Answer:
D. f^-1(x) = log2(x -6)4x^2 -3 . . . . x ≤ 0B. √(x^5) -3√(x^3) -18√xStep-by-step explanation:
1. When you replace f(x) by x and x by y, you have
... x = 2^y + 6
The first thing you do is subtract 6; then you take the base-2 logarithm:
... (x -6) = 2^y
... log2(x -6) = y = f^-1(x)
You know that to get the y-term by itself, you must subtract 6. Anything else you do will operate on (x-6). Only answer choice D has that sort of construction.
2. When you swap x and y and solve for y, you have ...
... x = -1/2√(y+3)
... -2x = √(y +3) . . . . . . multiply by -2
... (-2x)^2 = y +3 . . . . . square
... 4x^2 - 3 = y = f^-1(x) . . . . subtract 3
The range of f(x) is (-∞, 0], so that is the domain of f^-1(x). That is, f^-1(x) is defined for x ≤ 0.
3. The product of the two functions is ...
... (x -6)(√x)(x +3) = (√x)(x^2 -3x -18)
Every term will have a factor of √x, and the coefficients will be 1, -3, -18. Only selection B matches those conditions.
Answer:
Question One: log_2(x - 6) = y
Question Two: First blank: 4 Second blank 0
Question Three: B
Step-by-step explanation:
f(x) = 2^x + 6
y = 2^x + 6 Interchange the x and y
x = 2^y + 6 Subtract 6 from both sides
x - 6 = 2^y Take the log of both sides
log(x - 6) = log 2^y The power can be multiplied by the log of 2
log(x - 6) = y log(2) Divide by the log of 2
log(x - 6)/log(2) = y This to me is the preferred answer. It allows you to calculate what the actual number is or graph it on Desmos
The answer I have given is equivalent to using base 2 as your log, but calculating that is not always easy.
log_2(x - 6) = y
Answer: D
Problem Two
You want the inverse of y = - 1/2 sqrt(x + 3) x ≥ - 3
Note: you cannot have any number less than -3 because if you do, you will be taking the square root of -x which involves complex numbers. In addition x ≥ -3 is a domain. You have to keep that in mind when doing this question.
y = - 1/2 sqrt(x + 3) Interchange the x and yx = - 1/2 sqrt(y + 3) Multiply by - 2-2x = sqrt(y + 3) Square both sides(-2x)^2 = sqrt(y + 3)^2 4x^2 = y + 3 Subtract 3 from both sidesy = 4x^2 - 3The domain and range of this is a little harder to figure out. The range of f(x) becomes the domain of f-1(x)
The range of f(x) is 0 <=y < - infinity
So the domain of f-1(x) <= 0
Answer: The first blank is 4 and the second one is 0
Graph: the graph is given you below the question. What it shows is the f(x) and f^-1(x) are symmetrical about y = x. Most inverses are. If you want to check your work, it is best to include a graph when doing inverses.
Red OriginalBlue inverseBlack: y = xProblem Three
The best way to begin this problem is to apply the associative property of multiplication and start by rewriting the givens as x^(1/2)[(x - 6)(x + 3)]. Do what is in the square brackets first.
x^(1/2) [x^2 - 6x + 3x - 18]x^(1/2) [x^2 - 3x - 18]Now deal with the x^(1/2) which must be multiplied by all three terms in the square brackets.
x^(1/2)*x^2: x^(2 + 1/2) = x^(4/2 + 1/2) = x^(5/2)x^(1/2)*(-3x): - 3 x^(2/2 + 1/2) = - 3x^(3/2)x^(1/2)*(-18): - 18x^(1/2)Result: x^(5/2) - 3x^(3/2) - 18x^(1/2)
Answer: √(x^5) - 3√x^3 - 18√x
Answer: B
Find the slope of:2y+8x=6
Answer:
-4
Step-by-step explanation:
The slope of the line given by the equation 2y + 8x = 6 is -4. This was found by converting the equation into slope-intercept form, y = mx + b.
