Answer:
f(x) = 6ˣ⁻⁷-3
Step-by-step explanation:
The basic transformations of an exponential function from the parent function can be given by the equation:
f(x) = b^x [parent exponential function]
f(x) = ab^((x/c)-h) + k [transformation of parent exponential function]
Where b is the parent growth or decay, a is the vertical stretch or compression, c is the horizontal stretch or compression, h is the horizontal translation, and k is the vertical translation.
Given a translation down 3 units, and another translation right 7 units, we are only using h, and k.
Given that our original function is g(x) = 6ˣ. We know our parental growth or b is 6. So just substitute our quantities and solve:
f(x) = g(x-7) - 3 → (1)6^((x/1)-7) - 3 → 6^(x-7) - 3 → 6ˣ⁻⁷-3.
Answer:
f(x) = 6ˣ⁻⁷-3
Step-by-step explanation: I took the test
The elephant's foot was discovered a couple months after the meltdown. This was the result of the reactor Melting creating lava
Answer:
Ok, that‘s not a question, it‘s a statemen. So what‘s your point
Step-by-step explanation:
The concentration C of certain drug in a patient's bloodstream t hours after injection is given by
C(t)= t/3t^2+5
Required:
a. Find the horizontal asymptote of C(t). (Answer must be in slope-intercept form.)
b. Determins what happens to the concentration of the drug as t increases. As t increases, what value will c(t) approach.
c. Determine the time at which the concentration is highest.
Answer:
a) The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) The time at which the concentration is highest is approximately 1.291 hours after injection.
Step-by-step explanation:
a) The horizontal asymptote of [tex]C(t)[/tex] is the horizontal line, to which the function converges when [tex]t[/tex] diverges to the infinity. That is:
[tex]c = \lim _{t\to +\infty} \frac{t}{3\cdot t^{2}+5}[/tex] (1)
[tex]c = \lim_{t\to +\infty}\left(\frac{t}{3\cdot t^{2}+5} \right)\cdot \left(\frac{t^{2}}{t^{2}} \right)[/tex]
[tex]c = \lim_{t\to +\infty}\frac{\frac{t}{t^{2}} }{\frac{3\cdot t^{2}+5}{t^{2}} }[/tex]
[tex]c = \lim_{t\to +\infty} \frac{\frac{1}{t} }{3+\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{\lim_{t\to +\infty}\frac{1}{t} }{\lim_{t\to +\infty}3+\lim_{t\to +\infty}\frac{5}{t^{2}} }[/tex]
[tex]c = \frac{0}{3+0}[/tex]
[tex]c = 0[/tex]
The horizontal asymptote of [tex]C(t)[/tex] is [tex]c = 0[/tex].
b) When t increases, both the numerator and denominator increases, but given that the grade of the polynomial of the denominator is greater than the grade of the polynomial of the numerator, then the concentration of the drug converges to zero when time diverges to the infinity. There is a monotonous decrease behavior.
c) From Calculus we understand that maximum concentration can be found by means of the First and Second Derivative Tests.
First Derivative Test
The first derivative of the function is:
[tex]C'(t) = \frac{(3\cdot t^{2}+5)-t\cdot (6\cdot t)}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}-\frac{6\cdot t^{2}}{(3\cdot t^{2}+5)^{2}}[/tex]
[tex]C'(t) = \frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right)[/tex]
Now we equalize the expression to zero:
[tex]\frac{1}{3\cdot t^{2}+5}\cdot \left(1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} \right) = 0[/tex]
[tex]1-\frac{6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]\frac{3\cdot t^{2}+5-6\cdot t^{2}}{3\cdot t^{2}+5} = 0[/tex]
[tex]5-3\cdot t^{2} = 0[/tex]
[tex]t = \sqrt{\frac{5}{3} }\,h[/tex]
[tex]t \approx 1.291\,h[/tex]
The critical point occurs approximately at 1.291 hours after injection.
Second Derivative Test
The second derivative of the function is:
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}-\frac{(12\cdot t)\cdot (3\cdot t^{2}+5)^{2}-2\cdot (3\cdot t^{2}+5)\cdot (6\cdot t)\cdot (6\cdot t^{2})}{(3\cdot t^{2}+5)^{4}}[/tex]
[tex]C''(t) = -\frac{6\cdot t}{(3\cdot t^{2}+5)^{2}}- \frac{12\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
[tex]C''(t) = -\frac{18\cdot t}{(3\cdot t^{2}+5)^{2}}+\frac{72\cdot t^{3}}{(3\cdot t^{2}+5)^{3}}[/tex]
If we know that [tex]t \approx 1.291\,h[/tex], then the value of the second derivative is:
[tex]C''(1.291\,h) = -0.077[/tex]
Which means that the critical point is an absolute maximum.
The time at which the concentration is highest is approximately 1.291 hours after injection.
How many yards will the players have run ?? Please help
Answer:
125.3 yards
Step-by-step explanation:
He wants them to run the so 110^2+60^2 =which is 125.3.
Hope this helps plz mark brainliest :D
14) Find the product of seven times five and two
thousandths.
Answer:
35.015
Step-by-step explanation:
see attached image
What type of dance does a geometry teacher like
Answer:
line dancing, square dancing, etc
Step-by-step explanation:
Answer: square dancing, circle dancing, line dancing.
Hope this helps... Stay safe and have a great day/night!!! :D
I have 12 coins x of them are R5 coins and the rest are R1 coins. An expression in the in terms of x for the number of R1 coins I have is
Answer:
ans= 12-x=r1 coin...
Step-by-step explanation:
hope u can do..
3
If a is 63% of x and c is
8
the closest equivalent of the ratio of a to c?
ã of x, which of the following is
O
С C
E
Answer:
The closest equivalent of the ratio of a to c will be:
a/c=1.680
Step-by-step explanation:
As 'a' is 63% of x
so
[tex]a=0.63x[/tex]
As 'c' is 3/8 of x
so
c=3/8
Thus, the closest equivalent of the ratio of a to c will be:
a/c = (0.63x)/(3/8x)
= 1.680
Therefore, the closest equivalent of the ratio of a to c will be:
a/c=1.680
Subtract 52.35 − 1.58 =
(5 points)
Answer:
52.35-1.58= 50.77
Step-by-step explanation:
change 0.18 into a ratio
What is the slope of the line shown below?
Answer:
m=-2
Step-by-step explanation:
Rewrite the equation -3x+6y=42 in slope intercept form. Show all steps to receive full credit
Answer:
-3x+6y=42
-3x+6y-42=0
-x+2y-14=0
x-2y+14=0
Answer:
Step-by-step explanation:
Slope intercept form: y = mx + c
-3x + 6y = 42
6y = 3x + 42
y = [tex]\frac{3}{6}x + \frac{42}{6}[/tex]
y = [tex]\frac{1}{2}x + 7[/tex]
which table represents a proportional relationship that has a constant proportionality equal to 0.8
Answer:
1x0.8=0.8 ,10x0.08=0.8 and 100x0.008=0.8
Step-by-step explanation:
please help asap question 3****
Answer:
answer is c
Step-by-step explanation:
C is the only one with the correct slope
David cycled 4 laps on a bicycle path surrounding a lake. Each lap was the same length. If he cycled a total of 13.2 mi, what was the length of each lap around the lake? Write your answer in feet.
it's probably 17424 feet
Question
9. Deb ordered a set of red and yellow pins. She received 220 pins, and 40% of them were red. How many yellow pins did Deb
receive?
I’ve never been good with math, can u help?
Which ratio is equivalent to the ratio 7 : 350?
Answer:
Choice D. 17:850
Answer:
D
Step-by-step explanation:
17/7=2.42857142857
multiply 350 by that big number=850 So D
Marty collects colorful paper clips. Each week he is sure to add exactly five new paper clips to his collection. Make a table representing this situation. Is the number of paper clips and arithmetic or geometric sequence? How do you know? I need the answer by today please. Whoever answer is correct I will make brainliest
Answer:
all of them
Step-by-step explanation:
please make a word problem out of this equation x + 3 > 2
like someone make a word problem like bob had this much apples something like that with that equation.
please and Thankyou
Answer:
Bob had x apples and Mary had 2 apples. After Bob received 3 more apples from his mother, Bob had more apples than Mary. How many apples did Bob have at first?
Step-by-step explanation:
The inequality sign > shows that x + 3 is more than 2.
School lunch costs $1.25 per day. If there are 21 school days
this month, how much would it cost to eat at school all
month?. SHOW YOUR WORK., i need help asap
Answer:
$26.25
Step-by-step explanation:
1.25 per day
21 days
1.25 × 21 = 26.25
What is the volume of a cylinder ft, with a height of 9 feet in a base diameter of 16ft? Round to the nearest tenths place ?
1809.56ft³ <<<<<<<<<<<<<<<<Answer
Answer:
452.7 ft³
Step-by-step explanation:
sooooo first you find the radius of the base.
Radius=16/2=8
now you find the area of the base:
Area of a circle=2(pi)(radius)=50.3 ( rounded up to the nearest 10ths)
now to get the volume:
volume of a cylinder=Base*hight=50.3*9= 452.7 ft³
PLZ ANSWER THIS AND GIVE AN EXPLANATION!!!
I WILL MARK BRAINLIEST!!!
Answer:
-3+(-5)=-8
-5+(-3) is also -8
Step-by-step explanation:
if the parenthesis is separating the + and - then you just add the numbers and add the symbol.
In the following expression, both A and B are variables that can take positive values.
2\sqrt(A)-(B)/(5)
Which of these actions will cause the expression's value to increase?
Choose 2 answers:
(Choice A)
Keeping A constant and increasing B
(Choice B)
B
Keeping A constant and decreasing B
(Choice C)
C
Increasing A and keeping B constant
(Choice D)
D
Decreasing A and keeping B constant
Answer:
(Choice B) Keeping A constant and decreasing B
(Choice C) Increasing A and keeping B constant
Step-by-step explanation:
Let us analyze these two options.
2√a - b /5
(Choice B) Keeping A constant and decreasing B
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
But if A is kept constant and B is decreased to 20
2√100 - 20/5
= 2(10) - 4
= 20 -4= 16
We see the expression value has increased from 14 to 16.
Similarly analyzing Option C
(Choice C) Increasing A and keeping B constant
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
Now increasing A to 121 and keeping B constant would give
Let a = 100 and b= 30
2√121 - 30/5
= 2(11) - 6
= 22 -6= 16
This also increases the expression's value
But the other two choice A and D do not give the same result.
Let a = 100 and b= 30
2√100 - 30/5
= 2(10) - 6
= 20 -6= 14
(Choice A)
Keeping A constant and increasing B
2√100 - 40/5
= 2(10) - 8
= 20 -8= 12
This decreases the value .
Also
(Choice D)
Decreasing A and keeping B constant
2√81 - 40/5
= 2(9) - 8
= 18 -8= 10
This also decreases value
The correct choices are B and C
Answer:
the acutal solution is B and D
Find the next three terms of the sequence: 33, 25, 18, 12, …….
a) 7, 2, -1
b) 8, 3, 0
c) 7, 3, 0
d) 6, 2, -1
pls help and show work
The required terms are 7, 3 and 0. The correct option is (c).
What is an arithmetic sequence?
An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given sequence is as below,
33, 25, 18, 12, …….
The difference between the consecutive terms is given as,
D₁ = 25 - 33
= -8
D₂ = 18 - 25
= -7
D₃ = 12 - 18
= -6
It is clear that the difference between the consecutive terms are in arithmetic progression.
