Answers
Answer: C) 2/3
========================================================
Explanation:
Let's cross multiply and then get everything to one side
x/(2x-1) = (2x+1)/(x+2)
x(x+2) = (2x-1)(2x+1)
x^2+2x = 4x^2-1
0 = 4x^2-1-x^2-2x
0 = 3x^2-2x-1
3x^2-2x-1 = 0 .... see note below
x^2-(2/3)x-1/3 = 0
In that last step, I divided everything by the leading coefficient 3. That way, the leading coefficient becomes 1.
It turns out that anything in the form x^2-px+q has roots m and n such that
p = m+n
q = m*n
In short, the roots add to the negative of the middle coefficient, and they also multiply to the constant term. Again this only applies to quadratics where the leading coefficient is 1.
Comparing x^2-(2/3)x-1/3 with the form x^2-px+q, we see that
p = 2/3
q = -1/3
Therefore, p = m+n = 2/3
If you're curious why this works, it's because (x+a)(x+b) expands out to x^2+(a+b)x+ab, and note how the roots here are x = -a and x = -b.
-------------------------
Note: Another route would be to solve 3x^2-2x-1 = 0 for x using any method you prefer (I recommend the quadratic formula). You would get the two solutions x = -1/3 and x = 1. They add to (-1/3)+1 = (-1/3) + (3/3) = (-1+3)/3 = 2/3.
Related Questions
Grissom draws different sized spheres in a notebook. He knows there is a relationship between the volume of the sphere and the length of its diameter. What is the independent quantity in the situation?
Answers
Answer:
The independent quantity in the situation is the length of the diameter.
Step-by-step explanation:
Consider a relationship between two variables.
Of the two variables one variable is dependent upon the other.
Dependent variables are those variables that are under study, i.e. they are being observed for any changes when the other variable values are changed.
Independent variables are the variables that are being altered to see a proportionate change in the dependent variable.
In this case, it is provided that Grissom knows there is a relationship between the volume of the sphere and the length of its diameter.
With every sphere that Grissom draws, the volume of the sphere changes according to its diameter length.
That is the volume of the sphere depends upon the length of its diameter.
Thus, the independent quantity in the situation is the length of the diameter.
Write 6 x 10 x 10 x 10 x 10 with an exponent.
Answers
Answer:
the answers is 6x 10 4
Step-by-step explanation:
The expression 6 x 10 x 10 x 10 x 10 with an exponent would be written as 6(10^4).
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
We have been given an expression as
6 x 10 x 10 x 10 x 10
Here we can see the base 10 multiplied by itself 4 times.
Exponentiation(the process of raising some number to some power) have some basic rules as:
[tex]a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\\\ a^b \times a^c = a^{b+c} \\\\^n\sqrt{a} = a^{1/n} \\\\(ab)^c = a^c \times b^c\\\\a^b = a^b \implies b= c \: \text{ (if a, b and c are real numbers and } a \neq 1 \: and \: a \neq -1 )[/tex]
The expression 6 x 10 x 10 x 10 x 10 with an exponent would be written as 6(10^4).
Learn more about exponentiation here:
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Scott imports a car from Japan for $12,500. He places an advertisement to sell the car in the newspaper and sells it for $26,800 How much profit has he made ?
Answers
Answer:
14,300
Step-by-step explanation:
Set of the equation
X+9=26
Answers
Answer:
17
Step-by-step explanation:
subtract 9 from 26 and you should get the answer
determine the quotient of 2/3 ÷ 4/5
Answers
Answer:
5/6
Step-by-step explanation:
It might make the problem easier to understand if we were to rewrite it as:
2
----
3
======
4
----
5
In this expression, we're dividing by a fraction, the fraction 4/5. We can get the same result by inverting this divisor fraction, 4/5, and then multiplying 2/3 by 5/4:
5 2
----- * -----
4 3
This reduces to
5 1
----- * ----- = 5/6
2 3
Solve for b. A=1/2(b+h)
Answers
Answer:
b = 2A - hStep-by-step explanation:
A = 1/2(b+h)
×2 ×2
2A = b + h
- h - h
2A - h = b
b = 2A - h
is 65.4279 Rational or Irrational
Answers
Answer:
Irrational
Step-by-step explanation:
Not repeating
I hope this helps
Will Give Brainliest
Big Water Canoeing Company rents canoes for $75 per hour. Explain why the point (0, 0) and (1, 75) are on the graph of the relationship and what these points mean in the context of the problem.
Answers
Answer: Unit Rate= 75 they are on the graph because that is where the unit rate starts. In the context they mean the rent goes up by $75.
Step-by-step explanation: I hope this helps im still a little confused myself, if it doesnt help im sorry.
Which angles are corresponding angles?
Check all that apply.
8 5
7
6
4
1
3
2
D A. 7 and 3
B. 1 and 5
O c. 1 and 6
O D. 5 and 4
D E. 8 and 1
O F. 1 and 4
Answers
Answer:
A. 7 and 3
&
B. 1 and 5
Step-by-step explanation:
Corresponding angles are a pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
The answers are:
•8 and 4
•5 and 1
•7 and 3
•6 and 2
I hope this helps! I'm sorry if it's wrong.
All good football players are over 200 pounds. Earl is 230 pounds. Kaylie concludes Earl is a good football player. Is her conclusion valid? Explain.
Answers
Answer:
I don't think so
Step-by-step explanation:
If being over 200 lbs makes you a good football player, then Earl could be a good player. But you need to be skilled at football to be good at it. Your weight doesn't make you good at something. So in my opinion, I don't think Kaylie's conclusion is valid.
I hope this answer helped you
which is not a correct name to name an angle
Answers
Answer:
<TGE
Step-by-step explanation:
it must connect
In a binomial experiment, if there are two possible outcomes and P(S) = 0.36, what is P(F)?
a 0.06
C. 0.36
b. 0.74
d. 0.64
Answers
Answer:
D. 0.64
Step-by-step explanation:
The reason I got this answer is because the problem tells us that there is a success rate of .36, so you would subtract .36 from 1 to get .64. The success rate and failure rate should always be equal to 1.
Urgent!!! Brainliest ,25 points and a thanks for the first to answer.
Answers
Answer:
1) 8
2) 6
3) 7
4) 0
5) 5
6) 1
7) 3
8) 2
9) -14
10) 12
11) -9
12) -6
13) -11
14) 1
15) -6
16) -12
17) -1/2
18) 9/11
19) 7/13
20) 9/7
21) -5/13
22) -13/25
Step-by-step explanation:
-1/2x-1/4(10x-9)=-(-7/4x+2)-x
Answers
Answer:
x= 17/15
Step-by-step explanation:
−1/2 x- 1/4 (10x−9)=−( -7/4 x+2)−x
The cross-sectional areas of a right pyramid and a right cylinder are congruent. The pyramid has a height of five units, and a right triangle has a height of three units. Which conclusion could be made from the given information
Answers
Answer:
the volume of the right cylinder is 1.8 times the volume of the pyramid
Step-by-step explanation:
The volume of a pyramid is
[tex]V = \dfrac{1}{3} \times B\times H[/tex]
where the height of the pyramid is 5
[tex]V = \dfrac{1}{3} \times B\times 5[/tex]
[tex]V = \dfrac{5}{3} B \ units ^3[/tex]
On the other hand, the volume of a right cylinder is
V = BH
where the height of the right cylinder = 3 units
V = 3 B units³
Since we know that the cross-sectional areas are congruent, comparing the two-volume, we have the ratio of their volumes to be:
[tex]\dfrac{V_p}{V_c}= \dfrac{\dfrac{5}{3}B}{3B}[/tex]
[tex]\dfrac{V_p}{V_c}= \dfrac{5}{9}[/tex]
[tex]9 V_p = 5 V_c[/tex]
[tex]V_c = 1.8 \ V_p[/tex]
Hence, the volume of the right cylinder is 1.8 times the volume of the pyramid
A muffin recipe calls for 3 cups of flour for 24 muffins. If you want to make 108
muffins, how many cups of flour will you need? *
Answers
Answer:
13.5
Step-by-step explanation:
3 cups for 24 muffins
x cups for 108 muffins
x=(108*3)/24
x=13.5
A ladder leans against a house making a 30 degree angle with the ground. If the ladder touches the house at a point 10 feet high, how long is the ladder?
Answers
Answer:
20ft.
Step-by-step explanation:
Sine = Opposite / Hypothenuse
Opposite = Height = 10ft
Hypothenuse = Length of ladder
Therefore, sin30° = 10ft / Length = 1/2
Length = 20ft
Ava has 34 candy bars. If
a box contains 5 bars and she has 4 extra candy bars
determine how many boxes
She has?
Answers
[tex]\bf Step-by-step~explanation:[/tex]
If Ava has 34 candy bars, and each box can hold 5 bars, then we need to find out how many boxes that are filled up.
[tex]\bf Step~1:[/tex]
Divide the number of candy bars (34), by the number each box can hold (5)
[tex]\bf\frac{34}{5}=6.8[/tex]
Since we cannot have 6.8 boxes, we have to round down to 6.
[tex]\boxed{\bf Our~final~answer:~6~boxes}[/tex]
[tex]\bf Check~our~answer:[/tex]
To check our answer, we multiply the number of boxes (6), by the number of bars in each box (5), to get 30. We add Ava's extra bars (4), and we get the number we started off with: 34. This proves our answer is correct!
5x (x+8)= - 7 quadratic or not? explain,
Answers
Answer:
Step-by-step explanation:
Yes it is a quadratic equation
5x^2 + 40x = -7
5x^2 + 40x + 7 = 0
a = 5
b = 40
c = 7
-40/10 + (sqrt(1600 - 4(5)(7)))/10
-4 + (sqrt(1600-160))/10
-4 + (sqrt(1440))/10
-4 + 12(sqrt(10))/10
-4 + 6/5(sqrt(10))
Owen knows he only has three pencils in his backpack, and they are all yellow. He reaches into his backpack without looking and takes out a pencil. What is the probability that the pencil was yellow? Answer options with 5 options A. 0-thirds B. 1-third C. 2-thirds D. 3-thirds E. 3 over 1 I NEED ACTUAL ANSWERS NOT JUST STUPID PEOPLE WITH A POOR SENSE OF HUMOR
Answers
Answer:
D; 3-thirds
Step-by-step explanation:
Here is a probability question.
Firstly, we need to understand that the probability of any event is between 0 and 1; it cannot be negative and cannot be more than 1.
So the probability we want to calculate here is simply the probability of drawing a yellow pencil.
The way to go about this is by dividing the number of yellow pencils by the total number of pencils
Mathematically;
Probability of bringing out a yellow pencil= Number of yellow Pencils/ Total number of pencils
From the question, we are told that the number of pencils = number of yellow pencils = 3
Thus the probability will be 3/3 = 1
This cannot be found in the options right?
1 is the same as 3-thirds meaning 3 * 1/3 = 1
How are the solutions of an inequality different from the solutions of an equation?
Answers
Answer:
Step-by-step explanation:
+
What is the x-coordinate of the solution to the following system of equations?
x − y = −3
x + 3y = 5
x = −2
x = −1
x = 1
x = 2
Answers
The {x} coordinate of the solution to the following system of equations is - 1.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the system of equations as -
x − y = − 3
x + 3y = 5
We can write -
x - y = - 3
y = x + 3
So, we can write -
x + 3(x + 3) = 5
x + 3x + 9 = 5
4x = - 4
x = - 1
Therefore, the {x} coordinate of the solution to the following system of equations is - 1.
To solve more questions on algebraic expressions, visit the link below -
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-14 could be classified as all of these EXCEPT?
Rational
Real
Whole
Integer
Answers
Answer:
it is a rational number, a integer, and a real number. It is NOT a whole number
Step-by-step explanation:
Answer:
It is not a whole number when compared to other answers.
Please help ALGEBRA 1 !
Answers
Answer:
B. 36 root7 = area of the rectangle
Solve the equation for x.
1/4(2x + 8) = –16
A)
-18
B)
-24
D
-28
D)
-36
Answers
Answer:
D
Step-by-step explanation:
Given
[tex]\frac{1}{4}[/tex] (2x + 8) = - 16
Multiply both sides by 4 to clear the fraction
2x + 8 = - 64 ( subtract 8 from both sides )
2x = - 72 ( divide both sides by 2 )
x = - 36
Answer:
The answer is option DStep-by-step explanation:
[tex] \frac{1}{4} (2x + 8) = - 16[/tex]First multiply through by 4
That's
[tex]4 \times \frac{1}{4}(2x + 8) = - 16 \times 4 \\ 2x + 8 = - 64[/tex]Subtract 8 from both sides
We have
[tex]2x + 8 - 8 = - 64 - 8 \\ 2x = - 72[/tex]Divide both sides by 2
That's
[tex] \frac{2x}{2} = - \frac{72}{2} [/tex]We have the final answer as
x = - 36Hope this helps you
A van can travel 18 miles on each gallon of gasoline. At that rate, how many miles can the van travel on 15 gallons of gasoline? 33 miles 83 miles 120 miles 270 miles Mark this and return
Answers
Answer:
270 miles
Step-by-step explanation:
if 1 gallon = 18 miles
then 15 gallons = x miles
cross multiply
1 × x = 15×18miles
x = 270 miles
so it travels 270 miles on 15 gallons of gasoline
six plus what equals -2
Answers
Answer: -8
Step-by-step explanation:
6+ -8 = -2
Last year, Gena’s food cart business was $225 in debt. This year, the debt has tripled. Which expressions show how much Gena’s business is currently in debt? Check all that apply.
225(3)
(3)(–225)
–225 + 3
3 – 225
–225(3)
Answers
Answer:
first one cause 225 times 3
Step-by-step explanation:
Answer:
answers 2 and 5
Step-by-step explanation:
How can 3.14159 be based on a multiple on the divisor?
Answers
Answer:
Here the value is similar to the value of pi ([tex]\pi[/tex])
Step-by-step explanation:
22 / 7 = [tex]\pi[/tex]
22 / 7 = 3.14159
So it is based on a multiple on the divisor 7
Is figure B a scaled copy of figure A?
Answers
Answer:
Yes
Step-by-step explanation:
Figure B is doubled in size
Answer:
Yes
Step-by-step explanation:
Because every length of each of the shape is just doubled:
Bottom of figure A=4
Bottom of figure B=8
Right Side of figure A=2
Right Side of figure B=4
Left Side of figure A=2
Left Side of figure B=4
Top of figure A=3
Top of figure B=6