The equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
How to determine the circle equation?The given parameters are:
Center, (a,b) = (1, -9)
Radius, r = 12
The circle equation is calculated as:
(x - a)^2 + (y- b)^2 = r^2
This gives
(x - 1)^2 +(y + 9)^2 = 12^2
Evaluate the exponent
(x - 1)^2 +(y + 9)^2 = 144
Hence, the equation of the circle is (x - 1)^2 +(y + 9)^2 = 144
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Given the parent graph
f(x) = 4^x
explain all transformations to the parent
graph given the new functions
f(x) =-1/3 • 4x
Using translation concepts, it is found that the new function was reflected over the x-axis and vertically compressed by a factor of 3.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The functions are given as follows:
Parent: [tex]f(x) = 4^x[/tex].Translated: [tex]f(x) = -\frac{1}{3} \times 4^x[/tex].The translated function was multiplied by -1/3, hence it was reflected over the x-axis(multiplication by negative number) and vertically compressed by a factor of 3(fraction of 1/3).
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Write a paragraph describing the business venture and what kind of algebra or other calculations and formulas might help someone in that endeavor. Also include ways in which the business might operate differently with those tools than without them.
Answer:
Starting a business can be a daunting task, but with a little algebra and some careful planning, it can be a successful endeavor. Algebra can help you determine how much start-up capital you will need, as well as how to price your products or services. It can also help you track your expenses and calculate your profits. Without these tools, it would be difficult to know if your business is viable or if you are making a profit.
the wacky widget company can make 120 of their wackiest widgets in 90 minutes. How many hours will it take them to complete a special order of 450 wackiest widgets?
The number of hours it would take to make 450 wackiest widgets is 4 hours 30 minutes.
How many hours would it take to make 450 widgets?The first step is to determine how many minutes it would take to make 1 widget.
Minutes it would take to make 1 widget ; 90 / 120 = 3 / 4 minutes
Number of minutes it would take to make 450 widgets: 3/4 x 450 = 270 minutes
Now convert minutes to hours : 270 / 60 = 4 hours 30 minutes
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Which statement best explains whether △ABC is similar to △DEF?
a. There is not enough information to determine whether the triangles are similar.
b. The triangles are similar because 820=1025.
c. The triangles are similar because 613=820.
d. The triangles are not similar because 613≠820.
Answer:
d. The triangles are not similar because 6/13 ≠ 8/20.
Step-by-step explanation:
△ABC is similar to △DEF ,If the length of their corresponding sides are proportional.
ie : 6/13 = 8/20 = 10/25
Since , 6÷13 = 0.461538461538 ≠ 0.4 = 8÷20
Then
6/13 ≠ 8/20
Therefore , the triangles are not similar.
confused someone explain please!
Answer:
[-7, + ∞) is domain
Step-by-step explanation:
Domain is all of the 'x' values a function has
this one goes from -7 to + inf
100000/222
solve with proper steps and find the remainder
Answer: 450 rest 100
Step-by-step explanation:
So, we need to calculate this division 100.000/222 and get the rest.
Well, 222 enters in 1000 by 4 times.
222 times 4 is 888
So, 100.000/222 = 4
888-
We subtract 888 from 1000.
That will be 112
100.000/222 = 4
888
112
Now, get the next 0 down next to 112
100.000/222 = 4
888
1120
222 get in 1120 by 5 times.
5 times 222 = 1110
divide 1120 by 1110
100.000/222 = 45
888
1120
1110
That will be 10
100.000/222 = 45
888
1120
==10
Get the next zero down
100.000/222 = 45
888
1120
==100
222 gets in 100 by 0 times.
100.000/222 = 450
888
1120
==100
0
100 subtracted by 0 is 100
100.000/222 = 450
888
1120
==100
0
100
The rest is 100 and the result is 450
Now, you can do the verification:
222 time 450 is 99,900.
If you add the rest to 99,900 it will be 100.000. So the result is good
in one hour, the human body processes about 11.5% of the caffeine in the blood. if your teacher drank a cup of coffee with 175 mg of caffeine 3 hours ago, how much caffeine remains in her blood
121.3 grams of caffeine is remaining in her blood
How to determine the amount of caffeine?The given parameters are:
Initial, a = 175 mgRate, r = 11.5%Time, t = 3 hoursThe amount of caffeine is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 175 * (1 - 11.5%)^t
At 3 hours, we have:
A(3) = 175 * (1 - 11.5%)^3
Evaluate
A(3) = 121.3
Hence, 121.3 grams of caffeine is remaining in her blood
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The sum of angles in a triangle is 180 prove
three angles= 180
180/3
60
A radio tower, 27 m tall, is supported by two guy wires, each on opposite sides.. The angles of elevation to the top of the radio tower are 13° and 21°. To the nearest tenth of a metre, how far apart are the guy wires? Select one: a. 16.6 m b. 196.4 m c. 46.6 m d. 187.3 m
The distance apart of the two guy wire is 187.7 metres
How to find the distance apart of the two wires?The distance apart of the two wires can be found using trigonometric ratios.
Therefore,
tan ∅ = opposite / adjacent
Therefore,
tan 13 = 27 / x
x = 27 / tan 13 = 27 / 0.23086819112 = 117.391304348
tan 21 = 27 / y
y = 27 / tan 21
y = 70.338144115
Therefore,
distance apart of the guy wire = 117.391304348 + 70.338144115 = 187.728144115 = 187.7 metres
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The following graph shows a proportional relationship.
What is the constant of proportionality between yyy and xxx in the graph?
The constant of proportionality of the given graph is gotten as 4.
How to find the constant of proportionality?The constant of proportionality here is simply the slope of the graph.
Now, we will take two points and use their coordinates to find the slope from the formula;
m = (y2 - y1)/(x2 - x1)
Let us pick 2 points which are;
(1, 4) and (2, 8). Thus;
m = (8 - 4)/(2 - 1)
m = 4/1
m = 4
Thus, the constant of proportionality of the graph is gotten as 4.
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4x-3/5 - 2x-3/2=-2
Solve for x
Answer:
I believe the answer should be -11/20
Step-by-step explanation:
Answer:
x = 14 1/2 or 14.5
Step-by-step explanation:
(4x-3)/5 - (2x-3)/2 = -2
make denominators match
2*(4x-3)/10 - 5*(2x-3)/10 = -2
(8x-6)/10 - (10x-15)/10 = -2
(8x-6-10x+15)/10 = -2
(-2x+9) = -2*10
-2x+9 = -20
-2x = -29
x = -29/-2
x = 14 1/2 or 14.5
gathmath
Find the quotient:
27y4 + 36y
——————
-9y
Answer: [tex]-3y^3 -4[/tex]
Step-by-step explanation:
[tex]\frac{27y^4 + 36y}{-9y}=-3y^3 -4[/tex]
What is the gradient of the graph shown?
Answer:
1
Step-by-step explanation:
Start at any point on the line, for example (0, 1).
Each unit up correspond to a unit right. The next easy to read point going up to the right is (1, 2).
difference in y: 2 - 1 = 1
difference in x: 1 - 0 = 1
gradient = (difference in y)/(difference in x) = 1/1 = 1
Answer:
[tex]\huge\boxed{\sf Slope = 1 }[/tex]
Step-by-step explanation:
Take any two co-ordinates from the line.
I will take (0,1) and (-1,0)
So,
[tex](x_1,y_1)=(0,1)\\\\(x_2,y_2)=(-1,0)[/tex]
Finding gradient/slope:[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{0-1}{-1-0} \\\\Slope = \frac{-1}{-1} \\\\Slope = 1 \\\\\rule[225]{225}{2}[/tex]
which choice is equivalent to the quotient below when -2<=x<2
square root of 4-x^2 divided by square root of 2-x
The choice which is equivalent to; √(4-x²)/√(2-x) is; √(2-x).
Which choice is equivalent to the quotient?According to the task content, it follows that the expression whose equivalent is to be determined can be evaluated as follows;
√(4-x²)/√(2-x) = √(4-x²)/(2-x)
Hence, the numerator can be evaluated by difference of two squares where;
(4-x²) = (2-x)(2+x)
Hence; we have; √(2-x)(2+x)/(2-x) = √(2-x).
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Answer:
sqrt 2+x
Step-by-step explanation:
Which expressions are equivalent to the one below? Check all that apply.
Answer:
0
Step-by-step explanation:
㏒₇1 = 0 and ㏒₅25 = 2, so the expression evaluates to 0.
Determine whether 8^2m/8^m2 is equivalent to each of the following expressions.
82m- 8m²
8m²-2m
82m-m²
64m-m²
Equivalent Not equivalent
By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)
What expression is equivalent to a exponential function?
In this question we must apply power properties to prove if a given expression have at least one equivalent. Now we proceed to show alternative forms:
[tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex]
[tex]8^{2\cdot m-m^{2}}[/tex]
By power properties the exponential expression [tex]\frac{8^{2\cdot m}}{8^{m^{2}}}[/tex] is only equivalent to [tex]8^{2\cdot m-m^{2}}[/tex]. (Correct choice: A)
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The quotient of (x4 5x3 – 3x – 15) and (x3 – 3) is a polynomial. what is the quotient?
The quotient of [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex] is (x+5).
Given expression [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3}-3[/tex] and we have to find the quotient of the first expression.
Quotient is any quantity produced by dividing two numbers. It can be of simple numbers or expressions also. Remainder is a number or expression that is left after division.
To find the quotient of [tex]x^{4}+5x^{3} -3x-15[/tex], we have to divide the expression by [tex]x^{3}-3[/tex].
We know that,
Divident=Divisor*quotient+remainder
[tex]x^{4}+5x^{3}-3x-15[/tex]=([tex]x^{3}-3[/tex])*(x+5)+0
By equating from the given formula we can find that the value of quotient is (x+5).
Hence the quotient of [tex]x^{2} +5x^{3} -3x-15[/tex] by dividing it by [tex]x^{3} -3[/tex] is (x+5).
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Question is incomplete as the expressions are incomplete. They should be like [tex]x^{4} +5x^{3} -3x-15[/tex] and [tex]x^{3} -3[/tex]
Sin^2x=1+cosx write your answer in radians in terms of pi. if there is more than one solution, separate them with commas.
The solution of the equation is union of x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.
What is a function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.
sin²x = cosx + 1
1 - cos²x = cosx + 1
cos²x + cosx = 0
cosx(cosx + 1) = 0
When cosx = 0
x = a(π/2) where a = 1,2,3......∞
When cosx = -1
x = n(π) where n = 1,3,5,7.......∞
Hence the solution of the equation will be the union of x = a(π/2) where a = 1,2,3......∞ and x = n(π) where n = 1,3,5,7.......∞.
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Emiliano necesita cortar dos cuerdas,una de 18m y la otra de 12 m en trozos iguales,,de manera que estos sean los mas grandes posibles ¿Cuanto debe medir cada trozo y cuantos sacara de cada cuerda?
Por descomposición factorial y el concepto de máximo común divisor, se tiene que cada trozo de cuerda debe medir 6 metros y que se debe preparar cinco trozos.
¿Cómo cortar cuerdas en segmentos de máxima e igual longitud?
En este problema debemos determinar la cantidad de segmentos de cuerda de igual y máxima longitud, la cual puede ser hallado por descomposición factorial a los números asociados a las longitudes:
18 = 2 × 3²
12 = 2² × 3
La máxima longitud posible se obtiene mediante el máximo común divisor, es decir, se encuentra que la máxima longitud es 2 × 3 = 6 metros. Por último, la cantidad de trozos iguales es:
x = (18 m + 12 m)/6 m
x = 30 m/6 m
x = 5
Por descomposición factorial y el concepto de máximo común divisor, se tiene que cada trozo de cuerda debe medir 6 metros y que se debe preparar cinco trozos.
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In one week, we sold 184 baskets at $3.25 each. The following week, we reduced the price of the basket to $2.
How many baskets were sold then?
The number of baskets that were sold for $2 is 299 baskets.
What is a word problem?A word problem is a method we used in denoting mathematical expressions and variables and it can be solved with the use of fractions, ratios, algebra, and arithmetic operations as the case may be.
From the given information:
If 184 baskets is sold for = $3.25; and (x) baskets is sold for = $2The number of baskets sold in the second week is obtained as follows
i.e.
x = (184 × 3.25)/2
x = 299 basket were sold for $2
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Please help! How can this set be expressed using inequalities?
The set is expressed using inequalities; [tex]0 < x\leq 3[/tex], option D is correct.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
A collection of inequalities for which we consider a common solution for all inequalities is called a system of inequalities.
The set be expressed using inequalities are;
[tex]0 < x\leq 3[/tex].
Thus, option D is correct.
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A consumer affairs investigator records the repair cost for 4 randomly selected washers. A sample mean of $52.63 and standard deviation of $22.01 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the washers. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval.
The critical z value which should be used in determining the confidence interval is z=1.29 and the confidence interval is (38.43355,66.82645).
Given sample mean of $52.63 and standard deviation of $22.01.
We have to construct the confidence interval of 80% for the mean repair cost for the washers.