To find the slope of the equation 2y + 8x = 6, we first need to convert it into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Start with the given equation: 2y + 8x = 6Isolate y by subtracting 8x from both sides: 2y = -8x + 6Divide everything by 2 to solve for y: y = -4x + 3In the slope-intercept form y = -4x + 3, the coefficient of x is the slope -4.Therefore, the slope of the line is -4.
A shopper wants to ensure he has enough cash to purchase a $59 coffee table, so he asks a clerk what the total will be with the sales tax included. The clerk tells him the total will be $61.36. What is the sales tax percentage?
Answer:
Step-by-step explanation:
First you have to subtract 59$ from 61.36 which will give you 2.36.Then you have to multiply 0.02 to 59 which equals 1.18.Then you multiply 0.04 by 59 which will give you the answer.Hope this helps!!!Your answer should be 0.04!!!Please Mark brainliest!!!!!
To find out the sales tax percentage, first find the amount paid in taxes by subtracting the original price from the total price. Then divide this tax amount by the original price and multiply by 100 to get the percentage, which is 4% in this case.
Explanation:To determine the sales tax percentage charged on the coffee table, we first calculate the total amount of sales tax paid. We subtract the original price of the table ($59) from the total amount paid with tax ($61.36) to find the amount of tax paid.
$61.36 - $59.00 = $2.36
Now, we'll convert the sales tax into a percentage of the original price. We do this by dividing the sales tax amount by the original price and then multiplying by 100 to get the percentage.
$2.36 ÷ $59 = 0.04 (rounded to two decimal places)
0.04 × 100 = 4%
Therefore, the sales tax percentage on the coffee table is 4%.
Learn more about Sales Tax Calculation here:https://brainly.com/question/18375545
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[tex] \frac{2}{3} - \frac{4}{10} = [/tex]
what is the answer?
Answer:
8/30 (Simplified answer: 4/15)
Step-by-step explanation:
Find common denominators. Note the what you do to the denominator, you do to the numerator.
Multiply 10 to both the denominator & numerator of 2/3, and multiply 3 to both the denominator & numerator of 4/10
(10/10)(2/3) - (3/3)(4/10)
Simplify.
(20/30) - (12/30)
Simplify. Combine the terms
(20/30) - (12/30) = (20 - 12)/30 = 8/30
Simplify the fraction
(8/30)/(2/2) = 4/15
~
Point C(3.6, -0.4) divides in the ratio 3 : 2. If the coordinates of A are (-6, 5), the coordinates of point B are .
A (5,-4)
B (5,-2)
C (10,-4)
D (10,-2)
If point D divides in the ratio 4 : 5, the coordinates of point D are .
A (62/9,-4)
B (58/9,-4)
C (62/9,-2)
D (58/9,-2)
QUESTION 1
The point C(3.6, -0.4) divides AB in the ratio 3 : 2.
The coordinates of A are (-6, 5).
Let the coordinates of B be [tex](x_2,y_2)[/tex]
We use the formula:
[tex]x=\frac{mx_2+nx_1}{m+n}[/tex] to determine the x-coordinate of B.
We substitute the known values to obtain:
[tex]3.6=\frac{3x_2+2(-6)}{3+2}[/tex]
[tex]3.6=\frac{3x_2-12)}{5}[/tex]
[tex]3.6\times 5=3x_2-12[/tex]
[tex]18=3x_2-12[/tex]
[tex]18+12=3x_2[/tex]
[tex]30=3x_2[/tex]
This implies that:
[tex]x_2=10[/tex]
We also use the formula:
[tex]y=\frac{my_2+ny_1}{m+n}[/tex] to find the y-coordinate.
[tex]-0.4=\frac{3y_2+2(5)}{3+2}[/tex]
[tex]-0.4=\frac{3y_2+10}{5}[/tex]
[tex]-0.4\times 5=3y_2+10[/tex]
[tex]-2-10=3y_2[/tex]
[tex]-12=3y_2[/tex]
[tex]-4=y_2[/tex]
The coordinates of B are (10,-4)
QUESTION 2.
If point D divides CD in the ratio 4 : 5.
