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]
A parallelogram has vertices at (-5, -1), (-2, -1), (-3, -4), and (-6, -4). What is the approximate perimeter of the parallelogram? Round your answers to the nearest hundredth.
a. 9.16
b. 12 units
c. 12.32 units
d. 14
e. 14.32
I NEED THE ANSWER ASAP!!
Answer:
option C
Step-by-step explanation:
We will call :
A=(-5, -1) B=(-2, -1) C=(-3, -4) D= (-3, -4)
Perimeter= 2*AB+2BC
Where AB= [tex]\sqrt{(-5+2)^{2} +(-1+1)^{2} } = \sqrt{9} =3\\[/tex]
BC =[tex]\sqrt{(-2+3)^{2} +(-1+4)^{2} } = \sqrt{10} =3.16\\[/tex]
So We have:
Perimeter=2*3+2*3.16= 12.32
Answer:
C.
Step-by-step explanation:
help pleaseeeee solve 3-x/2=>12
Answer:
x ≤-18
Step-by-step explanation:
3-x/2≥12
Subtract 3 from each side
3-3-x/2≥12-3
-x/2≥9
Multiply each side by -2 to clear the fraction. Remember to flip the inequality since we are multiplying by a negative
-3 * -x/2 ≤ -2 *9
x ≤-18
Answer:
x ≤ - 18
Step-by-step explanation:
Given
3 - [tex]\frac{x}{2}[/tex] ≥ 12
Multiply all terms by 2
6 - x ≥ 24 ( subtract 6 from both sides )
- x ≥ 18
Multiply both sides by - 1, remembering to reverse the sign as a consequence of multiply by a negative quantity.
x ≤ - 18
What is the slope of a line that includes the points (-5, 1) and (-2, 3).
Select one:A.2/3 b.-2/7 c.-2/3 d.3/2
Answer:
A
Step-by-step explanation:
Work with the two points
Formula
m = (y2 - y1)/(x2 - x1)
Givens
y2 = 3
y1 = 1
x2 = - 2
x1 = - 5
Solution
m = (3 - 1) / (-2 - - 5)
m = 2 / (-2 + 5)
m = 2 / 3
Answer: A
Answer:
[tex]\large\boxed{\text{A.}\,2/3}[/tex]
Step-by-step explanation:
In this question ,we're trying to find the slope with the given points.
We would use the slope-formula to find the slope.
Slope-formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
We would plug in the numbers to their right spots in the formula. The second y-coordinate going to y2, the second x coordinate going to x2, and etc.
Your equation should look like this:
[tex]m=\frac{3-1}{-2-(-5)}[/tex]
Now we solve:
[tex]m=\frac{3-1}{-2-(-5)} \\\\m=\frac{2}{-2-(-5)}\\\\\text{Carry the negative over to the 5, turning it to a positive 5}\\\\m=\frac{2}{-2+5}\\\\\text{Add the denominators}\\\\m=\frac{2}{3}[/tex]
When you're done solving, you should get 2/3
This means that the slope is 2/3
I hope this helped you out.Good luck on your academics.Have a fantastic day!If x= yand y = Z, which statement must be true?
Answer:
The answer is
B. x =>z
They all equal the same.
I Need Help Plz I’m Failingggg!!
Answer:
I believe it would be B
Step-by-step explanation:
take x and y values and figure it out what it is by itself
Given that the first term and the common difference of an arithmetic progression are 6 and 3 respectively. Calculate the sum of all terms from 4th term to the 14th term.
Answer:
330
Step-by-step explanation:
Evaluate the sum of 14 terms and subtract the sum of the first 3 terms
The sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], so
[tex]S_{14}[/tex] = 7 [ (2 × 6) + (13 × 3)]
= 7(12 + 39) = 7 × 51 = 357
[tex]S_{3}[/tex] = 6 + 9 + 12 = 27
Sum of terms from 4 th to 14 th = 357 - 27 = 330
Use the distributive property to evaluate 4(2x-1) when x=6 .
Answer:
44Step-by-step explanation:
The distributive property: a(b + c) = ab + ac
4(2x - 1) = (4)(2x) + (4)(-1) = 8x - 4
Put x = 6 to the expression:
8(6) - 4 = 48 - 4 = 44
The solution to the given expression is 44.
What is the distribution property of multiplication?The distributive property of multiplication states that when the sum of two (2) or more addends are multiplied by a given numerical value or factor, the same output would be produced as when each addend is multiplied respectively by the numerical value or factor, and the products are added together.
By applying the distributive property of multiplication to the given expression, we have:
4(2x - 1) = 4(2x) - 4(1)
4(2x - 1) = 8x - 4
when x = 6, we have;
8x - 4
8(6) - 4
48 - 4 = 44.
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A ball is released at a height of 27 inches to roll inside a half-cylinder. It rolls
to a height of 9 inches on the other side of the cylinder on roll 1. Each time it
rolls up a side of the cylinder, the ball reaches a point th
high as it
had reached on the other side.
This explicit formula models the height of the ball, in inches, the nth time it
rolls up a side of the cylinder.
How high does the ball roll on its 4th time up the cylinder's side?
Answer:
[tex]\frac{1}{3}\ in[/tex]
Step-by-step explanation:
we have
[tex]a(n)=9(\frac{1}{3})^{n-1}[/tex]
For n=4
substitute
[tex]a(4)=9(\frac{1}{3})^{4-1}[/tex]
[tex]a(4)=9(\frac{1}{3})^{3}[/tex]
[tex]a(4)=9(\frac{1}{27})[/tex]
[tex]a(4)=\frac{1}{3}\ in[/tex]
Answer:
1/3
Step-by-step explanation:
Three times a number increases by 4 is the same as four
times that number decreased by 11. Find the number.
Answer:
15 is your answer.
Step-by-step explanation:
Let "a number" = x
"Three times a number increase(d) by 4" = 3x + 4
"...is the same as" = "="
"four times that number decreased by 11" = 4x - 11
Set the equation:
3x + 4 = 4x - 11
Isolate the variable, x. Subtract 4x and 4 from both sides:
3x (-4x) + 4 (-4) = 4x (-4x) - 11 (-4)
3x - 4x = -11 - 4
Simplify. Combine like terms:
-x = -15
Isolate the variable, x. Divide -1 from both sides:
(-x)/-1 = (-15)/-1
x = (-15)/(-1)
x = 15
15 is your answer.
~
Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?
In the physics context of free fall, it would take an object approximately 7.67 seconds to fall from a 944-foot tower, neglecting air resistance. This is calculated using the formula for distance of a freely falling object s(t)=16t^2.
Explanation:The question deals with the physics concept of free fall, specifically directed to the time it would take an object to fall from a certain height. Given that the distance s(t) of a freely falling object is given by the equation s(t)=16t^2, we can find the time t for an object to fall from a height of 944 feet, which is the height of the specific tower.
Setting s(t) equal to the height of the tower, we get: 944=16t^2. Solving this equation for t, we'll get the square root of 944/16 which is approximately 7.67 seconds. Therefore, it would take an object about 7.67 seconds to fall to the ground from the top of the 944-foot tower, neglecting air resistance.
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To determine how long it takes for an object to fall from a 944-foot tower, we use the formula s(t) = 16t^2. Solving for t, we find that it takes approximately 7.68 seconds. Thus, the object hits the ground after 7.68 seconds.
Neglecting air resistance, the distance s(t) in feet traveled by a freely falling object is given by the function s(t)=16t^2, where t is time in seconds. The height of a certain tower is 944 feet. How long would it take an object to fall on the ground from the top of the building?
To solve this problem, we need to determine the time t it takes for the object to hit the ground. Given the height h = 944 feet, we'll use the formula for the distance fallen:
s(t) = 16t^2
We set s(t) equal to the height of the tower:
944 = 16t^2
Next, solve for t:
Divide both sides by 16:
944 / 16 = t^2
t^2 = 59
Take the square root of both sides:
t = √59
t ≈ 7.68 seconds
Therefore, it would take approximately 7.68 seconds for an object to fall to the ground from the top of the building.
What is most likely the correlation coefficient for the set of data shown
Answer:
0.19
Step-by-step explanation:
A correlation coefficient is a measure of how well the line of best fit fits the data. The higher the correlation coefficient, up to 1.0 or -1.0, the better the fit. A positive correlation coefficient means an increasing data set, while a negative correlation coefficient means a decreasing data set.
We can see that this line of best fit is increasing, so our correlation coefficient will be positive.
However we can also see that the points are fairly scattered; this means this is not a very good fit. This means that 0.19 is the better fit.
The isosceles triangle has a perimeter of 7.5 m which equation can be used to find the value of x if the shortest side, y measures 2.1 m ?
Answer:
7.5 = 2x + 2.1
Step-by-step explanation:
The perimeter of a triangle is the sum of the sides. In an isosceles triangle, two sides are the same length. If x is the length of the two sides and y is the length of the third side, then:
P = 2x + y
Given that P = 7.5 and y = 2.1:
7.5 = 2x + 2.1
Answer: The equation that can be used to find the value of x is
2x + 2.1 = 7.5
Step-by-step explanation: An isosceles triangle is a type of triangle which has two of its sides equal to each other. It also has two it's angles (the base angles) equal to each other.
From the question, the given triangle has the shortest side, y to be 2.1 m. This means side y is shorter than the other two sides. Hence, the other two sides must be the sides that are equal to each other. These other two sides are denoted by x ( see the attachment for an illustrative diagram).
The perimeter of a triangle is the sum of all its sides. Therefore, the perimeter (P) of the given triangle is
P = x + x + y
P = 2x + y
From the question, P = 7.5 m
and y = 2.1 m
Hence,
7.5 m = 2x + 2.1 m
2x + 2.1 m = 7.5 m
This equation can be used to find the value of x. The equation can also be written as:
2x = 7.5 m - 2.1m OR
x = (7.5 m - 2.1m) / 2
Which factor do 9x2 – 12x + 4 and 9x^2 – 4 have in common?
Answer:
3x-2
Step-by-step explanation:
[tex]9x^{2} -12x+4[/tex] can be factored using the perfect square rule into [tex](3x-2)^{2}[/tex]
and
[tex]9x^{2}-4[/tex] can be factored by using the difference of squares formula into [tex](3x+2)(3x-2)[/tex]
Both can be factored by (3x-2) so it is a common factor.
Hence, there are no common factors between the two equations.
What is a factor?factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
How to solve?given equation is [tex]9x^2-4[/tex]
solving for x,
[tex]9x^2=4\\x^2=\frac{9}{4} \\x=\frac{3}{2}, -\frac{3}{2}[/tex]
putting values of x in equation 1,
x = [tex]\frac{3}{2}[/tex],
[tex]\frac{81}{4}-12.\frac{3}{2}+4\\ \frac{25}{4}[/tex]Therefore, 3/2 is not a common factor
x=[tex]-\frac{3}{2}[/tex],
[tex]\frac{81}{4}+12.\frac{3}{2}+4\\ \frac{169}{4}[/tex]Therefore, -3/2 is not a common factor
Hence, there are no common factors between the two equations.
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If a graph of y=-4x +2 were changed to a graph of y=-4x+5, how would the y- intercept change?
Answer:
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
The y-intercept was (0,2) then it becomes (0,5) in the new line.
Step-by-step explanation:
The slope-intercept form a line is y=mx+b where m is the slope and the y-intercept is b.
Both of these equations given are in this form.
y=-4x+2 when compared to y=mx+b you see that m=-4 and b=2.
Since b=2 then the y-intercept is 2.
y=-4x+5 when compared to y=mx+b you see that m=-4 and b=5.
Since b=5 then the y-intercept is 5.
So if y=-4x+2 was changed to y=-4x+5, then the y-intercept would increase by 3.
What is the solution set of { x I x < -5} n { x I x> 5
For this case we have to:
[tex]x <-5:[/tex] Represents the solution of all strict minor numbers to -5.
[tex]x> 5:[/tex] Represents the solution of all strict major numbers to 5.
The global solution is given by the intersection of both sets. The symbol of intersection is denoted as: ∩
If we represent the solution in a numerical line, it gives us empty. do not intersect.
Answeer:
Empty set
The two spheres above have the same center. One has a radius of 4 cm, and the other has a radius of 5 cm
Answer:
Step-by-step explanation:
Lets assume that a sphere with greater radius = R = 5cm
And a sphere with smaller radius = r = 4cm
Volume of a sphere = 4/3 π * r³
To find the volume of a sphere with radius 5.
Put the value in the formula.
=4/3π * r³
=4/3π *(5)³
5³ = 5*5*5=125
=4/3π * 125
=4/3 *3.14 *125
=1570/3
=523.3 cm³
Now find the volume of sphere with radius= 4
4/3π*r³
=4/3π * 4³
4³= 4*4*4=64
=4/3*3.14*64
=803.84/3
=267.9cm³
Now to find the space between the spheres subtract the volume of smaller sphere from the volume of larger sphere.
We can write it as:
Space between the spheres = Volume of larger sphere - Volume of smaller sphere
= 523.3 cm³ - 267.9cm³
= 255.4cm³ ....
Do you guys know the answer for 3 and 4
Answer:
Problem 3: H. 350 = r * 5
Problem 4: rate of speed = 70 miles per hour
Step-by-step explanation:
Problem 3:
speed = distance/time
Multiply both sides by time.
speed * time = distance/time * time
speed * time = distance
distance = speed * time
distance = 350
speed = r
times = 5
350 = r * 5
Answer: H. 350 = r * 5
Problem 4:
350 = r * 5
Divide both sides by 5.
350/5 = r * 5/5
70 = r
r = 7
rate of speed = 70 miles per hour
Answer:
H. 350 = r*5
Her average rate: 70 miles
Step-by-step explanation:
When finding average rate, you are always either multiplying or dividing so all the choices except for H, won't work.
Also, r represents the rate so its how many miles per hour. So you would multiply the miles per hour by the amount of hours you have.
So r*5.
To find her average you would solve for r in the equation.
So r*5 = 350
You would divide 5 by itself and then by 350, because whatever you do to one side of the equation, you do to the other.
So 5/5 = 1 or just r
350/5 = 70
r = 70
what is the median of the following distribution?
Answer:
37
Step-by-step explanation:
So this is probably not the correct mathematical way to do it, but it is really easy so you'll probably understand quicker. So a median is the middle number, so how do you find it. First, I counted how many numbers there were (17). Then I subtracted by one to get an even number (if you already have an even number skip this step, and just divide by 2). So now we have 16, so I divided it by 2 to get 8 and just added that 1 that we took out and got 9. So i counted from 24 and the 9th number was 37. To double check I did the same from 56 and got 37.
(04.05 MC)
Which of the following is a solution to this inequality?
[tex]y < \frac{2}{3} x + 2[/tex]
A.(0,3)
B.(-3,1)
C.(3, 5)
D.(1,2)
Answer:
D
Step-by-step explanation:
Plug in and see.
Check A: Lets plug in (0,3) into y<2/3 x+2.
3<2/3 (0)+2
3<2 is not true so not A
Check C: Lets plug in (3,5) into y<2/3 x+2.
5<2/3 (3)+2
5<2+2
5<4 is not true so not C
Check B: Lets plug in (-3,1) into y<2/3 x+2.
1<2/3 (-3)+2
1<0 is not true so not B
Check D: Lets plug in (1,2) into y<2/3 x+2.
2<2/3 (1)+2
2<2/3+2 is true so D
Please Help.
Tracey built a small boat and recorded the distance it traveled. The table below shows the distance traveled (f) during the first 4 seconds after starting (p).
Elapsed Time
(seconds) Distance Traveled
(feet)
1 4.2
2 8.4
3 12.6
4 16.8
Which of the following equations represents the relationship between the distance traveled and the elapsed time?
p = 4.2f
f = 4.2p
p = 4.2 + f
f = 4.2 + p
Answer:
Expressing the distance from the shore by the time needed to reach that distance at an invariable speed of 4.2f/s then f=4.2 p
Answer:
f=4.2p
Step-by-step explanation:
Solve the inequality. 1/3+x+2/9>5/6
Answer:
5⁄18 < x
Step-by-step explanation:
Start by adding like-terms [⅓ and 2⁄9] with 9 being the Least Common Denominator [LCD]. Since 2⁄9 already has a 9 in the denominator, it does not get touched, so in order to make ⅓ a denominator of 9, we simply multiply both terms by 3, to get 3⁄9. So, adding that to 2⁄9 gives you 5⁄9, also giving you 5⁄9 + x > ⅚. Now, we have to find the LCD again because we have two unlike fractions. Now, our Least Common Denominator is 18, so multiply both terms in ⅚ by 3 [15⁄18] and multiply both terms in 5⁄9 by 2 [10⁄18]. Now you have two like fractions to work with, and you can clearly see that your answer is x > 5⁄18. Although the answer is written in reverse, it is still the same concept.
