Answers
The value of the function f(a+4) is [tex]\frac{7}{a^{2} +8a+11}[/tex]
What is a function?function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable called the dependent variable.
if f(x) = [tex]\frac{7}{x^{2} - 5}[/tex], which means this equation is a function of x,
To find another equation whose function is f(a + 4)
We substitute x for a + 4 in the above equation
f(a+4) = [tex]\frac{7}{(a+4) ^{2} - 5 }[/tex]
expanding [tex](a + 4)^{2}[/tex], and simplifying the denominator, we have
[tex]a^{2}[/tex] +8a + 16 - 5 = [tex]a^{2}[/tex] + 8a + 11
so the simplified form of the new function would be [tex]\frac{7}{a^{2} +8a+11}[/tex]
In conclusion, the function f(a +4) = [tex]\frac{7}{a^{2} +8a+11}[/tex]
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Related Questions
Please help me with this thank you :)))
Answers
Answer:
Step-by-step explanation:
Which expression is equivalent to 1 2/9 x 6/16
Answers
Answer:
0.45833333333 or 11/23
Step-by-step explanation:
1 2/9*6/16 is simply 11/23, cross multiply and simplify
What fraction is represented by .8 point is a blank which point represents 56 point blank represents 56
Answers
The fraction that represents 0.8 is 4/5 .
Fraction can be defined as a numerical quantity that is part of a whole number . it is written in the form of a/b , where a is called the numerator and b is called the denominator .
For Example , 1/2 , 3/8 4/9 are all fractions .
In the question ,
it is given that the point is 0.8 ,
we need to convert this point in fraction ,
the point 0.8 in fraction can be written as 8/10 ,
= 8/10
simplifying further ,
we get
= 4/5
Therefore ,The fraction that represents 0.8 is 4/5 .
The given question is incomplete , the complete question is
What fraction is represented by 0.8 ?
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The radius of a spherical ball is increasing at a rate of 2 cm/min. At exactly what rate (in cm2/min) is the surface area of the ball increasing when the radius is 6 cm?
Answers
The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Surface area of SphereThe surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]
Given;
S = surface area at time t, and r = radius at time t
radius of a spherical ball is increasing at a rate of 2 cm/min
radius: 6cm
Area of a sphere is A = 4π[tex]r^{2}[/tex]
Step 1: Differentiate area of a spherical ball
A = 4π[tex]r^{2}[/tex]
[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])
=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])
=4π2r [tex]\frac{dr}{dt}[/tex]
[tex]\frac{dA}{dt}[/tex] = 8πr
since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;
[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π
So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.
Note that measuring area unit is cm2/min
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A pool can be filled by one pipe in 3 hours and by a second pipe in 5 hours. How long will it take using both pipes to fill
the pool?
Answers
Answer:
i think it 8h
Step-by-step explanation:
perpendicular bisector of the line segment whose endpoints are 7,4) and (−9,−4).
Answers
Answer:
y=-2x-2
Step-by-step explanation:
If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:
[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.
Now we find the equation!
y=mx+b. Plug in -[tex]2[/tex] as the "m", or slope:
y=-[tex]2[/tex]x+b
Now, plug in the point (-1, 0):
0=-[tex]2[/tex]*-1+b
0=[tex]2[/tex]+b
b=-[tex]2[/tex]
So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!
y=-[tex]2[/tex]x-[tex]2[/tex]
Hope this helps!! :D
Use the graph below to answer the following questions.
⦁ Estimate the available territory at 20 years
⦁ Estimate the available territory at 15 years
⦁ Does this graph represent exponential growth or decay?
⦁ As the time decreases the available territory _______________
Answers
Answer:
a) about 190 acres
b) around 240 acres
c) exponential decay because the amount of land available is decreasing at an increasingly rapid rate over time.
Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.51 ⨯ 10−5
watts/cm2
Answers
The 2.51 × 10⁻⁵ Watts/cm² sound intensity of the sound from the rocket engine has a decibel level of 114 dB
What is a decibel?A decibel is a unit to measure the relative loudness of sound or to express the ratio electrical or acoustic power.
The intensity of the sound of the rocket engine = 2.51 × 10⁻⁵ Watts/cm²
Converting the unit of the sound intensity to Watts/m² gives;
1 cm² = 0.0001 m²
10,000 cm² = 1 m²
2.51 × 10⁻⁵ Watts/cm² = 10000 × 2.51 × 10⁻⁵ Watts/m² = 0.251 Watts/m²
The equation for the decibel from the power of sound is presented as follows;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{I}{I_0} \right)[/tex]
Where;
I₀ = 10⁻¹² W/m²
Which gives;
[tex]\beta\ (dB)=10\cdot log_{10}\left(\dfrac{0.251 }{10^{-12}} \right) = 113.9967373215 \approx 114[/tex]
The number of decibels for the power of the sound given to the nearest decibel by the rocket engine is 114 decibels
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The data to the right represent the cost of living for 20
states. The cost of living is a measure of the average
price paid for housing, utilities, groceries, healthcare,
transportation, and miscellaneous expenses. The
national average cost of living is 100. The data can be
used to compare a state to the national average and
to other states.
T
Use these data to construct a frequency distribution with a first class of 85.0-94.9. Fill in the missing classes and the frequency for each class belo
Cost of living
Number of states
9
85.0-94.9
125.0134.9
8-8
20
(Type integers or decimals. Do not round.)
151.2121.3 99.4 94.5 89.7
138.7120.1 96.7 94.5 89.6
132.1106.5 95.3 90.9 89.4
124.9101.6 95.2 90.1 89.2
Answers
The frequency distribution based on the information given is illustrated below.
What is the frequency distribution of table?
A frequency distribution table is the chart that summarizes all the data under two columns - variables/categories, and their frequency.
It should be noted that the distribution table has two or three columns and the first column lists all the outcomes as individual values or in the form of class intervals, depending upon the size of the data set.
Given the above information the frequency distribution table is:
Cost of living[tex]\begin{table}[]\begin{tabular}{ll}Cost of living & Number of States \\85.0 - 94.9 & 9 \\95.0 - 104.9 & 5 \\105.0 - 114.9 & 0 \\115.0 - 124.9 & 2 \\125.0 - 134.9 & 2 \\135.0 - 144.9 & 1 \\145.0 = 154.9 & 1 \end{tabular}\end{table}[/tex] Number of states
85.0 - 94.9 9
95.0 - 104.9 5
105.0 - 114.9 0
115.0 - 124.9 2
125.0 - 134.9 2
135.0 - 144.9 1
145.0 - 154.9 1
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Solve for x.
please help asap!
Answers
The sum of the first k positive integers is 990. What is k?
Pls give explaintion
Answers
Answer:
k=44
Step-by-step explanation:
1 + 2 + 3 + 4......+ k = 990
Arithmetic sequence with d = 1 a1 = 1
1 + 1+ 1 + 1 +2 ...... 1+ (k-1) = 990
ak = a1 + (k-1) <====formula for sequence
Sum of a sequence formula = Sk = k ( a1+ak)/2
990 = k ( 1 + (1 + k-1) /2
1980 = k^2 + k
k^2 + k - 1980 = 0 Use quadratic formula a = 1 b = 1 c = - 1980
to find k = 44
In an ecology experiment, a number of mosquitoes are placed in a container with water and vegetation. The population of mosquitoes, P, increases and can be modelled by the function:
P9T)=24*4^0.385t, t is greater than or equal to 0
Where t is the time, in days, since the mosquitoes were placed in the container.
(a) find the number of mosquitoes in the container after 5 days
The maximum capacity of the container is 5000 mosquitoes
(b) Find the number of days until the container reaches its maximum capacity.
Answers
Using the given exponential function, it is found that:
a) The number of mosquitoes in the container after 5 days is of: 346.
b) The number of days until the container reaches the maximum capacity is of: 10 days.
What is the exponential function?The exponential function that models this problem is presented as follows:
P(t) = 24(4)^(0.385t).
Hence, after five days, the number of mosquitoes is of:
P(5) = 24(4)^(0.385 x 5) = 346 mosquitoes.
The number of days that it takes for the container to reach it's maximum capacity of 5000 is obtained solving the exponential function with logarithms as follows:
[tex]5000 = 24(4)^{0.385t}[/tex]
[tex](4)^{0.385t} = \frac{5000}{24}[/tex]
[tex](4)^{0.385t} = 208.3[/tex]
[tex]\log{(4)^{0.385t}} = \log{208.3}[/tex]
Applying the power property of logarithms, we have that:
[tex]0.385t\log{4} = \log{208.3}[/tex]
[tex]t = \frac{\log{208.3}}{0.385\log{4}}[/tex]
t = 10 days.
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Differentiate the function with respect to x.
Answers
The differentiation of the given function is 12[tex]x^3[/tex](5[tex]x^2[/tex] +2).
In the given question we have to differentiate the given function with respect to x.
The given function is f(x) = [tex]2x^4(5x^2+3)[/tex]
Before differentiating the function we first simplify the given expression.
To simplify the expression we multiply the 2x^4 to each term under the bracket.
Now the function;
f(x) = [tex]2x^4\cdot5x^2+3\cdot2x^4[/tex]
As we know that if the base is same en power get added.
f(x) = [tex]10x^{4+2}+6x^4[/tex]
f(x) = [tex]10x^{6}+6x^4[/tex]
Now differentiating the function with respect to x.
f'(x) = d/dx([tex]10x^{6}+6x^4[/tex])
f'(x) = 10d/dx([tex]x^6[/tex]) + 6d/dx([tex]x^4[/tex])
As we know that d/dx of x^n =nx^(n-1). So
f'(x) = 10∙6 [tex]x^5[/tex] + 6∙4 [tex]x^3[/tex]
f'(x) = 60[tex]x^5[/tex]+24[tex]x^3[/tex]
Now taking 12x^3 common
f'(x) = 12[tex]x^3[/tex](5[tex]x^2[/tex] +2)
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Solve The Problem
All the students in grades 3, 4 and 5 are going on a field trip to Coney Island
Each grade has 125 students. The cafeteria needs to pack lunches. About how
many students are going on the trip? Represent the exact amount of student
in all three grades using an array, How many students are there altogether?
Answers
The number of Students going on the trip is 375.
In the question,
It is given that:
There are 125 students in Grade 3.
There are 125 students in Grade 4.
There are 125 students in Grade 5.
So, Total number of students going on trip = Number of students in Grade 3 + Number of students in Grade 4 + Number of students in Grade 5
= 125 + 125 + 125 = 375.
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A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.24t2 + 12t feet per second after t seconds (for 0 ≤ t < 30).
a.
Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time
t = 0.]
b.
Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.)
Answers
The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.
What is the relation between speed and distance?Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.
The speed formula is speed = distance/time.
We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).
Then the distance that it will travel from its starting point in the first t seconds is;
[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]
At zero it will be 12 feet.
b. the distance (in ft) that the car will travel in the first 10 seconds.
-0.48(10) + 12 = 16.8 feet.
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Please only answer if you know the answer for sure,
URGENT
Answers
Find point C on the x-axis so that AC + BC is a minimum.
A(-8,4), B(-1,3)
Answers
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
A(x₁,y₁) = (-8,4)
B(x₂,y₂) = (-1,3)
C(x, y ) = (x ,0)
equation of a line is given as:
y - y₁ = (y₂ - y₁)/ (x₂ - y₁) (x - x₁)
y - 4 = (3 - 4)/(-1 + 8)(x + 8)
y - 4 = -1/7(x + 8)
7(y - 4) = -1(x + 8)
7y - 28 = -x + 8
x + 7y - 36 = 0
when y = 0 then the value of x is given as:
x + 7y- 36 = 0
x + 7(0) - 36 = 0
x = 36
point C on the x-axis (x , 0) = (36,0)
The point C on the x-axis when A(-8,4), B(-1,3) so that AC + BC is a minimum is (36,0).
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A student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30. How many
more monthly payments must be maid to pay off the loan?
Answers
The number of months required to pay off the loan will be 15.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a student requests a loan for $1178.80. The monthly payment of the loan is $42.10. So far, the student has paid $547.30.
The number of the months will be calculated as,
N = ( 1178.8 - 547.30) / 42.10
N = 631.5 / 42.10
N = 15
Therefore, the number of months required to pay off the loan will be 15.
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Solve for the value of T
Answers
Step-by-step explanation:
4t - 7 + 83 = 180
4t + 76 = 180
4t = 104
t = 26
A standard toilet uses 1.6 gallons per flush. If a toilet is flushed two times per day, how much water will be used in a week (7 days)?
Answers
Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.
What is Multiplication?
In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.
Solution:
Given that,
The standard toilet uses 1.6 gallons of water per flush
Also, it is flushed twice a day
To Find, Total water used in a week i.e. 7 days
Since, flush uses 1.6 gallons water per flush
Total water used in a day is 2*1.6 = 3.2 gallons
This implies,
Total water used in 7 days = 7 * 3.2 = 22.4 gallons
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His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas
mileage in his new car?
Answers
The Xavier is not getting better mileage with his new car .
In the question ,
it is given that
distance travelled by Xavier's new car in 25 gallons = 528 miles
the mileage can be calculated using the formula = (distance travelled)/( gallons of fuel used) .
So , mileage of the new car = 528/25 = 21.12 miles per gallon ,
the milage of Xavier's former car = 20.28 miles per gallon .
From the above data , we can see that the mileage of former car is greater than new car .
Therefore , The Xavier is not getting better mileage with his new car .
The given question is incomplete , the complete question is
Xavier's new car uses 25 gallons for 528 miles , His former car was able to travel 20.28 miles per gallon. Is Xavier getting better gas mileage in his new car?
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A rectangular fish tank has a base that is 4 inches by 9 inches. How much water will it take to fill the tank to a depth of 3 inches? A 150 cubic inches B 685 cubic inches C 108 cubic inches 16 cubic inches
Answers
Answer:
C: 108 cubic inches
Step-by-step explanation:
This problem is simply asking us to calculate volume, and in a rectangular shape can be calculate as: length * width * height
Since we know that the base is 4 inches by 9 inches, we already have the length and width.
We're also given that the depth, which in this case is our height, as 3 inches.
So we multiply these three numbers: [tex]4 \text{ in} * 9 \text{ in} * 3\text{ in} = 108\text{ in}^3[/tex]
So our answer is 108 cubic inches
help me out thanks 10 ponits
Answers
Answer:
yes yes ...................
MIXED REVIEW
Directions: Arrange the numbers in order from least to greatest.
21) 32%, pi, 2 1/2 √9
22) -3.4, -4, -3, -2 1/2, -pi
23) 250%, 3.4, -%, 0
Answers
The solution is
a) The ascending order is 32 % < 2 1/2 < √9 < π
b) The ascending order is -4 < -3.4 < -3 < -2 1/2 < π
c) The ascending order is -5/8 < 0 < 250% < 3.4
What is Ascending Order?
When numbers are arranged in ascending order, they are done so from least to largest. We must first compare the numbers before we may arrange them in any order. Compare first, then order. Numbers arranged in ascending order: Determine how many digits each number has.
Given data ,
A)
32 % , π , 2 1/2 , √9
32 % = 32 / 100
= 0.32
π = 3.14
2 1/2 = 2.5
√9 = 3
So , arranging the numbers in ascending order we get ,
0.32 < 2.5 < 3 < 3.14
Hence , the ascending order is 32 % < 2 1/2 < √9 < π
B)
-3.4 , -4 , -3 , -2 1/2 , π
Hence , the ascending order is -4 < -3.4 < -3 < -2 1/2 < π
C)
250 % , 3.4 , -5/8 , 0
250 % = 2.5
-5/8 = -0.625
So , arranging the numbers in ascending order we get
-0.625 < 0 < 2.5 < 3.4
Hence , the ascending order is -5/8 < 0 < 250% < 3.4
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Graph the function with the given domain. Then identify the range of the function.
1) y = -6; domain: x ≥ 5
2) y = -x - 1; domain: -1 ≤ x ≤ 3
Answers
What is the solution to this system of equations?
3b + 4c = 3
8b+ 5c = 27
2b + 6c = 1
Answers
Here ya are hope this helps! :]]
Use a table of areas to obtain the shaded area under the standard normal curve.
Answers
The shaded area under the standard normal curve is 2.58%.
According to z-score table,
Area for < 2.23 = 0.9871
Area for >2.23 = 1 - 0.9871
= 0.0129
Area for < 2.23 = 0.0129
Total area = 0.0129 + 0.0129
= 0.0258
Area percent = 0.0258*100
= 2.58%
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What numbers are elements? -7, -4, 2, 14, 21, 34, 42
Answers
The answer is [14, 42].
The number 14 is even.
7 x 2 = 14
An even number, 42.
7 x 6 = 42
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Which of the following choices would move this curve to the RIGHT 17 units and up 4 units: y=(x+6)^2 - 2
Answers
If we start with the parent quadratic function, then the transformation is:
g(x) = (x - 17)^2 + 4
Which transformations move the graph in the desired way?The definitions of translations are:
Horizontal translation:
For a general function f(x), a horizontal translation of N units is written as:
g(x) = f(x + N).
If N is positive, the shift is to the left.If N is negative, the shift is to the right.
Vertical translation:
For a general function f(x), a vertical translation of N units is written as:
g(x) = f(x) + N.
If N is positive, the shift is upwards.If N is negative, the shift is downwards.
Then if the parent function is:
f(x) = x^2
The translation of 17 units to the right and 4 units up is:
g(x) = f(x - 17) + 4 = (x - 17)^2 + 4
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If A = 1
a.
-2 6 1
b.
-5
9 -6 and B= -2 -7
1
10
-99-9
-22 30 32
-16 -78 48
42 24 30
-32 72 30
-2
26 -20
-50
94 -58
9 6
4
-1
Ń
find-4A + 6B.
C.
d.
38
8
30
-78
-40
6 0
42
58
-96
8 0 -18
14
82 -52
Answers
The answer is option (a)
Hope this answer helps you
