Write the equation in standard form for the circle with center (0, -3) passing through (15/2 , 1)
Answers
Check the picture below, so the green line is really the radius of the circle, and we know its center.
[tex]~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad(\stackrel{x_2}{\frac{15}{2}}~,~\stackrel{y_2}{1})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[\frac{15}{2} - 0]^2 + [1 - (-3)]^2}\implies r=\sqrt{\left( \frac{15}{2} \right)^2 + (1+3)^2}\\\\\\r=\sqrt{\left( \frac{15}{2} \right)^2 +4^2}\implies r=\sqrt{\frac{225}{4} + 16}\implies r=\sqrt{\cfrac{289}{4}}\implies r=\cfrac{17}{2}\\\\[-0.35em]\rule{34em}{0.25pt}[/tex]
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\frac{17}{2}}{ r} \\\\\\\ [x-0]^2~~ + ~~[y-(-3)]^2~~ = ~~\left( \cfrac{17}{2} \right)^2\implies x^2+(y+3)^2 = \cfrac{289}{4}[/tex]
Related Questions
Which of the binomials below is a factor of this trinomial?
x^2 + 8x + 16
A. x + 4
B. x - 4
C. x + 8
D. x - 8
Answers
The answer is A.
Pick A.
Good luck
A very slow man walks
20 cm.in 0.5 left, what his
velocity in meter per second?
Answers
Time taken(t)= 30 s(1min=60 s)
Velocity (v)=?
We know that,
Velocity (v) = d/t
=0.0067
What is a2+b2+c2? Thank you for your help.
Answers
Answer:
Pythagoras theorem
Step-by-step explanation:
dhebbd
Larger is 32 ounces and sells for 2.99 and smaller is 18 ounce and sells for 1.59
What is the better buy
Answers
Divide price by size of each and compare the u it price:
2.99/32 = 0.0934 per ounce
1.59/18 = 0.0883 per ounce
The 18 ounce do $1.59 has a lower cost per ounce so is the better buy
Find the sum of a finite arithmetic sequence from n=1 to n=5 using the expression -3(4)^n-1
Answers
Answer:
Step-by-step explanation:
Arithmetic sequaence:
[tex]\sf a_n = -3(4)^n - 1\\\\a_1=-3*4^1 -1\\\\ = -3*4 - 1\\\\ = -12 - 1\\\\a_1=-13[/tex]
[tex]a_2 = -3*4^2-1\\[/tex]
= -3*16 -1
= -48 - 1
= -49
difference = second term - first term
= -49 -(-13)
= -49 + 13
d = -36
[tex]\boxed{S_n=\dfrac{n}{2}[2a + (n-1)d]}[/tex]
[tex]\sf S_5=\dfrac{5}{2}*[2*(-13} + 4*(-36)]\\\\ =\dfrac{5}{2}[-26-144]\\\\=\dfrac{5}{2}*(-270)[/tex]
= 5*(-135)
= -675
A 22° B 54° С What is the measure of AD? O 108° 0 27° 126 54°
Answers
Answer:
A. 108
sorry if im wrong but if u am I'm so sorry
Which of the following is true of the numbers 4 and 10?
A. The greatest common factor is
B. The least common multiple is
C. The greatest common factor is 20.
D. The least common multiple is 40.
Answers
Answer:
None
Step-by-step explanation:
Answer is isn't there
the gcf = 2
the LCM = 20
Find the simple interest on the loan of $2500 for 2 years at 5%.
$
(Simplify your answer. Round to the nearest cent as needed.)
Answers
Answer:
Step-by-step explanation:
simple interest=prt
p=principle amount
r=rate
t=time
here p=$2500
r=5 %=0.05
t=2 years
simple interest=2500×2×0.05=$250
The simple interest on the loan of $2500 for 2 years at 5% is $250
How to determine the value?The formula for calculating simple interest is expressed as;
I = PRT/100
Such that the parameters of the formula are;
P is the principal amountI is the simple interestR is the interest rateT is the timeNow, substitute the values, we get;
Simple interest = 2500 × 5 × 2/100
Multiply the values
Simple interest =25, 000/100
Simple interest =$250
Learn about simple interest at: https://brainly.com/question/25793394
#SPJ2
-0.5(14a - 22) = ? this for my work, please help me.
