For this case we have the following equations:
[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2-3x[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = \frac {1} {x ^ 2-3x}[/tex]
We must find the domain of f (g (x)). The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.
[tex]x ^ 2-3x = 0\\x (x-3) = 0[/tex]
So, the roots are:
[tex]x_ {1} = 0\\x_ {2} = 3[/tex]
The domain is given by all real numbers except 0 and 3.
Answer:
x other than 0 and 3
ANSWER
0 and 3
EXPLANATION
The given functions are
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} - 3x[/tex]
[tex]( f \circ g)(x) = f(g(x))[/tex]
[tex]( f \circ g)(x) = f( {x}^{2} -x )[/tex]
[tex]( f \circ g)(x) = \frac{1}{ {x}^{2} - 3x} [/tex]
Factor the numerator:
[tex]( f \circ g)(x) = \frac{1}{ x(x - 3)} [/tex]
The function will be undefined if the denominator is zero.
[tex]x(x - 3) \ne0[/tex]
[tex]x \ne0 \: and \: x \ne3[/tex]
Therefore 0 and not in the domain of the composed function.
Replacing only the minimum value in a data to a smaller number will also change the mean
A.always
B. Sometimes
C.never true
Answer:
Always.
Step-by-step explanation:
I can think of no example that makes always false.
Replacing the minimum value in a dataset with a smaller number can sometimes change the mean. Hence, the correct answer is B.
Sometimes, replacing only the minimum value in a dataset with a smaller number may change the mean.
For example, if the dataset is {1, 3, 4, 5} and you replace the minimum value 1 with 0, the mean changes from 3.25 to 3.
What is 1.16, 1 1/4, 1.37, and 1 1/10 from greatest to least?
Answer 1.37, 1 1/4, 1.16, 1 1/10
Step-by-step explanation:
1.37
1 1/4 (1.25)
1.16
1 1/10 (1.1)
Hello There!
-Ordered From Least To Greatest-
1 1/10 - 1.16 - 1 1/4 - 1.37
tell whether the angles are adjacent or vertical.
The angels are ADJACENT ANGELS
Answer:
21
(Side Note: I solved this for anyone who needs the answer.)
Definitions:
Adjacent: Congruent meaning same measure.
Vertical: Two angles that have a common side.
Explanation:
This equation is adjacent.
If we look at this problem and look to the bottom and see that tiny square, that means it is a right angle, right angles equal to 90 degrees.
Step-By-Step:
To solve for x, we need to put 25 degrees and x into a formula.
x + 35 = 90
Next and the last step is to subtract 90 and 35:
90 - 35 = 21
Our final answer is 21.
Hope this helps!
~Hocus Pocus
which is expression is equivalent to 6^4 • 6^3?
Answer:
C) (6x6x6x6)x(6x6x6)
Step-by-step explanation:
an exponent is the base multiplied by itself that many times, and another way to write 2 exponents multiplied by each other (and have the same base) is by simply adding the exponents, for example, 6^4x6^3 is 6^7 :D Hope this helps!
Answer:
The answer is C :)
Step-by-step explanation:
(3 + 5) * 2Y = (5 * 8) - (2 * 4)
Answer:
Y = 2
Step-by-step explanation:
Solve for Y:
(3 + 5)×2 Y = 5×8 - 2×4
3 + 5 = 8:
8×2 Y = 5×8 - 2×4
5×8 = 40:
8×2 Y = 40 - 2×4
-2×4 = -8:
8×2 Y = -8 + 40
8×2 = 16:
16 Y = 40 - 8
40 - 8 = 32:
16 Y = 32
Divide both sides of 16 Y = 32 by 16:
(16 Y)/16 = 32/16
16/16 = 1:
Y = 32/16
The gcd of 32 and 16 is 16, so 32/16 = (16×2)/(16×1) = 16/16×2 = 2:
Answer: Y = 2
for 6 days in a row, alyssa recorded the total amount of rain
Answer
if your looking for an answer try to be smart and actually show a picture I cant do nothing with just a name thats how we us experts find answers pictures.
Step-by-step explanation:
Solve for the variable x in the following equation. x2 = 100 x =±
Answer:
x = ±10
Step-by-step explanation:
x^2 = 100
Take the square root of each side
sqrt(x^2) = sqrt(100)
x = ±10
the endpoints of the double arrow are congruent triangles. what is the area of the figure.
