Answers
Answer:
Piecewise function;
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Step-by-step explanation:
Function graphed represents the piecewise function.
1). Equation of the line with y-intercept (-2) and slope 'm'.
Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{1}[/tex]
= 2
Therefore, equation of this segment will be in the form of y = mx + b,
⇒ y = 2x - 2 where x < 2
2). Equation of a horizontal line,
y = 4 where 2 ≤ x ≤ 5
3). Equation of the third line in the interval x > 5
Let the equation of the line is,
y = mx + b
Where m = slope of the line
b = y-intercept
Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{2}{2}[/tex]
= 1
Equation of this line will be,
y = 1(x) + b
y = x + b
Since, this line passes through (5, 6),
6 = 5 + b
b = 6 - 5 = 1
Therefore, equation of this line will be,
y = x + 1 where x > 5
Graphed piecewise function is,
y = 2x - 2 where x < 2
4 where 2 ≤ x ≤ 5
y = x + 1 where x > 5
Related Questions
The curvature of a plane parametric curve x = f(t), y = g(t) is $ \kappa = \dfrac{|\dot{x} \ddot{y} - \dot{y} \ddot{x}|}{[\dot{x}^2 + \dot{y}^2]^{3/2}}$ where the dots indicate derivatives with respect to t. Use the above formula to find the curvature. x = 6et cos(t), y = 6et sin(t)
Answers
Answer:
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Step-by-step explanation:
The equation of the curvature is:
[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]
The parametric componentes of the curve are:
[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]
The first and second derivative associated to each component are determined by differentiation rules:
First derivative
[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]
[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]
Second derivative
[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]
[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]
[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]
[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]
Now, each term is replaced in the the curvature equation:
[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]
And the resulting expression is simplified by algebraic and trigonometric means:
[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]
[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]
[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]
[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]
[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]
The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].
Which functions have an axis of symmetry of x = -2? Check all that apply. A. f(x) = x^2 + 4x + 3 B. f(x) = x^2 - 4x - 5 C. f(x) = x^2 + 6x + 2 D. f(x) = -2x^2 - 8x + 1 E. f(x) = -2x^2 + 8x - 2
Answers
Answer:
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Step-by-step explanation:
The axis of symmetry is found by h = -b/2a where ax^2 +bx +c
A. f(x) = x^2 + 4x + 3
h = -4/2*1 = -2 x=-2
B. f(x) = x^2 - 4x - 5
h = - -4/2*1 = 4/2 =2 x=2 not -2
C. f(x) = x^2 + 6x + 2
h = -6/2*1 = -3/2 = x=-3/2 not -2
D. f(x) = -2x^2 - 8x + 1
h = - -8/2*-2 = 8/-4 =-2 x=-2
E. f(x) = -2x^2 + 8x - 2
h = - 8/2*-2 = -8/-4 =2 x=2 not -2
Answer:
Hey there! The answer to this question is
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
10) BRAINLIEST & 10+ Points!
Answers
Answer:
20Solution,
Complement of 70°
=90°-70°
=20°
hope this helps...
Good luck on your assignment..
Answer:
20°
Step-by-step explanation:
Complement of 70° is 90°-70°= 20°
To determine the complement, subtract the given angle from 90.
What is the value of the angle marked with xxx?
Answers
Answer:
Here you go!! :)
Step-by-step explanation:
Given that the sides of the quadrilateral are 3.3
The measure of one angle is 116°
We need to determine the value of x.
Value of x:
Since, the given quadrilateral is a rhombus because it has all four sides equal.
We know the property that the opposite sides of the rhombus are equal.
The measure of the opposite angle is 116°
x = measure of opposite angle
x = 116°
Then, the value of x is 116°
Therefore, the value of x is 116°
Answer:
In the diagram, the measurement of x is 87°
Step-by-step explanation:
In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.
180 - 93 = 87
The measurement of x is 87°
Translate the following statements into symbolic form using capital letters to representaffirmative English statement.
If Maria Cantwell promotes alternative energy,then if Patty Murray supports wilderness areas, then Dianne Feinstein's advocating gun control implies that Susan Collins does so,too.
Answers
Answer:
Step-by-step explanation:
There are two distinct statements but put together, it is:
- If Maria Cantwell (MC) promotes Alternative Energy (AE) and if Patty Murray (PM) supports Wilderness Areas (WA) then Dianne Feinstein (DF) advocating Gun Control (GC), implies that Susan Collins (SC) does so too.
For Susan Collins, she advocates gun control too.
So the symbolic or algebraic representation is:
(SC = DF): (MC ~ AE), (PM ~ WA)
OR
(GC = GC): (MC ~ AE), (PM ~ WA)
Where ":" represents "such that" or "given that"
" ~ " represents "support or promotion of"
It can now be read thus;
Susan Collins has same or equal interest as Dianne Feinstein, given that Maria Cantwell promotes alternative energy and Patty Murray supports Wilderness Areas.
a water storage tank is in the shape of a hemisphere. If the radius is 29ft, approximate the volume of the tank in cubic feet
Answers
Answer:
The answer is 51080.2 cubic feetStep-by-step explanation:
Volume of a hemisphere is given by
[tex]V = \frac{2}{3} \pi {r}^{3} [/tex]
where r is the radius of the hemisphere
From the question
r = 29 ft
Substitute the value of r into the formula
That's
[tex]V = \frac{2}{3} \pi \times {29}^{3} [/tex]
[tex]V = \frac{48778}{3} \pi[/tex]
We have the final answer as
V = 51080.2 cubic feetHope this helps you
What is the greatest common factor of the polynomial below 12x^2-9x
Answers
Answer:
the greatest common factor of this is 3
Please answer this correctly without making mistakes
Answers
Answer: Anything above 2
Step-by-step explanation:
Answer: 3,4,5,6,7,8,9 (Any of these digits work)
Step-by-step explanation:
We want to find a digit that makes the number greater than 3260.2. There are many digits that can fit in there.
3318.7≥3260.2
Here, we plugged in a 3. that makes this sentence true because 3318.7 is greater than or equal to 3260.2. Since 3 works, we know that any digit greater than 3 would fit.
what is the gfc of 16 and 8
Answers
Answer:
Greatest common factor of 16 and 8 is 8 .....About 16.6% of Americans can speak Spanish. We obtain a random sample of seventy-five Americans and determine the proportion in the sample who speak Spanish. Find the probability that 25% or more in the sample speak Spanish.
Answers
Answer:
The probability that 25% or more in the sample speak Spanish is 76%.
Step-by-step explanation:
Sample of 75 Americans
If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.
The proportion of those who do not speak Spanish is 18 (24% of 75)
Therefore, the proportion of those who speak Spanish is 57 (75 - 19)
This implies that 57/75 x 100 = 76% of the sample speak Spanish.
This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.
Probability is the chance that an event may occur from many other events that could have occurred. It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.
The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = .000586 mm. Assume a random sample of 59 sheets of metal resulted in an x¯ = .2905 mm. Calculate the 95 percent confidence interval for the true mean metal thickness.
Answers
Answer:
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm
The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm
The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm
Which graph represents the function?
Answers
the answer is the bottom left option
PLEASE ANSWER FAST, THANKS! :)
Answers
Answer:
Step-by-step explanation:
k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8
k = 4; 2k + 2 = 2*4 + 2 = 8 +2 = 10
k =5; 2k + 2 = 2*5 +2 = 10+2 = 12
k=6; 2k +2 = 2*6 + 2 = 12+2 = 14
k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16
k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18
∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78
Which expression represents the phrase 4 times the sum of 9 and 6
A. 4x (9+6)
B.4x 9+6
C.9+ 6x4
D. 9+ (6x4)
Answers
Answer:
The answer is option A
4 x ( 9 + 6)
Hope this helps you
The vector matrix[ 27 ]is dilated by a factor of 1.5 and then reflected across the X axis if the resulting matrix is a B then a equals an VE
Answers
Correct question:
The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???
Answer:
a = 3
b = 10.5
Step-by-step explanation:
Given:
Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]
Dilation factor = 1.5
Since the vector matrix is dilated by 1.5, we have:
[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]
= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]
Here, we are told the vector is reflected on the x axis.
Therefore,
a = 3
b = 10.5
Answer:
a = 3
b = -10.5
Step-by-step explanation:
got a 100% on PLATO
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours.
Answers
Answer:
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
Step-by-step explanation:
Step(i):-
Given mean of the life time of a bulb = 510 hours
Standard deviation of the lifetime of a bulb = 25 hours
Let 'X' be the random variable in normal distribution
Let 'x' = 552
[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]
Step(ii):-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = P(Z>1.63)
= 1- P( Z< 1.63)
= 1 - ( 0.5 + A(1.63)
= 1- 0.5 - A(1.63)
= 0.5 -A(1.63)
= 0.5 -0.4485
= 0.0515
Conclusion:-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
Perform the indicated operation.
Answers
Answer:
√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.
Answer:
[tex] 7\sqrt{3} [/tex]
Step-by-step explanation:
[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]
Please answer this correctly
Answers
Answer:
[tex] \frac{1}{6} [/tex]
Step-by-step explanation:
the ways of choosing 2 cards out of 4, is calculator by
[tex] \binom{4}{2} = 6[/tex]
so, 6 ways to select 2 cards.
but in only one way we can have 2 even cards. thus, the answer is
[tex] \frac{1}{6} [/tex]
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answers
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Answers
Answer: a) additive inverse (addition)
b) multiplicative inverse (division)
Step-by-step explanation:
Step 2: 6 is being added to both sides
Step 4: (3/4) is being divided from both sides
It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:
Step 2: Addition Property of Equality
Step 4: Division Property of Equality
Please answer this correctly
Answers
Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.
what is 3(C - 5) = 48
Answers
Answer:
c=21
Step-by-step explanation:
[tex]3(c-5)=48\\3c-15=48\\3c=48+15\\3c=63\\c=63/3\\c=21[/tex]
Hope this helps,
plx give brainliest
Answer:
c=21
Step-by-step explanation:
3(c−5)=48
Divide both sides by 3.
c-5=48/3
Divide 48 by 3 to get 16.
c−5=16
Add 5 to both sides.
c=16+5
Add 16 and 5 to get 21.
c=21
1/3 times the difference of a number and five is -2/3 which equation best shows this
Answers
Answer:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Step-by-step explanation:
Let the number be x
Difference of a number & 5 : x-5
1/3 time the difference of a number & 5: 1/3 (x-5)
Equation:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Solution:
[tex]x-5=\frac{-2}{3}*\frac{3}{1}\\\\x-5=-2\\\\x=-2+5\\x=3[/tex]
A boat that can travel 18 mph in still water can travel 21 miles downstream in the same amount of time that it can travel 15 miles upstream. Find the speed (in mph) of the current in the river.
Answers
Hey there! I'm happy to help!
We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)
We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.
We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.
[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]
So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!
15(18+r)=21(18-r)
We use the distributive property to undo the parentheses.
270+15r=378-21r
We subtract 270 from both sides.
15r=108-21
We add 21 to both sides.
36r=108
We divide both sides by 36.
r=3
Therefore, the speed of the river is 3 mph.
You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!
Have a wonderful day!
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
Answers
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Population divided into groups. Some members of each group are surveyed. This is stratified sampling
i-Ready
Sofia
The area of a rectangle is 7/9 square feet. The width of the rectangle is 2 1/3 feet. What is the length of the rectangle?
Answers
Answer:
1/3 feet.
Step-by-step explanation:
The length = area / width
= 7/9 / 2 1/3
= 7/9 / 7/3
= 7/9 * 3/7
= 3/9
= 1/3 feet,
Now divide 7/9 with 7/3
Answer: 1/3
Check: 1/3*7/3=7/9
In 1998, the average price for bananas was 51 cents per pound. In 2003, the following 7 sample prices (in cents) were obtained from local markets:
50, 53, 55, 43, 50, 47, 58.
Is there significant evidence to suggest that the average retail price of bananas is different than 51 cents per pound? Test at the 5% significance level.
Answers
Answer:
[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]
The degrees of freedom are given by:
[tex]df=n-1=7-1=6[/tex]
The p value for this case would be given:
[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]
The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51
Step-by-step explanation:
Info given
50, 53, 55, 43, 50, 47, 58.
We can calculate the sample mean and deviation with this formula:
[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]
represent the mean height for the sample
[tex]s=5.014[/tex] represent the sample standard deviation for the sample
[tex]n=7[/tex] sample size
represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is equal to 51, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 51[/tex]
Alternative hypothesis:[tex]\mu \neq 51[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]
The degrees of freedom are given by:
[tex]df=n-1=7-1=6[/tex]
The p value for this case would be given:
[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]
The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51
SOMEBODY HELP
Jill bought 7 books more than Sam. If Sam and Jill together have 25 books, find the
number of books Sam has.
Answers
Answer:
Jill bought 16 books and Sam bought 9 books
Step-by-step explanation:
Let the number of books that Jill bought be j.
Let the number of books that Sam bought be s.
Jill bought 7 more books than Sam:
j = 7 + s
They bought 25 books altogether:
j + s = 25
Put j = 7 + s into the second equation:
7 + s + s = 25
7 + 2s = 25
2s = 25 - 7 = 18
s = 18/2 = 9 books
Therefore:
j = 7 + s = 7 + 9
s = 16 books
Jill bought 16 books and Sam bought 9 books.
vertex form of x^2+6x+3
Answers
Answer:
y = (x + 3)^2 - 6.
Step-by-step explanation:
The vertex formula is Y = a(x - h)^2 + k.
To find the vertex formula, we need to find h and k, by finding the vertex of x^2 + 6x + 3.
h = -b/2a
a = 1, b = 6.
h = -6 / 2 * 1 = -6 / 2 = -3
k = (-3)^2 + 6(-3) + 3 = 9 - 18 + 3 = -9 + 3 = -6
So far, we have Y = a(x - (-3))^2 + -6, so y = a(x + 3)^2 - 6.
In this case, the coefficient of x^2 of the given formula is 1, which means that a will be 1.
The vertex form of x^2 + 6x + 3 is y = (x + 3)^2 - 6.
To check our work...
y = (x + 3)^2 - 6
= x^2 + 3x + 3x + 9 - 6
= x^2 + 6x + 3
Hope this helps!
Solve: -1/2+ c =31/4 c=8 c=7 c=33/4 c=29/4
Answers
Answer:
c = 29/4Step-by-step explanation:
[tex] - \frac{1}{2} + c = \frac{31 }{4} \\ \\ c = \frac{31}{4} + \frac{1}{2} = \frac{31 - 2}{4} \\ \\ c = \frac{29}{4} [/tex]
Hope this helps you