The following graph represents the hourly commission of a home appliance salesperson, y, based on the number of salespeople that are
working the showroom floor, x. The graph of the hourly commission of the salesperson is a quadratic function. What is the equation for
the function in standard form if the vertex is 6.5,42.25 and the origin is the only other known point?
Answers
We have been given graph of a downward opening parabola with vertex at point [tex](6.5,42.25)[/tex]. We are asked to write equation of the parabola in standard form.
We know that equation of parabola in standard form is [tex]f(x)=ax^2+bx+c[/tex].
We will write our equation in vertex form and then convert it into standard form.
Vertex for of parabola is [tex]y=a(x-h)^2+k[/tex], where point (h,k) represents vertex of parabola and a represents leading coefficient.
Since our parabola is downward opening so leading coefficient will be negative.
Upon substituting coordinates of vertex and point (0,0) in vertex form, we will get:
[tex]0=-a(0-6.5)^2+42.25[/tex]
[tex]0=-a(42.25)+42.25[/tex]
[tex]-42.25=-a(42.25)+42.25-42.25[/tex]
[tex]-42.25=-42.25a[/tex]
[tex]a=1[/tex] Divide both sides by [tex]-42.25[/tex]
So our equation in vertex form would be [tex]f(x)=-(x-6.5)^2+42.25[/tex].
Let us convert it in standard from.
[tex]f(x)=-(x^2-13x+42.25)+42.25[/tex]
[tex]f(x)=-x^2+13x-42.25+42.25[/tex]
[tex]f(x)=-x^2+13x[/tex]
Therefore, the equation of function is standard form would be [tex]f(x)=-x^2+13x[/tex].
Related Questions
Which shows the correct substitution of the values ab and c from the equation 0 = - 3x ^ 2 - 2x + 6 into the quadrati formula?
Answers
The answer would look something like this:
[tex]\frac{2+-\sqrt{2^{2}-4(-3)(6) }}{2(-3)}[/tex]
There could also have a simplified version.
I hope this helps.
find the value of JW given that JW=6x+2 and JB=10x+1
Answers
The value of JW is 14 units.
What is a triangle?A triangle is a polygon with 3 sides. The area of a triangle with base b and height h is given by A = (1/2)bh.
Given that, JB is the median of the triangle and JW = 6x + 2 and JB = 10x + 1.
The distance between the centroid and a vertex of a triangle is 2/3 of the length of the median, therefore, it follows:
JW = (2/3)JB
Substitute the values:
6x + 2 = (2/3)(10x + 1)
18x + 6 = 20x + 2
2x = 4
x = 2
Substitute x = 2 into the expression for JW:
JW = 6(2) + 2
JW = 14
Hence, the value of JW is 14 units.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ2
-(8x) . 3x^2 please help
Answers
Answer:
− 24 x 3
This is if you multiply the expressions
What is the slope of the line of best-fit in the scatterplot below?
Answers
Answer:
Option C
Step-by-step explanation:
Using the slope formula and the points in the picture: (3,12) (6,19)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{19-12}{6-3}=\frac{7}{3}[/tex]
The slope of the line is 7/3.
Option C should be the correct answer.
Answer:
Your correct answer is option C. 7/3
Step-by-step explanation:
Devon started the week with $50 in his checking account. On Monday he took $20 out of the
account. On Tuesday, the balance of Devon's account changed to $0. Which value best
represents the change to his account balance on Tuesday?
Answers
Answer:
see below
Step-by-step explanation:
Starting with 50
Took out 20
50-20 = 30
Then the balance was 0
We need to subtract 30 to get to get to 0
30-30 = 0
Taking out 30
Withdrawing 30
Spending 30
All are ways of indicating taking out 30 dollars
Answer:
On Tuesday, Devon took 30 dollars out of his checking account.
Step-by-step explanation:
Starting with: $50 - Ending with $0
Monday: took out $20 or in other words -20 50-20=30
Tuesday: undetermined, but since that was his last day, it would correspond with $0 so, he must've took out $30 and then ended up with none in the end.
30-30=0
So, he took 30 dollars out on tuesday.
If the soccer team paid $5 for 15 hamburger, then what is the price of one hamburger?
Answers
Answer:
$0.33 per hamburger
Step-by-step explanation:
You know that the team paid $5 for 15 hamburgers, then you need to divide the cost of all the hamburgers, ($5) by the number of hamburgers. 5/15 = 0.33 repeating. This means that they paid $0.33 per hamburger.
Answer:The answer is 80
5, 10, 15, 20, 25, 30, 35,40, 45, 50, 55, 60, 65, 70, 75, 80.
please help! im desperate :))
Answers
Answer:
1a) C, D, E is over 600 cubic inches.
1b) x4.8 greater The sphere is x4.8 greater than the first cone.
Step-by-step explanation:
A) Smaller Right cylinder V≈565.49 cubic inches
B) Smaller cone V≈188.5 cubic inches
C) Cylinder right prism V≈1696.46 cubic inches
D) Right circular cone V≈565.49 cubic inches
E ) Sphere V≈904.78 cubic inches
1b) Volume of sphere/volume of smaller cone
is 904.78/188.5= 4.7998938992 = x4.80 greater.
what is the greatest common factor 30y^8 + 10y^4
Answers
Answer: 10y^4
Since it can go 10y^4(3y^4+1)
Step-by-step explanation:
Answer:
10y^4
Step-by-step explanation:
in order to solve you would have to find the prime factors of each term i order to find the GCF.
hope this helped ;)
Solve the simultaneous equations
2x - 3y = 18
5x + 9y = -10
Answers
Answer:
2x - 3y = 18 (1)
5x + 9y = -10 (2)
<=>
Multiply both sides of (1) by 5, and multiply both sides of (2) by 2, then:
10x - 15y = 90
10x + 18y = -20
Subtract (2) to (1):
=> 33y = -110 => y = -110/33
Substitute y back into (1):
=> 2*x - 3*(-110/33) = 18
=> 2*x + 10 = 18
=> 2*x = 8
=> x = 4
=> Solution: x = 4, y = -110/33
Hope this helps!
:)
Answer: x=4 y= -10/3
Step-by-step explanation:
Look at the attachment. It should explain.
f(x)=x/2-3 and g(x)=3²+x-6 find (f+g)(x)
Answers
Answer: X=3
Step-by-step explanation:
I need help PLZ!
I'm not too sure if I got the right answers or not.
I put, > < > > > (left to right). Is this right?
Answers
Answer:
yee
Step-by-step explanation:
yee
please answer asapppp!!! i will give brainliest to whoever helps and does it 100% please i need help.
Answers
2. The equations are parallel, here’s my work:
Need the answer to this one please
Answers
The answer is A.
I used a graphing calculator.
Answer:
the first one
Step-by-step explanation:
slope: use rise-over-run theorem. the slope of the graph rises -2 for every 1 unit over, so slope is -2x
intercept: the line crosses the y-axis at y=3, hence +3
put it together: y=-2x+3
A cylinder has a circular base with diameter of 20 inches. What is the volume of this cylinder with the height of 11 inches?
HELP PLEASE
Answers
Answer:
3455.75
Step-by-step explanation:
find an equation for the line that passes through the points (5, -4) and (1, -2)
Answers
Answer:
y=-3/2x-.5
Step-by-step explanation:
(5,-4) and (1,-2)
Step 1: find slope:
-4-2/5-1=-6/4=-3/2
y=mx+b
y=-3/2x+b
2.: Plug in point
(1,-2)
-2=-3/2*1+b
-2=-3/2+b
-2+3/2=b
b=-.5
Consider that the roots of a cubic equation with integral coefficients are 2, -1, and 4. Which choice is the cubic equation?
es )
A
x3 + 5x2 + 2x + 8 = 0
B)
x3 - 5x² + 2x + 8 =0
C)
x3 - 5x2 + 2x - 8 = 0
D)
x3 - 5x? –2x - 8 = 0
Answers
Help!!!
Explain to Noah Clue why the following logarithmic properties are true. Be sure to demonstrate with examples and explain it well enough so that Noah could relay the information to Atta Loss with authority.
log (a•b) = log (a) + log (b)
b
log (a ) = b•log (a)
Answers
noun phrase
verb phrase
adverbial phrase
Sentence
We worked on the framework for a very long time.
He has been playing the cello at schools for ages.
Fen people understood Michelle's exaggerated explanation.
Answers
Answer:
1.) Verb phrase
2.) Noun phrase
3.) Adverbial phrase
Extending Patterns What is the value of y when x = 0? When x = 0, y = .
HURRY PLS
Answers
Answer: 0
Step-by-step explanation: it would only be a different number if there’s an equation like y=2x 3
0000000000000000000000
Step-by-step explanation:
ray cuts out a figure that has 4 equal sides and no right angles. what is the best name for the figure?
Answers
Answer:
Trapezoid
Step-by-step explanation:
None
Answer:
trapezoid
Step-by-step explanation:
There were 144 people in attendance at the school football game last Friday. This week there were 346 people in attendance at the school football game.What is the percent of change from last week to this week?Round your answer to the nearest whole number
Answers
Answer: 140%
Step-by-step explanation:
STEP 1: FIND THE CHANGE IN # OF PEOPLE:
initial # of people: 144
final # of people: 346
change in # of people = (final - initial)
change in # of people = (346 - 144)
change in # of people = 202
STEP 2: FIND THE % CHANGE
202/144 = x/100
(100)(202/144) = x
100(1.4) = x
140% = x
Answer:
140 %
Step-by-step explanation:
(346-144)/144 * 100
(202/144) * 100
If sin a-b =1/2 and cos a+b =1/2 Find a and b
Answers
Answer:
[tex]a = \frac{1}{2} [/tex]
[tex]b = 0[/tex]
Step-by-step explanation:
[tex]a - b = \frac{1}{2} \\ a + b = \frac{1}{2} \\ \\ a - b + a + b = \frac{1}{2} + \frac{1}{2} \\ a + a = \frac{2}{2} \\ 2a = 1 \\ \frac{2a}{2} = \frac{1}{2} \\ a = \frac{1}{2} [/tex]
[tex]a + b = \frac{1}{2} \\ \frac{1}{2} + b = \frac{1}{2} \\ b = \frac{1}{2} - \frac{1}{2} \\ b = 0[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!!
What is the sum?
-5 + (20) =
Answers
Answer:
15
Step-by-step explanation:
-5+20=20-5
15
Please answer correctly !!!! Will mark BRAINLIEST !!!!!!!
Answers
Answer:
g(n) = [tex]\frac{11+5n}{3}[/tex]
Step-by-step explanation:
Given
3m - 5n = 11
Rearrange making m the subject
Add 5n to both sides
3m = 11 + 5n ( divide both sides by 3 )
m = [tex]\frac{11+5n}{3}[/tex] , thus
m = g(n) = [tex]\frac{11+5n}{3}[/tex]
Solve the equation for y: -8x + 4y = 20
es
A)
y = 2x - 5
B)
y = 2x + 5
)
y= {x+5
yox=20
D)
Answers
Answer:
Step-by-step explanation:
4y = 20 + 8x
y = 5 + 2x
Answer:
Option B
Step-by-step explanation:
-8x + 4y = 20
[tex]-8x+8x+4y=20+8x \leftarrow \text {Addition Property of Equality.}\\4y=20+8x\\\\\frac{4y}{4}=\frac{20+8x}{4} \leftarrow \text {Division Property of Equality.}\\y=5+2x\\\boxed {y=2x+5}[/tex]
Option B should be the correct answer.
7. How would you solve this equation: 9x = 153? *
Multiply
Divide
Add
Subtract
Answers
You would need to DIVIDE by 9
Answer:
x=17
Step-by-step explanation:
divide both sides of the equation by 9
On a coordinate plane, trapezoid A B C D has points (negative 3, negative 2), (negative 1, 2), (3, 2), and (5, negative 2). Trapezoid ABCD is graphed in a coordinate plane. What is the area of the trapezoid? 16 square units 24 square units 32 square units 48 square units
Answers
Answer:
Correct option: second one -> 24 square units
Step-by-step explanation:
First we need to find the length of each side of the trapezoid, and we do that finding the distance between points:
AB = sqrt( (-1 - (-3))^2 + (2 - (-2))^2) = 4.4721
BC = sqrt( (3 - (-1))^2 + (2 - 2)^2) = 4
CD = sqrt( (5 - 3)^2 + (-2 - 2)^2) = 4.4721
DA = sqrt( (-3 - 5)^2 + (-2 - (-2))^2) = 8
The points B and C have the same y-coordinate, and the points D and A also have the same y-coordinate, so they are the bases of the trapezoid.
The height of the trapezoid is the difference in y-coordinate of points B and A:
height = 2 - (-2) = 4
So the area of the trapezoid is:
Area = (BC + DA) * 4 / 2 = (4 + 8) * 2 = 24 square units
Correct option: second one
Answer:
Its B
Step-by-step explanation:
Which equation is represented by the graph below?
Answers
Answer:
Option 3 y=ex-3 hoping this helps
a boy is older than his sister by 3 years five years ago, the ratio of their ages was 4 : 3 find his present.
Answers
4x - 3x = 3
x = 3
They were 12 & 9.
Add 5 to that.
So he’s now 17 and she’s 14
Answer:
five years ago -- boy- x+3 years
sister --- x
ratio-- 4:3 so difference is 3 years
4-3-- 1 1--3
five years ago --- sister :3*3--9 brother : 4*3--12
present : sister 14 years and brother 17 years old
Step-by-step explanation:
Combine like terms to create an equivalent expression
-3.6 - 1.9t + 1.2 + 5.1t
Answers
Answer:
3.2t-2.4
Step-by-step explanation:
-3.6 - 1.9t + 1.2 + 5.1t
Combine like terms
-3.6+ 1.2 - 1.9t +5.1t
-2.4 + 3.2t
Answer: 3.2t-2.4
Step-by-step explanation:
First thing you need to do is do -1.9t+5.1t= 3.2t. Then you do -3.6+1.2= -1.2.
Then put all this together and you get 3.2t-1.2. (do not do 3.2t+-1.2 this incorrect because we left the subtracting sign