Answer:
[tex]\displaystyle x=-\frac{2}{3}[/tex]
Step-by-step explanation:
We want to solve the equation:
[tex]\displaystyle \sqrt{x^2-4x+8}+x=2-x[/tex]
We can isolate the square root. Subtract x from both sides:
[tex]\sqrt{x^2-4x+8}=2-2x[/tex]
And square both sides:
[tex](\sqrt{x^2-4x+8})^2=(2-2x)^2[/tex]
Expand:
[tex]x^2-4x+8=4-8x+4x^2[/tex]
Isolate the equation:
[tex]3x^2-4x-4=0[/tex]
Factor:
[tex]\displaystyle (3x+2)(x-2)=0[/tex]
Zero Product Property:
[tex]3x+2=0\text{ or } x-2=0[/tex]
Solve for each case. Hence:
[tex]\displaystyle x=-\frac{2}{3}\text{ or } x=2[/tex]
Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.
Testing x = -2/3:
[tex]\displaystyle \begin{aligned} \sqrt{\left(-\frac{2}{3}\right)^2-4\left(-\frac{2}{3}\right)+8}+\left(-\frac{2}{3}\right)&\stackrel{?}{=}2-\left(-\frac{2}{3}\right)\\ \\ \sqrt{\frac{4}{9}+\frac{8}{3}+8}-\frac{2}{3}&\stackrel{?}{=}2+\frac{2}{3} \\ \\ \sqrt{\frac{100}{9}}-\frac{2}{3}& \stackrel{?}{=} \frac{8}{3}\\ \\ \frac{10}{3}-\frac{2}{3} =\frac{8}{3}& \stackrel{\checkmark}{=}\frac{8}{3}\end{aligned}[/tex]
Since the resulting statement is true, x = -2/3 is indeed a solution.
Testing x = 2:
[tex]\displaystyle \begin{aligned}\sqrt{(2)^2-4(2)+8}+(2) &\stackrel{?}{=}2-(2) \\ \\ \sqrt{4-8+8}+2&\stackrel{?}{=}0 \\ \\ \sqrt{4}+2&\stackrel{?}{=}0 \\ \\ 2+2=4&\neq 0\end{aligned}[/tex]
Since the resulting statement is not true, x = 2 is not a solution.
Therefore, our only solution to the equation is x = -2/3.
Step-by-step explanation:
Hey there!
Given;
[tex] \sqrt{ {x}^{2} - 4x + 8} + x = 2 - x[/tex]
Take "X" in right side.
[tex] \sqrt{ {x - 4 + 8}^{2} } = 2 - 2x[/tex]
Squaring on both sides;
[tex] {( \sqrt{ {x}^{2} - 4x + 8 } )}^{2} = {(2 - 2x)}^{2} [/tex]
Simplify;
[tex] {x}^{2} - 4x + 8 = {(2)}^{2} - 2.2.2x + {(2x)}^{2} [/tex]
[tex] {x }^{2} - 4x + 8 = 4 - 8x + 4 {x}^{2} [/tex]
[tex]3 {x}^{2} - 4x - 4 = 0[/tex]
[tex]3 {x}^{2} - (6 - 2)x - 4 = 0[/tex]
[tex] 3 {x}^{2} - 6x + 2x - 4 = 0[/tex]
[tex]3x(x - 2) + 2(x - 2) = 0[/tex]
[tex](3x + 2)(x - 2) = 0[/tex]
Either;
3x+2 = 0
x= -2/3
Or;
x-2 = 0
x= 2
Check:
Keeping X= -2/3,
√(x²-4x+8 ) +X = 2-x
√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3
8/3 = 8/3 (True)
Now; Keeping X= 2
√{(2)²-4*2+8}+2 = 2-2
8 ≠0 (False)
Therefore, the value of X is -2/3.
Hope it helps!
Can someone help me with this math homework please!
Answer:
-1
Step-by-step explanation:
we match the input to the output to find that f(3) points towards -1
This is the last question for the 12 point
9514 1404 393
Answer:
WR ≅ WX
Step-by-step explanation:
To use the SAS postulate, you need congruent sides bounding a congruent angle.
Here, side WP is one side of one of the vertical angles, ∠PWR, so you need the other side of that angle: WR. The corresponding side in triangle VWX is WX. That is, for SAS, you need WR ≅ WX.
Write the equation of the graph y=
9514 1404 393
Answer:
y = 6^x -3
Step-by-step explanation:
The graph is that of an exponential function that has been translated downward. We notice the horizontal asymptote is -3, and a couple of points on the graph are (0, -2) and (1, 3).
The shifted parent function will look like ...
y = a·b^x +c
where c is the horizontal asymptote. Using the two points we found, we have ...
-2 = a·b^0 -3 . . . . . using (x, y) = (0, -2)
1 = a . . . . . . . . . . add 3 and simplify
Then using (x, y) = (1, 3), we have ...
3 = b^1 -3
6 = b . . . . . . . . . add 3 and simplify
So, the equation is ...
y = 6^x -3
How can I get the answer
Answer:
A.
Step-by-step explanation:
To find the inverse of a function, first make f(x) a y
So,
y = [tex]\frac{12}{x}[/tex] -18
Then switch the x and the y
x = [tex]\frac{12}{y}[/tex] - 18
Solve, for y
Why did U.S. leaders decide to create the Federal Reserve?
A. Economic panics showed that the banking system was not stable.
B. The United States needed to have a single type of currency.
C. Small banks requested additional government oversight.
D. State banks needed the power to create their own currencies.
Answer:
A
Step-by-step explanation:
A central bank was needed to oversee monetary policy
Answer:A
Step-by-step explanation:
I did the test
please help....Which fraction has the greatest value?
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
Any negative number couldn't count as more than a positive. 5 is more than 1, so the correct answer has to be 5/6.
Can someone please help me with this?
Answer:
x = 2/3
Step-by-step explanation:
-3x + 4 = 2
-3x = -2
x = 2/3
y = 2
(plug it into original equation)
(2/3. 2)
PLEASE HELP!! You are playing a game in which you must flip a coin and then roll a die. What is the probability of flipping a tails and then rolling a five?
===========================================================
Explanation:
1/2 is the probability of flipping tails because we have one side labeled tails out of 2 sides total.
1/6 is the probability of rolling a 5, because there's one side we want out of 6 total.
The two events (flipping the coin and rolling the die) are independent, allowing us to multiply those previously mentioned fractions:
(1/2)*(1/6) = (1*1)/(2*6) = 1/12
Find the lateral surface area of this
cylinder. Round to the nearest tenth.
r = 5 cm
5 cm
LSA = [ ? ] cm2
Enter
Answer:
[tex]A=157.07\ cm^2[/tex]
Step-by-step explanation:
Given that,
The radius of a cylinder, r = 5 cm
Height of the cylinder, h = 5 cm
We need to find the lateral surface area of the cylinder. The formula for the lateral surface area of the cylinder is given by :
[tex]A=2\pi r h[/tex]
Put all the values,
[tex]A=2\pi\times 5\times 5\\\\=157.07\ cm^2[/tex]
So, the lateral surface area of the cylinder is [tex]157.07\ cm^2[/tex].
PLEAS ANSWER ASAP If you like peanut butter and chocolate, then you will love Reese's.
What is the contrapositive of the statement?
Simplify the expression by combining like
terms:
2b + 7b2 - 2 + 3b - 1 + b
Answer:
[tex]7b^2+6b-3[/tex]
Step-by-step explanation:
Given:
[tex]2b+7b^2-2+3b-1+b[/tex]
Combine like terms.
[tex]7b^2+6b-3[/tex]
Hope this helps.
I need help with 7 and 8 please
Answer:
Can't See 7 clearly
8) (9,9)
Step-by-step explanation:
[tex]\frac{10+8}{2}[/tex] , [tex]\frac{10+8}{2}[/tex]
Add x's and divide by 2
Add y's and divide by 2
Like taking the average of the coordinates.
Write L if it is Likely to happen and Write U if it is unlikely to happen. Topic is probability
1. 2:3 __
2. 4:15 __
3. 3/10__
4. 13/21__
5. 6/16 __
6. 8:11 __
7. 9:20__
8. 11:25__
9. 5/16__
10. 7/12 __
11. 6:13__
12. 4:9__
13. 2:5 __
14. 19/45 __
15. 12/25__
Please make it quick
Answer:
1h b+h boi gate
Step-by-step explanation:
the sum of all the exponents on all the variables of a term
plsss answer
Answer:
Answer: for polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations to their solutions.
Answer:
Step-by-step explanation:
1). 2x + y = 12 -----(1)
x = 9 - 2y -------(2)
By substituting the value of x from equation (2) to equation (1)
2(9 - 2y) + y = 12
18 - 4y + y = 12
18 - 3y = 12
3y = 18 - 12
y = 2
By substituting the value of x in equation (2)
x = 9 - 2(2)
x = 9 - 4
x = 5
2). x + 2y = 9 ------(1)
2x + 4y = 20
x + 2y = 10 -------(2)
Since, both the equations are the parallel equations,
Therefore, No solutions will be the answer.
3). x + 3y = 16 -------(1)
2x - y = 11 ---------(2)
Multiply equation (2) by 3 the add to equation (1)
6x - 3y + (x + 3y) = 16 + 33
7x = 49
x = 7
From equation (1),
7 + 3y = 16
3y = 9
y = 3
4). y = 11 - 2x -------(1)
4x - 3y = -13 -------(2)
By substituting the value of y from equation (1) to (2),
4x - 3(11 - 2x) = -13
4x - 33 + 6x = -13
10x = 33 - 13
10x = 20
x = 2
From equation (1)
y = 11 - 2(2)
y = 7
5). y = 10 + x -------(1)
-3x + 3y = 30
-x + y = 10
y = 10 + x ------(2)
Equations (1) and (2) are same.
Therefore, Infinite solutions will be the answer.
6). 2x + y = 11 --------(1)
x - 2y = -7 ---------(2)
Multiply equation (1) by 2 then add to equation (2)
4x + 2y + (x - 2y) = 22 - 7
5x = 15
x = 3
From equation (2)
3 - 2y = -7
2y = 3 + 7
y = 5
Solve each system of equations by substitution. Clearly identify your solution.
Answer:
(-7,-2)
Step-by-step explanation:
y = 3x + 19
y = 5x + 33
Substitute in y. Basically set equal to each other.
3x + 19 = 5x + 33
-2x = 14
x = -7
y = 3 (-7) + 19
y = -21 + 19
y = -2
Answer:
y = -2
x = -7
Step-by-step explanation:
Substitute y= 5x + 33
5x + 33 = 3x + 19
Isolate x for 5x + 33 = 3x + 19: x = -7
For y = 5x + 33
Substitute x = -7
y = 5(-7) + 33
y = -2
So the solution is y= -2, x=-7
Instructions: Problem 2 ! Find the missing angle in the image below. Do not include spaces in your answers
Step-by-step explanation:
since angles in a triangle add up to 180
<vuw=180-(71+23)
=86°
since angles in a straight line add up to 180
<vuf=180-86
=94
Will mark brainlest helpppp pleaseeeee
Answer:
come to mya massanger dk khanal fb user
Step-by-step explanation:
i will teach you by sending picture
Solve for x, then choose
the correct graph.
- 3x > 12
answer:
-4
Step-by-step explanation:
-3x>12
x<-4
the correct graph is graph b
I tried figuring it out but its kinda hard not knowing what to make as an equation?
Write the trigonometric expression in terms of sine and cosine, and then simplify.
tan θ/(sec θ − cos θ)
Answer:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta} = \frac{1}{\sin\theta} = \csc\theta[/tex]
Step-by-step explanation:
We have the expression:
[tex]\displaystyle \frac{\tan\theta}{\sec\theta - \cos\theta}[/tex]
And we want to write the expression in terms of sine and cosine and simplify.
Thus, let tanθ = sinθ / cosθ and secθ = 1 / cosθ. Substitute:
[tex]=\displaystyle \frac{\dfrac{\sin\theta}{\cos\theta}}{\dfrac{1}{\cos\theta}-\cos\theta}[/tex]
Multiply both layers by cosθ:
[tex]=\displaystyle \frac{\left(\dfrac{\sin\theta}{\cos\theta}\right)\cdot \cos\theta}{\left(\dfrac{1}{\cos\theta}-\cos\theta\right)\cdot \cos\theta}[/tex]
Distribute:
[tex]\displaystyle =\frac{\sin\theta}{1-\cos^2\theta}[/tex]
Recall from the Pythagorean Theorem that sin²θ + cos²θ = 1. Hence, 1 - cos²θ = sin²θ. Substitute and simplify:
[tex]\displaystyle =\frac{\sin\theta}{\sin^2\theta} \\ \\ =\frac{1}{\sin\theta}[/tex]
We can convert this to cosecant if we wish.
Which equation in slope-intercept form represents a line that passes through the point (5,−1) and is parallel to the line y=2x-7?
Answer:
y = 2x - 11
Step-by-step explanation:
y = 2x + b
-1 = 2(5) + b
-1 = 10 + b
-11 = b
What is the equation of the following line?
Answer:
The equation of the line is y=7x
which point is on the graph of f(x) =5x?
Answer:
There is an infinite amount, but let say that x is 10, then:
5*10
y=50
A point(10, 50)
10. The sum of the digits of a two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27 . find the number
Answer:
Step-by-step explanation:
Let "ab" represent the digits of the number. The value of "ab" is 10a+b.
a+b = 7
The value of "ba" is 10b+a
(10b+a) - (10a+b) = 9b-9a = 27
b-a = 3
a+b = 7
b-a = 3
------------
2b = 10
b = 5
a = 2
The number is 25.
Question 5 can I have as much as you can do please
Answer:
x = 12
Step-by-step explanation:
The sum of angles in a triangle is 180°
Thus,
(x + 20) + (10x) + (x + 16) = 180°
Collect like terms
x + 10x + x + 20 + 16 = 180°
12x + 36 = 180°
12x = 180 - 36
12x = 144
Divide both sides by 12
x = 144 ÷ 12
x = 12
Substitute the value of x into the question
Therefore,
x + 20 = 12 + 20
= 32°
10x = 10(12)
= 120°
x + 16 = 12 + 16
= 28°
Amy earned $25 after babysitting for 3 hours if amy always charges the same rate,how much will she make after babysitting for 7 hours
24 is 8 times as great as q
2√4^3
find the rationalizing factor
Hello!
2√4³ =
2 × √4 ³ =
2 × 2³ =
2 × 8 = 16
Good luck! :)
Select three ratios equivalent to 4:34:34, colon, 3.Select three ratios equivalent to 4:34:34, colon, 3.
Answer:
A
C
D
Step-by-step explanation:
Select three ratios that are equivalent to 4:3.
Choose 3 answers:
(Choice A)
8:6
(Choice B)
9:12
(Choice C)
20:15
(Choice D)
32:24
(Choice E)
36:28
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
To determine which fractions are equivalent to 4:3 express the options in their lowest terms
option 1 - 8 : 6
To transform to the simplest form. divide the numbers by 2
4 : 3 this is equivalent
option 2 : 9 : 12
To transform to the simplest form. divide the numbers by 3
= 3 : 4 this is not equivalent
option 3 : 20:15
To transform to the simplest form. divide the numbers by 5
4 : 3 this is equivalent
option 4 : 32:24
To transform to the simplest form. divide the numbers by 8
4 : 3 this is equivalent
option 5 : 36:28
To transform to the simplest form. divide the numbers by 4
9 : 7 this is not equivalent