Answers
Answer:
-7a+11
Step-by-step explanation:
Each of students reported the number of movies they saw in the past year. Here is what they reported.
11,6 ,9 ,16 ,12 ,18 ,14
Find the mean number of movies that the students saw.
If necessary, round your answer to the nearest tenth.
Answers
Answer:
18+16+14+12+11+9+6=8686÷7=12.2812.28=13Answer:
12.3
Step-by-step explanation:
11+6 +9 +16 +12 +18 +14 =86
86/7 = 12.28571
Tenths is the place value of the digit that appears after the decimal. It represents the 1/10 position of the digit
(12.3) rounded to the nearest tenth.
What angles are acute GFE mlk dbc dba
Answers
Answer:
d and a
Step-by-step explanation:
an acute is an angle less than 90 degrees. a 90 degree angle is a right angle (klm) the only 2 angles smaller than (klm) are (gfe) and (dba)
help me please mark U as BRAINLIEST
Answers
Hope this helps. Good luck
A store sells a workout outfit that consists of a jacket, a t-shirt, and a pair of shorts. The store purchases the jacket for $34, the t-shirt for $9, and the shorts for $12. The percent of markup is 28%. Find the selling price of the outfit.
PS: include show work please I have to submit this in like 3 hours thankyou
Answers
Answer:
The Outfit costs $70.4.
Step-by-step explanation:
Add the selling price together
34 + 9 + 12 = 55
Multiply by the markup (Profit)
100% = 1
28% = 0.28
55 x 1.28 = 70.4
Please help i wan't a good grade but I can't figure this out.
Answers
Answer:
angle DCE
Angle DEC
Angle ABF
Step-by-step explanation:
you had the wrong order
How do you solve this?
2sinXcosX=sinX
Answers
2sinXcosX = sinX
Divide through by 2sinX
cosX = 1/2
X = cos-1(1/2)
X= 60°
Write the rate in lowest terms.
During a bad storm there was 2 in of rain in 4 hr.
The rate in lowest terms is_____?
Answers
Answer:
1/2 in/hr
Step-by-step explanation:
2 in / 4h = 1/2 inch per hour
112 is 80% of what number?
A. 140
B. 896
C. 1,400
D. 8,960
Answers
Answer:
A
Step-by-step explanation:
112/0.8 = 140
Answer:
A
Step-by-step explanation:
I am not sure about the answer
What’s the difference between 4, 7/9 and 2 1/2
Answers
[tex]\huge \mathbb \orange{ANSWER} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \mathsf \purple{4 \frac{7}{9} - 2 \frac{1}{2} }[/tex]
[tex] \blue\implies \mathsf \pink{ 2(\frac{43}{9}) - (\frac{5}{2} )9 }[/tex]
[tex] \blue \implies \mathsf \purple{ \frac{86}{18} - \frac{45}{18} }[/tex]
[tex] \blue \implies \mathsf \pink{ \frac{41}{18} = 2 \frac{5}{18} }[/tex]
What is the range of this data set?
36.6, 39.8, 33.3, 34.8, 35.8, 39.6, 36.7, 36.9, 37.5, 32.2, 33.1, 33.3
Answers
Answer:
Step-by-step explanation:
39.8 - 32.2 = 7.6
Range is subtracting the highest and lowest numbers by each other .
Based on the calculations, the range for this data set is equal to 7.6.
What is a range?In Mathematics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
Mathematically, range is calculated by using this formula;
Range = Highest number - Lowest number
From the given data set, we have:
Highest number = 39.8.Lowest number = 32.2.Substituting the given parameters into the formula, we have;
Range = 39.8 - 32.2
Range = 7.6.
Read more on range here: https://brainly.com/question/9393969
Which number is a common multiple of 3 and 4?
A) 8
B) 14
C) 32
D) 48
Answers
Answer:
LCM of 3 and 4 is 12
Step-by-step explanation:
This is your answer
Answer:
The answer is D.
Step-by-step explanation:
To find the common multiple you would divide each answer choice by both numbers & if the are whole numbers then there is your answer. If it is a number with a decimal somewhere then that is not the answer.
Let x and b be positive real numbers so that log_b(x^2) = 10. Find log_3sqrtb (1/x)
Answers
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b.
How to analyze and solve logarithmic expressionsLogarithms are trascendental functions, that is, functions that cannot be described algebraically.
In this question we must apply logarithm and algebraic properties to determine firstly the value of [tex]x[/tex] and later to find value of the latter logarithm. Now we proceed to find the value of [tex]x[/tex]:
[tex]\log_{b} x^{2} = 10[/tex]
[tex]2\cdot \log_{b} x = 10[/tex]
[tex]\log_{b} x = 5[/tex]
x = b⁵
Then, the value of the latter logarithm is:
log₃ (x⁻¹)[tex]^{1/b}[/tex]
- b⁻¹ · log₃ x
- b⁻¹ · log₃ b⁵
- 5 · b⁻¹ · log₃ b
The value of the logarithm log₃ (x⁻¹)[tex]^{1/b}[/tex] where x and b positive real numbers is - 5 · b⁻¹ · log₃ b. [tex]\blacksquare[/tex]
RemarkThe statement is poorly formated, correct form is described below:
Let [tex]x[/tex] and [tex]b[/tex] be positive real numbers so that [tex]\log_{b} x^{2} = 10[/tex]. Find [tex]\log_{3} \sqrt [b]{\frac{1}{x} }[/tex].
To learn more on logarithms, we kindly invite to check this verified question: https://brainly.com/question/3181916
A data set is normally distributed with a mean of 8.1 and a standard deviation of 3.8.
What percentage of the data is above 8.6?
Enter your answer as a number to the nearest whole percentage, like this: 42%
Answers
Answer:
45%
Step-by-step explanation:
Your graphing calculator, statistics app, or spreadsheet can tell you that 45% of the normally-distributed data is above 8.6 when the mean is 8.1 and the standard deviation is 3.8.
Given f(x) and g(x) = f(x) + k, use the graph to determine the value of k.
Answers
Answer:
k = 3
Step-by-step explanation:
The value of k is the amount by which the function f(x) is translated upward to give the function g(x). We can compare y-intercepts to see that the y-intercept of g(x) is 5 -2 = 3 units more than the y-intercept of f(x). This means ...
g(x) = f(x) +3
Comparing to ...
g(x) = f(x) +k
we see that k = 3.
A car travels 80 miles on 3 gallons of gas. At the same rate (in miles per gallon) l, how many miles will the car be expected to travel on 5 gallons of gas?
A. 48
B. 130
C. 133 1/5
D. 160
Answers
Answer:
C
Step-by-step explanation:
Which expression is equivalent to the following complex fraction?
Answers
Consider the fraction first ;
[tex]{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}[/tex]
[tex]{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}[/tex]
[tex]{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}[/tex]
Hence, Option B) is required answer
Use the distributive property to write the following expressions in expanded form. 4(x +y)
Answers
Answer:
4x+4y
Step-by-step explanation:
Answer:
4x + 4y
Step-by-step explanation:
To do this you need to know that the number (or variable) on the outside of the parenthesis must be multiplied to all of the numbers/variables on the inside of the parenthesis.
So here, you want to multiply x by 4:
4x
Then multiply y by 4:
4y
And because the expression is adding the x and y, it comes out as:
4x + 4y
i need help with this problem
Answers
Answer:
Disagree
Step-by-step explanation:
because it looks like less than 45
CAN SOMEONE HELP PLS?? I rlly dont get this.
Answers
The little square on the angle means that the entire angle is 90 degrees
The larger angle is made up of two angles of measure 'x - 18' and 'x'
Let's put that into an equation form:
(x - 18) + (x) = 90
2x - 18 = 90
2x = 108
x = 54
So x = 54
Hope that helps!
NEED HELP ASAP The salaries of Nathan and Trisha are in the ratio of 5:9. Trisha's salary is £16800 more than Nathan's. Find Nathan's salary.
Answers
Answer:
From the ratio
The difference is 9 - 5 = 4
Hence Trisha has 4 units more than Nathan and this resulted to 16800
Therefore 1 unit will be
16800 / 4 = 4200
Nathan’s salary is 5 units
5 * 4200 = 21000
Does anyone know the answers? Need help!!
Answers
Answer:
nice handwriting
Step-by-step explanation: