100 POINTS! Using the following equation, find the center and radius of the circle. You must show and explain all work and calculations to receive credit. Be sure to leave your answer in exact form.
Answers
Answer:
Center: (-4, 1)
Radius: √2
Explanation:
Circle general equation is represented by (x - h)² + (y - k)² = r²
where (h, k) is the center and "r" resembles radius
To write in general equation form, start completing square:
x² + y² + 8x -2y + 15 = 0
x² + 8x + y² - 2y + 15 = 0
(x + 4)² - 4² + (y - 1)² - (-1)² + 15 = 0
(x + 4)² + (y - 1)² - 16 - 1 + 15 = 0
(x + 4)² + (y - 1)² - 2 = 0
General equation form:
(x - (-4))² + (y - 1)² = (√2)²
From here, comparing with the formula equation.
It is determined: center: (-4, 1) and radius: √2
Answer:
center = (-4, 1)
radius = √2
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven equation:
[tex]x^2+y^2+8x-2y+15=0[/tex]
Subtract 15 from both sides to move the constant to the right side of the equation:
[tex]\implies x^2+y^2+8x-2y=-15[/tex]
Rearrange the left side to collect like variables:
[tex]\implies x^2+8x+y^2-2y=-15[/tex]
Add the square of half the coefficients of the variables x and y to both sides:
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2+y^2-2y+\left(\dfrac{-2}{2}\right)^2=-15+\left(\dfrac{8}{2}\right)^2+\left(\dfrac{-2}{2}\right)^2[/tex]
[tex]\implies x^2+8x+16+y^2-2y+1=2[/tex]
Factor the two perfect square trinomials on the left side:
[tex]\implies (x+4)^2+(y-1)^2=2[/tex]
Compare the found equation with the general form to find the center and radius of the circle:
center = (-4, 1)radius = √2Learn more about circle equations here:
https://brainly.com/question/27798599
https://brainly.com/question/27783217
Related Questions
The value of [tex]\sin ^{-1}\left(\frac{\sqrt{3}}{2}\right)-\sin ^{-1}\left(\frac{1}{2}\right)[/tex] is
Answers
Answer:
[tex]\displaystyle \frac{\pi}{6}[/tex]
Explanation:
According to the unit circle, [tex]\displaystyle \frac{\pi}{3}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are the radian measures you are looking for because all y-coordinates are associated with the sine function, so when evaluating, you will arrive at this:
[tex]\displaystyle \boxed{\frac{\pi}{3}} = \frac{\pi}{3} - \frac{\pi}{6}[/tex]
I am joyous to assist you at any time.
Drag each label to the correct location on the chart. Not all labels will be used. Given: and are supplementary and are supplementary Prove: The two linear pairs and one supplementary angle with values of 1, 2, and 3 Statements Reasons 1. and are supplementary 1. given 2. and are supplementary 2. given 3. 3. congruent supplements theorem Complete the flow chart to show the proof. vertical angles theorem given congruent complements theorem congruent supplements theorem
Answers
Based on the Congruent Supplements Theorem, <1 = <3 are congruent, given that <1 and <2 and <2 and <3 are supplements.
What does the Congruent Supplements Theorem say?The Congruent Supplements Theorem shows that when two angles are considered to be supplements of a certain angle, then those two angles must be congruent.
Filling in the chart would therefore be:
<1 and <2 are
supplementary <1 = <3
GIVEN Congruent Supplements Theorem
<2 and <3 are
supplementary
GIVEN
Find out more on the Congruent Supplements Theorem at https://brainly.com/question/17385360.
#SPJ1
How effective is it to go to your manager to request others take on some activities?
Answers
The effectiveness depends on your score of working.
How effective is it to go to your manager to request others take on some activities?
Certainty implies, indeed, that favorable things will happen and uncertainty implies favorable things won't happen.
