Answer:
D
Step-by-step explanation:
The + 6 moves it up 6 units.
The correct answer is (D) "The graph of g(x) is the graph of f(x) shifted 6 units up."
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
When we add a constant to a function, such as in the case of g(x) = f(x) + 6, it will shift the graph of f(x) upward by 6 units.
This is because, for any value of x, the value of f(x) will be added to 6, resulting in a vertical shift of the entire graph.
Option (A) is incorrect because adding 6 to f(x) would shift the graph up, not down.
Option (B) is incorrect because adding a constant to a function does not cause it to shift horizontally.
Option (C) is incorrect because adding 6 to f(x) would shift the graph right, not left.
D. The graph of g(x) is the graph of f(x) shifted 6 units up. Adding a constant term to a function will shift the graph of the function vertically. In this case, adding 6 to f(x) will shift the graph of f(x) upward by 6 units, resulting in the graph of g(x).
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ASAP there are three marbles in a bag. One is red and two are black. What is the probability of picking a black marble first, putting it back in the bag and then picking a black marble? Use the following probability to find the answer.
Answer:
[tex] \frac{4}{9} [/tex]
Step-by-step explanation:
[tex]p = \frac{favorable \: outcomes}{total \: outcomes} = \frac{4}{9} [/tex]
=============================================================
Explanation:
The probability you get a black marble on the first selection is 2/3 since we have 2 black marbles out of 2+1 = 3 total.
We put the marble back and then we have 2/3 as the probability of selecting another black marble on the second try. Nothing has changed because we put the marble back. That means the events are independent.
So we get (2/3)*(2/3) = 4/9 as the probability of selecting 2 black marbles in a row (with replacement).
Chung has 6 trucks and 5 cars in his toy box. Brian has 4 trucks and 5 cars in his toy box.
Which is the correct comparison of their ratios of trucks to cars?
StartFraction 6 Over 4 EndFraction less-than StartFraction 5 Over 5 EndFraction
StartFraction 6 Over 4 EndFraction greater-than StartFraction 5 Over 5 EndFraction
StartFraction 6 Over 5 EndFraction less-than StartFraction 4 Over 5 EndFraction
StartFraction 6 Over 5 EndFraction greater-than StartFraction 4 Over 5 EndFraction
Given:
Chung has 6 trucks and 5 cars in his toy box.
Brian has 4 trucks and 5 cars in his toy box.
To find:
The correct comparison of their ratios of trucks to cars.
Solution:
The ratio of trucks to cars is defined as:
[tex]\text{Ratio}=\dfrac{\text{Number of trucks}}{\text{Number of cars}}[/tex]
Chung has 6 trucks and 5 cars in his toy box. So, the ratio of trucks to cars is:
[tex]\text{Ratio}=\dfrac{6}{5}[/tex]
Brian has 4 trucks and 5 cars in his toy box.
[tex]\text{Ratio}=\dfrac{4}{5}[/tex]
We know that,
[tex]6>4[/tex]
[tex]\dfrac{6}{5}>\dfrac{4}{5}[/tex]
Therefore, the correct option is D.
Answer:
what the guy above me said
Step-by-step explanation:
so yeah he is right points
Find the distance between the pair of points: (0,1) and (1,0)
Answer:
sqrt(1^2 + 2^2)
[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Alec bakes spherical rolls of bread. Each roll is about 8cm
wide. What is the approximate volume of each roll? Use
3.14 to approximate a.
Answer:
Step-by-step explanation:
2143.57
9x5
pls help meeeeeeeeee
Answer:
45
hope this helps
Answer:
45
Step-by-step explanation:
9x5=45
3 3/4 × 2 2/9 please
Help ♀️♀️♀️
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: 8 \frac{1}{3}\:(or) \:8.333}}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]
[tex]3 \frac{3}{4} \times 2 \frac{2}{9} [/tex]
➺[tex] \: \frac{15}{4} \times \frac{20}{9} [/tex]
➺[tex] \: \frac{300}{36} [/tex]
➺[tex] \: \frac{25}{3} [/tex]
➺[tex] \: 8 \frac{1}{3} [/tex]
➺[tex] \: 8.333[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\pink{Mystique35 }}{\orange{❦}}}}}[/tex]
Differentiate the function. y = (2x - 5)^2 (5 - x)?
Answer:
[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x)
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor: [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4: [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative: [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x): [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms: [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor: [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer fast please and thanks!
Answer:
tan 30 = x / 15
General Formulas and Concepts:
Trigonometry
[Right Triangles Only] SOHCAHTOA[Right Triangles Only] tanθ = opposite over adjacentStep-by-step explanation:
Step 1: Define
Identify variables
Angle θ = 30°
Opposite Leg = x
Adjacent Leg = 15
Step 2: Solve for x
Substitute in variables [tangent]: tan 30 = x / 15Answer:
3rd one
Step-by-step explanation:
Recall that
Sin = opposite over hypotenuse
Cos = adjacent over hypotenuse
Tan = opposite over adjacent
For the angle with a measure of 30 degrees we are given it's adjacent side length and need to find it's opposite side length
When dealing with opposite and adjacent we use tangent
If tan = opposite over adjacent
Then tan30 = x / 15 and the correct answer choice is the third one
Solve the equation 2x^2 + 3 – 41 = –15 to the nearest tenth.
Hellllpppp
9514 1404 393
Answer:
x = {-4.4, +2.9}
Step-by-step explanation:
We assume you want to solve ...
2x^2 +3x -41 = -15
Adding 41 and factoring out the leading coefficient gives ...
2(x^2 +3/2x) = 26
Dividing by 2 makes it ...
x^2 +3/2x = 13
We can add the square of half the x-coefficient to "complete the square."
x^2 +3/2x +(3/4)^2 = 13 +(3/4)^2
(x +3/4)^2 = 13.5625 . . . . write the left side as a square
x +3/4 = ±√13.5625 . . . . . take the square root
x = -0.75 ±3.683 = {-4.433, +2.933} . . . . subtract 3/4 and evaluate
The solutions are approximately x = -4.4 and x = 2.9.
At the beginning of a population study, a city had 320,000 people. Each year since, the population has grown by 2.1%. Lett be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t.
Answer:
y = 320,000(2.1)^t
Step-by-step explanation:
uhm, im not very good at explaining, but everytime the year increases, the population will exponentially increase, that's why 't' is an exponent
Answer:
[tex]y=320000(1.021)^t[/tex]
Step-by-step explanation:
To increase something by x% mulitply it by (1+x)
in other words, to increase sometihng by 2.1% mulitply it by
(1+.021) or 1.021
because we are mulitplying 320000 by 1.021 each year we can write the equation as
y=320000(1.021)^t
The ice cream man just ended his shift for the day. Let 1/2x^2 6/11x + 8 represent the amount of chocolate ice cream bars he sold. Let 5/9x^2 + 2/3 represent the amount of vanilla ice cream bars he sold. Finally let 1/3x^2 + 4x + 4/3 represent the amount of strawberry ice cream bars he sold. Select all the statements that are true
a. The total amount of ice cream bars sold can be represented by the expression 25/18x^2+ 50/11x +10
b. The total amount of ice cream bars sold can be represented by the expression 25/18x^2 + 172/33x +28/3
c. He sold 1/6x^2 + 50/11x + 28/3 more chocolate than strawberry ice cream bars.
d. He sold 1/6x^2 - 38/11x + 20/3 more chocolate than strawberry ice cream bars.
Answer:
A and D
Step-by-step explanation:
Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.
=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)
=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)
Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]
= (1/6)x2 - (38/11)x +(20/3)
So, the correct options are A and D
Rewrite the equation by completing the square.
x^2 + 7x + 12 = 0
Answer:
x^2 + 7x + 12 = 0
x^2 + 7x = -12
(+3)(+4)=0
=−3
=−4
I also love r o blox
Hope This Helps!!!