Thus, the next differences can be found as,
D₄ = -6 + 1
= -5
D₅ = -5 + 1
= -4
And, D₆ = -4 + 1
= -3
The next three terms of the sequence can be written as,
12 - 5 =7, 7 - 4 = 3, 3 - 3 = 0.
Hence, the next three terms of the given sequence are 7, 3 and 0.
To know more about arithmetic sequence click on,
https://brainly.com/question/15412619
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(Ill give brainliest!! Pls explain your reasoning tho)
What is a reasonable estimate for the equation 9.8 ÷ 5 = ________?
A) 6
B) 5
C) 3
D) 2
Answer:
i think its C
Step-by-step explanation:
I dunno i just think its C
Solve for a.
Pythagorean Theorem: a^2+b^2=c^2
Answer:
square root of 16
Step-by-step explanation:
Declan has $45 dollars in his bank account. He accidentally breaks a glass and has to pay to replace it. He now has $9 in his bank account. What is the percent decrease?
Answer: The percent decrease is 98.44 brainliest please :)
In the diagram shown, M, N and P are collinear and QM=QN as shown. If mMQN = 48" and
mNQP = 33. Justify why QNP must be isosceles.
Answer/Step-by-step explanation:
Let's find the measure of the angles of ∆QNP.
∆QMN is am isosceles ∆, because it has two equal sides. Therefore, its base angles would be the same. Thus:
m<MNQ = ½(180 - 48) (one of the base angles of ∆QMN)
m<MNQ = ½(132) = 66°
Next, find m<QNP
m<QNP = 180° - m<MNQ (linear pair angles)
m<QNP = 180° - 66° (Substitution)
m<QNP = 114°
Next, find m<P
m<P = 180 - (m<QNP + m<PQN) (sum of ∆)
m<P = 180 - (114 + 33)
m<P = 180 - 147
m<P = 33°
Thus, in ∆QNP, there are two equal angles, namely, <P and <PQN.
An isosceles ∆ had two equal base angles. Therefore, ∆QNP must be an isosceles ∆.
An isosceles triangle is that the triangle must have two sides of equal length.
Triangle QNP is isosceles triangle because, QN = PN
In triangle QMN,
Since, QM = QN
So, ∠QMN = ∠QNM
By property of triangle:
∠MQN + ∠QNM + ∠QMN = 180
48 + 2 ∠QNM = 180
∠QNM = [tex]\frac{180-48}{2}[/tex] = 66 degree
So, ∠QMN = ∠QNM = 66 degree
from figure,
∠QNM + ∠QNP = 180
∠QNP = 180 - 66 = 114 degree.
In triangle QNP,
∠QNP + ∠PQN + ∠QPN = 180
∠QPN = 180 - 33 - 114 = 33 degree
Since, ∠QNP = ∠QPN = 33 degree
Therefore, triangle QNP is isosceles triangle.
Learn more:
https://brainly.com/question/19414224
Tell whether (1,-1) is a solution of y
9x - 10
Answer:
yes, it is
Step-by-step explanation:
plug in the point (1, -1) (x,y) into the equation y = 9x - 10
-1 = 9(1)-10
-1 = 9-10
-1=-1
Betty is making a scale model of her house as a project for her math class. The scale she is using is 1 inch: 4 feet. The actual house is 80 feet long. What will be the length of the model?
Answer:
20 inches
Step-by-step explanation:
80 / 4 = 20 !!!!! <3
combine like terms 2.4m- 125 + 1.8b+ 92.4
Answer:
2.4m+1.8b−32.6
Step-by-step explanation:
Group like terms together
1. 2.4 m + \left( - 125 + 92.4 \right) + 1.8 b2.4m+(−125+92.4)+1.8b
2 . Add or subtract the numbers
2.4 m- 32.6 + 1.8 b2.4m−32.6+1.8b
3 . Rearrange the expression
2.4 m + 1.8 b- 32.62.4m+1.8b−32.6
Answer:
2.4m+1.8b-32.6
Step-by-step explanation:
2.4m- 125 + 1.8b+ 92.4
2.4m+1.8b-32.6