Which function represents a parabola that is translated 2 units to the left and 6 units down from the parent function, f(x)=x^2
Translation involves moving a function along its coordinates
The image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]
How to determine the new functionThe parent function is given as:
[tex]f(x) = x^2[/tex]
When the function is translated 2 units left, we have:
[tex]f'(x) = (x + 2)^2[/tex]
When the function is translated 6 units down, we have:
[tex]f"(x) = (x + 2)^2 - 6[/tex]
Rewrite as:
[tex]g(x) = (x + 2)^2 - 6[/tex]
Hence, the image of the function is [tex]g(x) = (x + 2)^2 - 6[/tex]
Read more about translation at:
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The y- intercept is when x= ?
Answer:
The y-intercept is the point at which the graph crosses the y-axis. At this point, the x-coordinate is zero. To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.
Step-by-step explanation:
hope it helps
Zach worked 1,040 hours this year and made $9 per hour. How much money did he earn over the course of the year?
$9,060
$9,360
$10,360
$12,660
Answer:
$9,360
Explanation:
$9 per hour, rewrite: 1 hour he earned $9so for 1040 hours, he earned:
$9 * 1,040
$9,360
How do you solve this multiplying decimals problem 0.14 x 0.27 ?
Answer:
0.0378[tex]\begin{gathered} \: \end{gathered}[/tex]
[tex] \tt0.14 \times 0.27[/tex][tex] \tt = \red{0.0378}[/tex][tex]\begin{gathered} \: \end{gathered}[/tex]
what is the probability of spinning an A if you have 2 A on the 6 letter spinner?
Answer:
1/3
Step-by-step explanation:
p(A) = (number of A's on the spinner)/(total number of letters on the spinner)
p(A) = 2/6 = 1/3
A water pipe is leaking 2 1⁄4 litres of water every hour. How long will it take 5 2⁄5 litres of water?
Answer:
above is the solution to the question
If m aed is 48°, then possible measurements for arc ad and arc bc respectfully are:
Answer:
it's going to be 30 and 18
The possible measurements for arc AD and arc BC are 130° and 34° respectively.
What is Circle?Circle is a two dimensional figure which consist of set of all the points which are at equal distance from a point which is fixed called the center of the circle.
Given is a circle.
We have the outside angle formed by the two secants is ∠AED and the measure for it is 48°.
Outside Angle Theorem states that " the measure of an angle which is formed by joining two tangents, or two secants, or one of either of them is equal to the measure of half of the difference of the intercepted arcs.
Here outside angle, ∠AED = 48°
Intercepted arcs are AD and BC.
Using the theorem,
∠AED = (Arc AD - Arc BC) / 2
This holds only if AD = 130° and BC = 34°.
(130 - 34) / 2 = 48
Hence the correct option is D. 130° and 34°.
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4. Funds are like the ultimate in one stop shopping (investing)
True
False
50 POINTS // This graph represents a proportional relationship.
What is the constant of proportionality for this relationship?
•1/3
•1/2
•2
•I don't know
We need slope
(3,1)(6,2)[tex]\\ \rm\Rrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{2-1}{6-3}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{1}{3}[/tex]
This can be solved using two methods:
Method #1:
Rise/Run = Slope=> 1/3 = SlopeThe slope is 1/3.
Method #2:
y₂ - y₁/x₂ - x₁ = Slope=> 2 - 1/6 - 3 = Slope=> 1/3 = SlopeThe slope is 1/3.
Looking at the two methods, we can conclude that:
The slope of the line is 1/3.
HELPPPP IF YOU CAN pls?
Answer:
i'm not sure but here's some encouragement- YOU CAN DO IT
Step-by-step explanation:
Evaluate the expression 3× 2t if t equals 4
PLEASE HELP!!!!!!!!!!!!!!!!
Answer:
The answer is B 80.00 hope this helps
have a nice day
Step-by-step explanation:
Identify whether each phrase is an expression, equation, or inequality.
Answer:
Step-by-step explanation:
Expression => | -2 |
Equation => 6 - 1 = 2 + 3
Inequality => 8^m > 64
Answers:
Expression is [tex]|-2|[/tex]
Equation is [tex]6-1 = 2+3[/tex]
Inequality is [tex]8^m > 64[/tex]
====================================================
Explanation:
If it has an equal sign, then it's an equation.
If it has an inequality sign of one of the following [tex]< , \ > , \ \le, \ \ge[/tex], then it's an inequality.
Otherwise, it's an expression.
the tangent decimal of a 25-degree angle is .4463. what can be determined about the length of the angles opposite sides compared to the length of the angles adjacent sides?
heres a link hope it help you
https://www.journaldespalaces.com/carriere/offre-118597-Officier-de-restauration-Cafetier.html
What is the factored form for the quadratic function?
Answer:
Step-by-step explanation:
The factored form of a quadratic function is f (x) = a (x - p) (x - q) where p and q are the zeros of f (x).
with any set of scores that is normally distributed what percentage of the total area falls,
1. between the mean and a score that lies one standard deviation below the mean?
2. above a score that lies one standard deviation below the mean and one standard deviation above the mean?
3. between a score that lies two standard deviations below the mean and two standard deviations above the mean?
Answer:
1.) Approximately 68%We can summarize use of the standard deviation as a yardstick with the Empirical Rule, also known as the 68-95-99.7% Rule. In any normal distribution with mean μ and standard deviation σ : Approximately 68%of the data fall within one standard deviation of the mean.
Step-by-step explanation:
This table contains x and y values in equivalent ratios fil in the missing value in the table
Answer:
where is the table?
Step-by-step explanation:
._.
Can someone tell me what is 1350 divided by 225 step by step?
can you help me solve for slope
∫(2x^3-x^2-2x+4)/(1+x^2)dx
Simplify the integrand as
[tex]\dfrac{2x^3 - x^2 - 2x + 4}{1 + x^2} = \dfrac{(2x^3 + 2x) - (x^2 + 1) - 4x + 5}{x^2 + 1} \\\\ = \dfrac{2x(x^2 + 1) - (x^2 + 1) - 4x + 5}{x^2 + 1} \\\\ = 2x - 1 - \dfrac{4x - 5}{x^2 + 1}[/tex]
(in other words, compute the quotient and remainder)
We can further split up and prepare the remainder term for integration by rewriting it as
[tex]\dfrac{4x - 5}{x^2 + 1} = 2\times\dfrac{2x}{x^2 + 1} - \dfrac5{x^2 + 1}[/tex]
Now we integrate:
[tex]\displaystyle \frac{2x^3 - x^2 - 2x + 4}{1 + x^2} \, dx = \int \left(2x - 1 - 2\times\frac{2x}{x^2+1} + \frac5{x^2+1}\right) \, dx[/tex]
[tex]\displaystyle = x^2 - x - 2 \int \frac{2x}{x^2+1} \, dx + 5 \int \frac{dx}{x^2+1}[/tex]
In the first remaining integral, substitute y = x² + 1 and dy = 2x dx. In the last integral, recall that d/dx [arctan(x)] = 1/(x² + 1).
[tex]\displaystyle = x^2 - x - 2 \int \frac{dy}y + 5 \int \frac{dx}{x^2+1}[/tex]
[tex]\displaystyle = x^2 - x - 2 \ln|y| + 5 \arctan(x) + C[/tex]
[tex]\displaystyle = \boxed{x^2 - x - 2 \ln(x^2+1) + 5 \arctan(x) + C}[/tex]
estellano Rosales, FABIAN A cone and a cylinder with their dimensions are shown in the diagram. 8 in. 8 in. A - 6 in. - 6 in. Which measurement is closest to the difference between the volumes of these figures in cubic inches?
Answer:151 in.³
Step-by-step explanation:
you run a delivery service between two small islands which are connected by a bridge and connected to the mainland by several bridges as shown in the picture below. the river separates the top mainland from the bottom mainland. you cannot get from the top of the mainland to the bottom of the mainland without passing through an island.
Answer:
"Through" (and any subsequent words) was ignored because we limit queries to 32 words.
Point P is called the center of
Answer:
Point P is the center of Rotation.
