Answer:
Center (h,k) is (1,-2) and radius r = 2
Step-by-step explanation:
We need to find the center and radius of the circle of the given equation:
[tex]x^2-2x+y^2+4y+1=0[/tex]
We need to transform the above equation into standard form of circle
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
where(h,k) is the center of circle and r is radius of circle.
Solving the given equation:
[tex]x^2-2x+y^2+4y+1=0[/tex]
Moving 1 to right side
[tex]x^2-2x+y^2+4y=-1[/tex]
Now making perfect square of x^2-2x and y^2+4y
Adding +1 and +4 on both sides of the equation
[tex]x^2-2x+1+y^2+4y+4=-1+1+4[/tex]
Now, x^2-2x+1 is equal to (x-1)^2 and y^2+4y+2 =(y+2)^2
[tex](x-1)^2+(y+2)^2=4[/tex]
Comparing with standard equation of circle:
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
h = 1 , k =-2 and r =2 because r^2 =4 then r=2
So, center (h,k) is (1,-2) and radius r = 2
Which graph is the right graph
Answer:
x^2 +8x+16
Step-by-step explanation
Since you didn,t include the picture of the graph, I can still solve the equation for you
f(x+4)=(x+4)^2
=x^2 +8x+16
Find the corresponding graph in your exercise
Answer:
Im not sure what the option chocies are but I graphed both graphs online for you! :)
Solve the inequality
| 2x - 4|>-2
[tex]|2x-4|>-2\\x\in\mathbb{R}[/tex]
Reginald is distributing n boxes of paper to the copy rooms in an office building. If he places 6 boxes of paper in each copy room, there are 7 boxes left over. In order to place 7 boxes of paper in each room, he will need 2 more boxes. How many copy rooms are in the office building?
Answer:
The total number of copy rooms in the building is 9.
Step-by-step explanation:
With the given information we can compute the total number of copy rooms (let's call them r) and the boxes of paper Reginald has to distribute among them (already named n).
From the first arrangement we can see that if reginald gives 6 boxes of paper to each room, he will still have 7 boxes. We can write this as:
[tex]n = 6 \cdot r + 7[/tex]
From the second arrangement we can see that if reginald gives 7 boxes of paper to each room, he would still need 2 boxes. We can write this as:
[tex]n = 7 \cdot r - 2[/tex]
From the above, we have a 2x2 system of equations, which can be solved by any method. In this case, we can use equalization to easily find the number of rooms. From the 2 relations we can write:
[tex]6 \cdot r + 7 = 7 \cdot r - 2[/tex]
Puting known and unknowns on opposite sides, we get:
[tex]7+2 = (7-6) \cdot r [/tex]
Solving we get:
[tex]9 = r[/tex]
Therefor the total number of rooms is 9.
Pluging this solution into any of the 2 equations, we can obtain that the number of boxes of paper is 61.
As a reference, the following link is useful:
https://en.wikipedia.org/wiki/System_of_linear_equations
The number of boxes of paper exists at 61.
How to find the copy rooms in the office building?The whole number of copy rooms as r and the boxes of paper Reginald has to distribute among them (already named [tex]$\mathbf{n}$[/tex] ).
Reginald gives 6 boxes of paper to each room, he will always have 7 boxes. We can write this as:
[tex]$n=6 \cdot r+7$$[/tex]
Reginald shows 7 boxes of paper to each room, he would always require 2 boxes. We can write this as:
[tex]$n=7 \cdot r-2$$[/tex]
From the above equation, we have a [tex]$2 \times 2$[/tex] system of equations, which can be solved in any form. In this issue, we can utilize equalization to easily find the number of rooms.
From the 2 relations we can write:
[tex]$6 \cdot r+7=7 \cdot r-2$[/tex]
Putting known and unknowns on opposite sides, we get:
[tex]$7+2=(7-6) \cdot r$$[/tex]
Solving we get:
[tex]$9=r$$[/tex]
Thus the total number of rooms exists at 9.
Plugging this solution into any of the 2 equations, then we get
The number of boxes of paper exists at 61.
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HELP PLEASE!!!!!!!!!!!!!!!!! WILL GIVE BRAINLIEST!!! 6TH GRADE MATH
Which of the sets of ordered pairs represents a function?
A = {(–5, 5), (–2, 2), (2, –2), (5, –5)}
B = {(4, 2), (3, –2), (9, 4), (11, –3)} (4 points)
Only A
Only B
Both A and B
Neither A nor B
Answer:
The answer is both a and b
Answer:
both a and b is correct
The equation 3x2 = 6x - 9 has two real solutions
True
False
Answer: FALSE
Step-by-step explanation:
The first step is to rewrite the equation in the form [tex]ax^2+bx+c=0[/tex], then:
[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]
Now, we need to calculate the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
We can identify in the given equation that:
[tex]a=3\\b=-6\\c=9[/tex]
Then, we only need to substitute these values into the formula:
[tex]D=(-6)^2-4(3)(9)[/tex]
[tex]D=-72[/tex]
Since [tex]D<0[/tex] then the equation has no real solutions.
An ellipse has vertices along the major axis at (0, 8) and (0, -2). The foci of the ellipse are located at (0, 7) and
(0, -1). What are the values of a, b, h, and k, given the equation below?
Answer:
The values are a = 5 , b = 3 , h = 0 , k = 3
The equation is x²/9 + (y - 3)²/25 = 1
Step-by-step explanation:
* Lets revise the standard equation of the ellipse
- The standard form of the equation of an ellipse with center (h , k)
and major axis parallel to y-axis is (x - h)²/b² + (y - k)²/a² = 1 , where
-The length of the major axis is 2a
- The coordinates of the vertices are (h , k ± a)
- The length of the minor axis is 2b
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c), where c² = a² - b²
* Now lets solve the problem
∵ The vertices of the ellipse along the major axis are (0 , 8) , (0 , -2)
∴ The major axis is the y-axis
∴ The vertices are (h , k + a) and (h , k - a)
∴ h = 0
∴ k + a = 8 ⇒ (1)
∴ k - a = -2 ⇒ (2)
∵ The foci of it located at (0 , 7) , (0 , -1)
∵ The coordinates of the foci are (h , k + c) and (h , k - c)
∴ h = 0
∴ k + c = 7 ⇒ (3)
∴ k - c = -1 ⇒ (4)
- To find k and a add equations (1) and (2)
∴ (k + k) + (a + - a) = (8 + -2)
∴ 2k = 6 ⇒ divide both sides by 2
∴ k = 3
- Substitute the value of k in equation (1) or (2) to find a
∴ 3 + a = 8 ⇒ subtract 3 from both sides
∴ a = 5
- To find the value of c substitute the value of k in equation (3) or (4)
∴ 3 + c = 7 ⇒ subtract 3 from both sides
∴ c = 4
- To find b use the equation c² = a² - b²
∵ a = 5 and c = 4
∴ (4)² = (5)² - a²
∴ 16 = 25 - b² ⇒ subtract 25 from both sides
∴ -9 = -b² ⇒ multiply both sides by -1
∴ b² = 9 ⇒ take √ for both sides
∴ b = 3
* The values are a = 5 , b = 3 , h = 0 , k = 3
* The equation is x²/9 + (y - 3)²/25 = 1
Answer:
a=5, b=3, h=0, k=3
Step-by-step explanation:
The center of the circle is (0,3) therefore h is 0 and k is 3. If you use a graphing calculator and plot the points given you should find that a=5. Then try to c and use the equation c^2=a^2-b^2 to find b.
A triangular flag has an area of 493 square meters and a height of 17 meters. What is the length of the base
Answer:
58 meters
Step-by-step explanation:
We are looking for the length of the base of a triangle, given the height and area. The formula for the area of a triangle
A=1/2 bh
relates A= the area, b= length of the base, and h= the height of a triangle, so this is the formula we should use.
We are given that the area of the triangle is A=493 and the height h=17. Substitute this information into the formula and solve for b to find
A=493
493=1/2⋅b⋅17
493=17/2b
58=b
The length of the base is 58 meters.
The length of the base of the triangle is 58 meters.
Given,
A triangular flag has an area of 493 square meters and a height of 17 meters.
We need to find what is the length of the base.
What is the area of a triangle?The area is given by:
= 1/2 x base x height
Find the area of the triangle.
Area = 493 square meters
Height = 17 meters
Area = 1/2 x base x height
493 square meters = 1/2 x base x 17 meters
Multiply 2 on both sides.
2 x 493 = 2 x 1/2 x base x 17
986 = base x 17
Dividing both sides by 17.
986 / 17 = base
Base = 58 meters.
Thus the length of the base of the triangle is 58 meters.
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write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3
part 1:write the equation in point slope form
part 2: rewrite the equation in slope intercept form
part 3: rewrite the equation in a standard form
Answer:
[tex]\large\boxed{y-3=-\dfrac{1}{3}(x+6)-\text{point-slope form}}\\\boxed{y=-\dfrac{1}{3}x+1-\text{slope-intercept form}}\\\boxed{x+3y=3-\text{standard form}}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]m=-\dfrac{1}{3},\ (-6,\ 3)\to x_1=-6,\ y_1=3[/tex]
Substitute:
[tex]y-3=-\dfrac{1}{3}(x-(-6))\\\\y-3=-\dfrac{1}{3}(x+6)[/tex]
Convert to the slope-intercept form
[tex]y=mx+b[/tex]
[tex]y-3=-\dfrac{1}{3}(x+6)[/tex] use the distributive property
[tex]y-3=-\dfrac{1}{3}x-2[/tex] add 3 to both sides
[tex]y=-\dfrac{1}{3}x+1[/tex]
Convert to the standard form
[tex]Ax+By=C[/tex]
[tex]y=-\dfrac{1}{3}x+1[/tex] multiply both sides by 3
[tex]3y=-x+3[/tex] add x to both sides
[tex]x+3y=3[/tex]
The graph of which function will have a maximum and a y-intercept of 4?
0 fx) = 4x + 6x-1
f(x) = -4x2 + 8x + 5
f(x) ==x2 + 2x + 4
0 f(x)= x2 + 4x-4
Answer:
f(x) = -x² + 2x + 4Step-by-step explanation:
We have quadratic functions f(x) = ax² + bx + c.
c - y-intercept
If a > 0, then a parabola opens up and has a minimum in a vertex.
If a < 0, then a parabola opens down and has a maximum in a vertex.
The function has maximum and y-intercept of 4:
a < 0 and c = 4
The graph of the function which will have a maximum and a y-intercept of 4 is C. f(x) = x² + 2x + 4.
What is y Intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
Given are four functions.
We have to find the function which has a y intercept of 4.
This means that substitute x = 0 and then find the value of f(x).
A. f(x) = 4x² + 6x - 1
When x = 0, f(x) = -1 ≠ 4
B. f(x) = -4x² + 8x - 5
When x = 0, f(x) = -5 ≠ 4
C. f(x) = x² + 2x + 4
When x = 0, f(x) = 4
D. f(x) = x² + 4x - 4
When x = 0, f(x) = -4
Hence the function which has a y intercept of 4 is C. f(x) = x² + 2x + 4.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
You roll a number cube twice. Find P(even, then not 2). Write the probability as a fraction in simplest form.
Answer:
5/12
Step-by-step explanation:
First find the probability on the first roll
The possible results are 1,2,3,4,5,6
evens: 2,4,6
not 2 = 1,3,4,5,6
P(even)= number of evens/total = 3/6 = 1/2
P (not 2) = number of results not 2/ total = 5/6
Since the rolls are independent (do not depend on each other), we can multiply the probabilities
P(even, then not 2) = 1/2 * 5/6 = 5/12
Ghlj and gstu are both parallelograms why is angle L= angle T
Answer: By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation: This is the sample response on Edge.
Both parallelograms are <L ≅ < T
Because, by the parallelogram angle theorem, opposite angles of a parallelogram are congruent.
Given parallelograms, GHLJ and GSTU such the parallelogram GSTU is inscribed inside parallelogram GHLJ with angle G coinciding on the two parallelograms.
Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Therefore, ∠L ≅ ∠T
The parallelogramA parallelogram is a two-dimensional geometrical shape, whose sides are parallel to each other. It is a type of polygon having four sides (also called quadrilateral), where the pair of parallel sides are equal in length. The Sum of adjacent angles of a parallelogram is equal to 180 degrees.
Parallelograms are shapes that have four sides with two pairs of sides that are parallel. The four shapes that meet the requirements of a parallelogram are square, rectangle, rhombus, and rhomboid.
Four types of parallelogramsRectangles, rhombus, and squares are parallelograms. A trapezoid has at least one pair of parallel sides. The parallel sides are called the bases and the non-parallel sides are called the legs. There are three types of trapezoid - isosceles, right-angled, and scalene trapezoids.
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Fractions and decimals order least to greatest 1 3/4, 2.3, 2/5, 1.6
Answer: 2.3, 1 3/4, 1.6, 2/5
Step-by-step explanation: Convert each fraction into a decimal (or vise versa), then order.
1 3/4 = 1.75
2/5 = 0.4
Answer:
Answer is 2/5, 1 3/4, 1.6, 2.3
Step-by-step explanation:
Lets see: 1 3/4 = 7/4
2.3 = 23/10 or 2 3/10
2/5 is 2/5
and
1.6 is 8/5
so the least is 2/5, 1 3/4, 1.6, 2.3
Hope my answer has helped you in any way!
Let f(x) = x2 − 8x + 5. Find f(−1). (1 point) −3 14 −4 13
Answer:
f(- 1) = 14
Step-by-step explanation:
To evaluate f(- 1) substitute x = - 1 into f(x)
f(- 1) = (- 1)² - 8(- 1) + 5 = 1 + 8 + 5 = 14
Answer:
f(-1)=14
14-4=25
13=70
Step-by-step explanation:
Rachel received a $90 gift card for a coffee store. She used it in buying some coffee that cost $7.74 per pound. After buying the coffee, she had $66.78 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds
Step-by-step explanation:
What is the factored form of 2x^3 + 4x^2 - 4
Answer:
2 ( x ^3 + 2 x^ 2 − 2 )
Step-by-step explanation:
Factor 2 out of
2 x^ 3 + 4 x^ 2 − 4 .
Following Quotient expression
Answer:
Second choice
and the last 2 choices
Step-by-step explanation:
32m/16m=2 and our constant is 3 not 2 so not choice A
4m^2/2m=2m so possible 6m/2m=3 so choice B
4m/2m=2 and our constant is 3 not 2 so not choice C
10m/5m=2 same reason as A and C
10m^2/5m=2m possible...15m/5m=3 so choice E
32m^2/16m=2m and 48m/16m=3 so this last choice too
Solve for x
n(17+ x) = 34z - r
Answer:
[tex]x=\frac{34z-r}{n}-17[/tex]
Step-by-step explanation:
Given
[tex]n(17+x)=34z-r[/tex]
We have to isolate x on one side of the equation
Dividing both sides by n
[tex]\frac{n(17+x)}{n} =\frac{34z}{n}-\frac{r}{n}[/tex]
Taking LCM on left side
[tex]17+x = \frac{34z-r}{n}[/tex]
Subtracting 17 from both sides
[tex]17+x-17 = \frac{34z-r}{n}-17[/tex]
So, the value of x will be:
[tex]x=\frac{34z-r}{n}-17[/tex] ..
The answer is:
[tex]x=\frac{34z-r}{n}-17[/tex]
Why?To solve for "x" , we just need to isolate it from the equation.
So, we are given the equation:
[tex]n(17+x)=34z-r[/tex]
Then, isolating we have:
[tex]n(17+x)=34z-r\\\\17+x=\frac{34z-r}{n}\\\\x=\frac{34z-r}{n}-17[/tex]
Hence, the answer is:
[tex]x=\frac{34z-r}{n}-17[/tex]
Have a nice day!
The function relating the height of an object off the ground to the time spent falling is a quadratic relationship. Travis drops a tennis ball from the top of an office building 90 meters tall. Three seconds later, the ball lands on the ground. After 2 seconds, how far is the ball off the ground? 30 meters 40 meters 50 meters 60 meters
Answer:
Answer is 50 meters
Step-by-step explanation:
Solution:
Height of the building (h)= 90 meters.
Time taken by the ball to reach the ground (t) = 3 seconds
According to the statement;
h = kt²
90=k(3)²
90=k(9)
90=9k
Divide both the sides by 9
k=10
h=kt²
Put the value time (t)=2 in the equation
h=10(2)²
h=10(4)
h=40 meters
Distance from the ground = 90 - 40
=50 meters.
Thus the correct option is 50 meters....
Answer:
The answer is A) 50 meters
Step-by-step explanation:
An automobile's radiator has a capacity of fifteen quarts, and it currently contains twelve quarts of a thirty percent antifreeze solution. How many quarts of pure antifreeze must be added to strengthen the solution to forty percent?
2 quarts
3 quarts
4 quarts
Answer:
2 quarts
Step-by-step explanation:
We know that an automobile's radiator has a capacity of fifteen quarts and currently carries twelve quarts of a thirty percent antifreeze solution.
We are to find the number of quarts of pure antifreeze that must be added to strengthen the solution to forty percent.
We can write the following equation for this and solve it:
[tex] 12 + x = y \\ 12 (.30) + 1 x = y ( . 4 0 ) [/tex]
[tex]3.6 + x = 0.4y[/tex]
[tex]0.4(12 + x) = 3.6 + x&\\4.8 + 0.4x = 3.6 + x[/tex]
[tex]x-0.4x=4.8-3.6[/tex]
[tex]0.6x=1.2[/tex]
[tex]x=2[/tex]
Therefore, 2 quarts are needed.
For f (x) = 3x +1 and g(x) = x^2-6, find (g/f)(x)
Answer:
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
Step-by-step explanation:
We have the following functions
[tex]f (x) = 3x+1[/tex]
[tex]g (x) = x^2-6[/tex]
To find [tex](g/f)(x)[/tex] we must divide the function g(x) with the function f(x)
Then we perform the following operation
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
Finally we have that:
[tex](g/f) (x) =\frac{x^2-6}{3x+1}[/tex]
For [tex]x \neq -\frac{1}{3}[/tex]
the number line below represents the solution to which inequality?
<--|--|--|--|--|--O--|--|--|--|--|--|--|--|--|-->
__ -6__-4__-2 __0 __2 __4 __6
(Filled circle)
(Arrow pointing left from -2)
F. -2x + 7 > 8
_
G. 7x + 11 < 4
_
H. 6x - 9 < -21
_
J. -3x -15 < -27
_
The number line represents the solution to the inequality -2x + 7 > 8, and the solution is x < -0.5.
Explanation:The filled circle and the arrow pointing left on the number line indicate that the solution to the inequality is to the left of -2.
The inequality that represents this solution is -2x + 7 > 8.
To solve this inequality, we can subtract 7 from both sides to isolate the x variable.
This gives us -2x > 1. Finally, we divide both sides of the inequality by -2, remembering that when we divide by a negative number, the inequality sign flips.
So, the solution to the inequality is x < -0.5.
Thus, Correct option for the given number line is F. -2x + 7 > 8.
Final answer:
The number line indicates the solution to the inequality H. 6x - 9 < -21, where x < -2, including -2 (since the circle is filled). The solution matches the given number line plot.
Explanation:
The number line given indicates the solution to an inequality that includes all numbers to the left of – the filled circle on –2, which means –2 is included in the solution set. This represents an inequality that is of the form x ≤ a where a is –2 in this case. Now let's analyze each of the provided inequalities.
F. -2x + 7 > 8: Solving this we get –x > 1 or x < –1, which does not match the plot.
G. 7x + 11 < 4: Solving this inequality we get x < –1, which also is not a match.
H. 6x - 9 < -21: Resolving this inequality leads to x < –2, which matches the number line.
J. -3x - 15 < -27: Solving this we get x > 4, which is incorrect as per the number line plot.
Therefore, the correct inequality is H. 6x - 9 < -21.
A window is being replaced with tinted glass. The plan below shows the design of the window. Each unit length represents 1 foot. The glass costs $26 per square foot. How much will it cost to replace the glass? Use 3.14 for π.
g790432
The cost to replace the glass of the window is $
Answer:
Step-by-step explanation:
Okay first if each unit length is 1 ft then you need to find out what the total cost would be. Then use 3.14 and find the total area of £
Which statements are true ? Check all that apply ?
Answer: answers 1 and 5 are correct.
The mean monthly rent of students at Oxnard University is $890 with a standard deviation of $206. John's rent is $1,395. What is his standardized z-score?
Answer:
$299
Step-by-step explanation:
Rent+standard deviation 890+206= $1,096
John's rent: $1,395
Z-score: 1395 - 1096=$299
Answer: 2.4515
Step-by-step explanation:
Given : The mean monthly rent of students at Oxnard University is [tex]\mu=\$890[/tex] with a standard deviation of [tex]\sigma=\$206[/tex]
Using the formula , [tex]z=\dfrac{x-\mu}{\sigma}[/tex], we have the standardized z-value for x= 1395 as
[tex]z=\dfrac{1395-890}{206}=2.45145631068\approx2.4515\ \text{ [To the nearest four decimal places.]}[/tex]
Hence, the standardized z-score = 2.4515
write an expression without exponent that is equivalent to (2^3)(4^3)
Answer:
512
Step-by-step explanation:
Solve the parenthesis first. Note that:
2^3 = 2 * 2 * 2 = (4) * 2 = 8
4^3 = 4 * 4 * 4 = (16) * 4 = 64
Multiply:
8 * 64 = 512
512 is your equivalent expression.
~
Answer:
(2³)(4³) = 2³ x [tex]2^{6}[/tex] = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 512
Can someone please help me
Answer:
x < -7Step-by-step explanation:
<, ≤ - line to the left
>, ≥ - line to the right
<, > - open circle
≤, ≥ - closed circle
==================================
We have the line to the left and open circle.
The circle is on -7.
Therefore is x < -7
vertical angles must check all that apply
Answer:
Vertical angles must have the same vertex and be congruent as well.
Step-by-step explanation:
Answer:
Correct answer is B and C.
Step-by-step explanation:
Vertical angles are those angles opposite each other when two lines intersect. So, they have the same vertex.
When two lines intercept form 4 angles. Those that are opposite to each other are vertical angles, these angles are always congruent.
Someone please help
Answer:
[tex]\large\boxed{6\sqrt[5]{x^2y}=6x^\frac{2}{5}y^\frac{1}{5}}[/tex]
Step-by-step explanation:
[tex]\sqrt[n]{a^m}=a^\frac{m}{n}\\\\6\sqrt[5]{x^2y}=(6)(\sqrt[5]{x^2})(\sqrt[5]{y})=6x^\frac{2}{5}y^\frac{1}{5}[/tex]
Cylinder A has a radius of 1 m and a height of 4 m. Cylinder B has a radius of 2 m and a height of 4 m. What is the ratio of the volume of cylinder A to the volume of cylinder B?
a: 5:6
b: 1:4
c: 1:2
d: 1:1
Note: The volume of a cylinder is:
radius² × π × height
First lets work out the volume of Cylinder A:
Volume = 1² × π × 4
= 4π m³
Now lets work out the volume of Cylinder B
Volume = 2² × π × 4
= 16π m³
__________________________________________
Now lets compare the volumes ( Cylinder A : Cylinder B) :
4π : 16π
Lets simplify this by dividing both sides by 4π:
4π : 16π ( ÷ 4π)
----> 1 : 4
_____________________________________________________
Answer:
Option b) 1 : 4
Answer:
1:4
Step-by-step explanation:
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
[tex]\sqrt{x-2}[/tex] + 8 = x
Answer:
(17+√553)/2
and
(17-√553)/2
Step-by-step explanation:
Subtract 8 from both sides. This leaves you with
sqrt(x-2) = x-8. Square both sides to get rid of the sqrt,
leaving x-2=(x-8)^2
expanding gives x-2=x^2-16x+64
subtract x from both sides leaves
-2=x^2-17x+64
add 2 to both sides
x^2-17x+66=0
this cannot be factored, however, there are other techniques.
Completing the square is a bit annoying, so I will use the quadratic formula, to give the answer.
This gives you:
(17+√553)/2
and
(17-√553)/2
Hope this helps!