Convert this equation to standard form:
f(x) = -(x + 3)^2 + 1
Answers
The vertex of the parabola is at the point (3, -35). The standard form allowed us to determine that the parabola opens downwards and to find the vertex of the parabola at the point (3, -35).
To convert the given equation to standard form, we need to expand the square in the equation and simplify it.
f(x) = -(x + 3)^2 + 1
f(x) = -1(x^2 + 6x + 9) + 1
f(x) = -x^2 - 6x - 9 + 1
f(x) = -x^2 - 6x - 8
The equation is now in standard form, which is given by:
Ax^2 + Bx + C = 0
where A, B, and C are constants. In this case, A = -1, B = -6, and C = -8.
Note that standard form represents a quadratic equation in the form of a parabola. The value of A determines whether the parabola opens upwards (if A is positive) or downwards (if A is negative). In this case, A is negative, which means that the parabola opens downwards.
We can also determine the vertex of the parabola from the standard form. The x-coordinate of the vertex is given by:
x = -B / 2A
Substituting the values of A and B, we get:
x = -(-6) / 2(-1) = 3
The y-coordinate of the vertex can be found by substituting x = 3 into the equation:
f(3) = -3^2 - 6(3) - 8 = -35
Therefore, the vertex of the parabola is at the point (3, -35).
In summary, we converted the given equation f(x) = -(x + 3)^2 + 1 to standard form Ax^2 + Bx + C = 0 by expanding the square and simplifying. The standard form allowed us to determine that the parabola opens downwards and to find the vertex of the parabola at the point (3, -35).
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Related Questions
if RS=2x+6 ST=x+4 and RT=40 find RS
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
\(undefined\)Plz help I’ll give Brainliest!!!!
URGENT PLZ HURRY!!!!
Answers
Answer:
y= 4 , -4
Step-by-step explanation:
hope i helped
f(x) = x². What is g(x)?
A. g(x) = -x² – 3
B. g(x) = -3x²
C. g(x) = x² - 3
D. g(x) = -x²
Answers
Answer:
A
Step-by-step explanation:
because g(x) is the opposite of f(x) minus three steps
i need help asap please help me
Answers
Answer: yo wassup picture isn't straight cant see
Step-by-step explanation:
Given the points below, are the two lines parallel, perpendicular, or neither.
L1: (-4, 6) (-3,-1) L2: (8,9) (15, 10)
Answers
Answer:
perpendicular
Step-by-step explanation:
First we need to dtemine the slopes of the line
For line 1
L1: (-4, 6) (-3,-1)
m1 = y2-y1/x2-x1
m1= -1-6/-3+4
m1 = -7/1
m1 = -7
For line 2:
L2: (8,9) (15, 10)
m2 = 10-9/15-8
m2 = 1/8
Take their product
m1 * m2 = -7 * 1/7
m1m2 = -1
Since the product of their slopes is -1, hence they are perpendicular
ILL GIVE BRAINIEST TO WHO EVER IS CORRECT!! PLEASE HELP ASAP!!
Write an equation of a line in standard form that passes through points A(-3,4) and B(1,-2)
Answers
Answer:
Step-by-step explanation:
please help me i need help quick
Answers
Answer:
x = -2
y = -6
Step-by-step explanation:
Equating the equations :
x - 4 = 4x + 23x = -6x = -2y = -2 - 4y = -6Equate both
x-4=4x+2-4-2=4x-x-6=3xx=-2And
y=-2-4=-6Graph attached
Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
Answers
Answer:
\(\frac{1}{8}\)
Step-by-step explanation:
Since there are four answer choices for question one, the chance of picking the correct answer is \(\frac{1}{4}\). However, there is also another question. That question is a true-or-false question, meaning that there is only two options. Therefore, the probability of picking the correct answer is \(\frac{1}{2}\). To find the probability of picking both correctly, you multiply the two together. \(\frac{1}{4} * \frac{1}{2} = \frac{1}{8}\), so the answer is \(\frac{1}{8}\).
The table shows a pattern of exponents.
Powers of 5
59
52
Value
125
25
5
51
50
1
5-7
1
5
5-2
25
What is the pattern as the exponents decrease?
subtract 5 from the previous value
subtract 100 from the previous value
divide the previous value by 5
Save and Exit
Next
Answers
Answer: c. divide the previous value by 5
Step-by-step explanation:
Answer:
divide the previous value by 5
Step-by-step explanation:
Edge
A member has had an account for 9 days and asks for a prorated refund based on the time they did not use . they are signed up for our 180 usd a month plan( 45 usd a week). understanding that we are trying to provide a member with the best customer experience possible , how much would you refund for them ? why did you refund them this amount ?
Answers
Based on the calculation, no refund would be provided in this scenario.It's important to note that the calculation assumes a linear distribution of usage over time, which may not perfectly reflect the actual usage patterns of the member. However, for simplicity and fairness, proration calculations are often based on this linear assumption.
To determine the prorated refund amount for the member who has had an account for 9 days, we need to calculate the unused portion of their subscription.
The member is signed up for the $180 per month plan, which is equivalent to $45 per week.
Since the member has had the account for 9 days, we can calculate the unused portion of the weekly subscription as follows:
Unused portion = (Total weekly subscription - Used portion)
= ($45 - $45 * (9 days / 7 days))
Here, we divide the number of days the member has used by the total number of days in a week (7 days) to find the proportion of the week that they have used.
Using this formula, we can calculate the unused portion:
Unused portion = $45 - $45 * (9/7)
= $45 - $57.86
= -$12.86
The calculated unused portion is negative, indicating that the member has used more than the amount they have paid for the 9 days. In this case, a refund would not be appropriate as the member has already used more than the value of their subscription.
Therefore, based on the calculation, no refund would be provided in this scenario.
It's important to note that the calculation assumes a linear distribution of usage over time, which may not perfectly reflect the actual usage patterns of the member. However, for simplicity and fairness, proration calculations are often based on this linear assumption.
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simplifying with like terms; 2(3y + 10)
Answers
2 ( 3y + 10)
Use 2 to multiply both 3y and 10
Therefore, you have
2 x 3y + 2 x 10
6y + 20
A marksman at rest fires a 4.00 -kg gun that expels a bullet of mass 0.014 kg with a velocity of 181 m/s. the marksman’s mass is 81 kg. what is the marksman’s velocity after firing the gun?
Answers
The marksman's velocity after firing the gun is about -0.63 m/s (in the opposite direction of the bullet's velocity), as calculated using the conservation of momentum principle.
The conservation of momentum principle can be used to resolve this issue. The initial momentum of the system (marksman plus gun) is zero, and the final momentum is also zero because the bullet and the marksman have equal and opposite momenta. Therefore, we can write:
initial momentum = final momentum
\(0 = (M + m) * V + m * v\)
where M is the mass of the gun, m is the mass of the bullet, V is the velocity of the gun after firing, and v is the velocity of the bullet after firing (which is 181 m/s in this case).
Solving for V, we get:
\(V = - m * v / (M + m)\)
= \(\frac{- 0.014 kg * 181 m/s}{(4.00 kg + 0.014 kg)}\) ≈ -0.63 m/s
Therefore, the marksman's velocity after firing the gun is about -0.63 m/s (in the opposite direction of the bullet's velocity).
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Before changes to its management staff, an automobile assembly line operation had a scheduled mean completion time of 14.4 minutes. The standard deviation of completion times was 1.8 minutes. An analyst at the company suspects that, under new management, the mean completion time, u, is now less than 14.4 minutes. To test this claim, a random sample of 12 completion times under new management was taken by the analyst. The sample had a mean of 13.8 minutes. Assume that the population is normally distributed. Can we support, at the 0.05 level of significance, the claim that the population mean completion time under new management is less than 14.4 minutes? Assume that the population standard deviation of completion times has not changed under new management. Perform a one-tailed test.
a) State the null hypothesis H, and the alternative hypothesis.
b) Determine the type of test statistic to use.
c) Find the value of the test statistic. d) Find the p-value. e) Can we support the claim that the population mean completion time under new management is less than 14.4 minutes?
Answers
a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes. The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes. b) The type of test statistic to use is a one-sample z-test, since the sample size is small and the population standard deviation is known. c) The calculated test statistic is approximately -1.632. d) The p-value is slightly greater than 0.05. e) Based on the p-value being greater than the significance level (0.05), we fail to reject the null hypothesis.
a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes.
The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes.
b) Since the sample size is small (n = 12) and the population standard deviation is known, we will use a one-sample z-test.
c) The test statistic for a one-sample z-test is calculated using the formula:
z = (\(\bar x\) - μ) / (σ / √n), where \(\bar x\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Plugging in the values from the problem:
z = (13.8 - 14.4) / (1.8 / √12) ≈ -1.632
d) To find the p-value, we will compare the test statistic to the critical value from the standard normal distribution. At a significance level of 0.05 (α = 0.05), for a one-tailed test, the critical value is -1.645 (approximate).
The p-value is the probability of obtaining a test statistic more extreme than the observed test statistic (-1.632) under the null hypothesis. Since the test statistic is slightly larger than the critical value but still within the critical region, the p-value will be slightly greater than 0.05.
e) Since the p-value (probability) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the population mean completion time under new management is less than 14.4 minutes at the 0.05 level of significance.
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A spinner is evenly divided into red, yellow, blue, green and orange sections. What is the probability of spinning a yellow?
Answer (round) to the hundredth place value.
Answers
Answer:
The probability of spinning a yellow is 0.20
Step-by-step explanation:
red= 20%
yellow= 20%
blue=20%
green=20%
orange=20%
20%=0.20
The radius of a sphere is 5.5 inches. What is the surface area of the sphere? Express the answer in terms of Piin.Squared. Recall the formula S A = 4 pi r squared. 22 44 88 121
Answers
Answer:
121
Step-by-step explanation:
EDG 21
Answer:
121
Step-by-step explanation:
Shares of Sarah Corporation pay an annual dividend of $1.25, D₁.
This dividend grows at a rate of 4% per year. If the shares trade
at $22, what is the cost of common equity?
Answers
The dividend discount model calculates the cost of common equity based on the present value of expected future dividends .the cost of common equity is 9.68% (rounded to two decimal places)
The cost of common equity can be calculated using the dividend discount model. The dividend discount model is a technique that values the stock price based on the present value of expected future dividends. The formula for the dividend discount model is:
\($$P_0 = \frac{D_1}{r-g}$$\)
where P0 is the current stock price, D1 is the expected dividend for next year, r is the required rate of return, and g is the dividend growth rate. To calculate the cost of common equity, we need to solve for r.
Given:Shares of Sarah Corporation pay an annual dividend of $1.25, D1.This dividend grows at a rate of 4% per year.If the shares trade at $22, what is the cost of common equity?Solution:From the given information,
D1 = $1.25, g = 4%, and P0 = $22.Substituting the values into the dividend discount model formula, we get:\($$22 = \frac{1.25}{r - 0.04}$$\)
Multiplying both sides by r - 0.04, we get:
\($$22(r - 0.04) = 1.25$$$$22r - 0.88\)
\(1.25$$$$22r = 2.13$$$$r\)
\(= \frac{2.13}{22}$$$$r = 0.0968$$\)
Therefore, the cost of common equity is 9.68% (rounded to two decimal places).
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A new phone sells for $250 and a used one sells for $75. How many of each are sold if the sales for the day totals $625?.
Answers
The number of new phone sold is 1 and the number of old phone sold is 5, if the sales for the day totals $625.
It is given that
A new phone sells for $250
and a used one sells for $75
Let number of new phone is sold = x
and number of old phone is sold = y
Here the total profit for the day is $625
So, 250x + 75y = 625
or 10x + 3y = 25
Now the value of x and y satisfy the above equation, if we take x = 2 and more than 2, it is clear that it not satisfy the above equation. So we made a conclusion here x must be equal to 1 here.
Now, if x = 1
10(1) + 3y = 25
3y = 15
y = 5
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Point O is on line segment NP . Given NP=18 and , NO=10, determine the length OP .
Answers
18-10= 8
hope this helps!
Traci has a coupon for $2.50 off a box of name-brand cereal that normally costs $12.78. The store-brand cereal costs $10.98.
How much will Traci save it she uses her coupon and buys the name-brand cereal instead of store-brand cereal?
Answers
Gregory has 10 ways to choose 3 boxes of cereal.
A corporation or organization uses the purchasing process to buy products or services in order to achieve its objectives. Although many organizations make an effort to establish standards for the purchasing process, procedures can differ significantly between organizations.
According to data in the given question,
We have :
The purchase of 3 boxes and the store has 5 different varieties of munchie brand cereal.
The order in which the boxes of cereal are chosen is not important as Gregory can randomly choose any 3 different varieties. So, this is a combination problem.
Use the combination formula:
nCr = =n! / r! ( n- r)!
Putting n=5 (5 different varieties) and r=3 (3 different varieties). So, the number of ways Gregory choose 3 boxes of cereal is:
5C3 = 10
Therefore, the required answer is 10 ways.
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complete question:
gregory has a coupon for $1 off the purchase of 3 boxes of munchie brand cereal. the store has 5 different varieties of munchie brand cereal. how many ways can gregory choose 3 boxes of cereal?
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is.
Answers
The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
In the question ,
it is given that ,
number of items in the sample = 61 items
the mean of the sample is given as 23 ,
we have to find the degree of freedom(df) ,
the degree of freedom(df) can be solved using the formula
degree of freedom(df) \(=\) (number of observations) - 1
Substituting the values in the formula ,
we get ,
degree of freedom = 61 - 1
= 60
Therefore , The number of degree of freedom for reading the t values is 60 , the correct option is (c) .
The given question is incomplete , the complete question is
In order to determine an interval for the mean of a population with unknown standard deviation a sample of 61 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is ?
(a) 22
(b) 23
(c) 60
(d) 61
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3(x + 5)
Do y’all know the answer
Answers
Answer:
3x+15
Step-by-step explanation:
Solve this by Distributing
3 * x = 3x
3 * 5 = 15
Distribute
3(x + 5)
3x + 15
Answer:
3 x + 15
Consider a continuous random variable x, which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________. 0.50 0.075 0.75 1.00
Answers
The probability of x taking on a value between 75 to 90 is 0.25.
Given that x is a continuous random variable uniformly distributed between 65 and 85.To find the probability that x lies between 75 and 90, we need to find the area under the curve between the values 75 and 85, and add to that the area under the curve between 85 and 90.
The curve represents a rectangular shape, the height of which is the maximum probability. So, the height is given by the formula height of the curve = 1/ (b-a) = 1/ (85-65) = 1/20.Area under the curve between 75 and 85 is = (85-75) * (1/20) = (10/20) = 0.5Area under the curve between 85 and 90 is = (90-85) * (1/20) = (5/20) = 0.25.
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what is the square root of a perfect square always rational
Answers
Answer:
The square root of a perfect square will always be a whole positive or negative number
Step-by-step explanation:
solving systems of equations elimination
Answers
umm do you need to show work?
The price of an item yesterday was $60. Today, the price rose to 147. Find the percentage increase.
Answers
Answer:
145%
Step-by-step explanation:
percentage increase = [(final value - initial value) ÷ initial value] x 100
= [(147 - 60) ÷ 60] x 100
= 145%
A ladder 21 meters long is leaning against a wall. If the bottom of the ladder is being pushed horizontally towards the wall at 5 meters per second. How fast is the top of the ladder moving when the bottom is 10 meters from the wall?
Answers
the top of the ladder is moving downwards at a rate of approximately 3.95 meters per second when the bottom is being pushed towards the wall at 5 meters per second and is 10 meters away from the wall.
We can solve this problem using the related rates method. Let's call the distance between the bottom of the ladder and the wall "x", and the height of the ladder on the wall "y". We want to find the rate of change of y with respect to time, or dy/dt, when x = 10m and dx/dt = 5m/s.
Using the Pythagorean theorem, we know that:
x^2 + y^2 = 21^2
Differentiating both sides with respect to time t, we get:
2x(dx/dt) + 2y(dy/dt) = 0
Simplifying this equation, we get:
dy/dt = -x/y * dx/dt
Now we can substitute the given values for x and dx/dt into this equation, and solve for dy/dt:
dy/dt = -(10m)/(sqrt(21^2 - 10^2)m) * (5m/s) ≈ -3.95 m/s
Therefore, the top of the ladder is moving downwards at a rate of approximately 3.95 meters per second when the bottom is being pushed towards the wall at 5 meters per second and is 10 meters away from the wall.
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twice as many dimes as quarters I have a $1.80 total how many dimes do I have
Answers
Answer:
The answer is 8 dimes
Step-by-step explanation:
4 quarters x 2 = 8
8 dimes
1.00 + 0.80 = $1.80
What is the LCM and LCD of 60 and 13
Answers
Answer:
LCM=780
Step-by-step explanation:
The least common denominator, also called lowest common denominator (LCD), of 60 and 13 is 780. Here is a math problem example where you need to know the LCD of 60 and 13 to solve: 3/60 + 2/13 = 780
A fair 6 sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number?.
Answers
Answer: each time you roll a 6-sided die is 1/6 percent to get any number
Step-by-step explanation:
Solve the following equation. Express your answer as an integer, simplified fraction, or decimal rounded to two decimal places.
−1=−2v+15
Answers
Answer:
v=8
Step-by-step explanation:
in order to isolate the variable from the numbers, you add 2v to both sides. Then, you add 1 to both sides because you want to leave the numbers on one side, and the variables on the other. You then get 2v=16 and you divide both sides by 2 to get v by itself.
-1=-2v+15
+2v. +2v
-1+2v=15
+1. +1
2v=16
2v÷2=16÷2
v=8