Write f(x) = 2x2 – 44x 185 in vertex form. To write f(x) = 2x2 – 44x 185, factor out from the first two terms. Next, form a perfect square trinomial keeping the value of the function equivalent: f(x) = 2(x2 – 22x 121) 185 – 242 The function written in vertex form is f(x) = (x – )2.
The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x – 11)² – 57.
What is a quadratic equation?It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The quadrattic equation is f(x) = 2x² – 44x + 185.
Take common 2 from the equation, we have
[tex]f(x) = 2(x^2 - 22x )+ 185[/tex]
Add and subtract 121, we have
[tex]f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57[/tex]
And we know that the standard equation
f(x) = a(x - h)² + k
On comparing, we have
The vertex (h, k) is (11, -57).
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
Answer:
1. 2
2. 2
3. 11
4. -57
Step-by-step explanation: actual answers
Philip is a football player who runs a pass route that takes a right angle bend as shown in the diagram below. Which do you think will have the greater magnitude; the average speed or the average velocity? explain why
Answer:
Average velocity
Step-by-step explanation:
The average speed is only different from average velocity because it has direction.
The average speed will be calculated with the hypotenuse A_C, but average velocity will be calculated with the two directions AB_BC.
Ethan's living room is 11 feet wide and 16 feet long. He wants to put a border around the top of the room. The cost of the border is $1.00 per foot. How much will it cost to buy enough of the border to go around the room?
What is the solution to the equation below?
Answer:
C
Step-by-step explanation:
sqrt(2 - 3x)/sqrt(4x) = 2
sqrt(2 - 3x) = 2×sqrt(4x)
now let's just square both sides
2 - 3x = 4×4x = 16x
2 = 19x
x = 2/19
F(x)=x^2
G(x)=x^2-8x+16
In which direction and by how many units should f(x) be shifted to match g(x)?
Answer:
4 units right
Step-by-step explanation:
The question of shifts or other transformations can be more easily answered when the transformed function is written in vertex form.
g(x) = (x -4)²
Compared to f(x) = x², this is g(x) = f(x-4). That change corresponds to a right-shift of 4 units.
f(x) should be shifted right 4 to match g(x)
_____
Additional comment
The square of a binomial is (a -b)² = a² -2ab +b². The form of G(x) can be seen to match this form, so we know G(x) can be written as the square shown above.
Can anyone solve this correctly?
Answer:
24 cm³
Step-by-step explanation:
The volume of a triangular prism with triangular face 4 cm by 2 cm and height 6 cm is the product of the triangle area and the prism height:
V = BH
V = ((1/2)bh)H = 1/2(2 cm)(4 cm)(6 cm) = 24 cm³
The volume of the prism is 24 cubic centimeters.
_____
Additional comment
Note that this is half the volume of a rectangular prism of the same dimensions.
what is the difference in length beetween a 1 1/4 inch button and a 3/8 inch button
Answer:
7/8
Step-by-step explanation:
First you have to make the fractions into a common denominator. So I made 1 1/4 into 10/8. Now you just subtract 2/8 from 10/8 and get 7/8.
Aja can harvest a field in 13 hours. One day her friend Khia helped her and it only took 6.24 hours. How long would it take Khia to do it alone?
four friends earned $5.20 for washing a car They shared the money equally how much did each friend get.
Answer:
$1.30
Step-by-step explanation:
We need to figure out how much each friend gets out of the 5.20 so we will have to divide :)
5.20/4 = $1.30
Have an amazing day!!
Please rate and mark brainliest!!!
find the highest common factor (HCF) of 30 and 45
Answer:
The highest common factor of 30 and 45 is 15.
Step-by-step explanation:
factors of 30 = 1, 2, 3, 4, 5, 6, 10, 15, 30 ; factors of 45 are = 1, 3, 5, 9, 15, 45)
Greatest common factor is 15
Answer:
15.
Step-by-step explanation:
HCF is also called GCD. So, you divide both numbers with a common number that can divide both numbers at the same time without a remainder.
3 30 45
5 10 15
2 3
3 × 5 = 15
Blue Tide Swim Shop is having its annual summer sale, when every item in the store gets marked down. During the sale, rashguards sell for $5 less than full price. Miguel purchases 3 rashguards and pays a total of $60.
Which equation can you use to find how much money, f, each rashguard costs at full price?
How much does each rashguard cost at full price?
Original price be x
Discount price be y
The equation is
y=x-5So
y=3(x-5)60=3x-153x=75x=25$Answer:
3(f - 5) = 60
$25
Step-by-step explanation:
Let f = full price of rash-guard
Given:
during the sale, rash-guards sell for $5 less than full pricecost of 3 rash-guards during sale is $60Therefore, the equation you can use to find how much money each rash-guard costs at full price is:
3(f - 5) = 60
To calculate the full price of the rash-guard, solve the equation for f:
⇒ 3(f - 5) = 60
Expand:
⇒ 3f - 15 = 60
Add 15 to both sides:
⇒ 3f = 75
Divide both sides by 3:
⇒ f = 25
Therefore, the full price of each rash-guard is $25.
Guys, I’m giving you at least 100 points for you to answer to my angles, triangles, and quadrilaterals word problem homework package. So guys, please listen up and pay attention to me without ignoring my angles, triangles, and quadrilaterals word problem homework package for no reason! :D
Please read my 2 of the geometric word problem questions carefully in order to get the clear understanding in order for you to get the Brainliest award if your answer is the best efforts and step-by-step explanations all of the time and here’s an image for you to answer to my 2 of my geometric word problem questions.
Please answer to my geometric word problem questions as soon as possible with the best efforts and the best step-by-step explanations in order to get the Brainliest award of all the time! :D
Well anyways, guys, good luck on answering 3 math word problem questions of my my angles, triangles, and quadrilaterals word problem homework package in order to get the best Brainliest award of all of the time, and I will check the answers to see if it’s appropriate for me. :)
Step-by-step explanation:
For question 22: Notice the congruent symbol on sides AB and CB; this shows that the triangle is isosceles, and in an isosceles triangle, the angles opposite congruent sides are congruent. Thus, angle A actually equals angle C.
In other the find B, it is know that all of the interior angles of a triangle must add to 180; thus, this can be written as: angle A + angle B + angle C = 180.
Since you already know angles A and C, subtract angle A and angle C from 180 to get angle B.
For question 23:
Notice that triangle DBC is an isosceles triangle, and that angle D and angle C are opposite of congruent sides, indicating that they are equal. Since the interior angles of a triangle must add up to 180, and you know that angle D equals angle C, you can find angle DBC by doing 180 - (2 * angle D).
Now that you have angle DBC, you can find angle CBA; since these two angles form a straight line, you know they must add to 180 degrees. Thus, 180 - angle DBC equals angle CBA.
Now, notice that triangle CBA is also isosceles, and that angles CBA and angle A are opposite congruent sides, indicating that they are also congruent. Thus, angle A equals angle CBA.
Hope this helps :)
write -5 as a logarithim with a base of 4
Answer:
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Step-by-step explanation:
[tex]log_b(a) = c[/tex] ↔ [tex]b^c = a[/tex]
You are given [tex]b[/tex] = 4
You re also given [tex]c[/tex] = -5
To find a, use the exponential form:
[tex]b^c = a[/tex]
[tex]= (4)^{-5} = \frac{1}{4^5} = a[/tex]
Then you can convert into a logarithm.
[tex]log_4(\frac{1}{4^5}) = -5[/tex]
Answer:
There are multiple ways of writing this:
[tex]\sf -5log_4(4)=log_4(4^{-5})=log_4\left(\dfrac{1}{4^5}\right)=log_4\left(\dfrac{1}{1024}\right)[/tex]
Step-by-step explanation:
Log rule: [tex]\sf log_a(a)=1[/tex]
[tex]\sf \implies log_4(4)=1[/tex]
[tex]\sf \implies -5log_4(4)=-5[/tex]
Log rule: [tex]\sf c \cdot log_ab=log_a(b^c)[/tex]
[tex]\sf \implies -5log_4(4)=log_4(4^{-5})[/tex]
[tex]\sf = log_4\left(\dfrac{1}{4^5}\right)[/tex]
[tex]\sf = log_4\left(\dfrac{1}{1024}\right)[/tex]
Is the following relation a function yes or no
It's function of sinus
...........
Help please and thank you
20 possible points if anyone gets this correct
Answer:
13
Step-by-step explanation:
I counted the X's of 1-3 and got 13 in total.
(Let me know if that was correct) :)
Answer:
13 students
Step-by-step explanation:
To solve this you count the x's above 1, 2, and three.
I hope this helps!!
Please help i need quick answers
We see that 24 is split into 8q.
Therefore 8q equals 24 --> 8q = 24 --> q = 24/8 = 3.
So q = 3.
Hope it helped!
Which value, when placed in the box, would result in a system of equations with infinitely many solutions? y = -2x 4 6x 3y =
The missing value is 12 in a system of equations with infinitely many solutions conditions.
It is given that in the system of equations there are two equations given:
[tex]\rm y =n -2x+4\\\rm and \\\rm 6x+3y= ?[/tex]
It is required to find the missing value in the second equation.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
We have equations:
[tex]\rm y = -2x+4 ....(1)\\ \\\rm 6x+3y= ? ....(2)[/tex]
Let's suppose the missing value is 'Z'
We know that the two pairs of equations have infinitely many solutions if and if they have the same coefficients of variables and the same constant on both sides.
From equation (1)
[tex]\rm y = -2x+4 \\\\\rm 2x+y=4[/tex](multiply both the sides by 3)
[tex]\rm 6x+3y=12[/tex] ...(3)
By comparing the equation (2) and (3), we get
M = 12
Thus, the missing value is 12 in a system of equations with infinitely many solutions conditions.
Learn more about the linear equation.
brainly.com/question/11897796
SOOO CLOSEE TO BEING DONEEEE helppppp
[tex]423 \times 10 {}^{2} [/tex]
[tex]2 \times 10 {}^{3} [/tex]
[tex]92 \times 10 {}^{5} [/tex]
[tex]4 \times 10 {}^{3} [/tex]
[tex]80 \times 10 {}^{6} = 8 \times 10 {}^{7} [/tex]
[tex]32 \times 10 {}^{9} [/tex]
Answer:
4.23*10^4
2*10^3
9.2*10^7
4*10^3
8*10^7
3.2*10^10
a + b =c a + b + c = 36 given that a and b have the same value what is a,b and c
Answer:
a = 9 b = 9 c = 18
Step-by-step explanation:
a+b = c
a+ b + c = 36 but we know a+b = c sub that in
c + c = 36
c = 18 now a + b = c and a and b are the same
so a and b are = 9
Answer:
a is 9
b is 9
c is 18
Step-by-step explanation:
Let's list the information provided
a + b =c
a + b + c = 36
a=b
Knowing that a=b we can replace b with a in the equations
a+a is the same as 2a since a is being doubled
2a=c
Knowing this we can replace c with 2a
2a+2a=36
Now solve for a
[tex]2a+2a=36\\4a=36\\\frac{4a}{4} =\frac{36}{4} \\a=9[/tex]
Now let's sub this value of a into the equations to see what the other values are
a=b
9=b
2a=c
2(9)=c
18=c
100 points and brainliest if u answer this right
Consider this dilation
(a) Is the image of the dilation a reduction or an enlargement of the original figure? Explain.
(b) What is the scale factor? Explain.
Answer:
a) Enklargement, b) k = 2Step-by-step explanation:
a)
The original figure is ABC and the image is A'B'C'.
We can see the image is larger than the original figure.
It indicates that the dilation is an enlargement.
b)
Find the ratio of corresponding sides to find the scale factor.
First get the measure of corresponding line segments.
AC = 2 - (-2) = 4A'C' = 5 - (-3) = 8The scale factor is:
k = A'C'/AC = 8/4 = 2#1
Enlargement#2
Take two sides of both
BC=|-3-1|=4unitsB'C'=|-3-5|=8unitsScale factor:-
k=8/4=2Please solve for the value of 3
Answer:
P = 45
Step-by-step explanation:
180 - 90 = 90
90 / 2 = 45
P = 45
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
wich one' is the right answer need help
Answer:
C
Step-by-step explanation:
because density equal all the rest
Mai earns a salary of $200 per week plus an additional 5% commission on her sales. If
Mai's weekly salary increases by $25 and her commission increases to 6%, how much will
she earn if her weekly sales are $2,500?
so Mai had booming sales of $2500, now her commission used to be 5%, but since she rules it went up to 6%, how much is her commission on that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 2500}}{\left( \cfrac{6}{100} \right)2500}\implies 150[/tex]
since her salary which used to be $200 but is now 200 + 25 = $225, so for that week she earned 225 + commission or 225 + 150 = 375.
if the surface area of a sphere is 48.3cm^2, find its diameter. PLEASE HURRY
Answer:
Step-by-step explanation:
The diameter to answer 3.92 A=4 pi r2 d=2r
Need help on my problem
Answer:
Step 1: 2*5 - 4y = 2
Step 2: 10 - 4y = 2
Step 3: -4y = -8
Step 4: y = 2
Step-by-step explanation:
What is the volume of this cone? Use 3.14 for π and round your answer to the nearest tenth.
In your answer, give the volume of the cone rounded to the nearest tenth, and then explain how you calculated it.
The length of the base of a parallelogram is 18 centimeters. the parallelogram has an area of 450 square centimeters.
what is the height of the parallelogram?
enter your answer in the box
Answer:
h = 25 cm
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the height )
given A = 450 and b = 18 , then
18h = 450 ( divide both sides by 18 )
h = 25
Answer:
h = 25cm
Step-by-step explanation:
PLEASE HELP!
Will try to give the brainliest!
Answer:
L: (15+6x) W: 2
L: (10+4x) W: 3
L: (5+2x) W: 6
Step-by-step explanation:
We don't have any numbers here to do calculations, so probably this is just an exercise in FACTORING. Also to practice that area is length times width.
The area given,
30 + 12x
can be factored several ways to be able to fill in the table.
This kind of factoring is like "un-distributive property" where a common factor can be factored out of the expression. Usually its helpful to factor out the greatest common factor (GCF) but in this case any common factor will do.
Also, unless there are more directions, either factor may be the length or the width.
2(15+6x)
3(10+4x)
6(5+2x)
PLEASE HELP ME! THERE IS A PICTURE
Answer:
I think 10
letter C.
Step-by-step explanation:
divide *2
-4x + 3y = 29
5x + y = -3
solve by substitution
Step-by-step explanation:
please mark me as brainlest
Answer:
y = 7x = -2Explanation:
-4x + 3y = 29 __ equation 15x + y = -3make x the subject in equation 2,
5x + y = -3
y = -3 - 5x __ equation 2
using substitution method,
-4x + 3(-3 - 5x) = 29
-4x -9 -15x = 29
-19x = 38
x = -2
Find y,
y = -3 - 5x
y = -3 - 5(-2)
y = 7