Find the axis of symmetry and the vertex of the graph of y=3x^2+2x
Answers
Answer:
Vertex is (-1/3, -1/3) and the axis of symmetry is x = -1/3
Hope this helps :)
Related Questions
A picture frame has a perimeter of 100 cm. It’s width is 4 cm less than twice its length. What is the width of the picture
frame?
18 cm
32 cm
48 cm
50 cm
Answers
derivate (cos(3x^2). (5x^3 -1)^1/3 +sin 4x^3)^4
\( \: \: \: \: find \: first \: derivative \\ ( cos(3x {}^{2} ) \times ( \sqrt[3]{5x {}^{3} - 1} ) + \sin(4x {}^{3} ) {}^{4} \)
Answers
Answer:
Step-by-step explanation:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; \frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] --- eq(1)\)
Lets look at the derivative part:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)] \\\\= \frac{d}{dx}[cos(3x^2) \sqrt[3]{5x^3 -1} ] + \frac{d}{dx}[sin(4x^3)]\\\\=cos(3x^2) \frac{d}{dx}[ \sqrt[3]{5x^3 -1} ] + \sqrt[3]{5x^3 -1}\frac{d}{dx}[ cos(3x^2) ] + cos(4x^3) \frac{d}{dx}[4x^3]\\\\=cos(3x^2) \frac{1}{3} (5x^3 -1)^{\frac{1}{3} -1} \frac{d}{dx}[5x^3 -1] + \sqrt[3]{5x^3 -1} (-sin(3x^2))\frac{d}{dx}[ 3x^2] + cos(4x^3)[(4)(3)x^2]\)
\(=\frac{cos(3x^2) 5(3)x^2}{3(5x^3 - 1)^{\frac{2}{3} }} -\sqrt[3]{5x^3 -1}\; sin(3x^2) (3)(2)x + 12x^2 cos(4x^3)\\\\=\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)\)
Substituting in eq(1), we have:
\(\frac{d}{dx} [cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^4\\\\=4[cos(3x^2) \sqrt[3]{5x^3 -1} +sin(4x^3)]^3\; [\frac{5x^2cos(3x^2) }{(5x^3 - 1)^{\frac{2}{3} }} -6x\sqrt[3]{5x^3 -1}\; sin(3x^2) + 12x^2 cos(4x^3)]\)
Jenny and julian are hiking jenny starts at an elevation of 480 feet and is hiking down a mountain at a constant rate of 15 feet per minute so her elevation is decreasing 15 feet every minute at the same time julian starts at an elevation of 200 feet and is hiking at a rate of 5 feet per minute so her elevation is increasing at a rate of 5 feet every minute. the variable T represents the time in minutes they have been hiking. When will the two hikers be at the same elevation?
Answers
Answer:
Time taken for both hikers to be at the same elevation = 14 minutes
At that time, they will both be at an elevation of 270 feet
Step-by-step explanation:
Let us represent Jenny's current elevation by x and Julian's current elevation by y
Let T be the time taken when the hikers reach the same elevation
For Jenny
Initially Jenny's elevation is at 480 feetHer rate of descent (vertically) is 15 feet per minuteSo in T minutes she would have descended 15T feet. Jenny's elevation after T minutes = 480 - 15T feetFor Julian
Initial elevation = 200 feetRate of vertical ascent = 5 feet /minuteAfter T minutes, vertical ascent = 5T minutesHis elevation would be : 200 + 5TSince at this point in time, the elevation of both hikers is equal,200 + 5T = 480 - 15TAdd 15T to both sides:
200 + 5T + 15T = 480 - 15T + 15T
==> 200 + 20T = 480Subtract 200 from both sides:
200 - 200 + 20T = 480 - 200
20T = 280
T = 280/20 = 14 minutes
Check working
After 14 minutes, Jenny's elevation = 480 - 15 x 14 = 480 = 210 = 270 feet
After 14 minutes, Julian's elevation = 200 + 5 x 14 = 200 + 70 = 270 feet
So it checks out
Divide x3 – 3x2 + x-2) ÷ 10x414x3_10x2 + 6x = 10 The quotient is ____
The remainder is ____
Answers
Answer:
Im pretty sure X= 5/3
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
x3−3x2+x−2
10
x414)(x3)(0)x2+6x=10
0+6x=10
(6x)+(0)=10(Combine Like Terms)
6x=10
6x=10
Step 2: Divide both sides by 6.
6x
6
=
10
6
x=
5/3
HELP I NEEED ANSWER ASAP 95.11 = (100.50 + 78.35 + x)/3
Answers
Answer:
Here u go hoped it at least helped u !!!
