Answer:
um
Step-by-step explanation:
Rewrite each of the following expressions without using absolute value bars.
a
|x−4| if x>4
b
|x−y| if x
c
|3r−15| if r<5
a y=x-4 if x>4
b INCOMPLETE
c 3r-15 is r<5
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
7 increased by a number w
An expression is
Solve for x.
25(x−12)=−234 will name you the brainllest fastest answer
Answer:
2.64
Step-by-step explanation:
looked it up
Answer:
66/25 or 2.64
Step-by-step explanation:
times 25 and x to get 25x and then 25 and 12 to get -300, put it togather as an equation to get 25x-300= -234. Next move postive 300 to -234 do the math and get 66=25x. last divied 66 and 25 to get 2.64 or in a fraction 66/25
Fiona is taking some time to balance her check register at the end of the month. Use the check register to answer questions for 6 and 7. Based on the transactions, what was the balance in Fiona’s account after she deposited her birthday gift on 6/4?
$780
$690
$340
$430
Beth is half as old as Meg. Enter an algebraic expression based on this situation.
The algebraic expression for this is ____________
Answer:
b = 1/2m
Step-by-step explanation:
Let:
b = beth's agem = meg's ageThe prompt tells us that Beth is half as old as Meg. Therefore, mathematically, b = 1/2m.
Write the equation of the line that passes through the points (8,−7) and (−9,7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y + 7 = (-14/17)(x - 8)
Step-by-step explanation:
We want the equation of this line in the point-slope form y - k = m(x - h).
We are given two points (8, -7) and (-9, 7), and may arbitrarily choose one of them to serve as the point (h, k) in the point-slope form shown above. Then the other point is represented by (x, y) in the point slope form shown above:
Let (h, k) be 8, -7) and let (x, y) be (-9, 7). Then, y - k = m(x - h) becomes:
7 - (-7) = m(-9 - 8), so that 14 = m(-17), and the slope is thus m = -14/17
The desired equation is then y + 7 = (-14/17)(x - 8) (which is in point-slope form).
Another way to get this result would be to find m in the usual way:
rise 14
m = ------------- = --------- = -14/17 (same as before).
run -17
Find the sale price and then add tax.
Pete wants to buy a new PlayStation 5 controller that is on sale. The controller cost $70 and is on sale for 40% off. If the sales tax is 10.1% how much will he pay for the controller?
Answer:
Your answer is $52.2 :)
Step-by-step explanation:
First, we need to find the sale, which is 40% of $70, we can do that by doing this equation: (40% x $70) / 100 = 28. Now we minus 28 from 70 in this equation: 70 - 28 = 42. Now we do tax, which is 10.1% of $42. We can do the same equation, but with the new information, so the new equation is ($42 x %10.1) / 100 which is 4.2042, and since we are talking money, we can make 4.2042, 4.2 (Rounded 0.042 down). Lastly, we add $4.2 (Tax) and $48 (Discounted price) to get $52.2. You're welcome :D
Find the total cost with sale tax.
Show all your steps ( Works)
Holly has $15 to buy a gift for her brother. She found a stuffed animal that cost $12.50. With 10.1% sales tax added on, what is the sale tax? What is the total cost of the stuffed animal with tax included?
write 28 x 32 in distributive property
Answer: I'm not sure if anyone else has answered but ~ The Answer is 4* 14
Hoped this helped i'm learning the same thing
Step-by-step explanation:
Which expression is equivalent to
5
p
2
+
3
p
2
−
6
p
? first correct answer gets brainliest pog
Answer : The correct answer is 8p2 - 6p
12x12/12+12x3467 How knows the answer?
sterling plants a tree that is 4 3/4 feet tall. please do step by step!!!
Answer:
There's not really a question to answer there, you've only stated the information that we know. From what I can see the only conclusion I can make is that Sterling plants a tree that is 4 3/4 feet tall, but that's already written and with all the information provided that's really all I can say.
Sorry if that's not exactly what you were looking for, maybe if there's more to the question re-post it with the entire question?
PWEAS HELP ME ASAP
Line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A prime B prime. What is the length of A prime B prime? (5 points)
1 unit
2 units
3 units
5 units
Answer:
The correct option is C.
Step-by-step explanation:
It is given that line segment AB has a length of 3 units. It is translated 2 units to the right on a coordinate plane to obtain line segment A'B'.
Translation is a rigid transformation. It means the shape and size of preimage and image are same. In other words we can say that the preimage and image are congruent.
Corresponding sides of congruent figures are congruent.
The length of A'B' is 3 units. Therefore the correct option is C.
PLEASE HELP ASAP!! ILL GIVE BRAINLIEST IF CORRECT
Two linear functions are represented in different formats.
Function 1:
x y
0 5
2 11
5 20
8 29
Function 2: (image below)
Which statements are true?
Select each correct answer.
Function 1 has a greater rate of change than function 2.
Function 2 has a greater rate of change than function 1.
Function 1 has a greater y-intercept than function 2.
Function 2 has a greater y-intercept than function 1.
Answer:
Function 1 has a greater Y intercept than that of function 2
Step-by-step explanation:
Y intercept can be found by replacing x by 0 or
x = 0 0f the given function.
in this case Function 1 has a Y intercept of 5 when x =0
on the other hand, function 2 crosses the y axis once at -1 which is the y intercept.
you can now clearly see that
y = 5 > y = -1
---> 5>-1
so that's why we conclude that 1 has a greater Y intercept.
I'm so bad at prime numbers. Help please !
Answer:
35111723
Step-by-step explanation:
17, 3, 23, 5, 11
3, 5, 11, 17, 23
35111723
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: 1. 447
2. 572
3. 257
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
I need help due today
Answer:
Step-by-step explanation:
y=mx+b b= y-intercept y-intercept=where the line crosses the y-axis m=slope slope== rise/run or slope formula, m=y2-y1/x2-x1
For example, number 1's slope is 5/3. On a graph, you would go up 5 (not in block, but in numerical value) and right 3. The y-intercept is -2. This is where your line starts on the graph.
sorry, cant help ya there buddy
Multiplying Integers with Integer Tiles –5(–2) =
Answer:
-5 x -2 = 10
Step-by-step explanation:
- x - = +
5 x 2 = 10
Joe drove 538 miles in 9 hours 15 minutes. What was his average speed per hour? Round to the nearest whole number.
The First-person to answer gets brainliest.
The table shows values for a linear function, f (x ). What is an equation for f (x )?
Select the two values into the correct location.
Answer:
c
Step-by-step explanation:
I took the test
What is not an example of potential energy?
Question 3 options:
A stretched rubber band
A ball sitting high on a shelf
A pendulum at the top of its swing when it briefly stops
A car accelerating down a hill
Answer:
a car accelerating down a hill
Step-by-step explanation:
because if an object is moving at a speed, then it has kinetic energy because its moving, not potential energy. potential energy is strored energy meaning that it has the potential to move.
Find the selling price.
Markup ($) = percent markup (%) x original cost ($)
Selling price ($) = original cost ($) + markup ($)
A local gaming store bought a gaming console for $90. The gaming store sold the console, and the percent markup was 162%. What is the selling price?
The selling price is: $_________
Skip to navigation
Answer:
$145.80
Step-by-step explanation:
The original cost of the product was $90. There was a 162% markup. In order to get the selling price, I like to take away 100 percent and simply add original price+(original price*62%). After taking away 100%, I am left with 62%. I then multiply the original cost ($90) by the remaining percent (62%), getting 55.8. Following the steps that I originally wrote, I now add 90 to 55.8, getting 145.8.
Answer:$145.80
Step-by-step explanation:
Please answer when u can! (asap, pls in 5 or less minutes ;-;) No links pls
((THE QUESTION INFO) Marina, Cleo, and Paul are buying paper plates for a big cookout. A 4-pack of plates sells for $0.37 and a 48-pack sells for $3.84. They each use a different method to decide which option is the best buy. Decide which methods use correct reasoning. Write an equation relating the cost C to the number of plates p for the best option. )
question B. Write the equation for the best option, relating the cost C to the number of plates p.
Answer:
2+2=4
Step-by-step explanation:
PLEASE HELP FAST! DUE TODAY AND CANT HAVE A 0!
Answer:
ok so i think it is 5/9
Step-by-step explanation:
both equal 0.5 in decimal point
Answer:
The last option is correct
Step-by-step explanation:
Eg: i take -4/9
If your answer id 4/-9 , the negative sign will always go on the top so answer will be -4/9
Thus its similar
Hope you understood
if not I will explain again !
Your welcome !
will giver brainliest to the person with the most detailed answer. That means tell me how you got ur answer. And the person who answers with the most clear explanation as well. Good luck!! This is due in 8 minutes as well. And pls number ur answers in order so it is clear!!
Answer:
Step-by-step explanation:
Simplify each expression involving signed numbers.
-7 – 2 =
12 + (-4) =
-8(-6) =
18/-3=
Answer:
-5 , 8 , 48 , -6
Step-by-step explanation:
-7- -2 = -5
This complies with the rule that 2 negatives make a positive.
12 + (-4) = 8
You just ignore the brackets.
-8(-6) = 48
The -8 next to the bracket with no symbol means you need to multiply, and again 2 negatives make a positive.
18/-3 = -6
As the 18 is not negative, but -3 is, the answer is also a negative because one negative and one positive make a negative!
Hope this helps and have a good day!
Two quantities are related, as shown in the table:
x y
2 3
4 4
6 5
8 6
Which equation best represents the relationship?
A. y = 1/2x + 2
B. y = 1/2x + 1
C. y = x + 2
D. y = 2x + 1
Answer:
B. y = 1/2x + 1
Step-by-step explanation:
y is added up by 1, while it is split 1/2 from x.
hope this helps.
plz help me easy 10 points
Answer
21
Step-by-step explanation: