant rate of change.
The rate of change of either f(x) or g(x) must be 0.
From the first equation we know that both f (x) and g (x) must be of order 1 or of order 0, since the maximum exponent of X is 1. This indicates that both functions must have a constant rate of change , since the derivative of a function of order 0 or of order 1 is a constant.
From equation 2 we know that both f (x) and g (x) are composed of a single term, since the multiplication of both results in a single term (-9x). In addition, we verify that one of the functions is of order 0 and the other is of order 1, since the result of the product is of order 1.
If f (x) or g (x) are of order 0, which means that they are composed of only one constant, the rate of change of any of the 2 functions is 0.
Step-by-step explanation:
Answer:
B and D.
Step-by-step explanation:
We know that when we added the two functions together, we get:
[tex]h(x)=-x+9[/tex]
However, when we multiplied them together, we get:
[tex]j(x)=-9x[/tex]
Let's first consider what we can determine from this.
If we add them together, we get a linear equation. However, this doesn't mean that our two original functions are linear since if we have, say, -x^2 and x^2-x+9, they will cancel and form a linear equation if we add them together.
However, since we know that if we multiply the two functions together, we get a linear equation, this means that both our original functions must be linear.
But, if we multiplied two linear functions, then we should get a quadratic, since x times x will yield x².
Therefore, this means that one of our linear functions is a horizontal line with no x variable. This is the only way to have a linear equation when multiplied.
Therefore, we have determined that both of our original functions are linear functions, and one (only one of them) is a horizontal line.
Let's go through each of the answer choices.
A) Both functions must be quadratic.
This is false as we determined earlier. If this was true, then the resulting function should be a quartic and not a line. A is false.
B) Both functions must have a constant rate of change.
Remember that all linear equations have a constant rate of change.
Since we determined that both our original functions are linear equation, this means that both our functions will have a constant rate of change.
So, B is true.
C) Both functions must have a y-intercept of 0.
Remember that one of our functions is a horizontal line.
If the y-intercept was 0, then the equation of our horizontal line will be:
[tex]y=0[/tex]
And we know that anything multiplied by 0 will give us 0. However, the product of our function is -9x.
So, C cannot be true.
Rather, only our linear equation (not the horizontal line) may have a y-intercept of 0.
D) The rate of change of either f(x) or g(x) must be 0.
Remember that we determined that one of our lines must a horizontal.
Remember that horizontal lines have a slope of 0. In other words, the rate of change is 0.
So, D is true.
E) The y-intercepts of f(x) and g(x) must be opposites.
Well, since B and D is are true, this must be false since we can only select two options ;D
But, we can think about this. Note that if we multiply the two functions, we have a function without a y-intercept.
Remember that our horizontal line is not 0. So, the y-intercept of the horizontal line is a number.
So, the opposite of a number is another number.
So, if we multiply two non-zero numbers, we must get another number.
However, from our product, j(x)=-9x, we don't have another number. The y-intercept from this is 0.
Therefore, the two y-intercepts cannot be opposites of each other. If it was so, then we should have a y-intercept. So, E must be false.
In fact, this means that the y-intercept of our line (not the horizontal one) must be 0.
So, our answers are B and D.
And we're done!
Edit: Some (minor) errors in reasoning. Sorry!
Related Questions
Jamie’s string is 10 ft 1 in. long. Emma’s string is 6 ft 4 in. long. How much longer is Jamie’s string
Answers
Answer:
3 ft 9 in
Step-by-step explanation:
What is the length of segment VS?
O 3 units
11 units
13 units
O 15 units
Answers
From the diagram given, line TR and RV are equal, using the obtained value of x, the value of the segment VS is 15 units
5x - 4 = 2x + 5
5x - 2x = 5 + 4
3x = 9
x = 9/3
x = 3
TS = VS
Hence, VS = 6x - 3
Substitute the value of x to obtain the value of VS :
VS = 6x - 3
VS = 6(3) - 3
VS = 18 - 3
VS = 15 units
Hence, the length of the segment VS is 15 units.
Learn more : https://brainly.com/question/18293224
Answer:
15 units :)
Step-by-step explanation:
What’s 605,000 in scientific notation
Answers
This is the answer for what is 605,000 in scientific notation.
Answer:
6.05 × 10∧5Step-by-step explanation
make a decimal at the end if the Number. Move the decimal until the lest of it is more than one and less than ten. And since you move the decimal 5 times the five goes over the ten
The perimeter of a greeting card is 74 centimeters. The greeting card is 22 centimeters tall. How wide is it?
