i have the answer, 2-(3/x+2)
i got this from my calculator, however i need another line of working and i’m unsure of the process used to get there
Answers
Start with the answer format we want, and work your way toward forming a single fraction like so
[tex]a + \frac{b}{x+2}\\\\a*1+\frac{b}{x+2}\\\\a*\frac{x+2}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)}{x+2}+\frac{b}{x+2}\\\\\frac{a(x+2)+b}{x+2}\\\\\frac{ax+2a+b}{x+2}\\\\\frac{ax+(2a+b)}{x+2}\\\\[/tex]
Compare that last expression to (2x+1)/(x+2). Notice how the ax and 2x match up, so a = 2 must be the case.
Then we have 2a+b as the remaining portion in the numerator. Plugging in a = 2 leads to 2a+b = 2*2+b = 4+b. Set this equal to the +1 found in (2x+1)/(x+2) to have the terms match.
So, 4+b = 1 leads to b = -3
Therefore, a = 2 and b = -3
------------------------------------------------
An alternative route:
[tex]\frac{2x+1}{x+2}\\\\\frac{2x+1+0}{x+2}\\\\\frac{2x+1+4-4}{x+2}\\\\\frac{(2x+4)+1-4}{x+2}\\\\\frac{2(x+2)-3}{x+2}\\\\\frac{2(x+2)}{x+2}+\frac{-3}{x+2}\\\\2-\frac{3}{x+2}\\\\[/tex]
I added and subtracted 4 in the third step so that I could form 2x+4, which then factors to 2(x+2). That way I could cancel out a pair of (x+2) terms toward the very end.
------------------------------------------------
Other alternative methods involve synthetic division or polynomial long division. They are slightly separate but related concepts.
Answer:
a = 2
b = -3
Step-by-step explanation:
the secret is seeing that the numerator (top part of the division) contains 2x. that means 2 times the factor of x in the denominator (bottom part of the division).
so, we want to change the numerator that we can simply say the result is 2 and some rest (remainder).
2×(x+2) would be 2x + 4
aha !
and we have 2x+1 up there. so, what had to happen to get from 2x+4 to 2x+1 ? we had to subtract 3. it to get to 2x+4 we have to add 3.
but if we add 3, we need also to subtract 3 to keep the value of the whole expression the same.
therefore we get
(2x+1)/(x+2) = (2x+4)/(x+2) - 3/(x+2) =
= 2×(x+2)/(x+2) - 3/(x+2) = 2 - 3/(x+2)
Related Questions
Find the area of the following composite figure. Assume angles that look like they are a right angle are
right angles.
14 in
14 in
Q
Leave your answer in terms of . For example your answer might to 98 + 107.
square inches
NOTE: Figures are NOT to scale.
Answers
Answer:
7π + 7π + 196 ( could also be 14π + 196)
Step-by-step explanation:
14 is the length of the square. However it is also the diameter of the circle.
If you do diameter x π you will get the circumfrance. Which in this case is 14π. If your trying to find half of the circumfrance you would do 14π ÷ 2 which is 7π.
After finding 7π for one half a circle you do the same for the other and also get 7π
After finding the 2 half circles find the square which is 14 x 14 = 196
196 + 7π + 7π if you don't want bother pi's there it could also be seen as 196+ 14 π
What are the values of a, b, and c in the quadratic equation 0 = 1 / 3x² – 3x – 2?
O a = 3,6 =3, c= 2
O a = 1, b =-3, c= -2
O a= 2,6 = 3, c= -2
O a = 1, b = -3, c = 2
W
Answers
Answer:
[tex]a = \frac{1}{2} \\ b = - 3 \\ c = - 2[/tex]
Step-by-step explanation:
The explanation is in the picture!
Practice multiplying numbers by powers of 10.
Answers
Multiply (400 + 20 + 3) x 10000
Add 4 zeros to the end of 423
Step-by-step explanation:
423 x 10,000 = Adding the amount of zero’s in 10000 to 423
What is the length of BC? :(
Enter your answer in the box
Answers
Answer:
BC=22
Step-by-step explanation:
Hi there!
We are given an isosceles triangle (notice the markings on m<C and m<B), the length of the sides AB and AC as x-2 and 2x-24 respectively, and we want to find the length of BC (given as x)
In an isosceles triangle, the sides known as the legs (in this case, AC and AB), are congruent to each other
As they both contain x in their side lengths (remember that x=BC), let's set them equal to each other to find the value of x
2x-24=x-2
Add 24 to both sides
2x=x+22
Subtract x from both sides
x=22
So the length of BC is 22
Hope this helps!
Let the lengths of each side of △ABC having area equal to 1 be as follows: AB = 2, BC = a and CA = b. Let CD be a perpendicular line from point C to AB. Answer the following questions.
(1) Given AD = x, write a²+(2√3-1)b² in the form of x.
(2) Find the value of x at which a²+(2√3 - 1)b² is the lowest and the magnitude of ∠BAC.
Need help! Please show your work too. Thanks!
Answers
Answer:
Part 1)
[tex]\displaystyle \left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)[/tex]
Or simplified:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Part 2)
The value of x for which the given expression will be the lowest is:
[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]
And the magnitude of ∠BAC is 60°.
Step-by-step explanation:
We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.
Please refer to the diagram below.
Part 1)
Since we know that the area of the triangle is one:
[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]
Simplify:
[tex]\displaystyle CD = 1[/tex]
From the Pythagorean Theorem:
[tex]\displaystyle x^2 + CD^2 = b^2[/tex]
Substitute:
[tex]x^2 + 1 = b^2[/tex]
BD will simply be (2 - x). From the Pythagorean Theorem:
[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]
Substitute:
[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]
We have the expression:
[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]
Substitute:
[tex]\displaystyle = \boxed{\left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)}[/tex]
Part 2)
We can simplify the expression. Expand and distribute:
[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]
Simplify:
[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]
Simplify:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 2√3, b = -4, and c = (4 + 2√3).
Therefore, the x-coordinate of the vertex is:
[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]
Hence, the value of x at which our expression will be the lowest is at √3/3.
To find ∠BAC, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]
Therefore:
[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]
convert 17.25base base two to base 2
Answers
Answer:
could you explain your question better please
Hi, Which option is correct??
Answers
Answer:
B
Step-by-step explanation:
option B is not similar.
the ratio of each side isn't same
find the value of m if 3m/5+m/2=4/1+2/5
Answers
Answer: m = 3.89
Step-by-step explanation:
(3m/5)+(m/2) =(4/1)+(2/5)
= (taking LCM) (6m+5m)/10 = (20+1)/5
or, 11m/10 = 21/5
or, 55m = 210
or, m = 210/55
so, m = 3.89
Find the equation of the line that is parallel
to the line y = 3x + 9 and passes
through the point (2,1) Write the
equation in slope-intercept form.
Answers
Answer:
y = 3x - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 9 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes, then
y = 3x + c ← is the partial equation
To find c substitute (2, 1) into the partial equation
1 = 6 + c ⇒ c = 1 - 6 = - 5
y = 3x - 5 ← equation of parallel line
Please help will give brainliest
Answers
Answer:
16p - 2
Step-by-step explanation:
Answer:
20p - 2
Step-by-step explanation:
To find a perimeter, you take the values of each side and add them together.
Let's start there.[tex](p-8)+(9p-7)+(p-8)+(9p-7)[/tex]
Bring all values with a p to one side[tex]p+9p+9p+p-8+7-8+7[/tex]
Simplify, knowing values with an attached variable cannot be added to values without an attached variable.[tex]20p-8+7-8+7[/tex]
Simplify the other numbers.[tex]20p-2[/tex]
Write the following expression as a simplified polynomial in standard form.
(x-4)^2+3(x-4)+6
Answers
Answer:
x6−24x5+240x4−1280x3+3840x2−6144x+4102
Step-by-step explanation:
I don't know if this is right or not but there ig?
If s = 6 and t = 4, find the value of x.
x = 4 + s - t
Answers
Answer:
x = 6
Step-by-step explanation:
s = 6
t = 4
x = 4 + s - t
Substituting s and t in equation,
x = 4 + 6 - 4
x = 6
Answer:
6
Step-by-step explanation:
s=6
t=4
x= 4+6-4
x=10-4
x=6
Therefore; the final result is 6
The equations of four lines are given. Identify which lines are perpendicular.
Line 1: y=2
Line 2: y=15x−3
Line 3: x=−4
Line 4: y+1=−5(x+2)
Answers
Answer:
lines 1 and 3
Step-by-step explanation:
y = 2 is a horizontal line parallel to the x- axis
x = - 4 is a vertical line parallel to the y- axis
Then these 2 lines are perpendicular to each other
y = 15x - 3 ( in the form y = mx + c ) with m = 15
y + 1 = - 5(x + 2) ( in the form y - b = m(x - a) with m = - 5
For the lines to be perpendicular the product of their slopes = - 1
However
15 × - 5 = - 75 ≠ - 1
The 2 lines 1 and 3 are perpendicular
ASAPPPPPPPPPPPPPPPPPPPPPPP P P P P P P P P P P P P P P P P P P P P
Answers
Answer:
5 trees per day
Step-by-step explanation:
Answer:
5 trees per day
Step-by-step explanation:
(1, 5)
(2,10)
the day increases by 1 and the trees increase by 5
Describe and correct the error in finding the volume of the pyramid.
Answers
Match function with its corresponding graph
Answers
Answer:
Step-by-step explanation:
We can see that there are roots at (-2,0) and (-1,0)
also, the root at (-2,0) should bounce right off
and the root at (-1,0) should go through
With all that being said it has to be B
Solve, using the substitution method.
y = 3x + 5
4x – y = 5
10, 35)
(15, 10)
There are an infinite number of solutions.
There is no solution.
Answers
Answer:
the answer is (10,35)
Step-by-step explanation:
i took the quiz and im 100% sure
ty have a great day :)
I need help to find n =
Answers
Answer:
n = √108
Step-by-step explanation:
Use similar triangles or the right triangle altitude theorem.
18/n = n/6
n^2 = 18 * 6
n^2 = 108
n = √108
A real estate agent receives a 3%
commission for selling a house. Find the
commission that the agent earned for
selling a house for $131,000.
Answers
you just have to divide the value by 100 and then multiply by 3 (the order doesn't matter tho) so,
131000/100 = 1310 x 3 = 3930
the commission is $3930.00
hope it helps :)
Find the length of CV
Answers
Answer:
sinΘ = opposite/ hypotenuse
sin (37)= CV/55
55 sin (37) = CV
CV=33.1
OAmalOHopeO
ram can do a piece of work in 8 days. He work fir 6 days and left. If hari finish as the remaining work . how much work is done by hari?
Answers
Answer:
Hari finished the last two days of work that ram had left behind so that means that hari did 2 days of work.
2. Write down the supplementary angle of each of the following angles are 105 degree.
Answers
Answer:
75
Step-by-step explanation:
Answer:
75°Step-by-step explanation:
Supplementary angles add up to 180°.
The angle x, supplementary with 105°:
x + 105° = 180°x = 180° - 105°x = 75°Which is the best estimate for the percent equivalent of StartFraction 7 Over 15 EndFraction? 21% 22% 46% 47%
Answers
Answer:
47%
Step-by-step explanation:
StartFraction 7 Over 15 EndFraction = 7/15
Equivalent Percentage
7/15 × 100
= 0.4666666666666 × 100
= 46.666666666666%
Approximate to the nearest whole percentage
= 47%
The answer is 47%
Answer:7
Step-by-step explanation:
Solve for x. PLEASE HELP ASAP!!!
A. 8
B.4
C. 10
D. 7
Answers
Answer:
[tex]6(6+4)=5(5+x)[/tex]
[tex]6(10)=5(5+x)[/tex]
[tex]60=5(5+x)[/tex]
[tex]12=5+x[/tex]
[tex]x=7[/tex]
~OAmalOHopeO
Find the H.C.F of the following expressions.{x²-3x,x²-9}
Answers
Answer:
x2−3x+2=x2−2x−x+2
x(x−2)−1(x−2)=(x−2)(x−1)
Now
x2−4x+3=x2−3x−x+3
x(x−3)−1(x−3)=(x−3)(x−1)
Thus, the only common factor is (x-1)
Option A
hiiiii
Answer:
Step-by-step explanation:
x2−3x+2=x2−2x−x+2
x(x−2)−1(x−2)=(x−2)(x−1)
Now
x2−4x+3=x2−3x−x+3
x(x−3)−1(x−3)=(x−3)(x−1)
Thus, the only common factor is (x-1)
Option A
hope it helps
An exponential function fx) is reflected across the y-axis to create functiong(x). Which is a true statement
regarding fa) and g(x)?
The two functions have no points in common
The two functions have the same initial value
The two function have opposite output values of each other for any given input value
The graph of the two functions would look exactly the same
Intro
Answers
Answer:
The two functions have the same initial value
how to evaluate 4(x+2−5x) when x=2
Answers
Answer:
-24
Step-by-step explanation:
4(x+2−5x)
Combine like terms
4(2 -4x)
Distribute
8 -16x
Let x=2
8 - 16(2)
8 - 32
-24
how to evaluate 4(x+2−5x) when x=2
To Find :The value after evaluating Solution :We are provided that x equals 2 so have to put 2 instead of x to the desired result4(x + 2 - 5x)
Putting the value of x we get
4(2 + 2 - 5 × 2)
According to BODMAS multiplication comes first then addition
So 5 × 2 will be solved after that we will simplify 2 added with 2
4(2 + 2 - 10)
4(4 - 10)
4(-6)
- 24
Henceforth, the required answer is -24
Check the attached image
Answers
B
Step-by-step explanation:
Note: This doesn’t go to all systems of equation
++++++++++++++++++++++++++++++++++
Here we are given a graph where there’s basically a inequality and we are trying to find out: “Which point is a solution to the inequality?”
Answer + explanation:
Answer: O B. (0, 5)
It would be (0, 5)
Explanation:
Any point inside the shaded area of the inequality would be a solution to the system of equation
Note: The type of inequality that we are taking a look at is a dash line
What do I mean by that? That any point that is in the dash CANNOT be a solution
Therefore our answer is B
If V=πh²(r-h\3) make r subject of formula
Answers
Making r the subject of formula, we have; [tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]
In Mathematics, making a variable the subject of formula simply means making the particular variable to be equal to all the other variable contained in an algebraic expression or mathematical equation. Thus, the subject of a formula is typically on the left-hand side of a mathematical equation while the other variables on the right-side.
Given the mathematical expression;
[tex]V = \pi h^{2}(r \; - \;\frac{h}{3} )[/tex]
To make "r" subject of formula;
First of all, we would divide both sides by [tex]\pi h^{2}[/tex]
[tex]\frac{V}{\pi h^{2} } = r \; - \;\frac{h}{3}[/tex]
Next, we would rearrange the equation;
[tex]r = \frac{V}{\pi h^{2} } \; + \;\frac{h}{3}[/tex]
For more on subject of formula visit: https://brainly.com/question/17148850
The function f(t) = 4t2 − 8t + 7 shows the height from the ground f(t), in meters, of a roller coaster car at different times t. Write f(t) in the vertex form a(x − h)2 + k, where a, h, and k are integers, and interpret the vertex of f(t).
A) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 3 meters from the ground
B) f(t) = 4(t − 1)2 + 3; the minimum height of the roller coaster is 1 meter from the ground
C) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 2 meters from the ground
D) f(t) = 4(t − 1)2 + 2; the minimum height of the roller coaster is 1 meter from the ground
Answers
Answer:
A) f(t) = 4(t − 1)^2 + 3; the minimum height of the roller coaster is 3 meters from the ground
Step-by-step explanation:
f(t) = 4t^2 − 8t + 7
Factor out 4 from the first two terms
f(t) = 4(t^2 − 2t) + 7
Complete the square
(-2/2)^2 =1 But there is a 4 out front so we add 4 and then subtract 4 to balance
f(t) = 4( t^2 -2t+1) -4 +7
f(t) = 4( t-1)^2 +3
The vertex is (1,3)
This is the minimum since a>0
The minimun is y =3 and occurs at t =1
Answer:
The above answer is correct.
Step-by-step explanation:
