Answer:
y = 1/3 x + 5/3
Step-by-step explanation:
For rectangular to polar
x = rcosθ ... 1
y = rsinθ ... 2
Given the expression
r=5/3sinθ−cosθ
Cross multiply
r(3sinθ−cosθ) = 5
Expand
3rsinθ−rcosθ = 5 ..3
Substitute 1 and 2 into 3
3y - x = 5
Write in slope intercept form
3y = x + 5
Divide through by 3;
3y/3 = x/3 + 5/3
y = x/3 + 5/3
y = 1/3 x + 5/3
Hence the expression in slope-intercept form is y = 1/3 x + 5/3
question 2.
the center of a circle is located at (5,2) and a point in the circle is (-3,4) what is the radius of the circle?
Answer:
ss
Step-by-step explanation:
sas
The radius of the circle who center is at ( 5 , 2 ) and the point on the circle is ( -3 , 4 ) is given by r = 2√17 units
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be r
Let the center of the circle be A ( 5 , 2 )
Let the point on the circle be P ( -3 , 4 )
Now , standard form of a circle is
( x - h )² + ( y - k )² = r²
So , r² = ( 5 - ( -3 ) )² + ( 2 - 4 )²
On simplifying the equation , we get
r² = ( 8 )² + ( 2 )²
r² = 64 + 4
r² = 68
Taking square roots on both sides , we get
r = √68
r = 2√17
Hence , the radius of the circle is 2√17 units
To learn more about circle click :
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Find the x...............
Answer:
Step-by-step explanation:
Remark
You are going to use the Pythagorean Theorem. The trick is to find the length of the leg making up the base of the triangle.
That base is equal to the difference between the two bases.
Solution
The base of the triangle = 2x + 1 - (x + 3) Remove the brackets.
base = 2x + 1 - x - 3
base = x - 2
Now the height of the trapezoid is also the second leg of the triangle. Apply the Pythagorean Theorem.
c^2 = a^2 + b^2
a = x - 2
b = x + 4
c = 2x
4x^2 = (x - 2)^2 + (x + 4)^2 Expand the brackets
4x^2 = x^2 - 4x + 4 + x^2 + 8x + 16 Collect like terms
4x^2 = 2x^2 + 4x + 20 Subtract the right side from the left.
4x^2 - 2x^2 - 4x - 20 = 0
2x^2 - 4x - 20 = 0 Divide by 2
2x^2/2 - 4x/2 - 20/2 = 0
x^2 - 2x - 10 = 0
x = - b +/- sqrt(b^2 - 4*a*c)/ 2a
a = 1
b = - 2
c = - 10
x = (- -2 + / - sqrt((-2)^2 - 4*(1)*(-10) ) / 2
x = (2 + / - sqrt(4 + 40 ))/2 Only the plus root has any meaning.
x = ( 2 + sqrt(44 ) )/2
x = ( 2 + 2*sqrt(11) ) / 2
x = 1 + sqrt(11)
sqrt(11) = 3.3166
x = 1 + 3.3166
x = 4.3166
Given JKL: XYZ, find x.
Answer:
is there a pic to go along? i need more to this..
Solve 2 ≤ 2x + 4 < 10 for x.
–1 ≤ x < 3
1 < x < 3
–1 < x < 3
1 ≤ x < 3
Answer:
-1 ≤ x < 3
Step-by-step explanation:
2 ≤ 2x + 4 < 10
Subtract 4 from all sides
2-4 ≤ 2x + 4-4 < 10-4
-2 ≤ 2x < 6
Divide all sides by 2
-2/2 ≤ 2x/2 < 6/2
-1 ≤ x < 3
What is the solution to the system of equations?
Answer:
ans: D
Step-by-step explanation:
suppose
y = 3x +1 be equation••••••1
and
y = -2x - 4
-y= 2x + 4 be equation ••••••2
add equation 1 and 2 as
y = 3x + 1
-y = 2x + 4
0 = 5x + 5
so ,
5x = - 5
x = - 1
put x In either equation 1 or 2 to get y= - 2
OR,
since given equation intersects each other ,
use substitution method ,
Answer:
D
Step-by-step explanation:
The solution to a system of equations given graphically is at the point of intersection of the 2 lines.
The lines intersect at (- 1, - 2 ) ← solution → D
Please give a real answer.
No Docs/No files/No link
I will rate a 5-star and give the brainiest.
Answer:
3.5 m
Step-by-step explanation:
PQ = 5/(5+5) × 7
= 5/10 × 7
= 3.5 m
SOMEBODY PLEASE HELP
Answer:
x=40
Step-by-step explanation:
1/5x=8
x=8*5=40
x=40
Help me to do this set question
CAN SOMEONE HLEP ME OUT WITH THIS PLEASE AND THANK YOU
Answer:
12 5/24 thats the answer
Step-by-step explanation:
use this website for mixed number calculator: https://www.calculatorsoup.com/calculators/math/mixednumbers.php
3
If f(x) =
x
-VX-3, complete the following statement:
X + 2
than or equal to
The domain for f(x) is all real numbers.
3.
Answer here
SUBMIT
Answer:
Greater
Step-by-step explanation:
Because x-3 must be greater or equal zero and x must be not equal -2
Pls help me with this equation
Answer:
x = 20
Step-by-step explanation:
Given BD = CD then Δ BCD is isosceles and the 2 base angles are congruent
∠ CBD = ∠ BCD = 40° , then
∠ BDC = 180° - (40 + 40)° = 180° - 80° = 100° ← sum of angles in triangle
Sum the 3 angles of Δ ACD and equate to 180
20 + 100 + x + 40 = 180
160 + x = 180 ( subtract 160 from both sides )
x = 20
If x=9/4, then prove that(x root x)^x= x^x root x
Will give Brainliest...
Answer:
√x-9=4
square on both sides
x-9=4*4
x-9=16
x=16+9
x=25
.
.hope it helps
plz mark as brainliest
[tex]( {x \sqrt{x} })^{x} = {x}^{x \sqrt{x} } [/tex]
[tex]\large\mathfrak{{\pmb{\underline{\purple{Step-by-step\:explanation}}{\purple{:}}}}}[/tex]
Let us first solve for L. H. S.
Substituting the value [tex]x\:={ \frac{9}{4} } [/tex], we have
➼[tex]\:( { \frac{9}{4} \sqrt{ \frac{9}{4} } })^{ \frac{9}{4} } [/tex]
➼[tex] \: ({ \frac{9}{4} \sqrt{ \frac{( {3})^{2} }{( {2})^{2} } } })^{ \frac{9}{4} } [/tex]
➼[tex] \: ({ \frac{9}{4} \times \frac{3}{2} })^{ \frac{9}{4} } [/tex]
➼[tex] \: ( { \frac{3 \times 3 \times 3}{2 \times 2 \times 2} })^{ \frac{9}{4} } [/tex]
➼[tex] \: ({ \frac{ {3}^{3} }{ {2}^{3} } })^{ \frac{9}{4} } [/tex]
➼[tex] \: ({ \frac{3}{2} })^{ \frac{9 \times 3}{4} } [/tex]
➼[tex] \: ({ \frac{3}{2} })^{ \frac{27}{4} } [/tex]
Now let us find R. H. S.
➺[tex]\: {x}^{x \sqrt{x} } [/tex]
➺[tex]\: { \frac{9}{4} }^{ \frac{9}{4} \sqrt{ \frac{9}{4} } } [/tex]
➺[tex] \: ( { \frac{ {3}^{2} }{ {2}^{2} } })^{ \frac{9}{4} \sqrt{ \frac{ {3}^{2} }{ {2}^{2} } } } [/tex]
➺[tex] \: ({ \frac{3}{2} })^{ 2 \times \frac{9}{4} \times \frac{3}{2} } [/tex]
➺[tex] \: { \frac{3}{2} }^{ \frac{54}{8} } [/tex]
➺[tex] \: ( { \frac{3}{2} })^{ \frac{27}{4} } [/tex]
Since L. H. S = R. H. S
➝[tex] \: ({ \frac{3}{2} })^{ \frac{27}{4} } =( { \frac{3}{2} })^{ \frac{27}{4} } [/tex]
[tex]\boxed{Hence\:proved.}[/tex] ✔
[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]
I need help it says which of the following function is graphed below
Answer:
D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The right part of the function is a line and its equation must be linear (the exponent of the x must be 1)
The lines start at x = 1. We can say that because there is a black dot
the x of the second function keep decreasing
Thanks to these informations we can say that the answer is D
What's the Area of the Rectangle, Triangle and the entire shape?
Answer:
Rectangle = 48 un²
Triangle = 12 un²
Total = 60 un²
Step-by-step explanation:
Area rectangle = 8 x 6 = 48 un²
Area triangle = 1/2 ( 6 x 4) = 1/2 ( 24 ) = 12 un²
Total = 48 un² + 12 un² = 60 un²
To check the total area, find the area of the trapezoid:
1/2 ( 8 + 12) * 6 =
(20 * 6)/2 =
120 / 2 = 60
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
What is the answer to -4 + 10.
Negative 4 plus 10
Answer:
Six
Step-by-step explanation:
10 - 4 = 6
-4 + 10 = 6
Answer:
6
Step-by-step explanation:
[tex] - 4 + 10 = 6[/tex]
6
What is the solution of the following quadratic function?
A rectangle has an area of 40 square units. The length is 6 units greater than the width. What are the dimensions of the rectangle?
Answer:
[tex]W=2.58 unit[/tex]
[tex]L=15.5 unit[/tex]
Step-by-step explanation:
From the question we are told that:
Area [tex]A=40[/tex]
Equation
Length [tex]L=6LW[/tex]
Generally the equation for Area of a rectangle is mathematically given by
[tex]A=L*W[/tex]
[tex]A=W*(6W)[/tex]
[tex]A=6W^2[/tex]
[tex]W=\sqrt{40/6}[/tex]
[tex]W=2.58 unit[/tex]
Therefore Length is
[tex]L=6W[/tex]
[tex]L=6(2.58)[/tex]
[tex]L=15.5 unit[/tex]
Length = 10
Width = 4
The dimensions of the rectangle would be 10 by 4.
What is the answer to this question?
Answer:
32
Step-by-step explanation:
[tex]g(13) = 16 \\ f(16) = 32[/tex]
If the average, mode, and range of 5 different numbers are all 8, find the sum of all possible values of the second largest number.
I believe you meant:
If the average, mode, and range of 5 different numbers are all 8, find the sum of all possible values and the second largest number
Answer:
Sum of all possible values = 40
Second largest number= 8
Explanation:
Since our mean, mode, and range is 8, our sum is 40 and our second largest number is 8.
The sum of all the numbers is 40 since our mean is 8 and there are 5 numbers(8×5)
To find possible values, we already know the mode is 8 and so we know 8 must appear more than once. If we have 8 twice then we are left with 24(sum is 40). We have 3 numbers left and the range is 8 so we must have a maximum number and minimum number that has a difference of 8 and a third number, all adding up to 24(sum left). Within 24, only 12-4+8 satisfies the condition, hence our numbers are: 4,8,8,8,12.
‼️‼️‼️‼️HELPP‼️‼️‼️‼️
Answer:
I can't see the small numbers.post it again
Step-by-step explanation:
if y is inversely proportional to 2x + 1 and the difference in the values of y when x= 0.5 and x= 2 is 0.9, find the value of y when x = -0.25
Answer:
6
Step-by-step explanation:
answer is in photo above
Divisibility rules for 2, 5, and 10
Which numbers are divisible by 10?
A)222
B)185
C)847
or none of these
Answer:
none of these
Step-by-step explanation:
A number is divisible by 10 if the last digit of the number is 0. The numbers 20, 40, 50, 170, and 990 are all divisible by 10 because their last digit is zero, 0.
m^(2)-n^(2)+6n-9
Please factor this out completely and help me
Answer:
m^2-n^2+6n-9
m^2-6n^2-9
I am going to bye a three bags of plums and the cost of the plums are $4000 but I only have $300 how many more money do I need
well...
if all three bags cost $4,000 then you'll need $3,700.
but if one bag costs $4,000 then that'll equal to $12,000 which then you'll need $11,700.
i might've misundestood your question so please let me know if this is correct!
Can someone help me out with this at all?
Answer:
1 maps to 1
2 maps to 3
3 maps to 2
Step-by-step explanation:
the correctly assigned answer options describe everything.
there is not much else to say and explain.
these are all true statements due to the symmetry principle of a circle.
when 2 direct connections of two points on the circumference of a circle have the same length, then also their bent distances on the circumference of the circle are the same. and vice versa.
and yes, the perpendicular radius (or diameter) of the circle towards such a line cuts this line in half.
one fifth of the sum of four and m
Answer:
[tex]\frac{1}{5\/}[/tex](4+m)
Step-by-step explanation:
[tex]\frac{1}{5\/}[/tex](4+m)
Hope this helps!
B
47°
F
G
A
C
20
J
H Н
Answer:
FGAC 20 JH Н
Step-by-step explanation:
FGAC 20 JH Н
Marking brainliest need help
I’m purchasing tickets that are $40.00 but I have a discount which is 35% off. How much will I pay with that discount?
Answer:
26 ShillingStep-by-step explanation:
The amount to be paid = The new price
where;
New price = (100-x)/100 * Original price
Original price = 40.00
x = discount
Placing in formula100-35/100 * 40.00
65/100 *40
26 shilling
Therefore the amount you will pay for the discount is 26 shillingSomebody asked a teacher how many students do you have? I would like to send my son to your school The teacher asnwered if as many students as i have now join my school and half as many as i have join it and quarter as many and your boy comes to study with me as well i will have excactly 100 students
Answer:
So whats the question?
2 more after this help
Answer:
y = 1x-5
Step-by-step explanation:
We know two points so we can find the slope
(0,-5) and (5,0)
m = ( y2-y1)/(x2-x1)
= ( 0 - -5)/(5-0)
(0+5)/(5-0)
5/5
=1
We know the y intercept = -5
The slope intercept form is y = mx+b where m is the slope and b is the y intercept
y = 1x-5