Find the center and the radius of the circle.
(x-4)^2 + (y + 3)^2 = 74
Answers
Answer:
radius = [tex] \sqrt{74} [/tex]center = [tex](4,-3)[/tex]Step-by-step explanation:
We would like to calculate the centre and the radius of the circle . The given equation is ,
[tex]\longrightarrow (x - 4)^2+(y+3)^2=74 [/tex]
As we know that the Standard equation of circle is given by ,
[tex]\longrightarrow (x - h)^2+(y-k)^2=r^2[/tex]
where ,
[tex](x,y)[/tex] is a point on circle .[tex](h,k)[/tex] is the centre of circle .[tex]r[/tex] is the radius of the circle .We can rewrite the equation as ,
[tex]\longrightarrow (x-4)^2+\{ y -(-3)\}^2=(\sqrt{74})^2\\ [/tex]
Now on comparing to the standard form , we have ;
radius = [tex]r[/tex] = [tex]\sqrt{74}[/tex]center = [tex](h,k)[/tex] =[tex](4,-3)[/tex]Graph :-
[tex] \setlength{\unitlength}{7mm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\circle*{0.2}}\put(0.2, - .1){(4,-3)}\put(-1.2,0){\vector(0,1){5}}\put(-1.2,0){\vector(0, - 1){5}}\put(-1,0.7){\vector(1,0){5}}\put(-1,0.7){\vector( - 1,0){5}}\put(0,0){\line(-1,0){2.3}}\put( - 1.2,-0.7){$\sf \sqrt{74}$}\put(2,6){$\boxed{\sf \textcopyright \: RISH4BH }$}\end{picture} [/tex]
And we are done !
We are given the equation of circle (x - 4)² + (y + 3)² = 74 , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;
So, consider the equation of circle ;
[tex]{:\implies \quad \sf (x-4)^{2}+(y+3)^{2}=74}[/tex]
Can be further written as ;
[tex]{:\implies \quad \sf (x-4)^{2}+\{y-(-3)\}^{2}=({\sqrt{74}})^{2}}[/tex]
On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows
Centre = (4, -3)Radius = √74 unitsRelated Questions
Does anyone mind giving me a hand answering this question?
Answers
Answer:
A. x = 4
B. ∠C = 80°
Step-by-step explanation:
A.The sum of interior angles in a pentagon is 540°. We can write an equation for the sum of angles using this fact. Clockwise from lower left, we have ...
140° +(20x)° +100° +(16x +16)° +(160 -5x)° = 540°
31x +416° = 540° . . . . . . collect terms
31x = 124° . . . . . . . . . . subtract 416°
x = 4
__
B.The measure of angle C is found by substituting the value of x into the given expression for angle C.
(16x +16)° = (16(4) +16)° = 80°
Angle C is 80°.
_____
Additional comment
It can be useful to remember that the sum of interior angles of an n-gon is ...
(180°)(n -2)
This can be derived from the fact that the sum of exterior angles is always 360°.
These relations apply to convex polygons. YMMV when there are reflex angles or when sides cross each other.
100 students went on a field trip. Six busses were filled and 10 students traveled in
cars with their parents. How many students were on each bus?
Answers
Answer:
15 students in each bus.
Step-by-step explanation:
Subtract 10 from 100 and you get 90 then divide 90 by 6 and that gives you how many students in each bus
Find the fraction suitable for the blank. Show the method how you found.
Answers
Answer:
3/5Step-by-step explanation:
Let the blank is x, solve the equation for x:
(4 1/2 - x) × 1 3/13 = 4 4/5(9/2 - x) × 16/13 = 24/59/2 - x = 24/5 × 13/169/2 - x = 39/10x = 9/2 - 39/10x = 45/10 - 39/10x = 6/10x = 3/5Let that be x
(9/2-x)×16/13=24/5(9-2x)/2=24/5×16/13(9-2x)/2=39/1090-20x=7820x=12x=12/20x=6/10x=3/5Use the quadratic formula to solve the equation: y = x2 - 3x - 1
Group of answer choices
x = 5.6 and -1.3
x = 3.3 and -.3
x = -5.4 and -.4
x = 6.3 and 3.2
Answers
Answer:
3.3 and -0.3
Step-by-step explanation:
Using the quadratic formula plug in the a, b, and c values in this equation into the formula and you get 3.3 as a result. Not sure where the 0.3 part came from since it is not the opposite equation, but 3.3 is for sure correct. Work is linked below.