If we go to our manager, requesting that others should take some activities. It certainly depends upon the our score in the office. if we are hard working than in situations manager could approve our request and if our score is low or we are not a hard worker than result may no be in our favor.
Thus, the effectiveness depends on your score of working.
Learn more about certainty and uncertainty here:
https://brainly.com/question/23422212
#SPJ1
Clasify each polynomial based on the number of terms it contains
Answers
Answer:
Monomial - one term
Binomial - two terms
Trinomial - three terms
Polynomial - any polynomial with more than three terms
Brainliest, please :)
Your elderly neighbor places a bag of corn kernels on your doorstep each morning. The first day, the bag contained 1 kernel of corn, the second day it contained 2 kernels
of corn, 4 kernels of corn the third day, and so on. Each kernel of corn weighs 0.06 grams. How many kernels of corn will be in the bag on the 22nd day?
Answers
Answer:
2^25
Step-by-step explanation:
Given
On first day bag contained 1 kernels
on second bag contained 2 kernels of corn
on third day bag contained 4 kernels of corn
on n th day bag contains 2n-1 kernels of corn
thus on 26 th day bag contains 2^26= 2^25=33,554,432 kernel
Each kernel weigh 0.07 gm
Therefore 2^25 kernels weighs = 2^25 x 0.07
Therefore on 26 th day 2^25 kernel weighs 23,488.1024 kg
Suppose every interior angle in a regular polygon is approximately 128.57∘. What kind of polygon is this?
Answers
The polygon with 128.57° as every interior angle is a septagon.
How to determine the polygonIf the interior angle = 128. 57°
Using ( n-2) × 180 = sum of interior angles
Let's say n= 7
We have that,
(7-2) × 180 = 900
Let's find out the polygon
= 7 × 128.57
= 900
A polygon with seven sides is a septagon
Thus, the polygon with 128.57° as every interior angle is a septagon.
Learn more about polygons here:
https://brainly.com/question/1592456
#SPJ1
the data represented by the following stem-and-leaf plot range from to .
4|578
5|14
6|023
7|69
A. 45,76
B. 48,79
C. 45,79
D. 48,76
Answers
Considering the stem-and-leaf plot, the range of the data-set is given as follows:
C. 45,79
What is an stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
Considering the key format, the smallest value in this problem is 4|5 = 45, and the highest is 7|9 = 79, hence the range is given by:
C. 45,79
More can be learned about an stem-and-leaf plot at https://brainly.com/question/8649311
#SPJ1
Giving brainliest!!!!!
Answers
I think it is 49123.52
Step-by-step explanation:
Analyze and sketch the polynomial functions and complete the charts below. State the degree and sign of the leading coefficient of the polynomial functions. Determine the end behavior of the graph of the functions. For 5b, write the polynomial function as a product of linear factors (in factored form).
a. f(x) = –7(x + 2)^3(x – 1)^2(x – 3) Zeros Multiplicity Crosses/Touches
Degree Sign
End behavior
b. m(x) = x^3 – 4x^2
Factored form: m(x) =
Degree Zeros Multiplicity Crosses/Touches
Sign End behavior
Answers
See below for the properties of the functions
How to analyze the functions?The function f(x)
We have:
f(x) = –7(x + 2)^3(x – 1)^2(x – 3)
From the graph, we have the following features:
Leading coefficient: Negative, because -7 is negativeZeros: x = -2 at multiplicity = 3, x = 1 at multiplicity = 2 and x = 3 at multiplicity = 1Crosses = 2Touches = 3End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:-\infty \:[/tex]The function m(x)
We have:
m(x) = x^3 - 4x^2
Factor out x^2
m(x) = x^2(x - 4)
Factor out x
m(x) = x(x)(x - 4)
From the graph, we have the following features:
Leading coefficient: PositiveZeros: x = 0 at multiplicity = 2, x = 4 at multiplicity = 1Crosses = 1Touches = 1End behavior = [tex]\mathrm{as}\:x\to \:+\infty \:,\:m\left(x\right)\to \:+\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:m\left(x\right)\to \:-\infty \:[/tex]Read more about functions at:
https://brainly.com/question/12431044
#SPJ1
please help me with this math problem
will mark brainiest
Answers
Using the given exponential function, the age of the skull is 6,733 years old.
What is the exponential function for the skull's amount?It is given by:
[tex]N(t) = N(0)e^{-kt}[/tex]
In which:
N(0) is the initial amount.k is the decay rate.t is the time in years.In this problem, the parameters are given as follows:
N(t) = 0.51N(0), k = 0.0001.
Hence we solve for t to find the age.
[tex]N(t) = N(0)e^{-kt}[/tex]
[tex]0.51N(0) = N(0)e^{-0.0001t}[/tex]
[tex]e^{-0.0001t} = 0.51[/tex]
[tex]\ln{e^{-0.0001t}} = \ln{0.51}[/tex]
[tex]-0.0001t = \ln{0.51}[/tex]
[tex]t = -\frac{\ln{0.51}}{0.0001}[/tex]
t = 6,733 years old.
More can be learned about exponential functions at https://brainly.com/question/25537936
#SPJ1
The equation y minus 1 = negative 7 (x minus 3). is written in point-slope form. What is the y-intercept of the line? –4 –2 20 22
Answers
Answer:
22
Step-by-step explanation:
Hello!
We can convert it into slope-intercept form.
Slope - Intercept Form: [tex]y = mx +b[/tex]
m = slopeb = y-interceptConverty - 1 = -7(x - 3)y = -7x + 21 + 1y = -7x + 22The y-intercept of the line is 22.
RSTU is an isosceles trapezoid with bases RS and TU.
Find x and m/S if m/R=4x +11 and m/T=2x-5.
Answers
[tex]\angle R[/tex] and [tex]\angle S[/tex] are supplementary by the same-side interior angles theorem, and [tex]\angle S \cong \angle T[/tex] because of the properties of an isosceles trapezoid, meaning that [tex]\angle R[/tex] and [tex]\angle T[/tex] are supplementary.
[tex]4x+11+2x-5=180\\\\6x+6=180\\\\6x=174\\\\x=\boxed{29}\\\\\implies m\angle S=m\angle T=2(29)-5=\boxed{53^{\circ}}[/tex]
How is the graph of g(x)=-(3x)³ related to the graph of
f(x)=x³?
A. The graph of g(x) is vertical compression of
the graph f(x) by a factor of 3 and a
reflection across the x-axis.
B. The graph of g(x) is horizontal compression
of the graph f(x) by a factor of 3 and a
reflection across the y-axis.
1
C. The graph of g(x) is horizontal compression
of the graph f(x) by a factor of and a
reflection across the x-axis.
3
Answers
the transformation from f(x) to g(x) is (c) the graph of g(x) is horizontal compression of the graph f(x) by a factor of 1/3 and a reflection across the x-axis.
How to compare both functions?The functions are given as:
f(x) =x^3
g(x) = -(3x)^3
The minus sign in g(x) = -(3x)^3 implies that the function f(x) is reflected across the x-axis
The 3 in g(x) = -(3x)^3 implies that the function f(x) is stretched horizontally by 1/3
Hence, the transformation from f(x) to g(x) is (c)
Read more about transformation at:
https://brainly.com/question/13810353
#SPJ1
5) Solve the simultaneous equations log(x+y)=0 Solve the simultaneous equations 2logx=log(y+1)
Answers
Answer:
(1,0)
Step-by-step explanation:
Since log (x+y) = 0 you should know x+y = 1
so y = (1-x)
then 2 logx = log (y+1)
log x^2 = log (1-x +1) = log (2-x)
x^2 = 2-x
x^2 + x-2 = 0
(x+2)(x-1) = 0 so x = -2 or +1
then y = 3 or 0
-2,3 and 1,0 since you cannot have a log of a negative number
the only answer is (1,0)
If we approximate the function y=sin(x) with a0+a1 x a2 x^2 +a3 x^3, what is a0,a2,a2,a3?
Answers
The coefficients [tex]a_0,a_1,a_2,a_3[/tex] could be chosen to be the coefficients in the Maclaurin series of [tex]\sin(x)[/tex].
We have
[tex]y = \sin(x) \approx a_0 + a_1 x + a_2 x^2 + a_3 x^3 \\\\ \implies y(0) = 0 = a_0[/tex]
[tex]y' = \cos(x) \approx a_1 + 2a_2 x + 3a_3 x^2 \\\\ \implies y'(0) = 1 = a_1[/tex]
[tex]y'' = -\sin(x) \approx 2a_2 + 6a_3 x \\\\ \implies y''(0) = 0 = 2a_2[/tex]
[tex]y''' = -\cos(x) \approx 6a_3 \\\\ \implies y'''(0) = -1 = 6a_3[/tex]
It follows that [tex]a_0=0[/tex], [tex]a_1=1[/tex], [tex]a_2=0[/tex], and [tex]a_3 = -\frac16[/tex].
simplify: 5^2 x 5^4
A, 5^8
B. 5 x 8
C. 5^2
D. 5^6
Answers
2+4=6, so the answer is
5^6
Hope this helped :)
Answer:
D. 5^6
Step-by-step explanation:
[tex]5^2*5^4\\5^2^+^4\\5^6[/tex]
A certain 90-mile trip took 2 hours. Exactly 1/3 of the distance traveled was by rail and this part of the trip took 1/5 of the travel time. What was the average rate, in miles per hour, of the rail portion of the trip?
A. 71 B. 73 C. 74 D. 75
Answers
The average rate, in miles per hour, of the rail portion of the trip is; D: 75
How to calculate the average speed?Since exactly 1/3 of the distance travelled was by rail, then we can say that;
(1/3) * (90) = 30 miles
We are told that part of the trip took 1/5 of the travel time. Thus;
Time it takes to travel that distance is:
(1/5) * (2) = 2/5 of an hour
Average rate is;
30/(2/5) = 150/2 = 75 mph
Read more about Average speed at; https://brainly.com/question/4931057
#SPJ1
Find the x-intercept of the graph of the linear equation y = −1
2
x + 3.
x-intercept
Answers
Answer:
there is no x-intercept
Step-by-step explanation:
The graph of the equation y = -1 is a horizontal line that passes through (0, -1). The line is parallel to the x-axis. It never intersects the x-axis. There is no x-intercept.
What is the value of x in the triangle?
Answers
The value of x in the right triangle is 4 units.
How to find the side of a right triangle?The side x of the right triangle can be found using trigonometric ratios.
Therefore,
sin 30° = opposite / hypotenuse
sin 30 = x / 8
1 / 2 = x /8
cross multiply
8 = 2x
divide both sides by 2
8 / 2 = 2x / 2
x = 4
learn more on right triangle here: https://brainly.com/question/10060696
#SPJ1
Could someone help me out?
Answers
What is limit?
Limit, can be defined as the every nearby the value of a variable for a function exists, is called limits|
⇒ [tex]\lim_{h \to0 \zero} 46x^11+32xh^3+6x^15h+23[/tex]
When putting h = 0
⇒ [tex]46x^11+23[/tex]
Thus, the value of a function of its limit is given by [tex]46x^11+23[/tex]
Learn more about limits here:
https://brainly.com/question/18008819
#SPJ1
A school administrator bought 6 desk sets. Each set consists of one table and one chair. He pald $48.50 for each chair. If he pald a total of $663 for the 6 sets, the cost of each table Is
Answers
And cost of chairs is 6($48.50) = $291
Therefore;
$291 + 6(X) = $663
6x = $663 - $291
6x = $372
X = $372/6
X = 62
4 rows with circles and triangles, left to right. Row 1, circle, triangle, 2 circles, triangle. Row 2, triangle, circle, 2 triangles, circle, triangle. Row 3, circle, 2 triangles, circle, triangle. Row 4, triangle, 2 circles, 2 triangles. The ratio of the number of circles to the number of triangles in simplest form is . The number of circles that need to be added to make the ratio 1 : 1 is .
Answers
The ratio of circle to triangles is; 3:4 and the number of circles which should be added to make the ratio 1:1 is; 3.
What is the ratio of circles to triangles?It follows from the task content that the total number of circles and triangles in all 4 rows and can be counted and concluded as; 9 and 12 respectively.
Hence, the ratio of circles to triangles is 9 to 12 and in its simplest form is; 3:4.
However, to make the ratio 1:1, the number of circles and triangles must be equal. Hence, 3 circles must be added to make the ratio 1:1.
Read more on ratios;
https://brainly.com/question/13513438
#SPJ1
HELP, PLATO!!!!!!!
David proved the Law of Cosines with reference to ∆ABC using a different method. Arrange the steps of his proof in the correct sequence.
Answers
Answer:
the law of cosines with ABC
The graph of a system of inequalities is shown.
195
554-3-2-1
4
(5
-5-
-6
-7
-8
9
23 x
Which system is represented by the graph?
O
O
y> 2x
x+2y≤-8
y≥ 2x
x+2y<-8
y< 2x
x+2y²-8
y≤2x
x+2y>-8
Answers
Answer: Option (1)
Step-by-step explanation:
The line y = 2x is shaded above and is dotted, so it represents [tex]y > 2x[/tex].
This eliminates all the options except for option (1).
The graph of a system of inequalities is shown. The following system of inequations represents the graph:
y ≥ 2x;
x + 2y ≤ -8:
Inequality refers to a condition in which there's a lack of equivalency or aesthetics, frequently panning out in disparities or differences in chances, resources, treatment, or outcomes among individuals, groups, or associations. It encompasses various forms, including economic inequality, colonial inequality, and political inequality.
The blue region is on the left of the blue line of equation y = 2x so the region is represented by the line y ≥ 2x. The equality holds in this inequality as the region also includes the origin (0, 0).
The second option only has the inequality y ≥ 2x in its system of inequalities.
So, the correct answer is the second one. The system of inequation is
y ≥ 2x;
x + 2y ≤ -8:
Learn more about Inequality here:
https://brainly.com/question/30013680
#SPJ7
The question is down below
also I home school and have permission to post this question
Answers
Answer:
2448 ft²
Step-by-step explanation:
The surface area of the triangular prism is the sum of the areas of the triangular bases and the lateral area of the rectangular faces.
Base areaThe two right triangle bases together form a rectangle that is 24 ft wide and 18 ft tall. The total base area is ...
A = (24 ft)(18 ft) = 432 ft²
Lateral areaThe rectangular faces of the prism are each 28 ft wide and have a total width of 18 +24 +30 = 72 ft. Their total area is ...
LA = (28 ft)(72 ft) = 2016 ft²
Total surface areaThe sum of the base area and lateral area is ...
total area = (432 ft²) +(2016 ft²) = 2448 ft²
The surface area of the triangular prism is 2448 ft².
__
Additional comment
The area formula for the triangular base is ...
A = 1/2bh . . . . . . area of one triangle with base b and height h
Then the area of the two congruent triangular bases is ...
A = 2(1/2bh) = bh
This is the formula we used above. It skips the work of dividing by 2, then multiplying by 2 again.
b) The resale value of a piece of industrial equipment has been found to behave according to the function V=700,000e-0.02t.
i) What was the original value of the piece of equipment
Answers
The original value of the piece of equipment is 700000
How to determine the original value?The resale value is given as:
V=700,000e^(-0.02t)
The original value is when t = 0.
So, we have:
V=700,000e^(-0.02 *0)
Evaluate the product
V=700,000e^0
This gives
V=700,000 * 1
Evaluate
V=700000
Hence, the original value of the piece of equipment is 700000
Read more about exponential functions at:
https://brainly.com/question/11487261
#SPJ1
Which expression represents the distance Kelli traveled downstream?
0.1(x – 5)
0.1(x + 5)
Answers
The distance that Kelli can swim will be about 6.11 kilometers per hour.
How to calculate the distance?Here is the complete question:
Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth. Kelli can swim about km/hour.
To solve for x, you need to follow SADMEP. SADMEP is subtraction, addition, division, multiplication, exponents, and parentheses.
It follows the same rules as PEMDAS, but SADMEP is only used when solving algebraic equations.
x - 5 = 0.1(x + 5) (use the distributive property)
x - 5 = 0.1x + 0.5 (subtract 0.1x to both sides)
0.9x - 5 = 0.5 (add 5 to both sides)
0.9x = 5.5 (divide both sides by 0.9)
x = 6.11 km/hour.
Therefore, Kelli can swim about 6.11 kilometers per hour.
Learn more about distance on:
https://brainly.com/question/17273444
#SPJ1
Answer:
It's the first one for upstream and the other one for downstream
Step-by-step explanation:
PLS HELP ASAP
The graph shown below expresses a radical function that can be written in the form f(x)= a(x + k)^1/n +C. What does the graph tell you about the value of k in this function?
Answers
PLS ANSWERS QUCIK THANK YOU
Answers
Answer:
394.13cm²
Step-by-step explanation:
Formula: The area of a circle is found by A = πr²
Given:
radius is 11.2cm (shown in circle)π = 3.142Plug in:
A = πr² → A = (3.142)(11.2)²
→ A = (3.142)(125.44)
→ A = 394.13248
"2 decimal places", round up to 394.13
Learn more about Circles here: https://brainly.com/question/10368742
NO LINKS!!!! What is the transformation of f (x)= x^3:
PART 4:
THIS IS NOT MULTIPLE CHOICE!!!!
10. f(x)= (x+5)^3
11. f(x)= (1/5x)^3
12. f(x)= (-x)^3
Answers
Answer:
10. Left 5
11. Horizontal stretch by a factor of 5
12. Horizontal reflection
Step-by-step explanation:
Transformations of Graphs (functions) is the process by which a function is moved or resized to produce a variation of the original (parent) function.
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{a}[/tex]
[tex]y=-f(x) \implies f(x) \: \textsf{reflected in the} \: x \textsf{-axis}[/tex]
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Identify the transformations that take the parent function to the given function.
Question 10
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(x+5)^3[/tex]
Comparing the parent function with the given function, we can see that 5 has been added to the x-value of the parent function.
Therefore, the transformation is:
[tex]f(x+5) \implies f(x) \: \textsf{translated}\:5\:\textsf{units left}[/tex]
Question 11
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=\left(\dfrac{1}{5}x\right)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by ¹/₅.
Therefore, the transformation is:
[tex]y=f\left(\dfrac{1}{5}x\right) \implies f(x) \: \textsf{stretched parallel to the x-axis (horizontally) by a factor of} \: \dfrac{1}{\frac{1}{5}}[/tex][tex]\textsf{As }\dfrac{1}{\frac{1}{5}}=5 \implies \textsf{horizontal stretch by a factor of 5}[/tex]
Question 12
[tex]\textsf{Parent function}: \quad f(x)=x^3[/tex]
[tex]\textsf{Given function}: \quad f(x)=(-x)^3[/tex]
Comparing the parent function with the given function, we can see that the x-value of the parent function has been multiplied by -1.
Therefore, the transformation is:
[tex]y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}[/tex]
Learn more about graph transformations here:
https://brainly.com/question/27845947