Identify the vertex and the axis of symmetry of the graph of the function y=3(x+2)^2-3
Answers
we know that
The equation in vertex form of a vertical parabola is of the form
[tex]y=a(x-h)^{2}+k[/tex]
where
[tex](h,k)[/tex] is the vertex of the parabola
and
[tex]x=h[/tex] is the axis of symmetry
if [tex]a > 0[/tex] -----> open upward
if [tex]a < 0[/tex] -----> open downward
In this problem we have
[tex]y=3(x+2)^{2}-3[/tex]
[tex]a=3[/tex]
This is a vertical parabola open upward
The vertex is a minimum
therefore
the answer is
the vertex is the point [tex](-2,-3)[/tex]
the axis of symmetry is [tex]x=-2[/tex]
see the attached figure to better understand the problem
The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
Further Explanation:
The standard form of the parabola is shown below.
[tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
Here, the parabola has vertex at [tex]\left({h,k}\right)[/tex] and has the symmetry parallel to x-axis and it opens left.
Given:
The quadratic function is [tex]y=3{\left({x+2}\right)^2}-3[/tex].
Calculation:
Compare the [tex]y=3{\left({x+2}\right)^2}-3[/tex] with the general equation of the parabola [tex]\boxed{y=a{{\left({x-h}\right)}^2}+k}[/tex]
.
The value [tex]a[/tex] is [tex]3[/tex], the value of [tex]h[/tex] is [tex]-2[/tex] and the value of [tex]k[/tex] is [tex]-3[/tex].
Therefore, the vertex of the parabola is [tex]\left({-2,-3}\right)[/tex].
The function is symmetric about [tex]x=-2[/tex].
The vertex of the function [tex]y=3{\left({x+2}\right)^2}-3[/tex] is [tex]\boxed{\left({-2,-3}\right)}[/tex].
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
2. Learn more about non-collinear https://brainly.com/question/4165000
3. Learn more about binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Conic sections
Keywords: vertex, symmetry, symmetric, axis, y-axis, x-axis, function, graph, parabola, focus, vertical parabola, upward parabola, downward parabola,
Related Questions
explain how you could find 3/8% of 800
Answers
Also, you can see that 3/8 and 800 can easily be converted to a common denominator... 800. So, just add 2 zeros to 3, and you get 300!
If f(x) = 3x + 6, which of the following is the inverse of f(x)?
A. f –1(x) = 3x – 6
B. f –1(x) =
C. f –1(x) =
D. f –1(x) = 6 – 3x
Answers
To determine the inverse of the function f(x) = 3x + 6, you need to switch 'x' and 'f(x)', isolate f-1(x) on one side of the equation, then solve for f-1(x). The resulting inverse function is f-1(x) = (x - 6)/3.
Explanation:The function given is f(x) = 3x + 6. To find the inverse of this function, we first need to switch 'x' and 'f(x)', giving us: x = 3f-1(x) + 6. Next, we want to isolate f-1(x) on one side of the equation. To do this, we subtract 6 from both sides of the equation resulting in: x - 6 = 3f-1(x). Finally, we divide all terms by 3 to solve for f-1(x), which gives us f-1(x) = (x - 6)/3. So, the correct answer from the options given is not listed.
Learn more about Inverse Function here:https://brainly.com/question/17872426
#SPJ12
Which equation could you use to solve for x in the proportion 4/5=9/x ?
Answers
[tex] \frac{9}{x} = \frac{4}{5} [/tex]
dividing both sides by 9
[tex] \frac{1}{x} = \frac{4}{5 \times 9} [/tex]
rasing both sides to the power of -1
[tex]x = \frac{5 \times 9}{4} = \frac{45}{4} [/tex]
Answer:
4x = 45 Chi3 is completely wrong
Step-by-step explanation:
To solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction, you can use the cross multiplication method.
First, multiply the numerator of the left fraction (4) by the denominator of the right fraction (x). Then, multiply the denominator of the left fraction (5) by the numerator of the right fraction (9).
