Answer:
The general equation for a parabola is:
y = f(x) = a*x^2 + b*x + c
And the vertex of the parabola will be a point (h, k)
Now, let's find the values of h and k in terms of a, b, and c.
First, we have that the vertex will be either at a critical point of the function.
Remember that the critical points are the zeros of the first derivate of the function.
So the critical points are when:
f'(x) = 2*a*x + b = 0
let's solve that for x:
2*a*x = -b
x = -b/(2*a)
this will be the x-value of the vertex, then we have:
h = -b/(2*a)
Now to find the y-value of the vertex, we just evaluate the function in this:
k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c
k = -b/(4*a) - b^2/(2a) + c
So we just found the two components of the vertex in terms of the coefficients of the quadratic function.
Now an example, for:
f(x) = 2*x^2 + 3*x + 4
The values of the vertex are:
h = -b/(2*a) = -3/(2*2) = -3/4
k = -b/(4*a) - b^2/(2a) + c
= -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8
divide 64.050÷0.12. need whole process
Answer:
533.75
Step-by-step explanation:
Given the expression;
64.050÷0.12
Express first as a fraction
64.050 = 64050/1000
0.12 = 12/100
Divide both fractions
= 64050/1000÷12/100
= 64050/1000 *100/12
= 64050/10 * 1/12
= 64050/120
= 533.75
Hence the required answer is 533.75
Please help:
Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary
Statements and Reasons
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex] Given
[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex] Vertical Angles are Congruent
[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex] Linear Pair
[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex] Substitution
[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex] Substitution
[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex] Definition of Supplementary Angles
Integration of [(x+1)/(x-1)]dx
Hello!
∫[(x+1)/(x-1)dx
∫t+2/t dt
∫t/t + 2/t dt
∫1 + 2/t dt
∫1dt + ∫2/t dt
∫t + 2In (|t|)
x - 1 + 2In (|x-1|)
x + 2In (|x-1|) + C, C ∈ R
Good luck! :)
PLEASE HELP!!! Which number is a solution of the inequality x less-than negative 4? Use the number line to help answer the question. A number line going from negative 9 to positive 1.
Answer:
is it going to be 10.5
Step-by-step explanation:
I do not have any explanation
Answer: 0 (zero)
Step-by-step explanation:
Start Learning & start growing! edge2023
*DROPS THE MIC*
How to find B?
what type of angle is it?
Answer:
Obtuse angle; 57°
Step-by-step explanation:
b and 43° form a right angle. A right angle is 90°. Solution: 90°-43°=57°
43° is acute, so angle b must be obtuse.
jimmy had twice as many oranges as grapefruit, 5 more grapefruits than pineapples, how many of each fruit did jimmy have?
Answer:
Step-by-step explanation:
I think he has 7 oranges and 5 grapefruit and ten pineapples
8. Discount: An auto dealer paid $8730 for a
large order of special parts. This was not the
original price. The amount paid reflects a 3%
discount off the original price because the
dealer paid cash. What was the original price
of the parts?
Answer: 5,987
Step-by-step explanation:
Help! This is timed!
Answer: 5 ft i think so
Use the Pythagorean theorem
What is the measure of L?
A. 390
B. 25°
C. Cannot be determined
D. 32°
Answer:
∠L = 25°
Step-by-step explanation:
Two sides are equal. so , it is an isosceles triangle.
Angles opposite to equal sides are equal.
∠L = 25
If a student answered 77 exam questions correctly out of 100, what fraction
and what percentage of questions did the student answer incorrectly?
Choose two answers.
A. 0.77%
B.
20
100
IC
23
100
I D. 23%
O E. 77%
OF
77
100
Answer: 23%
Step-by-step explanation: 77 + 23 is 100
Answer:
77 out of 100
Step-by-step explanation:
For a fraction, it would look like 77/100,
and for percentage, 77%.
3. Determine the Area and Perimeter of the
shape below.
13
5
12
Answer:
Perimeter: 30 Area: 30
Step-by-step explanation:
Perimeter of a triangle= Add all sides = 5+12+13 = 30
Area of a triangle= (B*H)/2 = (5*12)/2 = 60/2 = 30
Hope this helps! :)
100 POINTS PLEASE HELP ON HW
Answer:
Solution given:
f(x)=x²
g(x)=x+5
h(x)=4x-6
now
23:
(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25
24:
(gof)(x)=g(f(x))=g(x²)=x²+5
25:
(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36
26:
(hof)(x)=h(f(x))=h(x²)=4x²-6
27;
(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1
28:
(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14
Answer:
the answer is 4x - 4
Step-by-step explanation:
1/4+3+11/2=
NEEED ANSWER ASAP BTW
Answer:
8.75 or 8 3/4
Step-by-step explanation:
To do this question, many do it differently. But for now, we will convert the fractions into decimals.
