Use the parabola tool to graph the quadratic function f(x)=x^2+10x+24.
Graph the parabola by first plotting its vertex and then plotting a second point on the parabol
Answers
Today we are just going to graph this quadratic function.
First let's find the vertex. There are two ways to find the vertex, but we will use the formula -b/2a today!
f(x)=x^2+10x+24
plug this into -b/2a where a=1 and b=10. (I found out what a and b equal by looking at the each term's coefficient.)
-10/2(1)
-10/2
-5
So the x value for our vertex is -5, so now to find the y-value, we need to plug in -5 in place of x in the equation...
f(x)=x^2+10x+24
f(-5)=(-5)^2+10(-5)+24
f(-5)=25-50+24
f(-5)=-25+24
f(-5)=-1
So the vertex is at (-5,-1)
Look at the table...
X] -5
Y] -1
Now we need to plug in number around the vertex to the equation.
X] -3 -4 -5 -6 -7
Y] -1
f(x)=x^2+10x+24
f(-4)=(-4)^2+10(-4)+24
f(-4)=16-40+24
f(-4)=-24+24
f(-4)=0
f(-3)=(-3)^2+10(-3)+24
f(-4)=9-30+24
f(-4)=-21+24
f(-4)=3
X] -3 -4 -5 -6 -7
Y] 3 0 -1
Now because the parabola is symmetrical, we don't have to plug in the other points to the equation. Watch what I do...
X] -3 -4 -5 -6 -7
Y] 3 0 -1 0 3
I really hope this helps!
Best wishes :)
Answer:
See the attachment
Step-by-step explanation:
You want a graph of the parabola defined by f(x) = x² +10x +24.
VertexWe can add and subtract the square of half the x-coefficient to put the equation into vertex form:
f(x) = x² +10x +24 . . . . . . . . . . given
f(x) = x² +10x +25 +24 -25 . . . . add and subtract (10/2)² = 25
f(x) = (x +5)² -1 . . . . . . . . . write in vertex form
Comparing to the vertex form equation f(x) = (x -h)² +k, we see that ...
(h, k) = (-5, -1).
These are the coordinates of the vertex.
Another pointThe coefficient of x² is 1, so another point can be found by adding (1, 1) to the vertex. That means a second point on the parabola is ...
(-5, -1) +(1, 1) = (-4, 0)
GraphThe attached graph shows the parabola with vertex (-5, -1) through point (-4, 0).
__
Additional comment
When the coefficient of x² is not 1, the process is a little different. If you start with f(x) = ax² +bx +c, you can factor 'a' from the first two terms to help you get vertex form.
f(x) = a(x² +(b/a)x) +c
f(x) = a(x² +(b/a)x +(b/(2a))²) + c - a(b/(2a))²
f(x) = a(x +b/(2a)x)² +(c -b²/(4a))
The vertex is (-b/(2a), c -b²/(4a)).
The second point can be found by adding (1, a) to the vertex coordinates.
Related Questions
Solve for x. 3.3x = 29.04 A) 8.0 B) 8.2 C) 8.6 D) 8.8
Answers
[tex]3.3x=29.04[/tex]
[tex]\frac{3.3x}{3.3} = \frac{29.04}{3.3} [/tex]
[tex]x = 8.8[/tex]
Your answer is D :)
Where a linear equation crosses the y-axis, that point is called the A) x-intercept. B) y-intercept. C) point of termination. D) point of translation.
Answers
Where a linear equation crosses the y-axis (the vertical axis), that point is called the y-intercept. This term is derived from 'the interception of the y-axis', in short 'y-intercept'.
Answer:
B) Y- Intercept
Step-by-step explanation:
I Took The USATP Quiz ^_^
your elapsed time is 9 and 3/4 and you finishrd at 6:00 pm. what ime did you start?
Answers
if the elapsed time is in minutes then you started at 5:50pm 15 seconds in
John bought 12 books 2/3 of the books are science fiction how many of the books are science fiction
Answers
Here are two ways to solve this problem. Way 1:
Convert the fraction to a decimal by dividing its numerator by its denominator.
2 ÷ 3 = 0.6666666667
Then, multiply the decimal by the total amount of books.
0.6666666667 × 12 = 8
Way 2:
Divide twelve by the denominator of the fraction, and then multiply it my the numerator.
