k/2+1/2=3
Move +1/2 to the other side. Sign changes from +1/2 to -1/2
k/2+1/2-1/2=3-1/2
k/2=3-1/2
Find the common denominator for 3 and -1/2.
Common denominator is 2
k/2=3(2)-1/2
k/2= 6/2-1/2
k/2=5/2
Multiply k/2 with 2. Multiply 2 with 5/2
k/2 (2/1)=2(5/2)
Cross out 2 and 2. Divide by 2. Cross out 2 and 2 for 5/2(2). Divide by 2
k=5
Which statement is true about lines a and b?
They are parallel lines.
They are perpendicular lines.
They are skew lines.
They will intersect.
It would be C. they are skew on ED :)
Answer: C
Step-by-step explanation: your welcome
4,792÷8 show your work
Answer:
4,792 ÷ 8 = 599Step-by-step explanation:
Look at the picture.
Use the long division.
Identify the explicit function for the sequence in the table.
1 9
2 14
3 19
4 24
5 29
,
O A. a[n) = 9+ (n - 1)•5
O B. a(n) = 5 + (n - 1)•9
O.C. a[n) = 9 (n-1)
O D. a(n) = 5(n-1)
Answer:
A.
[tex]a_n=9+(n-1)\cdot 5[/tex].
Step-by-step explanation:
The common difference is 5. The y values are going up by 5. So this is an arithmetic sequence since we have a common difference.
The explicit form for arithmetic sequence is:
[tex]a_n=a_1+(n-1) \cdot d[/tex] where d represents the commom difference and [tex]a_1[/tex] is the first term.
Here the first term is [tex]a_1=9[/tex] and we already determined the value for d which is 5.
Inputing these values for first term and common difference give:
[tex]a_n=9+(n-1)\cdot 5[/tex].
Answer:
the answer is A
Step-by-step explanation:
Select the equation of the line parallel to the equation 2x + 4y = -5 that passes through the point (-4, -8).
a). x + 2y = 16
b). 2x + y = -16
c). 2x + 4y = -9
d). x + 2y = -20
Answer:
D.
Step-by-step explanation:
First, put your original equation in slope-intercept form to find your slope.
[tex]y=mx+b\\2x+4y=-5\\4y=-2x-5\\y=-\frac{1}{2} x-\frac{5}{4}[/tex]
Now that you have your slope ([tex]-\frac{1}{2}[/tex]) and a point, you can use point-slope form to find your y-intercept.
[tex]y-y1=m(x-x1)\\y-(-8)=-\frac{1}{2} (x-(-4))\\y+8=-\frac{1}{2} (x+4)\\y+8=-\frac{1}{2} x-2\\y=-\frac{1}{2} x-10[/tex]
Your answer choices are all in [tex]Ax+By=C[/tex] form, so lets convert our equation into that form.
[tex]y=-\frac{1}{2} x-10\\1/2x+y=-10\\x+2y=-20[/tex]
If we multiply all of our terms by 2, we can get answer choice D.
If you can draw one straight line through a polygon and cross more than two sides, the polygon is _______________.
A. concave
B. convex
C. regular
D. equiangular
Answer:
If you can draw one straight line through a polygon and cross more than two sides, the polygon is concave - A.
finding whole number equal to fraction 8/1
Answer: 8
Step-by-step explanation: 8 divided by 1 is 8
8 is the whole number equal to fraction 8/1.
What is Number system?A number system is defined as a system of writing to express numbers.
The given fraction is 8/1
Eight divided by one.
A fraction represents a part of a whole or, more generally, any number of equal parts.
8 is the numerator and 1 is the denominator.
The complete set of natural numbers along with '0' are called whole numbers.
If a number is divided by another number then the result will be the numerator which is whole number.
8/1=8
Hence, 8 is the whole number equal to fraction 8/1.
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What is the complete factorization of the polynomial below x^3+5x^2-x-5
Answer:
(x+5)(x-1)(x+1)
Step-by-step explanation:
Let's attempt factoring by grouping:
So what this means we first want to group the first two terms together and second two terms together, like so:
(x^3+5x^2)+(-x-5)
Now we factor what we can from each pair:
x^2(x+5)+1(-x-5)
Notice x+5 doesn't appear to be the same as -x-5 so we should factor out -1 instead of 1 in the second pair of terms:
x^2(x+5)-1(x+5)
You have two terms: x^2(x+5) and -1(x+5); they have a common factor of (x+5) so we can factor it out:
(x+5)(x^2-1)
You can actually factor this more because x^2-1 is a difference of squares.
The formula for factoring a difference of squares is u^2-v^2=(u-v)(u+v).
So the factored form of x^2-1 is (x-1)(x+1).
So the complete factored form of our expression we had initially is
(x+5)(x-1)(x+1).
Answer:
[tex]\large\boxed{x^3+5x^2-x-5=(x+5)(x-1)(x+1)}[/tex]
Step-by-step explanation:
[tex]x^3+5x^2-x-5\qquad\text{distributive}\\\\=x^2(x+5)-1(x+5)\\\\=(x+5)(x^2-1)\\\\=(x+5)(x^2-1^2)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x+5)(x-1)(x+1)[/tex]
what is the equation of a line that contains the point (2,-5) and is parallel to the line y=3x-4
Answer:
y = 3x - 11
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 - 4 ← is in slope- intercept form
with slope m = 3
• Parallel lines have equal slopes, hence
y = 3x + c ← is the partial equation of the parallel line
To find c substitute (2, - 5) into the partial equation
- 5 = 6 + c ⇒ c = - 5 - 6 = - 11
y = 3x - 11 ← equation of parallel line
the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:
y = 3x - 11To find the equation of a line that is parallel to a given line and passes through a certain point, we need to use the concept that parallel lines have the same slope. The slope-intercept form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Given that the line is parallel to y = 3x - 4, it will have the same slope, which is 3. Thus the slope of our new line is also 3.
We want our line to pass through the point (2, -5). Plugging these values into the slope-intercept form, we get:
-5 = 3(2) + bwhich simplifies to:
-5 = 6 + bThus, the y-intercept b of our new line is:
-5 - 6 = bTherefore, the equation of the line that is parallel to y = 3x - 4 and passes through the point (2, -5) is:
y = 3x - 11There are 22 participants in a spelling bee. In how many ways can the top 5 participants finish? Use the formula for permutations to find your answer
Answer:
3,160,080Explanation:
The formula for permuations is nPk:
[tex]_nP_k=\frac{n!}{(n-k)!}=(n)(n-1)(n-2)...(n-k+1)[/tex]Where n is the total number of elements from which you must choose combinations of k number of elements, and where the order of selection is relevant.
In this case n = 22 (the number of participants), k = 5 (the number of top participants). Since, the order in which the participants finish is relevant, then you have to use the formula of permutations, such as the question states.
Calculations:
[tex]_{22}P_5=\frac{22!}{(22-5)!}=22.21.20.19.18=3,160,080[/tex]EXPLAIN!!!!!!!!!!!!!!
Answer:
111
Step-by-step explanation:
because the lines are parallel and they are on opposite sides its like having two angles on the same line but on different sides so they are supplementary meaning they add up to 180 and 180-69 = 111
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wht equation describes a parabola that opens up or down and whos vertex is at the point (h,v)
Answer:
[tex]f(x)=a(x-h)^2+k[/tex]
Vertex form.
Step-by-step explanation:
You are talking about the vertex form for a parabola.
[tex]f(x)=a(x-h)^2+k[/tex] tells us:
A) The vertex is (h,k).
B) Open up (if a is positive) or open down (if a is negative)
C) a also tells us how much it is vertically stretched or compressed.
Solve the equation 25x^2+121=0
Subtract 121 from both sides:
[tex]25x^2=-121[/tex]
Divide both sides by 25:
[tex]x^2 = -\dfrac{121}{25}[/tex]
The solutions would be
[tex]x = \pm\sqrt{-\dfrac{121}{25}}[/tex]
This expression cannot be evaluated using real numbers, because the square root of negative numbers are not allowed. If we're using complex numbers, the solutions are
[tex]x = \pm\sqrt{-\dfrac{121}{25}} = \pm\dfrac{11i}{5}[/tex]
PLEASE HELP!!!!!!!!!!!!
How does the graph of g(x) = −(x + 3)^4 compare to the parent function of f(x) = x^4
A) g(x) is shifted 3 units to the right and 1 unit up
B) g(x) is shifted 3 units to the right and 1 unit down
C) g(x) is shifted 3 units to the right and reflected over the x-axis
D)g(x) is shifted 3 units to the left and reflected over the x-axis
I would rlly appreciate it!!! :)
Answer: Option D
Step-by-step explanation:
If we have a main function [tex]f (x) = x ^ 4[/tex]
And we perform the transformation:
[tex]g (x) = f (x + h) = (x + h) ^ 4[/tex]
Then it is fulfilled that:
If [tex]h> 0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the left
If [tex]h <0[/tex] the graph of [tex]f(x)[/tex] moves horizontally h units to the right
If we have a main function [tex]f (x) = x ^ 4[/tex]
And we perform the transformation:
[tex]g (x) = -f(x) = -x ^ 4[/tex]
Then it is fulfilled that:
The graph of [tex]g(x)[/tex] is equal to the graph of [tex]f(x)[/tex] reflected on the x axis
In this case we have to:
[tex]g(x) = -(x + 3)^4[/tex] and [tex]f(x) = x^4[/tex]
Therefore [tex]h=3>0[/tex] and [tex]g(x) = -f(x)[/tex]
This mean that: g(x) is shifted 3 units to the left and reflected over the x-axis.
Type the correct answer in the box. For this item, any non-integer answer should be entered as a decimal rounded to the hundredths place. Statistics show that a certain soccer player has a 63% chance of missing the goal each time he shoots. If this player shoots twice, the probability that he scores a goal both times is_____ %.
Answer:
13.69%.
Step-by-step explanation:
The probability he scores in 1 shot = 1 - 0.63 = 0.37.
The probability that he scores twice in 2 shots = 0.37 * 0.37
= 0.1369
= 13.69%.
The probabilities are multiplied because the 2 events are independent.
Answer:
For plato user the answer is 13.69 %.
Step-by-step explanation:
If this player shoots twice, the probability that he scores a goal both times is
13.69 %.
How do u factor this?
Answer:(a+b)^2+(ab+a+b)2
Step-by-step explanation:
You break it up into two part, based on the exponents.
(a^2+b^2)+(2ab+2a+2b)
Now you can factor out from each...
(a+b)^2+(ab+a+b)2
Answer: (x+y+2)(x+y)
Step-by-step explanation:
Using square roots and factorising
Identify an equation in point-slope form for the line parallel to y = x-7 that
passes through (-3,-2).
Answer:
B. y + 2 = ½(x + 3)
Step-by-step explanation:
Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula [y - y₁ = m(x - x₁)], all the negative symbols give the OPPOSITE terms of what they really are, which is the reason why you see two "+" in the equation. The ordered pair of [-3, -2] has two negative numbers, therefore you need to make them both positive in the equation [see above answer].
I am joyous to assist you anytime.
What is the square root of -1?
Т -
ОООО
Т -
Answer:
i
Step-by-step explanation:
The square root of -1 is i which is an imaginary number
PLEASE HELP PLEASE
Which number is not divisible by either of the numbers 3 and 5?
A. 5000
B. 2374
C. 1203
D. 2505
Answer:
The answer is B. 2374
Answer:
B. 2374
Step-by-step explanation:
Division by 5: If a number ends in 0 or 5 it is divisible by 5.
A. 5000 is divisible by 5.
D. 2505 is divisible by 5.
Division by 3: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3.
B. 2374
Add the digits of 2374: 2 + 3 + 7 + 4 = 16. 16 is not divisible by 3, so 2374 is not divisible by 3. It is also not divisible by 5 since it does not end in 0 or 5.
C. 1203
Add the digits of 1203: 1 + 2 + 0 + 3 = 6. Since 6 is divisible by 3, 1203 is divisible by 3.
Answer: B. 2374
PLEASE HELP! I have three questions:
1. 4 students from a class of 15 are going to be chosen to be on the dance committee. Find the number of different 4-person committees that can be made.
2. Leslie has 7 books. There is enough space on a shelf for 3 books. In how many ways can 3 of the 7 books be arranged on the shelf? (For this one I keep getting the answer 35, but its coming up wrong on my assignment.)
3. Out of the 12 girls who tried out for the softball team, 10 will be chosen for the team. Find the number of different 10-person teams.
Thank you!!
Answer: 1. 3 can be made 2. i believe it is only one way to put three books on a shelf 3. 3 i believe, its been awhile since i studied this
Step-by-step explanation:
Solve for x.
A. 2
B. 4
C. 6
D. 8
The full length of one line times the length of the line outside the circle is equal the the other line.
(x-1) +5 x 5 = (2+x)+4 x 4
Simplify:
(x+4) x 5 = (x +6) x 4
5x +20 = 4x +24
Subtract 20 from each side:
5x = 4x +4
Subtract 4x from each side:
x = 4
The answer is B. 4
HELP ME WITH THIS QUESTION THANKS!✔✔
Answer:
-1 9/18 and then -32/40 and then 1 8/20
Step-by-step explanation:
The largest negatives is the least , then the second to least and then non-negative should be the greatest or the last
WILL GIVE BRAINLEST SUPER EASY A coyote can run up to 43 miles per hour while a rabbit can run up to 35 per hour. Write two equivalent expressions and then find how many more miles a coyote can run in six hours than a rabbit at these rates.
48 more miles
Coyote= 43h
Rabbit= 35h
Coyote= 43(6)= 258
Rabbit= 35(6)= 210
Now subtract 258 by 210
258-210= 48
In 46 years Christopher will be three times as old as he is right now. How old is he right now
Answer:
23
Step-by-step explanation:
Let his current age = x
Now if you add 46 to that, you will get x + 46.
x + 46
At which point he will be 3 times as old as he is now
x + 46 = 3x Subtract x from both sides.
x-x + 46 = 3x-x Combine
46 = 2x Divide by 2
46/2=2x/2 Do the division
23 = x
He is 23 right now
===============
It might be a little easier to see if you represent the situation a little more literally.
3x - 46 = x The answer comes to the same thing. You might think about which way you want to do it.
please Answer fast .......
Answer:
Option 3 [tex]\frac{67}{441}[/tex]
Step-by-step explanation:
step 1
Find the roots of the quadratic equation
we have
[tex]3x^{2}+5x-7=0[/tex]
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]3x^{2}+5x-7=0[/tex]
so
[tex]a=3\\b=5\\c=-7[/tex]
substitute in the formula
[tex]x=\frac{-5(+/-)\sqrt{5^{2}-4(3)(-7)}} {2(3)}[/tex]
[tex]x=\frac{-5(+/-)\sqrt{109}} {6}[/tex]
[tex]x=\frac{-5+\sqrt{109}} {6}[/tex]
[tex]x=\frac{-5-\sqrt{109}} {6}[/tex]
step 2
Let
[tex]\alpha=\frac{-5+\sqrt{109}} {6}[/tex]
[tex]\beta=\frac{-5-\sqrt{109}} {6}[/tex]
we need to calculate
[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]
step 3
Calculate [tex](3\alpha+5)^{2}[/tex]
[tex](3\alpha+5)^{2}=[3(\frac{-5+\sqrt{109}} {6})+5]^{2}[/tex]
[tex]=[(\frac{-5+\sqrt{109}} {2})+5]^{2}[/tex]
[tex]=[(\frac{-5+\sqrt{109}+10} {2})]^{2}[/tex]
[tex]=[(\frac{5+\sqrt{109}} {2})]^{2}[/tex]
[tex]=[(\frac{25+10\sqrt{109}+109} {4})][/tex]
[tex]=[(\frac{134+10\sqrt{109}} {4})][/tex]
[tex]=[(\frac{67+5\sqrt{109}} {2})][/tex]
step 4
Calculate [tex](3\beta+5)^{2}[/tex]
[tex](3\beta+5)^{2}=[3(\frac{-5-\sqrt{109}} {6})+5]^{2}[/tex]
[tex]=[(\frac{-5-\sqrt{109}} {2})+5]^{2}[/tex]
[tex]=[(\frac{-5-\sqrt{109}+10} {2})]^{2}[/tex]
[tex]=[(\frac{5-\sqrt{109}} {2})]^{2}[/tex]
[tex]=[(\frac{25-10\sqrt{109}+109} {4})][/tex]
[tex]=[(\frac{134-10\sqrt{109}} {4})][/tex]
[tex]=[(\frac{67-5\sqrt{109}} {2})][/tex]
step 5
substitute
[tex]\frac{1}{(3\alpha+5)^{2}}+ \frac{1}{(3\beta+5)^{2}}[/tex]
[tex]\frac{1}{[(\frac{67+5\sqrt{109}} {2})]}+ \frac{1}{[(\frac{67-5\sqrt{109}} {2})]}[/tex]
[tex]\frac{2}{67+5\sqrt{109}} +\frac{2}{67-5\sqrt{109}}\\ \\\frac{2(67-5\sqrt{109})+2(67+5\sqrt{109})}{(67+5\sqrt{109})(67-5\sqrt{109})} \\ \\\frac{268}{1764}[/tex]
Simplify
Divide by 4 both numerator and denominator
[tex]\frac{268}{1764}=\frac{67}{441}[/tex]
Answer:
3) 67/441
Step-by-step explanation:
Comparing the given equation to the expressions you need to evaluate, you find there might be a simplification.