Step-by-step explanation:
Answer:
106.480
I hope this helps!
Jose drove a total distance of 72,230.4 yd on a race track. He drove 12 laps where each lap was the same length. What was the length of each lap? Write your answer in miles.
Answers
Answer:6019.2
Step-by-step explanation: what you want to do is divide 72,230.4 by 12 and you'll get 6019.2
Which is the best estimate of the product of the fractions? StartFraction 4 Over 7 EndFraction times StartFraction 8 Over 9 EndFraction times StartFraction 14 Over 15 EndFraction
Answers
Answer:
Product = \(\dfrac{64}{135}\)
Step-by-step explanation:
The expression is as follows :
\(\dfrac{4}{7}\times \dfrac{8}{9}\times \dfrac{14}{15}\)
We need to find the product of the above expression
As 7 × 2 = 14
So, it will become :
\(4\times \dfrac{8}{9}\times \dfrac{2}{15}\\\\=\dfrac{4\times 8\times 2}{9\times 15}\\\\=\dfrac{64}{135}\)
So, the product of the given fractions is \(\dfrac{64}{135}\).
Answer:
64/135
Step-by-step explanation:
Boris started on the treadmill after setting timer for 99 minutes. The display says he have finished 43% of his run. How many minutes have gone by. Round to the nearest tenth
Answers
99 minutes * 0.43 = 42.57 minutes
Rounding to the nearest tenth, we can say that approximately 42.6 minutes have gone by.
What is the surface area of a storage box that measures 19 centimeters by 16 centimeters by 14 centimeters
Answers
Answer:
surface area = 2(length× breadth) +2(length ×height) +2(height×breadth
A community would like to add a brick paver border around their swimming pool. They created the following image to represent the pool with the border. A large rectangle with a length of 48 feet and a width of 28 feet. Inside of it is another rectangle with a length of 32 feet and a width of 12 feet. Part A: Find the total area of the brick paver border that surrounds the 12 ft by 32 ft pool. Show your work. (2 points) Part B: If brick pavers cost $8 per square foot, what is the total cost of the brick pavers needed for this project? Explain. (2 points)
Answers
Part A: The total area of the brick paver border is \(960\) square feet.
Part B: The total cost of the brick pavers needed for this project is $\(7,680\).
Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.
The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.
Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).
Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).
Note: The calculations provided assume that the border consists of a single layer of brick pavers.
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On 1 April mazibane has R540, 00 in his credit card account. He buys a lounge suit for R8300, 00 on credit. There is no interest on the debit amount for the first month. Thereafter the interest is 16% per year calculated daily but compounded monthly. On 1 June Mazibane pays R5000 into the account.
How much must Mazibane pay into the account on 30 June to have no debt in the account
Answers
According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.
How to calculate the amount Mazubane must pay on 30 June?To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.
Initial Debt:
On 1 April, Mazibane had a credit card debt of R8300.Interest Calculation:
The interest on the debt is 16% per year, calculated daily but compounded monthly. From 1 April to 1 June, a period of two months, there is no interest charged on the debt.Previous Payment:
On 1 June, Mazibane paid R5000 into the account.To determine the remaining debt on 1 June, we subtract the payment from the initial debt:
Remaining debt on 1 June = R8300 - R5000 = R3300.From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.
To calculate the interest for one month, we use the formula:
Interest = Principal x (1 + (rate/100))^(time/12) - Principal,where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).
Interest for one month = R3300 x (1 + (16/100)/12)^(1/12) - R3300.To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:
Total debt on 30 June = R3300 + Interest for one month.To have no debt on 30 June, Mazibane must pay the total debt amount:
Mazibane must pay R3300 + Interest for one month on 30 June.Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.
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I’m needing help with this question but all of the medals sums up over 400 medals overall
Answers
Answer:
H is an empty set;
\(H=\lbrace\rbrace\)Explanation:
Given the table in the attached image.
we want to write the set H, which consists of all the countries with fewer than 400 medals.
We can observe from the table that each of the given countries has more than 400 medals.
Therefore, there is no country with fewer than 400 medals.
So, H is an empty set;
\(H=\lbrace\rbrace\)
hich linear function has the steepest slope?
y = negative 8 x + 5
y minus 9 = negative 2 (x + 1)
y = 7 x minus 3
y + 2 = 6 (x + 10)
Answers
The function with the steepest slope is \(y = 7x - 3\).
The correct answer is C.
The linear function with the steepest slope is the one with the highest absolute value for the coefficient of x.
Let's compare the coefficients of x in each of the given functions:
\(y = -8x + 5\)
Slope: -8
\(y - 9 = -2(x + 1)\)
Simplifying, we get \(y - 9 = -2x - 2\)
Rearranging, we have \(y = -2x + 7\)
Slope: -2
\(y = 7x - 3\)
Slope: 7
\(y + 2 = 6(x + 10)\)
Simplifying, we get \(y + 2 = 6x + 60\)
Rearranging, we have \(y = 6x + 58\)
Slope: 6
Therefore, the steepest slope is the \(y = 7x - 3\).
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Use the gcf to factor the expression 40x+24y-56
Answers
Answer:
40x+24y-56=
8(5x+2y-7)
Step-by-step explanation:
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have only one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.a) The average baggage-related revenue per passenger is: $(please round to the nearest cent)b) The standard deviation of baggage-related revenue is: $(please round to the nearest cent)c) About how much revenue should the airline expect for a flight of 120 passengers?(please round to the nearest dollar)
Answers
Answer:
(a) The average baggage-related revenue per passenger is $15.70.
(b) The standard deviation of baggage-related revenue is $19.95.
(c) The expected revenue for 120 passengers is $1,884.
Step-by-step explanation:
Let the random variable X represent the baggage-related revenue per passenger.
It is provided that the baggage fees is $25 for the first bag and $35 for the second.
The probability model is:
X : 0 25 60
P (X) : 0.54 0.34 0.12
(a)
Compute the average baggage-related revenue per passenger as follows:
\(E(X)=\sum {X\times P (X)}\)
\(=(0\times 0.54)+(25\times 0.34)+(60\times 0.12)\\\\=0+8.50+7.20\\\\=15.70\)
Thus, the average baggage-related revenue per passenger is $15.70.
(b)
Compute the standard deviation of baggage-related revenue as follows:
\(E (X^{2})=\sum X^{2}\times P(X)}\\\\=(0^{2}\times 0.54)+(25^{2}\times 0.34)+(60^{2}\times 0.12)\\\\=0+212.50+432\\\\=644.5\\\)
\(SD(X)=\sqrt{E(X^{2})-(E(X))^{2}}\)
\(=\sqrt{644.5-(15.7)^{2}}\\\\=19.950188\\\\\approx 19.95\)
Thus, the standard deviation of baggage-related revenue is $19.95.
(c)
Compute the expected revenue for 120 passengers as follows:
\(E(R)=n\times E(X)\)
\(=120\times 15.7\\\\=1884\)
Thus, the expected revenue for 120 passengers is $1,884.
Samuel orders four DVDs from an online music store. Each DVD costs $9.89. He has a 25% discount code, and sales tax is 7.5%. Round sales tax amounts to the nearest cent. What is the total cost of his order?
Analyze information
Identify the important information.
The price of one DVD is $9.89.
The discount is 25% or 0.25.
The sales tax is 7.5% or 0.075.
Formulate a plan
Find the regular price for four DVDs. Then, calculate the amount discounted and subtract the discount from the price. Next, calculate the sales tax and then add that to the discounted price to find Samuel's final cost.
Solve
Regular price: 4 × $9.89 = $39.56
Discount: 0.25 × $39.56 = $9.89
Subtract the discount from the total.
Total − Discount = Discounted Price
$39.56 − $9.89 = $29.67
Calculate the sales tax on the discounted price.
Sales tax: 0.075 × $29.67 = $2.23
Add the sales tax to the discounted total to get the final price.
Discounted Total + Sales tax = Final Price
$29.67 + $2.23 = $31.90
The total cost of Samuel's order is $31.90.
Answers
What would the number 2.048503e+13 be without scientific notation?
Answers
Quadrilateral PEST has vertices (0, -5), (9, 2), (12, 13), and (3, 6), respectively.
a) Sketch a graph of the quadrilateral.
b) Classify the quadrilateral as a square, rectangle or rhombus.
c) Determine the intersection point of the diagonals.
will give brainliest :)
Answers
Answer:
what they said was correct just took the test
Step-by-step explanation:
Find the value of X.
Answers
Answer:
x = 36
Step-by-step explanation:
Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.
RelationThe product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.
24² = 12(12 +x)
2·24 = 12 +x . . . . . . . divide by 12
36 = x . . . . . . . . . subtract 12
<95141404393>
Share your own multi-step combination problem
Answers
My own multi-step combination problem is given below:
Amanda was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda create?How do you solve the multi-step combination?To solve this problem, Amanda need to use the formula for combinations and it is:
nCr = n! / (r! x (n-r)!)
where:
n = total number of items to select from
r is the number of items to select.
First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:
5C3
= 5! / (3! x (5-3)!)
= 10
Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be
4C2
= 4! / (2! x (4-2)!)
= 6
Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:
3C2
= 3! / (2! x (3-2)!)
= 3
To have the total number of dinner menus, we have to multiply these three numbers together:
= 10 x 6 x 3
= 180
Therefore, one can say that Amanda have 180 different dinner menus that she can be create.
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Find the final amount of money in an account if $ 2 ,100 is deposited at 2 % interest compounded annually and the money is left for 5 years.
Answers
\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2100\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 2100\left(1+\frac{0.02}{1}\right)^{1\cdot 5}\implies A=2100(1.02)^5 \implies A \approx 2318.57\)
Please help me with this question and please show me step by step and the frmula used.
Answers
By interpretating the graph of a quadratic equation, the initial height of the ball is equal to 5 feet above ground.
How to determine the initial height of the ball
In this problem we must determine the initial height of the ball according to a graph, whose form resembles quadratic equations. Graphically speaking, the initial height is the y-coordinate of the y-intercept. First, the coordinates of the y-intercept of the equation are:
(t, h) = (0 s, 5 ft)
Second, the final height of the ball is equal to:
h = 5 ft
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Is x2+8x+16 a perfect square?
Answers
Answer:
yes, it's factors are (x+4)²
Step-by-step explanation:
Answer:
It is a perfect square.
Step-by-step explanation:
Help solve for X
Please ignore the other scribbles in pencil.
Thanks
Answers
Answer:
The correct answer is X=5
I'm 10000000000% sure
Answer:
x = 5
Step-by-step explanation:
First, to get rid of the fraction, multiply both sides of the equation by x.
— (14.8/x + 2.4) * x = 5.36 * x
— 14.8 + 2.4x = 5.36x
Next, subtract 2.4x from both sides of the equation.
— 14.8 + 2.4x - 2.4x = 5.36x - 2.4x
— 14.8 = 2.96x
Now, divide both sides of the equation by 2.96.
— 14.8/2.96 = 2.96x/2.96
— 5 = x
Which graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1?
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = 1.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = 0, and the horizontal asymptote is at y = negative 1.
Mark this and return
Answers
The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.
On a coordinate plane, the graph of a hyperbola is shown.
In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.
The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.
The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.
A fraction with a denominator of zero cannot exist.
The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.
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Kareem borrowed money from a credit union for 6 years and was charged simple interest at an annual rate of 8%. The total interest that he paid was $240 . How much money did he borrow?
Answers
Answer:
I think 220.8
Step-by-step explanation:
"when reading a cd-rom disk 2.8 cm from its center the rotational speed is 726 rpm what is the rpm at 5.2cm
Answers
9514 1404 393
Answer:
726 rpm
Step-by-step explanation:
The angular speed is not dependent upon the radius. The rotational speed is 726 rpm at any radius.
500 POINTS PLEASE HELP ME I WILL GIVE ALL POINTS PLEASE PLEASE HELP ME ASAP
Answers
Answer:
its only says you will give 14 point so not ancering hahaha loser
Step-by-step explanation:
Answer:-_-
Step-by-step explanation:
Can someone help with this math problem?
Answers
Answer:
Hope it will help you a lot.
Kate is making biscuits. She uses flour, butter, and sugar in the ratio 5:3:2 Kate has 800 g flour 550 g butter. Kate wants to make the maximum number of biscuits possible. She works out how much sugar she needs. (a) How much sugar does Kate need? You must show working.
Answers
Answer:
800 grams flour ÷ 5 grams flour/biscuit = 160 biscuits
160 biscuits × 3 grams butter/biscuit = 480 grams butter
160 biscuits × 2 grams sugar/biscuit = 320 grams sugar
Katie needs 320 grams sugar.
Kate needs 270g of sugar to make the maximum number of biscuits possible.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Now, Based on the ratio of flour, butter, and sugar of 5:3:2, we can determine that Kate needs;
⇒ 800g + 550g
= 1350g of the mixture.
Hence, For find out the amount of sugar needed, we need to determine the proportion of sugar in the mixture.
We can do this by adding up the ratio numbers;
(5+3+2) = 10.
Then we can divide each ratio number by the total (10) to get the proportion of each ingredient.
So the proportion of sugar in the mixture is 2/10. To find out how much sugar Kate needs, we can set up a proportion:
2/10 = x/1350
We can solve for x by cross-multiplying:
2 × 1350 = 10x
2700 = 10x
x = 270
Therefore, Kate needs 270g of sugar to make the maximum number of biscuits possible.
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