Answer:
C. The x-coordinate of the vertex must be 6
Step-by-step explanation:
The parabola intercepts the x-axis when y = 0.
Therefore, if the quadratic equation has the points (2, 0) and (10, 0) then the x-intercepts or "zeros" are x = 2 and x = 10.
The x-coordinate of the vertex is the midpoint of the zeros.
[tex]\sf \implies midpoint=\dfrac{2+10}{2}=6[/tex]
Therefore, the solution is option C.
Additional Information
The leading coefficient of a quadratic tells us if the parabola opens upwards or downwards:
Positive leading coefficient = parabola opens upwardsNegative leading coefficient = parabola opens downwardsWe have not been given this information and so therefore cannot determine the way in which it opens.
As we do not know the way in which way the parabola opens, we cannot determine if the parabola will have a negative or positive y-intercept.
We have not been given the full quadratic equation, and so we cannot determine if the parabola is wider (or narrower) than the parent function.
Find the quadratic equation
[tex]\\ \rm\Rrightarrow (x-2)(x-10)=y[/tex]
[tex]\\ \rm\Rrightarrow y=x(x-10)-2(x-10)[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-10x-2x+20[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-12x+20[/tex]
Convert to vertex form of parabola
y=a(x-h)²+k[tex]\\ \rm\Rrightarrow y=x^2-2(6x)+20+16-16[/tex]
[tex]\\ \rm\Rrightarrow y=x^2-2(6x)+36-16[/tex]
[tex]\\ \rm\Rrightarrow y=(x-6)^2-16[/tex]
Vertex(h,k)=(6,-16)Option A and C is correct
if the prisms below are similar what is the ratio of the surface area of the smaller prism to the surface area of the larger prism
v=24
v=375
The ratio between the surfaces areas of the two prisms is equal to 6.25.
How to get the ratio of the surface areas?
The ratio between the volumes of the prisms is:
[tex]R_v = \frac{375 in^3}{24 in^3} = 15.625[/tex]
This number is equal to the cube of the scale of dilation applied to the dimensions of the smaller prism, so the scale factor is:
[tex]\sqrt[3]{15.625} = 2.5[/tex]
And the ratio between the areas should be the square of the scale factor, then we will have that the ratio between the surface areas of the two prisms is:
[tex]2.5^2 = 6.25[/tex]
If you want to learn more about scale factors, you can read:
https://brainly.com/question/3457976
What is the length of the Radius if AB is tangent to OB
Answer:
r = 5 units
Step-by-step explanation:
One way is to use the Pythag Theroem
12 ^2 + r^2 = (8+r)^2
144 + r^2 = 64 + 16r + r^2
80 = 16 r r = 5
Consider the diagram and proof by contradiction.
Given: △ABC with ∠B ≅ ∠C
Prove: AB ≅ AC
Triangle A B C is shown. Angles A B C and B C A are congruent.
Which would prove that AB ≅ AC?
converse of the isosceles triangle theorem
substitution
definition of congruency
converse of the triangle parts relationship theorem
Answer: converse of the isosceles triangle theorem
Step-by-step explanation:
Answer:
converse of the isosceles triangle theorem
Step-by-step explanation:
Took the test
Jared sold 194 Boy Scout chocolate bars. Matthew sold three times as many as Jared. Gary sold 297) few than Matthew. How many bars did Gary sell?
Answer:
285 choclate bars
Step-by-step explanation:
Jared: 194 choc. bars
Mathew: 3*jared=3*194=582
Gary: matthew-297=582-297=285 choc. bars
Solve:
5 = p/4
SOMEONE PLEASE HELP IM SO CONFUSED AND THEIR IS 90 QUESTIONS AND IM ONLY ON 50 AND ITS DUE THIS FRIDAY
Answer:
p = 20
Step-by-step explanation:
Note the equal sign, what you do to one side, you do to the other.
Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtraction
~
Isolate the variable, p, by multiplying 4 to both sides of the equation:
[tex]5 = \frac{p}{4}\\ 5 (* 4) = \frac{p}{4} (* 4)\\ 5 * 4 = p\\p = 20[/tex]
p = 20 is your answer.
~
Thursday: For the equation y=3x+5 what is the value of x when y=11? * *
Answer:
[tex]\huge\boxed{\bf\: 2 = x}[/tex]
Step-by-step explanation:
Given,
y = 11We need to find x.
Equation: y = 3x + 5.
On solving,
[tex]y = 3x + 5\\(11) = 3x + 5\\11 - 5 = 3x\\6 = 3x\\6 \div 3 = x\\\boxed{\bf\:2=x}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
I GOT THIS WRONG!! So what is the answer??
BOTS=BAN/REPORT
TROLL=BAN/REPORT
Use one of the sets and divide them to find the proportional relationship.
3 / 43.5 = 0.06896
Now since it's not in the answer choices, you round it.
0.06896 rounded to the nearest tenths is 0.7
Aliya lined up the interior angles of the triangle along line p below
When the measure of angle A increases in the triangle, what happens to angle A on line p?
It also increases.
Olt decreases
It stays the same.
It may increase, or it may stay the same.
Answer:
it also increases
Step-by-step explanation:
Solve the equation 1.37w=0
Hey there!
1.37w = 0
DIVIDE 1.37 to BOTH SIDES
1.37w/1.37 = 0/1.37
CANCEL out: 1.37w/1.37 because it give you 1
KEEP: 0/1.37 because it help solve for the w-value
NEW EQUATION: w = 0/1.37
SIMPLIFY IT!
w = 0
Therefore, your answer is: w = 0
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Use the portion of the exponential graph below to answer questions 7-8.
What is the domain?
What is the range?
Answer:
See below ~
Step-by-step explanation:
Domain = range of x values
Lowest value = -1Highest value = 3Domain ⇒ -1 ≤ x ≤ 3Range = range of y-values
Lowest value = 6Highest value = 27Range ⇒ 6 ≤ y ≤ 27HELP ASAP
The table shows how the number of sit-ups marla does each day has changed over time. At this rate, how many sit-ups will she do on day 12? Explain your steps in solving this problem
Day 1 - 12
Day 2 - 21
Day 3 - 25
Day 4 - 29
Day 5 - 33
Answer:
177
Step-by-step explanation:
just answered this for someone else but the number of sit-ups is going up in 4s so just add four to 33 7 times since thats how many days she has left til 12th day
Some of the dimensions of a square pyramid are shown in the diagram. The height of the pyramid is 7.5 meters.
square pyramid
What is the volume of the square pyramid in cubic meters?
Question 8 options:
40 m3
120 m3
360 m3
60 m3
DIGRAM BELOW
Answer:
40 m^3.
Step-by-step explanation:
Volume = 1/3 * 4^2 * 7.5
= 40 m^3.
stacy runs 16 miles is 4.5 hours. what is stacys average speed?
Answer: Stacy's average speed is 3.55555555556 or approximate 3.56 miles per hour. Speed ≈ 3.56
Step-by-step explanation: You simply solve by taking the number of miles dividing it by the number of hours and you get 16 ÷ 4.5 which gets your answer to be approximately 3.56 miles per hour (mph). I hope this helped you! Let me know if you need me to explain more!
16 miles in 4.5 hours.
to find:the average speed.
solution:[tex]speed = \frac{distance}{time} [/tex]
[tex]s = \frac{d}{t} [/tex]
[tex]s = \frac{16}{4.5} [/tex]
[tex] = 3.5555555556[/tex]
[tex] = 3.56m |hr[/tex]
therefore, the average speed of Stacy is 3.56 m/hr.
HELP! BRAINLIEST!
Which of the following represents vector w = 11i − 60j in trigonometric form?
w = 61❬sin 280.389°, cos 280.389°❭
w = 61❬cos 280.389°, sin 280.389°❭
w = 61❬cos 79.611°, sin 79.611°❭
w = 61❬sin 79.611°, cos 79.611°❭
Answer:
w = 61❬cos 280.389°, sin 280.389°❭
Step-by-step explanation:
The "trigonometric form" of a vector is ...
(magnitude)❬cos(angle), sin(angle)❭
This is sometimes abbreviated ...
magnitude cis(angle)
__
This form immediately eliminates choices A and D, as those have the trig functions reversed. The signs on the unit vectors i and j tell you the vector has a 4th-quadrant angle, so will be between 270° and 360°. Only answer choice B makes any sense.
w = 61❬cos 280.389°, sin 280.389°❭
_____
Additional comment
The angle is computed from ...
θ = arctan(y/x) = arctan(-60/11) = -79.611°
Expressed as a positive angle in the range [0, 360°), that will be ...
360° +(-79.611°) = 280.389°
__
The abbreviation "cis" is mentioned as an aid to remembering the (x, y) coordinates are the cosine and sine of the angle, in that order.
Which expression is equivalent to -7 + 5a ?
-2a
-12a
5a - 7
-5a + 7
Hey there!
-7 + 5a
We DO NOT have any LIKE TERMS so we can NOT do much to this equation
So, the one that seems about right would be: -5a + 7
Answer: -5a + 7 (Option D)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Name a diameter.
8
G
E
A
FG
С
CE
B.
AB
D
BO
Answer:
FG
Step-by-step explanation:
FG is the only line which goes straight across the circle through the centre
On an average day 1/40 of the students at Brown Middle School are absent during an outbreak of flu twice as many students are absent what fraction of students is this
sam has $37 to spend at a festival the price of admission is $10 and tickets to each attraction cost $0.75. how many tickets can he get
Answer:
37-10=27 then 27 / 0.75 = 36
Step-by-step explanation:
36 is your answer
A quadrilateral has two angles that measure 222° and 81°. The other two angles are in a ratio of 6:13. What are the measures of those two angles?
[tex]\sf\huge\underline{\star Solution:-}[/tex]
[tex]\rightarrow[/tex] Ratio of two angles are 6:13.
So, let the one angle be [tex]\sf{6x}[/tex] and another be [tex]\sf{13x.}[/tex]
As we know that,
Sum of all interior angles of a quadrilateral = [tex]\sf\pink{360°.}[/tex]
So let's sum up the given angles,
[tex]\rightarrow[/tex] [tex]\sf{222°+81°+6x+13x \:=\: 360°}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{303+19x \:=\: 360°}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 360-303}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{19x \:=\: 57}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{x \:=\: \frac{19}{57}}[/tex]
[tex]\rightarrow[/tex] [tex]\sf{x \:=\: 3}[/tex]
Hence, [tex]\sf{x \:=\: 3}[/tex]
So, First angle [tex]\sf{= \:6x\: = \:6×3 \:=}[/tex] [tex]\sf\purple{18°.}[/tex]
Second angle [tex]\sf{= \:13x\: = \:13×3 \:=}[/tex] [tex]\sf\purple{39°.}[/tex]
_________________________________
Hope it helps you:)
A parallelogram has one angle that measures 125°. What are the measures of the other three angles in the parallelogram?
Answer:
the other 3 sides are 125,55 and 55 - hope this helped :)
Step-by-step explanation:
side 1 = 125
side 2 = 125
side 3 and 4 = ?
360 - 250 = 110
110/2 = 55
side 3 and 4 = 55
Help! Khan academy geometry practice
if you invest 1500 today in a bank that gives you 5% annual interest eats, which of these items can you buy in two years
Which statement is true?
A. |-2.5| >|-3|
B. |-2.5| <|-3|
C. |-2.5| = |-3|
Answer:
A. |-2.5| >|-3|
Step-by-step explanation:
Which is a larger volume, a candle with a height of 6. 3 inches and a radius of 3. 1 inches, or a candle with both a height and a radius of 3. 9 inches?
Step-by-step explanation:
such candles are cylinders.
the volume of a cylinder is
pi×r²×height
the volume of candle 1 is
pi×3.1²×6.3 in³ = pi × 60.543 in³
the volume of candle 2 is
pi×3.9²×3.9 in³ = pi × 59.319 in³
so, candle 1 has the larger volume.
i dont know this and i think its going to be in our FSA please help THANK YOU.....
Answer:
You never put a screenshot
Step-by-step explanation:
Pls put screenshot :)
Matt wants to start zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint? Use specific numbers from the situation to justify or refute whether Matt’s design meets the slope constraint
There is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
We know the slope can be evaluated using:
[tex]\rm Slope = \frac{Change \ in \ y \ axis}{Change \ in \ x \ axis}[/tex]
Change in y-axis = difference in height
Change in y-axis = 16 - 10
= 10 feet
Change in x-axis = distance between tress
Since the data is not given.
So, the height difference is insufficient to keep the slope constraint.
Thus, there is no difference in height that is not sufficient to meet the slope constraint if Matt wants to start a zip line 16 feet high in one tree and end 10 feet high in the other tree is the difference in height sufficient to meet the slope constraint.
Learn more about the slope here:
https://brainly.com/question/3605446
#SPJ1
round 256.709 to the nearest tenth place
Answer: 256.7
Step-by-step explanation: the tenth place, (7) is rounded to 7 because when you round the number after the tenth place (7) the number has to be at 5 or greater inorder to change values.
Please help me find the angles marked in the above diagrams The first figure is 8cm,5cm
2. 8m,15m
3. 8.4m,6.3m
4. 105m,123m
Due yesterday
Even if ur sure its correct j send it, ill turn in anything
Answer:
A)8000
B) 1296a^4
C) 9x^2
D)100000000
E)0.00097656
F)x^⁶
G)y^11
Step-by-step explanation:
find the lateral area and surface area of each prism. please show your work.
[tex]\stackrel{\textit{\Large Lateral Area}}{\stackrel{\textit{area of the 6 sides}}{6(12)(15)}\implies 1080} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap~~ \begin{cases} a=apothem\\ p=perimeter\\[-0.5em] \hrulefill\\ p=\stackrel{6\times 12}{72}\\ a=10.39 \end{cases}\implies A=\cfrac{1}{2}(10.39)(72)\implies 374.04 \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{\Large Areas}}{\stackrel{lateral}{1080}~~ + ~~\stackrel{two~hexagons}{2(374.04)}}\implies 1828.08\qquad \leftarrow \textit{total surface area}[/tex]