The value of (fogoh)(x) is [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]
Here, we are given 3 functions as listed below:
f(x) = [tex]x^{3}[/tex] +8
g(x) = x - 2
and, h(x) = [tex]\sqrt{x}[/tex]
now, (fogoh)(x) can be written as follows-
f[g{h(x)}] = f{g([tex]\sqrt{x}[/tex])}
here, g([tex]\sqrt{x}[/tex]) = [tex]\sqrt{x}[/tex] - 2
Thus, f{g([tex]\sqrt{x}[/tex])} = f([tex]\sqrt{x}[/tex] - 2)
Substituting x = [tex]\sqrt{x}[/tex] - 2 in the function f(x) we get,
[tex](\sqrt{x} - 2)^{3}[/tex]+8
using the algebraic property [tex](a+b)^{3}[/tex] = [tex]a^{3} + b^{3}[/tex] + 3ab(a + b), we get-
= [tex]\sqrt{x^{3} }[/tex] - [tex]2^{3}[/tex] + 3[tex]\sqrt{x}[/tex](-2){[tex]\sqrt{x}[/tex] - 2} + 8
= [tex]\sqrt{x^{3} }[/tex] - 8 + 6x + 12[tex]\sqrt{x}[/tex] + 8
= [tex]\sqrt{x^{3} }[/tex] + 6x + 12[tex]\sqrt{x}[/tex]
Thus the value of (fogoh)(x) = [tex]\sqrt{x^{3} }[/tex] + 6x +12[tex]\sqrt{x}[/tex]
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What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%
The amount at the end of three years is 1.06 times the initial amount.
Simple interest is calculated using the following formula: = P × R × T, where P = principal, R = annual interest rate (%), T = hours, usually calculated as years. The interest rate is expressed as a percentage r% and written as r/100. Principal : Principal is the amount originally borrowed or invested by the bank. The capital is represented by P. Interest Rate : The interest rate is the rate at which the principal is given to someone for a period of time. The interest rate could be 5%, 10%, or 13%. The interest rate is represented by R. Time : Time is the length of time a principal is given to someone. Time is represented by T. Amount : When a person takes out a loan from a bank, he has to repay the amount of principal plus interest, and this repayment amount is called the amount.Rate = 2%
Time = 3 Years
Let the principal amount be P
Simple interest = P * R * T
SI = ( P * 2 * 3 ) / 100
= 6P/100
= 0.06P
Amount = P + SI
= P + 0.06P
= P(1 + 0.06)
= 1.06P
The amount at the end of three years is 1.06 times the initial amount.
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Solve the equation
22x+1 +2x+2 =12−2x
Answer:
x = (9/26)
Step-by-step explanation:
22x + 1 + 2x + 2 = 12 - 2x
24x + 3 = 12 - 2x
+2x +2x
26x + 3 = 12
-3 -3
26x = 9
÷26 ÷26
x = (9/26)
I hope this helps!
Please help!
Simplify the expression. Show all steps to simplify the expression.
Answer:
3^5
Step-by-step explanation:
substract the index of the number
I need some help please
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{5}{2}}(x-\stackrel{x_1}{(-6)}) \implies y +2= \cfrac{5}{2} (x +6) \\\\\\ y + 2 = \cfrac{5}{2}x + 15\implies y = \cfrac{5}{2}x+13[/tex]
Jane’s grocery receipt is shown. If the sales tax on these items is 6.25%, what is the amount of sales tax? Round to the nearest cent. Turkey- 21.55 Turkey gravy-2.25 Stuffing-3.89 Peas-1.95
hi
amount before tax :
21.55+2.25+3.89+1.95 = 26.94
as sales tax is 6.25 /100 = 0.0625
then amount of tax is : 26.94 *0.0625 ≈ 1.68
11. If F is the number of Faces, E is the number of Edges and V is the number of Vertices, calculate V - E + F for a hexagonal prism.
pls I really need help
The value of V-E+F=2
Euler's polyhedron formula, V−E+F=2
A hexagonal prism has 8 faces, F=8
A hexagonal prism has 12 vertices, V=12
A hexagonal prism has 18 edges, E=18
So, 12−18+8=2
V-E+F=2 is Euler's polyhedron formula.
F=8 for a hexagonal prism with 8 faces
V=12 is the number of vertices in a hexagonal prism.
E=18 is the number of edges on a hexagonal prism.
So, 12−18+8=2
A hexagonal prism is a three-dimensional prism with two parallel ends that have the same size and form. The hexagonal prism has six parallelogram-shaped faces on its six sides. Regular hexagonal prisms and irregular hexagonal prisms are the two types of hexagonal prisms. A hexagonal prism is a polyhedron with 8 faces, 18 edges, and 12 vertices, with 6 faces in the shape of rectangles and 2 faces in the shape of hexagons.
