The most common way to write a ratio is as a fraction, 3/6. We could also write it using the word "to," as "3 to 6." Finally, we could write this ratio using a colon between the two numbers, 3:6.
solve for x enter the solution from least to greatest (x - 1)^2 - 9 = 0 Lesser x = ___ greater x = ____
Answer:
X=4 or X=-2
Step-by-step explanation:
Step-1 : Multiply the coefficient of the first term by the constant 1 • -8 = -8
Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -2 .
-8 + 1 = -7
-4 + 2 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 2
x2 - 4x + 2x - 8
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-4)
Add up the last 2 terms, pulling out common factors :
2 • (x-4)
Step-5 : Add up the four terms of step 4 :
(x+2) • (x-4)
Which is the desired factorization
Equation at the end of step
1
:
(x + 2) • (x - 4) = 0
STEP
2
:
Theory - Roots of a product
2.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
2.2 Solve : x+2 = 0
Subtract 2 from both sides of the equation :
x = -2
Solving a Single Variable Equation:
2.3 Solve : x-4 = 0
Add 4 to both sides of the equation :
x = 4
Supplement : Solving Quadratic Equation Directly
Solving x2-2x-8 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
3.1 Find the Vertex of y = x2-2x-8
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 1.0000
Plugging into the parabola formula 1.0000 for x we can calculate the y -coordinate :
y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 8.0
or y = -9.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-2x-8
Axis of Symmetry (dashed) {x}={ 1.00}
Vertex at {x,y} = { 1.00,-9.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-2.00, 0.00}
Root 2 at {x,y} = { 4.00, 0.00}
Solve Quadratic Equation by Completing The Square
3.2 Solving x2-2x-8 = 0 by Completing The Square .
Add 8 to both side of the equation :
x2-2x = 8
Now the clever bit: Take the coefficient of x , which is 2 , divide by two, giving 1 , and finally square it giving 1
Add 1 to both sides of the equation :
On the right hand side we have :
8 + 1 or, (8/1)+(1/1)
The common denominator of the two fractions is 1 Adding (8/1)+(1/1) gives 9/1
So adding to both sides we finally get :
x2-2x+1 = 9
Adding 1 has completed the left hand side into a perfect square :
x2-2x+1 =
(x-1) • (x-1) =
(x-1)2
Things which are equal to the same thing are also equal to one another. Since
x2-2x+1 = 9 and
x2-2x+1 = (x-1)2
then, according to the law of transitivity,
(x-1)2 = 9
We'll refer to this Equation as Eq. #3.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-1)2 is
(x-1)2/2 =
(x-1)1 =
x-1
Now, applying the Square Root Principle to Eq. #3.2.1 we get:
x-1 = √ 9
Add 1 to both sides to obtain:
x = 1 + √ 9
Since a square root has two values, one positive and the other negative
x2 - 2x - 8 = 0
has two solutions:
x = 1 + √ 9
or
x = 1 - √ 9
Solve Quadratic Equation using the Quadratic Formula
3.3 Solving x2-2x-8 = 0 by the Quadratic Formula .
According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :
- B ± √ B2-4AC
x = ————————
2A
In our case, A = 1
B = -2
C = -8
Accordingly, B2 - 4AC =
4 - (-32) =
36
Applying the quadratic formula :
2 ± √ 36
x = —————
2
Can √ 36 be simplified ?
Yes! The prime factorization of 36 is
2•2•3•3
√ 36 = √ 2•2•3•3 =2•3•√ 1 =
± 6 • √ 1 =
± 6
So now we are looking at:
x = ( 2 ± 6) / 2
Two real solutions:
x =(2+√36)/2=1+3= 4.000
or:
x =(2-√36)/2=1-3= -2.000
953−105×4+118
Help plz :-( if right me give a lllllloooooot of points
Answer:
the awnser is 651 I hope this helps
HELLPP ME PLEASEEE
What was the unit rate for a drumstick in the 16 pack of drumsticks for $17.60?
Answer:
$1.10
Step-by-step explanation:
17.60 ÷ 16 and you have your answer 1.1 or $1.10
Help me I need it plz
Answer:
4 2/21
Step-by-step explanation:
2/3 and 3/7 have a common denominator, 21
so, 14/21 and 9/21
plug in the whole numbers: 1 14/21 and 2 9/21
which will give you: 3 23/21
so, simplify it which will give u the answer: 4 2/21
Write the standard form of the number shown.
two hundred thirty million, three hundred forty-four thousand, nine hundred ninety-six
Answer:
230,344,996 is my answer. Hope this could help you!
Solve for m.
m – 7/8 = 5
Write your answer as a fraction or as a whole or mixed number.
m = ____
Answer:
5 7/8
Step-by-step explanation:
Do the inverse operation.
5 + 7/8 = 5 7/8
Or, do this instead!
Add 7/8 to both sides of the equation. On the side before the equal sign, -78 and +78 cancel out, leaving m all by itself. Bring down the equals sign and we have m = 5 7/8!
Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which statement best describes triangle P′Q′R′?
Answer:
It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
Step-by-step explanation:
please help me with problem with clear explanation
Answer:
this doesn't even make any sense
Step-by-step explanation:
both -5.4 and 5.4 go off the m.f grid
Last time a bot answered but the question is below.
Answer:
True, true ,true, true?, false
Find The Area Of The Arrow Above Question Answered
Answer:
30 inches
Step-by-step explanation
because the other triangle is the same and its 30inches
The lengths of x and y are shown in the figure below.
Which number line shows the closest approximate values of x and y?
Answer:
x = 6.40312423743 y=12.8062484748
Step-by-step explanation:
To find the value of x, you must use the Pythagorean Therom.
a^2+b^2=c^2
5^2+4^2=c^2
25+16=c^2
41=c^2
Then find the square root of 41 so x = 6.40312423743.
Then to find y you must substitute the value of x in and use the triangle formula: 1/2(b)(h).
1/2(4)(6.40312423743)
y=12.8062484748
The answer is x = 6.40312423743 y=12.8062484748
Your final bill is $51.28. This includes a 12% tip. What was the bill without tip?
Answer:
$45.13
Step-by-step explanation:
what is 12% of 51.28 change 12% to a decimal by moving two spaces to left =0.12. multiple by 51.28= 6.15 that is the amount of the tip then subtract it from 51.28-6.15= $45.13 original amount before the tip.
I still dont understand slope can someone help?
[tex]m = slope\\(x1, y1) = coordinates of first point in the line\\(x2, y2) = coordinates of second point in the line[/tex]
Answer:
I don’t know the answer but I can try to help.
Step-by-step explanation:
The slope is the measurement of the steepness of a line, so all you would have to do is find the steepness of the line on that graph.
I hoped this helped :)
evaluate x+3 squared by 2 - 6 when x = 4
Answer:
43
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify.
(x + 3)² - 6
x = 4
Step 2: Evaluate
Follow Order of Operations.
Substitute in x [Equation]: (4 + 3)² - 6(Parenthesis) Add: 7² - 6Exponents: 49 - 6Subtract: 43Answer:
43
Step-by-step explanation:
Assuming you meant "evaluate x+3 squared - 6 when x = 4, we get:
(x + 3)^2 - 6
Substituting 4 for x, we get 7^2 - 6, or 43.
HELP DUE AT 9:00 PM!
What is the perimeter of a square with a side length of 14 m?
A. 46 m
B. 56 m
C. 70m
D. 196 m
Answer:
56m..................
Please help quick! Thanks! (NO LINKS!)
Answer:
i wish i could help i would of
Step-by-step explanation:
Answer:
The answer is 1.54 × 10^1.
Hope this helps. :D
Step-by-step explanation:
Pls mark brainliest.
HELPPP
What would be your pay per hour for working at Miracle Maintenance?
Answer:Hello Uhhhhcora,
Scotts Miracle-Gro Mechanical Maintenance Technicians earn $61,000 annually, or $29 per hour, which is 32% higher than the national average for all Mechanical Maintenance Technicians at $44,000 annually and 8% lower than the national salary average for all working Americans.
Step-by-step explanation:
Hoped i helped. Ask me anything for questions. ♥Please subscribe to Addie Nahoe.♥
Answer:
$27.66
Step-by-step explanation:
Write 28 x 32 in associative property
Answer:
32 * 28
Step-by-step explanation:
Just flip the positions of the two and you have your answer
there are 28 students and 22 of the students passed a resent test what percentage passed the test
THe answer to this problem is 78.57 percent.
PLz help me! We r doing semester finals and i need to get this lesson finished in 2 hours!
Answer:
Step-by-step explanation:
364000
may i please get help i beg you
Step-by-step explanation:
a) 108 - double the equation
b) -3 - divide by 3
C) -54 - multiply by -3
d) 6 - divide by 9
Please!! 10 points but adding 5 more!! so 15 points!!
need help on this will be helpful if help is here!
A transportation engineer wants to determine the number of vehicles that drive through an intersection on a given day. The following table shows the total number of vehicles that drove through the intersection over a 10-hour period.
The transportation engineer determines that the linear function that best models the data is, y = -16.7333 + 52.7515x where y represents the total number of vehicles that drove through the intersection and x represents the number of hours. The following graph shows the residuals for this function.
Answer:
510.7817 or 511
explanation:
First you’re going to have to substitute 10 in for x, so
Y= 52.7515(10) -16.7333
Y=527.515-16.7333
Then subtract
Y=510.7817
Can someone explain to me what this means, I can't quite understand it.
Jacki evaluated the expression below.
2 cubed (3 minus 1) + 4 (8 minus 12) = 2 cubed (2) + 4 (4) = 8 (2) + 16 = 16 + 16 = 32.
What was Jacki’s error?
Jacki should have simplified the exponent first.
Jacki should have multiplied 4 and 8 first.
Jacki did not subtract 12 from 8 correctly.
Jacki should not have multiplied 8 and 2
Answer: Jacki did not subtract 12 from 8 correctly
Step-by-step explanation: it should be -4
Answer: C
Step-by-step explanation:
Jacki didn’t subtract 12 from 8 correctly he was suppose to get a negative and not 12
A copy machine can print 480 copies every 4 minutes. A teacher printed 720 copies. How long did it take to print?
Answer:
6 minutes
Step-by-step explanation:
every minute is 120
720/120=6
· A ball is dropped from a height of 256 feet. After it hits the ground, it rebounds to a height that is 75% of its previous maximum height. Use proportional reasoning to complete the table. Bounce 1 2 4 3 Maximum Height (ft) 256 Height of Bounce (ft)
Answer:
The answer is 192 ft. :D
Step-by-step explanation:
PLEASE mark me brainliest! :)
Which of the following expressions is equal to P/17
Answer:
a and b would work in my opinion because it doesn't say in which specific order.
Answer:
the answer is b
Step-by-step explanation:
im sorry if it was wrong
What is the slope of the line in the graph?
On a coordinate plane, a line with a negative slope goes through points (0, 1) and (4, negative 2).
Negative four-thirds
Negative three-fourths
Three-fourths
Four-thirds
Answer:
Well all you need is 2 points to calculate slope
You can follow the equation,
{y2-y1 / x2-x1} = slope
-2-1=-3
4-0=4
-3/4
-3/4 is the slope