Using the given information, the equation of the circle with radius 2 and center at (-1 , -5) is (x + 1)^2 + (y + 5)^2 = 4.
The general 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.
Given the radius and center of the circle, substitute these values to the general form of the equation of the circle.
(x - h)^2 + (y - k)^2 = r^2
where (h , k) = (-1 , -5)
r = 2
(x - -1)^2 + (y - -5)^2 = 2^2
(x + 1)^2 + (y + 5)^2 = 4
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In a bag, the ratio of purple counters to green counters was 3:4. 8 more purple counters were then added to the bag, and the ratio of purple counters to green counters became 5 : 4. How many green counters are in the bag?
Answer:16
Step-by-step explanation:
since the increase is 2 units for purple counters
8 ÷ 2 = 4
4×4=16
Please help!!!
For questions 10-13 use f(x)=4(1/2)^x
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 21+19+17+ . . . ; n=8
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
The given series is 21+19+17+ . . .
On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.
So the formula will be (-2n +/- something).
Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.
So if n=0, our first term is 21
If n=1, our second term is 19
If n=2, our third term is 17
and so on.
So, we have the expression (21 - 2n).
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
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Simplify the expression.
16-12 / 15-11
The simplified expression for (16-12 / 15-11) is 1 .
The given expression is,
( 16-12 / 15-11 )
First we need to solve the numerator which is (16-12) and on simplifying the numerator we can write,
Numerator = ( 16 - 12 ) = 4 equation 1
Similarly, now we can proceed to solve the denominator which is (15 - 11) and on simplifying the denominator we write,
Denominator = (15 - 11) = 4 equation 2
Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 16-12 / 15-11 ) as,
(Numerator / Denominator) = (16-12 / 15-11) = (4/4) = 1
The simplified expression for (16-12 / 15-11) is 1 .
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A stop sign in the shape of a regular octagon is inscribed in a circle. Find following measure.
m < LRQ
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
The measure of < LRQ is 112.5.
What is an Intercepted Arc?
The term "intercepted arc" refers to an arc that is "cut off" or "lies between" the specified angle's sides.
An arc is a segment of a circle's circumference. An intercepted arc is thus one formed when one or two different chords or line segments cut across a circle and meet at a common point known as a vertex.
If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.
So, [tex]$m \angle L R Q=\frac{1}{2}(m \overparen{L N Q})$[/tex]
The sum of the measures of the central angles of a circle with no interior points in common is 360 .
Here, 360 is divided into 8 equal arcs and each arc measures
360/ 8 = 45.
Then, m LNQ = m LM + m MN + m NO + m OP + m PQ = 5(45) = 225.
[tex]$m \angle L R Q=\frac{1}{2}(225)=112.5$[/tex].
Therefore, the measure of < LRQ is 112.5.
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whats the slope for (-6,-3) and (0, -1.5) in fraction form?
The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
What is the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) as required in the task content?It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.
On this note, it follows from the slope formula that slope;
m = (y2 - y1)/(x2 - x1)
Therefore, the slope of the line segment joining the two points is;
m = (-1.5 - (-3))/(0 - (-6))
m = 1.5/6
m = 1/4.
Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.
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Write an algebraic expression that models each situation.
The piggy bank contained 25 , and 1.50 is added each day.
The algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x
Given,
The piggy bank contained = $25
The amount added in each day = $1.50
Consider number of days as x
Then the algebraic expression = 25+1.50x
Hence, the algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x
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Determine if 21 is rational or irrational and give a reason for your answer.
Simplify by combining like terms. -(3 z-5)+z
The simplification by combining like terms of -(3z -5) + z is -2z + 5.
According to the given question.
We have an expression -(3z -5) + z.
As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.
Since, we have to combine the like terms of the given expression -(3z - 5) +z.
Here -3z and z both are the like terms.
So, we subtract coeffcients of z to simplify the given expression.
Therefore, the simplification of the expression -(3z - 5) +z is given by
-(3z - 5) + z
= -3z + 5 + z
= -3z + z + 5
= -2z + 5
Hence, the simplification by combining like terms of -(3z - 5) + z is -2z + 5.
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factorise and hence evaluate :
2,014^2-2,012^2
Answer:
8,052
Step-by-step explanation:
(2,014 - 2,012) x (2,014 +2,012)
2 x 4,026
8,052
Find the measure of each numbered angle. (Lesson 4-2)
m ∠ 6
The measurement of angle ∠2 is 67.50°.
What exactly do we mean by an angle?In Euclidean geometry, an angle is a figure formed by two rays called the sides of the angle that share a common endpoint called the vertex of the angle.Angles formed by two rays are located in the plane in which the rays are located.When two planes intersect, angles are formed.These are referred to as dihedral angles.So,
An octagon has 8 sides.Sum of interior angles = 180° x (n-2) = 180° x (8-2) = 180° x 6 = 1,080°1,080° ÷ 8 sides = 135° interior angle.Angle 2 = 135° / 2 = 67.50°Therefore, ∠2 is 67.50°.
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The correct question is given below:
Given the regular polygon, find the measure of each numbered angle.
m ∠ 2
how can changing fractions to decimals make them easier to compare?
Answer:
They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.
Step-by-step explanation:
I'll give brainliest
What values of x and y satisfy the system of equations {x=−2y+13x+8y=11?
Enter your answer as an ordered pair, like this: (42, 53)
If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475), enter it like this: (42/53, 64/75)
If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."
The solution of the simultaneous equation is given by (-7 , 4) .
A pair of simultaneous equations is the most common representation of a pair of straight lines in the cartesian plane.
For solving a pair of simultaneous equation we can use various procedures such as the matrix method, substitution or the method of elimination.
The given pair of simultaneous equation is given as:
x=−2y+1
3x+8y=11
Let us solve the equations by the method of substitution:
From the first equation we take the value of x and put it in the second equation:
3x + 8y = 11
or, 3 ( -2y + 1 ) + 8y = 11
or, -6y +3 +8y = 11
or, 2y + 3 = 11
or, 2y = 8
or, y = 4
Substituting the value of y as 4 in the first equation we get:
x = − 2y + 1
or, x = - 2 × 4 +1
or, x = -8 +1
or, x = -7
Therefore the solution set of the pair of equations is given by (-7 , 4) .
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Find the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi. (PLEASE SHOW WORK IF POSSIBLE)
The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
Volume of a coneThe formula for calculating the volume of a cone is expressed according to the formula
V = 1/3 pir²h
where
r is the radius of the cone = 10/2 = 5in
h is the height = 2in
Substitute to have;
V = 1/3pi(5)² × 2
V = 50/3pi
Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
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Put the following numbers in order from least to greatest
1/2, -2, √5, -7/4, -24
Answer:
-24 < -2 < -7/4 < 1/2 < √5
Step-by-step explanation:
Negative integers are always less than 0 and positive integers. More the magnitude (numerical value) of a negative integer, lesser is that number.Hence the order of negativeintegers will be -24 < -2 < -7/4. 1/2 is 0.5 and root 5 is around 2.236. Hence, 1/2 < √5. The final order is -24 < -2 < -7/4 < 1/2 < √5Three integers have a mean of 8, a median of 8 and a range of 4.
Answer:
The 3 integers are 6 8 and 10
Step-by-step explanation:
Comment
Start with the median. That's the middle number of an ordered set of numbers.
a 8 b is what you have so far.
Now the range between a and b is 4 which means that a and b differ by 4.
a + 4 = b
The mean will solve this quickly. Put a + 4 for b
[(a + 8 + a + 4)]/3 = 8 Combine like terms
(2a + 12)/3 = 8 Multiply both sides by 3
3 (2a + 12)/3 = 8 *3
2a+12 = 24 Subtract 12 from both sides
2a + 12 - 12 = 24-12 Combine
2a = 12
a = 6
but we know that the range between a (which is 6 ) and b is a + 4 = 10
So b must equal 10
A meeting room is set up with 16 rows of seats. The number of seats in a row increases by two with each successive row. The first row has 12 seats. What is the total number of seats?
a. How can you find the number of seats in each row using an explicit formula?
The most commonly used explicit of an arithmetic sequence is given as,
an = a + (n - 1) d
Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,
2nd row seat = 12+ 1x2
3rd row seat = 12 + 2 x2
nth seat = 12 + (n-1) x 2
16th row seat = 12 + (16–1) x2 = 42
Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows
Average number of seats per row = (12 +42)/2= 27
So total seats = average per row x number of rows
= 27 x 16 = 432.
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Can someone provide a justification?
The piecewise function that best models her weekly pay h(t) is given by:
h(t) = 12t, 0 ≤ t ≤ 40.h(t) = 480 + 18t.What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, we have that:
The input is the number of hours worked.The output is the weekly pay.Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:
Standard hours: t ≤ 40.Overtime hours: t > 40.For up to 40 hours, she receives the standard wage of $12, hence:
h(t) = 12t, 0 ≤ t ≤ 40.
For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:
h(t) = 480 + 18t.
Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:
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Evaluate the function at each specified value of the independent variable and simplify.
f(x) = x² + 1
a) f(1) =
b) f(-3) =
c) ƒ (6³) =
d) f (x - 1) =
name all the sets of numbers to which each real number belongs.
1. 12
2. -15
3. 1 1/2
4. 3.18
5. square root 48
6. 9.3
7. -2 7/9
8. square root 25
9. square root 3
10. negative square root 64
11. negative square root 12
12. 8/4
These are the description of the real numbers.
According to the statement
We have to explain all about the real numbers.
So, For this purpose, we know that the
Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.
From the given information:
Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.
• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.
• Whole numbers include all positive integer values including 0.
• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)
• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)
Using the definitions above :
• 12 = Natural, integer , integer and rational (12/1)
• -15 = Integer, rational (-15/1)
• 1 1/2 = 3/2 = Rational
• 3.18 = rational (terminating decimal)
• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)
• 9.3 = rational (terminating decimal)
• -2 7/9 = -25/9 = rational (a/b)
• root 25 = √25 = ±5 = integer, rational (5/1)
• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .
• negative root 64 = - √64 = - 8 = integer, rational (-8/1)
• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)
• 8/4 = 2 = natural, number, rational, integer
So, These are the description of the real numbers.
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Write the correct messurement indicated by the arrows on the lines to the left
Answer:
Step-by-step explanation:
It is given that we need to find the correct measurement indicated by the arrows on the lines to the left.
Now, let us have a look at the figure;
6 inches5.2 inches4.6 inches4.3 inches4 inches3.6 inches3.1 inches2.6 inches2.3 inches1.7 inches1.4 inches1.2 inches1.1 inches0.5 inches0.3 inches0.2 inches0.1 cm0.7 cm1.7 cm2.3 cm3.1 cm3.4 cm4.2 cm4.7 cm5.5 cm6.4 cm7.2 cm8.2 cm8.5 cm9.1 cm9.6 cmTo know more about this topic, click here:
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Does the infinite series converge or diverge? If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
Does the infinite series converge or diverge? The series converges.
If it converges, what is the sum?
a. 1/2 + 3/4 + 9/8 + . . . . .
The sum of the infinite series is -1
What is the sum of the infinite series?
Given:
[tex]a(\text{ the first term})=\frac{1}{2} \\\\r(\text{ thecommon ratio})=\frac{a_2}{a_1} =\frac{3}{2}[/tex]
Since ,[tex]\vert r\vert < 1[/tex], the infinite series converges.
The sum of infinite geometric series is:
[tex]S_\infty=\frac{a }{1-r} ; -1 < r < 1\\\\S_\infty=\frac{\frac{1}{2}}{1-\frac{3}{2}}=-1[/tex]
The sum of the infinite series is -1
What is an infinite geometric series?
The result of an endless geometric sequence is an infinite geometric series.There would be no conclusion to this series.The total of all finite geometric series can be determined.However, if the common ratio of an infinite geometric series is bigger than one, the terms in the sequence will grow steadily larger, and adding the larger numbers together will not yield a solution.To learn more about infinite geometric series, refer:
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Find the eighth term of each geometric sequence. 3,9,27, . . . . .
Answer:
6561
Step-by-step explanation:
You multiply by 3 each time.
→
List all the 4-digit even numbers
that can be created by
rearranging
these number tiles.
3472
Determine the probability of following event, flipping a coin and not landing on heads
According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}
Therefore, the probability can be written as:
Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]
Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Draw a line representing the rise and representing the run of the line. State the slope of the line in simplest form.
A diver is 7.5 meters above water. she takes her dive 1.7 meters below the surface. how far does the dive take her.
The diver take her at a distance of 9.2 meters.
What is distance?A resultant displacement can be used to quantify distance. It involves measuring the coordinate values of the beginning and ending positions. The distance is measured in quantities like meters, centimeters, kilometers, etc.
A diver descends 1.7 meters below the surface of the water while suspended 7.5 meters above it, according to the question.
According to fundamental mathematics, values that are less than zero can be represented as negative values.
She will thus descend (-1.7) meters as she dives below the surface.
The formula may now be expressed as follows: Total Distance = 7.5 - (-1.7) = 9.2 meters.
As a result, the diver descends 9.2 meters below the surface with her.
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A plant that manufactures metal plates has a quality control team to check that the plates are the right size. A rectangular plate advertised as 5 cm by 3 cm must have a length within 0.25 cm of 5 cm. Use the solution to the equation |x − 5| − 0.25 = 0 to find the minimum and maximum area, in sq. cm, of the plates.
The minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
What is area of rectangle?In mathematics, area of rectangle refers to the product of length of the rectangle and width of the rectangle. The unit is in square units. Area shows the extent a surface or a plane covers
Given data
size of rectangular plate = 5 cm by 3cm.
the length should be within = 0.25 of 5 cm
How to solve for the minimum and maximum areaThis means the length, L of the rectangular plate can be mathematically represented as
5 - 0.25 ≤ L ≤ 5 + 0.25
4.75 ≤ L ≤ 5.25
Area of rectangle = Length × Width.
Width = 3
minimum length = 4.75
maximum length = 5.25
minimum length
= 4.75 * 3
= 14.25 cm^2
maximum length
= 5.25 * 3
= 15.75 cm^2
Therefore, the minimum area is 14.25 cm^2while the maximum area is 15.75 cm^2
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book. With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book. For how many books produced will the costs from the two methods be the same?
The number of books published by a small publishing company is 3240.
Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of books be x.
With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.
That is, 44,714+11.50x
With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.
That is, 17,174+20x
Now, the number of books produced will the costs from the two methods be the same.
So, 44,714+11.50x=17,174+20x
⇒ 44,714-17,174=20x-11.50x
⇒ 8.5x = 27540
⇒ x=3,240
Therefore, the number of books published by a small publishing company is 3240.
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Which expression is equal to this expression, according to the associative property? 5+(3-1)
Answer:7
Step-by-step explanation:
3-1= 2
5+2=7
