The function in vertex form that is equivalent to the equation f(x) = x^2 + 8 - 16x from the given options is given by: Option A: f(x) = (x-8)^2 -56
What is vertex form of a quadratic equation?If a quadratic equation is written in the form
[tex]y=a(x-h)^2 + k[/tex]
then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)
Since it is specified that the options are in vertex form, so let we convert the given equation to vertex form.
The specified equation is: [tex]f(x) = x^2 + 8 - 16x[/tex]
Converting to vertex form:
[tex]f(x) = x^2 + 8 - 16x\\\\f(x) = x^2 -16x + 8\\[/tex]
(let we make terms such that it becomes (a+b)^2 's formula).
[tex]f(x) = x^2 -16x + 8\\f(x) = x^2 -2\times8x + (-8)^2 -(-8)^2 + 8\\f(x) = (x-8)^2 -64 + 8\\f(x) = (x-8)^2 -56[/tex]
Thus, the function in vertex form that is equivalent to the equation f(x) = x^2 + 8 - 16x from the given options is given by: Option A: f(x) = (x-8)^2 -56
Learn more about vertex form of a quadratic equation here:
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Answer:
A
Step-by-step explanation:
Find the lateral area of the prism
Answer: 50, 208 mm²
Step-by-step explanation:
The lateral area is the surface area excluding the bottom, also known as the base. This means we will be solving for two rectangles and two triangles.
[The Rectangles]
They are both congruent, so I will do the following;
A = 2(L * W)
A = 2(7 mm * 24 mm)
A = 2(168 mm)
A = 336 mm²
[The Triangles]
The area of a triangle is [tex]\frac{B * H}{2}[/tex] However, they are both congruent. I will do the following;
A = B * H
A = 24 mm * 2,078 mm
A = 49,872 mm²
[The Total]
Lastly, I will add them together.
336 mm² + 49,872 mm² = 50, 208 mm²
What is the sum of the geometric sequence 1, 3, 9, ... if there are 11 terms? (5 points) 29,524 55,987 87,381 88,573
Answer:
S₁₁ = 88573
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{3}{1}[/tex] = 3 , then
S₁₁ = [tex]\frac{1(3^{11}-1) }{3-1}[/tex] = [tex]\frac{1}{2}[/tex] (177147 - 1) = [tex]\frac{1}{2}[/tex] × 177146 = 88573
Colin put a pie in the oven at 1:35 p. M. He took the pie out at 2:17 p. M. How long was the pie in the oven?
Answer:
42 minutes
Step-by-step explanation:
there are 60 minutes in one hour.
from 12 pm, 1 hour and 35 minutes have passed to get to 1:35 pm
from 12 pm, 2 hours and 17 minutes have passed to get to 2:17 pm
we are trying to figure out the start to end time, or the difference between the times
2 hours and 17 minutes - 1 hour and 35 minutes
1 hour = 60 minutes
if we convert everything to minutes we can get a definitive time in one single unit
2 hours = 1 hour * 2 = 60 minutes * 2 = 120 minutes
1 hour = 60 minutes
plug these in
(120 + 17) minutes - (60 + 35) minutes
= 137 minutes - 95 minutes
= 42 minutes as our answer
What is the trigonometric ratio for cos D ?
Answer:
Here,
H=75P=72B=21We know that cosD= b/h
=21/75
=7/25
please help, thank you if you do
Step-by-step explanation:
q3) if the given sequence is 1, 2, 4, 8, 16..., then it is not arithmetic one. The common ratio is 2: 16/8=8/4=4/2=2/1.
q4) if it is given -34; -64; -94; -124; -154..., then it is arithmetic sequence, where the difference is -64--34=-94--64=-124--94=-154--124= -30
find the mean of 3,2,2,5,1,3,2,0,5
Answer:
2.56
Step-by-step explanation:
(3+2+2+5+1+3+2+0+5)/9=2.55555555556...
Fill in the Blanks:
To factor p^2 - 5p -14 we need to find ___ of ____ that will also add to equal ____.
Answer:
We need to find Factors of 14 that will also add and equal to 5
Step-by-step explanation:
Trinomial factorising
Answer:
see explanation
Step-by-step explanation:
p² - 5p - 14
We need to find the factors of the constant term (- 14) that will also add to give the coefficient of the p- term (- 5)
the factors are - 7 and + 2 , since
- 7 × + 2 = - 14 and - 7 + 2 = - 5
then
p² - 5p - 14 = (p - 7)(p + 2) ← in factored form
The width w is less than 10 inches
Answer:
w - 10
Step-by-step explanation:
Substract 10 from W --> w - 10
What would be the BEST formula to model the volume of the flower planter shown?
A)
volume of a cone
B)
volume of a cylinder
c
volume of a triangular prism
D
volume of a rectangular prism
Answer:
B
Step-by-step explanation:
if it's one plant it's b, if it means more than one then probably D
Answer:
D) Volume of a rectangular prism
Step-by-step explanation:
I would like it if I could get a accurate answer.
Answer:
60°
Step-by-step explanation:
the triangle need to have 180°. The up right corner is 60 because 120 + 60 = 180. Then I extended to rhombus where you have two sets of same angles. 125 + 55 = 180. 125 + 125 = 250. 360 - 250 = 110. 110 ÷ 2 = 60
Josh calculated the mean absolute deviation of the points he earned throughout the year in four of his classes: science, math, Spanish, and art. science: MAD of 1.14 math: MAD of 1.6 Spanish: MAD of 1.2 art: MAD of 1.93 In which class were his scores the closest together?
Answer:
science
Step-by-step explanation:
k12 test
i need help with this
y= 2x+5 what is the gradient and y-intercept?
The awse is b) :B...... ur welcum
Juan's family and Ethan's family go to a food stand.
• Juan's family buys three hot dogs and four drinks for $18.50.
• Ethan's family buys five hot dogs and four drinks for $25.50.
What is the cost of one drink at the food stand?
Answer:
1 hotdog is $3.5.
1 drink is $2.
Step-by-step explanation:
18.50= 3x+4y(times 5)
25.50=5x+4y(times -3)
92.5=15x+20x
-76.5=-15x+-12y
16=-8y
2=y
18.50=3x+4(2)
10.50=3x+8
10.50=3x
3.5=x
(2y^2 – 3y + 1) = (y - 2)
Answer:
see below
Step-by-step explanation:
Move R side to the L side to get
2y^2 -4y +3 = 0
Use quadratic formula to find y = 1 +- i sqrt (2) / 2
PLEASEE HELPPPPPPP!!!!!!!!!!!
Answer:
6
Step-by-step explanation:
[tex]h \sqrt{28 } \\ \sqrt{28} = \sqrt{4 \times 7} \\ \sqrt{28} = \sqrt{4} \times \sqrt{7} \\ 2 \sqrt{7} \\ 8 \sqrt{7} - 2 \sqrt{7} = 6 \sqrt{7} [/tex]
hope this helps :D have a good day
There are two mechanics who work on cars. For each mechanic, the relationship between x, the number of hours worked, and y, the total cost, in dollars, is described below. • The equation y = 36x represents the total cost charged by Mechanic A for the number of hours worked. The graph shown below represents the total cost charged by Mechanic B for the number of hours worked.
Answer:
B
Step-by-step explanation:
if you divide the 2/88 you should get a price of 44. So Mechanic B charges $44 while Mechanic A charges $36. Subtract 44-36 and get 8. Since Mechanic B charges more, it would give you the answer listed in B.
The equation satisfies option B, Mechanic B charges $8 more per hour then mechanic A.
What is graph?a collection of all points whose coordinates satisfy a given relation (such as a function) a diagram that represents the variation of a variable in comparison to that of one or more other variables, such as a series of one or more points, lines, line segments, curves, or areas
The fundamental subject of graph theory is graphs.
Given the Equation for cost charged by Mechanic A
y = 36x
where y = total cost and x = hours worked
graph shows the total cost charged by Mechanic B
from graph we the coordinates (0, 0) and (2, 88)
when x = 0, y = 0 and when x = 2, y = 88
the equation satisfy the condition is
y = 44x
cost for one hour for Mechanic A
y = 36x (x = 1)
y = $36
cost for one hour for Mechanic B
y = 44x (x = 1)
y = $44
Mechanic B is $8 more than Mechanic A
Hence Mechanic B charges $8 more per hour then mechanic A.
Learn more about graph;
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Find LJ and mGM if KP=PL and GH=36 ft
find m^gm
y (y + 2) = y2 - 6
also
2 [x - (1-3x)] = 3 (x + 1)
Answer:
Step-by-step explanation:
y(y+2)=y²-6
y²+2y=y²-6
2y=-6
y=-3
2[x-(1-3x)]=3(x+1)
2[x-1+3x]=3x+3
2(4x-1)=3x+3
8x-2=3x+3
8x-3x=3+2
5x=5
x=1
Will mark brainlyest!! Please help.
