The equation of the circle that passes through the given points and has its center lying on this line 2x + y = 7 is equal to x² + y² - 10x + 6y - 6 = 0.
The equation of a circle.Mathematically, the standard form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.How to determine the equation of this circle?Assuming the center of this circle lies at (h, k), then we have the following expressions that models the distance from the center of the given circle:
(h - 7)² + (k - 3)² = (h - 11)² + (k - (-1))²
(h - 7)² + (k - 3)² = (h - 11)² + (k + 1)²
(h - 7)² - (h - 11)² = (k + 1)² - (k - 3)²
(h - 7 + h - 11)(h - 7 - h + 11) = (k + 1 + k - 3)(k + 1 - k + 3)
(2h - 18)(4) = (2k - 2)(4)
8h - 72 = 8k - 8
8h - 8k = 64
h - k = 8 .......equation 1.
Since (h, k) lies at 2x + y = 7, we have:
2h + k = 7 .......equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
h - k = 8
2h + k = 7
3h = 15
h = 15/3
h = 5.
For the value of k, we have:
h - k = 8
5 - k = 8
k = 5 - 8
k = -3.
Next, we would determine the radius of this circle:
Radius, r² = (h - x)² + (k - y)²
Radius, r² = (5 - 7)² + (-3 - 3)²
Radius, r² = (-2)² + (-6)²
Radius, r² = 4 + 36
Radius, r = √40.
Now, we can write the equation of this circle:
(x - h)² + (y - k)² = r²
(x - 5)² + (y - (-3))² = 40
(x - 5)² + (y + 3)² = 40.
x² - 5x - 5x + 25 + y² + 3y + 3y + 9 - 40 = 0
x² - 10x + 25 + y² + 6y - 31 = 0
x² - 10x + y² + 6y - 6 = 0
x² + y² - 10x + 6y - 6 = 0.
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Evaluate using the order of operation. Enter the answer in simplest form.
The answer of the given expression [tex]\frac{1}{2} +\frac{3}{4} \times16[/tex] is 25 / 2 .
PEMDAS is word form accustomed mention the order of operations to be followed whereas determination expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.PEMDAS or order of operations may be a set of rules to perform operations in AN arithmetic expression. There ar completely different situations wherever everything goes through numerous steps during a mounted sequence.
We have given an expression [tex]\frac{1}{2} +\frac{3}{4} \times16[/tex] .
According to PEDMAS , we will first solve the multiplication term which on solving gives 3/4 (16) = 3 × 4 = 12.
Now we will solve the addition term which is given by
1/2 + 12 = 1 + 24 /2
= 25 / 2
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Help 66 points show your work and I’m giving brainliest
Based on the calculations on the given expressions, the correct answers are as follows:
Expression = -5.Quotient = 60/12.x = 48.Expression = 13/20.Prime factorization of 64 = 2⁶.Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.The graph of x = 3.5 is shown in the image attached below.Number of bags = 5 bags.Expression = 100.What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
How to evaluate the given expression?When x = 6, we have:
Expression = 9 + x + 5 - 20
Expression = 9 + 6 + 5 - 20
Expression = 15 - 20
Expression = -5.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
How to interpret and simplify the word problem?The quotient of 60 and 12:
Quotient = 60/12
How to solve the given equation?x/12 = 4
Cross-multiplying, we have:
x = 12 × 4
x = 48.
How to evaluate the given expression?1/20 + 3/5 =
Lowest common multiple (LCM) = 20;
(1 + 12)/20 = 13/20.
How to write the prime factorization of 64?Factors of 64 = 1, 2, 4, 6, 8, 16, and 32
Prime factorization of 64 = 2 × 2 × 2 × 2 × 2 × 2 = 2⁶.
What are factors?Factors can be defined as the fundamental building blocks of a number. This ultimately implies that, factors refers to numbers which can be multiplied together to get another number.
List of all the factors of 100.Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, and 100.
How to calculate the number of boxes?In order to calculate the number of boxes that Doritos can buy, we would apply direct proportion:
1 box = $8
X box = $40
Cross-multiplying, we have:
8X = 40
X = 40/8
X = 5 bags.
Number of bags = 5 bags.
How to simplify the given expression?In order to simplify this expression, we would apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.
Expression = 100 + 2(25 - 5²)
Expression = 100 + 2(25 - 25)
Expression = 100 + 2(0)
Expression = 100.
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Answer this question please
Answer:
See below
Step-by-step explanation:
This means
x < 3 or
-x < 3 <==== multiply both sides by -1 <=== this reverses the <
x > -3
so combining the two underlined
-3 < x < 3
Answer:
Step-by-step explanation:
we can expand the inequality to x>-3 or x<3 meaning x should be between -3 and 3 mathematically we can say -3<x<3
hope this helps
1.A rectangle is placed around a semicircle as shown below. The width of the rectangle is 9mm. Find the area of the shaded region.
Use the value3.14 for pi , and do not round your answer. Be sure to include the correct unit in your answer.
2.A rectangular paperboard measuring 29 in long and 22in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.
3.The radius of a cylindrical construction pipe is 2. If the pipe is 19 long, what is its volume?
Use the value 3.14for pi , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
PLS HALP
Answer:
Since figure is not given, assume drawing a rectangle and label it from left top to right top as A and B. Similarly label it as C and D from bottom left to right. Draw a semicircle starting from C to D inside the rectangle.
You are asked to find area of shaded region which I assume is semicircular part.
Area of a circle is determined by Pi × r ^2
r is the radius of circle which is half of diameter. The diameter of circle is same as width of rectangle. So radius = 7/2 = 3.5 mm And area of shaded region is
1/2(Pi×r^2) = 1/2(3.14×3.5^2) = 19.2325 sq mm
Step-by-step explanation:
2(4)-5=
i dont know what the answer is but i need help now bc it is a timed test someone pls help pls
Answer:
3
Step-by-step explanation:
what is 4320 divided by 27
Answer:
160
Step-by-step explanation:
Answer:
160
Step-by-step explanation:
José put $1,500 into a savings account. He earns 3% interest every year. How much simple interest will he earn at the end of 3 years?
He would have a total of: $1639.09
In intrest alone he would've made 1639.09
Step-by-step explanation:
3%= 0.03
The first thing you do is multiply $1,500 by the %3 (0.03).When your done multiplying, you should get 45.Add 45 to 1500Now you have 1545Then you repeat the process over, two more times. However the numbers will change.PLZ ANSWER ASAP!!!
A parallelogram ABCD , with I as the middle point of AC and EF is a line that goes through I. Show that IE=IF.
Answer:
IE = IF (By CPCT)
Step-by-step explanation:
Given:
ABCD is a parallelogram
So,
LINE AC || DC
Computation:
IN ΔAIE and ΔCIF
∠AIE = ∠CIF (Vertical opposite angle)
AI = IC (I is midpoint of line AC)
∠IAE = ∠ICF (Alternate angle)
So,
ΔAIE ≅ ΔCIF
So,
IE = IF (By CPCT)
Kelly makes fruit juice each morning. She uses 2 1/3 pints of strawberries and 1 2/5 pins of grapes in her juice how many more pints of strawberries than pints of grapes does she use?
Two angles are supplementary. One has a measure that is five times as large as the other. Find the two angle measures.
Answer:
30° and 150°
Step-by-step explanation:
supplementary means that the sum of the measures = 180
let's say 1 angle is labled ∠A and the other ∠B
m∠A + m∠B = 180°
however, m∠A = 5 * m∠B
so, by substituting that:
5*m∠B + m∠B = 180°
6*m∠B = 180°
m∠B = 30°
m∠A = 150°
In a sample of 80 Americans, 55% wished that they were rich. In a sample of 90
Europeans, 45% wished that they were rich.
a) At a = 0.01, is there difference in the proportions?
b) Find the 99% confidence interval for the differences of the two proportions
Answer:
hjgkulihjoj;l
Step-by-step explanation:
PLEASE HELP
Find the unit rate.
12 slices from 2 cakes =
Answer:
1 cake 6 slice
Step-by-step explanation:
just divide
12/2=6
2^5 is equal to 2•5.
Group of answer choices
Answer:
32≠10
False
Step-by-step explanation:
.
If each 10 x 10 unit square represents one whole, then what
percent is represented by the shaded region?
. In the model above, 25% represents a quantity of 10
students. How many students does the shaded region
represent?
Answer: 125% and 50 students.
write 7x7x7 as a base and an exponent (2ps possilbe)
Answer:
[tex]7^{3}[/tex]
Step-by-step explanation:
7 is being multiplied by itself 3 times meaning it's to the power of 3 so the base is 7 while the exponent is 3.
Solve the following 3/4+2/8
Answer:
28
Step-by-step explanation:
3x4 is 12
2x8 is 16
16+12 is 28
Answer:
1
Step-by-step explanation:
In order to add fractions they have to have a common denominator.
In this case we can multiply the fraction 3/4 by 2 to get 6/8.
Now we can add them:
[tex]\frac{6}{8} + \frac{2}{8} = \frac{8}{8} = 1[/tex]
Therefore, the answer to the question is 1.
I hope this helps!!
- Kay :)
Lily deposited $500 in a savings account. At the end of 1 year, she had eamed $20 in simple interest What interest rate did she receive?
Answer:
4% compounded yearly
Step-by-step explanation:
20 / 500 = 0.04
0.04 * 100 = 4%
Ok ok ok ok ok ok ok ok ok ok
Answer:
53%
Step-by-step explanation:
No Com
A certain shade of paint is made by mixing 5 parts blue paint with 2 parts white paint. To get
the correct shade, how many quarts of white paint should be mixed with 8.5 quarts of blue
paint?
Answer:
5.5
Step-by-step explanation:
8.5-5=3.5
so you need to add 3.5 to the amount of white paint.
2+3.5 is 5.5
The answer is 5.5
What is the Volume of this Cube?
Answer:
1 cubic cent
Step-by-step explanation:
Cause the volume of a cube is V^3. So, 1x1x1 = 1
Answer:
The answer is 1 cubic centimeter.
Step-by-step explanation:
Shep Company’s records show the following information for the current year:
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Determine net income (loss) for each of the following separate situations. (For all requirements, losses should be entered with a minus sign.)
a. Additional common stock of $4,600 was issued, and dividends of $8,600 were paid during the current year.
b. Additional common stock of $15,400 was issued, and no dividends were paid during the current year.
c. No additional common stock was issued, and dividends of $13,600 were paid during the current year.
.
The determination of the net income for each of the following separate situations is as follows:
Situation A Situation B Situation C
Net income $21,800 $2,400 $31,400
Data and Calculations:Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Situation A:
Common Stock issued = $4,600
Dividend paid = $8,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 4,600
Dividend paid (8,600)
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$21,800 ($47,400 - $29,600 - 4,600 + 8,600)
Situation B:Common Stock issued = $15,400
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued 15,400
Dividend paid
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$2,400 ($47,400 - $29,600 - 15,400)
Situation C:Dividends paid = $13,600
Beginning of year End of year
Total assets $ 53,200 $ 84,000
Total liabilities $ 23,600 $ 36,600
Equity $29,600 $47,400
Common Stock issued
Dividend paid $13,600
Net Income = Ending Equity - Beginning Equity - Additional stock + Dividend Paid)
$31,400 ($47,400 - $29,600 + 13,600)
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A nurse assesses a 66 - year - old client who is attempting to quit smoking . The client states , " I started smoking at age 16 , and smoked one pack each day until 10 years ago . Then I decreased to a half of a pack per day . " How many pack - years should the nurse document for this client ?
The nurse should document for this client as 45 pack years.
Pack year is determined by dividing the quantity of packs smoked daily by the number of years the smoker has smoked.
total years of smoking = current age of the client - the year he started smoking
= 66 - 16
50 years of smoking
For 40 years he smoked 1 pack per day but then he reduced it to a half pf a pack per day
= 40 x 1 + 10 x 0.5
= 45 pack- years
The nurse should document for this client as 45 pack years as the client has started smoking at age 16 , and smoked one pack each day until 10 years ago then he had decreased to a half of a pack per day.
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A music club has 35 drum players. If 25% of the total number of members in the club are drum players, what is the total number of member in the club?
Answer:
140
Step-by-step explanation:
Since 25% is 1/4 of 100, that means that 35 is 1/4 of the total amount of members in the club. So, 35 times 4 is 140.
Answer:
140
Step-by-step explanation:
hope this helps get a 100%
Certain types of songs tend to have a call-and-response structure because_________.
A. It can have many different sections
B. It is easy to remember and suitable for groups
C. Only very musical people can learn it
Certain types of songs tend to have a call-and-response structure because A. It can have many different sections
What is call and response?A call and response in music is a series of two independent phrases that are typically composed in separate portions of the piece, with the second phrase being heard as a direct remark or answer to the first.
Direct imitation between instruments, a questioning phrase and subsequent response, a statement of affirmation from one instrument to another, or variations on a direct call by a group of instruments are examples of call and response.
Therefore, certain types of songs tend to have a call-and-response structure because it can have many different sections
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if a²-b²=21 and a²+b²=29, which of the following could be the value of ab?
1. -10
2. 5√2
3. 10
Answer:
ab = 10 or -10
Step-by-step explanation:
........
.
Find the perimeter of abc with vertices (1,-6) (1,-3) (-4,-6)
Answer:
8+√34
Step-by-step explanation:
use distance formula d =√(x2-x1)² +(y2-y1)² to find the sides
√ (1 -1)²+( -6+3)² = √9 = 3
√ (1+4)²+( -6+6)² = √25 =5
√ (1+4)² + (-3+6)² = √25+9 =√34
Perimeter is P = 3+5+√34 = 8+√34
What is the surface area of the rectangular prism below?
Answe: there is no pic
Step-by-step explanation:
What ratio is equivalent to the ratio 14:7 A 1:7 B2:7 C2:1
Answer:
c 2:1
Step-by-step explanation:
If you simplify 14:7 it is 2:1 (divide by 7)
Answer:
14:7 is the same as 2:1 because 7 can go into 14 two times and into 7 once
so your answer would be C
A rectangular garden has a walkway around it. The area of the garden is 6(3.5x+1.5). The combined area of the garden and the walkway is 7.5(6x+5). Find the area of the walkway around the garden as the sum of two terms.
Answer:
[tex]A_w=24x+28.5[/tex]
Step-by-step explanation:
The rectangular garden is surrounded by a walkway.
The combined area of both is 7.5(6x+5) and the area of the garden alone is 6(3.5x+1.5).
The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:
[tex]A_w=7.5(6x+5) -(6(3.5x+1.5))[/tex]
Removing parentheses:
[tex]A_w=45x+37.5 -21x-9[/tex]
Simplifying:
[tex]\mathbf{A_w=24x+28.5}[/tex]
If x varies directly as y and z and inversely as the square
of r, and x = 16 when y = 3, z = 12 and r = 3, find
x when y = 5, z = 30, and r
r =10
Answer:
x = 6
Step-by-step explanation:
Take the statement x varies directly as y and z
This means value of x is directly proportional to the value of y and z represented as x ∝ yz which can be represented as x = k.y.z where k is a constant known as the constant of proportionality
If x varies inversely as the square of r we represent this as x ∝ 1/r² or in equation form x = k/r²
Since the value of x is dependent on the values of y, z and jointly we have a single equation of proportionality:
[tex]\bold{x= k\cdot\frac{yz}{r^{2}}}[/tex]
Given the values for x, y, z and r we can compute the proportionality constant and determine the value of x for any value of y, z or r
x = 16 when y = 3, z = 12 and r = 3
[tex]16 = k\cdot \frac{3\cdot 12}{3^2} \\\\16 = k\cdot \frac{3\cdot 12}{9}\\\\16 = k\cdot4\\\\k = 16/4 = 4\\[/tex]
So the constant of proportionality is k = 4. Us this value in the proportionality equation along with y, z and r to get the value of x
[tex]x = 4\cdot \frac{5\cdot 30}{10 \cdot 10}\\\\x = 4\cdot\frac{150}{100}\\\\x = \frac{600}{100} = 6\\\\[/tex]
So x = 6 is the answer