The equation of the circle is x² - 24x + y² + 14y + 144 = 0
We have,
The center of the circle is at (12, -7), so the coordinates of the center give us the values of h and k in the equation of the circle:
(x - h)² + (y - k)² = r²
where (h,k) is the center and r is the radius.
Substituting the given values, we get:
(x - 12)² + (y + 7)² = r²
The diameter of the circle is 14, so the radius is half of that, or 7.
Substituting this value into the equation above, we get:
(x - 12)² + (y + 7)² = 7²
Expanding the left side and simplifying, we get:
x² - 24x + 144 + y² + 14y + 49 = 49
Combining like terms, we get:
x² - 24x + y² + 14y + 144 = 0
Therefore,
The equation of the circle is x² - 24x + y² + 14y + 144 = 0
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in the cost equation tc = f + vx, x is best described as the:
The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.
In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.
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what is the sum of all the even numbers between 30 and 36?
Answer:
30 + 32 + 34 + 36 = 132
Hope this helps!!
What is an equation of the line that passes through the points (-3,-1) and (6, 2)?
Put your answer in fully reduced form.
Answer:
1/3
Step-by-step explanation:
(2-(-1))/(6-(-3)) = 3/9 = 1/3
Answer:
y=1/3x
Step-by-step explanation:
Find the slope: 2-(-1)
6-(-3)
slope = 1/3
Point Slope Form: y-2= 1/3 (x-6) plug one of the coordinates into the equation
y-2= 1/3x -2
y=1/3x
car A is traveling east at a steady speed of 60 miles per hour after 2 hours, it is 130 miles east of Johnstown. car B is traveling east on the same road. its distance east of Johnstown is represented by the graph.
plzzzzzzzzzzzzzzzzz help mee
Answer:
There's no numbers on this graph. it you can tell me where it is, ill gladly update my answer. Other than that, I know exactly what they are saying, I just need numbers.
Step-by-step explanation:
need help pleeassseeee !!
Answer: 5
Step-by-step explanation: f(3) = 2x - 1
substitute the x with 3. 2(3)-1
6-1
5
Answer:
The answer is 5, hope you like!
I need help with Trigonometric Ration
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry, trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The trigonometry ratios for a specific angle ‘θ’ is given below:
Trigonometric Ratios
Sin θ Opposite Side to θ/Hypotenuse
Cos θ Adjacent Side to θ/Hypotenuse
Tan θ Opposite Side/Adjacent Side & Sin θ/Cos θ
Cot θ Adjacent Side/Opposite Side & 1/tan θ
Sec θ Hypotenuse/Adjacent Side & 1/cos θ
Cosec θ Hypotenuse/Opposite Side & 1/sin θ
Note: Opposite side is the perpendicular side and the adjacent side is the base of the right-triangle. Also, check out trigonometric functions to learn about each of these ratios or functions in detail.Trigonometric Identities
Definition
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
The three sides of the right triangle are:
Hypotenuse (the longest side)
Perpendicular (opposite side to the angle)
Base (Adjacent side to the angle)
what is greater 23/20 or 110%
Answer:
23/20
Step-by-step explanation:
110% of 20 is 22/20, so 23/20 is more.
Step-by-step explanation:
23/20 = 1,15
110% = 1,1
1,15 > 1,1
⇒ 23/20 > 110%
Find WX please help is very much appreciated
Answer:
WX = 6
Step-by-step explanation:
1. Approach
First, one must find the value of the variable (x). This can be done by using the Tangent-Line-intersection-theorem (many people refer to it by another name, but the theory is the same). This theory essentially states that when two lines are tangent to a circle and are non-parallel, the distance between the point of tangency, and the point of intersection of those two lines are the same for each line. After finding the value of (x), one can substitute it back into the given equation for the value of (WX), and solve it.
2. Finding (x)
The two segments; (WX) and (XY) are tangent to the given circle. Meaning that they only make contact with the circle at a single point. The space between their point of tangency and the point at which they intersect will be equal. Essentially meaning that the length of (WX) and the length of (XY) are the same. Therefore the equation
(XY) = (XW)
Can be formed. Substitute in the given values;
7x - 29 = 2x + 16
Inverse operations,
7x - 29 = 2x + 16
-2x -2x
5x - 29 = 16
+29 +29
5x = 45
/5 /5
x = 9
3. Solve for (WX)
Now substitute back in to find the length of (WX)
7x = 29
x = 5
7(5) - 29
35 - 29
6
which expression is equivalent to 7(a+2) when a equals 6?
7(6)
9(6)
7(6)+2
7(6)+14
plz help ty
Step-by-step explanation:
When a = 6,
7(a + 2) = 7(a) + 7(2) = 7(6) + 7(2) = 7(6) + 14.
Answer:
7(6)+14
Step-by-step explanation:
7(6+2) = 7(6) + 7(2) = 7(6) + 14
The general form of the solutions of the recurrnce relation with the following characteristic equation is:
(r-1)(r-4)=0
A. an=a1(1)n-a2(4)n
B. None of the above
C. an=a1(-1)n+a2(4)n
D. an=a1(-1)n+a2(-4)n
The characteristic equation for the recurrence relation is (r-1)(r-4)=0. This equation has two roots:
r=1 and r=4. Therefore, the general form of the solution is an = a1(1)n + a2(4)n. Therefore, the correct answer is A.
The recurrence relation can be written as an = an-1 + 4an-2. Substituting the general form of the solution into th
is equation, we get a1(1)n + a2(4)n = a1(1)n-1 + a2(4)n-1 + 4a1(1)n-2 + 4a2(4)n-2. Dividing both sides by 4n-2, we get (a1/4)(1)n-2 + a2(1)n-2 = (a1/4)(1)n-3 + a2(4)n-3 + a1(1)n-4 + a2(4)n-4. This equation holds for all n. Therefore, equating coefficients of like terms, we get a1/4 = a1/4, a2 = 4a2, a1 = a1/4, and a2 = 4a2. Solving these equations, we get a1 = a1/4 and a2 = 4a2.
Therfore, the general form of the solution is an = a1(1)n + a2(4)n.
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The general form of the solutions of the recurring relation with the following characteristic equation is ( an=a1(1)n-a2(4)n.
The general form of the solutions of the recurrence relation with the characteristic equation (r-1)(r-4)=0 is a linear combination of the form an=a1(1)n+a2(4)n, where a1 and a2 are constants determined by the initial conditions of the recurrence relation.
This can be seen by factoring the characteristic equation into two linear factors: r-1=0 and r-4=0, which correspond to the two possible roots of the characteristic equation.
The solution to the recurrence relation is a linear combination of these two roots raised to the power of n, with the coefficients determined by the initial values of the sequence.
Therefore, the correct answer is A.
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I need the steps and answers please
Answer:
Number 2: -3/10 (I think)
Number 4: 10a-5b-4
Number 6: x=5/2
Number 8: x=6
Step-by-step explanation:
Number 2:
3ysquared/2y-4x2
3(-1)squared/2(-1)-4x2
3x1/2(-1)-4x2
3x1/-10
-3/10
(I might be wrong with this one though)
Number 4:
10a-3b-4-2b
10a-5b-4
Number 6:
2(-3x+8)=4x-9
-6x+16=4x-9
-6x+16-16=4x-9-16
-6x=4x-25
-6x-4x=4x-25-4x
-10x=-25
-10x/-10=-25/-10
x=5/2
Number 8:
1(4x-8)/4=-x+10
4x-8/4=-x+10
4x-8/4+x=-x+10+x
8x-8/4=10
4x8x-8/4=4x10
8x-8=4x10
8x-8=40
8x-8+8=40+8
8x=48
8x/8=48/8
x=6
please this is due tomorrow
Answer:
289m = 2,890dm
Step-by-step explanation:
you multiply the meters by 10
can yall help me with this
In solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
What are fractions?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.There are three main categories of fractions in mathematics. 'Proper fractions, incorrect fractions, and mixed fractions are these three types. The expressions with a numerator and a denominator are called fractions.So, the wrong step will be:
(4/7) ÷ (-1/2)Then, the next step should be:
(4/7) × (-2/1)But, the steps it is given as:
(4/7) × (-2/-1)Which makes the error.
Therefore, in solving the following fraction, step (A) (4/7) × (-2/-1) is wrong and the correct step should be (4/7) × (-2/1).
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A number cube is tossed 60 times. outcome frequency 1 12 2 13 3 11 4 6 5 10 6 8 determine the experimental probability of landing on a number greater than 4.
The experimental probability of landing on a number greater than 4 is 0.25 or 25%.
To find this probability, we need to determine the number of successful outcomes (landing on a number greater than 4) and divide that by the total number of trials (60).
The successful outcomes are 5 and 6, with a frequency of 10 and 8 respectively. To add these two frequencies together, we can use 10 + 8 = 18.
So, the experimental probability is 18/60 = 0.3 or 25%.
It's important to note that experimental probability is based on the outcomes of an experiment or a sample and it may not be the same as a theoretical probability which is based on the ratio of favorable outcomes to the total number of outcomes in a theoretical model.
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the answer in fraction form is 18/60
if thats what you are looking for.
10. Which of the following situations represents a proportional relationship?....
F. A pizza is $7.95 plus $1.00 for each additional topping.
G. A pool fills at a rate of 90 gallons per hour.
H. A health club charges a $40.00 membership fee plus $25.00 per month.
J. A bank account begins with $350.00 and gains $30.00 per month.
Answer:
G A pool fills at a rate of 90 gallons per hour
Step-by-step explanation:
i dont know
a grain silo consists of a cylindrical main section and a hemispherical roof of the total volume of the silo (including the part inside the roof section) is 10,000 find.the.cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot?
The radius of the silo which is in the shape of cylinders and spheres , correct to the nearest tenth of a foot, is approximately 10.3 feet.
To find the radius of the silo, we need to determine the radius of the cylindrical section.
The volume of the cylindrical section can be calculated using the formula:
\(V_{cylinder} = \pi * r^2 * h\)
where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.
Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:
\(V_{cylinder} = \pi * r^2 * 30\)
To find the radius, we can rearrange the formula:
\(r^2 = V_{cylinder} / (\pi * 30)\)
Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:
\(r^2 = 10,000 / (\pi * 30)\)
Simplifying further:
\(r^2 = 106.103\)
Taking the square root of both sides, we find:
\(r = \sqrt{106.103} = 10.3\)
Therefore, the radius of the silo which is in the shape of cylinders and spheres , correct to the nearest tenth of a foot, is approximately 10.3 feet.
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Given that sin63= 0. 891 enter the cosine of a complementary angle
The cosine of a complementary angle to an angle with sine 0.891 is also 0.891.
The sine and cosine functions are trigonometric functions that are related to each other through complementary angles. Complementary angles are angles whose sum is 90 degrees or π/2 radians.
In this case, we are given that sin(63) = 0.891. To find the cosine of the complementary angle, we can use the identity: sin(θ) = cos(90 - θ).
Since sin(63) = 0.891, we know that sin(90 - 63) = 0.891. Therefore, the complementary angle to 63 degrees is 90 - 63 = 27 degrees.
Now, we can find the cosine of the complementary angle. Using the identity mentioned earlier, we have: cos(27) = sin(90 - 27) = sin(63) = 0.891.
Hence, the cosine of the complementary angle to an angle with sine 0.891 is also 0.891.
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Use additive inverses and their properties to find the equivalent expressions.
3+(-3)
3-5
3+(-3)
-3+3
-3+5
5-3
The values of the equivalent expressions are 0, -2, 0, 0, 2 and 2 respectively.
What is the equivalent expressionTo find equivalent expressions, we can use the property of additive inverses, which states that the sum of a number and its additive inverse is always equal to zero. That is:
a + (-a) = 0
We can use this property to rewrite the expressions as follows:
a. 3 + (-3) = 0
b. 3 - 5 = 3 + (-5) = -2
c. 3 + (-3) = 0
d. -3 + 3 = 0
e. -3 + 5 = 2
f. 5 - 3 = 5 + (-3) = 2
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Hi, can you help me to solve this problem please!
f(12) will be: substituting 12 into the expression above
\(\begin{gathered} f(12)=\frac{12}{2}-5 \\ =6-5 \\ =1 \\ Final\text{ answer:} \\ f(12)=1 \end{gathered}\)What is the slope of y=-5+4xy=−5+4xy, equals, minus, 5, plus, 4, x?
Answer:
-5/4
Step-by-step explanation:
The slope of a line y=4x-5 is 4.
The equation of a line is y=-5+4x.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y2-y1)/(x2-x1)
The standard form of equation of line is y=mx+c
m is a slope of a line and c is y-intercept
Compare the equation y=4x-5 with y=mx+c, we get m=4
Therefore, the slope of a line y=4x-5 is 4.
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The table and the graph show information about students enrolled in spanish and french classes at a high school. use the graph to determine after how many years there will be equal enrollment in spanish and french classes
Answer:
after 6 years
Step-by-step explanation:
thats when the lines intersect, (6,300)
There will be equal enrollment in Spanish and French classes after 6 years from now.
The red line shows the number of students enrolled in French class each year from now and blue line shows the number of students enrolled in Spanish class each year from now.
The point of intersection of the lines is the point which lies in both the line.
So, it represents the point or time when there are same number of students enrolled in both French and Spanish classes.
From the graph, we can see that the two lines at a point \((6,300)\). The value on the \(x\)-coordinate shows the years from now. So, we can say that there will be equal number of students enrolled in two classes after 6 years.
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Find the integer that exceeds –5 by the same amount that 13 exceeds –1. \
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
Answer:
Step-by-step explanation:
Answer:
7
Step-by-step explanation:
13 exceeds - 1 by - 1 + 13 = 12, then
- 5 + 12 = 7
Enter the value that belongs in the
green box.
57°
Х
Z
33
25
tan 33
Answer:
x
Step-by-step explanation:
tan33° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{25}\)
A county reported the following data on breast cancer for the past year. what is the prevalence rate per 100,000? number of new cases: 1,774; number of total cases: 4,192; population: 5,977,906
The prevalence rate per 100,000 is 99.8%
We know that the prevalence rate is the proportion of persons in a population who have a particular disease over a specified period of time.
In this question, we have been given a data on breast cancer for the past year:
number of new cases: 1,774;
number of total cases: 4,192;
population: 5,977,906
We need to find the prevalence rate per 100,000
The total number of infected people = 1,774 + 4192
= 5966
Chance of infection in the whole population would be,
5,977,906/ 5966 ≈ 1002
This means, chances of having breast cancer is 1 in every 1002 people.
A prevalence rate is calculated by dividing total number of infected people by the total population. The result is then multiplied by 100,000
Now we calculate the prevalence rate per 100,000
= (5966 / 5,977,906) × 100,000
= 0.000998 × 100,000
= 99.8 %
Therefore, the prevalence rate per 100,000 is 99.8%
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HELPPP PLSS What is the solution to the equation
Answer:
\(a=3\frac{1}{3}\)
Step-by-step explanation:
\(a+5\frac{2}{3} =9\)
\(a+5\frac{2}{3}-5\frac{2}{3}=9-5\frac{2}{3}\)
\(a=3\frac{1}{3}\)
A single number that estimates the value of an unknown parameter is called a _______ estimate.
Answer:
A single number that estimates the value of an unknown parameter is called a point estimate.
Step-by-step explanation:
Don't see the point (haha) of elaborating
use he multiplyer method to increase 88 by 14%
Answer:
£100.32
Step-by-step explanation:
114% of £88
= 114/100 * 88
= 10032/100
= 100.32
Step-by-step explanation:
use he multiplyer method to increase 88 by 14%
100 + 14% = 114% = 1.14
88 * 1.14 = 100.32
A=h/3(a+b)
I need the answer for h please
Answer: Pretty sure H would be
h = 3 a/a+ b
As I said I am not sure, tell me I'm if wrong?
Formula One race cars can reach speeds of approximately 100 meters per second. What is this speed in meters per minute? 0. 6 meters per minute 1. ModifyingAbove 6 with Bar meters per minute 600 meters per minute 6,000 meters per minute.
Answer:
1.6667 meters per minute
Step-by-step explanation:
To convert meters per second into meters per minute, let's first think about the difference between seconds and minutes.
There are 60 seconds in one minute, so to find our meters per minute speed, we will divide the distance by 60.
100 / 60 = 1.6667 meters per minute
Hope this helped!
Answer:
it is d my guy :)
Step-by-step explanation:
how does the number googol look like?
The solution is, Number of zeroes in product = 102.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
A googol is a large number that is the digit 1 followed by one hundred zeros
1 googol = 1 x 10¹⁰⁰
Now we need to multiply googol by 100
googol x 100
= 1 x 10¹⁰⁰ x 100
= x 10¹⁰²
Number of zeroes in googol x 100 = 102
Number of zeroes in product = 102
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Complete question:
A googol is a large number that is the digit 1 followed by one hundred zeros. if you multiply a googol by 100, how many zeros will that product have?