12 ÷ 3 = 4
12 × 2 = 8
Thus, 8 of the 12 books are science fiction.
in an election for sheriff 210 people voted if there where 1260 possible voters write a ratio to compare the number of people who voted to the numbernof possible voters
Answers
The ratio of the number of people who voted to the number of possible voters in the sheriff election is 1:6 after simplifying the original ratio of 210:1260.
Explanation:In an election for sheriff where there are 1260 possible voters and only 210 people voted, the ratio of the number of people who voted to the number of possible voters can be written as 210:1260. To simplify this ratio, you divide both numbers by the greatest common divisor, which in this case is 210. So, when you divide both 210 and 1260 by 210, the simplified ratio is 1:6. This means that for every one person who voted, there were six possible voters.
The number of people who voted is 210 and the number of possible voters is 1260. So the ratio is 210:1260. Simplifying this ratio by dividing both numbers by their greatest common divisor, which is 30, we get 7:42. Therefore, the ratio to compare the number of people who voted to the number of possible voters is 7:42.
Mailboxes plus sends packages overnight for $5 plus $0.25 per ounce. United packages cost $2 plus $0.35 per ounce. Mr.Molinari noticed that his package would cost the same to maill using either service. How much does his package weigh?
Answers
x=5+0.25w
y=2+0.35w
Since the prices (x and y) end up being the same, we can set the equations equal to each other:
5+0.25w=2+0.35w
Now, we can simplify and solve for w, the weight.
3=0.1w
30=w
So, his package weighs 30 ounces.
By setting up an equation equating the cost of shipping with both Mailboxes Plus and United Packages, we determine that Mr. Molinari's package weighs 30 ounces.
Mailboxes Plus charges a flat rate of $5 plus $0.25 per ounce, while United Packages charges $2 plus $0.35 per ounce. Since the cost is the same for either service, we can equate the two expressions and solve for the weight of the package in ounces.
Let x represent the weight of the package in ounces. The cost for Mailboxes Plus is then $5 + $0.25x, and for United Packages, it is $2 + $0.35x. Setting these two expressions equal to each other, we get:
$5 + $0.25x = $2 + $0.35x
Now, we will solve for x:
Subtract $2 from both sides: $3 + $0.25x = $0.35xSubtract $0.25x from both sides: $3 = $0.35x - $0.25xCombine like terms: $3 = $0.10xDivide both sides by $0.10: $3 / $0.10 = xSimplify: 30 ounces = xTherefore, Mr. Molinari's package weighs 30 ounces.
Brian spent 60% of a weeks time working on drawings for a new apartment building. If Brian spent 18 hours working on projects other than the apartment building, compute the total hours worked
Answers
Let's say he spent t hours working on everything. So .4t=18
t = 45
Total hours worked is 45. He spent 27 hours on the apartment building.
The circumference of a circle is 6.28 meters. What is the circle's radius? C=6.28 m Use 3.14 for pi
Answers
The radius of the circle is 1 meter.
We have,
The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, r is the radius, and π is a constant equal to approximately 3.14.
We are given the circumference of the circle as 6.28 meters, so we can substitute this value into the formula:
6.28 = 2πr
Dividing both sides by 2π gives:
r = 6.28 / (2π)
r = 6.28 / (2 x 3.14)
r = 1
Therefore,
The radius of the circle is 1 meter.
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Final answer:
To find the circle's radius with a circumference of 6.28 meters using π=3.14, use the formula C=2πr. By rearranging and solving for r, the radius is found to be 1 meter.
Explanation:
The question is about finding the radius of a circle when the circumference is given as 6.28 meters and using 3.14 for π (pi). To find the radius, we use the formula for the circumference of a circle, C = 2πr, where C is the circumference, r is the radius, and π is Pi. Given C=6.28 m and π=3.14, we rearrange the formula to solve for r: r = C / (2π).
Plugging in the given values, r = 6.28 / (2×3.14) = 6.28 / 6.28 = 1. Therefore, the radius of the circle is 1 meter.
144=8x what is the answer please help me
Answers
To solve for x in this equation, we need to divide both sides of the equation by 8 to isolate x.
144/8=8x/8
18=x
x=18
Hope this helps!
Here, it is multiplied by 8. We perform the inverse operation, divide by eight (or multiply by one eighth), on both sides of the equation.
[tex]144=8x[/tex]
[tex] \dfrac{144}{8}= \dfrac{8x}{8} [/tex]
[tex]x=18[/tex]
Anita sees in her nutrition book that a 7.5-ounce cake has 900 calories how many calories will she save if only takes 2.5-ounce piece help please
Answers
7.5/900 = 2.5/x
x = 900 * 2.5 / 7.5
x = 900 * (1/3)
x = 300
But that is not the answer. The question is what does she save.
900 - 300 = 600
You could get the answer more directly. She does not eat 5 oz cake, so solve for that.
5/x = 7.5/900 Cross multiply
5 * 900 = 7.5 x
4500 = 7.5x Divide by 7.5
4500/7.5 = x
600 = x
1 tin of 500ml blue paint costs $11.50. to finish a bedroom i need 4litre of blue paint. how much wi this cost me.
Answers
Knowing this, all we need to do is multiply $23 • 4 which should give us $92.
So, the total of how much you will need to pay in this scenario to paint a room is $92 for 4 litres of blue paint.
Good luck!
Simplify: 4x + 4y + 4z A) 4 + xyz B) 4x3y3z3 C) 4xyz D) 4x + 4y + 4z
Answers
change one letter in the word cave to solve it: A curved stick_______
Answers
By changing the 'v' in 'cave' to 'n', we solve the clue: A curved stick, given by the word 'cane'. Although a concave mirror was mentioned, it doesn't fit in this context.
Explanation:The question asks you to change one letter in the word 'cave' to solve the clue: A curved stick. If we change the letter 'v' in 'cave' to 'n', we get the word 'cane'. A cane is typically curved at the top, resembling a stick. Although the reference to a concave mirror is interesting, it does not fit in this context as a concave mirror is a spherical mirror with its reflecting surface on the inner side of the sphere, forming a 'cave' shape. A useful tip to remember for distinguishing between concave and convex is: concave means caved in.
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(4u)(5v^2)-2u+uv^2-4uv^2
Answers
plz put graph form
1) 2x - y = -13
y = x + 9
2)3x + 2y = 10
6x - y = 10
3)4x - 3y = 5
3x + 2y = -9
4)x + y = 7
x - y = -1
Answers
Three is about as complicated as they get.
Multiply the top equation by 2 or 2(4x - 3y = 5) = 8x - 6y = 10
Multiply the bottom equation by 3 or 3(3x + 2y = - 9) = 9x + 6y = - 27
8x - 6y = 10
9x + 6y = - 27 Now add these two
17x = - 17 Divide both sides by 17
x = - 1
You can solve for y
8(-1) - 6y = 10
-8 - 6y = 10 Add 9 to both sides.
-6y = 18
y = - 3
(-1,-3) is the point where this crosses.
What you want to see is here.
Find the function y1 of t which is the solution of 16y′′−81y=0 with initial conditions y1(0)=1,y′1(0)=0.
Answers
Make a design according the local requirements.
13 is 20% of what number
Answers
65 is your answer
(5 because 20 * 5 is 100)
13 ÷ .20 = 65
65 × .2 = 13
Answer: 65
Clara's savings account has an APR of 10.95% calculates interest daily and pays interest at the end of the month if during the month of september her balance was $700 for the first 10 days of the month, $1900 for the next 10 days of the month, and $1400 for the last 10 days of the month, how much total interest did clara earn in september
A. $12.78
B. $11.20
C. $12.00
D. $11.30
Answers
.. (700*10 +1900*10 +1400*10)/30 = 1333.33
The interest paid on that balance was
.. 30/365*0.1095*$1333.33 = $12.00 . . . . . matches selection C
Answer:
The correct option is C. $12.00
Step-by-step explanation:
Annual Principal Rate = 10.95%
= 0.1095
Time duration = 10 days
[tex]\text{Time duration in years =}\frac{10}{365}=0.027\:\:years[/tex]
First finding interest rate for $700
Interest = 700 × 0.1095 × 0.027
= $2.10
Now finding interest rate for $1900
Interest = 1900 × 0.1095 × 0.027
= $5.70
Then finding interest rate for $1400
Interest = 1400 × 0.1095 × 0.027
= $4.20
Total Interest paid = 2.10 + 5.70 + 4.20
= $12.00
Hence, The correct option is C. $12.00
can someone help me please
Answers
The first step to solve this problem is to compute first for the area of the bigger rectangle:
A = LW
A = 12m (10m)
A = 120 m^2
Next step is to find the area of the smaller rectangle:
A = LW
A = 7m (2m)
A = 14 m^2
The last step is to deduct the area of the smaller rectangle to the area of the larger rectangle:
Area of larger rectangle – Area of the smaller rectangle = Area of the shaded region
120 m^2 – 14 m^2 = 106 m^2
Therefore, the area of the shaded region is 106 square meters.
Yesenia took three tests in her accounting class. She scored 91 points on her first test and 73 points on her second test. If her average for the three tests is 79, what score did she get on her third test?
Answers
you just set it up at 73+91+x=79 and solve
Let Yesenia's score in the third test be represented by the letter "x".
Now, we know that, by definition, the average in our case is the ratio of the sum of the points scored in the tests to the total number of tests taken.
We know that Yesenia scored 91 points on her first test and 73 points on her second test.We also know that Yesenia's average is 79. We have already assumed that she scored "x" in the third test. Thus, by definition of average, we get the following equation as:
[tex] 79=\frac{91+73+x}{3} [/tex]
Cross multiplication gives us:
[tex] 79\time 3=164+x [/tex]
Thus, [tex] x=237-164=73 [/tex]
Thus, Yesenia got a score of 73 in her third test.
sin(a)+sin(b)=sqrt(5/3) and cos(a)+cos(b)=1. Compute cos(a-b).
I drew out triangles and modeled the sines and cosines of a and b, but that doesnt help me find cos(a-b). What do I do?
Answers
(sin(a) +sin(b))^2 = sin(a)^2 +2sin(a)sin(b) +sin(b)^2 = 5/3
(cos(a) +cos(b))^2 = cos(a)^2 +2cos(a)cos(b) +cos(b)^2 = 1
Adding, we have
sin(a)^2 +cos(a^2) +2(cos(a)cos(b) +sin(a)sin(b)) +sin(b)^2 +cos(b)^2 = 2 2/3
Of course, the first and last pairs of terms are 1 and 1, and the middle product is 2cos(a-b), so you have
1 + 2cos(a-b) +1 = 2 2/3
cos(a-b) = 1/3
HELP ME PLZ I BEGG I GIVE BRAINLIEST
For what value of x:
is the square of the binomial x+1 twenty greater than the square of the binomial x–3?
Answers
(x - 3)^2 = x^2 - 6x + 9
x^2 +2x + 1 = x^2 - 6x + 9 + 20 Cancel the x^2. add 9 and 20 together.
2x + 1 = -6x + 29 Add 6x to both sides.
2x + 6x + 1 = 29
8x + 1 = 29 Subtract 1 from both sides.
8x = 29 - 1
8x = 28 Divide by 8
x = 28/8
x = 3 4/8 = 3 1/2
mr. Dell taught the six members of the chess club to play chess. each member taught three classmates. each classmate taught two more friends. how many people were taught to play chess?
Answers
Mr. Dell taught six members of the chess club who then taught 18 classmates, and those classmates taught 36 friends, resulting in 60 people being taught how to play chess in total.
To find the total number of people taught, we compute as follows:
First level (by Mr. Dell): 6 members
Second level (6 members x 3 classmates each): 18 classmates
Third level (18 classmates x 2 friends each): 36 friend
To determine the total number of people taught to play chess, we sum the three levels: 6 members + 18 classmates + 36 friends = 60 people. Therefore, a total of 60 people were taught to play chess
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression.
Answers
Answer:
Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended.
The variable, c, represents Central's score before the three-pointer. Express the total points scored in the game as a variable expression. Check all that apply.
Step-by-step explanation:
The total points scored in the game as a variable expression is 2c + c + 3.
What are equivalent expressions?Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
It is given that Central High School plays Eastern High School in a basketball game. Eastern had double the score of Central before Central scored a three-pointer as the game ended:
Let consider Central High School score be c
We knowt that the variable, c, represents Central's score before the three-pointer.
So, when Eastern doubled the score of Central, it is 2c
A Central scored a three-pointer as the game ended, it is + 3
To get the total points scored in the game, add all the actual variables
= (Eastern double points + Central single point + Central three-pointer)
= 2c + c + 3
So, the total points scored in the game as a variable expression is 2c + c + 3.
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Carter is playing a video game he needs to score more than a hundred points to move on to the next level write an inequality to show how many points Carter needs to earn
Answers
We have then:
x: number of points to go to the next level.
We write the inequality based on the following fact:
"I need to score more than a hundred points"
The inequation is:
x> 100
Answer:
an inequality to show how many points Carter needs to earn is:
x> 100
Felicia paid $2,879 for a new wall oven with her credit card. Felicia’s credit card has an APR of 13.89%, compounded monthly. It took Felicia seven years of identical monthly payments to pay for her oven, and she made no other purchases with her card until it was paid off. Over the ten years that she kept the oven, it used an average of $2.97 per week in electricity. Between the electricity and the interest, which component of the lifetime cost of the oven was greater, and how much greater was it? (Round all dollar values to the nearest cent.) a. The interest cost $94.12 more than the electricity. b. The interest cost $1,638.52 more than the electricity. c. The electricity cost $1,334.60 more than the interest. d. The electricity cost $463.32 more than the interest.
Answers
P= PV x i / 1- (1+i)^-n
PV= 2879
I= .1389/12
N= 84 (7 years x 12)
=53.78 x 84 = 4517.52
4517.52 - 2879 = 1638.52
1638.52 - 1544.40 = 94.12
The lifetime cost of the oven shows that A. The interest cost $94.12 more than the electricity.
How to calculate the cost?From the given information, over ten years that she kept the oven, it used an average of $2.97 per week in electricity. This will be calculated as:
= 2.97 × (10 × 52)
= 2.97 × 520
= $1544.30
Then, using the interest, the computed value will be:
= [(53.78 × (12 × 7)] - 2879
= (53.78 × 84) - 2879
= 1638.52 - 1544.40
= $94.12
Therefore, the interest cost $94.12 more than the electricity.
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The school is having a bake sale and the math club is bringing cupcakes. They have 180 total cupcakes, both chocolate and strawberry. The number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes. Which system of equations can be used to find the number of chocolate cupcakes, c, and the number of strawberry cupcakes, s? A. c + s = 180 s = 2c - 18 B. c + s = 180 c = 2s + 18 C. c - s = 180 s = 2c + 18 D. c = 2s c - 180 = s
Answers
The number of chocolate and strawberry together make 180. c+s=180.
The number of chocolate is 18 more than twice the number of strawberry; c=2s+18.
From our problem we know that the total number of cupcakes is 180, so [tex]c+s=180[/tex]. We also know that the number of chocolate cupcakes is eighteen more than twice the number of strawberry cupcakes, so [tex]c-18=2s[/tex], or solving for [tex]c[/tex]: [tex]c=2s+18[/tex].
Know we have our system of equations:
[tex] \left \{ {{c+s=180} \atop {c=2s+18}} \right. [/tex]
We can conclude that the correct answer is B. c + s = 180 c = 2s + 18.
Lets solve our equations to find how many cupcakes of each they have:
from our second equation we know that [tex]c=2s+18[/tex]; lets replace that value in our first equation to find the number of strawberry cupcakes:
[tex]2s+18+2=180[/tex]
[tex]3s=162[/tex]
[tex]s= \frac{162}{3} [/tex]
[tex]s=54[/tex]
Now that we know the number of strawberry cupcakes, lets replace that value in our second equation to find the number of chocolate cupcakes:
[tex]c=2(54)+18[/tex]
[tex]c=108+18[/tex]
[tex]c=126[/tex]
As a bonus, we can conclude that the math club have 126 chocolate cupcakes and 54 strawberry cupcakes.
Ms. O bought 2 1/2 pounds of blueberries on Monday. She Gavs 1/4 of the blueberries to her students before school ended A. How many pounds of blueberries did she give to students on monday B.How many blueberroes were left? C. On Tuesday she ate 1/3 of the remaining blueberries. How many did she eat on Tuesday? D. Did Ms.O eat more blueberries on Monday or on Tuesday? Explain your reasoning
Answers
2 1/2 - 5/8 = 1 7/8, so she had 1 7/8 pounds of blueberries left.
1/3 of 1 7/8 is 5/8 so she ate 5/8 pound of blueberries out of the 1 7/8 left.
Mrs. O gave the same amount of blueberries on Monday and ate the same amount of blueberries on Tuesday. (5/8 = 5/8)
What is the mean of the data set un the box below?
- 7,- 10,- 1,0,- 4,- 7,3,- 2,1
Answers
The data set is: (-7), (-10), (-1), 0, (-4), (-7), 3, (-2),1
You find mean by adding up all of the values and dividing them by the number of values.
-7 + -10 + -1 + 0 + -4 + -7 + 3 + -2 + 1 = -27
you divide this by 9 because there are 9 seperate values.
-27/9 = -3
The mean of the data set is -3
Hope I helped!
Let me know if you need anything else!
~ Zoe
Which is greater 770 meters or 7 kilometers
Answers
7 km = 7000 m
770 m < 7000 m