The graph of $y = ax^2 + bx + c$ is shown below. Find $a \cdot b \cdot c$. (The distance between the grid lines is one unit.)
Answers
Answer:
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Step-by-step explanation:
Vertex is the minimum or maximum point of parabola
Vertex of parabola is (h,k)
Therefore, from given graph (-3,-2) is the lowest point.
Vertex of parabola is at (-3,-2).
Standard equation of parabola
[tex]y-k=a(x-h)^2[/tex]
Substitute the values
[tex]y-(-2)=a(x-(-3))^2=a(x+3)^2[/tex]
[tex]y+2=a(x+3)^2[/tex]
(-1,0) lies on the parabola.
Therefore, it satisfied the equation of parabola.
[tex]0+2=a(-1+3)^2=4a[/tex]
[tex]a=2/4=1/2[/tex]
Now, using the value of a
[tex]y+2=1/2(x+3)^2=1/2(x^2+6x+9)[/tex]
[tex]y+2=\frac{1}{2}x^2+3x+\frac{9}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9}{2}-2[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{9-4}{2}[/tex]
[tex]y=\frac{1}{2}x^2+3x+\frac{5}{2}[/tex]
By comparing with
[tex]y=ax^2+bx+c[/tex]
We get
[tex]a=\frac{1}{2}, b=3, c=5/2[/tex]
[tex]a\cdot b\cdot c=\frac{1}{2}\times 3\times \frac{5}{2}[/tex]
[tex]a\cdot b\cdot c=\frac{15}{4}[/tex]
Related Questions
Simplify 7t · s · 3rt.
Answers
Answer:
21 s t^2
Step-by-step explanation:
7t · s · 3rt
Multiply the coefficients
7*3 =21
t*t = t^2
s
Multiply back together
21 s t^2
Select THREE expressions that are equivalent to -16x - 68.
A. -4(4x - 17)
B. -2(8x + 34)
C. 2( - 8x - 34)
D. 4( - 4x - 17)
E. 8( - 2x - 8)
got it wrong the first time :(
Answers
Answer:
b, c, d
Step-by-step explanation:
What is 12% and 22% of 600 added together?
Answers
Answer:
204
Step-by-step explanation:
600 * .12 = 72
600 * .22 = 132
72 + 132 = 204
Have a great day!
Which is most applicable when continuous inspection is used? I-chart, P-chart, c-chart C-bar chart
Answers
There are various charts which represents mathematical and statistical data with graphical representation.
The correct answer for the given question is ,
I - Chart
Since this chart is used to present data for continuous inspection.
The charts are used for representation of inspected data in to structure way which helps understand the changes easily.
I chart is usually used when there is continuous inspection for the data. This type of chart used to monitor the process when measuring data at regular intervals.
Learn more at https://brainly.com/question/24366019
Type the correct answer in the box. Use numerals instead of words.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function p(g) =
.
Answers
Answer:
1g - 50 = p(g)
Step-by-step explanation:
The profit function is,
⇒ p(g) = g - 50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Betty sets up a lemonade stand and charges $1 per glass.
It cost her $50 to set up the stand.
And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.
Now, The number of glasses of lemonade sold = g,
And, A profit, p by function p(g)
Setup cost = $50
Since, Charges for 1 glass = 1 $
Hence, Charges for g glasses = 1.g = $g
Here, The cost = $50
Hence, Profit = $g - 50
⇒ p(g) = g - 50
Therefore, The profit function is,
⇒ p(g) = g - 50
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
A game involves rolling a number cube. You get one point if you roll an even number and negative one point if you roll an odd number.
A 7-column table has 3 labeled rows. The first row is labeled Roll with entries 1, 2, 3, 4, 5, 6. The second row is labeled Probability with entries one-sixth, one-sixth, one-sixth, one-sixth, one-sixth, one-sixth. The third row is labeled Point(s) with entries negative 1, 1, negative 1, 1, negative 1, 1.
Which statements are true regarding this scenario? Check all that apply.
The sample space is {1, 2, 3, 4, 5, 6}.
The expected value for the game is 0.
The expected value for the game is One-half.
The game is fair because the expected value is equal to 0.
The game is unfair because the expected value does not equal 0.
Answers
Answer:
A. B. D.
Step-by-step explanation:
There are 6 possible values to roll. Since 3 values are even and 3 values are odd, the game should be 0.
Answer:
A, B, D
Step-by-step explanation:
EDG 2021
Brainliest?
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Which phrase matches the expression 2v?
A. v divided by 2
B. twice v
C. 2 decreased by v
D. 2 more than v
Answers
Answer:
B) twice v
Step-by-step explanation:
because if there is no any sign between a number and a variable then you know that there is sign of multiplication
Choose the best answer that represents the property used to rewrite the
expression.
log root(12, 125x ^ 3) = 1/4 * log 5x
Answers
Answer:
commutative properties
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answers
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
write 1.4888... as a mixed number
Answers
Answer:
1861÷1250
Step-by-step explanation:
This is the simplified version
A contractor construct to build a house in 30 days. He employed 10 men to build the house. After 20 days. They completed only 1 /3 of the total work. How many more men will be required to finish the remaining work within due time?
Answers
Answer:
30
Step-by-step explanation:
First, we can say that because the men do 1/3 of the work in 20 days,
for 10 men:
20 days = 1/3 total work
Because we need the house built in 30 days, and 20 days have already passed, we only have 30-20=10 days left. Furthermore, 20/2=10, so in our equation of 20 days = 1/3 total work, we can divide both sides by 2 to get
10 days = 1/6 total work
The amount of work we need to get done in 10 days is (all of it) - (1/3 of total work) = 1 - 1/3 = 2/3 = 4/6
Since 10 men can do 1/6 of the work in 10 days, 10*4 =40 men can do 1/6 * 4 = 4/6 of the work in 10 days. This is the amount of work that needs to get done. Therefore, the contractor needs 40 (total workers) - 10 (current workers) = 30 new workers to finish the remaining work in due time
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. (Help ASAP)
Is it a, b, c or d?
Answers
Answer:
C.
Step-by-step explanation:
212/4 = 53, so 53/1, or 53 miles are driven every hour.
Check all that apply.
4x2 + 4x + 1 = 0
O A. X=
1
2
1
B. X= -2
c. x=-1
O D. x = 2
O E. x=
=
3
2
O F. X = 3
Answers
Answer:
x = -1/2
Step-by-step explanation:
4x^2 + 4x + 1 = 0
Factor
(2x+1)(2x+1) =0
Using the zero product property
2x+1 = 0 2x+1 =0
2x = -1 2x=-1
x = -1/2 x = -1/2
what is x increased by 10 divided by 4 as an expression?
please help need answer, I ask you don't answer if you don't know the answer, thank you!
Answers
Answer:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Step-by-step explanation:
We want to write an expression for the phrase: "x increased by 10 divided by 4."
If x is being increased by 10, the expression is:
[tex]x+10[/tex]
And if it is then divided by 4, we can place the entire expression over four. Hence:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Our expression is:
[tex]\displaystyle \frac{x+10}{4}[/tex]
In the diagram below, PQ is parallel to MN. Solve for 2. Round your answer to the
nearest tenth if necessary.
X=
Answers
At 11:00 a.m., John started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Jimmy started driving along the same highway in the same direction as John at the constant speed of 65 miles per hour. At what time will Jimmy catch up with John?
Answers
Answer:
12:05 pm
Step-by-step explanation:
Let z be the number of hours, from 11:00 am, when Jimmy would catch up with John. The time that Jimmy will have to drive to catch up with John is z - 1/4 as he started a quarter of an hour late. When Jimmy would catch up with John, they would have traveled the same distance. Hence
50 z = 65 (z - 1/4)
Solve for t
50z = 65z - 65/4
z = 65/60 = 1.083 hours = 1 hour and 5 minutes
Jim will catch up with John at
11:00 am + 1 hour 5 minutes = 12:05 pm
Answer From Gauth Math
Find the length of PR from the given figure ( step by step ).
Answers
Answer:
PR = 39 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
PR² + PQ² = QR² , that is
PR² + 80² = 89²
PR² + 6400 = 7921 ( subtract 6400 from both sides )
PR² = 1521 ( take the square root of both sides )
PR = [tex]\sqrt{1521}[/tex] = 39
Answer:
[tex]PR=39[/tex]
Step-by-step explanation:
The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:
[tex]a^2+b^2=c^2[/tex]
Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,
[tex]a^2+b^2=c^2[/tex]
Substitute,
[tex]a^2+b^2=c^2[/tex]
[tex]PQ^2+PR^2=QR^2[/tex]
[tex]80^2+PR^2=89^2\\[/tex]
Simplify,
[tex]80^2+PR^2=89^2\\[/tex]
[tex]6400+PR^2=7921[/tex]
Inverse operations,
[tex]6400+PR^2=7921[/tex]
[tex]PR^2=1521\\\\PR=39[/tex]
Mrs. Vacarro sliced a banana into 5 pieces. After eating one slice, she gave ⅘ of the original total to her toddler. After her child was finished, there were ⅖ of the banana slices left. What expression would you use to find out what fractional amount of banana Mrs. Vacarro's toddler ate?
Answers
Explanation: there were 5 existing pieces, mrs. Vacarro had 1 and gave the rest to her toddler which were 4 pieces. The remaining pieces were 2 which means the toddler ate 2/5 pieces
The fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Mrs. Vacarro sliced a banana into 5 pieces.
Number of slices she gave to her toddler = 4/5
Number of slices left after her toddler had finished eating = 2/5
Thus number of slices toddler ate,
⇒ [tex]\frac{4}{5} -\frac{2}{5}[/tex]
⇒ [tex]\frac{4-2}{5}[/tex]
⇒ [tex]\frac{2}{5}[/tex]
Hence we can conclude that the fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.
Learn more about word problems here
brainly.com/question/20594903
#SPJ2
Giải phương trình
2x+6=0
Answers
Answer: x = -3
[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]
Answer:
x= -3
Step-by-step explanation:
Solve the equation:
2x +6 = 0
We have isolate 'x'.
First subtract 6 from both sides
2x = 0-6
2x = -6
Divide each side by 2
x = -6/2
x = -3
find the surface area
Answers
Answer:
160π in²
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πrh + 2πr²
From here we can plug in what we know (r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
The surface area of a cylinder is 160π in².
What is the surface area of a cylinder?The surface area of a cylinder is also called the total surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
The formula for the surface area of a cylinder is:
A = 2πrh + 2πr²
From here we can plug in what we know that,
(r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
Hence, the surface area of a cylinder is 160π in².
Learn more about lateral surface area of a cylinder here:
https://brainly.com/question/11385509
#SPJ5
find the inverse f(x)=2x/x+3 x≠-3
Answers
Answer:
f^(-1)(x) = 3x/(2-x)
Step-by-step explanation:
f(x) = 2x/(x+3)
f(x)*(x+3)=2x
x(2-f(x))=3f(x)
x=3f(x)/(2-f(x))
f^(-1)(x) = 3x/(2-x)
200 students in a class took an examination in French and English. 180 of them passed in English and 80 passed in both French and English. 40 students did not pass in any of the subjects Illustrate the information on a Venn diagram How many passed in French? What is the probability of meeting a student who passed in one subject only?
