Answers
Given:
The quadratic equation is
[tex]y=3x^2-18x+15[/tex]
To find:
The x-coordinate and y-coordinate of the vertex.
Solution:
If a quadratic function is defined by [tex]f(x)=ax^2+bx+c[/tex], then the vertex is defined as:
[tex]Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)[/tex]
If [tex]a<0[/tex], then the function has a maximum at the vertex and ff [tex]a>0[/tex], then the function has a minimum at the vertex.
We have,
[tex]y=3x^2-18x+15[/tex]
Here, [tex]a=3,b=-18,c=15[/tex].
Since [tex]a=3>0[/tex], therefore the function has a minimum at the vertex. So, fill min in first blank.
Now,
[tex]\dfrac{-b}{2a}=\dfrac{-(-18)}{2(3)}[/tex]
[tex]\dfrac{-b}{2a}=\dfrac{18}{6}[/tex]
[tex]\dfrac{-b}{2a}=3[/tex]
Putting x=3 in the given function, we get
[tex]y=3(3)^2-18(3)+15[/tex]
[tex]y=27-54+15[/tex]
[tex]y=-12[/tex]
Therefore, the vertex is at point (3,-12).
Related Questions
A furniture salesman makes 3.5% commission. Her monthly sales are $18,545. Her annual salary is $18,995.80. What’s her monthly pay? Write just the value that represents your answer.
Answers
Using proportions, it is found that her monthly salary is of $1,528.9.
What is a proportion?A proportion is a fraction of total amount.
In this problem, her monthly sales are $18,545, with a commission of 3.5%, hence, in commission, the amount she makes is:
0.035 x 18545 = 649.075
Her annual salary is $18,995.80, of which 18995.80 - 649 = $18,346.8 she receives in 12 payments, hence:
18,346.8/12 = $1,528.9.
Her monthly salary is of $1,528.9.
You can learn more about proportions at https://brainly.com/question/24372153
True or false? The graph represents a function
5
-5
A True
B. False
Answers
Answer:
True
Step-by-step explanation:
It passes the vertical line test, meaning you can draw a vertical line anywhere on the graph and it will only intersect at one point
this means that for every input (x value) there is only one output (y value)
Yes, The graph represents a function.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to show a graph.
Now, We know that;
The vertical line test, meaning you can draw a vertical line anywhere on the graph and it will only intersect at one point, then it represent a function.
Here, The graph satisfy vertical line test, this means that for every input (x value) there is only one output (y value).
Thus, The graph represents a function.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
A recipe for cookies called for 2/3 of a cup of sugar per batch.Elena used 5 1/3 cups of sugar to make multiple batches of cookies. How many batches did she make?
Answers
Answer: 8 batches
explanation: 5 1/3 divided by 2/3 equals 8. To find out how many batches were made, you need to divide the total amount used by the amount needed for one batch.
Answer:
8 batches
Step-by-step explanation:
I divided 2/3 by 5 1/3
Name the solid figure formed by the net.
Answers
Answer:
square
Step-by-step explanation:
it is a square because all the shapes/parts are the same size
it also has 6 faces, 12 vertices
HELP HELP HELP ME PLEASE-
Answers
the answer is C or E lol because it's asking I've you put > in between both of them which one would be wrong if you put > in between them I look over them it would be c or e
A beach resort has 29 jet skis for guests to rent. Of these, 14 are two-person skis, 18 haveturbo packs, and 10 are both for two persons and have turbo packs. LetTbe the event that a jetski, randomly chosen, is a two-person ski, and letPbe the event that the ski has a turbo pack.A jet ski is chosen at random for rental. Find the probability for each of the following events.
Answers
Questions:
a. The jet ski is for two persons and has turbo packs.
b. The jet ski is not for two persons but has turbo packs.
Answer:
[tex]P(P\ and\ T) = \frac{10}{29}[/tex]
[tex]P(P\ and\ T') = \frac{270}{841}[/tex]
Step-by-step explanation:
Given
[tex]n=29[/tex] --- Total
[tex]T = 14[/tex] --- Two person skis
[tex]P = 18[/tex] --- Turbo packs skis
[tex]P\ and\ T = 10[/tex] --- Two person ski and Turbo packs
Solving (a):
This is represented as: [tex]P(P\ and\ T)[/tex]
This is calculated as:
[tex]P(P\ and\ T) = \frac{n(P\ and\ T)}{n}[/tex]
[tex]P(P\ and\ T) = \frac{10}{29}[/tex]
Solving (a):
This is represented as: [tex]P(P\ and\ T')[/tex]
This is calculated as:
[tex]P(P\ and\ T') = P(P)\ and\ P(T')[/tex]
[tex]P(P\ and\ T') = P(P)\ *\ P(T')[/tex]
Using the complement rule, we have:
[tex]P(T') = 1 - P(T)[/tex]
The equation becomes:
[tex]P(P\ and\ T') = P(P)\ *\ [1 - P(T)][/tex]
[tex]P(P\ and\ T') = \frac{n(P)}{n}\ *\ [1 - \frac{n(T)}{n}][/tex]
[tex]P(P\ and\ T') = \frac{18}{29}\ *\ [1 - \frac{14}{29}][/tex]
[tex]P(P\ and\ T') = \frac{18}{29}\ *\ \frac{29-14}{29}[/tex]
[tex]P(P\ and\ T') = \frac{18}{29}\ *\ \frac{15}{29}[/tex]
[tex]P(P\ and\ T') = \frac{18*15}{29*29}[/tex]
[tex]P(P\ and\ T') = \frac{270}{841}[/tex]
You are given data on number of radio ads and sales for a local department store. You had observations for 20 months. The correlation between ads and sales is 0.40. Does this indicate a positive and significant relationship between ads and sales at the 5% level of significance
Answers
Answer:
"No" would be the appropriate response. A further explanation is provided below.
Step-by-step explanation:
According to the question,
Number of observations,
n = 20
Significance level,
d = 5%
i.e.,
= 0.05
Calculated correlation,
= 0.40
Critical correlation value will be:
= 0.444
According to the question, we can see that the calculated correlation i.e., "0.40" is far less than the critical correlation value i.e., "0.444". The null hypothesis has always been not rejected. Thus it doesn't indicate the significant relationship.So the above it the right response.
Plllllssssssss Brainliest yo first answer pleassseeee
Answers
Answer:
26 mm
Step-by-step explanation:
Answer:
26
Step-by-step explanation:
you use the Pythagorean theorem so it look like: 10^2 + 24^2 = c^2
then u solve with algebra
If 2/3x - 1 = 4 , then x =
Answers
Answer:
2/5
Step-by-step explanation:
After solving the given equation, we get the value of x is
What is Equation?"An equation is a statement of equality between two expressions consisting of variables and/or numbers."
Solve the given equation, to find the value of x
[tex]\frac{2x}{3}-1 =4\\\frac{2x-3}{3}=4\\ 2x-3=12\\2x=15\\x=\frac{15}{2}\\ x=7.5[/tex]
Hence, the value of x is 7.5
To learn more about equation here
https://brainly.com/question/27661633
#SPJ2
10 POINTS PLS ANSWER
Answers
Answer:
Step-by-step explanation:
FGE is a straight line, and striaght lines measure 180 by definition. Therefore, x, angle BGA, and 55 all add together to equal 180. But notice that x and 55 are both marked with a single swish, meaning they are the same measure. So:
180 - 55 - 55 = x, so
x = 70
Is it against the law to be a Communist in the United States of America?
Answers
Answer:
no.
Step-by-step explanation:
Answer:
I don't believe there is any laws specifically saying that its illegal, but its probably not advised.
how many different ways can officers be appointed
Answers
Select the correct answer. The graph of the rational function f is shown. Which graph is the graph of g(x)=-f(x)?
Answers
Answer:
see picture
Step-by-step explanation:
Which of the following applications of undefined terms made use of the concept of point as a location in space?
A RADAR. C laser beam
b tip of needle. D mole o a face
Answers
Question on imagine
Will give 95 points if answer quickly
Answers
Answer:
B its 40cm^2
Step-by-step explanation:
break this odd shape up into two smaller ones like a 5x4 box and a 2x10 rectangle and add those two area together
Answer:
C).
Step-by-step explanation:
PLEASE HELP ME AND MY FRIEND WITH THIS PROBLEM!!
Answers
Answer:
36 possible outcomes
Step-by-step explanation:
Jessica's school bus stop is 60 yards from her house. For a normal school week, how many feet will Jessica walk to and from the bus stop.
Answers
Answer:
1,800 feet
Step-by-step explanation:
Assuming that the normal school week is 5 days, she will walk for 5 days to and from. Each day she will walk 120 yards to and from the stop. Multiply that number by 5 and you get your answer of 600 yards. The answer is wanted in feet, so you have to consider yards to feet conversions. 1 yard is three feet. Therefore, you multiply 600 by 3 and you get your answer in feet.
pls and this question
Answers
Answer:
-4
Step-by-step explanation:
that number cannot be simplified
If you receive 25\% off an item costing $22.00, how much money do you save?
Answers
Answer:
5.50
Step-by-step explanation:
They save 5.50
Answer:
$5.50
Step-by-step explanation:
Hello! This is an easy one. If we are trying to find how much she is saving all we would need to do is multiply.
$22.00 * 25% = $5.50
If we are trying to find out the total with the discount all we would need to do is subtract.
22 - 5.5 = $16.50
Hope this helps!!
Roger has to place cookies in plastic bags for a bake sale. He has 84 sugar cookies and 66 chocolate chip cookies. He wants to place the same number of cookies in each bag, wants to make sure that only one type of cookie goes into each bag, and wants to put the most cookies he can in each bag. How many cookies should be in each bag
Answers
Answer:
6 cookies
Step-by-step explanation:
Roger wants to place 84 sugar cookies and 66 chocolate chip cookies into plastic bags. Each bag must have the same number of cookies and only one type of cookie must be in each bag.
For the 84 sugar cookies:
number of cookies : 1 2 3 4 6 7 12 14 21 28 42 84
number of bags : 84 42 28 21 14 12 7 6 4 3 2 1
For the 66 chocolate cookies:
number of cookies : 1 2 3 6 11 22 33 66
number of bags : 66 33 22 11 6 3 2 1
The maximum common factor between 84 and 66 is 6.
Therefore 6 cookies should be placed in each bag. For sugar cookies, 6 cookies would be placed in each of the 14 bags while for the chocolate cookies, 6 cookies would be placed in each of the 11 bags.
choose yes or no to tell whether each of the following describes a convenience sampling method
Answers
In short, we have these answers in this exact order: No, No, Yes, Yes.
I need help with question 8
Answers
Answer:
the answer is B!
Step-by-step explanation:
because :
Jerry has = 150$
he "*DEPOSITED*" = 50$
(When the word deposit comes, it basically means we need to ADD)
therefore, 150 +50x = 500
(7 weeks) so,
150 + 50 * 7 = 500
see! my answer is correct !
mark me brainliest now pweasee! ;)) ♡♡♡
The length, width, and height of the wooden box are 12.3 inches, 6.4 inches, and 7.5 inches respectively. The cost of painting the box is $0.25 per square inches. Find the total cost of painting the box.
Answers
Answer:
Step-by-step explanation:
Formula
The first thing you must do is find the surface area. The formula is right below this sentence.
Surface area = 2*L*w + 2*L*h + 2 * w * h Substitute givens into this formula
L = lengthw = widthh = heightThe choice of what to make the Length, width and height is arbitrary
Givens
L = 12.3 inchesw = 7.5 inchesh = 6.4 inchesSolution
Surface area = 2*12.3*7.5 + 2*12.3*6.4 + 2*7.5*6.4
Surface area = 184.5 + 157.44 + 96
Surface area = 437.94 in^2
Cost of Paint
The question is not really about Surface Area. The question is about the cost of paint given that 1 square inch costs 0.25 dollars.
Cost = Surface Area * 0.25
Cost = 109.485 dollars or
Cost = 109.49 rounded.
You buy shrimp at the market.
The shrimp cost $34.99 for two 2.5-pound bags.
What is the unit rate of the shrimp in dollars per pound?
Find the unit rate to the nearest dollar.
Options: $30 per pound $0.14 per pound $7 per pound $14 per pound
Answers
34.99/5 pounds = 6.998 or $7/pound
Determine the area of the composite figure to the nearest whole number.
26 cm2
B)
38 cm?
46 cm2
85 cm2
Answers
Step-by-step explanation:
Area of rectangle= l×b
= 4cm×6cm
= 24cm²
Area of circle. = πr²
radius of circle = diameter÷2=6÷2=3cm
Area of circle. = 3.14×3²=3.14×9
Area of circle. = 28.26cm²
[tex]area \: of \: composite \: figure = area \: of \: circle \: + area \: of \: rectangle[/tex]
Area of........... = 28.26cm²+24cm²
= 52.26cm²
PLEASE MARK BRAINLIEST.
The area of the composite shape is: B. 38 cm²
What is the Area of a Composite Shape?Area of a composite shape = sum of the area of each shape that makes up the composite shape.
Thus:
Area of composite shape = area of semicircle + area of rectangle
= 1/2πr² + length × width
Radius (r) = 1/2(6) = 3 cm
Length = 6 cm
Width = 4 cm
Substitute
Area of composite shape = 1/2(3.14)(3²) + 6 × 4
Area of composite shape = 38 cm²
Learn more about area of composite shape on:
https://brainly.com/question/8408690
Can someone help me please
Answers
9514 1404 393
Answer:
{Segments, Geometric mean}
{PS and QS, RS}
{PS and PQ, PR}
{PQ and QS, QR}
Step-by-step explanation:
The three geometric mean relationships are derived from the similarity of the triangles the similarity proportions can be written 3 ways, each giving rise to one of the geometric mean relations.
short leg : long leg = SP/RS = RS/SQ ⇒ RS² = SP·SQ
short leg : hypotenuse = RP/PQ = PS/RP ⇒ RP² = PS·PQ
long leg : hypotenuse = RQ/QP = QS/RQ ⇒ RQ² = QS·QP
I find it easier to remember when I think of it as the segment from R is equal to the geometric mean of the two segments the other end is connected to.
__
segments PS and QS, gm RS
segments PS and PQ, gm PR
segments PQ and QS, gm QR
What is the next number in the following geometric sequence? *
{1, 3, 9,...}
A 3
B 27
C 2
D 1
Answers
Answer:
B. 27 Is the answer
Step-by-step explanation:
hope it helped u
PLEASE HELP. I NEED TO GET THIS RIGHT
Answers
Ciro is right
Gerard is wrong
Gunther is also wrong
Equal expression:
1 - 2(40x - 12)
PLEASE HELP ITS DUE IN 39 minutes
For each graph below state weather it represents a function
Graph 1
Graph 2
Graph 3
Graph 4
Graph 5
Graph 6
Answers
Answer:
Graph 4
Step-by-step explanation:
What is the equation of an exponential function?
1)y=mx+b
2)a=b+c
3)y=a (b)^x
4)y=ax^2+bx+c