Answer:
(x-2)²+(y-3)²=5².
Step-by-step explanation:
1. the equation of line through points (5;7) and (2;-2) is:
[tex]\frac{x-5}{3} =\frac{y-7}{9}; \ => \ 3x-y-8=0.[/tex]
2. to find the equation of the line, which is perpendicular to the line 3x-y-8=0:
the vector (3;-1) is perpendicular to the line 3x-y-8=0 and it is the vector-pointer for the requred line, and if |n₁|*|n₂|=0 (where n₁ is normal vector to the line 3x-y-8=0 and n₂ is normal vector to the required line), then 3*x-1*y=0 (where 'x' and 'y' any numbers). x=1; y=3, then n₂(1;3), then the required line is x+3y+C=0, where C - is unknown number.
3. to find the equation of the line, which is perpendicular to the line 3x-y-8=0 and passes through the middle point of (5;7) and (2;-2):
middle point is (7/2;5/2), then after substitution of coordinates of the middle point into the equation x+3y+C=0 it will be 3.5+3*2.5+C=0, ⇒ C= -11.
the required equation is x+3y-11=0
4. to calculate the intersection point of x+3y-11=0 and 2x-y=1:
[tex]\left \{ {{2x-y=1} \atop {x+3y=11}} \right. \ => \ (2;3)[/tex]
the point (2;3) is the centre of the required circle.
5. to calculate the radius² of the required circle:
r²=(5-2)²+(7-3)² or r²=(2-2)²+(2+3)², then r²=5².
6. if the centre of the required circle is (2;3) and its r²=25, then it is possible to make up the equiation of the circle:
(x-2)²+(y-3)²=5².
A giant prepared a big feast. If he invites another giant, they will finish the feast in 10 hours. He decides to invite 4 giants. How many hours will it take him and giant friends to finish the feast?
Answer:
1 1/4
Step-by-step explanation:
3 T-shirts cost $12. How
much will 50 T-shirts
cost?
Answer:
$200
Step-by-step explanation:
First, find the unit rate:
12/3= 4
Then multiply:
4*50= 200
Hope this helps!
or
Joey bought 3 packs of white T-shirts and 5 packs of blue T-shirts for his basketball team. The white T-shirts come in packs of 9, and the blue T-shirts come in packs of 7. How many T-shirts did Joey buy in all?
An isosceles triangle has two sides of equal lenght. The length of the third side is 1 ft less than twice the length of one of the equal sides find the length of each side when the perimeter is 23 ft, answer as a comma separated list
Answer: An isosceles triangle has two sides of equal length. The length of one of the equal sides is two more than 3 times the length of the third side. If the perimeter is 46m, find the length of each side.
Step-by-step explanation:
Hope this helps!
Answer:
Step-by-step explanation:
The perimeter is equal to the lengths of all the sides.
Let x equal the two sides that are equal to each other.
Then the 3rd side is 2x - 1 which is 2 times the length of the equal side minus 1.
So the perimeter 23 = x + x + (2x-1)
Now solve for x
23 = x + x + 2x - 1
add 1 to both sides
24 = x + x + 2x
24 = 4x
x = 6
The two equal sides would be 6 feet each
The other side would be 2(6) - 1 = 11
The perimeter is 6 + 6 + 11 = 23
Georgina cooked a 10 1/5 pound turkey in 2 3/5 hours. How many hours per pound did it take to cook the
turkey? Express and explain your answer as a unit rate.
13/51 hours per pound
EXPLANATION
= 2 3/5 hours : 10 1/5 pound
= 13/5 hours : 51/5 pound
= 13/5 × 5/51 hours per pound
= 65/255 hours per pound
= 13/51 hours per pound
#LearnWithEXO
sumi bought 3 tickets that cost $7 each. She paid with a $50 bill. How much change should she receive?
Answer:
$29
Step-by-step explanation:
The area of a rectangular decki: 15. 75 ft?. If the width
of the deck is 1 foot shorter than the length, what are
the dimensions of the deck?
A 3.0ft by5.25ft
B 3.5 by 4.5ft
C 4.5ft by 5.5ft
D5.5ft by 4.75ft
E 7.5 by 6.5 ft
Right answers please asap
Answer:
B. 3.5 ft by 4.5 ftStep-by-step explanation:
Let the width is x, then the area is:
x(x + 1) = 15.75x² + x - 15.75 = 0Solving we get:
x = 3.5So correct choice is B
What is the prime factorization of 7
Answer:
since 7 is a prime number, the prime factors are 1 and 7.
Step-by-step explanation:
Answer:
1 and 7
Step-by-step explanation:
Since 7 is a prime number (meaning that there are no other factors that can be multiplied to equal 7) the prime factors of 7 would be 1 and itself.
I attached a photo below that shows the factor tree for 7.