Answers
Answer:
500
Step-by-step explanation:
Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x+2y=23 (1/2)-y=4
Answers
Answer:
x = 7.75 y = -0.125
Step-by-step explanation:
3x + 2y = 23 1/2x - y = 4
2(1/2x - y) = (4)2 1x - 2y = 8
3x + 2y = 23
+ 1x - 2y = 8
4x = 31
x = 7.75
3(7.75) + 2y = 23
23.25 + 2y = 23
2y = -0.25
y = -0.125
simplify each radical expression pleaseeee help i haven’t done algebra in 2 years
Answers
Answer:
4. 12√3
5. -35√2
6. 5√2/2
Step-by-step explanation:
4. 3√12+2√27
= 3√(4×3) + 2√(9×3)
= 6√3+6√3
= 12√3
5. 5√8-9√50
= 5×2√2-9×5√2
= 10√2-45√2
= -35√2
6. 5/√2
= 5×√2/(√2×√2)
= 5√2/2
Answered by GAUTHMATH
what is photography????
Answers
Answer:
the art or practice of taking and processing photographs.
Step-by-step explanation:
question came up for me and i chose this and it was right.
Answer:
photography ... is a item that is a visual representation of something.
if you really don't know the word it is taking a picture of something (a "selfie").
Photo = light .... Graph = image so technically speaking a
photograph is "making a image using light"
Step-by-step explanation:
Plzzzzzzzzz help 10 points and will mark brainiest
Answers
Answer:
Hello,
[tex]Answer:\ 2.8 < x < 5.4[/tex]
Step-by-step explanation:
The simpliest is to use the triangular inequality:
in a triangle, a side must be inferior to the sum of the 2 others sides.
[tex]\left\{\begin{array}{ccc}4.1& < &x+1.3\\1.3&< &4.1+x\\x & < & 4.1+1.3\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}2.8& < &x\\1.3-4.1&< &x\ not\ used\\x & < & 5.4\\\end{array}\right.\\\\\\Finaly:\ 2.8 < x < 5.4[/tex]
Answer:
2.8 < x < 5.4
Step-by-step explanation:
Given 2 sides of a triangle then the third side is in the range
difference of 2 sides < x < sum of 2 sides , that is
4.1 - 1.3 < x < 4.1 + 1.3 , then
2.8 < x < 5.4
CAN SOME HELP PLS I NEED HELP PASSING PYTHAGOREAN THEOREM
Answers
Answer:
Step-by-step explanation:
[tex]a^2+b^2=c^2\\8^2+15^2=c^2\\64+225=c^2\\289=c^2\\c=17\\\\17+15+8 = 40 meters[/tex]
Sequence Problem Below
Answers
Answer:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]
Step-by-step explanation:
[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]
A number is raised to the 4 th power, then divided by half the of the original number, and finally increased by 141/2. If the result is 100, what was the orginal number
Answers
Answer:
the number is 2.45
Step-by-step explanation:
let the original number = n
[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]
Therefore, the number is 2.45
help on the circled problems, will mark brainliest :D
Answers
Answer:
see explanation
Step-by-step explanation:
(1)
x - (9x - 10) + 11 = 12x + 3(- 2x + [tex]\frac{1}{3}[/tex] ) ← distribute parenthesis on both sides
x - 9x + 10 + 11 = 12x - 6x + 1 ← collect like terms on both sides
- 8x + 21 = 6x + 1 ( subtract 6x from both sides )
- 14x + 21 = 1 ( subtract 21 from both sides )
- 14x = - 20 ( divide both sides by - 14 )
x = [tex]\frac{-20}{-14}[/tex] = [tex]\frac{10}{7}[/tex]
(3)
- 4x - 2(8x + 1) = - (- 2x - 10) ← distribute parenthesis on both sides
- 4x - 16x - 2 = 2x + 10
- 20x - 2 = 2x + 10 ( subtract 2x from both sides )
- 22x - 2 = 10 ( add 2 to both sides )
- 22x = 12 ( divide both sides by - 22 )
x = [tex]\frac{12}{-22}[/tex] = - [tex]\frac{6}{11}[/tex]
(7)
8(2x + 9) = 56 ( divide both sides by 8 )
2x + 9 = 7 ( subtract 9 from both sides )
2x = - 2 ( divide both sides by 2 )
x = - 1