μ=52.63
σ=22.01
n=4
First we have to find the value of z for the confidence level of 80% from z table and which is 1.29.
Margin of error is the difference between the calculated values and real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where μ is mean
σ is standard deviation
n is sample size
z is z value for the confidence level
Margin of error=1.29*22.01/[tex]\sqrt{4}[/tex]
=14.19645
Confidence interval =mean ±margin of error
Upper level=mean +margin of error
=52.33+14.19645
=66.82645
Lower level=mean-margin of error
=52.33-14.19645
=38.43355
Hence the confidence interval is (38.43355,66.82645) and the critical value used is z=1.29.
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Can you help me find the missing number I have an exam tomorrow and I really need to know the answer
(2/3)^ =16/81
Find the answer for ^
Hello,
[tex]( \frac{2}{3} ) {}^{n} = \frac{16}{81} [/tex]
[tex]nln( \frac{2}{3} ) = ln(\frac{16}{81})[/tex]
[tex]n = \frac{ln( \frac{16}{81} )}{ln( \frac{2}{3} )} = 4 [/tex]
Answer : 4
Answer:
^ is 4
Step-by-step explanation:
as you can see, [tex]\frac{16}{81}=\frac{2^4}{3^4}=(\frac{2}{3})^4[/tex]
For f(x) = 4x+1 and g(x)=x²-5, find
O A.
OB.
O C.
4x+1
th
x²-5
4x+1
-5>**+-√/5
√√5
4x+1
²²-5
OD. ²-5
4x+1
g
(x).
Answer:
OA=4x²-19
Step-by-step explanation:
4(x²-5)+1
4x²-19
9x-1=1/2(15x-47) I need help
Answer:
The answer is x= -15
HELP ME PLEAS ON PLATO I WANT TO FINISH SUMMER SCHOOL PLEASE ITS A LIVING HELL
The parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)
How to arrange the parabolas?The parent function is given as:
f(x) = x^2
The parabolas are given as:
y = f(x - 4), y = f(x + 3), y = f(x - 7), y = f(x + 2) and f = (x - 1/2)
The transformation from the parent function to each of the parabola is a horizontal translation.
This means that the y coordinate of their vertices are the same.
Arrange the parabolas starting from the left translations
y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)
Hence, the parabolas with respect to their positions are y = f(x + 3), y = f(x + 2), y = f(x - 1/2), y = f(x - 4) and f = (x - 7)
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Find a in degrees.
a
6
√11
5
[?]°
Round to the nearest hundredth.
Answer: [tex]33.56^{\circ}[/tex]
Step-by-step explanation:
[tex]\sin \alpha=\frac{\sqrt{11}}{6}}\\\\\alpha=\sin^{-1} \left(\frac{\sqrt{11}}{6}} \right)\\\\\alpha \approx 33.56^{\circ}[/tex]
Answer:
33.56
Step-by-step explanation:
Solve the system and enter the smallest x-coordinate first
PLEASE HELP ASAP I WILL GIVE BRAINLIEST!!!!!!!!
8:54 am
9:12 am
9:24 am
10:24 am
11:18 am
Light A flashes every 12 minutes, and Light B flashes every 18 minutes. The two lights flash at the same time at 8:00 am. At how many of the times listed above will they again both flash at the same time?
Answer:
9:12 10:24
Step-by-step explanation:
First find their least common divisor which is 36. which means every 36 minutes they will flashes together.
just add the 36 to the time where they flash at the same time which is 8:00am
8:36 9:12 9:48 10:24 11:00 11:36
Answer: 9:12 and 10:24
Step-by-step explanation:
if we start from 8 am and add 12 minutes for light A in intervals and do the same for Light B we can see where the times are the same
Light A: 8:00, 8:12, 8:24, 8:36, 8:48, 9:00, 9:12, 9:24, 9:36, 9:48, 10:00, 10:12, 10:24, 10:36, 10:48, 11:00, 11:12, 11:24
Light B: 8:00, 8:18, 8:36, 8:54, 9:12, 9:30, 9:48, 10:06, 10:24, 10:42, 11:00, 11:18
9:12 and 10:24 are the correct answers because this is when the two lights flash at the same time
Translate this phrase into an algebraic expression.
47 decreased by twice a number
Use the variable n to represent the unknown number.
Answer:
47 - 2n
Step-by-step explanation:
An algebraic expression is an idea of representing numbers using letters or alphabet.
From the question above,
The variable = n
twice the number = 2× n = 2n
Translating:
47 - 2n