URGENT! Please help me solve this question with full solutions
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.
Determine the slope of the line passing through the points (9,8) and (1,3).
slope =
Answer:
5/8
Step-by-step explanation:
slope: (y₂ - y₁) / (x₂ - x₁)
(3 - 8) / (1 - 9) = -5/-8 = 5/8
Answer:
m= 5/8
Step-by-step explanation:
The slope of a line can be found using the following formula:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }[/tex]
where (x₁, y₁) and (x₂, y₂) are the points the line passes through.
The points given are: (1,3) and (9,8). Therefore,
[tex]x_{1}=1 \\y_{1}=3 \\x_{2}=9 \\y_{2}=8[/tex]
Substitute the values into the formula.
[tex]m=\frac{8-3}{9-1}[/tex]
Perform the operation in the numerator. Subtract 3 from 8.
[tex]m=\frac{5}{9-1}[/tex]
Perform the operation in the denominator. Subtract 1 from 9.
[tex]m= \frac{5}{8}[/tex]
The slope of the line is 5/8
Can anyone Help please.
Answer:
D
Step-by-step explanation:
The remaining material can be calculated as
volume of larger cube - volume of smaller cube
= a³ - b³ ← difference of cubes which factors in general as
= (a - b)(a² + ab + b²) → D
Complete the explanation for why 2−3 is the same as 1 23 . Look at the pattern below. As the exponent goes down by , the value is of what it was before. 23 = 8, 22 = 4, 21 = 2, 20 = 1, x−x = 1 2 , x−x = 1 4 , x−x = 1 8 = 1 23
[tex]2^{-3}[/tex] is the same as [tex]\frac{1}{2^3}[/tex] because of the rule [tex]x^{-k} = \frac{1}{x^k}[/tex]
The negative exponent says to take the reciprocal of the base to make the exponent positive. The original base is 2, of which the reciprocal is 1/2.
Jon borrows $4.50 from his friends to pay for snacks, and $13.65 from his sister to go to the movies. How much money does he reed to repay?
Answer:
$18.15
Step-by-step explanation:
What is the value of y? Find the following angle measures. m
Answer:
10
Step-by-step explanation:
(10y+6) + (8y-6) =180
18y=180
y=10
JKM=10y+6=10(10)+6=106
MKL=8y-6=8(10)-6=74
Answer:
Step-by-step explanation:
10y+6+8y-6=180
then,y=10
therefore,
angle(JKM)=106
angle(MKL)=74
Find three consecutive numbers whose sum is 84.
You need 3 numbers, divide the total by 3:
84/3 = 28
This is the middle value.
Now you use the one lower and the one higher:
27 + 28 + 29 = 84
The numbers are 27, 28, 29
Answer: 26, 28, 30
Step-by-step explanation:
26, 28, and 30 follow each other in consecutive order without haps of more than two and are arranged smallest to largest.
Evaluate the stacked function machines for an input of 21*
Which expression is equivalent to 8 + n? 8n n - 8 n + 8 n = 8
Answer:
n+8
Step-by-step explanation:
8n=8(n)
n-8=n-8 (Since there is no commutative property in subtraction)
n=8 means 8=n
n+8=8+n
Because of commutative property in addition.
Hope this helps ;) ❤❤❤
Each expression with the appropiate property:
Answer:
it denotes distributive property of multiplication over addition
distributive property of multiplication over addition. The distributive property states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products together.
Sam takes the bus 3/5 of the distance from home to school. He then walks one block to his friends house and rides with the friend the remaining seven blocks to school. What fractional part of the trip did he ride with his friend?
Answer:
2/5
Step-by-step explanation:
3/5 + ____ = 5/5
2/5
PLZ ANSWER ASAP. DUE IN 1 HOUR. DIRECTIONS ARE ON THE SCREENSHOT
Answer:
DBH is an obtuse angle.
Step-by-step explanation:
D is around the 15 degree mark. h is around the 144 degree mark. Subtract 15 by 15 and 144 by 15 degrees, so that way angle D would be on the 0. You would get 129 degrees, which still makes it obtuse because is greater than 90 degrees
I hope this helps
please help me its due soon
Answer:
it is 17.2 + 16.4
Step-by-step explanation:
because 8.6x2= 17.2
then 5.2x2=10.4
then 3+3=6
lastly 10.4+6= 16.4
so that makes it 17.2+16.4
Kevin went to see his favorite sports team play his car can go 320 miles on one lank of gas. If he used 20% of a full tank of gas, how many miles did he travel?
Answer:
64 miles
Step-by-step explanation:
If he used 20% of the gas, he can go 20% of the miles
20% of 320 miles
.20 * 320
64 miles
Answer:
[tex]\huge\boxed{\sf 64\ miles}[/tex]
Step-by-step explanation:
A total tank travels to 320 miles
Let the miles be x
He used 20% of the full tank
=> 20% of the full tank = x
=> [tex]\frac{20}{100} * 320 = x[/tex]
=> 2 * 32 = x
=> x = 64 miles
So, He traveled 64 miles in 20% of the tank.
LM has one endpoint
L(-2,-9) and a midpoint
P(3,2). Find the
coordinates of the
other endpoint, M.
Thank you!
Answer:
coordinate of M (8,13)
Step-by-step explanation:
LM has L(-2,-9), P(3,2) mid point of LM
coordinate of mid point= x=x1+x1/2 and y=y1+y2/2
x1=-2 , x2 is the x of point M
xof P= (-2+x2)/2
3(2)=-2+x2
6=-2+x2 ⇒ x2=6+2=8
y of P= y1+y2/2
2=-9+y2/2
y2=2(2)+9⇒ y2=13
coordinate of M (8,13)
Can someone please tell me how to simplify [tex](2r^2t/4t^2)^2[/tex], please?
You are skiing down a mountain with a vertical height of 800 feet. The distance from the top of the mountain to the base is 1600 feet. What is the angle of elevation from the base to the top of the mountain?
Answer:
θ = [tex]30^{0}[/tex]
Step-by-step explanation:
Since the vertical height of the mountain is 800 feet, and the distance from the top to its base is 1600 feet. Let the angle of elevation be represented by θ, applying the required trigonometric function;
Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]
Sin θ = [tex]\frac{800}{1600}[/tex]
= 0.5
θ = [tex]Sin^{-1}[/tex] 0.5
θ = [tex]30^{0}[/tex]
Thus, the angle of elevation from the base to the top of the mountain is [tex]30^{0}[/tex].
Point R is on line segment \overline{QS} QS . Given QR=4,QR=4, QS=4x,QS=4x, and RS=5x-9,RS=5x−9, determine the numerical length of \overline{RS}. RS .
Answer:
RS = 16
Step-by-step explanation:
The segment addition theorem tells you ...
QR +RS = QS
4 + (5x-9) = 4x
x = 5 . . . . . . . . . . . add 5-4x
Then the length of RS is ...
RS = 5(5) -9
RS = 16
HELP ASAP!!!!! The expression 300n gives the number of 2.) calories in n cups of dry oatmeal. What is the number in 2 ¼ cups of dry oatmeal? (hint: just multiply)
Answer:
675 calories
Step-by-step explanation:
I don't know about you but for me it's easier to multiply with decimals. I turned 2 1/4 to 2.25 and because n is right next to 300 we multiply (2.25 x 300) to get 675.
Hope that helps, and have a great day!
WILL GIVE BRIANLIEST!!!!!!!!!!!!!!!!!!!!! picture down below ↓↓↓↓↓↓
Answer:
C
Step-by-step explanation:
A and c are parallel
B and d are parallel
A and c are intersecting
One month Abdul rented 3 movies and 5 video games for a total of . The next month he rented 6 movies and 2 video games for a total of $18 . Find the rental cost for each movie and each video game.
Answer:
Video Games = $5.25
Movies = $1.25
Step-by-step explanation:
(3x + 5y = 30)2
6x + 2y = 18
Video Games (y) = 5.25
6x + 10y = 60
- 6x + 2y = 18
(8y)/8 = (42)/8
6x + 2(5.25) = 18
6x + 10.5 = 18
6x = 7.5
x = 1.25
Double Check by plugging in the numbers
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
midpoint (-5,18), endpoint (3,13)
Answer:
Hey there!
If the midpoint is (-5, 18) and the endpoint is (3, 13) the other endpoint is (-13, 23)
Let me know if this helps :)
Using the remainder theorem, which quotient has a remainder of 20?
OA (3r4 – 573 + 5x + 2) = (x - 2)
O B. (3r3 + 702 + 5x + 2) = (x - 2)
Oc. (13 + 5x2 4r + 6) = (x + 5)
OD. (74 – 812 + 16) = (x + 4)
Answer:
The answer is A. (3x^4-5x^3+5x+2) =(x-2)
Step-by-step explanation:
we see that the polynomial that gives the remainder as 20 is
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)
Option A is our correct answer.
What is the remainder theorem?The remainder theorem states that when a polynomial p(x) is divided by
(x - a), then the remainder = f(a).
We have,
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2) ____(1)
We can directly find the remainder as:
x - 2 = 0
x = 2
Putting x = 2 in (1) we get,
= 3 x 16 - 5 x 8 + 5 x 2 + 2
= 48 - 40 + 10 + 2
= 20
The remainder is 20.
(3x³ + 7x² + 5x + 2) ÷ (x - 2) ) _______(2)
x - 2 = 0
x = 2
Putting x = 2 in (2) we get,
= 3 x 8 + 7 x 4 + 5 x 2 + 2
= 24 + 28 + 10 + 2
= 64
The remainder is 64.
(x³ + 5x² - 4x + 6) ÷ (x + 5) ______(3)
x + 5 = 0
x = -5
Putting x = -5 in (3) we get,
= - 125 + 5 x 25 - 4 x (-5) + 6
= -125 + 125 + 20 + 6
= 20 + 6
= 26
The remainder is 26.
([tex]x^{4}[/tex] - 8x² + 16) ÷ (x + 4) _______(4)
x + 4 = 0
x = -4
Putting x = -4 in (4) we get,
= 256 - 8 x 16 + 16
= 256 - 128 + 16
= 144
The remainder is 144.
Thus we see that the polynomial that gives the remainder as 20 is
(3[tex]x^{4}[/tex] - 5x³ + 5x + 2) ÷ (x - 2)
Option A is our correct answer.
Learn more about the remainder theorem here:
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Find the Greatest Common Factor between 42 and 45
Answer:
3
Step-by-step explanation:
The Greatest Common Factor between 42 and 45 is 3.
What is The Greatest Common Factor (GCF)?Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.
Given two numbers are 42 and 45,
42 = 7*2*3
45 = 5*3*3
GCF = 3
Hence, The Greatest Common Factor between 42 and 45 is 3.
For more references on Greatest Common Factor, click;
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2,568 + (-1,452) pls help me asap !!! we are doing adding rational numbers
Answer:
1,116
Step-by-step explanation:
2568 + ( - 1452)
= 2568 - 1452 ( because + × - makes -)
= 2568 - 1452
= 1,116
Answer:
the answer is 1116 I hope it's right
What is being constructed based in the markings in the following diagram?
Answer:
Perpendicular line through a point off a line
Step-by-step explanation:
Based on the markings in the diagram, we have;
Marking points E and F along AB extended forms two points equidistant from the point C on the line AB
Construction of the line HI by using equal arc lengths from E and F creates two points equidistant from E and F on either side of the line AB such that HI passes through C forming a perpendicular bisector from C to AB.
Therefore, a perpendicular line has been constructed from the point C off the line AB to the line AB
Hence the correct option is the construction of a perpendicular line through a point off a line.
Answer:
C. Perpendicular line through a point off a line (its off not on) Took the test and got it right
Step-by-step explanation:
the sum of a number and -43 is 102.what is the number
Answer: 145
Step-by-step explanation:
Answer: 145
Step by step explanation:
15 - [10 + (3 - 2)2] + 6
Answer:
9
Step-by-step explanation:
Use PEMDAS
Parentheses (Bracketts go after parentheses but are not included in PEMDAS)
Exponents
Multiplication
Division
Addition
Subtraction
Answer:
3
Step-by-step explanation: 15-(10+(3-2)2)+6
3-2=1x2=2+10=12 15-12=3
Determine the value of g-1(4).
help with this plz
Answer:
g-1(4)=-5
Step-by-step explanation:
because inverse mean that you will switch every x and y on the original graph
for example; point( 4,-2) inverse will be (-2,4)
so to find x=4 on the inverse than just find y=4 on the origin graph
Sarah has a wooden board that is 12 feet long. If she cuts three 28-inch pieces from the board, how many inches of board will she have left?
Answer:
60 inches
Step-by-step explanation:
12 feet=144 inches
28in x 3 = 84
144-84= 60
Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.
What do we mean by conversion of units?The conversion of units is the process of converting a quantity between multiple units of measurement, usually using multiplicative conversion factors.
What are the conversion factors between inch and foot?The conversion factor between inch and foot are:
1 foot = 12 inches,
or, 1 inch = 1/12 feet.
How do we solve the given question?We are informed that Sarah has a wooden board that is 12 feet long.
We are asked that if she cuts three 28-inch pieces from the board, how many inches of the board will she have left.
To solve the problem, we convert the length of the wooden board from feet to inches.
The board is 12 feet long. We know 1 foot = 12 inches.
∴ 12 feet = 12*12 inches = 144 inches.
∴ Length of the board = 144 inches.
Size of the piece cut by Sarah = 28 inches.
She cuts 3 such pieces,
∴ Total piece of board cut = 3*28 inches = 84 inches.
∴ Length of the board Sarah is left with = Total length of the board - Total piece cut from the board = 144 - 84 inches = 60 inches.
∴ Sarah is left with 60 inches of the board, after cutting three pieces of 28 inches of the board from 12 feet long board which is equal to 144 inches converted using the conversion factor.
Learn more about the conversion of units at
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