Then the coordinates of D are:
[tex](\frac{4(10)+5(3.6)}{4+5}, \frac{4(-4)+5(-0.4)}{4+5})[/tex]
[tex](\frac{58}{9}, \frac{-18}{9})[/tex]
The coordinates of D are [tex](\frac{58}{9}, -2)[/tex]
30 points!!! Plzz help!!! Will give Brainliest!!!! Need help ASAP!!!!
Using the diagram shown, select all that apply to the pair of angles, 1 and 2.
A. acute
B. right
C. obtuse
D. adjacent
E. vertical
F. complementary
G. supplementary
Gary ordered 30 pizzas for a party. 60% of the pizzas have 12 slices each. The remaining 40% of the pizzas have 10 slices each. Complete the model. Then complete the statements to find the total number of slices of pizza.
Answer:
60% of 30 is 18 and 40% of 30 is 12
18 x 12 = 216
12 x 10 = 120
216 + 120 = 336
Step-by-step explanation:
Answer: IN ORDER: 18,12,216,120,336
Step-by-step explanation: Got it right on TTM
You put 230 dollars in an account. The annual interest is 12% in 3 years. What is the principal you put into this account? PLEASE GIVE A FULL EXPLANATION!! I NEED HELPP
The complement of an angle is 53 degrees. What is the measure of an angle?
You can spend at most $10 at the mall. You want to buy a book that costs $6.75 and a cold drink. Write and solve an inequality to represent the amount of money you can spend on your cold drink.
Plzz Hellp me!!!;(
Answer:
the amount of money you can spend on the drink is no more than 3.25
Step-by-step explanation
total is greater than/equal to cost of book plus cost of drink
10>/=6.75+x (x represents the drink)
x</=3.25
Answer: 10.00-6.75=find out yourself, EASY
Step-by-step explanation:
Since you have 10 dollars and you find a book and a cold drink for all 6.75
you will need to subtract the numbers to find your answer
please help me!!!!!! I cant do it
Average rate of change formula:
[tex]\dfrac{\Delta y}{\Delta x}[/tex]
[tex]\Delta y=6-1=5\\\\\Delta x=4.95-0.40=4.55[/tex]
[tex]\dfrac{\Delta y}{\Delta x}=\dfrac{5}{4.55}=\dfrac{500}{455}=\dfrac{100}{91}\approx1.1[/tex]
which property is used below?
Distributive property
multiplication property of inequality
Subtraction property of inequality
Associative property of multiplication
Answer:
multiplication property of inequality
Step-by-step explanation:
-1/3 x - 2/3 ≥ 7x+3
We can multiply by 3 on each side to clear the fraction by the Multiplication property of inequality
Since c>0
and a≥b
ac ≥ bc
solve for x -3x+6=2x-24
-30
-6
6
30
-3x + 6 = 2x - 24.
Add 3x to both sides.
6 = 5x - 24.
Add 24 to both sides.
30 = 5x.
Divide it all by 5.
x = 6.
Three times the sum of a number and 2 is the same as the number minus 4
Answer:
3* ( n+2) = n-4
n=-5
Step-by-step explanation:
Three times the sum of a number and 2 is the same as the number minus 4
3* ( n+2) = n-4
Distribute
3n +6 = n-4
Subtract n from each side.
3n-n +6 =n-n-4
2n +6 = -4
Subtract 6 from each side.
2n +6-6 = -4-6
2n = -10
Divide by 2 on each side.
2n/2 = -10/2
n = -5
How do you do long division on 0.54?
Answer:
you put your divisor and add Dividend and see what that adds up to and get your answer
Step-by-step explanation:
Answer:
You add more 0
Step-by-step explanation:
Aria walked down a trail into a valley. V(d) models Aria's vertical distance from the top of the valley (in kilometers) after walking d kilometers along the trail. What does the statement V(3)<3 mean?
Answer:
When Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3 km
Step-by-step explanation:
Remember that V(d) denotes Aria's vertical distance from the top of the valley V after she has walked d kilometers along the trail.
This means that V(3) is Aria's vertical distance from the top of the valley after she has walked 3km.
Therefore, V(3)<3 means that Aria's vertical distance from the top of the valley after she has walked 3km, is less than 3km
In other words, the statement means that when Aria had walked 3km along the trail, her vertical distance from the top of the valley was less than 3km
V(3) < 3 means Aria's vertical distance from the top of the valley is less than 3 kilometers after walking 3 kilometers along the trail. It shows her descent into the valley is not more than 3 kilometers vertically at that point.
The inequality V(3) < 3 means that after Aria has walked 3 kilometers along the trail, her vertical distance from the top of the valley is less than 3 kilometers. In other words, Aria has descended into the valley, but her descent after 3 kilometers along the trail is not greater than 3 kilometers vertically. This provides a way to understand her position relative to the top of the valley based on the distance she has walked.
Which tables represent constant functions?
A function is a law that tells you how to associate inputs (x values) and outputs (y values).
In the case of constant functions, it doesn't matter which input you choose, the ouput must always be the same.
So, a constant function has always the same output (y values) for every input (x values) you feed.
Answer:
Third and last choices represent constant functions.Step-by-step explanation:
A constant function refers to those functions that only have one variable, which is constant. For example, x=2, y=4, x=-1, are constant function, because they don't variate.
From the given tables, the third and last choices are constant function, because you can observe that one variable doesn't variate. The third function has y=3 as the constant value, and the last table has y=-1 is the constant function.
Therefore, the right choices are third and last table.
I need the answer :(
Answer:
z = 62
y = 117
Step-by-step explanation:
Z
118 and z are supplementary.
z + 118 = 180 Supplementary angles add to 180. Subtract 118 from both sides.
z = 180 - 118 Do the subtraction
z = 62 Answer
Y
The interior angles of all quadrilaterals (convex) add up to 360 degrees.
y + z + 84 + 97 = 360 Given
62 + y + 84 + 97=360 Add
y + 243 = 360 Subtract 243 from both sides
y = 360 - 243 combine
y = 117 Answer
Which expressions are equivalent to -6n+(-12)+4n
Answer:
-2n - 12
Step-by-step explanation:
Combine like terms. Note that each term has one variable (n). Also note that one negative sign and one positive sign results in a negative sign.
-6n + (-12) + 4n = -6n + 4n - 12 = -2n - 12
-2n - 12 is your answer
~
Answer:
A
Step-by-step explanation:
4(n-3)-6n
Which lines are parallel if m angle 1= m angle 2 ?
Jane moved from a house with 58 square feet of closet space to an apartment with 29.58 square feet of closet space. What is the percentage decrease of Jane's closet space? A. 96% B. 39% C. 49% D. 51% R
(WILL GIVE BRAINLIEST)Find the polynomial function with real coefficients that has zeros 1, 1 , 2+ i sqrt 3
Answer:
[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]
Step-by-step explanation:
We have given that this polynomial has the given zeroes of 1, 1, and [tex]2+i\sqrt{3}[/tex], we can express the polynomial in a factored form where each zero has the form x-a (where a is our zero):
polynomial= [tex](x-1) (x-1) (2+i\sqrt{3})[/tex]
=[tex](x^2+1-2x) (2+i\sqrt{3})[/tex]
=[tex]x^3-x^2(4+i\sqrt{3} )+x(5+i2\sqrt{3} )-(2+i\sqrt{3} )=0[/tex]
I have no idea how to do this someone helped me with this and got the right answer which is 11/17 but I got a totally different answer!! Please help! Explain.
Answer:
Step-by-step explanation: The reason is is because when adding and subtracting integers, you flip the operation sign that will be used to solve the problem.So when you flip the sign of this equation, you subtract. So that's how your answer was 11/17. Also it is positive because the biggest number is positive so that is what the solution will be.
Please mark brainliest!!!!!!
First twelve mulitples of 4
Answer:
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
Step-by-step explanation:
4*1 = 4
4*2 = 8
4*3 = 12
and so on...
Answer:
4,8,12,16,20,24,28,32,36,40,44, and 48
Step-by-step explanation:
4*1=44*2=84*3=124*4=164*5=204*6=244*7=284*8=324*9=364*10=404*11=444*12=48which property is used to simplify the expression 5+(6+-6)=5+0
additive inverse property
additive identity property
associative property of addition
commutative property of addition
Answer:
additive inverse property
Step-by-step explanation:
which property is used to simplify the expression 5+(6+-6)=5+0
additive inverse property
x+-x = 0
additive identity property
0+8=8
associative property of addition
a+(b+c) = (a+b)+c
commutative property of addition
a+b=b+a
Answer: additive inverse property
Step-by-step explanation: i looked it up lol
The measures of the angles of a hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9. What is the measure of the smallest angle in the hexagon?
Answer:
[tex]72^{\circ}[/tex] is the measure of the smallest angle in the hexagon.
Step-by-step explanation:
As, we know that the sum of all the angles is 720 degrees.
Given: The measures of the angles of the hexagon are in the extended ratio 4 : 5 : 5 : 8 : 9 : 9.
Let x be the number used to simplify the size of each angle.
Sum of all the measure angles is 720 degrees
⇒[tex]4x+5x+5x+8x+9x+9x = 720^{\circ}[/tex]
Combine like terms;
[tex]40x = 720^{\circ}[/tex]
Divide both sides by 40 we get;
[tex]x = \frac{720}{40} = 18[/tex]
The measure of angles are:
[tex]4x = 4 \times 18 = 72^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\5x = 5 \times 18 = 90^{\circ}\\8x = 8 \times 18 = 144^{\circ}\\9x = 9 \times 18 = 162^{\circ}\\9x = 9 \times 18 = 162^{\circ}[/tex]
Therefore; the measure of the smallest angle in the hexagon is, [tex]72^{\circ}[/tex]
Nathan took his car in for service and repairs. He had a coupon for 10% off. Original Prices • Labor $218.97 • Parts $303.47 • Other $77.78 Which amount is closest to Nathan's total costs after the 10% discount and including 6% sales tax? [Assume tax is applied after the discount is applied.] A. $573 B. $508 C. $540 D. $504
Answer:
C PLEASE GIVE BRAINLIEST
Step-by-step explanation:
218.97 + 303.47 + 77.78 = $600.22
600.22 x .10 = 60.02 (amount of discount)
600.22 - 60.02 = $540.20 (amount he owes)
Answer is C
Answer:The answer should be D
Step-by-step explanation:
p(x)=x^2-x-6 q(x)=x-3 What is p(x)-q(x)
Answer:
[tex]x^{2} -2x-3 or the factored form (x+1)(x-3)[/tex]
Step-by-step explanation:
p(x) -q(x)=
[tex]x^{2} -x-6-x+3\\=x^{2} -2x-3[/tex]
Is a triangle congruent
Answer: Yes
Step-by-step explanation:
When two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they are there.
what is another way to write the expression P x (10 - 2)
A. 10 x 2 - P
B. (10 x 2) x P
C. (P x 10) - (P x 2)
D. (10 x 2) - P
how do the graphs of the function f(x)=(3/2)x and g(x)=(2/3)x compare
Answer:
f is a line through 0 and (2,3)
g is a line through 0 and (3,2)
Step-by-step explanation:
f and g are proportional linear functions. They each have the form y=mx+b where b=0 and m is a fraction. The m or slope tell us the form the function takes on the graph. It is a straight line through 0 with steepness m.
[tex]f(x)=\frac{3}{2} x[/tex] has steepness 3/2. Starting at (0,0) or the origin, move up three grid lines on the y-axis and then over 2 grid lines. Mark your point at (2,3). Then connect and draw arrows on the end.
[tex]g(x)=\frac{2}{3}x[/tex] has steepness 2/3. Starting at (0,0) or the origin, move up two grid lines on the y-axis and over 3 grid lines. Mark your point at (3,2). Then connect and draw he arrows on the end.
Answer:
The graphs are reflections of each other over the y-axis. The graph of g(x) shows exponential decay, while the graph of f(x) shows exponential growth.
Step-by-step explanation: