Answer:
3(x - 2)² - 17
Step-by-step explanation:
The equation of a quadratic in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Using the method of completing the square.
Given
3x² - 12x - 5 ← factor out 3 from the first 2 terms
= 3(x² - 4x) - 5
To complete the square
add/subtract ( half the coefficient of the x- term)² to x² - 4x
= 3(x² + 2(- 2)x + 4 - 4 ) - 5
= 3(x - 2)² - 12 - 5
= 3(x - 2)² - 17 ← in vertex form
Back Next
Check
Question 1
Indicate the answer choice that best completes the statement or answers the que
Solve s 3. Graph the solution on a number line.
Ву
+ +
0 1 2 3 4 5 6 7 8 9
-1
Oa
十一
0 1 2 3 4 5 6 7 8 9
Ob.
+
0 1 2 3 4 5 6 7 8 9
Ос.
0 1 2 3 4 5 6 7 8 9
Od
Answer:
C
Step-by-step explanation:
✔️First, solve for r:
r/2 ≤ 3
Multiply both sides by 2
r/2 × 2 ≤ 3 × 2
r ≤ 6
This implies that possible value of r is equal to 6 or less than 6.
Graphing this on a number line, the line with a shaded circle, indicating that 6 is included, starts at 6 and points to the left.
This indicates that value of r ranges from 6 and below.
The graph is C.
HELP I NEED HELP ASAP
Answer:
C
Step-by-step explanation:
Answer:
exponential;increase
Step-by-step explanation:
answer is C
What is the maximum volume in cubic inches of an open box to be made from a 10- inch by 20-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative.
Answer:
192.5 in³
Step-by-step explanation:
The cardboard is 10 by 20 before removing a square from each end. Assuming that the square is x inches wide. Therefore, the 20 in side gets reduced by x inches on both sides, or say it becomes 20 - 2x inches. On the other hand, the 10 in side is also reduced by 2x. The x value we get happens to be the height of the box when the sides are folded up.
Thus the volume V = lbh =
V = (20-2x)*(10-2x)*(x)
V = 4x³ - 60x² + 200x
On differentiating, we have dv/dx to be
dv/dx = 12x² - 120x + 200
Using general formula to find the roots of this equation, we can solve that x = 7.886 and x = 2.113
This roots we got are possible values of x, the square we cut. Since 7.886 * 2 = 15.772 inches, this is more than the 10 inch side, henceforth x = 2.113 inches.
You cut 2.113 inches from each corner to obtain the maximum volume.
The sizes of the cubes are
20 - (2 * 2.113) = 15.774
10 - (2 * 2.113) = 5.774
2.113
The volume of the cube is 15.774 * 5.774 * 2.113 = 192.5 cubic inches.
Adrianna is two years older than Fernando, while Lucy is triple Fernando's age. If the sum of their ages is eighty-two, how old is Adrianna?
HELPPPP MEEEEE!!!!!!
Answer:
18
Step-by-step explanation:
x + (2+x)+ (3x) =82
x+x+3x= 82-2
5x=80
x= 16
Fernando is 16
Adrianna is 2 years older so she is 18
And Lucy is 3x 16=48
together 82
what do you observe about the form of the equation of any circle whose center is at the point of origin
Ce clasă ești sa văd daca te pot ajuta
How far is the portion of her route from A to D? Round to the nearest whole number. Explain. I NEED IT BY TONIGHT SO PLSS SOMEONE HELP ME!
9514 1404 393
Answer:
A to D is about 2087 ft
Step-by-step explanation:
For the portion of the path of interest, the sine and cosine relations apply.
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
__
AB is the adjacent side to the angle marked 33°, with hypotenuse 975 ft.
cos(33°) = AB/(975 ft)
AB = (975 ft)cos(33°) ≈ 817.70 ft
BC is the opposite side in the same triangle.
sin(33°) = BC/(975 ft)
BC = (975 ft)sin(33°) ≈ 531.02 ft
CD is the hypotenuse of the right triangle BCD. The side BC that we know is opposite the given angle, so the sine relation applies.
sin(46°) = BC/CD
CD = BC/sin(46°)
CD = (531.02 ft)/sin(46°) ≈ 738.21 ft
__
Now we know the segments of the path of interest:
A–D = AB +BC +CD
A–D = 817.70 ft + 531.02 ft + 738.21 ft = 2086.93 ft
A–D ≈ 2087 ft
_____
Additional comments
The attachment shows all of the segments computed working counterclockwise from A. The angles in triangle DEF are computed using the Law of Sines from sides DF and DE and angle DEF. Segments EG and GH are computed using the Law of Cosines.
When we get to points F, G, H, we find that there is some inconsistency with the locations that would be computed working clockwise using AB and angle BFA. This inconsistency shows up in an error in the 119° angle in the attached figure.
This means that segments on the back side of the route, along path EFGHA, will vary somewhat depending on how they're computed.
We assume that points B, C, F, G are collinear.
Ten people put 63 boxes on a red truck and 38 boxes on a blue track About how many boxes did they load in all
Answer:
63+38=101
Step-by-step explanation:
helpppp meeee plz...
Answer:
3 coefficient po
Step-by-step explanation:
sana maka tulong
please help me guys!
its blur
how can we read it if your picture is blur
On which number line do the points represent negative seven and one over two and +1? (4 points)
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers.
Answer:A i did the test i got A correct
Step-by-step explanation:
PLS HELP!!
Solve for a side in right triangles
BC = ???
round your answer to the nearest hundredth
Answer:
39 centimeters
Step-by-step explanation:
I am very sorry if I'm wrong! ✿✿✿
help me with this question for my homework pls
Answer:
4 1/12 is your answer
Find a common denominator, 12. Multiply the many times you did to the denominator to get 12 to the numerator so 3/4 would be 9/12 and 2/3 would be 8/12 so 9/12 - 8/12 is 1/12 and as you know already 10 - 6 = 4 so 4 1/12 would be your answer.
What additional information would you need to prove
Answer:
A
Step-by-step explanation:
We use the Hypotenuse Leg Theorem
When we know the hypotenuse and a leg of a triangle.
We know The Hypotenuse (TO) so we need to know A leg of the triangle which the only leg is TM and OR.
6 1/4 - 2 3/4 = ?
please help lol
Answer:
3 1/2
Step-by-step explanation:
Rewriting our equation with parts separated
=6+1/4−2−3/4=6+1/4−2−3/4
Solving the whole number parts
6−2=4/6−2=4
Solving the fraction parts
1/4−3/4=−2/4 1/4−3/4=−2/4
Reducing the fraction part, 2/4,
−2/4=−1/2−2/4=−1/2
Combining the whole and fraction parts
4−1/2=3 1/2
please help with this question
==========================================================
Work Shown:
The diagram is below.
In this diagram, we have KN and LM as opposite sides. For any parallelogram, the opposite sides are parallel (as shown by the arrow markers) and they are congruent to each other. In other words, KN and LM are the same length.
This means KN = LM and we can solve for x like so
KN = LM
3x-11 = x+15
3x-x = 15+11
2x = 26
x = 26/2
x = 13
Then we can find side KL
KL = 2x-4
KL = 2*13-4
KL = 26-4
KL = 22
Charmaine has 17 cars available to rent. Let C be the number of cars she would have left after renting R of them.
Answer:
C = 17 - R
Step-by-step explanation:
In this scenario, 17 cars would be the initial starting point. While C would be the final number of cars, meaning that our equation would have to equal C. If she rents R number of cars then this number is being subtracted from the initial number of cars because Charmaine would no longer have them in his/her possession. Therefore, it is being subtracted. Using this information we can create the following equation.
C = 17 - R
Type the expression that results from the following series of steps:
Start with
x
, add 3, then times by 6.
Answer:
6x+18
Step-by-step explanation:
(x+3) * 6= 6(x+3)=6x+18
Answer:
6(x+3) or 6x +18
Step-by-step explanation:
x
add 3
x+3
times by 6
6(x+3)
simplify
6x+18
What is the value of the expression 1/2 divided by 6
Answer: the answer is to divide and you will come up with the answer 1/12
Step-by-step explanation:
Answer:
here is 1/2 divided displayed mathematically
1/2 ÷ 6
1= numerator
2= denominator
3= whole number
to make it fraction from the answer you keep the
numerator by the whole number to make a new
denomiter
___1___ = _1_
2×6 12
thus the answer to 1/2 divided by 6 on fraction form is
1/2 is the answer
Express each ratio as a fraction in simplest form.
26:169 and 36 to 78
Answer:
Step-by-step explanation:
1. 26/169 = 2/13
2. 36/78= 6/13
A children's ride at the amusement park has a rule that a person must be
shorter than 4 feet tall to ride it.
Create an inequality that shows the height, x, in feet, a person must be to go
on this ride.
Answer: the answer would be X<4
Step-by-step explanation: tell me if im wrong and i hope this helps you!
Turn y=-1/5x-4 into standard form
Jacob has 3 times as many football cards as Eli. Eli has 39 football cards. Tara has 111 football cards. Who has more football cards, Jacob or Tara? How many more?
Answer:
Jacob
Step-by-step explanation:
39*3 = 117
because it says Jacob has 3 times as many football cards as eli... Eli has 39 so 39*3 is 117 and 117 is more than 111
Quest
A teacher is peeling an orange at the front of a classroom. Where in the room
are the molecules from the orange most concentrated?
A. At the back of the room
B. In the second row of students
C. Near the orange
O D. By an open window
SUBMIT
2/3z=-6
Help please!!
Answer:
z = -9
Step-by-step explanation:
[tex]\sqrt{2x-3} =5[/tex]
Which of the following ordered pairs is not in the solution set of y < 2x − 5
Answer:
(4,3)
Step-by-step explanation:
Solve the equation:
3<2(4)-5
3<8-5
❌3<3 ❌
3 is not less than three, hence this is the phony
i hope this helps!
What is the additive inverse of -7?
O A. -7
O B. 7
C. -|-7|
D. -(-(-7))
Answer:
B
Step-by-step explanation:
Zach is a high school student who has an after school job at a grocery store. How much will he earn if he earns 75$ a week for 5 weeks?
HELP THIS IS DUE TODAY
I'm stuck on this.
Step-by-step explanation:
couldn't find the answer but try to get photo math on your phone it would surely help
Answer:
x = 0, y = -4
x = 1, y = -1
x = 2, y = 2
x = 3, y = 5
Step-by-step explanation:
just plug in the x value to get the y smh
if u get it wrong its not on me
f(x) = 4/9x + 7
linear or nonlinear?
Answer:
linear. :)
Step-by-step explanation:
Answer:
It depends on what you meant. See below.
Step-by-step explanation:
What you wrote means this:
[tex] f(x) = \dfrac{4}{9}x + 7 [/tex]
This is linear.
If you meant this
[tex] f(x) = \dfrac{4}{9x} + 7 [/tex]
or this
[tex] f(x) = \dfrac{4}{9x + 7} [/tex]
then it's non-linear.
An x in the denominator makes a function non-linear.