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Just double checking my work did i select all that applied?
Answer:
i think yes but do whatever you want
Name the quadrant in which the angle below is located.
Tan theta = -4/5 and sin theta is positive
Quandrant I, Quadrant II, Quadrant III or IV?
The quadrant in which the angle theta as described in the task content is located is; Quadrant II.
Which quadrant is the angle theta located?It follows from the task content that the angle theta described has; it's tan value to be negative and it's sine value to be positive.
Hence, since only sine of angles is positive in quadrant II while tan and cosine values are negative, it follows that the quadrant where theta is located is; Quadrant II.
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Write a quadratic function that includes the given point. If not possible state why.
Please help and explain
According to the question, the given points for the expression of the quadratic function are as: (2, 1) (-1, -2).(3,-10)
The standard form of the quadratic equation is: f(x) = [tex]ax^{2} +bx+c=0[/tex]
Using coordinate points the quadratic equation can be written as:
[tex]ax^{2} +bx+c=0[/tex] ⇒[tex]4a+2b+c=0[/tex]; [tex]a-b+c=0[/tex]; [tex]9a+3b+c=0[/tex]
Solving above three equation by the method called substitution and calculated the values of the variable. The calculated values are zero.
Therefore, the formed quadratic function is not quadratic function.
What is quadratic function?
The quadratic function is the polynomial expression and the formed curve is parabola on the graph. The direction of the parabola is either downward or upward or in the direction of left or right. It represent the equation steepness.
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206 × 34 helpppoppoo
Answer: 7004
Step-by-step explanation:
i used a calculator queen
Answer:
7004
Step-by-step explanation:
NO LINKS!! Please help me with this one
Answer:
[tex]\textsf{d)} \quad \dfrac{5}{6}, \quad \dfrac{25}{6}[/tex]
Step-by-step explanation:
Given:
[tex]12 \cos \left(\dfrac{2 \pi}{5}x\right)+10=16, \quad \textsf{when}\; \left(\dfrac{2 \pi}{5}x\right)\; \textsf{is in radians}.[/tex]
Subtract 10 from both sides of the given equation:
[tex]\implies 12 \cos \left(\dfrac{2 \pi}{5}x\right)=6[/tex]
Divide both sides of the equation by 12:
[tex]\implies \cos \left(\dfrac{2 \pi}{5}x\right)=\dfrac{1}{2}[/tex]
Take the inverse of cosine of both sides:
[tex]\implies \dfrac{2 \pi}{5}x = \cos^{-1}\left(\dfrac{1}{2}\right)[/tex]
[tex]\implies \dfrac{2 \pi}{5}x =\dfrac{\pi}{3}+2 \pi n, \dfrac{5 \pi}{3}+2 \pi n[/tex]
Multiply both sides by 5:
[tex]\implies 2 \pi x=\dfrac{5 \pi}{3}+10 \pi n, \dfrac{25 \pi}{3}+10 \pi n[/tex]
Divide both sides by 2π:
[tex]\implies x=\dfrac{5 \pi}{6 \pi}+\dfrac{10 \pi}{2 \pi}n, \dfrac{25 \pi}{6 \pi}+\dfrac{10 \pi}{2 \pi}[/tex]
Simplify:
[tex]\implies x=\dfrac{5}{6}+5n, \dfrac{25}{6}+5n[/tex]
The two smallest possible solutions for x are when n = 0:
[tex]\implies x=\dfrac{5}{6}, \quad x=\dfrac{25}{6}[/tex]
Give the equation of the line parallel to line 1 which passes through (-8,-5)
The equation of the line is y = 5x + 35
How to find the equation of a line?The equation of a line can be represented in a slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, line that are parallel have the same slope.
Therefore, if line one slope is 5, then the slope of the unknown line will be 5.
Hence,
y = 5x + b
let's find the y-intercept using (-8, -5)
-5 = 5(-8) + b
-5 = -40 + b
b = -5 + 40
b = 35
Therefore, the equation of the line is y = 5x + 35
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Gabriel draws a shape with 8 vertices and exactly 2 square square faces which shape does Gabriel draw
Answer: square prism
Step-by-step explanation: It is a square prism. All angles are 90°. rectangular faces and 2 square faces, 8 vertices and 12 edges. It is also a prism because it has the same cross-section along a length.
Dress shoes of a specific style for women come in sizes ranging from 6 to 10. A retailer believes that this range of
sizes is adequate for all but 5% of its female customers.
(a) What normal model for sizes is consistent with the opinion of the retailer? (Assume that the model is centered on
the given range.)
(b) If the retailer uses a normal model, then should it order more shoes of sizes 6 and 7 or more shoes of sizes 9 and
10?
(c) Can a normal model possibly be the right model for the proportion of shoe sizes of the retailer's female
customers?
(a) The normal model with μ = and o=
(Round to the nearest integer as needed.)
CCC
is consistent with the opinion of the retailer.
Normal model for sizes is (7,1)
Here 5% of female customer have foot size in between 6-10
a)We were told that there are dress shoes in sizes 6 to 10 point, and the tailor believes that, with the exception of 5% of his female customers, the shoe would fit almost everyone. As a result, it accounts for 95 percent of female customers or women who try on his shoes, and we've been asked to determine what standard model for sizes is consistent.
b)The mean is 8 and the standard deviation is 2 points. So, we can say that x follows a normal model with a mean of 8 and a variance of 4 point right and in part b, we were asked whether a retailer should order more shoes in sizes 4 and 5 or more shoes in sizes 11 and 12 point so the best way to do this is to draw a balk curve or the symmetric table. So let's try to graft that together. draw it out to begin with so an important feature of the normal curve of the ball curves that it's always symmetric about the mean.
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At store A for 2 pineapples is $5 if at store B the price for 2 pineapples is $5 what is the unit rate for each store
What are the correct answers ABCD?
Answer:
the answer would be D. x/7=9
Step-by-step explanation:
-
Layla and Amelia are making bracelets. It takes Layla 45 minutes to make 9 bracelets on her own. Together, Layla and Amelia can make 9 bracelets in 20 minutes. How long will it take Amelia to make 9 bracelets?
Answer:
Step-by-step explanation:
It takes Layla 45 minutes to make 9 bracelets on her own.
45 divided by 9 equals 5. It takes Layla 5 minutes to make one bracelet.
Layla and Amelia can make 9 bracelets in 20 minutes.
20 divided by 9 equals 2 and 2/9.
5 - 2 2/9= 2 7/9
2 7/9 times 9 equals 25
Amelia can make 9 bracelets in 25 minutes
So it takes Layla 56 minutes to make 9 ( 45 divided by 9 = 5) so that means in 20 minutes Layla will make 4 bracelets.
this means it will piece together as Layla would make 4 while Amelia makes 5. So i think on Amelia's own it'll take her 40 minutes.
so sorry if i'm wrong :(
With wireless Internet (WiFi) gaining popularity, the number of public wireless Internet access points (in thousands) is projected to grow from 2003 to 2008 according to the equation - 105x+3y=114 where x is the number of years after 2003. Find the slope of the linear equation.
Answer:
The slope is 35===========================
Given line
- 105x + 3y = 114Convert this into slope-intercept form:
y = mx + b, where m is the slope, b is the y-intercept-105x + 3y = 1143y = 105x + 114y = 105x/3 + 114/3y = 35x + 38The slope is 35
Question 2: How can you tell just by looking that the following system that it has infinitely many solutions?
x+y=5
2x+2y=10
In September 2022, Mr. Fishman noted that his age was 11 years less than twice his younger sister's age and he
was 2 years younger than his older sister. He also noted that his two sisters are 20 years apart in age. Let x be the age of Mr. Fishman's younger sister. Create at least one equation in order to determine
the younger sister's age in September 2022. Then use the equations you created to solve for all of their ages.
The younger sister is 29.
The older sister is 49.
Mr Fishman's age is 47.
What are their ages?Let:
x = older sister's age x = younger sister's age c = Mr. Fishman's ageThe difference between the older sister and younger sister's age: y - x = 20 equation 1
Mr Fishman's is 11 years less than twice his young sister's age: 2x - 11 = c equation 2
The difference between Mr Fishman and his older sister's age : y - c = 2
y - 2 = c equation 3
Let equation 2 and 3 be equal : 2x - 11 = y - 2
2x - y = 11 - 2
2x - y = 9
-y + 2x = 9 equation 4
The two equations that would be used are:
y - x = 20 equation 1
-y + 2x = 9 equation 4
Add both equations together
x = 29
Substitute for x in equation 1
y - 29 = 20
y = 29 + 20
y = 49
y - c = 2
49 - c = 2
c = 49 - 2
c = 47
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what is the domain of the relation { ( − 1 , 1 ) , ( 8 , 8 ) }
Answer:
{-1 , 8}
Step-by-step explanation:
The domain is simply all of the x values. Since the ordered pairs are written as (x, y) ...Find the domain by listing all the x values from the relation (which in this case is the first value in each of the parentheses).
What is the x-intercept of the line with this equation -3x+1/2y=18
Answer:
Step-by-step explanation:
for the x-intercept this is where the y value is equal to 0But before that by inspection you can see that your equation is not in the standard form of a straight lineMake y the the subject of the equation[tex]\frac{-3x+1}{2y}(2y) =18(2y)\\-3x+1=36y\\y=\frac{-3x+1}{36}[/tex]Now plug in y=00=-3x+1-3x=-1[tex]x=\frac{1}{3}[/tex]Find the 12th term of the geometric sequence 2,10,50
12th term of the geometric sequence is 97,656,250
In the given statement is:
Find the 12th term of the geometric sequence 2,10,50
What is Geometric Sequence?
A Geometric Sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.
Now, to find the 12th term of geometric sequence:
Formula of Geometric Sequence:
[tex]a_{n} =a_{1}r^n^-^1[/tex]
a = first term of the geometricr = common ratio of the geometric sequence[tex]a_{n}[/tex] = nth term[tex]a_{1}=2\\ \\[/tex]
r = 10/2 =5
[tex]a_{12}=2(5)^1^2^-^1\\ \\a_{12}=2(5)^1^1\\\\\\a_{12}=2(48,828,125)\\ \\a_{12} = 97,656,250[/tex]
Therefore, 12th term of the geometric sequence is 97,656,250
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I need help with this please
solve this maths pls 17-0.9
Answer:
16.1 is the answer
Step-by-step explanation:
17.0-0.9= 16.1
Answer:
16.1
Step-by-step explanation:
take 0.9 from 17=16.1
25 divided by 5
90 divided by 5
and how would it look like?
Answer:
Hope this helps :)
1. 25 ÷ 5 = 5
2. 25
---- <----- fraction bar means divide too
5
1. 90 ÷ 5 = 18
2. 90
---- <------- fraction bar means divide too
5
There are 48 people art a party. There are seven times as many adults as children. There are twice as many females as males. If there are 5 girls at the party, how many men are there?
48 persons make up a party. There are seven times more adults than children in the world. Males outnumber females two to one. If the party has five girls. The total number of male adults are15
The total number of people are in the party is equal to 48
Let the number of children be x
So, the number of adults in the party is equal to 7 x
x + 7 x =48 ( This is a linear equation)
So, the number of children in the comes to be 6
Number of adults in the party = 6 * 7 = 42
Now let number of males be y
So total number of females = 2 y
Y+2y = 48 ( This is a linear equation)
Y=16
Therefore, the number of males is 16 and number of females is 32
Number of children in the party is 6 and female child is equal to 5
Then, number of male children =6-5 = 1
So total males in the party is equal to 16
Adult males =total number of males - number of male children
=16 - 1 = 15
Hence the total number of male adults =15
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Tarek buys a pomegranate with 314 seeds. He buys a second pomegranate that has more seeds. The number of seeds in the second pomegranate is made of the digits 6, 3, 1, and 4, but not in that order.
Part A
If the value of 1 is 100 times greater in the second pomegranate, in
what place should the 1 be written in the second number? Explain
how you know.
Answer:
thousands place: 4th one to the left of the decimal point, 1000.
Step-by-step explanation:
You want the number place of a 1 that has a value 100 times that of the 1 in 314.
Place valueThe digit 1 in the number 314 is in the "tens place." It signifies 1 ten is part of the value of the number 314.
The value of a digit 1 that is 100 times that will be ...
10 × 100 = 1000
That is, the digit will be found in the "thousands place," two digits to the left of the location in the number 314.
Thousands placeThe 1 with a value of 1000 is written in the thousands place, the 4th place to the left of the decimal point.
if y= 0 what is y+10+10
Given:
y=0, y+10+10
statement of equality between two expressions consisting of variables and/or numbers
to solve the equation y+10+10, if y=0
substitute the value y=0, in the equation
which is equal to y+10+10= 0 +10 + 10 = 20
so the final answer is 20.
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How to solve 5x + 7y = 1790 and 1x + 1y = 290 algebraically
Answer:
Step-by-step explanation:
Answer: x=120; y=170.
Step-by-step explanation:
1) it is possible to make up the the system of two equations from these two given equations:
[tex]\left \{ {{5x+7y=1790} \atop {x+y=290}} \right.[/tex]
2) the solution of the system above:
[tex]\left \{ {{5x+7y=1790} \atop {5x+5y=1450}} \right. \ = > \ \left \{ {{2y=340} \atop {x+y=290}} \right. \ = > \ \left \{ {{y=170} \atop {x=290-y}} \right. \ = > \ \left \{ {{y=170} \atop {x=120}} \right.[/tex]
3) finally, (120;170).