Answer:
The area of the figure is [tex]56\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the figure is equal to the area of two triangles plus the area of rectangle
so
[tex]A=2[\frac{1}{2}(b)(h)]+(L)(W)[/tex]
we have
[tex]b=1+4+1=6\ cm[/tex] ----> the base of triangle
[tex]h=2\ cm[/tex] ---> the height of triangle
[tex]L=11\ cm[/tex] ----> the length of rectangle
[tex]W=4\ cm[/tex] ----> the width of rectangle
substitute
[tex]A=2[\frac{1}{2}(6)(2)]+(11)(4)[/tex]
[tex]A=56\ cm^{2}[/tex]
PLEASE ANSWER RIGHT AWAY
Answer:
The sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is t2 = 4 and recursive definition is tn+1 = 2 tn - 2 ⇒ 4th answer
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ The recursive definition is tn+1 = 2 tn - 2 and t2 = 4
- Look to the answer we have three answer with second term = 4,
1st , 2nd and 4th
- Lets find the 1st term
∵ t2 = 2 t1 - 2
∵ t2 = 4
∴ 4 = 2 t1 - 2 ⇒ add 2 to the both sides
∴ 6 = 2 t1 ⇒ divide the two sides by 2
∴ t1 = 3
- We have two answer with first term = 3, 2nd and 4th answers
* Lets find the third term
∵ t3 = 2 t2 - 2
∵ t2 = 4
∴ t3 = 2 (4) - 2 = 8 - 2 = 6
∴ The 4th answer has the third term = 6
* The 4th sequence 3 , 4 , 6 , 10 , 18 described by the 2nd term is
t2 = 4 and recursive definition is tn+1 = 2 tn - 2
Which functions represent a horizontal translation to the left of the parent function f(x) = ln x?
Check all that apply.
g(x) = 3 ln(x − 1) + 6
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
s(x) = −3 ln(x) − 3
p(x) = ln(x + 2) − 2
A horizontal shift happens when you add or subtract a value from the input value of x.
To shift left the number would be added to the x.
The answers are:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Answer:
h(x) = 3 ln(x + 3) + 1
r(x) = −3 ln(x + 1) + 3
p(x) = ln(x + 2) − 2
Step-by-step explanation:
The parent function given to us is: [tex]f(x)=\ln x[/tex].
A horizontal translation to the left k units is of the form [tex]y=\ln (x+k)[/tex].
This implies that;
h(x) = 3 ln(x + 3) + 1, is a horizontal translation to the left by 3 units.
r(x) = −3 ln(x + 1) + 3, is a horizontal translation to the left by 1 unit.
p(x) = ln(x + 2) − 2, is a horizontal translation to the left by 2 unit.
Which of the following describes the roots of the polynomial function K x) - (x+ 2)(x-4)(x+1)3?
Answer:
It's the first option.
Step-by-step explanation:
(x + 2)^2 gives a duplicate (multiplicity 2) root. (because (x + 2)^2 = 0 so x = -2 multplicity 2)
(x - 4) gives one root of 4.
(x + 1)^3 gives x = -1 with multiplicity 3.
Answer:
-2 with multiplicity 2, 4 with multiplicity 1, and -1 with multiplicity 3.
Step-by-step explanation:
The given polynomial function is: [tex]f(x)=(x+2)^2(x-4)(x+1)^3[/tex].
To find the roots of this polynomial, we equate each factor to zero.
This implies that;
i. [tex](x+2)^2=0[/tex], [tex]\implies x=-2[/tex], the multiplicity of this root is 2, because the factor repeats twice
ii. [tex]x-4=0[/tex], [tex]\implies x=4[/tex], the multiplicity of this root is 1, because the factor repeats once.
ii. [tex](x+1)^3=0[/tex], [tex]\implies x=-1[/tex], the multiplicity of this root is 3, because the factor repeats three times.
Someone please help I will mark brainlest!!
Answer:
I would say A, binocular vision. ((Not sure though.))
Step-by-step explanation:
Process of elimination. Opposable thumbs could help, but not as much as being able to spot your prey from far away. And what does singular births and just being a mammal help with being a predator? The answer that makes most sense is A. Hope this helps.
Answer:
I believe binocular vision or opposable thumbs
Step-by-step explanation:
Probably opposable thumbs because it helps predators grab things
I need help with this question
Answer:
The answer should be D. It is -2 on the inside because it is backwards of what you may think and because it is inside the square root. The -3 represents a down shift of 3
Answer: Last option.
Step-by-step explanation:
Below are shown some transformation for a function f(x):
[tex]f(x) + k[/tex] shifts the function k units upward.