Answers
Answer:
15cm
Step-by-step explanation:
the width is xcm
22 + 22 + 2x = 74
44 + 2x = 74
2x = 30
x = 15
the width is 15cm
help me please i’ll give you brainly thingy
Answers
Answer:
Step-by-step explanation:
Answer:
the answer is b
Step-by-step explanation:
because 8/10 divided by 1/5 equals 4
Which of the following is the correct factorization of 7x2-36x+5
Answers
then the answer should be (7x-1)(x-5)
By how much does 5 exceed -4?
(a) 1
(b)-1
(c) 9
(d) -9
Answers
Answer:
C
Step-by-step explanation:
-4+9=5
3 letters without replacement 4 letters A B C D how many ways can this be done if the order of the choices matters
Answers
Answer:
Since the order of choice matters, we will permute the values. a bit more explanation for this:
If the order of choice did NOT matter, ABC and BCA will be counted as one since order of choice does NOT matter
Since order of choice does matter, ABC , BCA and CAB are all different possibilities for the arrangement of the same 3 letters
Since we have 3 slots:
___ ___ ___
Now, for the first slot. You can out either one if the 4 alphabets in the first slot since no slot has been used as of now
So:
_4_ ___ ___
**Keep in mind that the 4 is the possible number of values this slot can have**
Now that one slot has been used, one of the 4 alphabets has been used and since we are not allowed to repeat the same alphabets, we are left with 3 more alphabets
we can put any one of the 3 alphabets in this second slot, Hence:
_4_ _3_ ___
Now that 2 of the 4 alphabets have been used, we are left with only 2 alphabets, so there are only 2 possible alphabets for slot 3
Therefore:
_4_ _3_ _2_
Now that we know the possible alphabets for all 3 slots, we will multiply them with each other to get the total possible number of 3 - alphabet words we can make with 4 alphabets
Total possible words = 4 * 3 * 2
Total possible words = 24
We could've used the formula for Permutation as well
Find the values of x and y
Answers
Answer:
Corresponding angles are equal
therefore y = 134°
Angles on a straight line add up to 180°
x = 180° - y
x = 180° - 134°
x = 46°
and please I need brainliest
Which of the lines shown is a line of symmetry?
Answers
The length of a rectangle is 5 cm less than three times its width. If the perimeter of the rectangle is 54 cm, find the LENGTH of the rectangle. *
Answers
Answer:
Hi there!
Your answer is
The length is 19
Step-by-step explanation:
L=3w-5
P=54
Perimeter formula
L+L+W+W=P
(3w-5)+(3w-5) +w+w = 54
8w-10=54
+10
8w=64
/8
w=8
Plug in width in Length formula
L=3w-5
L= 3(8)-5
L=19
Write an explicit rule for the geometric sequence:
3, -12, 48, -192
please help and thank you!
Answers
Answer:
I think you would just multiply by -4
Step-by-step explanation:
3 x -4 = -12
-12 x -4 = 48
48 x -4 = -192
Please let me know if I've done anything wrong!
21+5f=61 hnhnuihnh hun h
Answers
Answer:
f=8
Step-by-step explanation:
21+(5 times 8=40) = 61
. What would be the new coordinates if (-2,-4) is translated 5 units up and
7 units to the left.
Answers
Answer:
(-9, 1)
Step-by-step explanation:
translating UP is to increase on the y axis, so -4+5=1
translating to the LEFT is to subtract on the x axis so-2-7=-9
7. All of the following are perfect square trinomials EXCEPT one. Which is it?
A. 4x2 + 12xy + 9y2
C. xy2 - 4x2y2 + 4x2y2
B. 9a? - 36a + 36
D. a²b2 + 4a3b + 4a?
Answers
Answer:
All answers EXCEPT answer C. are perfect square trinomials.
Step-by-step explanation:
A perfect square trinomial is polynomial that satisfies the following condition:
[tex](a+b)^{2} = a^{2}+2\cdot a \cdot b + b^{2}[/tex], [tex]\forall\,a,b\in\mathbb{R}[/tex]
Let prove if each option observe this:
a) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex]
1) [tex]4\cdot x^{2} + 12\cdot x\cdot y + 9\cdot y^{2}[/tex] Given
2) [tex](2\cdot x)^{2}+ 2\cdot (2\cdot x)\cdot (3\cdot y)+(3\cdot y)^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 2\cdot x[/tex], [tex]b = 3\cdot y[/tex] Definition of perfect square trinomial/Result.
b) [tex]9\cdot a^{2}-36\cdot a + 36[/tex]
1) [tex]9\cdot a^{2}-36\cdot a + 36[/tex] Given.
2) [tex](3\cdot a)^{2}-2\cdot (3\cdot a)\cdot 6 + 6^{2}[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = 3\cdot a[/tex], [tex]b = 6[/tex] Definition of perfect square trinomial/Result.
c) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex]
1) [tex]x\cdot y^{2}-4\cdot x^{2}\cdot y^{2}+4\cdot x^{2}\cdot y^{2}[/tex] Given
2) [tex]x\cdot y\cdot (1-4\cdot x+4\cdot x)[/tex] Distributive property.
3) [tex]x\cdot y \cdot 1[/tex] Existence of the additive inverse/Modulative property.
4) [tex]x\cdot y[/tex] Modulative property/Result.
d) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex]
1) [tex]a^{2}\cdot b^{2}+4\cdot a^{3}\cdot b + 4\cdot a^{4}[/tex] Given
2) [tex](a\cdot b)^{2}+2\cdot (a\cdot b)\cdot (2\cdot a^{2})+(2\cdot a^{2})[/tex] Definition of power/Distributive, associative and commutative properties.
3) [tex]a = a\cdot b[/tex], [tex]b = 2\cdot a^{2}[/tex] Definition of perfect square trinomial.
All answers EXCEPT answer C. are perfect square trinomials.
Find g(h(x))
f(x) = 4x – 6
g(x) = 5/3x + 1
h (x) = -12x^2 - 6x
Answers
Answer:
g(h(x))
Step-by-step explanation:
g(h(x))=
[tex](5 \div 3)( (- 12) {x}^{2} - 6x) + 1 = \\ (5 \times( - 12) {x}^{2} ) \div 3 - (5 \times 6x) \div 3 + 1 = \\ (5 \times (- 4) {x}^{2} ) -( 5 \times 3x) + 1 = \\ - 20 {x}^{2} - 15x + 1[/tex]
Help anyone ??????!!!!!! Plz
Answers
Answer:
n = 12
Step-by-step explanation:
You first write it out as in equation and get 3n-7=2n+5
You then do addition property of equality to add 7 on both sides, and gets 3n=2n+12
Then you subtract 2n from both sides to get
n=12
Hope this helps!
2x-3y=-12 solve for y
Answers
Answer:
y intercept is 4
Step-by-step explanation:
Can someone please help me solve these word problems?
Answers
Answer:
7. 39
Jim is 39 years younger.
{10, 12, 14, 16, 18, ...} What is the formula ?
Answers
Answer:
+2
Step-by-step explanation:
Graph the compound inequality on the number line.
x2 and x <8
-10.98
53
12
8 9 10
ILL GIVE BRAINLIEST
Answers
put your point on 2 and make sure it isn’t open bc it is greater than or equal to (looks like “•”) then you draw your arrow to 8 bc it can’t be greater than that
Simplify and divide the following radical expression: √3/ 6√7
Step by step please
Answers
Answer:
19
√
5
+
45
Step-by-step explanation:
Multiply:
√
2
⋅
√
6
.
Multiply:
3
√
9
⋅
3
√
6
.
2
√
3
⋅
5
√
2
.
Answer
[tex]21[/tex]/6 write the square root sign with 21 inside /6 (I cant make the sign
[tex]\sqrt{x} 3[/tex]/6 x 7
[tex]\sqrt{x} 3[/tex][tex]\sqrt{x} 7[/tex] /6 TAKE THE X's OUT) ok i cant make the sign alone Draw a line
and put the 6 under the 3 and 7
[tex]3 x 7[/tex] /6 Put the 3x7 under one square root sign /over 6
21/6 Put the 21 inside the square root sign / over 6
Step-by-step explanation:
does that make sense? i cant make the square root symbol so dont put the x's with the numbers
PLEASE HELP THIS MAKES MY BRAIN HURT
Answers
23x+7=122
23x=115
Answer
X=5
Which equation has the correct sign on the product?
A. 27(-5) = -135
B. (-4)(-4) = -16
C. (-61)(3) = 183
D. 22.4 = -88
Answers
Answer:
A
Step-by-step explanation:
27 x -5 = -135
Answer: A
Step-by-step explanation: Hope I helped you.
Guess my rule......
Answers
Answer:
The rule in what is shown to be a graph and a in-out machine is:
y = 2x + 5
Step-by-step explanation:
2(5) + 5 = 15
10 + 5 = 15
15 = 15
TRUE RULE
2(7) + 5 = 19
14 + 5 = 19
19 = 19
TRUE RULE
2(8) + 5 = 21
16 + 5 = 21
21 = 21
TRUE RULE
y = 2x + 5 is your rule!
Answer:
Step-by-step explanation:
y = 2x + 5
Find the midpoint of the segment with the given endpoints.
(-4,-9) and (-2,1)
Answers
Answer:
it is -2,1 I really hope that helps
John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and found a job that will allow him to purchase a car to finally catch Roadrunner. He can either buy a new car at a cost of $22,000, buy a used car for $12000 or lease a new car for one year at a cost of $8,500 (assume total cash purchase up front, no financing or monthly payments required). The new car has a 20% chance of a serious break down resulting in a permanent impairment to the trade-in value. The trade-in value for the new car without a serious break down after one year is $18,000 but only $10,000 if the break down occurs. On the other hand, the used car has a 40% chance of suffering a major break down with a $8,000 decrease in the resale value. However, if it does not break down, Wile can sell it to a friend one year from now for $9,000 cash (assume he can also sell it to the friend for $4,000 if the breakdown occurs). Finally, the leased car has a 10% chance of breaking down with a repair cost of only $2,000, and if it doesn’t, Wile will not gain or lose anything by returning the car at the end of a one year lease period. NOTE: For the new and used car purchases all related repair costs resulting from a breakdown have been netted against the trade-in / resale value.
a. Construct a decision tree for Wile
b. What is the expected value of the new car?
c. What is the expected value of the used car?
d. What is the expected value of leasing the car?
Answers
Answer: See explanation
Step-by-step explanation:
a. Construct a decision tree for Wile
The solution to the question has been attached.
b. What is the expected value of the new car?
= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000
= $2000 + $14400 - $22000
= $16400 - $22000
= -$5600
c. What is the expected value of the used car?
= [(0.4 × $4000) + (0.6 ×$9000] - $12000
= $1600 + 5400 - $12000
= $7000 - $12000
= -$5000
d. What is the expected value of leasing the car?
= [(0.1 × -$2000) + (0.9 ×0)] - $8500
= -$200 - $8500
= -$8700
the mount of money earned on a jop is directliy propotional to the number of the hours worked.if 70$is earned in 5 hours how much money earned in 22hours of work
Answers
Answer:
$308
Step-by-step explanation:
Easy, find how much is earned in 1 hour. Therefore 70/5 = 14 dollars per hour
and multiply the amount of hours work therefore 14 times 22 = $308
Answer:
308
Step-by-step explanation:
Because if you have 70$ in 5 hours
it means that you have 14$ every hours
so, you have 308$ in 22 hours
22x14=308
Mr. Ratchett, an elderly American, was found murdered in his train compartment on the Orient Express at 7 AM. When his body was discovered, the famous detective Hercule Poirot noted that Ratchett had a body temperature of 28 degrees. The body had cooled to a temperature of 27 degrees one hour later. If the normal temperature of a human being is 37 degrees and the air temperature in the train is 22 degrees, estimate the time of Ratchett's death using Newton's Law of Cooling.
Answers
Answer:
Time of Death = 2 : 49 : 45 AM
Step-by-step explanation:
The formula for Newton's Law of Cooling is written as follows:
dT/dt = - K(T - Ts)
where,
dT = change in temperature
dt = time interval
K = cooling constant
T = Final Temperature of object
Ts = Surrounding Temperature
First, we will use the data of cooling of body from 28°C to 27°C to find the cooling constant of the body:
dT = 27°C - 28°C = -1°C
dt = 1 hr = 3600 s
K = ?
T = 27°C
Ts = 22°C
Therefore,
-1 °C/3600 s = - K(27 °C - 22 °C)
K = 1 °C/(3600 s)(5 °C)
K = 5.55 x 10⁻⁵ /s
Now, we use data for cooling of body from 37 °C to 28 °C to find the time of death:
dT = 28°C - 37°C = -5°C
dt = ?
K = 5.55 x 10⁻⁵ /s
T = 28°C
Ts = 22°C
Therefore,
- 5 °C/dt = - (5.55 x 10⁻⁵ /s)(28 °C - 22 °C)
dt = 5 °C/(5.55 x 10⁻⁵ /s)(6 °C)
dt = 1.5 x 10⁴ s
dt = 4.17 h = 4 h 10 min 15 s
Therefor,
Time of Death = 7 : 00 : 00 AM - 4 : 10 : 15
Time of Death = 2 : 49 : 45 AM
A person bikes 2 1/2 miles in 1/8 of an hour how far do they bike in 1 whole hour
Answers
Answer:
The person will bike 20 miles.
Step-by-step explanation: