Answer:
[tex]\large\boxed{-2(10r+4)+10(7r+2)=50r+12}[/tex]
Step-by-step explanation:
[tex]-2(10r+4)+10(7r+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=(-2)(10r)+(-2)(4)+(10)(7r)+(10)(2)\\\\=-20r-8+70r+20\qquad\text{combine like terms}\\\\=(-20r+70r)+(-8+20)\\\\=50r+12[/tex]
Who was the 35th president
Answer:
John F. Kennedy
Which of the following is a trino
Answer:
Option 1
Step-by-step explanation:
Tri means 3. An expression which has 3 terms and the terms are separated by plus or minus:
c^2+c+6
Thus option 1 is correct....
For this case we have that by definition, a trinomial is an algebraic expression formed by the sum or difference of three terms or monomials.
Example:
[tex]ax ^ 2y + cx + dy[/tex]
Thus, the correct option is option 1.
[tex]c ^ 2 + c + 6[/tex]
Three terms are observed.
Answer:
Option 1
At most, how many unique roots will a third-degree polynomial function have?
Answer: 3
Step-by-step explanation: I jus got it right on a pex
the length of a rectangular garden is 3 times its width. if the perimeter of the garden is 40 yards, what is the area
Answer:
75 yd^2.
Step-by-step explanation:
If the width = x yards, the length will be 3x yards.
The perimeter = 2 * length + 2 * width
= 2* 3x + 2*x = 40
6x + 2x = 40
8x = 40
x = 5
So the width is 5 and the length is 15 yards.
The area = 5 * 15 = 75 yd^2.
Answer:
75
Step-by-step explanation:
x=breadth
3x=length
perimeter=2(x+3x)=8x
40=8x
x=5
length=15
breadth=5
area=15*5=75
What is the greatest common factor of the numbers 12 and 54?
Answer:
6
Step-by-step explanation:
54=2x3x3x3
12=2x2x3
common factors are 2 and 3 so 2x3=6
The sum of two integers is 45. If one of them is (-200). Find the other.
Step-by-step explanation:
Let the number be x
ATQ,
-200+x =45
x=45+200
x=245
The other integer is equal to 245.
Explanation:We know that [tex]x+y=45[/tex]. We also know that [tex]x=-200[/tex].
Substitute the value into the equation. [tex]-200+y=45[/tex]
Add 200 to both sides of the equation. [tex]y=45+200=245[/tex]
Now, you have the answer. [tex]y=245[/tex]
emily has earned the following grades A, c+, a-,b- and b+. what grade must she earn in her biology class to keep her 3.2 gpa?
Answer:
B+
Step-by-step explanation:
Grades earned in five subjects are;
A,C+,A-,B- and B+
Remaining subject is biology
Total number of subjects will be=6
3.2 gpa as a percentile =86
For her to maintain 3.2 gpa total sum of percentile in the 6 subjects should be at least
6×86=516
Emily total sum of subjects in percentile is 93+77+90+80+87=427
Find the difference , 516-427=89
89 is grade B+
Emily should earn a grade of B+ to keep her 3.2 gpa
Need help with question number 55
Answer:
1) The profit of the company dropped by -15% compared to last year.
2) The temperature of Alaska was -5 degrees yesterday.
3) John had 1,000$ dollars deposited in the bank, and then made a poor investment, causing him to owe the bank 5,000$, making his account -4,000$
Step-by-step explanation:
With each scenario you have to try to find a new way to express a negative number which is primarily through loss. In which ways can you unique express loss of a value below zero in real world is the question, and you can do so with examples like money and temperature.
Which expression could be used to determine the product of -4 and 3
A. (-4)(3) × (-4) 1/4
B. (-4)(3)+(-4) 1/4
C. (3)(-4)x(3) 1/4
D. (3)(-4)+(3)(1/4)
Answer ASAP!
Answer:
I think that the answer is A.
Answer:
No options is correct.
Step-by-step explanation:
Given : The product of -4 and 3.
To find : Which expression could be used to determine the product ?