This gives you the equation: 4x = 5 * 9.
Simplifying the equation, you get: 4x = 45.
To isolate x, divide both sides of the equation by 4: x = 45/4.
So, the correct equation to solve for x in the given proportion is 4x = 45.
The GCF of any two even numbers is always even. true or false?
Answers
What inequality represents the verbal expression? 1. all real numbers less than 69?
Answers
Mr. Carandang sold a total of 1,790 prints of one of his drawings. Out of all 1,273 unframed prints that he sold, 152 were small and 544 were medium-sized. Out of all of the framed prints that he sold, 23 were small and 42 were extra large. Of the large prints that he sold, 188 were framed and 496 were unframed. Small Medium Large Extra Large Total Framed 23 264 188 42 ? Unframed 152 544 496 81 1,273 Total 175 808 684 123 1,790 Which number is missing from the two-way table?'
Answers
small 23 152 175
medium 264 544 808
large 188 496 684
ex-large 42 81 123
total 517 1273 1790
The missing number in the two-way table is the total number of framed prints, which is 517. This is calculated by subtracting the total unframed prints from the total prints sold and then summing the known framed prints.
To find the missing number of prints in the table, we need to determine the total number of framed prints sold by Mr. Carandang. We know the following from the table:
Total prints sold: 1,790Unframed prints: 1,273To find the total number of framed prints:
Total framed prints = Total prints - Total unframed prints
Total framed prints = 1,790 - 1,273 = 517
Now we need to sum the known framed prints:
Framed small: 23Framed medium: 264Framed large: 188Framed extra large: 42The total of known framed prints is:
23 + 264 + 188 + 42 = 517
Thus, the total framed prints value was missing and it is 517.
12 PTS!!!
John ordered two kinds of pizza for a party: sausage pizzas and veggie pizzas. He ordered three pizzas of each kind. The pizzas cost a total of $99. If the cost of each veggie pizza is $18, what is the cost of a sausage pizza?
Answers
Answer: 27
1 veggie pizza cost 18 so 3 cost 18*3 = 54
99-54 = 45 for the 3 sausage pizzas
45/3 = 15 dollars each for sausage
Find all values of x that are simultaneously a solution to the congruences x ≡ 2 (mod 3), x ≡ 1 (mod 5), x ≡ 3 (mod 29).
Answers
Let's start by supposing [tex]x=2+3+3=11[/tex]. Modulo 3, we end up with 2 as needed.
But modulo 5, we want to get 1, so we'd need to multiply the first and last terms by 5 and the second term by the inverse of 3 modulo 5. We have [tex]3\times2\equiv6\equiv1\pmod5[/tex], so we multiply by 2:
[tex]x=2\times5+3\times2+3\times5=31[/tex]
But now modulo 3, the first term gives a remainder of 1, so simply multiply by 2:
[tex]x=2\times5\times2+3\times2+3\times5=41[/tex]
Next, modulo 29, we can force the first two terms to vanish by multiplying them by 29, but the last term still yields 15. We want to get 3 on its own, so we could just multiply the third term by the inverse of 5 modulo 29. We have [tex]5\times6\equiv30\equiv1\pmod{29}[/tex].
[tex]x=2\times5\times2\times29+3\times2\times29+3\times5\times6=844[/tex]
Now, [tex]844\equiv1\pmod3[/tex], so we need to multiply the first term by 2 one more time; [tex]844\equiv4\pmod5[/tex], so we need to multiply the second term by the inverse of 4 modulo 5, which would be 4 since [tex]4^2\equiv16\equiv1\pmod5[/tex]; and [tex]844\equiv3\pmod{29}[/tex], so the last term is okay.
[tex]x=2\times5\times2\times29\times2+3\times2\times29\times4+3\times5\times6=1946[/tex]
We know 1946 is a possible solution because we engineered it that way, but it's not the smallest positive solution. We have
[tex]1946\equiv206\pmod{3\times5\times29}\equiv206\pmod{435}[/tex]
The general solution to the system is then [tex]x=206+435n[/tex], where [tex]n\in\mathbb Z[/tex].