[tex]f(x) - k[/tex] shifts the function k units downward.
[tex]f(x+k)[/tex] shifts the function k units to the left.
[tex]f(x-k)[/tex] shifts the function k units to the right.
Then, knowing that the graph of the function [tex]y=\sqrt{x}[/tex] is shifted 3 units down and 2 units rights, the function that represents the new graph is:
[tex]y=\sqrt{x-2}-3[/tex]
Which is the last option.
The price of a ring was increased by 30% to £325. What was the price before the increase?
Divide the new price by 1 + percent of increase:
325 / 1.30 = 250
The original price was £250
Simplify √25. please answer
Your answer is 5! (:
Answer:
5
Step-by-step explanation:
A square root of a number n is a number r such that r2=n. in the case 25 we find that 52=25 , so 5 is a square root of 25. sorry if this is confusing. found this from google.
Oliver plans to purchase a $1,500 certificate of deposit (CD) at his bank. The CD will earn 2.3% interest, compounded semi-annually.
Write an exponential expression in the form a(b)c, where b is a single value, to find the value of the CD, in dollars, after t years. Round any decimals to the nearest ten-thousandth. Do not include dollar signs or percent symbols in the expression.
Answer:
1500(1.0115)^(2t)
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.
__
Using the given values in the formula, we have ...
A = 1500(1 +0.023/2)^(2t)
Simplifying a bit, this is ...
A = 1500(1.0115)^(2t) . . . . . CD value after t years
I’d really appreciate help with these...
Answer:
+- 5 and +- 3
Step-by-step explanation:
qn 2:
4r² = 91 + 9
4r² = 100
r² = 25
r = +- 5
qn 3:
4r² = 29 + 7
4r² = 36
r² = 9
r = +- 3
Answer:
Q2. (±5)Q3. (±3)Step-by-step explanation:
[tex]\bold{Q2.}\\\\4r^2-9=91\qquad\text{add 9 to both sides}\\\\4r^2-9+9=91+9\\\\4r^2=100\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{100}{4}\\\\r^2=25\to r=\pm\sqrt{25}\\\\\boxed{r=\pm5}[/tex]
[tex]\bold{Q3.}\\\\4r^2-7=29\qquad\text{add 7 to both sides}\\\\4r^2-7+7=29+7\\\\4r^2=36\qquad\text{divide both sides by 4}\\\\\dfrac{4r^2}{4}=\dfrac{36}{4}\\\\r^2=9\to r=\pm\sqrt9\\\\\boxed{r=\pm3}[/tex]
Which graph has a slope of 13?
The top right graph has a slope of 1/3
Answer:
top right
Step-by-step explanation:
If angle g measures 117º, what is the measure of angle h?
The complete question is given below.
If angle g measures 117º, what is the measure of supplementary angle h?
Angle g and angle h are the Supplementary angles. Then the measure of the angle ∠h will be 63°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
If angle g measures 117º.
Then the measure of angle h will be
We know that angle g and angle h are the Supplementary angles. Then we have
∠g + ∠h = 180°
117° + ∠h = 180°
∠h = 63°
More about the angled link is given below.
https://brainly.com/question/15767203
#SPJ2
The cost to rent an instrument is $65 for the first month. It costs $30 for each additional month, x, that the instrument is rented. Which expression represents the total cost of renting the instrument?
A. 30 + 65x | B. x + 35 | C. 65 + 30x | D. x + 95
Final answer:
The total cost of renting the instrument is represented by the expression 65 + 30x, which accounts for the initial rental fee and the additional cost per subsequent month.
Explanation:
The expression that represents the total cost of renting the instrument is C = 65 + 30x, which is option C. To understand this, consider that there is a flat rental fee of $65 for the first month and an additional cost of $30 for each subsequent month an instrument is rented. The variable x represents the number of additional months the instrument is rented. Therefore, the total cost is given by the initial cost plus the cost for additional months, which in algebraic terms is 65 + 30x.
Justin and David were comparing text messages. For every 8 messages Justin sent, David sent 12 messages. Together Justin and David have sent 450 messages last month. How many messages did each person send?
Answer:
The number of messages sent by Justin was [tex]180\ messages[/tex]
The number of messages sent by David was [tex]270\ messages[/tex]
Step-by-step explanation:
Let
x-----> number of messages sent by Justin
y----> number of messages sent by David
we know that
[tex]\frac{x}{y}=\frac{8}{12}[/tex]
[tex]x=\frac{8}{12}y[/tex] ----> equation A
[tex]x+y=450[/tex] -----> equation B
substitute equation A in equation B and solve for y
[tex]\frac{8}{12}y+y=450[/tex]
[tex]\frac{20}{12}y=450[/tex]
[tex]y=450*12/20=270\ messages[/tex]
Find the value of x
[tex]x=\frac{8}{12}(270)=180\ messages[/tex]
therefore
The number of messages sent by Justin was [tex]180\ messages[/tex]
The number of messages sent by David was [tex]270\ messages[/tex]
What is the missing information in the paragraph proof?
inscribed angle
polygon interior angle sum
quadrilateral angle sum
angle bisector
Answer:
Inscribed angle
Step-by-step explanation:
Use the expression below to write an equivalent expression in standard form, and collect like terms.
Show all of the steps in your process.
(1.) 5x + 5 ( x-3y ) + 1/2 (4x - 6y)
The expression 5x + 5 ( x-3y ) + 1/2 (4x - 6y) simplifies to 12x - 18y by distributing the multiplication over addition, combining like terms, and checking the answer for reasonableness.
Explanation:To simplify the algebraic expression 5x + 5 ( x-3y ) + ½ (4x - 6y), let's start by distributing the multiplication over addition for each term inside the parentheses:
Multiply 5 by each term inside the first set of parentheses: 5 × x and 5 × (-3y), which gives us 5x - 15y.
Multiply ½ by each term inside the second set of parentheses: ½ × 4x and ½ × (-6y), resulting in 2x - 3y.
Now, combine the like terms:
The x-terms: 5x + 5x + 2x = 12x.
The y-terms: -15y - 3y = -18y.
So, the expression in standard form is 12x - 18y.
Lastly, we should check the answer to see if it is reasonable:
No like terms are left to combine.
The coefficients are summed up correctly.
The expression is simplified as much as possible.
Please help me with this!!
Step-by-step explanation:
To find the y-coordinate points we need to evaluate the function for all the [tex]x[/tex] values in the table. In other words, we need to replace [tex]x[/tex] with each value in our given function and simplify.
- For x = 0
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(0)=(0-2)^2-5[/tex]
[tex]f(0)=(-2)^2-5[/tex]
[tex]f(0)=4-5[/tex]
[tex]f(x)=-1[/tex]
Since [tex]x=0[/tex] and [tex]y=-1[/tex], our first point is (0, -1)
- For x = 1
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(1)=(1-2)^2-5[/tex]
[tex]f(1)=(-1)^2-5[/tex]
[tex]f(1)=1-5[/tex]
[tex]f(x)=-4[/tex]
Our second point is (1, -4)
- For x = 2
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(2)=(2-2)^2-5[/tex]
[tex]f(2)=(0)^2-5[/tex]
[tex]f(x)=-5[/tex]
Our third point is (2, -5)
- For x = 3
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(3)=(3-2)^2-5[/tex]
[tex]f(3)=(1)^2-5[/tex]
[tex]f(3)=1-5[/tex]
[tex]f(x)=-4[/tex]
Our fourth point is (3, -4)
- For x = 4
[tex]f(x)=(x-2)^2-5[/tex]
[tex]f(4)=(4-2)^2-5[/tex]
[tex]f(4)=(2)^2-5[/tex]
[tex]f(4)=4-5[/tex]
[tex]f(x)=-1[/tex]
Our fifth point is (4, -1)
Now we just need to plot each point in our coordinate plane and join them with the parabola as you can see in the attached picture.
how do you do this - with work - using pythagorean identities?
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identities
• 1 + tan²x = sec²x
• cot x = [tex]\frac{1}{tanx}[/tex]
Given
secΘ = [tex]\frac{4}{3}[/tex], then
tan²Θ = sec²Θ - 1 = ([tex]\frac{4}{3}[/tex] )² - 1 = [tex]\frac{16}{9}[/tex] - 1 = [tex]\frac{7}{9}[/tex], hence
tanΘ = ± [tex]\sqrt{\frac{7}{9} }[/tex] = ± [tex]\frac{\sqrt{7} }{3}[/tex]
Since 270° < Θ < 360° ← fourth quadrant where tanΘ < 0
Hence tanΘ = - [tex]\frac{\sqrt{7} }{3}[/tex]
and
cotΘ = [tex]\frac{1}{-\frac{\sqrt{7} }{3} }[/tex] = - [tex]\frac{3}{\sqrt{7} }[/tex] = - [tex]\frac{3\sqrt{7} }{7}[/tex]
Which integers are opposites
14 and -4
17 and -17
33 and -23
15 and -51
17 and -17. The opposite of a number is usually the negative or positive version of that #
Write a proportion and show work
for this case we must write a proportion that shows the earnings obtained from Mrs. Miller for the sale of the house.
By making a rule of three we have:
179000 ------------> 100%
x -----------------------> 6%
Where "x" represents the gains obtained.
So:
[tex]x = \frac {6 * 179000} {100}[/tex]
Writing the proportion:
[tex]\frac {x} {179000} = \frac {6} {100}[/tex]
The earns were:
[tex]x = 10740[/tex]
ANswer:
[tex]\frac {x} {179000} = \frac {6} {100}\\x = 10740[/tex]
Answer:
$10,740
Step-by-step explanation:
You know that Mrs. Miller sells a house for $179,000. Then the cost of the house will be the 100%.
Knowing that she earns 6% of comission, you can set up the following proportion (Let be "x" the amount of money she earns), then:
[tex]\frac{\$179,000}{100}=\frac{x}{6}[/tex]
Now you need to solve for "x". Therefore, you get:
[tex](6)(\frac{\$179,000}{100})=x[/tex]
[tex]x=\$10,740[/tex]
3 + 4x - 11 = -32
What does x equal?
Add/subtract common factors.
3 - 11 + 4x = -32
-8 + 4x = -32
4x = -32 + 8
4x = -24
Then, isolate the x by using division/multiplication. But for this problem, use division.
x = -24 / 4
x = -6
Joe’s department store sells pens for 60 cents each and pencils for 40 cents each. Diane purchased a total of 17 items (pens and pencils) for $8.20. How many pens did Diane purchase?
Answer:
Diane purchased 7 pens
Step-by-step explanation:
Let
x----> the number of pens
y----> the number of pencils
we know that
x+y=17
y=17-x -----> equation A
0.60x+0.40y=8.20 -----> equation B
Solve the system of equations by substitution
Substitute equation A in equation B and solve for x
0.60x+0.40(17-x)=8.20
0.60x+6.8-0.40x=8.20
0.20x=8.20 -6.8
x=1.4/0.2=7 pens
Answer: The number of pen purchased by Diane is 7.
Step-by-step explanation: Given that Joe’s department store sells pens for 60 cents each and pencils for 40 cents each.
Diane purchased a total of 17 items for $8.20.
We are to find the number of pen that Diane purchased.
We know that
1 cent = $ 0.01.
Let x and y represents the number of pen and pencils that Diane purchased.
Then, according to the given information, we have
[tex]60\times0.01x+40\times 0.01y=8.20\\\\\Rightarrow 0.6x+0.4y=8.20\\\\\Rightarrow 6x+4y=82~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
and
[tex]x+y=17\\\\\Rightarrow y=17-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
Substituting the value of y from equation (ii) in equation (i), we get
[tex]6x+4y=82\\\\\Rightarrow 6x+4(17-x)=82\\\\\Rightarrow 6x+68-4x=82\\\\\Rightarrow 2x=82-68\\\\\Rightarrow 2x=14\\\\\Rightarrow x=\dfrac{14}{2}\\\\\Rightarrow x=7.[/tex]
Thus, the number of pen purchased by Diane is 7.
What are the zeros of the function? f(x)=x3+4x2−12x
Set the function equal to 0 and solve for
x=0,2,-6
Answer:
The solutions are:
[tex]x= 0[/tex] and [tex]x= 2[/tex] and [tex]x = -6[/tex]
Step-by-step explanation:
1) Make the function equal to zero
[tex]f(x)=x^3+4x^2-12x = 0[/tex]
2) Take x as a common factor
[tex]x(x^2+4x-12) = 0[/tex]
3) Factor the expression [tex]x^2+4x-12[/tex]
The sought-after factors are such numbers that when multiplying them obtain as result -12 and when adding both numbers obtain as result 4.
The numbers that meet this condition are
6 and -2
Because
[tex]6*(-2) = -12\\\\6 -2 = 4[/tex]
Then the factors are
[tex]x^2+4x-12=(x-2)(x+6)[/tex]
4) Solve the equation for x
[tex]x(x-2)(x+6) = 0[/tex]
The solutions are:
[tex]x= 0[/tex] and [tex]x= 2[/tex] and [tex]x = -6[/tex]