Answers
The center of the circle will be equal to (-3,4) equation of the circle x²+y²+6x-8y+16=4
What is circle?The circle is defined as the locus of the point traces around a fixed point called as the center and is equidistant from the out trace.
The general form of the equation of the circle is:-
(x-x₁)²+(y-y₁)²=r²
here x1 and y1 are the center of the circle
Now we will convert our equation in the general form:-
x²+y²+6x-8y+16=4
x²+6xy²-8y+16-4=0
x²+3x+3x+9-9+y²-4y-4y+16-16-4=0
(x+3)²+(y-4)²-9-16+16-4=0 (x+3)²+(y-4)²=13
By comparing with the general form we can see that the coordinate of the center of the circle will be {-3,4)
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Related Questions
Enter an equation for which the solution is the speed of the train, in miles per hour, where the train's distance from the departing station is 162 miles and it has traveled for 3 hours. what is the equation for the speed of the train?
Answers
Answer:
Step-by-step explanation:
Formula
speed = distance / time
Givens
speed = ?
distance = 162 miles.
Time = 3 hours.
Solution
speed = 162 / 3
speed = 54 miles per hour.
Jacob wants to find the volume of a roll of paper towels.
Which composition produces a solid with the same shape and dimensions as the roll of paper towels?
A.
a difference between two cylinders with the same height and different radii
B.
a difference between a hemisphere and a cylinder with the same radius
C.
a difference between two cylinders with the same radius and different heights
D.
a difference between two hemispheres with the same center
Answers
A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The correct option is A, the difference between two cylinders with the same height and different radii.
What is a cylinder?A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centres overlap each other to form a right cylinder.
Since the shape of a paper towel is like a cylinder, therefore, the composition that produces a solid with the same shape and dimensions as the roll of the paper towel is a difference between two cylinders with the same height and different radii.
Hence, the correct option is A.
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PLEASE HELP 5 POINT ASSIGNMENT (LEASE TO GREATEST PROBLEM)
Order, 1/2, 5/6, 2/3, and 3/5 from least to greatest
Answers
Answer:
1/2 < 3/5 < 2/3 < 5/6
Step-by-step explanation:
Using the given inputs:
1/2 5/6 2/3 3/5
The least common denominator (LCD) is: 30.
Rewriting as equivalent fractions with the LCD:
1/2 5/6 2/3 3/5
15/30 25/30 20/30 18/30
Sorting this table by the numerators of the equivalent fractions in order from least to greatest:
1/2 3/5 2/3 5/6
15/30 < 18/30 < 20/30 < 25/30
Therefore, the sorted inputs in order from least to greatest is:
1/2 < 3/5 < 2/3 < 5/6
If f(x)=X²-3, what is the value of f(-3)?
Answers
__________________________________________________________
Hello! In this question, we are trying to solve the expression with a given value.
__________________________________________________________
Explanation:
In this question, we were given our f(x) equation: f(x) = x² - 3
We were also given the value of our variable "x": -3
To solve the expression, we would plug in our "x" value, -3, into the "x" variables in our expression and solve.
Solve:
f(x) = x² - 3
f(-3) = (-3)² - 3
= 9 - 3
= 6
Therefore, the value of f(-3) is 6.
__________________________________________________________
Answer:
f(-3) = 6
__________________________________________________________
To solve this problem, you will substitute an existing value into a function in order to find the y-coordinate at that x-coordinate.
SubstituteGiven the function f(x) = x² - 3, evaluate the function at f(-3) by substituting in x = -3:
[tex]f(-3) = -3^2-3[/tex]
Use Order of OperationsUse BPEMDAS, which stands for:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
First, evaluate -3².
[tex]-3\times-3=9[/tex]
Then, evaluate the rest of the expression by subtracting 3 from 9:
[tex]9 - 3 = \boxed{6}[/tex]
The final answer is f(-3) = 6.
need help with sigma notation
Answers
Answer:
114126Step-by-step explanation:
The given expression describes the GP with
The first term:
t = 80(1.23²⁻²) = 80(1.23⁰) = 80The common ratio:
r = 1.23It is required to find the sum of the terms from 2 (the bottom number of sigma) through 29 (the top number of sigma)
The number of terms is
n = 29 - 2 + 1 = 28The sum of the first 28 terms is
Sₙ = t(rⁿ - 1)/(r - 1) S₂₈ = 80(1.23²⁸ - 1)/(1.23 - 1) = 114125.75573 ≈ 114126 (rounded)Answer:
114,126 (nearest whole number)
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
Given:
[tex]\displaystyle \sum^{29}_{n=2}80(1.23)^{n-2}[/tex]
The sigma notation means to find the sum of the given geometric series where the first term is when n = 2 and the last term is when n = 29.
First term (a)
Determine the first term by substituting n = 2 into the given expression:
[tex]n=2 \implies 80(1.23)^{2-2}=80[/tex]
Common ratio (r)
From inspection, the common ratio is 1.23.
nth term
As the first term is when n = 2 and the last term is when n = 29, there is a total of 28 terms.
Therefore:
a = 80r = 1.23n = 28Sum of the first n terms of a geometric series:
[tex]S_n=\dfrac{a(1-r^n)}{1-r}[/tex]
Substituting the given values into the formula:
[tex]\implies S_{28}=\dfrac{80\left(1-1.23^{28}\right)}{1-1.23}=114125.7556[/tex]
Therefore, the sum of the given geometric series is 114,126 (nearest whole number)
The graphs below have the same shape. f(x) = x².
What is the equation of the graph of g(x)?
Answers
Answer:
C. g(x) = (x - 4)²
Explanation
g(x) is f(x) right 4 units
When shifted right, x - a, a is the distance
So g(x) = (x - 4)² is the answer
HOPE THIS HELPS AND HAVE A NICE DAY <3
Luis is flying a kite, holding his hands a distance of 3.75 feet above the ground and letting all the kite’s string play out. He measures the angle of elevation from his hand to the kite to be 35^{\circ} ∘ . If the string from the kite to his hand is 140 feet long, how many feet is the kite above the ground? Round your answer to the nearest tenth of a foot if necessary.
Answers
The height of the kite above the ground to the nearest tenth of a foot is 84.1 ft
Using the angle of elevation to find height?The situation forms a right angle triangle.
Therefore, the length of the string is the hypotenuse of the triangle formed.
Hence, using trigonometric ratios,
sin 35 = opposite / hypotenuse
sin 35 = h / 140
cross multiply
h = 140 sin 35
h = 140 × 0.57357643635
h = 80.3007010891
Height of the kite above the ground = 80.3007010891 + 3.75 = 84.0507010891
Height of the kite above the ground = 84.1 ft
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A catalog with 625 pages has 6 pages with tables.
What percent of the pages have tables?
0.16%
0.96%
1.28%
1.92%
Answers
Answer:
0.96%
Step-by-step explanation:
We are looking for the percent that represents "6 out of 625"
Divide to find the decimal answer:
6/625 means
6 ÷ 625
= 0.0096
Then multiply by 100 to change to a percent.
0.0096 × 100
= 0.96%
A class of 50 students votes for a class president.
Candidate A receives 19 votes.
Candidate B receives 31 votes.
Use this information to answer the questions below.
Answers
Answer:
[tex] \frac{31}{50} \\ \frac{31}{50} \times 100 = 62\% [/tex]
19+31= 50 students
Question #1: will be B/ total students which is 31/50
Question #2: to find percentage I like to cross multiply. X= total percentage voting 31/50 * x/100
31*100= 3,100
3,100/50= 62
X=62%
A cuboid with dimensions 45 cm by 16 cm by 12 cm is cut to form smaller cubes of
length 4 cm. What is the maximum number of cubes that can be obtained?
Answers
Answer:
135 cubes
Step-by-step explanation:
Volume of cuboid :
45 x 16 x 12720 x 128,640 cm³Volume of a small cube :
(4)³64 cm³Number of cubes :
n = 8,640/64n = 135 cubesfind the dot product of the pair of vectors and determine whether they are normal. (4,-3) and (-3,-4)
Answers
Answer:
normal
Step-by-step explanation:
Dot Product of Vectors
Multiply x-values with x-values and same for the y-values4(-3) + (-3)(-4)-12 + 120As the dot product of the vectors equals 0, the vectors are normal.
Find the length of side X in the simplest radical form of the rational denominator
Answers
[tex]~~~~~~~\cos 45^{\circ} = \dfrac{\text{Base}}{\text{Hypotenuse}}\\\\\\\implies \dfrac 1{\sqrt 2} = \dfrac{\sqrt 3}{x}\\\\\\\implies x = \sqrt 3 \cdot \sqrt 2\\\\\\\implies x = \sqrt {3 \times 2}\\\\\\\implies x = \sqrt 6[/tex]
HELP!!
Which of the statements below are true for linear functions? Select all that apply.
1. The general equation is y = mx + b.
2. The general equation is y = ax^2 + bx + c
3. The general equation is y = ab^x
4. The graph contains a vertex
5. The slope of the graph is constant and can be defined as rise over run.
Answers
[tex]\rule{60}{1}\:\:\:\rule{60}{1}\:\:\:\rule{60}{1}\:\:\:\rule{60}{1}[/tex]
[tex]\diamond\large\blue\textsf{\textbf{Given question:-}}}[/tex]
Which of the statements below are true for linear functions?
Select all that apply.
[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}[/tex]
The general equation for linear functions is [tex]\bold{y=mx+b}[/tex].
The equation [tex]\bold{y=ax^2+bx+c}[/tex] is the general equation for quadratic functions.
The equation [tex]\bold{y=ab^x}[/tex] is the general equation for exponential functions.
Linear functions don't have a vertex, they have slope (m) and y-intercept (b).
One way we can define the slope of a linear function is
[tex]\bold{Slope=\dfrac{Rise}{Run}}[/tex]
So we conclude that the right options are
[tex]\square\!\!\!\!\checkmark[/tex] The general equation is y=mx+b.
[tex]\square\!\!\!\!\checkmark[/tex] The slope of the graph is constant and can be defined as rise over run.
Good luck with your studies.[tex]\rule{300}{1}[/tex]
Suppose 60% of a herd of cattle is infected with a particular disease. let p = the number of non diseased cattle in a sample of size 5. the distribution of y is
Answers
The distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]
How to determine the distribution?The given parameters are:
Probability of success, p = 60%
Sample size, n = 5
The distribution of y is represented as:
[tex]P(y) = ^nC_y * p^y * (1 - p)^{n-y}[/tex]
So, we have:
[tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]
Hence, the distribution of y is [tex]P(y) = ^5C_y * (60\%)^y * (1 - 60\%)^{5-y}[/tex]
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Find the measure of exterior angle 1
Answers
Write a cosine function that has a midline of 3, an amplitude of 4 and a period
of pi.
Answers
Answer:
[tex]f(x)=4\cos(2x)+3[/tex]
Step-by-step explanation:
Using the general equation [tex]f(x)=a\cos(bx+c)+d[/tex], we already know that [tex]a=4[/tex] and [tex]d=3[/tex], but we need to find [tex]b[/tex] from the period:
[tex]\frac{2\pi}{|b|}=\pi\\ 2\pi=b\pi\\2=b[/tex]
Hence, the cosine function is [tex]f(x)=4\cos(2x)+3[/tex]
3.2 Tshego also intends tiling the dining room and lounge floors. The dimensions of the lounge floor are 4 m by 5 m and of the dining room floor 3 m by 4 m. Information and cost: Tshego intends using tiles that are 35 cm by 35 cm. One box of 4 tiles costs RI43,84. Tile cement costs R99,90 per 20 kg bag, which covers 3 m². She needs 4 bags of tile grout at R89,90 per 5 kg bag. The cost of labour is R2 500. Tshego's total budget for the tiling project is R15 000. Use the information above to answer the questions that follow. 3.2.1 Show that the total floor area to be tiled is 32 m². You may use this formula: Area of a rectangle = length x width (2)
Answers
Using the area of a rectangle, the total floor area to be tiled = area of the dinning room + area of the lounge floor = 32 m²
What is the Area of a Rectangle?The area of rectangle = (length)(width).
Total floor area to be tiled = area of the dinning room + area of the lounge floor
Total floor area to be tiled = (4)(5) + (3)(4)
Total floor area to be tiled = 20 + 12
Total floor area to be tiled = 32 m²
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Michael has a room in his house that is shaped like a parallelogram the length of the room measures 16 feet and the width measures 26 what is the perimeter of the
Answers
Answer:
84 ft
Step-by-step explanation:
16 + 16 + 26 +26 = 84
A cable extends from the top of a radio tower to a point 360 feet from the base of the tower. If the
cable is 850 feet long, how tall is the tower?
Answers
Step-by-step explanation:
we have a right-angled triangle :
the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.
then the ground distance (360 ft) and the height of the tower are the 2 legs.
so, we can use Pythagoras
c² = a² + b²
with c being the Hypotenuse.
in our case
850² = 360² + height²
height² = 850² - 360² = 592,900
height = 770 ft
the tower is 770 ft tall.
Answer:
770 feet
Step-by-step explanation:
Given
Cable = 850 feet longExtends from radio tower to a point 360 feet from the base of a towerSolving
Using the Pythagorean Theorem, we can find the height(distance from base)² + (height)² = (length of cable)²height² = (850)² - (360)²height² = 722,500 - 129,600height² = 592,900height = √592,900height = 770 feetFind the arc length of an arc with a Central angle of 2π/3 radians and a radius of 6 units
Answers
Answer:
Step-by-step explanation:
Please help me!!? Number 6
Answers
Answer:
the b believes in me
Step-by-step explanation:
B)75km etc
1hr
[tex]\frac{75 \text{ km}}{1 \text{ hr}} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ hr}}{60 \text{ min}} \times \frac{1 \text{ min}}{60 \text{ sec}}[/tex]
========================================================
Explanation:
We'll use the following facts (either memorized or written on a reference sheet somewhere)
1000 m = 1 km1 hr = 60 min1 min = 60 secEach of those equations will form conversion factors to help us go from km/hr to m/s. Each conversion factor is a fraction connecting the two sides of the equation. Example: The equation 1000 m = 1 km forms the conversion factor of [tex]\frac{1000 \text{ m}}{1 \text{ km}}[/tex]
In choice B, notice how the fractions are set up. The "km" units cancel when dividing. The same goes for the "hr" and "min" units.
Check out the screenshot below where I show this cancellation in action. The color-coding helps show how the terms pair up and cancel.
Choice A comes close to what choice B is saying, but we don't have the "min" units cancel. So choice A is eliminated as an answer.
Choices C and D are also eliminated because of the "75 km" in the denominator. It should be 1 km.
Here is Diya's work writing the expression 6 - 2x + 5 + 4x with fewer terms. Describe the mistake that Diya made.
Diya's Work
6- 2x + 5 + 4x
4x +
9x
13x Write an expression equivalent to 6 - 2x + 5 + 4x that has two terms.
Answers
Answer:
Below.
Step-by-step explanation:
This is the correct solution:
6 - 2x + 5 + 4x
= -2x + 4x + 6 + 5
= 2x + 11.
It looks like they added unlike terms together (4x + 5) to give 9x (incorrect) then added the 4x to give 13x.
please help mee i will give brainliest
Answers
Answer:
420*3/2 = 630
630/60 = 10.5
=> B direction isn't relevant with velocity
Answer:
A. 10.5
Step-by-step explanation:
I divided 450 by 40 for the velocity of 10.5 brainliest please!!
If the coordinates of point Q are (−12,√32), then what is the value of tan(m) ?
Answers
Vector components are expressed in the form (x, y). The measure of tan m given the coordinate Q is -√32/12
Direction of a vectorVector components are expressed in the form (x, y). Given the coordinates of point Q are (−12,√32), the measure of the angle is expressed as;
m = arctan(y/x)
m = arctan (-√32/12)
Take the tan of both sides
tan m = tan arctan(-√32/12)
tan m = -√32/12
Hence the measure of tan m given the coordinate Q is -√32/12
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Please help ASAP!!
see attachment below!
Answers
7C5 = 7 x 6 x 5 x4x3/5 x 4 x 3 x2x1 = 7
Hence option d is correct z
_x 11 = 99 what is the missing number?
Answers
Answer:
9 x 11 = 99
Step-by-step explanation:
if the number 11 is being multiplied by is under 10 its just that number twice.
11x1 = 11
11x2 = 22
11x3 = 33
ya know?
How many 4-digit numbers are neither multiples of 2 nor multiples of 5?
Answers
Multiples of 2 end in 0, 2, 4, 6, and 8. There are 9*10*10*5 = 4500 four-digit multiples of 2.
Multiples of 5 end in 0 or 5. There are 9*10*10*2 = 1800 four-digit multiples of 5.
There is redundancy between the two sets of numbers, namely those that end in 0, which are both multiples of 2 and 5. There are 9*10*10*1 = 900 four-digit multiples of both 2 and 5.
Then there are 4500 + 1800 - 900 = 5400 total four-digit numbers that are either multiples of 2 or 5, which means the remaining 4600 numbers are neither multiples of 2 nor 5.
Answer:
3,600
Explanation:
There's nine thousand numbers here, 4,500 of which are even, you will need to subtract mutiples of five from this number, making it even smaller.
subtract the non-even five's (exactly half of the 1800 hundred fives that fit in our little original number, (900!) ) 4,500-900= 3,600. Which should be your answer. :D
Step-by-step explanation:
A bus stops at a bus stop every 45 minutes. Once a person gets to the bus stio, what is the probability they will wait for no more than 20 minutes?
Answers
Answer:
≈ [tex]44.4%[/tex][tex]%[/tex]%
Step-by-step explanation:
The person will wait for no more than 20 minutes if they arrive when the bus is going to stop in 20 minutes, which means that they must arrive 25 minutes after the previous bus stops. So the probability that the person will not wait for more than 20 minutes will be [tex]\frac{20}{45}[/tex] which is about 44.4%.
ark. (iv). 2(x-3)-3(5x-2) ≤ 6(3-2x)
[tex]2( \times - 3) - 3(5 \times - 2) \leqslant 6(3 - 2x)[/tex]
Answers
Answer:
x ≥ 18
Step-by-step explanation:
2(x-3)-3(5x-2) ≤ 6(3-2x)
⇔ 2x - 6 - 15x + 6 ≤ 18 - 12x
⇔ 2x - 15x ≤ 18 - 12x
⇔ -13x ≤ 18 - 12x
⇔ -13x + 12x ≤ 18
⇔ -x ≤ 18
⇔ x ≥ 18
⇔ x∈[18 , ∞)
Teenegers were asked how many times a week they were reminded to do chores. The responses are shown in the graph. What is the mean of the number of times per week that they were reminded?
Answers
Answer:
i could help but i don't see the graph chart
Step-by-step explanation:
