Answer:
taking the square root of both sides of the equation
Step-by-step explanation:
The operation which is performed in the derivation of the quadratic formula moving from Step 6 to Step 7 is taking the square root of both sides of the equation.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given two steps in deriving the quadratic formula which is used to find the roots of a quadratic equation.
The first step is,
step 6 : (b² - 4ac) / (4a)² = (x + b / 2a)²
step 7 : ± √(b² - 4ac) / 2a = x + b / 2a
We have to find which step is done in between to transform from step 6 to step 7.
It is clear that square root is taken.
When the square root is taken in step 6,
±√[(b² - 4ac) / (4a)²] = √[(x + b / 2a)²]
√(b² - 4ac) / √(4a)² = √(x + b / 2a)²
± √(b² - 4ac) / 2a = x + b / 2a
Hence the step performed is taking the square root on both sides.
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can someone tell me if is this a function or not?
Answer:
Yes, it is a function.
Step-by-step explanation:
As long as there are no more than one point in a single x-value, it is considered a function.
Translate and solve: 58% of what number is 145?
Answer:
58% of 250 is 145.
Step-by-step explanation:
145 * 100/58
= 250
Answer:
250
Step-by-step explanation:
I will give brainiest to whoever answers correctly !!
Answer:
0.50 %
Step-by-step explanation:
= profit/cost x 100%
= 11.95 - 7.95 = 4
= 4/7.95 x 100 %
= 0.50 %
Which of the following decimals is greater than .4 and less than .65? Select all that apply. *
0.06
0.76
0.41
0.37
0.5
Answer:
0.41 and 0.5 are both greater than .40 and less than .65
Step-by-step explanation:
Bottles of sparkling water usually cost $1.69 each. This week they are on sale for 4 for $5. How much would it cost to pay for 4 bottles of water LAST week?
Answer:
$6.76
Step-by-step explanation:
A kangaroo hops 2 kilometers in 3 minutes at this rate how far does the kangaroo travel in 2 minutes
Answer:
2 1/2 or 2 and a half
Step-by-step explanation:
if you divide it it will come out to be that (I hope its right but i don't know if it is
Answer to this question: "A kangaroo hops 2 kilometers in 3 minutes at this rate how far does the kangaroo travel in 2 minutes"
2.50
Using the formula from part a, calculate the retail price for each quantity range.
Answer:
You have to answer to other question before answering this one, just in case anyone was confused
Step-by-step explanation:
Paul needs to buy 5/8 pound of peanuts. The scale at the store measures parts of a pound in sixteenths. What measure is equivalent to 5/8 pound?
Answer:
10 / 16
Step-by-step explanation:
10/16
5 x 2 = 10
8 x 2 = 16
Please help me answer this
Explain you’re answer
Will give braisnlt
Answer: I think its a
Step-by-step explanation:
Translate into an inequality or equation and solve: A number "n" minus 6 is no greater than 20. Write and
solve an equation or inequality.
Answer:
Therefore, n is smaller than 26 (n < 26).
Step-by-step explanation:
First, you have to form an inequality. With the given informations, the inequality will be :
[tex]n - 6 < 20[/tex]
Next, you have to solve it, by adding 6 to both sides :
[tex]n - 6 < 20[/tex]
[tex]n - 6 + 6 < 20 + 6[/tex]
[tex]n < 26[/tex]
Answer:
N-6≤20 N≤26
Step-by-step explanation:
n-6≤20
n-6=20
+6 +6
n≤26
How many whole numbers are on the highlighted part of a number line?
I'm solving for UW. And we're using pythagorean theorem.
Answer:
6^2+x^2 = 9^2x^2 = 9^2-6^2 = 81-36 = 45
x = √45
UW = √45 ft
what is F?
H is 5m
I is 8m
G is 10m
Answer: F is 11m.
Step-by-step explanation: Because H,I,G are all increasing their numbers like plus 3, plus 2, and the last one has to be plus 1.
Poor c cups never had a chance to have a d cup its ok others feel your pain
Answer:
uuuuuuuuuuuuuummmmmmmmmmmmm what
Step-by-step explanation:
the screen size of a television is determined by the length of the diagonal of the rectangular screen. Traditional TVs come in a 4:3 format, meaning the ratio of the length to width of screen is 4 to 3. what is the area of a 27-inch traditional tv screen? what is the area of a 27 inch LCD tv who's screen is in a 16:9 format? which screen is larger
Answer:
Area of 27" 4:3 screen = 349.92 square inches
Area of 27" 16:9 screen ≅ 311.5 square inches
Traditional 4:3 screen is larger
Step-by-step explanation:
The Traditional TVs is larger than LCD tv screen
What is diagonal of rectangle?The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices.
The length of diagonals of a rectangle can be calculated as:
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
According to the question
The screen size of a television is determined by the length of the diagonal of the rectangular screen.
Traditional TVs
Ratio of the length to width = 4:3
Let a be the constant for both length and width
therefore
Length of Traditional TVs = 4a
Width of Traditional TVs = 3a
The area of a 27-inch traditional tv screen
i.e
Diagonal of Traditional TVs = 27
Now applying formula of diagonal of rectangle
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
substituting the values
27 = [tex]\sqrt{(4a)^{2} + (3a)^{2} }[/tex]
27 = [tex]\sqrt{16a^{2} + 9a^{2} }[/tex]
27 = [tex]\sqrt{25a^{2} }[/tex]
27 = ± 5a
a cannot be -ve
a = 5.4
now,
Length of Traditional TVs = 4* 5.4 = 21.6 inches
Width of Traditional TVs = 3 * 5.4 = 16.2 inches
Area of Traditional TVs = Length * width
= 21.6 * 16.2
= 349.92 [tex]inches^{2}[/tex]
LCD TVs
Ratio of the length to width = 16:9
Let a be the constant for both length and width
therefore
Length of LCD TVs = 16a
Width of LCD TVs = 9a
The area of a 27-inch LCD TVs screen
i.e
Diagonal of LCD TVs= 27
Now applying formula of diagonal of rectangle
Diagonal of rectangle = [tex]\sqrt{Length^{2} + Breath^{2} }[/tex]
substituting the values
27 = [tex]\sqrt{(16a)^{2} + (9a)^{2} }[/tex]
27 = [tex]\sqrt{256a^{2} + 81a^{2} }[/tex]
27 = [tex]\sqrt{337a^{2} }[/tex]
27 = ± 18.357a
a cannot be -ve
a = 1.47
now,
Length of LCD TVs = 16*1.47 = 23.53
Width of LCD TVs = 9*1.47 = 13.23
Area of Traditional TVs = Length * width
= 21.6 * 16.2
= 311.30 [tex]inches^{2}[/tex]
Hence, the Traditional TVs is larger than LCD tv screen .
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A toy jet is 4 inches in length. And it's made using the scale 1 inch = 12.25 feet. What is the length of the actual jet?
Answer:
It is 49
Step-by-step explanation:
multiply 12.25 by 4 since 1 inch is 12.25 and 4 inches times 12.25 is 49
A sample of a radioactive isotope had an initial mass of 540 mg in the year 1991 and decays exponentially over time. A measurement in the year 1996 found that the sample's mass had decayed to 420 mg. What would be the expected mass of the sample in the year 2000, to the nearest whole number?
Using the decay constant on the exponential function, the mass of the sample that will be left in 2013 is 35g
What is an Exponential Function?An exponential function is a function that can be expressed in the form f(x) = b^x, where b is a positive real number and x is a real number. The graph of an exponential function is a curve that increases or decreases rapidly as x increases or decreases.
here, we have,
In the exponential decay, the decay function can be given as;
y = ae⁻ⁿˣ
a = initial mass of sample
n = disintegration constant
x = time
The disintegration constant is also know as the rate of decay and we can calculate it as;
260 = 470e⁻ⁿ⁽³⁾
n = 0.197
n = 0.2
The disintegration constant is 0.2
The amount left in 2013 will be;
y = 470e⁻⁽⁰.²⁾⁽¹³⁾
y = 34.90
The mass in 2013 is 35g
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complete question:
A sample of a radioactive isotope had an initial mass of 470 mg in the year 2000 and decays exponentially over time. A measurement in the year 2003 found that the sample's mass had decayed to 260 mg. What would be the expected mass of the sample in the year 2013, to the nearest whole number?
A company purchased 10,000 pairs of men's slacks for $19.36 per pair and marked them up $22.33 What was the selling price of each pair of slacks? Use the formula
Answer:
$41.69
Step-by-step explanation:
The computation of the selling price of the each pair of slacks is as follows:
Given that
Cost = $19.36 per pair
Markup = $22.33
As we know that
Markup = Sell Price - Cost
So,
Sell Price = Cost + Markup
= $19.36 + $22.33
= $41.69
Hence, the selling price is $41.69
Stephanie has a 3⁄4 pound bag of sand that she will pour into 4 vases. Each vase will have the same amount of sand. How many pounds of sand will each vase have? Write your answer as a fraction.
Answer:
3/16 pound
Step-by-step explanation:
hope it helps the picture show how its done
FAST
Which statements about the system are true? Select two options
Y=1/3x-4 3y-x=-7
The system has one solution
The system consists of parallel lines
Bothsire tave the same slope,
Both ties have the same y-Intercept
The equations represent the same line
Answer: The system consists of parallel lines
Step-by-step explanation:
Given system of lines :
[tex]y=\dfrac13x-4[/tex]
[tex]3y-x=-7[/tex]
Substitute [tex]y=\dfrac13x-4[/tex] in [tex]3y-x=-7[/tex], we get
[tex]3(\dfrac13x-4)-x=-7\\\\\Rightarrow\ x-12-x=-7\\\\\Rightarrow\ -12=-7[/tex] , which is not true.
That means , system has no solution.
i.e. they are representing parallel lines. [Parallel lines do not intersect and hence they do not have solution.]
3. The graph shows the Millennium Falcon traveling from Jakku to Takodan.
What is the average speed of the Millennium Falcon on this journey?
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type a whole number.)
A. 874÷23=?
B. 874÷23=? R ?
In the answer B the reason why i put an R is because they it also asks for an a remainder. And plz take ur time on this i'm in no rush and DONT JUST BE HERE FOR POINTS.! So plz help me on this and take ur time plz. I'll help u with anything u need.<3
Answer: 38 think
Step-by-step explanation:
Answer:
ok so
Step-by-step explanation:
874÷23=38
yw:)
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $9 monthly fee and charges an additional $0.13 for each minute of calls. The second plan has a $16 monthly fee and charges an additional $0.09 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal
Answer:
the number of minutes of call when the two cost plans would be equivalent to each other is 175 minutes
Step-by-step explanation:
The computation of the number of minutes of call when the two cost plans would be equivalent to each other is shown below:
Let us assume the number of minutes be x
Now the equation is
$9 + 0.13x = $16 + $0.09x
0.13x - 0.09x = $16 - $9
0.04x = $7
x = $7 ÷ 0.04
= 175 minutes
Hence, the number of minutes of call when the two cost plans would be equivalent to each other is 175 minutes
1. In the following statement, express the first number as a percentage of the second number.
The full-time year-round median salary for U.S. men in 2010 was $42,900, and the full-time year-round salary for U.S.
women in 2010 was $35,500.
% of the full-time year-round median
The full-time year-round median salary for U.S. men in 2010 was
salary for U.S. women in 2010.
(Round to the nearest tenth as needed.)
9514 1404 393
Answer:
120.8%
Step-by-step explanation:
Maybe you want to find $42,900 as a percentage of $35,500.
That is ...
42900/35500 × 100% = 120.8%
__
Comment on the question
The question is easier to read if you don't shuffle the phrases. Copying and pasting often requires a check and edit step afterward.
One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN = 1/2 PR.
The coordinates of Q are:
The coordinates of R are:
The slope of MN is:
The slope of PR is:
The line segments are (select)
MN =
PR =
Answer:
See the proof below
Step-by-step explanation:
Given the following coordinates
P(2, −1)
Midpoint of PQ M(3, 0)
We can get the coordinate point Q using the midpoint formula;
M(X,Y) = (x1+x2/2, y1+y2/2)
X = x1+x2/2
3 = 2+x2/2
6 = 2+x2
x2 = 6-2
x2 = 4
Y = y1+y2/2
0 = -1+y2/2
0 = -1 + y2
y2 = 0+1
y2 = 1
Hence the coordinate of Q is (4, 1)
Next is to get the coordinate of R
Given the midpoint of QR to be N(5, 3)
(5,3) = (4+x2/2, 1+y2/2)
5 = 4+x2/2
10 = 4+x2
x2 = 10-4
x2 = 6
1+y2/2 = 3
1+y2 = 6
y2 = 6-1
y2 = 5
Hence the coordinate of R is (6,5)
Given the coordinates M(3, 0) and N(5, 3)
Slope is expressed as:
m = y2-y1/x2-x1
m = 3-0/5-3
m = 3/2
Slope of MN = 3/2
Get the slope of PR
Given the coordinates P(2, −1) and R (6,5)
Slope of PR = 5-(-1)/6-2
Slope of PR = 5+1/4
Slope of PR = 6/4 = 3/2
Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR
To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:
For MN with coordinates M(3, 0) and N(5, 3)
MN = √(x2-x1)²+(y2-y1)²
MN = √(5-3)²+(3-0)²
MN = √2²+3²
MN = √13
Get the length of PR where P(2, −1) and R (6,5)
PR = √(6-2)²+(5+1)²
PR = √4²+6²
PR = √16+36
PR = √52
PR = √4*13
PR = √4*√13
PR = 2√13
Since MN = √13
PR = 2MN
Divide both sides by 2
PR/2 = 2MN/2
PR/2 = MN
Hence MN = 1/2 PR (Proved!)
Select the expression that is equivalent to 2x3+11x2−21xx2+3x for x ≠ −3 or 0 .
Answer:
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]
Required
Select equivalent expression
[tex]\frac{2x^3+11x^2-21x}{x^2+3x}[/tex]
Factorize the numerator and denominator
[tex]\frac{x(2x^2+11x-21)}{x(x+3)}[/tex]
Divide by x/x
[tex]\frac{2x^2+11x-21}{x+3}[/tex]
Expand the numerator
[tex]\frac{2x^2+14x-3x-21}{x+3}[/tex]
Factorize the numerator
[tex]\frac{2x(x+7)-3(x+7)}{x+3}[/tex]
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]
Hence, the equivalent expression is:
[tex]\frac{(2x-3)(x+7)}{x+3}[/tex]
What is the equation of the line that is parallel to the line y = 2x + 3 and
passes through the point (-2, 1)?
O A. y = 2x + 5
O B. y--3x+2
O C. y=-3x
O D. y = 2x-5
What is the slope? (IXL)
Answer:
2/3
Step-by-step explanation:
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 290 engines and the mean pressure was 7.6 pounds/square inch (psi). Assume the population standard deviation is 0.8. The engineer designed the valve such that it would produce a mean pressure of 7.5 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Answer:
z(s) = - 2,15 We accept H₀
Step-by-step explanation:
Assume Normal Distribution.
Sample size n = 290
Sample mean μ = 7,6
Sample standard deviation s = 0,8
Level of significance 0,02 ( CI = 98 % )
population mean μ₀ = 7,5
α = 0,02 the valve could fail under and above the spec value ( 7,6 ) therefore we must develop a two-tail test
α/2 = 0,01
Hypothesis Test
Null hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
for α = 0,01 z(c) = - 2,3
To calculate z(s)
z(s) = ( μ - μ₀ ) / s/√n
z(s) = ( 7,5 - 7,6 ) /0,8/√290
z(s) = - 0,1 * 17 /0,8
z(s) = - 1,7 / 0,8
z(s) = - 2,15
Comparing z(s) and z(c)
- 2, 15 < - 2,3
|z(s)| < | z(c)|
Then z(s) is in the acceptance region. We don´t have evidence to reject H₀
I clearly don't know how to do it if i did i wouldn't be asking for help.
Answer:
132 degrees
Step-by-step explanation:
answer : 48 degrees
method
1. opposite angles are the same , so CFG os the same as GAC - these two added up are 132 + 132 = 264
2. angles add up to 360 in a quadrilateral , so the sum of the two remaining angles is 360 - 264 = 96
3. because the two remaining angles , ACF and FGA , are opposite , those are equal too. so u just half to get one of them : 96 / 2 = 48
