The equation of the circle (x + 8)^2 + (y + 3)^2 = 121 has a radius of 11 and a center located at (-8 , -3).
The standard form of the equation of circle is given by
(x - h)^2 + (y - k)^2 = r^2
where (h , k) is the location of the center and r is the radius of the circle.
On the other hand, the general form of the equation of circle is given by
x^2 + y^2 + Dx + Ey + F = 0
where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.
If the equation of the circle in standard form is (x + 8)^2 + (y + 3)^2 = 121, then
h = -8
k = -3
r = √121
r = 11
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Solve each system by elimination.
4x+2y = 4 , 6x + 2y = 8
By elimination, the solution of the system of equations, 4x + 2y = 4 and 6x + 2y = 8, is (2 , -2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Subtracting the two equations will eliminate the variable y.
6x + 2y = 8 (equation 2)
4x + 2y = 4 (equation 1)
2x + 0y = 4
x = 2
Substitute the value of x to any of the two equations and solve for y.
6x + 2y = 8 (equation 2)
6(2) +2y = 8
2y = 8 - 12
2y = -4
y = -2
Hence, the solution of the system of equations is (2 , -2).
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Find the distance between each pair of points.
A(14,-3), B(9,-9)
Answer: (24, -12)
because 14 + 9 is 24 ob. and -3 + -9 will be 3+9 with the - so it's -12
C=(r+z / 3) h
what does r equal
Answer:
r= 3C/h - z
Explanation:
divide each side to isolate the variable.
Bob got a mean of 7.8 marks in his last 4 tests. How many marks did he get in total?
Answer:
78
Step-by-step explanation:
Answer:
31.2
Step-by-step explanation:
7.8x4=31.2
so he got in total of 31.2 out of 40 if all test is combined
SOMEONE HELP ASPAPPP. POLELASEEEE BEGING
THANKS
Answer:
29
Step-by-step explanation:
b is also 97
97 + 54 = 151
180 - 151 = 29
A number line can represent positions that are north and south of a truck stop on a highway
Positive positions are north of the truck stop and negative positions are south of the truck stop. What is the value, in miles, of each position on a number line?
1. The truck stop ______
2. 5 miles north of the truck stop _____
3. 3.5 mlles south of the truck stop ____
WILL GIVE BRAINLIEST, TYYY !
Using integer numbers, the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
In the context of each problem, integer numbers may have different representations, and for this problem, we have that:
The truck stop is the origin, that is, position zero.Positions north of the truck stop will be represented by positive values.Positions south of the truck stop will be represented by negative values.Hence:
5 miles north is represented by the integer 5.3.5 miles south is represented by the integer -3.5.Hence the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
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What is the answer to the following questions: 2 x 5
Answer:10
Step-by-step explanation:
Answer:
2x5=10 . .............
Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. how many laps around the park mayumi ride ? write your answer as a whole number of laps plus a fraction of a lap you can use the model to help.
Two expression with equal sign in between is equation. If Mayumi rides her bike around a park . each lap around the park is two/ three . Mayumi rides of total of three. Then 4 1/2 laps around the park mayumi ride.
What is Equation?
Two expression with equal sign in between is called as Equation.
Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. The number of laps around the park mayumi ride be x.
We convert this given data as a expression as given
2x/3=3
Apply cross multiplication.
2x=9
x=9/2,
We need to write answer as a whole number of laps plus a fraction of a lap.
x=4 1/2
Therefore 4 1/2 laps around the park mayumi ride.
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Answer: Mayumi Rides 4 whole laps, plus 1/2 of a lap.
Step-by-step explanation:
A trapezoidal deck has dimensions as shown.
a. What is a formula for the area of this trapezoid?
What is the Area of Trapezoid?
The area of a trapezoid is the total space covered by its sides. An interesting point to be noted here is that if we know the length of all sides we can simply split the trapezoid into smaller polygons like triangles and rectangles, find their area, and add them up to get the area of the trapezoid. However, there is a direct formula that is used to find the area of a trapezoid if we know certain dimensions.
Area of Trapezoid Formula :
The area of a trapezoid can be calculated if the length of its parallel sides and the distance (height) between them is given.
The formula for the area of a trapezoid is expressed as,
A = 1/2 (a +b) h
where (A) is the area of a trapezoid, 'a' and 'b' are the bases (parallel sides), and 'h' is the height (the perpendicular distance between a and b)
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One of the planet Saturn's rings has a diameter of approximately 2.5 × 105
kilometers. What is the diameter of the ring, in kilometers, written in standard
notation?
A.
2,500
B.
25,000
C. 250,000
D. 2,500,000
The diameter of the ring, in kilometers, written in standard notation is 250000 kilometers
What is the diameter of the ring, in kilometers, written in standard notation?The given parameters are:
Diameter = 2.5* 105 kilometers
Rewrite properly as
Diameter = 2.5* 10^5 kilometers
Express 10^5 as 100000
So, we have:
Diameter = 2.5* 100000 kilometers
Evaluate the product
Diameter = 250000 kilometers
Hence, the diameter of the ring, in kilometers, written in standard notation is 250000 kilometers
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You find 400 mg of a substance that has a half-life of 20 days. What is it's daily rate of decay? Round answers to four decimal places.
The daily rate of decay is approximately equal to 0.0347 days⁻¹.
What is the rate of decay of a substance?
According to the statement, we find that a substance is under a decay process, whose differential equation is introduced below:
dm(t) / dt = - k · m(t) (1)
Where:
m(t) - Current mass of a substance, in miligrams.k - Rate of decay, in 1 / day.The half-life of the substance is the time needed for a substance to decrease its mass by half. The rate of decay can be found in terms of half-life:
k = (㏑ 2) / t' (2)
Then, the daily rate of decay of the substance is:
k = (㏑ 2) / (20 days)
k ≈ 0.0347 day⁻¹
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Evaluate the expression
8
-
d
+3 when d = 4
Answer:
8-d+3
8-4+3
4+3
=7
this is the expression but this is very essay
WRITING IN MATH Explain why the order of the vertices is important when naming congruent triangles. Give an example to support your answer.
Because we are saying that the angles/edges in corresponding positions for each triangle are congruent.
Consider the triangle congruence statement below:
△ABC≅△DEFThis is actually a collection of six—yes, six—congruence statements.
They are as follows:
∠A≅∠D∠B≅∠E∠C≅∠FAB≅DEAC≅DFBC≅EFAs an example, consider the first congruence: ∠A≅∠D
This is implied by the fact that A and D are both listed first in their triangles (in the statement △ABC≅△DEF ). Similarly, B and E are in second place, so that's how we get ∠B≅∠E.A similar logic applies to the sides that have corresponding vertices.If the triangle congruence statement was as follows:
△ABC≅△FED
Then,
∠A would-be congruent to ∠F∠B would be congruent to ∠E∠C would be congruent to ∠DWe can see how changing the order of the triangle names changes which angles/edges are implied to be congruent.
This is why we must be cautious to name the triangles in the correct order. Otherwise, we risk claiming that two angles (or line segments) are congruent when they are not.Therefore, we are saying that the angles/edges in corresponding positions for each triangle are congruent.
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6 Sasha thinks of a number.
She adds 1 to her number then multiplies the result by 5.
a Use a mapping to write this as a function.
The answer Sasha gets is 11.
b Use inverse functions to work out the number Sasha thought of in the beginning.
Show all your working.
Solve the equation. Check your solution.
8.32=4.1z+10.5
Pls help.
Answer:
z = -0.5317073
Step-by-step explanation:
Get variable on left and all constants on right
-4.1z = 10.5 - 8.32
-4.1z = 2.18
Divide both sides by -4.1
z = -0.5317073
To check:
8.32 = 4.1(-0.5317073) + 10.5
3/7 divided by 11/21 = 3/7 x
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
What is the solution to the given equation?Given the equation in the question;
3/7 divided by 11/21 = 3/7 x
3/7 ÷ 11/21 = (3/7)x
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
3/7 ÷ 11/21 = (3/7)x
3/7 × 21/11 = (3/7)x
( 3 × 21 )/( 7 × 11 ) = (3/7)x
63/77 = (3/7)x
Remove the parenthesis
63/77 = (3/7) × x/1
63/77 = ( 3 × x )/( 7 × 1)
63/77 = 3x/7
Cross multiply
63 × 7 = 3x × 77
441 = 231x
231x = 441
Divide both sided by 231
231x/231 = 441/231
x = 441/231
x = 21/11
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
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Which set of numbers are irrational number
Answer:
numbers like 9.58596638927, pi, square root of 2, or square root of 11
Find equations that enclose a region such that when rotated about the x -axis, a solid is produced with a volume of 18π cubic units.
∫45 πy2 dx is that enclose a region such that when rotated about the x -axis, a solid is produced with a volume of 18π cu units .
How do you determine a region's volume?
Depending on the axis of revolution, r=f(x) or r=f(y) and V=Adx or Ady, where A denotes the usual disc's area. The volume of the solid produced by a region under f(y) (to the left of f(y)) that is rotated around the y-axis and is bounded by the horizontal lines y=c and y=d.Volume of the solid = ∫45 πy2 dx
= π ∫45 4x dx
= 4π (x2 / 2)45
= 18π cu units
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Determine a base area and height for each shape
You have to show the picture of what your talking about. Please do so if you want someone to answer your question.
A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m< RLQ
The measure of arc NPQ is 180° while the measure of m <AOB is 69°.
What is the inscribed of a circle?An inscribed angle of a circle is an angle whose vertex is a point A on the circle and whose sides are line segments (called chords) from A to two other points on the circle.
An octagon is known to be a type of polygon that is said to have up to 8 sides. the octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane. A regular octagon will have all its sides equal in length. Each interior angle of a regular octagon is equal to 135°. Therefore, the measure of exterior angle becomes 180° – 135° = 45°.
The measure of arc NPQ is 180° while the measure of m <AOB is 69°.
The complete question is:
A stop sign in the shape of a regular octagon is inscribed in a circle.
What is the measure of arc NPQ?
A. 45°
B. 90°
C. 135°
D. 180°
2. In the figure at the right points A, B, C are on 00, and m<ACB = 690
What is the m<AOB?
A. 69°
B. 138°
C. 2780
D. 360°
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Help marking brainlest and worth 20 points
let x^3-2x^2-6x+7=0 be a polynomicsl equation
Find all potential rational solutions using the rational route therom. Separate multiple solutions with commas if necessary.
Find all the distinct actual rational solutions. Separate multiple solutions with commas if necessary. If no solutions exist, enter none
The solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
What is a polynomial?
A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given equation is x³ - 4x² - 7x + 10 = 0. The equation will be solved as,
x³ - 4x² - 7x + 10 = 0
x³ - 3x² - 10x - x² + 3x + 10 = 0
( x² - 3x - 10) ( x - 1 ) = 0
( x² -5x + 2x - 10 ) ( x- 1) = 0
( x - 5 )( x + 2 )( x - 1 ) = 0
Therefore, the solution of the third degree polynomilal x³ - 4x² - 7x + 10 = 0 will be ( x - 5 )(x + 2 )( x - 1 ).
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A group of friends wants to go to the amusement park. They have $89.50 to spend on parking and admission. Parking is $7.75, and tickets cost $27.25 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
7.75 +27.25p = 89.50p = 3; 3 people can go the the amusement parkStep-by-step explanation:
Given parking costs $7.75 and admission costs $27.25, you want an equation and its solution for the number of people (p) who can go to the amusement park for $89.50.
EquationThe equation relates the total of costs to the total of funds available. The cost will be the total of 7.75 for parking and 27.25p for admission for p people.
7.75 +27.25p = 89.50
SolutionThis 2-step equation is solved by subtracting 7.75, then dividing by the coefficient of p.
7.75 +27.25p = 89.50 . . . . . equation
27.25p = 81.75 . . . . . . . . . . . subtract 7.75
p = 3 . . . . . . . . . . . . . . . . . . . divide by 27.25
3 people can go to the amusement park for $89.50.
<95141404393>
8(x-5)-3x
i need help someone tell me
Answer:
5x - 40
Step-by-step explanation:
8(x-5)-3x
Distribute
8x - 40 - 3x
Combine like terms
5x - 40
Distribute
-(8j-1)
(Show work)
Answer:
-8j + 1
Step-by-step explanation:
-(8j -1) = (-1 x 8j) - (-1 x 1) = -8j - (-1)
subtracting a negative creates a positive so:
-8j + 1
Beau buys a 3-pound of trail mix for a hike. he wants to make one-ounce bag of trail mix for his friends with whom he is hiking how many one-ounce bags can he make?
Using conversion, Beau can make 48 one-ounce bags of trail mix from the 3-pound trail mix he bought for the hike.
To know how much one-ounce bags of trail mix can he make from the 3-pound trail mix, convert first the amount of trail mix in pounds to ounce.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
Converting pounds to ounce,
1 pound = 16 ounces.
If Beau has 3 pounds of trail mix, equivalently, converting pounds to ounces, he has:
1 pound = 16 ounces
3 pounds = 3(16 ounces)
3 pounds = 48 ounces
If he wants to make one-ounce bag of trail mix from the 3-pound of trail mix (= 48 ounces), divide it by one ounce to get how many bags he can make.
number of one-ounce bag = 48 ounces/1 ounce
number of one-ounce bag = 48
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i think i know the answer but i still need help…
The solutions for 'u' are u ≤ -5 and u ≤ 1
How to solve the inequality
Given the inequalities;
-3u ≤ 15 2u - 1 ≤ 1Let's solve for u in the expression
-3u ≤ 15
Make 'u' the subject
-3u/3 ≤ 15/ -3
u ≤ -5
Let's solve for 'u' in the expression
2u - 1 ≤ 1
collect like terms
2u ≤ 1 + 1
Add like terms
2u ≤ 2
Make 'u' the subject
u ≤ 2/ 2
u ≤ 1
Thus, the solutions for 'u' are u ≤ -5 and u ≤ 1
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9.
(9x + 25)*
(13x - 19) /(17y + 5),
m
After simplification the solution of the given expression (9x + 25)(13x - 19)/(17y + 5) is 117x² + 154x - 475/(17y + 5).
What are expressions?In mathematics, an expression is a sentence that contains at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.You must substitute a number for each variable and perform arithmetic operations to evaluate an algebraic expression. Because 6 + 6 = 12, the variable x in the preceding example is equal to 6. We can evaluate the expression after replacing the variables with their values if we know their values.So, (9x + 25)(13x - 19)/(17y + 5):
(9x + 25)(13x - 19)/(17y + 5)9x(13x - 19)+ 25(13x - 19)/(17y + 5)117x² - 171x + 25(13x - 19)/(17y + 5)117x² - 171x +325x - 475/(17y + 5)117x² + 154x - 475/(17y + 5)Therefore, after simplification, the solution of the given expression is 117x² + 154x - 475/(17y + 5).
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What is the difference between an arithmetic sequence and an arithmetic series?
Answer:
arithmetic sequence is a sequence where the difference between a successive terms is constant
Step-by-step explanation: arithmetic series is the sum of the terms of an arithmetic sequence
PLEASE HELP!!!!!!!!!!
Answer:
m∠ FHC = 87°
Step-by-step explanation:
Hello!
Angle EHD and FHC are vertical angles, meaning they are non-adjacent angles formed by intersecting lines.
The two intersecting lines are EF and DC, and angles EHD and FHC are formed as non-adjacent angles.
Vertical Angles are congruent in measure.
Therefore, Angle FHC is also 87°.
Solve x² + 2x - 15 = 0.
The solutions to the equation are x = -5 and x = 3
How to solve the equation?The equation is given as
x^2 + 2x - 15 = 0
Expand the equation
So, we have
x^2 + 5x- 3x - 15= 0
Factorize
(x + 5)(x - 3) = 0
Solve for x
x = -5 and x = 3
Hence, the solutions to the equation are x = -5 and x = 3
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