1/4 = 0.25
11/2= 5.5
0.25 + 3 + 5.5
3.25 + 5.5 =
8.75
The answer is 8.75 or 8 3/4
Answer:
[tex] \frac{35}{4} \: \: \: or \: \: \: 8 \frac{3}{4} [/tex]Decimal form :
8.75
Step-by-step explanation:
Hope it is helpful....
URGENT PLEASE I NEED HELP
Answer:
1. <1 and <2 are congruent
Step-by-step explanation:
✔️Statement 1 is NOT TRUE:
Rationale: with the information given, we cannot determine the measure of each of the angles.
✔️Statement 2 is TRUE:
Rationale: complementary angles add up to 90°. The sum of both angles equals 90°
✔️Statement 3 is TRUE:
Rationale: the red little box indicates a right angle
✔️Statement 4 is TRUE:
Rationale: adjacent angles share a common side. Both angles share a common side, so they are adjacent to each other.
Please tell me the answer I have no idea how to do this
Answer:
60 degrees
Step-by-step explanation:
So we see there's a 90 degree angle and a 150 degree larger angle including it.
So to find out the part that the 150 degree large angle that's not a part of the 90 angle we would do: 150 - 90, and we get 60.
So the bottom right angle is 60 degrees.
Now since we have a straight line from the left to right horizontally, we know that one side has to equal 180 degrees. On the side which the x is on, we already have 2 angles: 90 and 30. 90 + 30 = 120.
Since a straight line equals 180, x + 120 has to equal 180.
So now we do simple algebra.
x + 120 = 180
x = 180 - 120
x = 60
So x is equal to 60 degrees.
where is the location of the incenter of triangle abc is
Answer:
The point of intersection of angle bisectors of the 3 angles of triangle ABC is the incenter (denoted by I). The incircle (whose center is I) touches each side of the triangle.
Answer:
Step-by-step explanation:
we need a photo..
Lorena and Julio purchased a home for $205,950. Their loan amount was $164,760, and the assessed value is now $200,500. Their tax rate is 1.5%. How much will their monthly taxes be?
Answer:
Monthly taxes = $250.63 (Approx.)
Step-by-step explanation:
Given:
Amount of purchase = $205,950
Loan amount = $164,760
Assessed value = $200,500
Tax rate is 1.5%
Find:
Monthly taxes
Computation:
Tax always calculated on Assessed value
Annual tax amount = 200,500 x 1.5%
Annual tax amount = 3,007.5
Monthly taxes = Annual tax amount / 12
Monthly taxes = 3,007.5 / 12
Monthly taxes = 250.625
Monthly taxes = $250.63 (Approx.)
A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative constant. The mean life M of an atom in the substance is
[infinity]
M = âk â« te^kt dt.
0
For the radioactive carbon isotope, 14C, used in radiocarbon dating, the value of k is -0.000121. Find the mean life of a 14C atom.
Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
[tex]m = mo e^{kt}[/tex]
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]
Find the volume (in cubic feet) of a cylindrical column with a diameter of 6 feet and a height of 28 feet. (Round your answer to one decimal place.)
Answer:
[tex]791.7\:\mathrm{ft^3}[/tex]
Step-by-step explanation:
The volume of a cylinder with radius [tex]r[/tex] and height [tex]h[/tex] is given by [tex]A_{cyl}=r^2h\pi[/tex].
By definition, all radii of a circle are exactly half of all diameters of the circle. Therefore, if the diameter of the circular base of the cylinder is 6 feet, the radius of it must be [tex]6\div 2=3\text{ feet}[/tex].
Now we can substitute [tex]r=3[/tex] and [tex]h=28[/tex] into our formula [tex]A_{cyl}=r^2h\pi[/tex]:
[tex]A=3^2\cdot 28\cdot \pi,\\A=9\cdot28\cdot \pi,\\A=791.681348705\approx \boxed{791.7\:\mathrm{ft^3}}[/tex]
Find the value of y.
Please help :(
F(x) = x2. What is g(x)?
need help asap!!!
Answer:
Dear the answer is 100% D
Good luck
answer quick it's urgent
Expand : (5xy+7)(5xy-7)
Answer:
[tex](5xy + 7)(5xy-7) = 25x^2 y^2 - 49[/tex]
Step-by-step explanation:
[tex](a - b)(a +b ) = a^2 - b^2 \\\\From \ given \ expression \ a = 5xy \ , \ b = 7\\\\Therefore , (5xy + 7 )(5xy - 7 ) = ( 5xy)^2 - ( 7)^2 \\[/tex]
[tex]= 25x^2 y^2 - 49[/tex]
Answer:
25x²y² - 49
Step-by-step explanation:
We can do this by using the a+b formula:
(a+b)(a-b)= a² - b²
So,
(5xy+7)(5xy-7)
=(5xy)² - 7²
= 25x²y² - 49
Another way we can do this by expanding the algebraic expression:
(5xy+7)(5xy-7)
= 5xy(5xy-7) + 7(5xy-7)
= 25x²y² - 35xy + 35xy - 49
= 25x²y²- 49
Write the sum of three odd consecutive integers if the last one is m-2
Answer:
the sum is 3m-12
Step-by-step explanation:
The nunbers are:
[tex]m-2\\m-4\\m-6\\the~sum~is:\\sum=(m-2)+(m-4)+(m-6)\\sum=m-2+m-4+m-6=m+m+m-2-4-6\\sum=3m-12[/tex]
The sum of three odd consecutive integers is 3m - 12
What are odd integers?"These are the integers which are not divisible by 2."