1. which expression is equivalent to 8 × 8 × 8 × 8?
A. 8 × 4
B. 8^5
C. 8^4
D. 4^8
2. which expression is equivalent to 4 × 4 × 4 × 4 × 4 × 4 × 4?
3. which expression is equivalent to 7 × 7 × 7 × 7 × 7 × 7?
4. which expression is equivalent to 4 × 4 × 4?
5. which expression is equivalent to 3 × 3?
Answers
2. 4×7
3. 7×6
4. 4×3
5. 3×1 or 3×2 it's probably 3×2 tho
What is the value of |−25|?
Answers
The answer to this is |-25| = 25.
Hope this helped!! ☺♥
Which unit would you use to measure the length of a football field mm cm m or km?
Answers
Find the rate of change of the area of a square with respect to the length z , the diagonal of the square. what is the rate when z=2?
Answers
z = xSqrt(2), its rate of change is just Sqrt(2)
The rate of change of Area, A with respect to the diagonal length, z and the rate of change when z = 2 is :
[tex]\frac{dA}{dz} = z [/tex][tex]\frac{dA}{dz} = 2 \: when \: z = 2 [/tex]The area of a square is rated to its diagonal thus :
Area of square = ALength of diagonal = zThe relationship between Area and diagonal of a square is : [tex]A \: = 0.5 {z}^{2} [/tex]
The rate of change of area with respect to the length, z of the square's diagonal ;
This the first differential of Area with respect to z
[tex] \frac{dA}{dz} = 2(0.5)z \: = z[/tex]
Therefore, the rate of change of area, A with respect to the length, z of the diagonal is [tex]\frac{dA}{dz} = z [/tex]
The rate of change [tex]\frac{dA}{dz} [/tex] when z = 2 can be calculated thus :
Substitute z = 2 in the relation [tex]\frac{dA}{dz} = z [/tex]
Therefore, [tex]\frac{dA}{dz} = 2 [/tex]
Learn more :https://brainly.com/question/3122130?referrer=searchResults
5x^7y^4+25xy^2+15xy^3/5xy^3
Answers
5x^7y^4+3x^2y^6+25xy^2
Toby exercises 14 hours a week. John exercises 20% more than Toby and Jenny exercises two more hours than John. Which expression represents how much Jenny exercises? (w represents weeks)
Answers
Jenny exercises two more hours than John. So the number of hours that Jenny exercises per week is 16.8 + 2 = 18.8.
So an expression representing the number of hours that Jenny exercises after w weeks is 18.8w.
the answer is 18.8w
Toby 14w
John 14(1.2)w
Jenny 14(1.2)w + 2w
thus, Jenny exercise
14(1.2)w + 2w
16.8w + 2w
18.8w
How many different 4-digit sequences can be formed using the digits 0, 1,..., 6 if repetition of digits is allowed
Answers
0 through 6 is 7 total numbers
1st digit can be 0-6 = 7 numbers
2nd digit can be 0-6 = 7 numbers
3rd digit can be 0-6 = 7 numbers
4th digit can be 0-6 = 7 numbers
7 * 7 *7 *7 = 2401 different combinations
If s = {r, u, d} is a set of linearly dependent vectors. if x = 5r + u + d, determine whether t = {r, u, x} is a linearly dependent set
Answers
[tex]c_1\mathbf r+c_2\mathbf u+c_3\mathbf x=c_1\mathbf r+c_2\mathbf u+c_3(5\mathbf r+\mathbf u+\mathbf d)[/tex]
[tex]=(c_1+5c_3)\mathbf r+(c_2+c_3)\mathbf u+c_3\mathbf d[/tex]
[tex]=c_4\mathbf r+c_5\mathbf u+c_6\mathbf d[/tex]
We know [tex]\mathbf r,\mathbf u,\mathbf d[/tex] are linearly dependent, which means there must exist some choice of not all zero constants [tex]c_4,c_5,c_6[/tex] such that the combination above gives the zero vector. So [tex]T=\{\mathbf r,\mathbf u,\mathbf x\}[/tex] is a set of linearly dependent vectors.
Express 9.21212121212... as a rational number, in the form pq
Answers
[tex]100x=921.212121\ldots=921.\overline{21}[/tex]
[tex]99x=921.\overline{21}-9.\overline{21}=921-9=912[/tex]
[tex]\implies x=\dfrac{912}{99}=\dfrac{304}{33}[/tex]
A machine is set to fill the small-size packages of m&m candies with 56 candies per bag. a sample revealed: three bags of 56, two bags of 57, one bag of 55, and two bags of 58. to test the hypothesis that the mean candies per bag is 56, how many degrees of freedom are there?
Answers
In statistics, the amount of degrees of freedom is the quantity of values in the final computation of a statistic that are free to differ. In this case, you can get the answer by adding the number of bags and subtracting 1.
So in computation, this would look like: 3 + 2 + 1 + 2 - 1 = 7
Therefore, 7 is the degrees of freedom.
Final answer:
The number of degrees of freedom for the hypothesis test that the mean candies per bag is 56 is 7, calculated by subtracting one from the total number of sampled bags.
Explanation:
To calculate the number of degrees of freedom for the hypothesis test that the mean candies per bag is 56, we use the sample size minus one. The sample size is the number of observations, which is the total count of bags sampled. In this case, we have a total of 8 bags (three bags of 56, two bags of 57, one bag of 55, and two bags of 58). Therefore, the degrees of freedom for this test would be 8 - 1 = 7.
Given e(x + 4) = 10 and e[(x + 4) 2 ] = 116, determine (a) var(x + 4), (b)μ= e(x), and (c)σ 2 = var(x).
Answers
b. [tex]\mathbb E(X+4)=\mathbb E(X)+\mathbb E(4)=\mathbb E(X)+4=10\implies\mathbb E(X)=6[/tex]
c. [tex]\mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2[/tex]
[tex]\mathbb E((X+4)^2)=\mathbb E(X^2+8X+16)=\mathbb E(X^2)+8\mathbb E(X)+\mathbb E(16)[/tex]
[tex]\implies116=\mathbb E(X^2)+48+16\implies\mathbb E(X^2)=52[/tex]
[tex]\implies\mathbb V(X)=52-6^2=16[/tex]
In the given statements, first 'x' is derived from the equation e(x + 4) = 10, then it is plugged into e(x) to find μ and the variance formula to obtain σ².
Explanation:The question presents a scenario with two equations: e(x + 4) = 10 and e[(x + 4) 2 ] = 116 .To solve these equations, you would need to employ various algebraic and statistical concepts. Given this information, let's procede as follows:
To find (a) var(x + 4), we first need to determine the value of 'x' which can be derived from the given e(x + 4) = 10. After calculating 'x', we can work out (b)μ= e(x) by inserting our calculated 'x' into the e(x) formula. Finally, σ 2 = var(x) can be computed by applying 'x' in the variance formula.
Please note, this solution requires a good understanding of the properties of exponential functions and the statistical representation of variance (var), mean (μ), and standard deviation (σ²). Due to the complexity of these equations, I recommend using a calculator to accurately work out each part.
Learn more about Exponential Functions & Statistics here:https://brainly.com/question/14587068
#SPJ11
Use an algebraic rule to describe a translation right 4 units and down 2 units.
Answers
(x, y)⇒(x+4, y-2)
Which ordered pair would form a proportional relationship with the point graphed below?
(–10, 30)
(30, –15)
(–30, 10)
(80, –30)
Answers
The (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The point (60, -20) is shown in the graph:
As we know from the definition of the proportional relationship:
y = kx
Here k is the constant of proportionality.
k = y/x
k = -20/60
k = -1/3
y = -x/30
Plug x = -30
y = 10
(–30, 10)
Thus, the (–30, 10) ordered pair would form a proportional relationship with the point graphed option (C) is correct.