3x² +5x -7 = 0 . . . . . given equation
3x² +5x = 7 . . . . . . . add 7
x(3x +5) = 7 . . . . . . . factor
3x +5 = 7/x . . . . . . . . divide by x
Now, we can substitute into the expression you are evaluating to get ...
1/(3α +5)² +1/(3β +5)² = 1/(7/α)² +1/(7/β)² = (α² +β²)/49
__
We know that when we divide the original quadratic by 3, we get
x² +(5/3)x -7/3 = 0
and that (α+β) = -5/3, the opposite of the x coefficient, and that α·β = -7/3, the constant term. The sum of squares is ...
α² +β² = (α+β)² -2αβ = (-5/3)² -2(-7/3) = 25/9 +14/3 = 67/9
Then the value of the desired expression is ...
(67/9)/49 = 67/441
25. Tom and Jerry must stuff and mail 1000
envelopes for a new marketing campaign. Jerry
can do the job alone in 6 hours. If Tom helps,
they can get the job done in 4 hours. How long
would it take Tom to do the job by himself?
A. 4 hours
B. 5 hours
C. 8 hours
D. 12 hours
Answer:
12
Step-by-step explanation:
The general formula for this is
Formula
1/t1 + 1/t2 = 1/t_tot
givens
t1 = 6 hours
t2 = x
t_tot = 4 hours
Solution
1/6 + 1/x = 1/4 Subtract 1/6 from both sides.
1/6-1/6 + 1/x = 1/4 - 1/6 Change to 12 as your common denominator
1/x = 3/12 - 2/12 subtract
1/x = 1/12 Cross multiply
x = 12
Tom would need 12 hours to do the job alone.
Answer:
Option D. 12 hours
Step-by-step explanation:
Let the work done by Tom to do the job alone = x hours
So per hour work done by Tom = [tex]\frac{1}{x}[/tex]
Jerry can do the job alone in the time = 6 hours
Per hour work done by Jerry = [tex]\frac{1}{6}[/tex]
Similarly job done by both together in the time = 4 hours
Per hour work done by both together = [tex]\frac{1}{4}[/tex]
Now we know,
Per hour work done by both together = per hour work done by Tom + Per hour work don by Jerry
[tex]\frac{1}{4}=\frac{1}{x}+\frac{1}{6}[/tex]
[tex]\frac{1}{x}=\frac{1}{4}-\frac{1}{6}[/tex]
[tex]\frac{1}{x}=\frac{3-2}{12}[/tex]
[tex]\frac{1}{x}=\frac{1}{12}[/tex]
x = 12 hours
Option D. will be the answer.
When you multiply a function by -1, what is the effect on its graph?
Step-by-step explanation:
[tex]\dfrac{a}{b}\cdot(-1)=-\dfrac{a}{b}[/tex]
On the number line, fractions a/b and -a/b lie on the opposite sides of the number 0, at the same distance (look at the picture).
Determine the area and perimeter of figure described:
square with sides of length 9mm
Answer:
Perimeter= 36mm
Area= 81mm
Step-by-step explanation:
3) Find the length of a rectangular lot with a perimeter of 92 m if the length is 8 m more than
the width.
Answer:
26 m
Step-by-step explanation:
Perimeter = 92 m
Length = 8 m more than width
Width: 20 m
Therefore,
length=26 mThe width of the rectangular lot is 19 m and the length is 27 m.
Explanation:The subject of this question is the calculation of the length of a rectangular lot. The perimeter of a rectangle is the sum of all its sides, given by the formula 2*(length + width). From the question, we know that the perimeter is 92 m, and the length is 8 m more than the width. Suppose 'w' is the width. Thus the length is 'w + 8' m.
So, we can set up the equation 2*(w + w + 8) = 92. Solving this equation will give us the value for the width (w) and consequently, the length by adding 8 to it.
Step-by-step solution:Combine like terms on the left side to get 2*(2w + 8) = 92.Then, distribute 2 to get 4w + 16 = 92.Subtract 16 from both sides to have 4w = 76.Finally, divide by 4 to find w = 19 m.The length (w+8) will then be 19m + 8m = 27m.Learn more about Rectangular Lot Dimensions here:https://brainly.com/question/34270507
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PLEASE ANSWER 9 and 10
GEOMETRY SOLVING FOR MISSING ANGLE
Answer:
9. 75°
10. 60°
Step-by-step explanation:
Note the angle-intercept theorem. If you create an angle in the opposite side of a circle from 2 points on other side, the arc will have a measure TWICE that of the intercepted angle created on other side.
Question 9
Arc WX has a measure 76, thus the angle created is Angle V, which should be HALF of that. So angle V is 76/2 = 38
Now looking at the triangle inside the circle, we know three angles of a triangle add up to 180, thus we can write and solve for "?" angle:
X + W + V = 180
? + 67 + 38 = 180
? + 105 = 180
? = 180 - 105 = 75°
Question 10
Using the theorem we can say that Angle B is HALF of ARC XYZ.
So,
2*Angle B = Arc XY + Arc YZ
2*102 = Arc XY + 124
204 = Arc XY + 124
Arc XY = 204 - 124 = 80°
Also, Arc BX + Arc XY is twice that of Angle Z (which is 70), thus
Arc BX + Arc XY = 70 *2
Arc BX + Arc XY = 140
Arc BX + 80 = 140
Arc BX = 140 - 80 = 60°
raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the circle. Write the equation of the circle.
Answer:
Equation:
[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]
The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.
Step-by-step explanation:
We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).
The center of this circle is the midpoint of (-3, 4) and (5, -2).
We use the midpoint formula:
[tex]( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )[/tex]
Plug in the points to get:
[tex]( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )[/tex]
[tex]( \frac{ -2}{2}, \frac{ 2}{2} )[/tex]
[tex]( - 1, 1)[/tex]
We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:
[tex]r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} } [/tex]
[tex]r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} } [/tex]
[tex]r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} } [/tex]
[tex]r = \sqrt{ 36+ 1 } = \sqrt{37} [/tex]
The equation of the circle is given by:
[tex](x-h)^2 + (y-k)^2 = {r}^{2} [/tex]
Where (h,k)=(-1,1) and r=√37 is the radius
We plug in the values to get:
[tex](x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2} [/tex]
[tex](x + 1)^2 + (y - 1)^2 = 37[/tex]
We expand to get:
[tex] {x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37[/tex]
[tex]{x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0[/tex]
[tex]{x}^{2} + {y}^{2} + 2x - 2y - 35= 0[/tex]
We want to find at least four points on this circle.
We can choose any point for x and solve for y or vice-versa
When y=0,
[tex]{x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0[/tex]
[tex]{x}^{2} +2x - 35= 0[/tex]
[tex](x - 5)(x + 7) = 0[/tex]
[tex]x = 5 \: or \: x = - 7[/tex]
The point (5,0) and (-7,0) lies on the circle.
When x=0
[tex]{0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0[/tex]
[tex] {y}^{2} - 2y - 35= 0[/tex]
[tex](y - 7)(y + 5) = 0[/tex]
[tex]y = 7 \: or \: y = - 5[/tex]
The point (0,-5) and (0,7) lie on this circle.