Given f and g in the graph, what is f(g(2)) ?
The required value of function f(g(2)) = 1.
What is a composite function?
When the result of one function is utilized as the input for another, this is known as a composite function.
Typically, a composite function is a function that is embedded within another function. The process of creating a function involves replacing one function for another.
Given, to find the value of the given function f(g(2))
First, we need to find the value of g(2) from the given graph
i.e. g(2) = 4 (i.e. x = 2)
Then, the above value is an input for function f.
So, f(4) = 1 (from the graph at x = 4)
Hence, the value of function f(g(2)) = 1.
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6. Simplify (x + 7)(x + 5).
Answer:
[tex]x^{2} +12x+35[/tex]
Step-by-step explanation:
Distribute
(X+7)(X+5)
x^2+5x+7x+35
X^2+12x+35
Hopes this helps please mark brainliest
Answer:
x^2 + 12x + 35
Step-by-step explanation:
Hi! I solved this using the FOIL, or firsts, outsides, insides, and lasts, to simplify:
The firsts, or F, would be: x*x which equals x squared (x^2)
The outsides, or O, would be: x*5 which equals 5x
The insides, or I, would be 7*x which equals 7x
The lasts, or L, would be 7*5 which equals 35
Then, the FOIL method says to add up all the answers you got together:
x^2+5x+7x+35
and then you simplify and get:
x^2+12x+35
I hope this made sense! :)
If g(x) is the image of y=−2x^2−20x+2 after a translation right 4 units and up 2 units, write the equation of g(x) in the standard form of a quadratic function and describe its graph.
Enter the quadratic expression in standard form, a(x−h)2+k .
The standard form equation is g(x)=
The image of y = −2x^2 − 20x + 2 after a translation right 4 units and up 2 units is written in:
the form a(x−h)^2 + k is -2(x + 1)^2 - 107standard form of the equation is g(x) = -2x^2 - 4x - 108The graph will be a vertical parabola opening downwards
How to get the transformation imagewhen the function y = −2x^2 − 20x + 2 translates right 4 units it gives
y = -2(x - 4)^2 − 20(x - 4) + 2
going up two units
y = -2(x - 4)^2 − 20(x - 4) + 2 + 2
simplifying the equation further gives
y = -2(x - 4)(x - 4) − 20(x - 4) + 4
y = -2(x^2 - 8x + 16) - 20x - 80 + 4
y = -2x^2 + 16x - 20x - 32 - 80 + 4
y = -2x^2 - 4x - 108
completing the square
-2x^2 - 4x - 108 = 0
-2x^2 - 4x = 108
-2x^2 - 4x + (4/4)^2 = 108 -(4/4)^2
-2x^2 - 4x + (1)^2 = 108 - 1
-2(x + 1)^2 - 107
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Patricia and Sandra have some apples.
Patricia says to Sandra, "If you give me 14 of your apples, I will have twice the number of apples left with you".
Sandra replies, "if you give me 14 of your apples I will have the same number of apples left with you".
Find the the number of apples with Patricia and Sandra separately.
Answer:
28
Step-by-step explanation:
Because 14 times 2 is 28, and 28 divided by 2 is 14.
A colony of bacteria grows by 5% every hour. How long does it take for the colony t
double in size?
Answer: 20 hrs
Step-by-step explanation:
Find an equation of the line described. Write the equation in slope-intercept form if possible.
Slope −2, through (−5, −2)
Please help it would make my day.
Answer:
part A=329.99=25.72+23.50x
part B=12.95=13 weeks
Step-by-step explanation:
need=329.99
have=25.72
save=23.50 per week
equation329.99=25.72+23.50x
23.50x=(329.99-25.72)
23.50x=304.24
x=12.95
=x =13
Differentiate the function with respect to x. Shot steps
The differentiation of the function f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
What is function?Function is a combination of different types of variable and constants.
A function is denoted by f(x).
The given function is,
f(x) = sin⁻¹(3x⁵)
Differentiate the given function with respect to x
f'(x) = d/dx(sin⁻¹(3x⁵))
The differentiation of sin⁻¹x is [tex]1/\sqrt{1-x^2}[/tex],
f'(x) =[tex]1/\sqrt{1-(3x^5)^2}\cdot d/dx(3x^5)[/tex]
= [tex]1/\sqrt{1-9x^{10}}\cdot 15x^4[/tex]
= [tex]15x^4/\sqrt{1-9x^{10}}[/tex]
The differentiation of f(x) = sin⁻¹(3x⁵) is [tex]15x^4/\sqrt{1-9x^{10}}[/tex].
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What does this mean in the context of the situation?
The value of h(46) is 168.13.
h(46) means the height of a female whose femur has a length of 46 is 168.13
What is the value of H(46)?The equation that can be used to determine height is a linear function. A linear function is a function that increases at a constant rate. A linear function has a single variable that is raised to the power of one.
The given equation is: h(x) = 61.41 + 2.32x
Where:
61.41 = intercept 2.32 = slope x represents the length of the femurh(46) means the height of a female whose femur has a length of 46.
61.41 + 2.32(46)
61.41 + 106.72 = 168.13
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Simplify.
-6,602 - (-4,899)
The value of -6,602 - (-4,899) is -1703.
What is simplification?
Simplification of expressions means rewriting the same algebraic expression with no like terms and in a compact manner. Making something simpler is making it less complex.
simplify mathematical expressions by grouping and combining similar terms. This makes the expression easily understandable and solvable.
Given,
-6,602 - (-4,899)
And to simplify it,
we know -(-) = +
we get, after simplification
-6,602 + 4,899 = -1703.
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I really need help!! These fractions are confusing me !
The values of the composite functions f(g(x)) and g(f(x)) are (x/4) and (4x - 9),respectively.
We are given two functions, f(x) and g(x). The function f(x) is defined as 1/(x - 3). The function g(x) is defined as (4/x) + 3. A function connects an input to an output. It is analogous to a machine with an input and an output. And the outcome is somehow connected to the input. We need to find the composition of the functions.
The first composition is f(g(x)). The composite function is solved below.
f(g(x)) = f((4/x) + 3)
f(g(x)) = 1/([(4/x) + 3] - 3)
f(g(x)) = 1/(4/x)
f(g(x)) = x/4
The second composition is g(f(x)). The composite function is solved below.
g(f(x)) = g(1/(x - 3))
g(f(x)) = (4/[1/(x - 3)]) + 3
g(f(x)) = 4(x - 3) + 3
g(f(x)) = 4x - 12 + 3
g(f(x)) = 4x - 9
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Question 13 of 50
If the graph of a system shows two parallel lines, it means that the system has:
no solution.
one solution.
three solutions.
two solutions.
an infinite number of solutions.
Answer:
Step-by-step explanation:
No solution. This is because they do not cross.
1. Jason runs 11 km every day. How far will he run in a week?
Answer: 77 km
Step-by-step explanation:
There are 7 days a week. If Jason runs 11 km each day, the equation for how far he'll run in a week is 7 x 11 km.
7 x 11 km = 77 km.
Which of the following graph(s) can be used to show data in intervals? (Check all that apply.)
frequency table
histogram
line plot
stem-and-leaf plot
The graph that shows data in intervals is the: B. histogram.
What is an Histogram?An histogram is a graph which is used to visualize data in intervals, as rectangular bars. The image attached below is a typical example of an histogram. The graph shows the data in intervals.
A frequency table can also show a set of data that are given in intervals, however, it is not a graph. It can rather be used to create graphs that have intervals, such as a histogram.
Line plot and stem-and-leaf plot are both graphs that show individual data points rather than show the data in intervals.
The answer is therefore: B. histogram.
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Evaluate the exponential function f(x)=12^x
Answer:
f(3) = 1728
f(-2) = 1/144
f(1/2) = 2sqrt(3)
Step-by-step explanation: all you is replace x with what ever is in the parenthesis
Estimate L4 and R4 over [0,7] for the function f(x) = 6x^2
The value of L4 and R4 over [0,7] for the function f(x) = 6x² will be 2[2√0 + 2√2 + 2√4 + 2√6] and 2[2√2 + 2√4 + 2√6 + 2√8] respectively.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that the function is,
I'm assuming that you mean the left and right Riemann sums with four equal subintervals when you refer to L4 and R4.
If so, then Δx = (8-0)/4 = 2, and f(x) = 2√x.
L4 = f(0)Δx + f(2)Δx + f(4)Δx + f(6)Δx
L4 =2[2√0 + 2√2 + 2√4 + 2√6]
R4 = 2[2√2 + 2√4 + 2√6 + 2√8]
Thus, the value of L4 and R4 over [0,7] for the function f(x) = 6x² will be 2[2√0 + 2√2 + 2√4 + 2√6] and 2[2√2 + 2√4 + 2√6 + 2√8] respectively.
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HELP ASAP PLEASE
The following angles are supplementary to each other.
m∠A = (2x − 27)° and m∠B = (3x + 27)°
Determine x.
55
36
18
9
Two angles A and B are supplementary when the value of x is 36°.
What are supplementary and complementary angles?Two angles are said to be supplementary if their sum is 180°.
Two angles are said to be complementary if their sum is 90°.
Given, m∠A = (2x − 27)° and m∠B = (3x + 27)° are supplimentary to each other.
∴ (2x - 27)° + (3x + 27) = 180°.
2x + 3x - 27 + 27 = 180°.
5x = 180°.
x = 36°.
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PLEASE HELP!
100 POINTS + BRAINLIEST IF CORRECT
Answer:
a = 0
b = 0
c = 0
Step-by-step explanation:
Select all expressions that are equivalent to the following: 6x - 2 - 8x + 13
Answer:
-2x + 11
Step-by-step explanation:
13 - 2 = 11
6x - 8x = -2x
You used 8 cups of sugar while baking
three dozen cookies and one cake. If you
used 1.25
cups of sugar for the cake and
the same amount of sugar for each dozen
of cookies, how much sugar was used for
each dozen of cookies?
Answer:
2.25 cups of sugar per dozen cookies
Step-by-step explanation:
8 - 1.25 = 6.75
6.75 ÷ 3 = 2.25
Which number sentence is true?
A.
B.
C.
D.
Answer: D
Step-by-step explanation:
The square root of 50 is less than 8.34, the square root of 15 is less than the absolute value of 4.32, 2.3x10^1 is greater than 2 2/5.
The absolute value of 5.43 is less than 2.1x10^1.
The function C(x) represents the cost, in dollars, of renting a bicycle for x hours.
Which statement BEST represents the statement C(5) = 15?
15 bicycles can be rented for 5 hours.
The cost of renting 5 bicycles is 15 dollars.
A
B
C
D
The cost of renting a bicycle for 5 hours is 15 dollars.
The cost of renting a bicycle for 15 hours is 5 dollars.
The best represents the statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.
What is a function?
A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
Here, we have
Given the function C(x) represents the cost, in dollars, of renting a bicycle for x hours.
So, the best statement that represents the given statement C(5) = 15 is the cost of renting a bicycle for 5 hours is 15 dollars.
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Does anybody know this!
Complete (assume $60,000 of overhead to be distributed): (Enter amount of overhead allocated as whole dollar amounts. Round your ratio answers to the nearest hundredth.) Sq. Ft. Ratio Amount of Overhead Allocated Dept. A 10,000 A B Dept. B 30,000 C D
The completion of the ratios, resulting from the square feet occupied by Departments A and B, and the amounts of allocated overhead costs to the two departments are as follows:
Ratio Amount
Department A 0.25 $15,000
Department B 0.75 $45,000
What is the ratio?The ratio is the proportion of the whole shared by two or more numbers.
Ratios are fractional values like proportions.
Ratios, depicted in fractions, decimals, and percentages, show how much a value or variable is contained in another.
Total distributable overhead = $60,000
Ratios = 10,000:30,000
= 1:3
Sum of Ratios = 4
OR
= 0.25:0.75
Sum of Ratios = 1
Overhead Allocation:Department Square Feet Ratio Amount of Overhead Allocated
Dept. A 10,000 A = 1 B = $15,000 ($60,000 x 0.25)
Dept. B 30,000 C = 3 D = $45,000 ($60,000 x 0.75)
Thus, based on the cost driver ratios, Department A bears $15,000, while Department B will be allocated $45,000 of the distributable overheads.
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........hELP pLEASE........
The total amount that Ms. Henderson must pay, given the penalty and the amount of taxes is $1, 478.75
How to find the total amount to be paid?First, find the total penalty on the taxes, to Ms. Henderson.
= Tax amount x Penalty percentage
= 1, 400 x 11 ¹ / ₄%
= $157.50
Because she paid in 6 months, but the penalty is for a year, Ms. Henderson's tax penalty is:
= 157.50 / 2
= $78.75
The total amount to be paid is:
= Taxes owed + Penalty
= 1, 400 + 78. 75
= $1, 478.75
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n a certain city, it was found out that there are 100 residents who are employed
in the office of the city mayor. They are classified as follows:
48 female employees
46 married employees
34 employees with more than 15 years of service
19 married females
18 married with more than 15 years of service
17 female with more than 15 years of service
8 married female with more than 15 years of service
Questions:
1.How many are married female employees with less than 15 years of service?
2.How many are married male with more than 15 years of service?
3.How many are female single employees with more than 15 years of service?
4.How many are married female with more than 15 years of service?
5.How many are male single employees with less than 15 years of service?
Answer:
1. 11 married females because out of the 19 married, only 8 had more than 15 years of service and 19 - 8 = 11.
2. 10 married males because of out the 18 married with more than 15 years of service, 8 were females and 18 - 8 = 10.
3. 9 single females because out of the 17 with more than 15 years of service, 8 were married and 17 - 8 = 9.
4. 8 married females because it literally says, "8 married female with more than 15 years of service".
gotta go hope this helps sry
given that the hcf of two numbers is 16 and their product is 6,400 determine there LCM
Given that the HCF of two numbers is 16 and their product is 6,400 then LCM is 400.
What is the relation between product of numbers, LCM and HCF?
The relation between LCM, HCF and product of two numbers is as follows:
LCM x HCF = Product of two numbers
According to the given question:
Let the numbers be x and y
Product of the numbers, x*y = 6400
HCF of the numbers is 16
Now according to the relation between numbers, LCM and HCF
LCM x 16 = 6400
LCM = 6400/16
LCM = 400
Hence LCM of the numbers is 400
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Elena's mother's painting service charges $10 per job and $0.20 per square foot. If she earned $50 for
painting one job, how many square feet did she paint at the job? Write an equation and solve.³
Answer:
so the total charge for the job was $50,
so all we need is the finding of x (# of square feet):
10 + 0.20x = 50
Step-by-step explanation:
Solving for x:
0.20x = 50 - 10
0.20x = 40
x = 40/0.20
x = 200 square feet
hope it helps!
reduce the following ratio to their lowest terms 1km to 250m
The ratio in their lowest terms is 4:1
What is a ratio?
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The proportion of lemons to oranges is also 6:8.
We are given two values 1km and 250m
We known that 1km = 1000m
Hence we have to find the ratio of the value 1000m to 250m
To find the ratio just Divide the two numbers we get
1000/250
=4/1
=4:1
Hence the smallest ratio for the term is 4:1
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ook at the figure:
An image of a right triangle is shown with an angle labeled x.
If tan x° = e divided by 8 and sin x° = e divided by f, what is the value of cos x°?
cos x° = 8 divided by f
cos x° = f divided by 8
cos x° = 8f
cos x° = 8e
The value of cos x° is 8 divided by f
How to find the value of cos x°?
We will use trigonometrical ratios to solve this problem. Below are the definitions of the trigonometrical ratios:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent or tan = sin/cos
The opposite is the side the angle of consideration is facing
The hypotenuse is the side the right angle is facing
The adjacent is the side left after determining the opposite and hypotenuse
Given: tan x° = e/8 and sin x° = e/f
Since tan = opposite/adjacent, that means in tan x° = e/8, opposite = e and adjacent = 8. Also, sin = opposite/hypotenuse, so in sin x°= e/f, hypotenuse = f
And cos = adjacent/hypotenuse. Thus, cos x° = 8/f.
Therefore, the value is cos x° = 8 divided by f is the answer. Pick the first option
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