For given question,
We need to find the sum of three consecutive odd integers.
Let x, x + 2, x + 4 be three consecutive odd integers.
We have been given the last one is m - 2
This means x + 4 = m - 2
So, the second odd integer would be,
x + 2 = m - 4
and the first odd integer would be,
x = m - 6
, we find the sum of the three odd consecutive integers.
⇒ (m - 6) + (m - 4) + (m - 2)
= m + m + m - 6 - 4 - 2
= 3m - (6 + 4 + 2)
= 3m - 12
Therefore, the sum of three odd consecutive integers is 3m - 12
Learn more about the odd integers here:
https://brainly.com/question/18365251
#SPJ2
What is the domain of the given
set of ordered pairs?
(2, 4), (5,5), (8, 6), (11, 7)
Answer:
2, 5, 8, 11
Step-by-step explanation:
The domian is the x axis points thingy
A pizza dough recipe calls for 6 1/2 cups of flour. The recipe makes 37 1/2 ounces of dough. How many ounces of dough does 1 cup of flour make?
Answer:
[tex]n = 5\frac{10}{13}[/tex]
Step-by-step explanation:
Given
[tex]Call = 6\frac{1}{2}[/tex] cups
[tex]Recipe = 37\frac{1}{2}[/tex] ounce
Required
Number of ounces per cup (n)
To do this, we simply divide the Recipe by the call
So, we have:
[tex]n = \frac{Recipe}{Call}[/tex]
[tex]n = 37\frac{1}{2} \div 6\frac{1}{2}[/tex]
Express as improper fraction
[tex]n = \frac{75}{2} \div \frac{13}{2}[/tex]
Rewrite as:
[tex]n = \frac{75}{2} * \frac{2}{13}[/tex]
[tex]n = \frac{75}{13}[/tex]
[tex]n = 5\frac{10}{13}[/tex]
express the ratio as a fraction in the lowest terms 100cm:5m
Step-by-step explanation:
we know that 1m=100cm
so 1m:5m(final)
1:5
Answer:
1/5
Step-by-step explanation:
Since 100cm = 1m
then
100cm:5m becomes 1m:5m
which in fraction is 1/5
HELP PLEASE! I tried everything from multiplying, dividing, adding, and subtracting but still no correct answer. Can someone please help me out here?
=============================================================
Explanation:
There are a few ways to do this.
One method involves drawing a horizontal line to form three rectangles as show below. Note the labels A,B,C.
Rectangle A in the upper left corner has area of base*height = 6*7 = 42 square miles. I'll let A = 42 since we'll use it later.Rectangle B is 20 miles across horizontally (base) and 2 miles tall vertically (height). The 2 miles is from 9-7 = 2. The area of rectangle B is 20*2 = 40 square miles. Let B = 40.Then finally, C = 28 because rectangle C is 4 miles across and 7 miles tall, so 4*7 = 28.Add up those three sub areas found: A+B+C = 42+40+28 = 110 square miles
----------------
There are other methods you could do. A second method is to draw two vertical lines to form 3 other rectangles, then add up the sub areas to get 110.
A third method is to draw a horizontal line across the top to form one large rectangle (20 mi by 9 mi) and subtract off the area of the 7 mi by 10 mi inner rectangle (the empty space), so you'd say 20*9 - 7*10 = 180-70 = 110
Mischa wrote the quadratic equation 0=_x2+4x-7 in standard form. If a = -1, what is the value of c in her equation?
C=-7
C= 1
c=4
c=7
Answer:
A. c = -7
Step-by-step explanation:
Standard form of a quadratic equation is given as ax² + bx + c = 0, where,
a, b, and c are known values not equal to 0,
x is the variable.
Given a quadratic equation of -x² + 4x - 7, therefore,
a = -1
b = 4
c = -7
Find the scale ratio for the map described below.
1cm (map) 50km (actual)
The scale ratio is 1 to .....?
Answer:
50,000 : 0.01
multiply by 100...
5000000 : 1
1:5,000,000
Step-by-step explanation:
The ratio of girls to boys in a classroom is 3:5. Kevin says there must be 8 students in the classroom. Which explains whether Kevin is correct?
Answer:
Kevin is correct.
Step-by-step explanation:
3 girls + 5 boys = 8 students.
Answer:
he is incorrect since in a ratio you don't add them together instead what this ratio means is for every 3 girls there is 5 boys
Hope This Help!!!