Hope this explanation clears up any confusion you may have had! Let me know if you have any other questions :D
The graph below shows four straight lines, A, B, C, and D: graph of line A going through ordered pairs negative 2, negative 3 and 2, 5. Graph of line B going through ordered pairs negative 2, negative 4 and 2, 4. Graph of line C going through ordered pairs negative 2, negative 5 and 3, 5. Graph of line D going through ordered pairs 0, negative 4 and 4, 4 Which line is represented by the function f(x) = 2x + 1? (1 point) Group of answer choices Line A Line B Line C Line D
Answer:
Line A is represented by the function f(x) = 2x + 1.
Step-by-step explanation:
HELP PLSSSS!!! I will mark you as brainlyist
How to tell if a graph is a function in algebra
Answer:
Inspect the graph to see if any vertical line drawn would intersect the curve more than once.
Step-by-step explanation:
If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.
find the center and radius of the circle whos equation is (x+5)^2+(y-3)^2=9
9514 1404 393
Answer:
center (-5, 3)
radius 3
Step-by-step explanation:
Compare the given equation to the standard form equation of a circle:
(x -h)² +(y -k)² = r² . . . . . . circle with center (h, k) and radius r
This shows us that ...
-h = +5 ⇒ h = -5
-k = -3 ⇒ k = 3
r² = 9 ⇒ r = √9 = 3
Then the circle center is (h, k) = (-5, 3), and the radius is r = 3.
o differences between constructing an inscribed regular hexagon and constructing an inscribed square.
Answer:
a daddy
Step-by-step explanation:
9) What 2 numbers have a total of 28 and a difference of 6?
Answer:
Sum: 17 + 11 = 28
Difference: 17 - 11 = 6
Step-by-step explanation:
The sum of x and y is 28. In other words, x plus y equals 28 and can be written as equation A:
x + y = 28
The difference between x and y is 6. In other words, x minus y equals 6 and can be written as equation B:
x - y = 6
Now solve equation B for x to get the revised equation B:
x - y = 6
x = 6 + y
Then substitute x in equation A from the revised equation B and then solve for y:
x + y = 28
6 + y + y = 28
6 + 2y = 28
2y = 22
y = 11
Now we know y is 11. Which means that we can substitute y for 11 in equation A and solve for x:
x + y = 28
x + 11 = 28
X = 17
Summary: The sum of two numbers is 28 and their difference is 6. What are the two numbers? Answer: 17 and 11 as proven here:
Sum: 17 + 11 = 28
Difference: 17 - 11 = 6
Answer:
17 +11 = 28
hope this helps
Find the slope of the tangent line to the given polar curve at the point specified by the value of θ
r = 9 + 8 cos(θ), θ = π/3
The given curve has equation
r(θ) = 9 + 8 cos(θ)
and its derivative is
dr/dθ = -8 sin(θ)
When θ = π/3, we have r (π/3) = 13, and dr/dθ (π/3) = -4√3.
Differentiate these with respect to θ :
dy/dθ = dr/dθ sin(θ) + r(θ) cos(θ)
dx/dθ = dr/dθ cos(θ) - r(θ) sin(θ)
In polar coordinates, we have
y(θ) = r(θ) sin(θ)
x(θ) = r(θ) cos(θ)
and when θ = π/3, we have y (π/3) = 13√3/2 and x (π/3) = 13/2.
The slope of the tangent line to the curve is dy/dx. By the chain rule,
dy/dx = dy/dθ • dθ/dx = (dy/dθ) / (dx/dθ)
dy/dx = (dr/dθ sin(θ) + r(θ) cos(θ)) / (dr/dθ cos(θ) - r(θ) sin(θ))
When θ = π/3, the slope is
dy/dx = (-4√3 sin(π/3) + 13 cos(π/3)) / (-4√3 cos(π/3) - 13 sin(π/3))
dy/dx = (-4√3 (√3/2) + 13 (1/2)) / (-4√3 (1/2) - 13 (√3/2))
dy/dx = - 1/(17√3)
So, the tangent line has slope -1/(17√3) and passes through (13/2, 13√3/2). Using the point-slope formula, its equation is
y - 13√3/2 = -1/(17√3) (x - 13/2)
y = -(x - 338)/(17√3)
Rewrite as a simplified fraction.
0.87 = ? But 87 is repeating
Answer:
87 / 100 I do believe will be your answer.
Step-by-step explanation:
1 is the greatest common divisor of 87 and 100, and therefore the result can't be further reduced. I hope this helps!
28. Suppose that the CPI in Year 1 is 150 and the CPI in Year 2 is 200. The rate of
inflation between Year 1 and Year 2 is:
a) 14.28%.
I b) 25%
c) 33.33%
d) 50%
The rate of inflation between year 1 and year 2, based on the CPI, is c. 33.33%.
The Consumer Price Index (CPI) allows us to calculate inflation. To find the inflation across these years, use the formula:
= (CPI₂ - CPI₁) / CPI₁ x 100%
Solving gives us:
= (200 - 150) / 150 x 100%
= 33.3%
In conclusion, the inflation is 33.3%.
Find out more at https://brainly.com/question/17329174.
Solve the photo above ⬆️
Btw these one's are gonna be a bit more confusing for me, so expect me to atleast probably send 7 more ^^|l|l
Answer:
7¹⁰ :) hope this helps you!!
3and3/4th divided by 2and 1/2
Answer:
1.5
Step-by-step explanation:
3 3/4 ÷ 2 1/2
3/2
= 1.5
Paige bought 1.06 pounds of what is 42.05 what does the lettuce cost per pound pounder to the nearest cent help please
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
1.6 pounds of lettuce costs :
$ 42.051 pound of lettuce costs :
$ 42.05 ÷ 1.06$ 39.66 per poundNO LINKS PLEASE HURRY I REALLY NED HELP!!!
Answer:
The answer is D
Step-by-step explanation:
-7.6+4.17= -3.43x
3.54-1.32= 2.22
5. Ken was at bat 120 times during the baseball season. If he hit the ball
15% of the time, how many times did he have a hit?
Am i correct on this problem if not please tell me why im not.
9514 1404 393
Answer:
A
Step-by-step explanation:
Reflection across a line reverses the orientation of the figure from CW to CCW, or vice versa. Each point on the image is the same distance from the line of reflection as the corresponding point on the preimage.
These characteristics are manifested in figure A.
__
Figure B represents a translation to the right; Figure C represents both rotation and translation. Figure D is translation up and to the right.
_____
Additional comment
When vertices of a figure are labeled, their orientation (CW or CCW) is easy to identify. When they are not, it isn't always easy. It helps when the figure has no particular symmetry, as here. We can, for example, consider the sides in order from shortest to longest. That would make the orientation CCW on the left of figure A, and CW on the right. Figure A is the only figure in which the orientation changes.
CW=clockwise; CCW=counterclockwise
tan(-x) cos(-x) =
Simplify the expression
Answer:
- sin (x)
Step-by-step explanation:
hope this helps :)
Answer: tan(-x) cos(-x) = -sin(x)
Step By Step Explanation:
tan(-x) cos(-x)
Use the negative angle Identity to get:
Cos (x) (-tan(x))
Remove the parenthesis to get:
-Cos (x) tan (x)
Express with sin,cos to get:
-sin(x)
I got my explanation from www.symbolab.com
https://www.symbolab.com/solver/simplify-calculator/tan%5Cleft(-x%5Cright)%20cos%5Cleft(-x%5Cright)%20%3D?or=input
, Hope this Helps :)
Have a great day!!
Pls give me an answer with step by step explanation
Solve for Rational Inequality.
(x+3)(X+5)x+2≥0
Use the formula below to find the 10th term in the geometric sequence.
an = (-2)(3)^n-1
A. -13,122
B. -39,366
C. -118,098
D. -354,294
Answer:
uhhhh I can't explain how but the answer is B. -39,366.
hello there
I am looking for some help on this thank you.
Answer:
rational
irrational
rational
rational
irrational
rational
rational
rational
Step-by-step explanation:
irrational numbers are square roots of numbers that aren't perfect squares (creates non-repeating non-terminating decimals) and pi.
please help!
Question 8 of 10 Allowable tax deductions do not include O A. personal vacation expenses B. charitable donations O c. home mortgage interest costs O D. educational expenses
Answer:
A. Personal vacation expenses
Step-by-step explanation:
Because everything else either helps the community or is a required expense
The ages of three brothers are consecutive, even integers. If the sum of the first even integer, three times the second even integer and twice the third even integer is fifty. Find the ages of all three brothers
Answer:
The ages of all three brothers are 4,6,8 years.
Step-by-step explanation:
Here n is the smallest of the three consecutive even integers, the condition gives you this equation
2n + 3*(n+2) + (n+4) = 34.
2n + 3n + 6 + n + 4 = 34
6n = 24
n = 4.
Answer. The ages are 4, 6 and 8 years.
Hope this helps you.
The ages of the three brothers are 6, 8, and 10 years, respectively.
How to determine ages of the three brothersLet the ages of the three brothers be \(x\), \(x+2\), and \(x+4\).
The sum of the first even integer, three times the second even integer, and twice the third even integer is fifty:
\[x + 3(x+2) + 2(x+4) = 50\]
Simplify the equation:
\[x + 3x + 6 + 2x + 8 = 50\]
Combine like terms:
\[6x + 14 = 50\]
Subtract 14 from both sides:
\[6x = 36\]
Divide by 6:
\[x = 6\]
So, the ages of the three brothers are 6, 8, and 10 years, respectively.
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