Answers
Answer:
[tex]\textsf{C)}\quad g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
Vertex = (8, -8)
Step-by-step explanation:
Standard form: [tex]y=ax^2+bx+c[/tex]
Vertex form: [tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex
Intercept form: [tex]y=a(x-p)(x-q)[/tex]
where p and q are the x-intercepts
Therefore, the form that most quickly reveals the vertex is
[tex]g(x)=\dfrac{1}{2}(x-8)^2-8[/tex]
The vertex is (8, -8)
Related Questions
please help me solve this
Answers
[tex]~~~~~\sin 30^{\circ} = \dfrac{x}{6}\\\\\implies \dfrac 12 = \dfrac x6\\\\\implies x = \dfrac 62 \\\\\implies x= 3.0~ \text{cm}[/tex]
[tex]\huge\underline\mathcal{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]
The question can be easily solved applying trigonometry ~
We know that ,
[tex]\bold{ \sin(\theta) = \frac{perpendicular}{hypotenuse}} \\ [/tex]
Given - θ = 30° and hypotenuse = 6cmTo find - the perpendicular , i.e. , value of xSubstituting the values in the formula of sin θ
[tex] \sin(30\degree) = \frac{x}{6} \\ [/tex]
now , we know that sin 30° = 1/2
[tex]\therefore \: \implies \frac{1}{2} = \frac{x}{6} \\ [/tex]
on cross multiplying ,
[tex]\implies \: 2x = 6 \\ [/tex]
dividing both sides of the equation by 2 ,
[tex] \implies \: \cancel \frac{2x}{2} = \cancel\frac{6}{2} \\ \\ \implies \: \boxed{x = 3 \: cm}[/tex]
hope helpful ~
Desmond opened a savings account and deposited $600.00 as principal. The account earns
6% interest, compounded annually. What is the balance after 6 years?
Use the formula A = P(1+r/n)^nt
where A is the balance (final amount), P is the principal
(starting amount), r is the interest rate expressed as a decimal, n is the number of times per
year that the interest is compounded, and t is the time in years. Round your answer to the nearest cent.
Answers
Answer:
$826.28
Step-by-step explanation:
Given:
[tex]P = 600[/tex]
[tex]r = 6% or 0.06[/tex]% or [tex]0.06[/tex]
[tex]t = 6[/tex]
Work:
[tex]A=Pe^{rt}[/tex]
[tex]A=600e^{0.06*6}[/tex]
[tex]A=600e^{0.36}[/tex]
[tex]A=826.28[/tex]
Therefore, the balance after 6 year is 826.28.
There are 6 options on the dessert menu at a restaurant. Akira and Paula like all of the choices equally, so they each choose a dessert at random from the menu. What is the probability that Akira will choose apple pie and Paula will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
Answers
Answer:
1/6 = 0.17 Step-by-step explanation:
Find the sum of the first 8 terms of the geometric sequence that begins: 12, 18, 27, ...
Answers
Answer:
times it bye 1.5 to get the next 8 terms
Step-by-step explanation: divide them all so 27.18 and 18/12 that will give you the same two answers thats what you times bye to get the next terms
Two men walk at rates of 6 miles per hour and 10 miles per hour, respectively. Simultaneously, they started from the same place walking in opposite directions. In how many hours will they be 200 miles apart?
Answers
The time taken by the two men will be equal to 26 hours
What is speed?The speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance.
here two men are walking at different speeds like
v₁=6 miles per hour
v₂=10 miles per hour
The time taken by them to separated by the distance of 100 miles each so that both of them separated by the distance of 200 miles.
t₁= {100}/{6}=16.66 hours
t₂= {100}/{10}=10 hours
total time taken will be
t₁+t₂=16.66+10=26.66 hours
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Find the surface area and the volume of the cylinder below.
Answers
Answer:
70
Step-by-step explanation:
10x7=70. basically, bxh base 10 height 7
Volume is 549.78cm^3
The table below shows the different times it takes paula to drive to her grandmother’s house depending on the rate at which she drives. rate vs. time rate (mph) 30 40 50 60 time (h) 2.5 1.875 1.5 1.25 if one day paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, how long should it take her? 2.625 hours 2.75 hours 3.125 hours 3.75 hours
Answers
Paula will take 3.125 hours to reach the grandmother's house if the constant rate of the scooter is 24 miles per hour, option third is correct.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
Let's suppose the distance between Paula's home to her grandmother's house is x miles
Then x = 30×2.5 (Distance = speed×time)
x = 75 miles
If one day, Paula rides a scooter to her grandmother’s house at a constant rate of 24 miles per hour, the time she takes:
= 75/24
= 3.125 hours
Thus, Paula will take 3.125 hours to reach the grandmother's house if the constant rate of the scooter is 24 miles per hour, option third is correct.
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Answer:
c
Step-by-step explanation:
What is the surface area of the composite solid? a rectangular prism with a length of 2 meters, width of 8 meters, and height of 2 meters. a rectangular prism with a length of 2 meters, with of 3 meters, and height of 11 meters. 119 m2 146 m2 162 m2 174 m2
Answers
Using the formula for the surface area of a rectangular prism, the surface area of the composite solid is: C. 162m²
What is the Surface Area of a Rectangular Prism?Surface area of a rectangular prism = 2(wl+hl+hw)
Surface area of the composite shape = surface area of the larger prism + surface area of the smaller prism - area of the face both prisms are joined together
Surface area of the larger prism = 2(wl+hl+hw) = 2(2×3 + 9×3 + 9×2) = 102 m²
Surface area of the smaller prism = 2(wl+hl+hw) = 2(2×8 + 2×8 + 2×2) = 72 m²
Area of the face both prisms are joined together = 2(l×w) = 2(3 × 2) = 6 m²
Surface area of the composite shape = (102 + 72) - 12 = 162m²
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Answer:
its c
Step-by-step explanation:
i took the test
Find the area of the irregular figure.
4 in.
6 in.
A = [? ]in.²
10 in.
7 in.
11 in.
6 in.
Answers
Answer:
160 square inches
Step-by-step explanation:
You can split the irregular figure up into regular shapes:
the top 4x6 inch rectangle
the middle section can be a 18x6 rectangle (added 7+11 for the length)
the bottom 4x7 rectangle (sibtracted 10-6 for the width)
Then, find the area of each section with the equation A = lw.
A= 4(6) = 24 square inches
A = 18(6) = 108 square inches
A = 4(7) = 28 square inches
Add these areas up to get the total area of the irregular figure.
24 + 108 + 28 = 160 square inches
Please help me!!? Number 6
Answers
Answer:
the b believes in me
Step-by-step explanation:
B)75km etc
1hr
[tex]\frac{75 \text{ km}}{1 \text{ hr}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}}[/tex]
========================================================
Explanation:
We'll use the following facts (either memorized or written on a reference sheet somewhere)
1000 m = 1 km1 hr = 60 min1 min = 60 secEach of those equations will form conversion factors to help us go from km/hr to m/s. Each conversion factor is a fraction connecting the two sides of the equation. Example: The equation 1000 m = 1 km forms the conversion factor of [tex]\frac{1000 \text{ m}}{1 \text{ km}}[/tex]
In choice B, notice how the fractions are set up. The "km" units cancel when dividing. The same goes for the "hr" and "min" units.
Check out the screenshot below where I show this cancellation in action. The color-coding helps show how the terms pair up and cancel.
Choice A comes close to what choice B is saying, but we don't have the "min" units cancel. So choice A is eliminated as an answer.
Choices C and D are also eliminated because of the "75 km" in the denominator. It should be 1 km.
Ms. Lewis is hiring a carpenter to repair her shed. The cost of Carpenter L is shown in the table.
A table titled Carpenter L Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred eighty-seven dollars. Two hours, two hundred fifty-nine dollars. Three hours, three hundred thirty-one dollars.
Part A. What is the initial cost and hourly rate of Carpenter L?
Part B. Write an equation to represent the function shown in the table.
Part C. Carpenter N charges $60 per hour and an additional $195 for the materials needed. What is the difference in cost between Carpenter N and Carpenter L if the repair takes 6 hours?
Enter the correct answers in the boxes.
Answers
Answer:
A. $115; $72/hour
B. c = 72h + 115
C. $8
Step-by-step explanation:
Part A.
1 hour: $187
2 hours: $259
2 hours - 1 hour = 1 hour
$259 - $187 = $72
$72/hour
The hourly rate is $72/hour.
Since for the first hour he charges $187, and only $72 comes from the hourly rate, then the initial cost is $187 - $72 = $115.
The initial cost is $115.
Part B.
c = 72h + 115
Part C.
Carpenter L for 6 hours:
c = 72(6) + 115 = 547
$547
Carpenter N for 6 hours:
60(6) + 195 = 555
$555
Difference: $555 - $547 = $8
what is the anwer to 81 = 27x-4
Answers
Answer: x= [tex]\frac{85}{27}[/tex]=x
Step-by-step explanation:
1. Add 44 to both sides.
81+4=27x
2. Simplify 81+4 to 85.
85=27x
3. Divide both sides by 27.
[tex]\frac{85}{27}[/tex]=x
4. Switch sides.
X= [tex]\frac{85}{27}[/tex]
Decimal form: 3.148148
A right triangle has legs of 21 inches and 28 inches whose sides are changing. The
short leg is decreasing by 7 in/sec and the long leg is shrinking at 7 in/sec. What is
the rate of change of the hypotenuse?
Answers
Using the Pythagorean Theorem, it is found that the rate of change of the hypotenuse is of -9.8 in/sec.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
Applying implicit differentiation, the rate of change of the hypotenuse is given by:
[tex]2h\frac{dh}{dt} = 2l_1\frac{dl_1}{dt} + 2l_2\frac{dl_2}{dt}[/tex]
[tex]h\frac{dh}{dt} = l_1\frac{dl_1}{dt} + l_2\frac{dl_2}{dt}[/tex]
In this problem, we have that the parameters are given as follows:
[tex]l_1 = 21, \frac{dl_1}{dt} = -7, l_2 = 28, \frac{dl_2}{dt} = -7[/tex]
[tex]h = \sqrt{l_1^2 + l_2^2} = \sqrt{21^2 + 28^2} = 35[/tex]
Hence, the rate of change of the hypotenuse, in inches per second, is given by:
[tex]h\frac{dh}{dt} = l_1\frac{dl_1}{dt} + l_2\frac{dl_2}{dt}[/tex]
[tex]35\frac{dh}{dt} = 21(-7) + 28(-7)[/tex]
[tex]\frac{dh}{dt} = \frac{21(-7) + 28(-7)}{35}[/tex]
[tex]\frac{dh}{dt} = -9.8[/tex]
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Need to know this asap number 6 and 7
Answers
The equation that does not assign one value to y is [tex]\frac 5y = 7x + \frac{10}{2y}[/tex] and the points that do not represent a function is (c)
The equation that does not assign one value to yTo do this, we simply make y the subject of formula.
So, we have:
[tex]\frac 5y = 7x + \frac{10}{2y}[/tex]
Simplify
[tex]\frac 5y = 7x + \frac{5}{y}[/tex]
Subtract 5/y from both sides
[tex]0 = 7x[/tex]
Rewrite as:
[tex]x = 0[/tex]
This means that the value of x is 0 irrespective of the value of y
Hence, the equation that does not assign one value to y is [tex]\frac 5y = 7x + \frac{10}{2y}[/tex]
The points that do not represent a functionFor a set of point to represent a function, the points must represent a one-to-one or many-to-one relationship.
From the list of options, option (3) represents a one-to-many relationship.
This is so because one x value has 3 y values
Hence, the points that do not represent a function is (c)
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if this is a perfect square trinomial factor it
A: (x-6)^2
B: (x+6)^2
C: (x(6)(x-12)
D: it's not a perfect square trinomial
Answers
Answer:
Option B: [tex](x + 6)^2[/tex]
Step-by-step explanation:
Hello!
We can simply expand each option to find which one matches the trinomial [tex]x^2 +12x + 36[/tex]
A: (x - 6)²(x - 6)(x - 6)x² - 6x - 6x + 36x² - 12x + 36It does not match.
B:(x + 6)²(x + 6)(x + 6)x² + 6x + 6x + 36x² + 12x + 36Option B matches, so it is the right solution.
An aquarium in a restaurant is a rectangular prism and measures 3.5 feet by 4 feet by 3 feet. What is the volume of the aquarium?
A) 42 cubic feet
B) 15.5 cubic feet
C) 36 cubic feet
D) 10.5 cubic feet
Answers
The elevator at the local mall has a weight limit of 1,800 pounds and requires that the maximum person allowance be no more than nine people. let represent the number of people. write an inequality to describe the maximum allowance of people allowed in the elevator at one time.
Answers
Answer: 9? I’m not sure but it seems like it’s 9 as it mentions it in the problem
Factor completely.
Show all work.
a) ²−7−18
b) 2²−26+24
c) 10²+37+7
d) ²−25
e) 42−4+1.
f) 144²−36
Answers
Answer: First find the GCF ( greatest Common Factor):-
GCF of 16, 24 and 48 is 8
GCF of the x terms is x^3
GCF of the y terms is y^4
So GCF is 8x^3y^4
Factoring:-
= 8x^3y^4 ( 2x^6y^4 - 16x^2y^2 + 3) answer
Step-by-step explanation:
NEED HELP WITH THIS!!!you survey your fellow algebra students and find out how many assignments they have copied from online sources and their score in their final exam. You find a correlation coefficient of -.089. How accurate will your predictions be with future students and why. Also, what does a negative correlation coefficient mean in terms of the relationship between how many assignments students have cheated on and their final exam score?
Answers
Answer:
Not very. The closer the value of your correlation coefficient is to 0, the weaker the correlation. Here, our correlation coefficient is only 0.089 away from 0 - in other words, there's not much correlation in the number of plagiarized assignments and the score on their final exam. If you were to plot this data on a graph, it would look like a pretty sparse "blob" of dots, where with a higher correlation, we'd expect a tighter grouping around the line of best fit. See the illustration for an example of strong/weak correlation in both negative and positive directions.
The sign of our correlation coefficient is negative, which means that generally, for what weak correlation we have, the score on the final exam goes down as the number of copied assignments go up. This makes sense - the more assignments you copy, the less you tend to retain.
A can of vegetables with no label has a 1/8 chance of being green beans, and a
1/5 chance of being corn. What is the probability the can is green beans or
corn?
Answers
Answer:
13/40.
Step-by-step explanation:
We add the probability in this case.
So it is 1/5 + 1/8
= 8/40 + 5/40
= 13/40.
4 - 5 5g > 39
What is the solution set for the inequality?
Answers
Answer:
g < -7
Step-by-step explanation:
Check image below
Avani is trying to find the height of a radio antenna on the roof of a local building. She stands at a horizontal distance of 21 meters from the building. The angle of elevation from her eyes to the roof ((point AA)) is 27^{\circ} ∘ , and the angle of elevation from her eyes to the top of the antenna ((point BB)) is 37^{\circ} ∘ . If her eyes are 1.54 meters from the ground, find the height of the antenna ((the distance from point AA to point BB)). Round your answer to the nearest tenth of a meter if necessary.
The answer is 5.1.
Answers
Answer:
Avani is the tiktoker everyone adores. however 49499 +4939+ 4969 is not the answer your looking for you. you have to subtract 39 from 129 to get the exact meters. and round it to the nearest tenth.
Step-by-step explanation:
4 kg of bananas and 3 kg of apples cost £7.50. 3kg of bananas and 5 kg of apples cost £8.10. work out how much 2kg of bananas and 2kg of apples cost
Answers
Answer:
£4.20
Step-by-step explanation:
Let :
cost of 1 kg banana = xcost of 1 kg apple = yEquations formed :
4x + 3y = 7.50 [Equation 1]3x + 5y = 8.10 [Equation 2]Multiply Equation 1 by 5 and Equation 2 by 3 :
20x + 15y = 37.509x + 15y = 24.30Subtract the newly formed equations :
11x = 13.20x = 1.20Finding y :
4(1.20) + 3y = 7.504.80 + 3y = 7.503y = 2.70y = 0.90Then :
Cost of 1 kg banana = £1.20Cost of 1 kg apple = £0.90Cost of 2 kg bananas and 2 kg of apples :
2(1.20) + 2(0.90)2(2.10)£4.20Please help me with this. Brainliest for right answer
Answers
Answer:
40
Step-by-step explanation:
This is part of Ivan's homework. A line segment, AB, goes from the point A(4, 7) to the point B(9, 3). AB is translated 3 squares left and 2 squares down. The image of AB is AB. Work out the coordinates of A' and B. Solution A' is at (7, 5). B' is at (12, 1). Ivan has worked out the coordinates of A' and B' incorrectly.
Explain the mistake that he has made.
Answers
Ivan mixed up left and right.
He mistakenly added 3 to the x coordinate to shift the points 3 units right, when instead he should have subtracted 3 from the x coordinate to go 3 units left.
Luckily, Ivan correctly shifted the points 2 units down.
The coordinates of A' and B' should be (1,5) and (6,1) respectively.
Refer to the diagram below.
if sally drives to work 25% faster than she did yesterday, what would be her
percentage decrease in the time it takes her to get to work
Answers
Answer:
50 percent
Step-by-step explanation:
because sally was tried yesterday and went 25 percent faster today.
there are 18 sweets in a packet. 8 of the sweets are mint what fraction of the sweets are not mint
Answers
Answer:
10/18 of the sweets are not mint
you can also simplify this fraction and say 5/9
Given that a/b = 3/5 and b/c = 4/5
Find a:b:c
Answers
Answer:
12:20:25
I thnk this is it. I'm not sure though
ANOTHER QUESTION! please help! will make branliest
Answers
Answer: Total: 10 3/4
Step-by-step explanation:
I need a answer for this:
What causes a wagon to speed up when going down a hill?
Answers
Answer:
supermax makes it go fast
Step-by-step explanation: