Answers
The error is when she added 4 to both sides.
Instead, she should divide both sides by -4 to undo the multiplication. Specifically, the multiplication between the -4 term and the (x-2)^2 term.
This is one possible correction of what her steps could look like.
[tex]y = -4(x-2)^2\\\\\\0 = -4(x-2)^2\\\\\\\frac{0}{-4} = \frac{-4(x-2)^2}{-4}\\\\\\0 = (x-2)^2\\\\\\(x-2)^2 = 0\\\\\\\sqrt{(x-2)^2} = \sqrt{0}\\\\\\x-2 = 0\\\\\\x-2+2 = 0+2\\\\\\x = 2\\\\\\[/tex]
In the third step, I'm dividing both sides by -4. In the sixth step, I'm applying the square root to both sides to undo the squaring operation. Then two steps later, I'm adding 2 to both sides to undo the "-2", which helps fully isolate x.
The only solution is x = 2, so it's the only x intercept. You can verify this answer by plugging x = 2 back into the original equation at the very top. You should end up with y = 0.
Note: The term "root" is another name for "x intercept".
Related Questions
HELP ASAP
TYSM TYSM What is the surface area of the square pyramid?
I put a picture!
⬇️
Answers
Answer:
the surface area is 133cm.
7 x 7 is 49
7 x 6 is 42.
42 divided by 2 is 21.
21 x 4 is 84
So 84 + 49 is 133.
solve the inequality [tex]\frac{\sqrt{9-x} - |3x-4|}{\sqrt{x+2}-|3x-4|}\leq 1[/tex]
Answers
Find the expected value of the winnings from a game that has the following payout probability distribution:
Payout ($) 0 4 6 8 10
Probability .5 .2 .15 .1 .05
Answers
Answer:
3
Step-by-step explanation:
What is the area of the figure to the nearest tenth?
Answers
Answer:
93.8 in
Step-by-step explanation:
9, 7, 9, 8, 4, 5, 2,4
Mean__
Median__
Mode__
Range__
Answers
Answer:
Mean= Summation /number of terms
= 48/8
=6.
Median
To do this
arrange all terms from smallest to biggest
That is
2,4,4,5,7,8,9,9
The two middle numbers are
5 and 7.
To get the median
add both and divide by 2
5+7 = 12... 12/2 =6
Median=6
Mode.... This is the number that appears most
Mode = 4 and 9.(Bimodal) Both appear equally.
Range: Highest - Lowest
= 9-2 =7.
Answer:
mean = 6 median = 6 mode 9 and 4 range = 7
Step-by-step explanation:
mean = 2+4+4+5+7+8+9+9÷ 8 = 6
median = 5+7÷2
mode = 9 and 4
range = 9-2=7
The distance between D(-3,5) and E(x, 9) is 15. Find the value(s) of the
missing coordinate.
Answers
9514 1404 393
Answer:
x ≈ -17.457 or 11.457
Step-by-step explanation:
The distance formula can help.
d = √((x2 -x1)² +(y2 -y1)²)
Substituting given values, we have ...
15 = √((x -(-3))² +(9 -5)²)
225 = (x +3)² +16 . . . . . . . . square both sides
209 = (x +3)² . . . . . . . . . . . subtract 16
±√209 = x +3 . . . . . . . . . take the square root
-3 ± √209 = x . . . . . . . . subtract 3
x ≈ -17.457 or 11.457
A plane takes off from a runway given as the path with points A and B. Find the midpoint if point A is at (-1, 2) and point B is at (-2, -4)
Answers
Answer:
a
Step-by-step explanation:
Answer:
(-1.5, -1)
Step-by-step explanation:
Here, you would essentially find the respective means of the x and y coordinates.
For x:
(-1 + (-2)) = -3
[tex]\frac{-3}{2}[/tex] = -1.5
For y:
(-4 + 2) = -2
[tex]\frac{-2}{2} \\[/tex] = -1
Thus, the midpoint would be (-1.5, -1)
HELP!!! I WILL MARK BRAINLEST!
Answers
you take 4•.25 and 8•.25
you get (1, 2)
Help!!
What is the slope of the line?
Answers
Answer:
2
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Slope = Change in y over change in x
Looking at the graph, as y goes up 4 x goes up 2
Thus, slope = 4/2 or 2
A survey found that 52% of middle school students needed extra help in class.
If a total of 300 students took the survey, how many students said they
needed extra help in class?
There were
students that said they needed extra help in class.
Answers
Answer:
Your answer is 156
Step-by-step explanation:
300*.52=156
Solve each equation using the substitution method.
8+=56
Answers
Answer:
I think u got yr question incomplete
there is no any equation
stay safe healthy and happy.Explanation: X=56
can someone explain the full answers
Answers
A) 2x+5=9 then if x=1
2+5=9 which is wrong then A is wrong
B) x=2
2×2+5=9
4+5=9
then B is correct
C) x=3
2×3+5=9
6+5=9
then C is wrong
D) 2x+5<9
2×1+5<9
2+5<9
7<9
D is correct
E)x=2
2×2+5<9
4+5<9
9<9
E is wrong
F) x=3
2×3+5<9
6+5<9
11<9
F is wrong
Hey please help me please help please
Help help please
1. What operation would you perform to express a measure given in the first unit as a measure in the second unit?
a) metres to centimetres _________________________
b) metres to millimetres __________________________
c) kilograms to grams ____________________________
d) litres to millilitres
2. Will each number be larger or smaller than the given number? Then fill in the blank.
larger smaller a) 3 m = ________ cm
larger smaller b) 28 cm = _________mm
larger smaller c) 2.4 km = _________m
larger smaller d) 485 mm = _________cm
larger smaller e) 35 cm = ____________m
larger smaller f) 2.4 m = _____________km
larger smaller g) 2495 mm = __________m
Answers
1.
a) metres to centimetres :
multiply length by 100
b) metres to millimetres:
multiply length by 1000
c) kilograms to grams:
multiply the mass value by 1000
d) litres to millilitres :
multiply volume by 1000
2.
a) 3 m = 3× 100 = 300 cm
b) 28 cm = 28 × 10 = 280 mm
c) 2.4 km = 2.4 × 1000
= 24 × 10^-1 × 10^3
= 24 × 10^2 =2400 m
d) 485 mm =485 / 10
= 485 / 10 ^1
= 485 × 10 ^-1
= 48.5 cm
e) 35 cm = 35 / 100
= 35 /10^2
= 35 × 10 ^ -2
= 0.35 m
f) 2.4 m = 2.4 / 1000
= 24 × 10 ^-1 / 10^3
= 24 × 10^-1 × 10 ^-3
= 24 × 10 ^ -4
= 0.0024 km
g) 2495 mm = 2495 /1000
= 2495 /10^ 3
= 2495 × 10 ^-3
=2.495 m
Simplify (4x - 6) + (3x + 6)
Answers
4x-6+3x+6
4x+3x
7x
Answer:
The simplified form would be 7x.
Step-by-step explanation:
(4x - 6) + (3x + 6)
4x - 6 + 3x + 6
4x + 3x -6 + 6
4x + 3x
= 7x
Decide whether the sequence is arithmetic, type yes or no. If so, find the common difference.
4,7, 10, 13, 16, ....
Answers
Answer:
arithmetic sequence
Step-by-step explanation:
There is a common difference between consecutive terms , that is
d = 7 - 4 = 10 - 7 = 13 - 10 = 16 - 13 = 3
This indicates the sequence is arithmetic with common difference d = 3
If the hypotenuse is 20 and one of the legs is 12, what is the length of the missing leg?
Answers
Answer: 16
Step-by-step explanation:
6 1/2 = 1 1/4 + n. Which statements are correct. Check all that apply.
Answers
Answer:
n = 5.25
Step-by-step explanation:
6.5 = 1.25 + n
6.5 - 1.25 = 1.25 - 1.25
5.25 = n
Calculation: 2/3 - 1/2 - fraction calculator. The result is 1/6 ≅ 0.1666667 = onesixth. ... Solve problems with two, three, or more fractions and numbers in one ... From a 1 meter ribbon, Ericka cut 2/4 meter for her hat and another 1/4 meter for ...
brainliest and 50 extra points
Answers
Answer:
The sunflower is doing this because it is following the direction of the sun, which is a key factor in photosynthesis.
Step-by-step explanation:
Answer:
a sunflower bends down to East in morning because the sun rises in east. all flowers grows towards the light of the sun. during 12 noon sun is middle of east and west so its growing towards the light at straight way. during 4 o' clock in afternoon became sun goes down to west so the sunflower bends down to the light.
A grocery store sells avocados for $2.35 per pound how much would it cost to buy 7.4 pounds of avocados from this store
Answers
Answer: cost to buy 7.4 pounds of avocados from this store=$17.39
Step-by-step explanation:
Sale of avocados per pound in the grocery= $2.35
Sale of 7.4 pounds of avocados= $2.35 x 7.4 pounds =$17.39
Therefore, the cost to buy 7.4 pounds of avocados from this store=$17.39
Please explain how. Thanks in advance
Answers
Answer:
A kite has only 1 pair of opposite congruent sides, whereas a parallelogram has 2 pairs of opposite congruent sides
Hope this helps!
what does coplanar mean ?
Brainliest
Answers
—Examples—
•] three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique.
Marking brainliest
Use human rights as a sentence
Don’t use the internet pls!!
Answers
Answer:
the human right movement was leaded by my father who if very good at his job
Step-by-step explanation:
Kenny'sofficehadalreadyrecycled29kilogramsthisyearbeforestartingthenewrecyclingplan,andthenewplanwillhavetheofficerecycling1kilogramofpapereachweek.HowmanyweekswillittakeKenny'sofficetorecycleatotalof43kilogramsofpaper?
Answers
Answer:
hi people of the 21 century
Step-by-step explanation:
HOW TO DO THIS QUESTION
Answers
Answer:
see explanation
Step-by-step explanation:
The dot above the 5 indicates the 5 is repeating , that is
2.7555...
We require 2 equations with the repeating 5 placed after the decimal point.
let x = 2.7555,,, ( multiply both sides by 10 and 100 )
10x = 27.55... → (1)
100x = 275.55... → (2)
Subtract (1) from (2), thus eliminating the repeating 5
90x = 248 ( divide both sides by 90 )
x = [tex]\frac{248}{90}[/tex] = [tex]\frac{124}{45}[/tex]
What is 8x-2y=6 is slop-intercept form
Answers
Answer:
y= 4x -3
Step-by-step explanation:
1) add -8x at both members
8x - 2y - 8x = 6 - 8x
-2y = -8x + 6
2) divide both members by -2
y = 4x -3
hi please help i’ll give brainliest
Answers
Answer:
1. 8 families with 3 kids
2.25 families
3.20 families
Find the value of KL
Answers
Answer:
40.5
Step-by-step explanation:
!
A triangle has two sides of length 18 and 4. What is the smallest possible whole-number length for the third side?
Answers
==================================================
Explanation:
Let a = 4 and b = 18 be the two known sides of the triangle.
Let c be the remaining side
We'll use a version of the triangle inequality theorem to set up the possible range of values for c.
The range of values for c is determined by the following
b-a < c < b+a
18-4 < c < 18+4
14 < c < 22
Telling us that the third side c is between 14 and 22, excluding both endpoints. This means c = 14 and c = 22 are not allowed. If either value were to happen, then the triangle becomes a single line instead. Try it out with slips of paper.
Because c = 14 is not allowed, we must go to the next whole number up. Therefore, c = 15 is the smallest possible length for the third side, when the third side is a whole number.
If the third side wasn't a whole number, then we could have something like c = 14.1 or c = 14.01 or c = 14.001 or c = 14.0001, and so on. We could steadily get closer and closer to 14, but never actually arrive to it. In short, there is no "smallest third side". This is likely why your teacher is focusing on the whole numbers so there is a smallest value of c possible.
Extra info: As you can probably guess, the largest side possible is c = 21, which is one less than 22. Like above, this is only possible if c is a whole number.
Answer:15
Step-by-step explanation: i got it right
6. If the measure of an arc is 68, what is the measure of its central angle?
Answers
Answer:
68
Step-by-step explanation:
Measure of arc = Measure of corresponding central angle
Thus, if the measure of an arc = 68, then the measure of its central angle also = 68
PLEASE HELPPPPPPPPPPPPPPPP
Answers
Answer:
$720
Step-by-step explanation:
(4000)(0.03)(6)