Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true?
Answers
Answer:
a = -1, b = 10Step-by-step explanation:
Given the function h(x) = (x – 1)³ + 10 so that h(x) = (g°f)(x). If f(x) = x + a and g(x) = x³ + b, then;
g(f(X)) = g(x+a).
To get g(x+a), we will have to replace the variable x with x+a in g(x) as shown;
g(x+a) = (x+a)³ + b
g(f(x)) = (x+a)³ + b
Since h(x)= g(f(x)) = (x – 1)³ + 10
g(f(x)) = (x+a)³ + b = (x – 1)³ + 10
Hence (x+a)³ + b = (x – 1)³ + 10
On comparing the coefficients to get the value of a and b;
(x+a)³ = (x-1)³
Take the cube root of both sides
∛(x+a)³ = ∛(x-1)³
x+a = x-1
x+a-x = -1
a = -1
Also on comparing, b = 10
Hence the values of a and b would make the composition true are -1 and 10 respectively.
Answer:
a: -1
b: 10
edge 2020
Related Questions
A. Write an expression to represent the difference between the two points shown on the number line. B. Find the distance between the two points. [Hint: Remember that distance is always positive.]
Answers
Answer:
Step-by-step explanation:
A: The distance is the sum of |-1.6| and 0.3: |-1.6| + 0.3
B. This distance is 1.6 + 0.3 = 0.9
Eileen is trying to test if the function f(x) = x2 + 2x + 5 is even, odd or neither. She produces the following work: f(– x) = (–x)2 + 2(–x) + 5 = x2 – 2x + 5 What conclusion can she reach? f(x) is even f(x) is odd f(x) is neither f(x) is both even and odd
Answers
Answer:
f(x) is neither
Step-by-step explanation:
The given function is neither even nor odd. The correct option is B.
What are odd and even functions?When the value of the function is negative after putting the value of the variable negative in the function then the function is odd and if the value of the function is positive after putting the negative value of the variable then the function is even.
Given that Eileen is trying to test if the function f(x) = x² + 2x + 5 is even, odd or neither. She produces the following work: f(– x) = (–x)² + 2(–x) + 5 = x² – 2x + 5.
The function will be solved as below:-
f(x) = x² + 2x + 5
f(– x) = (–x)² + 2(–x) + 5
f(-x) = x² – 2x + 5.
Here the resultant function is not giving any clear information the given function is neither even nor odd. The correct option is B.
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Is the equation (3x^2+2)=9x+4 always, sometimes, or never true? Explain.
Answers
always true
Step-by-step explanation:
Assuming that you mean by true that it has solutions
we have
[tex]3x^2-9x-2=0[/tex]
to know if it has real solutions we need to know if
[tex]b^2-4ac[/tex]
is greater, equal or less than zero
if it's greater it's always
if it's equal it's sometimes
if it's less it's never
so
b=-9
a=3
c=-2
[tex](-9)^2-4(3)(-2)\\\\=81+24\\\\=105[/tex]
so it's always
The equation (3x² +2) = 9x + 4 is sometimes true.
What is an equation ?An equation is an mathematical expression stating that left hand side and the right hand side are equal.
The equation (3x² +2) = 9x + 4 is only true for the roots of the formed equation
3x² + 2 = 9x + 4
3x² = 9x + 2
3x² - 9x -2 = 0
∴ x = (3 + [tex]\sqrt{105}[/tex])/2 OR (3 - [tex]\sqrt{105}[/tex])/2
Only for these values of x the equation 3x² + 2 = 9x + 4 are true except these two values it is never true.
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Evaluate (-3) to the power of 4
Answers
Answer:
-81
Step-by-step explanation:
Write it out, so it's more clear: [tex]-3^{4}[/tex] Because the base number of the equation (-3) is a negative, we know the answer will be a negativeMultiply -3 by itself 4 times: -3 × 3 × 3 × 3 -3 × 3 × 3 × 3 = -81
Write an expression for: half of w
2-w
2w
W/2
2/w
Answers
Answer:
w/2
Step-by-step explanation:
Calculating half of something is the same as dividing it by 2. In this case, the "something" is w so the answer is w/2.
The mapping diagram shows a functional relationship.
Domain
Range
Complete the statements.
f(4) is
f(x) = 4 when x is
و بہادن دا
8
2
3
11
3
4
1
2
Answers
Answer:
f(4) is 1/2
f(x)= 4 when x is 8
The manager of a factory collected data in order to analyze the relationship between the number of hours of training a worker receives and
the worker's error rate. The line of best fit for the collected data is y=01 -0.005r where x is the number of hours of training a worker
receives and y is the error rate.
What approximate error rate should the manager expect for a worker who receives 6 hours of training
Answers
Answer:
The approximate error rate the manager should expect for a worker who receives 6 hours of training is 0.07 error rate
Step-by-step explanation:
The given relation between the number of hours of training a worker receives, x and the worker's error rate y can be presented follows;
y = 0.1 - 0.005·r
Therefore, the approximate error rate the manager should expect for a worker who receives 6 hours of training can be given as follows;
When x = 6 hours, we have
y = 0.1 - 0.005 × 6 = 0.07
The approximate error rate the manager should expect for a worker who receives 6 hours of training is 0.07.
Which is an error rate o 7%
Which of the following expressions has three factors?
5(p+6)(q-4)
2(7-b)
(d-3)(c+9)
x+y-4
Answers
Answer:
5(p + 6)(q - 4)
Step-by-step explanation:
Factors are a set of numbers, alphabets or both that when multiplied would give a certain expression.
The expression with three factors is: 5(p + 6)(q - 4)
So that;
5(p + 6)(q - 4) = (5p + 30)(q - 4)
Then,
(5p + 30)(q - 4) = 5pq - 20p + 30q - 120
Therefore, the factorization of 5pq - 20p + 30q - 120 gives the factors; 5(p + 6)(q - 4).
Answer:
5 (p+6) (q−4)
'
In a mixture of 60 litres, the ratio of milk to water is 2:1. If this ratio is to be 1:2,then find the quantity of water to be further added.
Answers
Answer:
Quantity of milk = 60 x 2/3 litres = 40 litres.
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = 40 /20 + x
Now, 40 /20 + x = 1/2
20 + x = 80
x = 60.
Quantity of water to be added = 60 litres.
Scouts of D.P.S Sharjah made to run around a regular hexagonal ground fig 9, of perimeter 270 m .If they started running from point X and covered two fifth (2/5th) of the total distance.Which side of the ground will they reach?
Answers
Answer:
Side 3 or side 4
Step-by-step explanation:
The ground has 6 sides
Each side is:
270 m / 6 = 45 mIt is assumed that total distance is one cycle of 270 m.
Since no diagram attached, the start point X is the beginning of side 1.
Then the distance covered is:
270 m * 2/5 = 108 mAs
2*45 m = 90 m < 108 m < 3*45 m = 135 mthe scouts reached the side 3 or side 4 of the ground depending on direction of movement (clockwise vs anti-clockwise)
Solve for x. Evaluate and round your answer to 1 decimal place(tenths place). 10x=1200
Answers
Answer:
x = 3.1Step-by-step explanation:
[tex] {10}^{x} = 1200[/tex]To solve first take logarithm to both sides
That's
[tex] log_{10}(10) ^{x} = log_{10}(1200) [/tex][tex] log_{10}(10)^{x} = x log_{10}(10) [/tex]But
[tex] log_{10}(10) = 1[/tex]So we have
[tex]x = log_{10}(1200) [/tex]
Write 1200 as a number with the factor 100
That's
1200 = 100 × 12
So we have
[tex]x = log_{10}(100 \times 12) [/tex]Using the rules of logarithms
That's
[tex] log_{a}(x \times y) = log_{a}(x) + log_{a}(y) [/tex]Rewrite the expression
That's
[tex]x = log_{10}(100) + log_{10}(12) [/tex][tex]x = log_{10}(10)^{2} + log_{10}(12) [/tex][tex]x = 2 log_{10}(10) + log_{10}(12) [/tex][tex] log_{10}(10) = 1[/tex][tex]x = 2 + log_{10}(12) [/tex]x = 3.079
So we have the final answer as
x = 3.1 to one decimal placeHope this helps you
Give the coordinates of a point on the line whose equation in point-slope form is y − (−3) = 1 4 (x − 9).
Answers
Answer:
Below
Step-by-step explanation:
● y -(-3) = (1/4) (x-9)
Replace 1/4 by 0.25 to make it easier
● y + 3 = 0.25(x-9)
● y + 3 = 0.25x - 2.25
Add 3 to both sides
● y +3-3 = 0.25x -2.25-3
● y = 0.25x -5.25
To the coordinates of a point from this line replace x by a value.
The easiest one is 0.
● y = 0.25×0 -5.25
● y = 5.25
5.25 is 21/4
So the coordinates are (0, 21/4)
The coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)
The equation of a line in point-slope form is expressed as;
[tex](y-y_0)=m(x-x_0)[/tex] where:
m is the slope
[tex](x_0, y_0)[/tex] is the point on the line.
Given the equation in the point-slope form expressed as
[tex]y - (-3) = 1/4 (x - 9)[/tex]
Comparing the general equation with the given equation:
[tex]y_0 = -3\\x_0 = 9[/tex]
Hence the coordinate of a point on the line whose equation in point-slope form is y − (−3) = 1/4 (x − 9) is (9, -3)
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Write two expressions for the perimeter of the figure.
2x
7
3x
172
16
Note: The figure is not drawn to scale.
(a) Use all five side lengths.
perimeter - ] + + + +
(b) Simplify the expression from part (a).
perimeter =
Х
$ ?
Answers
Answer:
Two expressions for the perimeter would be
22x+23 and 2x+3x+17x+7+16
Step-by-step explanation:
you want to add the variables of the same kind in this case
2x
3x 7
17x 16
_________
22x + 23
i need help someone= R-7=1
Answers
Answer: R=8
Step-by-step explanation:
-7 is added to 1 making it R= 1+7 resulting in R=8
Answer:
[tex]\huge \boxed{R=8}[/tex]
Step-by-step explanation:
[tex]R-7=1[/tex]
Adding 7 to both sides of the equation.
[tex]R-7+7=1+7[/tex]
[tex]R=8[/tex]
Which step is the same when constructing an inscribed square and an inscribed equilateral triangle?
Answers
Answer: B.Construct a circle of any arbitrary radius.
Step-by-step explanation:
had to complete the question first.
A.Connect every arc along the circle.
B.Construct a circle of any arbitrary radius.
C.Set the compass width to greater than half the diameter of the circle.
D. Set the compass width to the radius of the circle.
Explanation:
when constructing an inscribed square and an inscribed equilateral triangle, the most important step and which turns out to be same for both procedures is the constructio of of a circle of an arbitrary radius. Because it’s is within this circle both the triangle and square would be drawn. Just their method of construction are different.
A liter of water contains about (first image) molecules. A certain river discharges about (second image) L of water every second. About how many molecules does the river discharge every minute? Write your answer in scientific notation.
Answers
================================================
Work Shown:
1 second = 2.3 * 10^7 liters of water
60*1 second = 60*2.3* 10^7 liters of water
60 seconds = 138 * 10^7 liters of water
1 minute = (1.38 * 10^2) * 10^7 liters of water
1 minute = 1.38 * (10^2*10^7) liters of water
1 minute = 1.38 * 10^(2+7) liters of water
1 minute = 1.38 * 10^9 liters of water
The river discharges 1.38 * 10^9 liters of water per minute.
--------------------------------
1 liter = 3.35 * 10^25 molecules
1.38 * 10^9*1 liter = 1.38 * 10^9*3.35 * 10^25 molecules
1.38 * 10^9 liters = (1.38*3.35) * (10^9*10^25) molecules
1.38 * 10^9 liters = 4.623 * 10^(9+25) molecules
1.38 * 10^9 liters = 4.623 * 10^34 molecules
1 minute = 4.623 * 10^34 molecules
-------------------------------
Every minute, about 4.623 * 10^34 molecules of water are discharged from the river.
Enter what that means?
Help someone.
Answers
[tex]\frac{x^2}{3}[/tex] is the same as [tex]\frac{1}{3}x^2[/tex]
Dividing by 3 is the same as multiplying by the fraction 1/3
A student scores on a geography test and on a mathematics test. The geography test has a mean of 80 and a standard deviation of . The mathematics test has a mean of 300 and a standard deviation of . If t
Answers
Complete question is;
A student scores 56 on a geography test and 267 on a mathematics test. The geography test has a mean of 80 and a standard deviation of 20. The mathematics test has a mean of 300 and a standard deviation of 22.
If the data for both tests are normally distributed, on which test did the student score better?
Answer:
The geography test is the one in which the student scored better.
Step-by-step explanation:
To solve this question, we will make use if the z-score formula to find the w test in which the student scored better. The z-score formula is;
z = (x - μ)/σ
Now, for geography, we are given;
Test score; x = 56
Mean; μ = 80
Standard deviation; σ = 20
Thus, the z-score here will be;
z = (56 - 80)/20
z = -1.2
Similarly, for Mathematics, we are given;
Test score; x = 267
Mean; μ = 300
Standard deviation; σ = 22
Thus, the z-score here will be;
z = (267 - 300)/22
z = -1.5
Since the z-score for geography is lesser than that of Mathematics, thus, we can conclude that the geography test is the one in which the student scored better.
Directions: Simplify each expression by distributing
1. 8(x + 5) =
3.-2(3m + 9) =
Answers
Answer:
8x +40-6m-18Step-by-step explanation:
[tex]8(x + 5) = \\ 8(x) + 8(5) \\ = 8x + 40[/tex]
[tex] - 2(3m + 9) \\ = - 2(3m) - 2(9) \\ = - 6m - 18[/tex]
Find the side of a square, whose area is equal to the area of a rectangle with sides 6.4m and 2.5m. Also find the perimeter of the square.
Answers
Answer:
side: 4 metres
perimeter: 16 metres
Step-by-step explanation:
Let's first find the area of this rectangle.
The area of a rectangle is denoted by A = lw, where l is the length and w is the width. Here, the length is l = 6.4 and the width is w = 2.5. Plug these in:
A = lw
A = 6.4 * 2.5 = 16 metres squared
We want to find the side of a square with area 16. Suppose the side length is x. The area of a square is denoted by A = x * x = x², so set this equal to 16:
x² = 16
x = √16 = 4
Thus, the side length is 4 metres.
The perimeter of a square is denoted by P = 4s, where s is the side length.
Here the side length is 4 metres, as we found, so:
P = 4s = 4 * 4 = 16
Hence the perimeter is 16 metres.
Hi... can anyone pls help
Answers
Answer: A globe shows all the countries with landmass and water bodies but a map shows only a specific country with its size shape and features .
Step-by-step explanation:
Josh weighed cantaloupes he picked from his garden. This line plot shows the cantaloupe weights. What is the total weight of all the cantaloupes that weigh no more than 2 pounds? 712 lb 10 lb 15 lb 20 lb
Answers
Answer:
Step-by-step explanation:
From the plot line you have (1x3) + (2x 1 1/4) + (3x 1 1/2) = 10
The total weight of all the cantaloupes that weigh no more than 2 pounds should be 10.
Calculation of the total weight:Since Josh weighed cantaloupes he picked from his garden.
So here the total weight should be like
[tex]= (1\times 3) + (2\times 1\ 1\div 4) + (3\times 1\ 1\div 2)[/tex]
= 10
hence, The total weight of all the cantaloupes that weigh no more than 2 pounds should be 10.
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Solve the system by using a matrix equation.
--4x - 5y = -5
-6x - 8y = -2
Answers
Answer:
Solution : (15, - 11)
Step-by-step explanation:
We want to solve this problem using a matrix, so it would be wise to apply Gaussian elimination. Doing so we can start by writing out the matrix of the coefficients, and the solutions ( - 5 and - 2 ) --- ( 1 )
[tex]\begin{bmatrix}-4&-5&|&-5\\ -6&-8&|&-2\end{bmatrix}[/tex]
Now let's begin by canceling the leading coefficient in each row, reaching row echelon form, as we desire --- ( 2 )
Row Echelon Form :
[tex]\begin{pmatrix}1\:&\:\cdots \:&\:b\:\\ 0\:&\ddots \:&\:\vdots \\ 0\:&\:0\:&\:1\end{pmatrix}[/tex]
Step # 1 : Swap the first and second matrix rows,
[tex]\begin{pmatrix}-6&-8&-2\\ -4&-5&-5\end{pmatrix}[/tex]
Step # 2 : Cancel leading coefficient in row 2 through [tex]R_2\:\leftarrow \:R_2-\frac{2}{3}\cdot \:R_1[/tex],
[tex]\begin{pmatrix}-6&-8&-2\\ 0&\frac{1}{3}&-\frac{11}{3}\end{pmatrix}[/tex]
Now we can continue canceling the leading coefficient in each row, and finally reach the following matrix.
[tex]\begin{bmatrix}1&0&|&15\\ 0&1&|&-11\end{bmatrix}[/tex]
As you can see our solution is x = 15, y = - 11 or (15, - 11).
Two students were asked to use estimation strategies to find a reasonable solution to this question: Heather has four envelopes with money in them. The first has $246, the second has $405, the third has $105, and the fourth has $514. Estimate the total amount of money in the four envelopes. From the choices below, select the student with the more reasonable solution.
Answers
Answer:
417 $
b h h h h h h h h h h h h
8 = 3а – 4
How do I solve this problem
Answers
Next you calculate -3a=-4-8 then
Next you will Divide both sides by -3
-3a=-12 then your answer would get a=4
given that x+1 is a factor of 3x³-14x²-7x+d, show that d= 10
Answers
Answer:
3x³ - 14x² - 7x + d = (x + 1)(ax² + bx + c)
--------------------------
(x + 1)(ax² + bx + c)
= ax³ + bx² + cx + ax² + bx + c
= ax³ + (a + b)x² + (b + c)x + c
--------------------------
ax³ + (a + b)x² + (b + c)x + c = 3x³ - 14x² - 7x + d
=> a = 3
a + b = -14
b + c = -7
c = d
=> a = 3, b = -17, c = 10, d = 10
CHAIRS A local furniture store sells two versions of the same chair: one for adults, and one for children. Find the value of x such that the chairs are similar.
Adult chair= 18,16
Kid Chair x,12
Answers
Answer:
Idek
Step-by-step explanation:
Ya I just need points
Answer:
13.5
Step-by-step explanation:
Use fractions to help. 12/16 = x/18.
12/16 simplifies to 3/4, so now divide 18 by 4 and multiply by 3.
18 / 4 = 4.5
4.5 x 3 = 13.5
Which value goes in the empty cell?
Answers
Answer:
[See Below]
Step-by-step explanation:
If you replace the x with -1 and evaluate the function you get -5.
*ANSWER ASAP PLEASE* What is the volume of a hemisphere-shaped coffee if the width of the coffee cup is about 16.51 centimeters? (Use 3.14 for pie)
Answers
Answer:
1177.58 cm³
Step-by-step explanation:
The volume of a sphere is given by V = (4/3)πr³. In this case, if the width (diameter) of the cup is 16.51cm, then the radius is 8.255 cm. So the volume of the cup, if it were a sphere, would be:
V = (4/3) * 3.14 * (8.255)³ ≈ 2355.1557 cm³
But since this is a hemisphere (i.e., half a sphere), we cut that value in half to get the volume of the cup:
2355.1557 / 2 ≈ 1177.58 cm³
What is the difference written in scientific notation?
Answers
Answer:
Step-by-step explanation:Cuando un número se escribe en notación científica, el exponente te dice si el término es un número muy grande o muy pequeño. Un exponente positivo indica un número grande y un exponente negativo indica un número muy pequeño que está entre 0 y 1.
Answer:
Below
Step-by-step explanation:
● 1.3×10^6 - 6.8 × 10^5
● 13 × 10^5 - 6.8 × 10^5
● 10^5 (13 -6.8)
● 6.2 × 10^5