Answers
Step-by-step explanation:
Standard form:
y = ax² + bx + cVertex form:
y = (x - h)² + kIdentity used:
(a ± b)² = a² ± 2ab + b²6 - 7)
Standard to vertex form conversion by completing the square
y = x² - 3x + 16
= x² - 2*1*3/2 + (3/2)² - (3/2)² + 16
= (x - 3/2)² - 9/4 + 16 =
= (x - 1.5)² + 13.75
8 - 9)
Same as above
y = x² - 2x + 3
= x² - 2*1*x + 1² - 1² + 3
= (x - 1)² + 2
10 - 12)
Vertex to standard for conversion by opening parenthesis and simplification
y = (x - 11)² + 15
= x² - 22x + 121 + 15
= x² - 22x + 136
13-15)
Same as above
y = (x - 4)² + 11
= x² - 8x + 16 + 11
= x² = 8x + 27
Related Questions
Can someone please show me their working on these on how to work out?
Answers
To rationalize essentially means to get rid of the radical.
The trick to all of these it to multiply the top and bottom by a radical that will turn the radical you have into the square root of a perfect square.
Part a: [tex]\dfrac{1}{2\sqrt{5}}[/tex]
One approach that will always work, but not be the smallest radical, is to just multiply by the radical that is already there.
In the case of [tex]\dfrac{1}{2\sqrt{5}}[/tex], you can multiply the top and bottom by [tex]\sqrt{5}[/tex], so you'll really do this:
[tex]\dfrac{1}{2\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}} = \dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}}[/tex]
But in the bottom, [tex]\sqrt{5}\cdot\sqrt{5} = \sqrt{25}=5[/tex], so your work finishes out like this:
[tex]\dfrac{1\cdot\sqrt{5}}{2\sqrt{5}\sqrt{5}} = \dfrac{\sqrt{5}}{2\sqrt{25}} = \dfrac{\sqrt{5}}{2\cdot5} = \dfrac{\sqrt{5}}{10}[/tex]
Part b: [tex]\dfrac{4}{5\sqrt{2}}[/tex]
In the case of [tex]\dfrac{4}{5\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], so you'll really do this:
[tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:
[tex]\dfrac{4}{5\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{5\sqrt{4}}=\dfrac{4\sqrt{2}}{5\cdot{2}}=\dfrac{4\sqrt{2}}{10}[/tex]
Sometimes the fraction can be reduced, so this should be reduced to [tex]\dfrac{2\sqrt{2}}{5}[/tex].
Looking at all the others, they'll follow this same approach and they will all reduce at the end.
Here's part c, for one more example.
Part c: [tex]\dfrac{3}{3\sqrt{2}}[/tex]
In the case of [tex]\dfrac{3}{3\sqrt{2}}[/tex], you can multiply the top and bottom by [tex]\sqrt{2}[/tex], but you should also reduce the initial fraction first.
[tex]\dfrac{3}{3\sqrt{2}} = \dfrac{1}{1\cdot\sqrt{2}} = \dfrac{1}{\sqrt{2}}[/tex]
And now proceed with rationalizing:
[tex]\dfrac{1}{\sqrt{2}} \cdot\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
But in the bottom, [tex]\sqrt{2}\cdot\sqrt{2} = \sqrt{4}=2[/tex], so your work finishes out like this:
[tex]\dfrac{1}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}} = \dfrac{1\cdot\sqrt{2}}{\sqrt{4}}=\dfrac{\sqrt{2}}{{2}}[/tex]
And you're done.
Hopefully that helps you finish the rest of those.
To check your answers, here is the answer key for the rest:
part d:[tex]\dfrac{2\sqrt{6}}{5}[/tex]
part e:[tex]\dfrac{4\sqrt{2}}{3}[/tex]
part f:[tex]\dfrac{4\sqrt{5}}{7}[/tex]
part g:[tex]\dfrac{5\sqrt{10}}{3}[/tex]
part d:[tex]\dfrac{5\sqrt{2}}{3}[/tex]
Answer:
Step-by-step explanation:
(a) 1/(2 sqrt5) x (sqrt 5)/(sqrt5) = (sqrt 5)/10
(b) 4/(5bsqrt2) x (sqrt2)/(sqrt2) = (4sqrt2)/10 = (2sqrt2)/5
(c) 3/(3 sqrt2) x (sqrt2)/(sqrt2) =(sqrt2)/2
(d) 12 /(5 sqrt6) x (sqrt6)/(sqrt6) = (12sqrt6)/30 = (2sqrt6)5
(e) 8/(3 sqrt2) x (sqrt2)/(sqrt2) = (8 sqrt2)/6 = (4 sqrt2)/3
(f) 20/(7 sqrt5) x (sqrt5)/(sqrt5) = (20 sqrt5)/35 = (4 sqrt5)/7
(g) 50/(3 sqrt10) x (sqrt10)(sqrt10) = (50 sqrt10)/30 = (5sqrt10)/3
(h) 10/(3 sqrt2) x (sqrt2)/(sqrt2) = (10 sqrt2)6 = (5 sqrt2)/3
100 POINTS IF YOU ANSWER ALL OF THESE AND NO LINKS!
Answers
Answer:
divide 8/3
8/3 = 2
and for -11/3 it = -4 because it would originally = to -3.66666666667 and u have to round it.
----------------------------------
for the second picture
make it into an improper fraction
-2 1/2 = -5/2
and for 6 1/2 it = to 13/2
now, to plot it on the line you have to divide
divide -5/2 = -2.5
and divide 13/2 = 6.5
------------------------------------
Hope this helps!
Which of the following is true when constructing a line graph?
Each axis has even spacing.
Each point represents a data pair.
The vertical axis shows increments of time.
The scale starts at the minimum value and goes to the maximum value. please help fast!!!!
Answers
Answer:
B
Step-by-step explanation:
Answer:
Each axis has even spacing.
Each point represents a data pair.
I took the test
Subtract.
3−(−5)−(−2)
Plot the solution on the number line.
Answers
Answer:
10
Step-by-step explanation:
Answer: Its 10, so plot it on 10 in the number line
Step-by-step explanation: Since the subtraction signs cancel out, they make a addition sign. Henceforth its " 3+5+2" which would mean the sum is 10.
which is equivalent to 2 5/6?
A. 5/3
B. 12/5
C. 7/6
D. 17/6
(IF YOU ARE ABLE TO, PLEASE PROVIDE AN EXPLANATION FOR THE ANSWER)
Answers
what is the answer for 4|x+7|=16
Answers
Answer:
-3
Step-by-step explanation:
hope it helps
PLEASE NO ONE WILL HELP ME WITH THIS
Find a sequence of rotations, reflections, translations, and dilations showing that one figure is similar to the other.
BE SPECIFIC: give the amount and direction of a translation, a line of reflection, the center and angle of a rotation, and the cent and scale factor of a dilation.
Answers
Answer:
ABCD dilates in a scale of 1/3 by the center of A followed by a reflection of C.
AD/AD = 1/3
Step-by-step explanation:
La suma de cuatro números consecutivos es 938 cuál es el valor del número menor
Answers
De acuerdo con los cálculos realizados en el presente desarrollo, el valor del número menor es 233.
Dado que la suma de cuatro números consecutivos es 938, para determinar cuál es el valor del número menor se debe realizar el siguiente cálculo:
X + X + 1 + X + 2 + X + 3 = 9384X + 6 = 9384X = 938 - 6X = 932 / 4X = 233233 + 234 + 235 + 236 = 938Por lo tanto, el valor del número menor es 233.
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the population in a town is 10,000. The population is growing at a rate of 0.08. what will the population be in 10 years
Answers
Hope this helps have a nice day!!!!
Circle each input value. Underline each output value. 1. {(1, 1), (2, 3), (3,5)} 2. {(6,2), (5, 3), (4,8)}
Answers
Answer:
The first numbers in the sets are input and the second numbers are outputs.
1. {(1, 1), (2, 3), (3,5)}
Input = 1, 2, 3Output = 1, 3, 52. {(6,2), (5, 3), (4,8)}
Input = 6, 5, 4Output = 2, 3, 8La puntuación media de un examen final fue de 72 y la desviación típica de 9. El 10%
de los mejores alumnos recibió la calificación A. ¿Cuál es la puntuación mínima que
un estudiante debió tener para recibir un A?
Answers
Answer:
I don't know what to do sorry
Two cars leave the same point at the same time traveling in opposite directions. One car travels west at 20 mph and the other travels east at 60 mph. In how many hours will they be 280 miles apart?
Answers
9514 1404 393
Answer:
3.5 hours
Step-by-step explanation:
The separation distance is increasing at the rate of 20 mph + 60 mph = 80 mph. It will be 280 miles after ...
time = distance/rate
time = (280 mi)/(80 mi/h) = 3.5 h
The two cars will be 280 miles apart after 3 1/2 hours.
Refer to the rectangular prism
Answers
Answer:
Properties of a Rectangular Prism : A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal.
Step-by-step explanation:
Two gasoline stations along an expressway have six gas pumps each. An experiment involves determining how many pumps are in use at a particular time for each station. Describe S by listing the elements.
Answers
The sample space is used to prepare a list of all possible outcomes or element in an experiment. The sample space containing all elements attainable for the number of working pumps at a particular station is listed below :
Number of stations = 2 Number of pumps per station = 6Let the number of pumps in use at each station be listed on the row and column respectively :
P1/P2_0 _ 1__ 2 __ 3 __ 4 __ 5 __ 6
0__ 0,0 _0,1 _0,2 _0,3 __0,4_ 0,5_0,6
1__ 1,0 __1,1 _1,2 __1,3 __1,4 __1,5_ 1,6
2__2,0 _2,1 _2,2 _2,3 __2,4 __2,5_2,6
3__3,0_3,1 _3,2 _ 3,3 __3,4 __3,5 _3,6
4__4,0_4,1 _4,2 _ 4,3 __4,4 __ 4,5 _4,6
5__5,0_5,1 _5,2 _ 5,3 __5,4 __ 5,5 _5,6
6__6,0_6,1 _6,2 _ 6,3 __6,4 __ 6,5 _6,6
Therefore, all possible outcomes relating to the number of working pumps are available in the sample space created.
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Factor the following polynomial x^2-9
Answers
Answer:
(x+3)(x-3)
Step-by-step explanation:
We know that [tex](a+b)(a-b)=a^2+b^2\\[/tex]
So, here we have x² and 9, which can be written as 3².
Therefore, we can have x=a and 3=b
So we get
(x+3)(x-3)
To check that we are correct, we can expand the brackets:
x²-3x+3x-9
=x²-9
solve for x and y in the following equation.
2x - 3y = 9.......(I)
2x + y = 13.......(ii)
x + 7y = 10.......(I)
3x - 2y = 7.......(ii)
5x + y = 10.......(I)
7x - 3y = 14......(ii)
Answers
Answer:
just rearrange the equation. I did the first one. Do the same for the rest.
2x - 3y = 9
-3y = -2x + 9
y = -2/-3x + 9/-3
y = 2/3x - 3
Step-by-step explanation:
PLEASE HELP! I Would appreciate it
Answers
Long answer: So this question is a probability problem, so we take the number we’re looking for and divide it by the whole. Which in this case would be 285/980 Getting us 0.290816326530612 which can be rounded to 0.2908, or in percentage form %29.0816.
Please mark brainliest
Write the equation of the line parallel to y=6 that passes through the point (2, -3). Write your answer in slope-intercept form.
Answers
Answer:
Y=-3
You see y=-3 does pass through 2,3 and is also parallel to y=6
State if the triangle are congruent by sss sas asa aas or not congruent
Answers
Answer:
(a) SSS
................................
P(x) = 4x3 + 5x + 9, D(x) = 2x + 1
Two polynomials P and D are given. Use either synthetic or long division to divide
P(x)
by
D(x),
and express P in the form
P(x) = D(x) · Q(x) + R(x)
Answers
Suzy can type 85 words in 2 minutes. How many minutes will it take her to type her to type 500 word paper?
Answers
Answer:
11,765
Step-by-step explanation: 1 word make up 0,024 minute so 500 words 500.0,024 = 11,765 minutes
Solve.
34.2 = 13.4 + 9.6x
Enter your answer as a mixed number in simplest form in the box.
x =
Answers
34.2-13.4=9.6x
20.8=9.6x
X=20.8/9.6
X=2.167
(5x+4)-3x
Solve it.
No scam
Answers
Answer:
=2x+4
Step-by-step explanation:
Let's simplify step-by-step.
5x+4−3x
=5x+4+−3x
Combine Like Terms:
=5x+4+−3x
=(5x+−3x)+(4)
=2x+4
Answer:
2x+4...
Step-by-step explanation:
Hopefully it helps
Hey can you please help me
Answers
Answer:
dont understand
Step-by-step explanation:
Let
A
=
{
1
,
2
,
6
}
and B={x
|
x is an odd whole number less than 8},
Answers
Answer:
I think the answer is 1. The problem is unclear though
HELP WILL GIVE BRANLIEST
Answers
The two lines below are parallel. If the slope of the red line is 1, what is the
slope of the green line?
Answers
solve for w
6w+2=9w+14
Answers
Answer:
w = 4
Step-by-step explanation:
6w+2=9w+14
9w-6w=14-2
3w=12
w=12/3
w=4
Write the equation in the standard linear equation form (Ax+By=C) if possible. Is the equation linear? y/3+x=5
Answers
Answer:
3x + y = 15
Step-by-step explanation:
y/3 + x = 5
You can first move the x and y variable around so it fits the standard linear equation format.
x + y/3 = 5
In order to make it look more like the standard format, you can multiply both sides of the equation by 3 to get rid of the 3 in the denominator of the y variable. It would look like this:
3 ( x +y/3) = 3 ( 5 )
When you multiply this out, you get this:
3x + y = 15
each big square below represents one whole. what percent is represented by the shaded area?
Answers
Answer:
43%
Step-by-step explanation:
mark me as brainliest please