Learn more about the proportional here:
brainly.com/question/14263719
#SPJ2
what is the factor expression of 27 + 33
Answers
The ____ function can be used to ensure that a number has the appropriate number of decimal places.
Answers
The cost function for a particular product is given by C(x)=0.0001 x^3−0.015x^2+13.1x+120 dollars, where 0≤x≤60. Find the minimum marginal cost of the product, rounded to the nearest cent.
Answers
Final answer:
To find the minimum marginal cost, differentiate the cost function to get the MC function, find its critical points, and evaluate it at these points within the interval.
Explanation:
To find the minimum marginal cost of the product, we need to differentiate the cost function C(x) with respect to x to find the marginal cost function, then find the critical points within the given interval by setting the derivative to zero and solving for x.
The cost function is C(x) = 0.0001x^3 - 0.015x^2 + 13.1x + 120. The marginal cost (MC) function, MC(x), is the first derivative of the cost function with respect to x:
MC(x) = dC/dx = 0.0003x^2 - 0.03x + 13.1.
To find the minimum marginal cost, we need to differentiate the MC function to find its critical points:
dMC/dx = 0.0006x - 0.03
Setting dMC/dx equal to zero and solving for x gives us:
0.0006x - 0.03 = 0
x = 50
After finding the critical point, we check if it is within the interval [0,60] and evaluate the MC function at x = 50 to find the minimum MC. Rounding it to the nearest cent, we have:
MC(50) = 0.0003(50)^2 - 0.03(50) + 13.1
The final minimum marginal cost of the product is calculated and rounded to determine the minimum cost to produce one more unit of output.
What is the perimeter of a parallelogram if it has a base width of 3x+9 and it has a height length of 4x-5?
Answers
2*length + 2*width
Or, in this case, once you substitute everything in,
2 * (3x + 9) + 2 * (4x - 5)
Use the distributive property, to distribute the 2s to everything inside the parenthesis.
2 * 3x + 2 * 9 + 2 * 4x + 2 * -5
6x + 18 + 8x - 10
Then just add everything
14x + 8 = perimeter
what is the equation for a line that passes through (-7, 2) and is perpendicular to the graph of y=-1/2x+3
Answers
[tex]\bf y=\stackrel{slope}{-\cfrac{1}{2}}x+3[/tex]
well, then, a line perpendicular to that line, will have a slope that is negative reciprocal to that one, so if the slope of that graph is -1/2, then
[tex]\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -\cfrac{1}{2}\\\\ slope=-\cfrac{1}{{{ 2}}}\qquad negative\implies +\cfrac{1}{{{ 2}}}\qquad reciprocal\implies + \cfrac{{{ 2}}}{1}\implies 2[/tex]
so, we're really looking for the equation of a line whose slope is 2, and runs through -7, 2.
[tex]\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -7}}\quad ,&{{ 2}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies 2 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=2[x-(-7)] \\\\\\ y-2=2(x+7)\implies y-2=2x+14\implies y=2x+16[/tex]
Use the given point to find the y-intercept "b" in y = mx+b
y = 2x + b
2 = 2(-7) + b
2 = -14 + b
2 + 14 = b
16 = b
final equation :
y = 2x + 16
In Miss Marshalls classroom 6/7 of the students play sports of the students who play sports for fifth also play instruments if there are 35 students in her class how many play sports and instruments
Answers
24 students do both.
We wish to choose 7 cards from a usual deck of 52 playing cards. In how many ways can this be done if we are required to choose the cards in the following ways?
(a) with no restriction.
(b) all cards come from the same suit.
(c) exactly 3 Aces and exactly 3 Kings are chosen.
(d) all 7 cards have values between 2 and 7 inclusive.
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
Answers
(a) with no restriction.
If there is no restriction and different order is not important, then the possible way should be: 52!/ (52-7)!7!= 52!/45!7!= (52* 51* *50*49*48*47*46)/(7*6*5*4*3*2*1) = 674274182400/5040= 133,784,560 ways
(b) all cards come from the same suit.
If all card has to come from the same suit, that means you will only have 13 possible cards for each suit.
Then the possible ways for each suit: 13!/(13-7)!7!= (13*12*11*10*9*8*7)/ (7*6*5*4*3*2)= 8648640/5040= 1716 ways per suit.
Since there are 4 suits then the possible way= 1716 * 4= 6864
(c) exactly 3 Aces and exactly 3 Kings are chosen.
In this case, we will have 3 aces, 3 kings, and one random card. There are 4 aces/kings in one deck and we have to choose 4.
The possible ways for 3 aces or 3 kings would be: 4!/3!(4-3)!= 4 ways.
After choosing the 3 aces and 3 kings, the deck should have 52-3-3 = 46 card left. That mean there will be 46 possible ways for the random card.
The total possibilities should be: 4 * 4* 46= 736 ways
(d) all 7 cards have values between 2 and 7 inclusive
There are four cards with each value. The value between 2 and 7 inclusive should be 7-2+1= 6 different value. Since each value has 4 cards and we have 6 different value, then the total possible card is 6*4= 24
Then, we take 7 cards from those 24 cards. The possible should be: 24!/7!(24-7)!= (24*23*22*21*20*19*18) / 5040= 1744364160/5040= 346104
(e) all 7 cards all have different values (where Jacks are different from Queens, etc.).
There is 4 card with same value. For the first take, you will have 52 different ways. But for the second take, you will only have 52-4=48 different ways. That was because you can use:
1. one card that you take earlier.
2. three cards with the same value.
Then the possible ways become like this: 52*48*44*40*36*32*28/ 7!= 28,114,944
What is the sum of 1.53 + 2.786 + 3.3 written with the correct number of significant figures?
Answers
7.616
:D
Answer:
1.53 + 2.786 + 3.3 = 7.6
Step-by-step explanation:
Significant figures is the number of digits that carry precision in a number.
In mathematical operations involving significant figures, an answer is no more precise that the least precise number used to get the answer.
For addition, look at the places to the decimal point. Add in the normal fashion, then round the answer to the least number of places to the decimal point of any number in the problem.
To find the sum of 1.53 + 2.786 + 3.3 you must:
[tex]1.53 + 2.786 + 3.3\\4.316 + 3.3\\7.616\\[/tex]
Because 3.3 is the number with the smallest sig figs, the result should have as many decimal places as the number with the smallest sig figs. Therefore, 7.6.
A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 18 m above ground level?
Answers
h = elevation of rider
A = angle of elevation of rider with respect to center of ferris wheel
dA/dt = 2pi/2 = pi rads/min
h = 13sin(A) + 13
dh/dt = 13cos(A)dA/dt
when h = 18 m
18 = 13sin(A) + 13
sin(A) = 5/13
cos(A) = sqrt(1 - (5/13)^2)
cos(A) = 12/13
dh/dt = 13*12/13*pi
dh/dt = 12pi m/min
To find the speed at which the rider is rising, we use trigonometry and differentiation to calculate the rate of change of the height with respect to time. The speed is approximately -8.14 m/min.
Explanation:To find the speed at which the rider is rising, we need to find the rate of change of the height of the rider with respect to time. This can be done using the concept of trigonometry and differentiation.
Since the Ferris wheel completes one revolution every 2 minutes, the angular speed is given by 2π radians per 2 minutes, which simplifies to π radians per minute.
The height of the rider can be represented by a sinusoidal function, and by taking the derivative of this function, we can find the rate of change of the height with respect to time. In this case, the derivative would be -13sin(t), where t is the time in minutes.
Substituting t = 18 minutes into the derivative equation, we can calculate the rate at which the rider is rising. Plugging in the value, we get a speed of -13sin(18) m/min, which is approximately -8.14 m/min.
Learn more about Rate of Change here:https://brainly.com/question/31226174
#SPJ3