A right square pyramid has a volume of 12 cubic centimeters. If the height remains fixed but the sides of the base are multiplied by 3, what is the volume of the new pyramid?
A. 36 cm³
B. 48 cm³
C. 108 cm³
D. 72 cm³
Answers
Answer:
36 cm^3
Step-by-step explanation:
Because you need to multiply 12x3 giving you 36.
Answer:
its a
Step-by-step explanation:
i took the test
Find the value of the expression.
Answers
[tex]( (\frac{3}{5}) {}^{0} ) {}^{ - 2} = (1) {}^{ - 2} = \frac{1}{1 {}^{2} } = \frac{1}{1} = 1[/tex]
Find the edge length of the cube. 0.064m\
Answers
The length would be 0.4
please it’s not hardHow many points are contained on a line?
infinitely many
20.000
none
Answers
Answer:
Infinitely many
Step-by-step explanation:
Infinitely many points are contained on a line.
Answer:
infinitely many
Step-by-step explanation:
A line consists of infinitely many points.
hope this helps!! p.s. i really need brainliest :)
Which reason best explains why m^10n^3 is NOT equal to (mn)^13?
Answers
Answer:This law of exponents can only be used when the bases are equal.
Step-by-step. explanation:
A baker has 3 pounds of dried fruit. Each batch of a recipe she is making uses 1/2 pound of the fruit. How many batches can she make?
Answers
The sum of 3 times a number and 7 equals 4.
Answers
Answer: x = -1
Step-by-step explanation:
The problem is asking you the sum (+) of 3 times of a unknown number (let the unknown number be x) and 7, as in 3x + 7
According to the problem this expression is equal to 4,
3x + 7 = 4
1. Subtract 7 from both sides
3x = -3
2. Divide 3 on both sides
x = -1
Your final answer would be negative 1
Find the length of AB.
Answers
Answer:
6.286
Step-by-step explanation:
♢C=⊙/360x 22/7x D
=45/360x22/7x16
=6.286
Yesterday, Salma had 387 baseball cards. Today, she gave 141 away. How many cards does Salma have left?
Answers
Answer:
387-141=246
Step-by-step explanation:
387
- 141
-------------
246
solve this to get brainiest
Answers
Answer:
1 a. commutative property of multiplication
b. distributive property of multiplication
2 x=23\12
-x = -23\12
-23\12+23\12=0
thus -(-x)+x
Answer:
See below ↓
Step-by-step explanation:
1.
a) commutative propertyb) commutative property2.
Given : x = 23/12To verify = -(-x) = x⇒ -(-(23/12)) ⇒ -1 x -1 x 23/12⇒ 1 x 23/12⇒ 23/12⇒ VerifiedCaleb placed 3 yellow balls and 4 red balls in a row.
How many visually distinct rows are possible?
A)210
B)70
C)144
D)35
Answers
Answer:
I think it's C)144. because I think it's C
Caleb placed 3 yellow balls and 4 red balls in a row. The possible visually distinct rows are 144.
What is the combination?Each of the different groups or selections can be formed by taking some or all of a number of objects, irrespective of their arrangments is called a combination.
It is given that Caleb placed 3 yellow balls and 4 red balls in a row.
So, visually distinct rows are possible
= 4 x 3 x 2 x 3 x 2
= 144
Thus, The possible rows are 144.
Learn more about combinations;
https://brainly.com/question/19692242
It takes _____________ for the minute hand to travel from one number to the next.
A) 10 minutes
B) 15 minutes
C) 1 minute
D) 5 minutes
Answers
Answer:
D)
Step-by-step explanation:
Because -12 to 1 is 5 min.
Answer:
it takes five minutes for the minute hand to travel from one number to the next
Step-by-step explanation:
5
Daito and Shoto are earning money to grow their College Savings Accounts. Daito has $780 in the College Savings Account and adds $47 each month. Shoto has $220 in the College Savings Account and adds $82 each month. How long until they have the same amount of money? What is the total amount of money they will both have in their COLLEGE SAVINGS ACCOUNTS?