Answer:
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
Step-by-step explanation:
Given
x² + 7x + 12 = 0
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² + 7x
x² + 2([tex]\frac{7}{2}[/tex] )x + [tex]\frac{49}{4}[/tex] - [tex]\frac{49}{4}[/tex] + 12 = 0
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{49}{4}[/tex] + [tex]\frac{48}{4}[/tex] = 0 , that is
(x + [tex]\frac{7}{2}[/tex] )² - [tex]\frac{1}{4}[/tex] = 0
If using the method of completing the square to solve the quadratic equation x^2+15x+21=0, which number would have to be added to "complete the square"?
Step-by-step explanation:
the answer is in the above image
Answer:
my answer is 225/5 sorry comments for wrong
the sum of two consecutive numbers is 2x+3. What are the numbers
Answer: 2 and 3
Step-by-step explanation:
its numbers
(View attachment)
a) Write ordered pairs.
b) Write the domain and range.
c) Why isn't the relation a function?
d) Which ordered pair should be removed to make the relation a function?
Answer:
in a relationship that maps elements from one set (the inputs) into elements from another set (the outputs), the usual notation for the ordered pairs is:
(x, y), where x is the input and y is the output.
In this case, the point where the arrow starts is the input, and where the arrow ends is the output.
a)
The ordered pairs are:
(28, 93)
(17, 126)
(52, 187)
(34, 108)
(34, 187)
b) The domain is the set of the inputs, in this case the domain is the set where all the arrows start, then the domain is:
{17, 28, 34, 52}
And the range is the set of the outputs, in this case the range is:
{93, 108, 126, 187}
c) A function is a relationship where the elements from the domain, the inputs, can be mapped into only one element from the range.
In this case, we can see that the input {34} is being mapped into two different outputs, then this is not a function.
d) We can remove one of the two ordered pairs where the input is {34},
So for example, we could remove:
(34, 108)
And then the relation would be a function.
Simplify the expression
Answer:
6
Step-by-step explanation:
3 sqrt(20) / sqrt(5)
We know that sqrt(a) /sqrt(b) = sqrt(a/b)
3 sqrt(20/5)
3 sqrt(4)
3 *2
6
A trinomial is a perfect square when two terms are
a. Positive
b.negative
c. Neither positve
d. Either negative
Answer:
a trinomial is a perfect square trinomial if it can be factorized into a binomial multiplies to itself. In a perfect square trinomial, two of your terms will be perfect squares.
please help me please help me please help me please help me please help me please help me please
Answer:
Q3. 9
Q4. 6
Step-by-step explanation:
Gỉaỉ pt
2x^2×(2x^2+3)=2-x^2 ai giải giúp vs
2x²×(2x²+3)=2-x²
[tex]x = \frac{1}{2} , - \frac{1}{2} ,i \sqrt{2} , - i \sqrt{2} [/tex]
A right rectangular container is 10 cm wide and 24 cm long and contains water to a depth of 7cm. A stone is placed in the water and the water rises 2.7 cm. Find the volume of the stone.
Answer:
The volume of the rock is 648 cm^3
Step-by-step explanation:
Likely the only dimension that is free to move is the depth of 7 cm.
Volume of the Rock = L * W * h1
L = 24
W = 10
h1 = 2.7
V = 24 * 10 * 2.7
V = 648 cm^3
If f(x) = - 2x +5 and g(x)=x2-1, then f(-3)+g(2) =
Answer:
[tex]{ \tt{f(x) = - 2x + 5}} \\ { \boxed{ \bf{f( - 3) = - 2( - 3) + 5 = 11}}} \\ \\ { \tt{g(x) = {x}^{2} - 1}} \\ { \boxed{ \bf{g(2) = {2}^{2} - 1 = 3}}} \\ f( - 3) + g(2) = 11 + 3 \\ = 14[/tex]
Solve for y.
r/3-2/y=s/5
Answer:
y = 2 / (r/3 - s/5)
Step-by-step explanation:
r/3 - 2/y = s/5
add 2/y to both sides
r/3 = s/5 + 2/y
Subtract s/5 from both sides
r/3 - s/5 = 2/y
multiply both sides by y
y(r/3 - s/5) = 2
Divide both sides by r/3 - s/5
y = 2 / (r/3 - s/5)
differentiate loge(x/x^2+7)
Answer:
1+1=11 2+2=22 ok na yan kuya or ate
1/6 of ______ equals 9
What is the blank?
Answer:
54
Step-by-step explanation:
1/6 × y = 9
y ÷ 6 = 9
y ÷ 6 × 6 = 9 × 6
y = 54
Hi, could someone help me solve this. so the question says to find the area of the shaded part (in black) , in terms of pie (π). the length of the square is 12 cm. the radius of the circle is 6cm. i came with the answer of (144-36π)/4. is this ok? below is the picture of the question.
Answer:
yes but can be simplified
Step-by-step explanation:
area of shaded part = ( area of square - area of circle ) / 4
= [tex]\frac{12^2-\pi (6)^2}{4}[/tex]
= [tex]\frac{144-36\pi }{4}[/tex]
= [tex]\frac{144}{4}[/tex] - [tex]\frac{36\pi }{4}[/tex]
= 36 - 9π
Rectangle ABCD translates 4 units down and 2 units to the right to form rectangle A'B'C'D'. The vertices of rectangle ABCD are labeled in alphabetical order going clockwise around the figure. If AB = 3 units and AD = 5 units, what is the length of B'C'?
Answer:
The length of BC is 14 units.Step-by-step explanation:
[tex]hope \: \: it \: \: helps} \beta \alpha \infty [/tex]
The length of B'C' is 0 units.
What is translation?It is the movement of the shape in left, right, up, and down direction.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
The length of AD = 5 units.
Since the rectangle translates down by 4 units,
The length of A'D' =5 units.
The width of the original rectangle is AB, which is 3 units.
Since the rectangle translates to the right by 2 units,
The width of the new rectangle = 3 units.
Now,
The length of B'C' is the same as the length of AD', which is 5 units.
Subtracting 5 units from 5 units gives us a length of 0 units.
Thus,
The length of B'C' is 0 units.
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which equation is the inverse of 5y+4=(×+3)^2+1/2?
Answer:
The inverse is -3 ±sqrt(5x+7/2)
Step-by-step explanation:
5y+4=(x+3)^2+1/2?
To find the inverse, exchange x and y
5x+4=(y+3)^2+1/2
Solve for y
Subtract 1/2
5x+4 -1/2=(y+3)^2+1/2-1/2
5x+8/2 -1/2=(y+3)^2+1/2-1/2
5x+7/2 = (y+3)^2
Take the square root of each side
±sqrt(5x+7/2) =sqrt( (y+3)^2)
±sqrt(5x+7/2) = (y+3)
Subtract 3 from each side
-3 ±sqrt(5x+7/2) = y+3-3
-3 ±sqrt(5x+7/2) = y
The inverse is -3 ±sqrt(5x+7/2)
Find an equation for the line parallel to 3x-5y=2 with y-intercept (0,1/5). Write the answer in slope-intercept form.
Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0
The answer is 32/3. But how do I get to that answer?
Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
Consider the graph below: Point T(-2; 3) is a point on the Cartesian Plane such that B is the angle of inclination of OT. T(-2;3) у х 2.1 Calculate the following without the use of a calculator: a) tanſ b) 13 sin B.cosB (2)
Answer:
(a) - 3/2
(b) - 78/25
Step-by-step explanation:
According to the trigonometry, the tangent of any angle is the ratio of rise to the run of the right angle triangle .
The sine of an angle is the ratio of rise to the hypotenuse of the right angle triangle.
The cosine of an angle is the ratio of run to the hypotenuse of the right angle triangle.
(a)
[tex]tan\beta = \frac{3}{-2} = \frac{-3}{2}[/tex]
(b)
[tex]13 sin\beta cos \beta = 13\times \frac{3}{\sqrt{3^2+2^2}}\times\frac{-2}{\sqrt{3^2+2^2}}\\\\13 sin\beta cos\beta = \frac{- 78}{25}[/tex]