Solution :
The product of -4 and 3 is [tex]-4\times 3=-12[/tex]
To know which expression we solve each options and get whose result is same as ours,
A) [tex](-4)(3)\times (-4)(\frac{1}{4})[/tex]
Solve,
[tex](-4)(3)\times (-4)(\frac{1}{4})= -12\times -1=12[/tex]
B) [tex](-4)(3)+(-4)(\frac{1}{4})[/tex]
Solve,
[tex](-4)(3)+(-4)(\frac{1}{4})= -12+(-1)=-13[/tex]
C) [tex](3)(-4)\times (3)(\frac{1}{4})[/tex]
Solve,
[tex](3)(-4)\times (3)(\frac{1}{4})=-12\times\frac{3}{4}=-9[/tex]
D) [tex](3)(-4)+(3)(\frac{1}{4})[/tex]
Solve,
[tex](3)(-4)+(3)(\frac{1}{4})=-12+\frac{3}{4}=-11.25[/tex]
From the given options, No options will get the product.
A square has an area of 100. What is the length of each side?
Answer:
One side is 10
Step-by-step explanation:
10*10 is equal to 100
What is the measure of AC?
Answer:
AC = 26
Step-by-step explanation:
AD = DC . . . . . .these segments are marked congruent
8x-1 = 6x+9 . . . substitute the given expressions
2x = 10 . . . . . add 1-6x
x = 5
__
AC = 2·AB = 2(3x-2) = 2(3·5-2) . . . . substitute into expression for AB
AC = 26
Gloria has 11 markers in a backpack. One of them is purple and one is gray. Find the probability Gloria will reach into the backpack without looking and grab the purple marker and then reach in a second time and grab the gray marker. Express your answer as a fraction in simplest form.
Answer:
Step-by-step explanation:
She has 1 in 11 chances of getting the purple one
One of her choices is gone after she takes out the purple one. She has a 1 in 10 chance of taking out the gray one.
1/11 * 1/10 = 1/110
The probability that Gloria will draw the purple marker first and then the gray marker from her backpack on consecutive tries without replacement is 1/110.
The question asks to find the probability that Gloria will pull the purple marker and then the gray marker out of the backpack on consecutive tries without replacement. To calculate the combined probability of two independent events happening in succession, you multiply the probability of each event occurring separately.
On the first draw, the probability of selecting the purple marker is 1 out of 11 markers, or 1/11. After drawing the purple marker, it is not replaced, so there are now only 10 markers left, one of which is gray. The probability of drawing the gray marker on the second draw is then 1 out of the remaining 10 markers, or 1/10.
To find the overall probability of both events happening, multiply the two probabilities: (1/11) x (1/10) = 1/110.
The probability that Gloria will draw the purple marker first and then the gray marker is 1/110.
You need a 30% alcohol solution. On hand, you have a 90 mL of a 45% alcohol mixture. How much pure water will you need to add to obtain the desired solution?
You will need
_____ mL of pure water
to obtain
______ mL of the desired 30% solution.
Answer:
45ml of pure water to obtain 135ml of the desired 30% solution
Step-by-step explanation:
45% of 90 = 40.5
So, 40.5ml of alcohol in 90ml
We want 30% and therefore need a ratio of 3:7
40.5÷3=13.5
so one part of our ratio is 13.5
we then times this by 7
13.5 x 7 = 94.5
so, 94.5ml of water
to work out how much we already have, we should do 90ml- 40.5ml = 49.5ml
and then 94.5- 49.5 = 45ml
We need 45ml of water and the total mo of the desired solution will be 90+45=135ml
To dilute a 45% alcohol solution to a 30% alcohol solution by adding pure water, you will need to add 45 mL of pure water to the initial 90 mL to achieve a total volume of 135 mL with the desired 30% alcohol concentration.
To dilute a 45% alcohol solution to a 30% alcohol solution using pure water, we can use the concept of concentration dilution in chemistry. This involves calculating the amount of diluent (in this case, water) to add to an existing solution to achieve a desired concentration.
Let's denote the amount of pure water to add as x mL. The initial volume of the alcohol solution is 90 mL with a 45% concentration, meaning it contains 40.5 mL of pure alcohol. Since adding water doesn't change the amount of alcohol, the final mixture's alcohol volume remains at 40.5 mL.
To find the final volume of the solution and the amount of water needed, we use the formula for the final concentration: Final Concentration = (Volume of Solute) / (Final Volume of Solution). Substituting the given and desired values gives us 30% = 40.5 mL / (90 mL + x).
Rearranging and solving for x gives: x = (40.5 / 0.3) - 90 = 135 - 90 = 45 mL. Therefore, 45 mL of pure water must be added to the original solution to get a 30% alcohol solution.
In conclusion, adding 45 mL of pure water to the 90 mL of 45% alcohol mixture yields a total volume of 135 mL of the desired 30% solution.
what is the simplified form of the expression 3(7/5x+4)-2(3/2-5/4x)?
Answer:
Step-by-step explanation:
distribute the first part of each term
(21/5x+12)+(-3+5/2x)
combine the xs and the numbers
9+6.7x
For this case we must simplify the following expression:
[tex]3(\frac{7}{5}x+4)-2(\frac{3}{2}-\frac{5}{4}x)=\\\frac{3*7}{5}x+ 3*4-\frac{2*3}{2} +\frac{2*5}{4}x=\\\frac{21}{5}x +12-\frac{6}{2} +\frac{10}{4}x=\\\frac{21}{5}x +12-3+ \frac{10}{4}x=[/tex]
We add similar terms:
[tex]\frac{21}{5}x+ \frac{10}{4}x+ 9=\\(\frac{21}{5} +\frac{10}{4})x +9=\\\frac{67}{10}x +9[/tex]
ANswer:
[tex]\frac{67}{10}x+9[/tex]
What do I do for this?
if EF ≅ WV and JK is intersecting both at a right-angle, the distances OK = JP and likewise PG = GO, namely
[tex]\bf 2(4x-3)-8=4+2x\implies 8x-6-8=4+2x\implies 8x-14=4+2x \\\\\\ 6x-14=4\implies 6x=18\implies x=\cfrac{18}{6}\implies x=3[/tex]
Find the value of each variable.
Answer:
see explanation
Step-by-step explanation:
Using the exact values of the trigonometric ratios
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex], cos60° = [tex]\frac{1}{2}[/tex]
sin45° = cos45° = [tex]\frac{1}{\sqrt{2} }[/tex]
Using the sine ratio on the right triangle on the left
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{4\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]
Cross- multiply
2a = 4[tex]\sqrt{3}[/tex] × [tex]\sqrt{3}[/tex] = 12 ( divide both sides by 2 )
a = 6
Using the cosine ratio on the same right triangle
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{c}{4\sqrt{3} }[/tex] = [tex]\frac{1}{2}[/tex]
Cross- multiply
2c = 4[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
c = 2[tex]\sqrt{3}[/tex]
------------------------------------------------------------------------------------------
Using the sine/cosine ratios on the right triangle on the right
sin45° = [tex]\frac{a}{b}[/tex] = [tex]\frac{6}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]
Cross- multiply
b = 6[tex]\sqrt{2}[/tex]
cos45° = [tex]\frac{d}{b}[/tex] = [tex]\frac{d}{6\sqrt{2} }[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]
Cross- multiply
[tex]\sqrt{2}[/tex] d = 6[tex]\sqrt{2}[/tex] ( divide both sides by [tex]\sqrt{2}[/tex] )
d = 6
------------------------------------------------------------------------------------------------
a = 6, b = 6[tex]\sqrt{2}[/tex], c = 2[tex]\sqrt{3}[/tex], d = 6
A cat keeps eating to gain weight while a dog keeps doing exercise.Later, the cat's weight increases by 20% and the dog's weight decrease such that their weights become the same. By what percentage is the cat weight less than the dog's original weight?
The feline expanded in weight compared with the canine's underlying weight which is steady with the data given.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let c be the feline's unique weight. Let c* be the feline's new weight.
Let d be the canine's unique weight. The d* be the canine's new weight.
The equation is given as,
c = 1.2 c
d = .9 d
c = d
The other equation is given as,
p = (d - c)/d = 1 - c/d
We know that the given condition,
c = d = 0.9 d
Then the equation is written as,
p = 1 - 0.9d/d
p = 1 - 0.9
p = 0.1 or 10%.
Hence, toward the beginning, the rate contrast compared with the canine was,
q = (d - c)/d = 1 - 0.75 = 0.25 or 25%.
That is, the feline weighed not exactly like the canine toward the beginning. Since p < q, the feline expanded in weight compared with the canine's underlying weight — which is steady with the data given.
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A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer than the side along the building. the third side is 7 feet longer than the side along the building. find the length of all three sides of the reflecting pool
Answer:
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft
Step-by-step explanation:
In the question, the shape of the pool is right triangle.
Let the leg side along the wall to be the x ft
Let the other leg side to be 7+x ft
Let the longest side/hypotenuse to be x+9 ft
Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse
This means;
[tex]x^2 +(x+7)^2=(x+9)^2\\\\[/tex]
Expand the terms in brackets
[tex]x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81[/tex]
collect like terms
[tex]x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0[/tex]
solve for x in the quadratic equation by factorization
[tex]x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8[/tex]
Taking the positive value of x;
x=8ft
Finding the lengths
Leg side along the wall = x ft = 8 ft
The other leg side = 7+x ft = 7+8=15 ft
The Hypotenuse =9+x ft = 9+8 = 17 ft
A waitress sold 12 steak dinners and 27 grilled salmon dinners, totaling $554.98 on a particular day. Another day she sold 26 ribeye steak dinners and 9 grilled salmon dinners, totaling &584.36. How much did each type of dinner cost?
Answer:
the cost of rib eye steak dinner = $22.47
the cost of grilled salmon dinners= $10.57 .....
Step-by-step explanation:
Let x be the rib eye steak dinner.
Let y be the grilled salmon dinner.
According to the first given statement:
12x+27y= $554.98 (equation 1)
According to the second statement:
26x+9y=$584.36 ( equation 2)
Lets take a look at the 1st equation:
12x+27y= $554.98
12x=$554.98- 27y
x=$554.98- 27y/12
Now substitute the value of x in 2nd equation:
26x+9y=$584.36
26($554.98- 27y/12)+9y=$584.36
26(554.98- 27y)+9y=584.36*12
14429.48-702y=7012.32
-702y=7012.32-14429.48
-702y= -7417.16
y= 7417.16/702
y=$10.57
Now substitute the value of y in equation 1:
12x+27y= $554.98
12x+27(10.57)=554.98
12x+285.39 = 554.98
Move the constant to the R.H.S
12x=554.98-285.39
12x=269.59
Divide both the terms by 12
12x/12=269.59/12
x=$22.47
Thus the cost of rib eye steak dinner = $22.47
the cost of grilled salmon dinners= $10.57 .....
20 POINTS!
Use the graph of the line to answer the questions.
1. What is an equation of the line in point-slope form?
2. How can the point-slope form be written in function notation?
Answer:
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form
[tex]f(x)=\dfrac{1}{3}x-\dfrac{1}{3}[/tex] - function notation
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
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (-2, -1) and (1, 0).
Substitute:
[tex]m=\dfrac{0-(-1)}{1-(-2)}=\dfrac{1}{3}[/tex]
[tex]y-(-1)=\dfrac{1}{3}(x-(-2))[/tex]
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] - point-slope form
[tex]y+1=\dfrac{1}{3}(x+2)[/tex] use the distributive property
[tex]y+1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex] subtract 1 = 3/3 from both sides
[tex]y=\dfrac{1}{3}x-\dfrac{1}{3}[/tex]
Answer:
1. 3rd option
2. 2nd option
Step-by-step explanation:
A new candle is 12 inches tall. It burn at a rate of 0.75 inches an hour. How tall will it be after 4.6 hours?
Answer:
8.55 inches
Step-by-step explanation:
We can use the slope intercept form to write this equation
y = mx+b where m is the lope and b is the y intercept
The y intercept, b, is how tall the candle is when we start, 12 inches
The slope is the rate at which it is burning or -.75 (the negative is because it is burning or getting smaller)
y = -.75x+12
or rewriting
t = 12-.75h where h is the hours and t is how tall
We are burning for 4.6 hours
t = 12-.75(4.6)
t = 12 -3.45
t= 8.55
Classify the following triangle. Check all that apply.
A. Right
B. Equilateral
C. Isosceles
D. Scalene
E. Obtuse
F. Acute
Answer:
This is an obtuse, isosceles triangle.
Step-by-step explanation:
The largest angle is greater than 90 degrees (obtuse), and two sides are equal as you can tell by two equal angles (isosceles).
The given triangle can be classified as isosceles and acute triangle.
What is Triangle?A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.
Sum of the interior angles of a triangle is 180 degrees.
Given is a triangle.
The three angles of the triangle are 41°, 41° and 98°.
That is, two angles of the triangle are equal. So the sides opposite these two angles are also equal.
So this is an isosceles triangle.
Obtuse triangle has one of the angles greater than 90°.
Acute triangle has all the angles less than 90°.
Here all the angles are less than 90°.
So it is acute.
Hence the given triangle is acute and isosceles triangle.
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the formula for the volume of a pyramid is V = 1/3 BH ,where B is the area of the base and H is the height rearrange the formula to solve for the height
The formula for the volume of a pyramid, V = 1/3 BH, can be rearranged to solve for the height, 'H', by multiplying both sides of the equation by 3 and then dividing by 'B'. This gives the formula H = 3V/B.
Explanation:The formula for the volume of a pyramid can be rearranged to solve for the height, 'H' as follows:
The formula is: V = 1/3 BH (where 'V' is the volume, 'B' is the base and 'H' is the height). To isolate 'H', we must first eliminate the constant from the right side of the equation. The constant here is 1/3. How? By multiplying every side of the equation by its reciprocal, which is 3. In other words, multiply both sides by 3. This gives us: 3V = BH. Finally, to get 'H', we divide both sides by 'B'. Therefore, H = 3V/B. So, the height of the pyramid can be found by multiplying the volume by 3 and then dividing by the area of the base.Learn more about Rearranging formula here:
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Which statement correctly describes the solution to this scenario?
Answer: Choice C
x represents time and x is positive; y value is 45 times more than the x value
==================================
Explanation:
The inequality y > 45x is the same as y > 45*x
We have y greater than 45*x meaning that y is 45 times more than the x value.
As an example, if x = 2, then 45*x = 45*2 = 90 meaning that y must be larger than 90 if you picked x = 2. In this scenario, x = 2 means that if you traveled for 2 hours then you must have gone more than 90 miles in total distance.
On a map, two cities are 4 and 1/4 inches apart. The scale of the map is 1/2 inch = 3 miles. What is the actual distance between the towns?
Answer:
25,5 miles
Step-by-step explanation:
4.25 inch on map
4.25/0.5 = 8,5
8,5 * 3 = 25,5 miles
Final answer:
To find the actual distance between two towns on a map, set up a proportion using the given scale. By solving the proportion, you can determine the real distance between the towns.
Explanation:
To find the actual distance between the two towns, we can set up a proportion using the given scale:
1/2 inch on the map represents 3 miles in reality.4 1/4 inches on the map represent x miles in reality.Set up the proportion: (1/2 inch) / (3 miles) = (4 1/4 inches) / (x miles).Solve for x to find the actual distance between the two towns.Use the substitution method to solve the system of equations. Choose the
correct ordered pair.
2x + 3y = 11
y = x - 3
A. (3,0)
B. (5,2)
C. (1,3)
D. (4,1)
Answer:
D
Step-by-step explanation:
Given the 2 equations
2x + 3y = 11 → I(1)
y = x - 3 → (2)
Substitute y = x - 3 into (1)
2x + 3(x - 3) = 11 ← distribute parenthesis and simplify left side
2x + 3x - 9 = 11
5x - 9 = 11 ( add 9 to both sides )
5x = 20 ( divide both sides by 5 )
x = 4
Substitute x = 4 into (2) for corresponding value of y
y = 4 - 3 = 1
Solution is (4, 1 ) → D
The correct ordered pairs for the equations 2x+3y=11, y=x-3 is (4,1)
What is a substitution method?In the substitution method we have to calculate the value of one variable by putting the value of another variable in terms of first variable.
How to use substitution method?We are having two equations
2x+3y=11.......1
y=x-3........2
Put the value of y from2 in 1
2x+3(x-3)=11
2x+3x-9=11
5x=20
x=4
put the value of x=4 in 2
y=4-3
y=1
Hence the ordered pairs becomes (4,1)
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a kids skipping rope is 210 cm long. how many ropes could i cut from a 10 meter long piece of rope?
Answer:
4 ropes.
Step-by-step explanation:
There are 100 cms in a meter.
So 10 meters = 10* 100
= 1000 cms.
1000 / 210 = 4 ropes with 160 cms remaining.
Many credit card companies charge a compound interest rate of 1.8% per month on a credit card balance. Nelson owes $950 on a credit card. If he makes no purchases or payments, he will go deeper and deeper into debt.
Which of the following sequences describes his increasing monthly balance
Answer:
the answer is A
Step-by-step explanation:
always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to
start with the 950 * .018 = 171.00
950 + 171.00 = 1121.00
then you follow this process
1121.00 * .018 = 201.78
1121.00 + 201.78 = 1322.78
The answer is A
What sequences describe his increasing monthly balance?Always multiply by the 1.8% (or .018) and then add it to the number you multiplied the .018 to
Start with the 950 *.018 = 171.00
950 + 171.00 = 1121.00
Then you follow this process
1121.00 * .018 = 201.78
1121.00 + 201.78 = 1322.78
Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.
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which expression is equivalent to ^5 square root 13^3
Answer:
[tex]\sqrt[5]{13^3} = 13^{\frac{3}{5}}[/tex]
Step-by-step explanation:
Answer:
D on EDGE
Step-by-step explanation:
Find the center of a circle with the equation: x2+y2−18x−14y+124=0
Answer:
(9,7)
Step-by-step explanation:
The goal is to write in standard form for a circle.
That is write in this form: [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex] is the center and [tex]r[/tex] is the radius.
So you have
[tex]x^2+y^2-18x-14y+124=0[/tex]
Reorder so you have your x's together, your y's together, and the constant on the other side:
[tex]x^2-18x+y^2-14y=-124[/tex]
Now we are going to complete the square using
[tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].
This means we are going to add something in next to the x's and something in next to y's. Keep in mind whatever you add on one side you must add to the other.
[tex]x^2-18x+(\frac{-18}{2})^2+y^2-14y+(\frac{-14}{2})^2=-124+(\frac{-18}{2})^2+(\frac{-14}{2})^2[/tex]
The whole reason we did is so we can write x^2-18x+(-9)^2 as (x-9)^2 and y^2-14y+(-7)^2 as (y-7)^2. We are just using this lovely thing I have I already mentioned: [tex]x^2+bx+(\frac{b}{2})^2=(x+\frac{b}{2})^2[/tex].
[tex](x-9)^2+(y-7)^2=-124+81+49[/tex]
[tex](x-9)^2+(y-7)^2=6[/tex]
Comparing this to [tex](x-h)^2+(y-k)^2=r^2[/tex] tells us
[tex]h=9,k=7,r^2=6[/tex]
So the center is (9,7) while the radius is [tex]\sqrt{6}[/tex].
Answer: (9,7)
Step-by-step explanation:
The equation of the circle in Center-radius form is:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where the center is at the point (h, k) and the radius is "r".
To rewrite the given equation in Center-radius form, we need to complete the square:
1. Move 124 to the other side of the equation:
[tex]x^2+y^2-18x-14y+124=0\\\\x^2+y^2-18x-14y=-124[/tex]
2. Group terms:
[tex](x^2-18x)+(y^2-14y)=-124[/tex]
3. Add [tex](\frac{-18}{2})^2=81[/tex] to the group of the variable "x" and to the right side of the equation.
4. Add [tex](\frac{-14}{2})^2=49[/tex] to the group of the variable "y" and to the right side of the equation.
Then:
[tex](x^2-18x+81)+(y^2-14y+49)=-124+81+49[/tex]
5. Finally, simplify and convert the left side to squared form:
[tex](x-9)^2+(y-7)^2=6[/tex]
You can identify that the center of the circle is at:
[tex](h,k)=(9,7)[/tex]