Answer:
Center: (3,-1)
Radius: 3
Step-by-step explanation:
Given:
[tex]\displaystyle \large{x^2+y^2-6x+2y+1=0}[/tex]
First, we have to convert the following standard circle equation to this:
[tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex]
where h is horizontal shift, k is vertical shift and r is radius.
That means we have to complete the square for both x-term and y-term.
Rearrange the equation:
[tex]\displaystyle \large{x^2-6x+y^2+2y+1=0}\\\displaystyle \large{(x^2-6x)+(y^2+2y+1)=0}[/tex]
For [tex]\displaystyle \large{y^2+2y+1}[/tex], can be converted to perfect square as [tex]\displaystyle \large{(y+1)^2}[/tex]. Hence:
[tex]\displaystyle \large{(x^2-6x)+(y+1)^2=0}[/tex]
For the x-terms, we have to find another value that can complete the square. We know that [tex]\displaystyle \large{(a\pm b)^2 = a^2 \pm 2ab + b^2}[/tex].
For [tex]\displaystyle \large{x^2-6x}[/tex] can be [tex]\displaystyle \large{x^2-2(x)(3)+3^2 \to x^2-6x+9}[/tex]. So our another value is 9.
[tex]\displaystyle \large{(x^2-6x+9-9)+(y+1)^2=0}[/tex]
From above, we add -9 because the original expression isn’t actual perfect square.
Separate -9 out of [tex]\displaystyle \large{x^2-6x+9}[/tex]:
[tex]\displaystyle \large{(x^2-6x+9)-9+(y+1)^2=0}[/tex]
Transport -9 to add another side:
[tex]\displaystyle \large{(x^2-6x+9)+(y+1)^2=9}[/tex]
Complete the square:
[tex]\displaystyle \large{(x-3)^2+(y+1)^2=9}[/tex]
Finally, we have our needed equation to find radius and center. The coordinate of center is defined as the point (h,k) from [tex]\displaystyle \large{(x-h)^2+(y-k)^2=r^2}[/tex] and the radius is defined as r.
Hence, from the equation:
The coordinate of center is (3,-1) with radius equal to 3.
What is the product of 3/4 and -6/7?
Answer:
-9/14
Step-by-step explanation:
Hey there!
Guide:
• Difference means subtract/subtraction
• Product means multiply/multiplication
• Sum means add/addition
• Quotient means divide/division
• Now that we know what “product” means… we can make the question/equation easier to solve.
3/4 × -6/7
= 3(-6) / 4(7)
= -18 / 28
= -18 ÷ 2 / 28 ÷ 2
= -9 / 14
Therefore, your answer is: -9/14
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50. What was the price before the tip?
Answer:
65.62
Step-by-step explanation:
Given:
After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50.
To find:
Price before tip
Solution:
87.50 × 25% = 21.875
~Round~: 21.875 to 21.88
87.50 - 21 .88 = 65.62
Thus the price before the tip is 65.62
Check Answer:
Formula: Higher number - Lower number ÷ original number × 100
Solve:
87.50 - 65.62 = 21.88
21.88 ÷ 87.50=0.25005714285
0.25005714285 × 100 = 25.0057142857
Round - 25%
~lenvy~
Math I need help I with it if you can help me out
Answer: 49.44807
Round that however you need to. Unfortunately the rounding instructions on the screenshot are cut off, so I cannot see what that part says.
=======================================================
Work Shown:
sin(angle) = opposite/hypotenuse
sin(22) = h/132
h = 132*sin(22)
h = 49.44807
A bag of chocolates is labeled to contain 0.384 pounds of chocolates. The actual weight of the chocolates is 0.3798 pounds. Are the chocolates heavier or lighter than the weight stated on the label?
Based on the information given the chocolates stated on the label is 0.0042-ounce lighter.
Weight:
Using this formula
Chocolate weight=Current weight-Actual weight
Where:
Current weight=0.384
Actual weight=0.3798
Let plug in the formula
Chocolate weight=0.384-0.3798
Chocolate weight=0.0042 ounce
In conclusion, the chocolates stated on the label are 0.0042-ounce lighter.
Find the value of x.
Answer:
6 .x = 121°
Sum of all interior angles of a 7 sided polygon is 900°.
Christy bought a 9- foot piece of lumber trim bookshelf. Altogether, she needs 100 inches of lumber. Did Christy buy enough lumber? Show your work and explain.
Answer:
Yes.
Step-by-step explanation:
because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.
find x correct to 2 decimal places
Answer:
Step-by-step explanation:
logariths, please help
Answer:
{ - 2 , 8 }
Step-by-step explanation:
[tex]log_{4}[/tex] ( x² - 6x ) = 2
4² = ( x² - 6x )
x² - 6x - 16 = 0
- 6 = - 8 + 2
- 16 = - 8 * 2
( x - 8 )( x + 2 ) = 0 ⇒ [tex]x_{1}[/tex] = - 2 , [tex]x_{2}[/tex] = 8
{ - 2 , 8 }
A manager drew this box-and-whisker plot to represent the ages of the company’s 240 employees. How many employees are younger than 42?
24
48
60
75
Answer:
its 60, need proof?
Step-by-step explanation:
Answer: 60
Step-by-step explanation: I took the test and got it right. Goodluck with the rest!
What is the factorization of the expression below?
16x^2 - 49
A. (4x + 7)(4x - 7)
B. (4x - 7)(4x - 7)
C. (8x - 7)(2x - 7)
D. (8x + 7)(2x - 7)
Answer:
[tex](4x+7)(4x-7)[/tex]
Step by step explanation:
[tex]16x^2 -49\\\\=(4x)^2-7^2\\\\=(4x+7)(4x-7)~~~~~~~~~~;[a^2-b^2 =(a+b)(a-b)][/tex]
Find the value of each variable in the parallelogram.
Answer:
x = 9 and y = 15
Step-by-step explanation:
this is the answer because each side is equivalent to the parallel line so y would be whatever is across from it
Answer:
y=15
x=9
Step-by-step explanation:
they are parallel and equal to the opposite sides
one way to test if a graph is a function or not is by doing a?
One way to test if a graph is a function or not is by doing a vertical line test.
The vertical line test is tested by testing if any vertical line is drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function, if there isn't any such line, the graph is a function.
Hope that helps!
Answer:
Vertical line test. (literally what it say)
Step-by-step explanation:
Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
Therefore you would have x value being the same for several points.
What is the division expression that is the same as 1/5 x 1/4?
A. 1/5÷4
B. 1/5÷5
C. 1/5÷3
D. 1/5÷2
[tex]=================================[/tex]
Option A is correct & here's why.
When dividing fractions, we take the first fraction and multiply it times the reciprocal of the second fraction (the second fraction flopped over)
So if we have 1/4, then its reciprocal is 4/1, or just 4.
Hence, Option A (1/5÷4) is correct.
[tex]==============================[/tex]
Notes:Hope everything is clear & let me know if you have any questions!Enjoy your day!Always remember: Knowledge is Power! :-)Answered by:~DiamonD~
A crate of a apples that usually cost 40$ is on sale for 20$ off. what is the sale price for the crate of apples?
Step-by-step explanation:
We are trying to find $40 on sale for 20$ off.
40*20/100
40*0.2
You save=$8
40-8
Final Price=$32
9. A quilt pattern will use the block shown in the graph with regular hexagon
ABCDEF that has points A(4,0) and D(-4, 0). What is the area of the hexagon
to the nearest tenth? Show all work. [5 points]
From the given coordinates of point A(4, 0), and D (-4, 0), the area of the hexagon is 33.94 units square.
How can the area of the hexagon be found?The given parameters are;
Shape of the quilt pattern = A regular hexagon
Coordinates of point A = A(4, 0)
Coordinates of point D = D(-4, 0)
Required;
The area of the hexagon
Solution;
The coordinates of the center of the hexagon, P = (0, 0)
A regular hexagon consist of six equilateral triangles.
The length of a side of the triangle = PA
Length of PA = 4 - 0 = 4
Therefore;
Length of a side of the triangle = 4
Height of the triangle = PA × sin(60)
Which gives;
Height of the triangle = 4 × (√3)/2 = 2•√3
Area of one triangle = (4 ÷ 2) × 2•√3 = 4•√2
Area of the 6 triangles is therefore;
A = 6 × 4•√2 = 24•√2
Area of the 6 triangles = Area of the hexagon
Therefore;
Area of the hexagon = 24•√2 = 33.94 square units.Learn more about the area of regular shapes here;
https://brainly.com/question/10572314
If told that |A|=48 what are the possible values for X.
Please help!
If the value of |A| is 48 the possible values for x in the matrix is 4 or -2.
How to use determinant to find a value in a matrix?The determinant of the matrix A is as follows:
|A| = 48
Therefore,
48 = (3x × 2x) - (4x × 3)
48 = 6x² - 12x
6x² - 12x - 48 = 0
3x² - 6x - 24 = 0
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2 -4(x + 2) = 0
(x - 4)(x +2) = 0
Therefore,
x = 4 or -2
learn more on determinant here: https://brainly.com/question/19206601
(Please show work and No links) If you bought 28 shares of stock at $30/sh and sold them at $25/sh. And How much did you net after selling the shares? Was it a profit or a loss?
Let C be the total cost;
[tex]c = 28 \times 30 = 840[/tex]
Let R be the total revenue;
[tex]r = 28 \times 25 = 700[/tex]
Let P be the net profit;
[tex]p = r - c[/tex]
[tex]p = 700 - 840 = - 140[/tex]
There was a 140$ net loss.
Out of 100 people sampled, 36 had kids. Based on this, construct a 95% confidence interval for the true
population proportion of people with kids.
Give your answers as decimals, to four places
This is the same as saying 0.2659 < p < 0.4541
=========================================================
Work Shown:
At 95% confidence, the z critical value is about z = 1.96 which is determined through a table or calculator.
x = number of people who had kids = 36
n = sample size = 100
phat = sample proportion of those who had kids
phat = x/n
phat = 36/100
phat = 0.36
E = margin of error
E = z*sqrt(phat*(1-phat)/n)
E = 1.96*sqrt(0.36*(1-0.36)/100)
E = 0.09408
This value of E is approximate because z = 1.96 is approximate.
-------------
L = lower bound
L = phat - E
L = 0.36 - 0.09408
L = 0.26592
L = 0.2659
U = upper bound
U = phat + E
U = 0.36 + 0.09408
U = 0.45408
U = 0.4541
The values of L and U are approximate since E is approximate.
-------------
The confidence interval in the format (L, U) is (0.2659, 0.4541)
This is equivalent to writing 0.2659 < p < 0.4541
which is the format L < p < U
We're 95% confident that the true population proportion (p) is somewhere between 0.2659 and 0.4541; i.e. we're 95% confident the true percentage of people who had kids is somewhere between 26.59% and 45.41%
What is the five-number summary of this data set?
{425, 255, 267, 507, 307, 435, 253, 250, 433}
What is the five-number summary of this data set?
{425, 255, 267, 507, 307, 435, 253, 250, 433}
Drag the numbers into the boxes to correctly complete the five-number summary.
Answer:
min250 max507 Q1=307 Q2=255 Q3=435
Step-by-step explanation:
The five-number summary of this data set is {250, 255, 307, 435, 507}
How to find the mean of a data set?
Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
[tex]\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}[/tex]
We are given that;
The data set= {425, 255, 267, 507, 307, 435, 253, 250, 433}
Now,
The five-number summary of a data set consists of the minimum, first quartile (Q1), median, third quartile (Q3), and maximum12.
To find the five-number summary of this data set, follow these steps:
Put the numbers in ascending order: {250, 253, 255, 267, 307, 425, 433, 435, 507}
Find the minimum: The smallest number is 250
Find the maximum: The largest number is 507
Find the median: The middle number is 307
Find Q1: The median of the lower half of the data is 255
Find Q3: The median of the upper half of the data is 435
Therefore, by the mean the answer will be {250, 255, 307, 435, 507}
Learn more about mean here:
https://brainly.com/question/16118626
#SPJ3
PLEASE HURRY AND HELP ME WITH THIS !! ILL GIVE BRAINLIEST
Answer:
C. Reflection, translation
Step-by-step explanation:
If we compare Figure A to Figure B, you might notice that they mirror each other. This means that Figure A was reflected. Now, if we take a look at Figure B and Figure C, you should see that both figures are the exact same shape, size, and facing the same direction. The only thing that changed was the location. So, this means that Figure B was translated.
I hope this helps! Have a lovely day!! :)
A total of 30000 tickets were sold for a concert of this amont 1/4 were sold for $1500 each 1/3 at $ 1000 each and the rest at $750 each .how many were sold at $750
Answer:
12,600
Step-by-step explanation:
1/3 = 4/12
1/4 = 3/12
Together they equal 7/12
The different is 5/12
5/12 = .416666 =.42
.42 x 30,000 = 12,600
Question
Write an equation of a line that passes through the point (4,3) and is perpendicular to the graph of the equation y=−1/3+4
Answer:
Step-by-step explanation:
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = -1/3 x +4
So : product for two slopes = -1 means : m×-1/3=-1
m = 3
now : y = 3 x+b
but this line :
through the point (4,3) : 3 =3(4)+b....... b=-9
conclusion :
the equation is : y =3x -9
PLSSS HELP WHOEVER DOES THE CORRECT WILL GET BRAINLIEST
Ray is x years old. His brother Ron is y years older than Ray.
How old was Ray 3 years ago?
Answer: x-3
Step-by-step explanation:
It’s a variable
In a small private school, 16 students are randomly selected from eighteen available students. What is the probability that they are the four youngest students?
Answer:
1/72
Step-by-step explanation:
16 * 18 = 288
4/288 = 1/72
Find the value of each variable in the parallelogram.
Answer:
b=10
C=99
D=140
Step-by-step explanation:
because it’s a parallelogram
if the log↓b(a)=0, what is the value of a?
explain why log↓0 (3) and log↓1 (3) do not exist.
Answer:
1. a = 1
2. See explanation below.
Step-by-step explanation:
First Question
Given:
[tex]\displaystyle \large{\log_b a = 0}[/tex]
Convert to exponential:
[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]
Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]
Evaluate:
[tex]\displaystyle \large{b^0 = a}[/tex]
We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.
Solution:
[tex]\displaystyle \large{a = 1}[/tex]
__________________________________________________________
Second Question
Given:
[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]
Let’s convert to an equation:
[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]
The variables represent unknown values of logarithm.
Convert to exponential:
[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]
Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.
Hence, no solutions for x and y.
Angle α is drawn on the unit circle in standard position. The terminal side of angle α intersects the unit circle at point (-0.292, 0.956). What is the approximate decimal value of tan(α)?
Using the unit circle, it is found that the approximate decimal value of tan(α) is given by -3.274.
What is the unit circle?For an angle [tex]\alpha[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\alpha}, \sin{\alpha})[/tex].
In this problem, we have point (-0.292, 0.956), hence [tex]\cos{\alpha} = -0.292, \sin{\alpha} = 0.956[/tex].
Applying the definition of the tangent, we have that:
[tex]\tan{\alpha} = \frac{\sin{\alpha}}{\cos{\alpha}} = \frac{0.956}{-0.292} = -3.274[/tex].
Hence the second option is correct.
More can be learned about the unit circle at https://brainly.com/question/16852127
The answer: -3.274.
Hope you got it right! :)
HELP ME OUT PLS!!!!!!!
The model represents an equation. What value of x makes the equation true?
A) 15/4
B) 15/8
C) -15/4
D) -15/8
Answer:
B
Step-by-step explanation:
-6x + 6 = 2x - 9
-6x + 15 = 2x
15 = 8x
x = 15/8
solve picture question
Answer:
As it ایس the correct answer is 45
78
7.90
Answer:
Its me Viktor Kozhanov may I have brainliest pleaseI also answered all you questions so give brainliest to those as well
Step-by-step explanation:
*Pls help me*
Yasmine is trying to find an outfit for the first day of school. She has to choose from 3 pairs of skirts: one black, one pink and one orange. She also has five blouses: one with flowers, one with polka-dots, one gray, one white and one with words saying I love New York! How many possible outfits can she choose from? *Hint-create a probability table.
Answer:
15 outfits
Step-by-step explanation:
Given
3 skirtsone blackone pinkone orange5 blousesone w/ flowersone w/ polka dotsone grayone whiteone w/ "I love New York!"Probability : No. of outfits
There are 3 elements in set A (skirts) and 5 elements in set B (blouses)Therefore possible outfits = A x B = 15 outfitsP.S. Sorry I couldn't create the probability table.