The Kaaba is one of Islam's holiest shrines. In what city is it located?
a.
Cairo
c.
Riyadh
b.
Medina
d.
Mecca
please help
1. If there is a decrease of 31 percent, what decimal do we multiply by to get the amount after the decrease?
2. If there is an increase of 16 percent, what decimal do we multiply by?
Answer:
1. 0.69
2. 1.16
Step-by-step explanation:
1.
Decrease of 31% = 100% - 31% = 69%
Convert 69% to a decimal = 69/100 = 0.69
2.
Increase of 16% = 100% + 16% = 116%
Convert 116% to a decimal = 116/100 = 1.16
what is the area of a square and a right triangle combined?
Answer:
you would have to separate the shapes and find out what the area of them both and add them together
Step-by-step explanation:
What is the area of a rectangle with a length of 214 inches and a width of 234 inches?
714 in²
6316 in²
4316 in²
3332 in²
Given :
The length of a rectangle is 214 inches and the width is 234 inches.⠀
To Find :
The area of the rectangle.⠀
Solution :
We know that,
[tex]\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:[/tex]
⠀
Now substituting the values :
[tex]\qquad {\dashrightarrow{ \sf{214 \: in\times 234 \: in = Area_{(rectangle)}}}}\:[/tex]
[tex]\qquad {\dashrightarrow \: { { \sf{50,076 \: {in}^{2} = Area_{(rectangle)}}}}\:}
[/tex]
⠀
Hence, The area of the rectangle is 50,076 in² .
The area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.
How to find the area of a rectangle?Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,
[tex]A=a\times b[/tex]
Here, (a)is the length of the rectangle and (b) is the width of the rectangle.
The rectangle given in the problem has,
A length of 2 1/4 inches. A width of 2 3/4 inches.Thus, the area of the rectangle is,
[tex]A=2\dfrac{1}{4}\times2\dfrac{3}{4}\\A=\dfrac{8+1}{4}\times\dfrac{8+3}{4}\\A=\dfrac{9}{4}\times\dfrac{11}{4}\\A=\dfrac{99}{16}\\\A=\dfrac{96+3}{16}\\A=6\dfrac{3}{16}[/tex]
Thus, the area of a rectangle with a length of 2 1/4 inches and a width of 2 3/4 inches is 6 3/16 in². Option C is correct.
Learn more about the area of rectangle here;
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Use the Factor Theorem to determine whether x-2 is a factor of P(x) = -x^4 + x^3 - x + 7.
Specifically, evaluate P at the proper value, and then determine whether x+2 is a factor.
P(?) =?
is x-2 a factor of P(x)
Is x-2 not a factor pf P(x)
Answer: WE have to find if x + 3 is a factor
Here's how we do it :
x + 3 = 0
x = -3
Plug that in :
(-3)^4 + 2(-3)^3 - 2(-3) - 6
81 - 54 + 6 - 6
27
So, when we divide, we get a remainder of 27. This is not zero.
So, since f(a) was not zero, (x - a) is not a factor
P(-3) = 27 ---> ANSWER
Thus here (x + 3) is NOT a factor ---> ANSWER
Let f(x)=cos(x)x^-2
F’(x)=
[tex]f(x)=cos(x)x^{-2}\implies f(x)=\cfrac{cos(x)}{x^2}\implies \cfrac{df}{dx}=\stackrel{\textit{quotient rule}}{\cfrac{-sin(x)\cdot x^2-cos(x)\cdot 2x}{(x^2)^2}} \\\\\\ \cfrac{df}{dx}=\cfrac{-x[x\cdot sin(x)+2cos(x)]}{x^4}\implies \cfrac{df}{dx}=\cfrac{-[xsin(x)+2cos(x)]}{x^3}[/tex]
Stephen rolls a fair dice 78 times.
How many times would Stephen expect to roll an odd number?
Answer:
Step-by-step explanation:
1 3 5 are all odd numbers.
There are 6 numbers all together on a die. 1 2 3 4 5 6
That means that 3/6 times, he should roll an odd number
3/6 * 78 = 39
He should get 39 rolls which are an odd number.