Answers
Answer:
16months
=$1532
Step-by-step explanation:
Daito
780+47x=220+82x
780-220=82x-47x
560=35x
x=16
=16 months
Matteo is following this recipe to make a cake.
He wants to make four of these cakes.
How much of each ingredient does he need?
Answers
Answer:
Step-by-step explanation:
First you would multiply 4x12 l
next you will get 36l
Finally you would divide it by some # to get your answer .
May someone please help me on this one
Answers
the greatest will be + 567
then 78 ; 0 ; - 6,7 ; - 6,78 ; - 45 and the least one = - 99
PLEASE EXPLAIN SO I CAN UNDERSTAND
Which of the following numbers
could be the absolute value of
another number?
A -425
B 1,200
C -1,300
D-2,525
Answers
Answer:
Step-by-step explanation:
Essentially, recall what an absolute value function is.
When you plug number into an absolute value function, or make it an absolute value, you will ALWAYS get a positive version of that number.
When the question asks, what number could be the absolute value of another number, it's asking you what is a possible outcome of making a number an absolute value.
Since we know that making any number an absolute value, makes that number positive. We can get rid of all of the negative answers.
You are left with B.
Answer:
B. 1200
Step-by-step explanation:
Absolute value is the non-negative version of a number/variable. Whether the sign is negative or positive, the absolute value is always positive.
Example:
|-4|=4
|2|=2
(1 point)
A hot air balloon is launched from the ocean beach. As it moves inland, it rises and then falls, having a path given by
p(x)= - 2x^2/2500 +0.7x where x is in metres. The land rises at a rate of 2 vertical metres for each 20 horizontal metres. See the
diagram
a. At what horizontal distance does the balloon reach maximum height above sea level?
b. What is the maximum height of the balloon above seal level?
c. What is the maximum height of the balloon above ground level?
m and
d. At what horizontal distance is the balloon 50 m above the ground? List the smaller value first.
Answers
The launching of the hot air balloon is from the ocean beach is an illustration of a projectile motion
The horizontal distance which it attains a maximum heightThe function is given as:
[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]
Differentiate
[tex]p'(x) =-\frac{4}{2500}x + 0.7[/tex]
Set to 0
[tex]-\frac{4}{2500}x + 0.7 = 0[/tex]
Subtract 0.7 from both sides
[tex]-\frac{4}{2500}x =- 0.7[/tex]
Multiply through by -2500/4
[tex]x =437.5[/tex]
Hence, the horizontal distance which a maximum height is attained is 437.5 meters
The maximum height above the sea levelIn (a), we have:
[tex]x =437.5[/tex]
Substitute [tex]x =437.5[/tex] in p(x)
[tex]p(437.5) =-\frac{2}{2500} * 437.5^2 + 0.7 * 437.5[/tex]
Evaluate
[tex]p(437.5) =153.125[/tex]
Hence, the maximum height above the sea level is 153.125 metres
The maximum height above the ground levelIn (b), the maximum height above the sea level is 153.125 metres
The ratio of the height on land and sea is given as:
Land : Sea = 2 m : 20 m
For the maximum height, we have:
Land : 153.125 m= 2 m : 20 m
Express as fraction
Land / 153.125 m = 2 /20
Multiply both sides by 153.125
Land = 15.3125
Approximate
Land = 15.3
Hence, the maximum height above the ground level is 15.3 meters
The horizontal distance where the balloon 50 m above the groundWe have:
[tex]p(x) =-\frac{2}{2500}x^2 + 0.7x[/tex]
Substitute 50 for P(x)
[tex]-\frac{2}{2500}x^2 + 0.7x = 50[/tex]
Using a graphing calculator, we have:
x = 78.465 and 796.535
Hence, the horizontal distances where the balloon 50 m above the ground are 78.465 and 796.535 meters
Read more about projectile motion at:
https://brainly.com/question/1130127
Alexandra deposited $1,000 in
a savings account
Her
savings account pays 3.5% simple
interest. How much interest will the
account earn in 5 years?
My answers are
A. 35.00
B. 145.00
C . 175.00
D . Not here
Answers
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 3.5\%\to \frac{3.5}{100}\dotfill &0.035\\ t=years\dotfill &5 \end{cases} \\\\\\ I = (1000)(0.035)(5)\implies I=175[/tex]
Which angles are alternate interior angles?
Answers
Answer:
Step-by-step explanation:
∠DEH=∠IHE (alternate angles)
Help help help help math
Answers
Answer:
It's 77, the absolute value bars will just make the number positive
Step-by-step explanation:
Can someone help me solve this please, I'm stuck.
Answers
The expression (3a + 2b)^7 is a binomial expression;
The coefficient of the fourth term is 15120
How to determine the coefficient fourth term?The equation is given as:
(3a + 2b)^7
The above expression is a binomial expression;
Assume the expression is:
(x + y)^n
The equation of the expansion is:
[tex](x + y)^n = ^nC_r * x^{n-k} * y^k[/tex]
When the expression is expanded, the parameters of the fourth term are
n = 7
r = 4
x = 3a
y = 2b
So, we have:
(3a + 2b)^7 = 7C4 * (3a)^(7-4) * (2b)^4
Evaluate each factor
(3a + 2b)^7 = 35 * (3a)^3 * (2b)^4
Evaluate the powers
(3a + 2b)^7 = 35 * 27a^3 * 16b^4
Evaluate the product
(3a + 2b)^7 = 15120a^3b^4
The coefficient of the above expression is 15120
Hence, the coefficient of the fourth term is 15120
Read more about binomial expressions at:
https://brainly.com/question/13602562
B. Solve the following. Write your solutions and final answers in your notebook.
1. To relieve her stress from work. Tina would always watch the fishes moves around her 90 cm wide, 70 cm high, and 45 cm long aquarium. If the aquarium is filled halfway through its height; how much volume of water is in it?
2. Elisha has a swimming pool in their house that measures 10 m long, 5 m wide and 1 m high. Approximately, how much will she be paying for the water supply of her swimming pool, if the water costs P27.25 per cubic liter?
3. Myla bought a jar shaped like a rectangular prism having a length of 130 cm, a width of 70 cm, and a height of 110 cm. How much water is needed to fill the jar?
4. A truck with dimensions 9 feet long, 7 feet wide, and 5 feet high is delivering sand for a sand sculpture competition. How many trips must the truck make to deliver 945 cubic feet of sand?
5. Create a problem on volume and prepare a solution to your problem based on the figure below:
I need best answer please
Answers
The volume of water contained in this aquarium that is filled halfway through its height is equal to 141,750 cm³.
The volume of a right prism.Mathematically, the volume of a right prism is calculated by using this formula:
Volume = length × width × height
Given the following data:
Length = 45 cm.Width = 90 cm.Height = 70 cm.Based on the information, the aquarium is filled halfway through its height. Thus, the height of water is given by:
H = 70 × 0.5
H = 35 cm.
Substituting the parameters into the formula, we have;
Volume = 45 × 90 × 35
Volume = 141,750 cm³.
How to calculate the volume?Mathematically, the volume of Elisha's swimming pool is given by:
Volume = length × width × height
Volume = 10 × 5 × 1
Volume = 50 m³.
Now, we can calculate the cost of water supply:
Cost = 27.25 × 50 × 10³
Cost = P1,362,500.
How to calculate the volume of water.Mathematically, the volume of a rectangular prism is given by this formula:
Volume = length × width × height
Volume = 130 × 70 × 110
Volume = 1,001,000 cm³.
How to calculate the number of trips.Firs of all, we would determine the volume of this truck:
Volume = length × width × height
Volume = 9 × 7 × 5
Volume = 315 ft³.
Now, we can calculate the number of trips:
Number of trips = 945/315
Number of trips = 3 trips.
Read more on rectangular prism here: brainly.com/question/3867601
How to write the slope intercept equation for points of (6,0) and (0,-5)?
Answers
Answer:
[tex]y=\frac{5}{6} x -5[/tex]
Step-by-step explanation:
Hi there!
We are given the points (6,0) and (0, -5), and we want to write the equation of the line containing those points in slope-intercept form
Slope-intercept form can be written as y=mx+b, where m is the slope and b is the y intercept
First, we need to find the slope of the line
The formula for the slope can be written as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We have everything we need to find the slope, but let's label the points to avoid confusion
[tex]x_1=6\\y_1=0\\x_2=0\\y_2=-5[/tex]
Now substitute these values into the formula
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{-5-0}{0-6}[/tex]
Subtract
m=[tex]\frac{-5}{-6}[/tex]
Simplify
m=[tex]\frac{5}{6}[/tex]
The slope of the line is 5/6
Let's plug this value into the formula for the equation of the line in slope-intercept form.
We substitute 5/6 for m in y=mx+b:
y=[tex]\frac{5}{6}x+b[/tex]
Now we need to find b
As stated before, b is the y intercept, which is the value where the line hits the y axis. The value of x at the y intercept is 0.
One of the points we were given is actually the y intercept; that point is (0, -5); notice how the value of x in this point is 0
The value of b is the value of y in this point, which is -5 in this case.
Substitute -5 as b in the formula.
[tex]y=\frac{5}{6} x -5[/tex]
Hope this helps!
See more on this subject here (n.b. the answer uses a different way of solving): https://brainly.com/question/20891204
enter order pairs for
y = 2x + 7
y= 3x – 3
Answers
Answer:
(10, 27)
Step-by-step explanation:
We have to solve the given set of equations :
y = 2x + 7y = 3x - 3As both equations are equal to y, equate the RHS of both of the equations.
2x + 7 = 3x - 3x = 10The x-coordinate is 10y = 3(10) - 3 = 27The y-coordinate is 27
Writing an ordered pair
The standard form of an ordered pair is given by (x, y) where x and y are x and y coordinates respectivelyTherefore, the answer is :⇒ (10, 27)Answer:
[tex]\displaystyle [10, 27][/tex]
Step-by-step explanation:
Set each equation equivalent to each other:
[tex]\displaystyle 3x - 3 = 2x + 7 \\ \\ \frac{-10}{-1} = \frac{-x}{-1} \\ \\ \boxed{10 = x, 27 = y}[/tex]
I am joyous to assist you at any time.
Aaron bought 14.6 gallons of gas for $1.98 per gallon. How much did he spend on gas?
Answers
Answer:
= 29$ (to the nearest dollar)
Step-by-step explanation:
14.6 gallons of gas
1 gallon = 1.98$
14.6 gallons = 14.6 × 1.98$
= 28.90800$
= 29$ (to the nearest dollar)
Roberto’s science grade is calculated using a weighted average quizzes are worth 25% homework is worth 10% unit tests are worth 30% and labs are worth 35%. Roberto earned an average of 94% on his quizzes, 99% on his homework, 92% on his unit test, and 94% on his labs. What is Roberto’s final science grade?
93.3%
93.9%
94.8%
95.3%
Answers
Answer:
the answer should be 93.9% let know if in wrong
Roberto's science grade as per weighted average is equals to 93.9%.
What is average?
" Average is defined as the ratio of total of all the given data to the total number of quantities in the data."
Formula used
Weighted average'W' = ( ∑[tex]w_{i} x_{i}[/tex] ) / ( ∑[tex]w_{i}[/tex] ) , where i = 1, 2,.... n
W= weighted average
n = number of terms to be averaged
w = weight applied to x values
x = data values to be averaged
According to the question,
Given,
Weight applied to quiz 'w₁' = 25%
Weight applied to homework 'w₂' = 10%
Weight applied to to unit tests 'w₃'= 30%
Weight applied to labs 'w₄' = 35%
Average on quiz Roberto earned 'x₁'= 94%
Average on homework Roberto earned 'x₂'= 94%
Average on unit test Roberto earned 'x₃'= 94%
Average on labs Roberto earned 'x₄' = 94%
Substitute the values in the formula we get,
Weighted average
= [ (25 × 94) +(10× 99) + (30 × 92) +(35 ×94)] / ( 25+10+30+35)
= (2350 +990 + 2760 + 3290) / 100
= 9390 / 100
=93.9%
Hence, Roberto's science grade as per weighted average is equals to 93.9%.
Learn more about weighted average here
https://brainly.com/question/18554478
#SPJ2