Answer:
The X-coordinates will decrease by 6 units because, anytime you move something to the left on a coordinate plane you are decreasing the x value
Answer:
The x-coordinates will decrease by 6.
Step-by-step explanation:
So when you look at a graph, the left side has smaller numbers than the right side because as you go down it becomes negative and the right means it is going positive. So if you are moving to the left you are getting smaller so you are decreasing. The other options with y-axis is not true because the y-axis is vertical.
what is the volume of a box with side lengths that are 20inches? use the formula V= s to the third power, where s is the length of one side
Answer:
8000 in^3
Step-by-step explanation:
V = s^3
= 20^3 = 8000 in^3
Annual snowfall (in inches):
20, 16, 20, 17.5, 19.5, 18, 23
Mean =
Median =
What is the mean and the median?
Answer:
Mean is all the numbers add up and divide how many number were there. The Median is to line up all in order and the middle on.
Step-by-step explanation:
Answer:
Mean =19.142857142857
Median =19.5
Step-by-step explanation:
I need help with math???
Answer:
oranges lasts for 9 days
Step-by-step explanation:
To find out the number of days, we have to divide the total oranges by the quatity of oranges used each day.
Number of days = Total oranges ÷ number of oranges used per day
[tex]\sf = 7\dfrac{7}{8} \ \div \dfrac{7}{8}\\\\ = \dfrac{63}{8} \ \div \dfrac{7}{8}\\\\ =\dfrac{63}{8} * \dfrac{8}{7}\\\\ = 9[/tex]
Fraction division:
Keep the first fraction
Change division to multiplication
Flip the second fraction
Answer:
9 days
write 7/8x9, put 1 under 9.
7x9=63
8x1=8
63/8 simplified is 7 7/8
Step-by-step explanation:
On an assignment, there are two true or false questions. You have no idea what the
correct answer is to either one so you guess.
What is the probability that you get both of them right by guessing?
HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
[tex]y=-\dfrac 14 x~~....(i)\\\\x+2y = 4~~...(ii)\\\\\text{Substitute}~~ y= -\dfrac 14 x ~~ \text{in equation (ii):}\\ \\ \\x+2\left(-\dfrac 14 x \right) = 4\\\\\implies 4x -2x = 16~~~~;\left[\text{Multiply both sides by 4} \right]\\\\\implies 2x = 16\\\\\implies x =\dfrac{16}2 \\ \\\implies x =8\\\\\text{Substitute x = 8 in equation (i);}\\\\y= -\dfrac 14 \cdot 8 = -2\\\\\text{Hence,}~ (x,y) = (8,-2)[/tex]
Answer:
[tex]y = - \frac{1 }{4} x \\ [/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]x + 2( - \frac{1}{4} x) = 4 \\ [/tex]
[tex]x + ( - \frac{2}{4} x) = 4 \\ [/tex]
[tex]x - \frac{1}{2} x = 4 \\ [/tex]
[tex] \frac{2x - 1x}{2} = 4 \\ [/tex]
[tex]2x - x = 8[/tex]
[tex]x = 8[/tex]
[tex]x + 2y = 4 \\ [/tex]
[tex]8 + 2y = 4[/tex]
[tex]2y = 4 - 8[/tex]
[tex]2y = - 4[/tex]
[tex]y = - 2[/tex]
If he is choosing one event and one time how many options does he have for his birthday party?
Answer:
6 options
Step-by-step explanation:
hes got 3 event options
and 2 time slots so
3 times 2 is 6
Sara bought 12 pencils for $1.44. What is the cost per pencil?
Answer:
Step-by-step explanation:
each pencil costs $8.33.
12÷$1.44=$8.33.
hope this helps!
mark me brainliest as well please.
i need help with this
i’ll mark Brainliest or whatever it is
Which expression is equivalent to m (n + p)?
O A. m X n + P
Ов. т Хр+п
OC, (m x n) + P
OD. (mx n) + (m xp)
m
O E. (m + n) x (m + p)
Answer:
A
Step-by-step explanation:
m( n+ p)
it's also known as m × n + p
Find the value of x.
Answer:
26
Step-by-step explanation:
im pretty sure this is it but sorry if it aint