I am joyous to assist you anytime.
Ben has 9 pizza’s with 8 slices each. 59 were eaten. How many slices are left?
Answer:
13 slices.
Step-by-step explanation:
To find your total amount of slices at the start, multiply your pizzas by your slices.
[tex]9*8=72[/tex]
Next, find the difference between your total amount of slices and the amount of slices which have been eaten.
[tex]72-59=13[/tex]
13 slices are left.
1. The table below shows the cost of some apples. Which function C(a) is represented in the table?
Apples
Cost
3
$1.95
6
$3.90
9
$5.85
A. C(a) = 0.65a
B. C(a) = 1.95a
C. C(a) = 3a
D. C(a) = 0.85a
2. Which function below translates the parent function f(x) = x4 five units to the right and seven units downward?
A. g(x) = (x – 7)4 – 5
B. g(x) = (x – 5)4 + 7
C. g(x) = (x – 5)4 – 7
D. g(x) = (x + 5)4 – 7
3. Use the mapping shown to show the value of the function f(x) at each point.
A. f(5) = –1, f(3) = 0, f(5) = 1, f(11) = 2, f(21) = 3
B. f(1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21
C. f(–1) = 5, f(0) = 3, f(1) = 5, f(2) = 21, f(3) = 11
D. f(–1) = 5, f(0) = 3, f(1) = 5, f(2) = 11, f(3) = 21
Detailed solution to math problems involving functions and mappings.
1. The function represented by the table:
Identify the pattern in the table to determine the function.
The cost increases by $1.95 for every 3 apples, so the function is C(a) = 0.65a (A).
2. Translating a function:
To shift f(x) = x^4 five units right and seven units down, the correct function is g(x) = (x+5)^4 - 7 (D).
3. Mapping the function:
Using the mapping provided, the correct values are: f(5) = 1, f(3) = 0, f(11) = 2, f(21) = 3 (A).
Convert 93 pints to quart
Answer:
Step-by-step explanation:
There are 2 pints in one quart.
93 pints = 93/2 = 46 quarts and 1 pint left over.
Answer:
46.5 quarts
Step-by-step explanation:
There are 2 pints in 1 quart.
Hence,
93 pints 1 quart
------------ * ------------- = 46.5 quarts
1 2 pints
Find the value of x in the picture please
Answer:
Option D 74°
Step-by-step explanation:
we know that
The measurement of the outer angle is the semi-difference of the arcs it encompasses.
so
The arcs that the outer angle encompasses are
254° and (360-254)=106°
therefore
∠x=(1/2)[254°-106°]
∠x=(1/2)[148°]
∠x=74°
What is solution to equation X-5/7=-3/7
A cube has side length 0.7 metres.
Work out the total surface area of the cube.
Give your answer in square centimetres
Answer:
2.94cm^2
Step-by-step explanation:
If you're referring to the mathswatch question, this gets you 2/3 :)
Jimmy spent $121.60 on shirts. Tee shirts cost $9.10 and long sleeve shirts cost $14.20. If he bought a total of 10, how many of each kind did he buy? Please answer
A set of equations is given below: equation C:y=5x+10 equation D:y=5x+2 which of the following best describes the solution to the given set of equations? One solution no solution two solutions infinitely many solutions
Answer:
The system has no solution
Step-by-step explanation:
we have
y=5x+10 -----> equation C
The slope of the equation C is m=5 and the y-intercept is b=10
y=5x+2 -----> equation D
The slope of the equation C is m=5 and the y-intercept is b=2
Remember that
If two lines are parallel, then their slopes are the same
Equation C and equation D are parallel lines with different y-intercept
therefore
The system has no solution (the lines do not intersect)
If z is a standard normal variable, find the probability.
The probability that z lies between –1.10 and –0.36
0.4951
–0.2237
0.2237
0.2239
Answer:
0.2237
Step-by-step explanation:
Use the Table of Standard Normal Probabilities for Negative z-scores.
For z= -0.36 NORMSDIST(-0.36)=0.3594 (read value from the table)
For z= -1.10 NORMSDIST(-1.10)=0.1357 (value from the table)
You know P(-1.10<z<-0.36) = 0.3594-0.1357=0.2237