Hi, so I know the answer to this problem (now that I got it wrong) but I'm not quite sure why I was wrong, help?
Answers
Answer:
[tex]-2x^2-x[/tex]. Your answer was wrong because "x-squared" terms didn't cancel.
Step-by-step explanation:
To solve this problem, set up an equation. We know something is supposed to be added to the expression [tex]2x^2+2x[/tex], and the result should be x. So:
[tex]2x^2+2x+(\text{ ? })=x[/tex]
We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.
It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".
[tex]2x^2+2x+(\text{ } y \text{ })=x[/tex]
...or just...
[tex]2x^2+2x+y=x[/tex]
Algebra allows us to solve the equation and find out what "y" is equivalent to.
To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.
Understanding "terms" & "like terms"
Terms
"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.
For example, the various terms in our equation above are
[tex]2x^2[/tex], [tex]2x[/tex], [tex]y[/tex], [tex]x[/tex]
You might ask why the last things, which don't have a number, are considered terms.
Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.
So, we can rewrite our equation:
[tex]2x^2+2x+1y=1x[/tex]
Like terms
"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the [tex]2x[/tex] and the [tex]1x[/tex] are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that [tex]2x[/tex] and [tex]2x^2[/tex] are not "like terms" because the "stuff" is different:
[tex]x[/tex] is different than [tex]x^2[/tex]
"Like terms" are important because only like terms can be "combined" into a single simplified term.
Solving equations
To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.
Starting with subtracting 2x from both sides of the equation:
[tex]2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x[/tex]
Subtraction is the same as "adding a negative":
[tex]2x^2+2x+1y+(-2x)=1x+(-2x)[/tex]
Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.
Thinking just about the number parts, since [tex]1+(-2)=-1[/tex], then [tex]1x+(-2x)=-1x[/tex].
Returning to our main equation, the right side simplifies:
[tex]2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x[/tex]
On the left side: [tex]2x[/tex] and [tex]-2x[/tex] are like terms.
Fact: [tex]2+(-2)=0[/tex]
So, [tex]2x+(-2x)=0x[/tex]
Since anything times zero is just zero, [tex]0x=0[/tex]. Furthermore, adding zero to anything doesn't change it. So when the [tex]2x[/tex] and [tex]-2x[/tex] terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)
So, [tex]2x^2+2x+1y+(-2x)=-1x[/tex] simplifies to:
[tex]2x^2+1y=-1x[/tex]
Similarly for the [tex]2x^2[/tex] term, we subtract from both sides:
[tex]2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)[/tex]
Combining like terms on the left, they disappear.
[tex]1y=-1x+(-2x^2)[/tex]
There are no like terms on the right.
Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:
[tex]1y=-2x^2+(-1x)[/tex]
Addition of a negative can turn back into subtraction, and simplify multiplication by 1.
[tex]y=-2x^2-x[/tex]
Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.
Verifying an answer
Verifying can double check an answer, and helps explain why the answer you chose doesn't work.
To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:
[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)[/tex]
Combining the "x-squared" terms, completely cancels...
[tex]2x+(-1x)[/tex]
Combining the "x" terms, and simplifying...
[tex]1x\\x[/tex]
So it works.
Why isn't the answer what you chose:
[tex]2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)[/tex]
Combining the x-squared terms, things don't completely cancel...
[tex]1x^2+2x+(-1x)[/tex]
Combining the x terms...
[tex]1x^2+1x\\x^2+x[/tex]
So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"
Related Questions
Triangle 304 degrees and 115 degrees work out x
Answers
a straight line make an angle of 180° ,
so 115+y=180
y=65°
for the top part of the triangle it makes an angle of 360° , so 304+y=360
y=56
sum measure of interior angles of triangle is 180° , According to this rule (n-2)180 ; where n is the no. of sides .
so
65+56+y= 180
121+y=180
y=59( the angle next to X)
X+59=180( together they make an angle of 180)
x=121°
Hope it helps
please give brainliest
What subjects together do more than half of the class like?
Math 9 people
Science 3 people
Art 5 people
Writing 3 people
History 1 person
Math and Writing
Science and History
Art and Science
History and Math
Answers
Answer:
Math and Writing
Step-by-step explanation:
Well if we add up all the people we get (9 + 3 + 5 + 3 + 1) = 21. Half of that is 10.5 so the sum of the two subjects must be at least 11. The amount of people that like Math and Writing is 11 people so the two subjects that more than half the class like are Math and Writing.
Answer:
Math and Writing
Step-by-step explanation:
Number of students who like each subject:
Math = 9Science = 3Art = 5Writing = 3History = 1Total number of students = 9 + 3 + 5 + 3 + 1 = 21
Half of 21 = 21 ÷ 2 = 10.5
Therefore, more than half the class would be > 10.5 students
Total number of students who like:
Math and Writing = 9 + 3 = 12Science and History = 3 + 1 = 4Art and Science = 5 + 3 = 8History and Math = 1 + 9 = 10Therefore, the only combination of subjects that more than 10.5 students like is Math and Writing as 12 > 10.5
what equation describes a linear function
Answers
Answer: y = f(x) = a + bx y = f(x) = a + bx y = f(x) =
explanation: The following is the formula for a linear function. y = f(x) = a + bx y = f(x) = a + bx y = f(x) = One independent variable and one dependent variable make up a linear function.
Answer:
I don't knowwwwwwwwwwwwwwww
4sin2xcosx+sin3x=sin<3,14+x>
Answers
The solution to 4sin2xcosx+sin3x=sin<3,14+x> is x = nπ, where n = ±{0, 0.5, 1, 1.5....}
How to solve the equation?The equation is given as:
4sin2xcosx+sin3x=sin<3,14+x>
Rewrite properly as:
4sin(2x)cos(x)+sin(3x)=sin(3.14+x)
Next, we split the equation as follows:
y = 4sin(2x)cos(x)+sin(3x)
y = sin(3.14+x)
Next, we plot the graph of both equations (see attachment)
From the attached graph, we have:
x = nπ, where n = ±{0, 0.5, 1, 1.5....}
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identify the coefficient of -24x7y3
Answers
Answer: -24
Step-by-step explanation:
See attached image.
The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Which of the following gives h–1(x)?
{(3, 5), (5, 7), (6, 9), (10, 12), (12, 16)}
{(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
{(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
{(5, 3), (7, 5), (9, 6), (12, 10), (16, 12)}
Answers
The inverse function will be h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}. Then the correct option is B.
What is inverse of a function?Suppose that the given function is
f:X → Y
Then the inverse of the considered function will be
f⁻¹: Y → X
The function h(x) is given below.
h(x) = {(3, –5), (5, –7), (6, –9), (10, –12), (12, –16)}
Then the coordinate of the inverse function gets swapped.
h⁻¹(x) = {(–5, 3), (–7, 5), (–9, 6), (–12, 10), (–16, 12)}
Then the correct option is B.
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A company making tires for bikes is concerned about the exact width of its cyclocross tires. The company has a lower specification limit of 22.8 millimeters and an upper specification limit of 23.1 millimeters. The standard deviation is 0.19 millimeters and the mean is 22.9 millimeters. What is the process capability index for the process? Note: Round your answer to 4 decimal places.
Answers
The process capability index for the process is 0.1754.
How to calculate the index?The first sided specification limit will be:
= (Upper specification limit - mean)/(3 × standard deviation)
= (23.1 - 22.9)/(3 × 0.19)
= 0.2/0.57
= 0.3508
The second sided specification limit will be:
= (22.9 - 22.8)/(3 × 0.19)
= 0.1/0.57
= 0.1754
The process capability index for the process is 0.1754 wine it's the lower value.
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difference between compounded annually, monthly and daily.
Answers
Answer:
With monthly compounding, the bank will calculate interest on your account just once per month. It will not update your balance on a daily basis when it calculates how much interest it owes you. Assuming that the APR is the same, accounts with monthly compounding offer a lower APY than accounts with daily compounding.
Make m the subject of the equation
(a) 5(m + y) = 4(m - 3y)
Answers
Answer:
m=(-5y-3y)
Step-by-step explanation:
5m+5y=4m-3y
5m-4m=-5y-3y
m(5-4)=-5y-3y
m=(-5y-3y)/1
The vertex of this angle is:
R
T
S
Answers
The vertex of this angle is point S.
i need help asapppppp
Answers
Answer:
a
Step-by-step explanation:
2^3 = 8; 4^3 = 64; 8/64 = 1/8
(g^5)^3 = g^15
(h^2)^3 = h^6
g^15/8h^6
I think of a number and divide it by 3. The result is 2 less than the number I first thought of. Find the number I first thought of.
Answers
Answer:
Let the number be x
so, x/4 = x-3
x = 4(x-3)
x= 4x-12
x-4x = -12
-3x = -12
x= 12/3
x = 4
Step-by-step explanation:
Hope this helps! (:
Please mark me Brainliest!please help me guys its math
Answers
I need help on this question don't understand this at all
Answers
Answer:
F (3)=-1
Step-by-step explanation:
The domain consists of the pre-images and the range has the images. We have the f (3)=-1 since -1 is the image of 3. When we are looking for the function of a number and we are given a diagram of such, we just need to take the value of the number it is pointing to.
Help yalllll question is in the pic
Answers
Step-by-Step Solution:
=> f(x) = 5x - 1
=> g(x) = 2x^2 + 1
=> Find value of (f * g)(-3)
First Substitute x as -3 in f(x) and g(x) :-
f(x) = 5x - 1
f(-3) = 5(-3) - 1
f(-3) = -15 - 1
=> f(-3) = -16
g(x) = 2x^2 + 1
g(-3) = 2(-3^2) + 1
g(-3) = 2(9) + 1
g(-3) = 18 + 1
=> g(-3) = 19
Now Multiply f(-3) with g(-3) :-
= f(-3) * g(-3)
= -16 * 19
=> -304
Therefore, (f * g)(-3) = -304
Raphael graphed the system of equations shown.
y = – 3
y = x – 0.8
A coordinate grid with 2 lines. The first line passes through the points (0, negative 0.1) and (0.8, 0). The second line is horizontal passes through the point (0, negative 3). The lines intersect at a point with a coordinate of slightly to the left of negative 2 and negative 3.
What is the best approximation for the solution to this system of equations?
(–3.2, –3)
(–2.9, –3)
(–2.2, –3)
(–1.9, –3)
–3x + StartFraction one-half EndFractiony = –3
b =
2
4
6
8
Answers
Answer:
C. (-2.2, -3)
HI PLEASE ANSWER THIS QUESTION THANK YOU!
(NO TROLLS PLEASE!)
Answers
Select the correct answer.
Using synthetic division, find (2x + 4x³ + 2x² + 8x + 8) + (x + 2).
O A. 2x3 + 2x + 4
OB.
2x4 + 2x² + 4x
OC. 2x3 + 2x + 4 +
I
OD.
2x3 + 2x² + 4
1
+ 2
Answers
The synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
Division of the polynomialThe division of the polynomial is determined as follows;
(2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2)
2x³ + 2x + 4
-------------------------
x + 2 √(2x⁴ + 4x³ + 2x² + 8x + 8)
- (2x⁴ + 4x³)
-------------------------------------
2x² + 8x + 8
- (2x² + 4x)
------------------------
4x + 8
- (4x + 8)
-------------------
0
Thus, the synthetic division of the polynomial, (2x⁴ + 4x³ + 2x² + 8x + 8) / (x + 2) = 2x³ + 2x + 4.
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Which graph represents the following piecewise defined function?
-2x, x<-2
g(x)= -x², -2
X, X >1
Answers
Answer: See Attachment
Step-by-step explanation: I wasn’t sure if you meant -2 < x, but that’s the work I did to get the answer. If you can, send a picture of the question itself in case you didn’t mean -2 < x.
The graph represents a function.
2
Which ordered pair can be plotted together with these four points, so that the resulting graph still represents a function?
O (2, -1) O (-5,2) O (2,-5) (-2,5)
Answers
(-5, 2) is the only point which we plot in given graph then it still represent a function.
What is Function?A function is a special type of relation in which each and every element of set A have a unique image in its codomain set B.
Here, Given points on graph
{(-4, 2), (-2, -3), (2, 3), (3, -1)}
2 and -2 are already available in given ordered pair.
so only (-5, 2) is the only option which satisfies the definition of function.
Thus, (-5, 2) is the only point which we plot in given graph then it still represent a function.
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Two boats left a base camp at bearing of S60°E and S50°W at speeds of 50km/h and 70km/h respectively. Find the distance between the both boats after two hours.
Answers
Answer:
197.93 kmStep-by-step explanation:
Let the base camp is point A and boats' locations after two hours are points B and C.
By connecting the three points together we get a triangle ABC with sides:
AB = 50*2 = 100 kmAC = 70*2 = 140 kmThe angle between AB and AC is:
60 + 50 = 110 degrees (opposite directions from south)We are looking for the distance BC, which can be found by using the law of cosines:
BC² = AB² + AC² - 2AB*AC*cos ∠BACBC² = 100² + 140² - 2*100*140*cos 110°BC² = 39176.56 (rounded)BC = √39176.56 = 197.93 km (rounded)The distance between the boats is 197.93 km.
Which pair of functions are inverses of each other?
Answers
f(x) = 10x -5 and g(x) = (x+5)/10 are inverses of each other , Option D is the correct answer.
What is a Function ?A function is a mathematical statement which relates two variables , a dependent and an independent variable.
The inverse of a function is found by replacing every y by x and vice versa , and then solve for y
The equation
f(x) = 4/x - 3
or
y= 4/x -3
Replacing y by x
x = 4/y -3
x +3 = 4/y
y = 4/(x+3)
Which do not correlate with the given inverse
f(x) = 10x -5
y = 10x -5
for finding inverse
10y -5 = x
10y = x+5
y = (x+5)/10
g(x) = (x+5)/10
Therefore , Option D is the correct answer.
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Given the function f(x) = −5x2 − x + 20, find f(3).
Answers
Answer:
-28
Step-by-step explanation:
put 3 where is x
f(x) = −5(3)^2 − (3) + 20
exponents flrst
(−5*9) − (3) + 20
-45 -3 +20
-48 + 20
-28
The sum of two consecutive even numbers is 38. What is the smaller number?
Answers
Even numbers = 2x +2
Consecutive even numbers = 2x+4
then
(2x+2) + (2x+4)= 38
2x + 2 + 2x + 4 = 38
2x + 2x + 2 + 4 = 38
4x + 6 = 38
4x = 38 - 6
x = 32 :4
x = 8
2x+ 2 = 2(8)+2 = 16 + 2 = 18
2x+4 = 2(8) +4 = 16 + 4 = 20
The smallest number is 18
[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
Answer:
18 is the smaller number
Step-by-step explanation:
Let us take X for the first even number (it will also be the smallest)
x, x+1, x+2, so on..
the consecutive even number of x+2 is the next even number after x.
so you now get this equation...
x+(x+2) = 38
2x + 2 = 38
2x = 36
x=18
please help me
I'll mark you brainlist
Answers
Answer:
There are 16 notes of 20 paise's and 12 notes of 5 paise's.
Explanation:
The amount of notes for of 20 paise and 5 paise coins are not given.
So let there be x 20 paise's coins and y 5 paise's coins.
Equation buildup:
20x + 5y = 380 ___eq 1
20y + 5x = 380 - 60
20y + 5x= 320 ___ eq 2
Make x the subject for both:
1st
[tex]\rightarrow \sf 20x + 5y = 380[/tex]
[tex]\rightarrow \sf 20x = 380-5y[/tex]
[tex]\rightarrow \sf x = 19-0.25y[/tex]
2nd
[tex]\sf \rightarrow 20y + 5x = 320[/tex]
[tex]\sf \rightarrow 5x = 320-20y[/tex]
[tex]\sf \rightarrow x= 64-4y[/tex]
Solve them simultaneously:
[tex]\sf \rightarrow 64-4y =19 - 0.25y[/tex]
[tex]\sf \rightarrow -4y+0.25y =19 -64[/tex]
[tex]\sf \rightarrow -3.75y =-45[/tex]
[tex]\sf \rightarrow y =12[/tex]
Find x:
[tex]\sf \rightarrow x = 64-4y[/tex]
[tex]\sf \rightarrow x = 64-4(12)[/tex]
[tex]\sf \rightarrow x = 16[/tex]
Asap please!!!!!!! if jkl=rst, which congruences are true by cpctc? check all that apply.
a. l=r
b. jk=rs
c. k=s
d. j=s
e. kl=st
f. jl=rs
Answers
Answer:
b, c e
Step-by-step explanation:
A congruence statement lists corresponding parts in the same order. CPCTC says corresponding parts are congruent.
__
To see if any particular statement is consistent with CPCTC, identify the locations of the referenced parts in the congruence statement. If they match, the congruence is true
a. l = r ... jkl = rst . . . . not in the same place
b. jk = rs ... jkl = rst . . . . a match; true
c. k = s ... jkl = rst . . . . a match; true
d. j = s ... inconsistent with (c)
e. kl = st ... jkl = rst . . . . a match; true
f. jl = rs ... inconsistent with (b)
Statements b, c, e are consistent with the congruence statement, and are true by CPCTC.
Work out the equation of line B. Give your answer in the form y = mx + c, where m and care integers or fractions in their simplest forms.
Answers
Answer:
y = -3x + 1
Step-by-step explanation:
The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.
You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.
DOWN3 and OVER1 is the slope -3/1, which is equal to -3.
Fill in -3 in place of the m in the equation.
y = -3x + 1
Done!
Answer:
y = -3x + 1
Step-by-step explanation:
The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)
The slope can be found by taking any two points on the line, (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)
If you look at the line 2 points on the line are P(2,-5) and (0,1)
Slope = (-5-1)/(2-0) = -3
The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1
Therefore equation is
y = -3x + 1
You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value
For example, in the graph we see that at x = 1, y = -2
Indeed -3(1) + 1 = -3 + 1 = -2 also
sally sweeps 20 floors in 4 hours , at the same rate , how many floors can sally sweep in 6 hours ?
Answers
Answer:
35 Floors in 6 Hours
Step-by-step explanation:
20 / 4 = X Floors Per Hour
floors per hour = 5
6*5 = 35 Floors
PLEASE PLEASE HELP WILL MARK BRAINLIEST!!
Which choice is equivalent to the product below when x > 0?
A. x/9
B. 1/3
C. x/3
D. 1/9
Answers
The equivalent expression to given expression is 1/3.
What is Equivalent Expression?Equivalent expressions are defined as algebraic expressions which give the same resulting expression. An algebraic expression (or) a variable expression is defined as a combination of terms by the operations such as addition, subtraction, multiplication, division.
Here, given expression
[tex]\sqrt{2/x^2} X \sqrt{x^2/18}[/tex]
= [tex]\sqrt{2 X x^2/18x^2}[/tex]
= [tex]\sqrt{1/9}[/tex]
= 1/3
Thus, the equivalent expression to given expression is 1/3.
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Which table represents a linear function?
2
3
4
5
(J1
10
15
20
25
Answers
Answer:
I think it’s C
Step-by-step explanation:
I think
