Answers
Answer:
(x-4)² + (y-3)² =29
Step-by-step explanation:
The equation of a circle is
(x-h)² + (y-k)² = r², where (h, k) is the center of the circle and r is the radius.
In this circle, the center is at (4, 3)
(x-4)² + (y-3)² = r²
and we have point (-1 ; 1)
r²=(-1-4)² + (1-3)² = 25+4=29
(x-4)² + (y-3)² =29
Answer:
(x - 4)² + (y - 3)² = 29
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (4, 3 )
The radius r is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (- 1, 1) and (x₂, y₂ ) = (4, 3)
r = [tex]\sqrt{(4+1)^2+(3-1)^2}[/tex]
= [tex]\sqrt{5^2+2^2}[/tex]
= [tex]\sqrt{25+4 }[/tex] = [tex]\sqrt{29}[/tex]
Then
(x - 4)² + (y - 3)² = ([tex]\sqrt{29}[/tex] )² , that is
(x - 4)² + (y - 3)² = 29 ← equation of circle
Related Questions
A business shipped 106 packages one day. Customers are charged 4.50 for each standard delivery and 7.50 for each express delivery
Answers
The question is incomplete:
A business shipped 106 packages one day. Customers are charged 4.50 for each standard delivery and 7.50 for each express delivery. Total shipping charges for the day were $600.00. How many of each kind of package were shipped?
Answer:
The business shipped 65 standard delivery packages and 41 express delivery packages.
Step-by-step explanation:
Since the business shipped 106 packages one day you can say that:
x+y=106, where:
x is the number of standard delivery packages
y is the number of express delivery packages
Also, you can say that the result of multiplying the price per each type of package for its amount and adding those would be equal to the total shipping charges for the day, which is:
4.50x+7.50y=600
So, you have the following equations:
x+y=106 (1)
4.50x+7.50y=600 (2)
Now, you can solve for x in (1):
x=106-y (3)
Then, you can replace (3) in (2) and solve for y:
4.50(106-y)+7.50y=600
477-4.50y+7.50y=600
3y=600-477
3y=123
y=123/3
y=41
Finally, you can replace the value of y in (3) to be able to find the value of x:
x=106-41
x=65
According to this, the answer is that the business shipped 65 standard delivery packages and 41 express delivery packages.
what is the probability that you will fail a test (pass or fail), draw a red ace, and then roll a 6?
Answers
Answer:
0.7890176%
Step-by-step explanation:
First, there is a 64% chance of failing a test.
Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces. You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.
Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%
Now we need to multiply each chance of something happening by one another
64% × 7.4% = 0.04736%
4.736% × 16.66% = 0.7890176%
So there is a 0.7890176% of all of these happening
The probability that you will fail a test, draw a red ace, and then roll a 6 is 0.7890176%
We have given that,
First, there is a 64% chance of failing a test.
We have to determine the probability
What is the probability?
Probability is an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Then there are 54 cards in a deck. There are two colors, red and black. There are two red aces and two black aces.
You have a 50% chance that the card is red. Then there are 27 cards of each color. Since there are 2 aces in those 27, there is a 2/27 or ~7.4%.
Lastly there are 6 sides on a die. Each side has the same chance of landing. So this gets you 16.66%
Now we need to multiply each chance of something happening by one another
64% × 7.4% = 0.04736%
4.736% × 16.66% = 0.7890176%
So there is a 0.7890176% of all of these happening
Therefore the probability that you will fail a test, draw a red ace, and then roll a 6 is 0.7890176%.
To learn more about the probability visit:
https://brainly.com/question/25870256
#SPJ2
A sphere with diameter of 12 cm is being painted. How much more paint is now needed to paint the sphere that has four times the original diameter.
4 times more paint
B 8 times more paint
16 times more paint
D 64 times more paint
Answers
Answer:
64 times more paint will be needed since the volume of the second is 64 times the volume of the first
Step-by-step explanation:
If the original sphere is 12 cm diameter
its radius will be half this measure which is 12/2 = 6 cm
The new diameter is 4 times this, so its radius would be 4 times this and it is 24 cm
Now, the volume of the sphere means we have to raise the power of the radius by 3
The other terms in the formula remains the same for both, so we are simply comparing the radii
so we will have the difference in volume in times of multiples as ;
(24/6)^3 = 4 * 4 * 4 = 64
Answer 15 points
( don’t answer if you don’t the answer )
Answers
Answer:
V=1/3hπr². Basically, 1/3 x height x 3.14 (pi) x radius squared.
Step-by-step explanation:
The formula of figure 2 would be 1/3 x 15 x 3.14 x 8 squared. The volume of figure 2 would be 1005.30965
the formula for figure 3 would be 1/3 x 15 x 3.14 x 4 squared. The volume of it would be 251.32741
hope this helps! (Also please make me brainliest if this helps u :) )
Find the area of the trapezoid
A. 168 in^2
B. 94.5 ft^2
C. 72 ft^2
D. 84 ft^2
Answers
Answer:
D. 84 ft^2
Step-by-step explanation:
Formula for area of a trapezoid:
[tex]A=\frac{a+b}{2} h[/tex]
where a and b = bases and h = height
The trapezoid shown has the following dimensions
base 1 = 9ft
base 2 = 12ft
height = 8ft
Using the following information we plug in the values into the formula
[tex]A=\frac{9+12}{2} \\9+12=21\\\frac{21}{2} =10.5\\10.5*8=84[/tex]
Hence, the area of the trapezoid is 84ft² and your answer is D
Select all correct ways of factoring –3x – 9.
Answers
-3(x+3)
Answer:
Some possible expressions, since there's no answer choices provided:
-3(x + 3)
3(-x - 3)
Step-by-step explanation:
Expression 1:
This uses a GCF of -3, since -3x and -9 are divisible by this. Let's divide -3x and -9 by this first:
-3x / -3 = x
-9 / -3 = 3
So now, we can add these terms and multiply them by -3 to get our answer:
-3(x + 3)
And just to check, we can expand it:
-3x + -3(3) = -3x - 9
Expression 2:
This uses a GCF of 3, like the last one but it's negative. -3x and -9 are also divisible by this. Let's divide both terms by this GCF first:
-3x / 3 = -x
-9 / 3 = -3
Now, we can add these terms and multiply them by -3 to get our final answer:
3(-x - 3)
To check, once again:
-3x + 3(-3) = -3x - 9
Which of the equations below shows the relationship in the table?
Answers
Answer:
Im Sure its A
Step-by-step explanation:
Describe, in words, the process you would use to find w.
Answers
Answer:
w = 52°
Step-by-step explanation:
We know that the sum of the angle of a triangle is equal to 180 degrees
In this figure,
w+w+76 = 180
As w = w (Vertically opposite angles)
So,
2w = 180-76
2w = 104
w = 52
So, the value of w is equal to 52°.
What is h?
Im so confused on this question
Answers
Answer:
i think h stands for height. I dont see it standing for any thing else
Step-by-step explanation:
Which equation represents a line which is parallel to the line y=7/2x-4
Answers
Answer:
y=-(7)/(2)x-5
Step-by-step explanation:
to make a parallel equation, you must make an equation that has the same slope, but different b intercepts. so, the equation must have 7/2x, and the b part can be any number.
Answer:
y = 7/2x + 2
Step-by-step explanation:
to make a parallel equation, you must make an equation that has the same slope, but different b intercepts. so, the equation must have 7/2x, and the b part can be any number.
Find all the zeroes of polynomial 2x4
– 9x3 + 5x2 + 3x – 1 ,if two of its zeroes are 2 + √3 & 2 - √3
Answers
9514 1404 393
Answer:
x ∈ {-1/2, 1, 2-√3, 2+√3}
Step-by-step explanation:
The given zeros mean that one of the quadratic factors of the given polynomial is ...
(x -2)^ -3 = x^2 -4x +1
When that is factored out (see first attachment), the remaining quadratic is ...
2x^2 -x -1
This can be factored as ...
= (2x +1)(x -1)
which has roots that make these factors zero: x = -1/2, x = 1.
So, all of the zeros of the given polynomial are ...
-1/2, 1, 2-√3, 2+√3 . . . all zeros
__
A graphing calculator can often point to the zeros of the function quite nicely.
_____
Additional comments
When p is a zero of a polynomial, (x-p) is a factor of it. The given zeros mean that factors are (x-2-√3) and (x-2+√3). The product of these factors is the difference of the squares (x-2)^2 and (√3)^2, so is (x -2)^2 -3.
Using the pattern for the square of a binomial, we see this is ...
(x-2)^2 = x^2 -2·2x +2^2 = x^2 -4x +4
The product of the given factor is then 3 subtracted from this square. The given zeros mean there is a quadratic factor of ...
(x-2-√3)(x-2+√3) = (x-2)^2 -3 = x^2 -4x +4 -3 = x^2 -4x +1
5x - y = -7
X + y = -5
Answers
Answer:
x = -2
y = -3
Step-by-step explanation:
5x - y = -7
x + y = -5
6x = -12
x = -2
x + y = -5
-2 + y = -5
y = -5 + 2
y = -3
Answer:
(-2,-3)
Step-by-step explanation:
x + y = -5
y = -x - 5
5x - (-x - 5) = -7
5x + x + 5 = -7
6x = -12
x = -2
x + y = -5
-2 + y = -5
y = -3
-7 2/3 + (-5 1/2) + 8 3/4 = ????
Answers
Answer:
-52/12 or -4 5/12
Step-by-step explanation:
hope this help there 2 ways
Answer:
-53/12 same as -4 4/12 same as -4,416
Step-by-step explanation:
convierte el numero mixto a una fracción impropia
-23/3 + (-5 1/2) + 8 3/4
cuando se encuentren un + en frente de una expresión dentro de un paréntesis, la expresión se mantiene igual
-23/3 - 5 1/2 + 8 3/4
convierte el numero mixto a una fracción impropia
-23/3 - 5 1/2 + 35/4
convierte el numero mixto a una fracción impropia
-23/3 - 11/2 + 35/4
calcula la suma o resta
-53/12
Determine the volume of the rectangular prism.
Answers
Answer:
132in
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
[tex]v = 4 \times 6 \times 5 \frac{1}{2} \\ v = 24 \times \frac{11}{2} = 132[/tex]
hope it helps
have a nice day
In a circle, an angle measuring 2π radians intercepts an arc of length 14π. Find the radius of the circle in simplest form.
Answers
Answer:
7 radians
Step-by-step explanation:
In a circle, an angle measuring 2π radians intercepts an arc of length 14π. Find the radius of the circle in simplest form.
Since our Angle in in radians
The formula for Arc length = S = rθ
S = 14π
θ = central angle = 2π radians
Hence
r = S/θ
r = 14π/2π radians
r = 7 radians
Radius = 7 radians
Which of the following represents the factorization of the trinomial below?
x² - 8x - 48
A. (X-6)(x-8)
B. (X+6) (x-8)
C. (x-4)(x-12)
D. (x+4)(x-12)
Answers
I just need help with the graphing!
Answers
Answer:
solution is in attachment
hope it helps
The lengths of the sides of the triangle are 3, 8, and 10. Is the triangle a right triangle, acute triangle, or an obtuse triangle?
Answers
Answer:
Obtuse
Step-by-step explanation:
You have to make sure it is a triangle by adding the smallest and the medium sides, if the result is greater than the bigger side then it is a triangle. you then use the Pythagorean theorem to check if the triangle is a right triangle, acute, or obtuse. If [tex]c^{2}[/tex] = [tex]a^{2} +b^{2}[/tex] then it is a right triangle. If [tex]c^{2} >a^{2} + b^{2}[/tex] then it is an obtuse triangle. if [tex]c^{2} < a^{2} +b^{2}[/tex] then it is an acute triangle. [tex]10^{2}[/tex] _ [tex]3^{2} + 8^{2}[/tex] 9+64_100 70_100 70<100in this case [tex]c^{2}[/tex] is greater than [tex]a^{2} +b^{2}[/tex] therefore, is it an obtuse triangle.
Solve the system of equations:
y = x + 2
y = x2 + 5x + 6
A.
(0, 2) and (2, 4)
B.
(–2, 0) and (–3, 0)
C.
(–2, 0)
D.
(0, 2)
Answers
Answer: C
Step-by-step explanation:
Since both equations are set equal to y, it follows that
[tex]x+2=x^2 + 5x+6\\\\x^2 +4x+4=0\\ \\ \\(x+2)^2 = 0\\\\x=-2\\\\\implies y=-2+2=0[/tex]
So, the solution is (-2, 0).
somebody helpp and ty
Answers
Answer:
45 degrees
Its on the first bar in the 45 degree angle which is half of 90
Find the next three terms in the pattern: 7, 3,-1, -5, -9.... Then, describe the pattem.
Answers
Answer:
Next three terms are: - 13, - 17, - 21
Step-by-step explanation:
Evety time it decreases by 4.
Answer:
-13, -17, -21
Step-by-step explanation: keep subtracting 4
2017 - Q13
13 Tivo identical number cubes are shown in the picture. The edge length of these number cubes
is 3 centimeters.
What is the combined volume of the two number cubes in cubic centimeters?
A 54 cm
B 18 cm
C 9 cm
D 27 cm
Answers
Answer:
Combined volume of the two number cubes = 54 cm³
Step-by-step explanation:
Given:
Side of a cube = 3 centimeter
Number of cubes = 2
Find:
Combined volume of the two number cubes
Computation:
If we combine two cube new figure will be a cuboid.
Length of new cuboid = 3 + 3 = 6 cm
Height of new cuboid = 3 cm
Width of new cuboid = 3 cm
Volume of cuboid = (l)(b)(h)
Combined volume of the two number cubes = (6)(3)(3)
Combined volume of the two number cubes = 54 cm³
One of the tallest living trees today is the Mendocino Tree found at
Montgomery Woods State Park, California. Its height is about 11,200
centimeters. What is this height in scientific notation?
Answers
Answer:
the height in scientific notation is 1.12 x 10^4 :)
Solve the inequality for t.
11 ≤ t + 4
Simplify your answer as much as possible.
Answers
Answer:
t≥7
Step-by-step explanation:
11≤t+4
4 moves to the other side hence its sign changes
11-4≤t
7≤t
they change sides
t≥7
the sign was facing t so this does not change
Answer:
Step-by-step explanation:
Here are some steps to help you
Step 1
11 ≤ t + 4 We are gonna simplify
Step 2
11 ≤ t + 4 simplify
t+4≥11
Step 3
t+4≥11 Subtract 4 from the sides
t≥7
So therefore, your answer will be t≥7
Hope this helps
Please help (;´༎ຶٹ༎ຶ`)
Answers
A jogger is running around a 3/4 mile track and is 2/3 of the way around the track. How far has the jogger traveled
Answers
Answer:
im literally doing the same exact thing right now
Step-by-step explanation:
a line with a slope of 1 passes through the point (5,10). what is the equation in this slope-intercept form?
Answers
Answer:
y=x+5
Step-by-step explanation:
So first you need to plug everything into the point-slope formula which is
y-y1=m(x-x1)
m being the slope and y1 and x1 being the point (5,10)
So once you plug it in it should look like this: y-10=1(x-5)
Now you solve it
First you need to distribute 1 in 1(x-5) which is (x-5)
Now you have y-10=x-5
Then you add 10 to both sides which is y=x+5
Your answer is y=x+5
7. A rectangular prism measures 7 1/2 cm by 12 cm by 15 1/2 cm. a. Calculate the number of cubes with edge length cm that fit in this prism. b. What is the volume of the prism in cm3? Show your reasoning. If you are stuck, think about how many cubes with -cm edge lengths fit into .
Answers
Answer:
a.The number of cubes with edge length 1/2 cm that fit in this prism= 2520
b. Volume of the prism= 315 cm³
Step-by-step explanation:
Volume of the rectangular prism = length *width * height
= 7 1/2 * 12 * 15 1/2
= 7 * 6* 15 1/2
= 7*3*15
= 315 cm³
Volume of the cube = length *width * height
= 1/2 *1/2 *1/2
= 1/8 cm³
Now number of cubes that would fit in the rectangular prism is given by
= Volume of the prism/ Volume of the cubes
= 315/1/8
= 2520
The number of cubes with edge length cm that fit in this prism= 2520
PLEASE HELP!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
i dont know
Step-by-step explanation:
is this quadrilateral a parallelogram? If yes, state the definition or theorem that justifies your answer.
Answers
Answer:
yeah its parallelogram.
quadrilateral whose diagonal bisect each other are parallelogram .