The rectangular form of the given equation r= 2 / 7sinθ−cosθ which is in polar form is 7x - y = 2 and the slope-intercept form is y = 7x - 2
How to convert from polar form to rectangular form?To convert from polar form to rectangular form we simply take the following steps:
x = rsinθy = rcosθWhat is slope-intercept form?The slope-intercept form is,
y = mx +c
where m is the slope made and c is the intercept both made by the straight line.
In the given question let's first rearrange it,
r × (7sinθ − cosθ) = 2
Multiplying the term (7sinθ−cosθ) with r we get,
7rsinθ - rcosθ = 2
Now we will follow the steps discussed above which is we will put x and y respectively in place of rsinθ and rcosθ.
7x - y = 2
So, the slope-intercept form will be,
y = 7x - 2
Therefore, the rectangular form is 7x - y = 2 and the slope-intercept form is y = 7x - 2.
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Let's simplify
Remember that rsinØ is x an rcosØ=y
r=2/7sinØ-cosØr(7sinØ-cosØ)=27rsinØ-rcosØ=27x-y=2Rectangle form or slope intercept form
y=7x-2First correct answer will get Brainliest, 30 mins to answer! 25 points
Dora has three candles, which will burn for 3, 4 and 5 hours, respectively. If she wants to keep two candles burning at all times, what is the greatest number of hours she can burn the candles? (Dora has a clock that she can use to time the candles.)
Answer:
4 hours
Step-by-step explanation:
As she wants to keep two candles burning so after3 hours only 2 candles will remain and after 4 hours only one but till 4 hours 2 candles would be burning that what she wanted so its 4 hours
If Dora burns candles that burn for 4 and 5 hours, they combine to burn for 9 hours.
What are permutation and combination?Combination and permutation are two alternative strategies for organizing elements of a set into subsets in mathematics. The subset's components can be recorded in any order when combined. The components of the subset are stated in a separate order in a permutation.
Dora has three candles that will burn for 3, 4, and 5 hours, respectively.
The combination of the hours of burning,
3 + 4 = 7 hours
4 + 5 = 9 hours
3 + 5 = 8 hours
So the greatest number is 9
Thus, if Dora burns candles that burn for 4 and 5 hours, they combine to burn for 9 hours.
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A prism has total surface area of 360 m2 and volume of 60 m². If the length, width,
and height are doubled their original sizes, what will be the new volume?
o 360 m3
o 480 m
o 120 m2
o 1,620 m
Answer:
480
Step-by-step explanation:
I did the test and this is what it said in the review.
The new volume of the prism is 480 m³, option B is correct
What is Three dimensional shape?A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The total surface area of the prism is given by:
2lw + 2lh + 2wh = 360
Dividing both sides by 2, we get:
lw + lh + wh = 180
The volume of the prism is given by:
lwh = 60
Multiplying both sides by 8, we get:
8lwh = 480
Substituting 2l, 2w, and 2h for l, w, and h, respectively, we get:
(2l)(2w)(2h) = 8lwh
(2l)(2w)(2h) = 480
Simplifying, we get:
(2l)(2w)(2h) = 8lwh
8lwh = 480
Therefore, the new volume of the prism is 480 m³, option B is correct
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A kangaroo hops 2 kilometers in 4 minutes. How far can the Kangaroo hop in 10 minutes?
Answer:
5 km
Step-by-step explanation:
10/4 = 2.5
2 x 2.5 = 5
Answer:
5 Kilometers
Step-by-step explanation:
Simply divide 2 by 4 and multiply the number you get by 10.
what is the Surface area
Answer:
104
Step-by-step explanation:
PLEASE HELP MEEEEEEEEEEEEE
Find the surface area of each pyramid round to the nearest tenth if necessary
Answer:
145.9
Step-by-step explanation:
Answer: 145.9 is your answer!
Step-by-step explanation:
give the person above me Brainliest~! ✪ ω ✪
Have a great rest of your day~ ヾ(•ω•`)/
x-(-7) = -10 as an addition equation
Answer: x=-17
Step-by-step explanation:
Given
x-(-7)=-10
Expand Parenthesis (REMEMBER to change signs)
x+7=-10
Subtract 7 on both sides
x+7-7=-10-7
x=-17
Hope this helps!! :)
Please let me know if you have any questions
Combine like terms for the following expressions:
5−2x+3+8x
Answer:
6x+8 is ur answer
finding the distance from (–6, 2) to the origin. Use (0, 0) as (x1, y1). d = StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot What is the difference of the x-coordinates, (x2–x1)? What is the difference of the y-coordinates, (y2–y1)? What is the distance from (–6, 2) to the origin?
Answer:
2√10
Step-by-step explanation:
Given the coordinates (-6, 2) and (0,0)
We are to find the distance between the coordinates. Using the distance formula;
d = √(x2-x1)²+(y2-y1)²
d = √(0-2)²+(0+6)²
d = √(-2)²+(6)²
d = √4+36
d = √40
d = √4*10
d = 2√10
Hence the required distance is 2√10
Sophie invested 5,000 into an account that will increase in value by 2.3% each year. Write a function to model this situation, then find the value of the investment after 15 years
Answer:
$6725
Step-by-step explanation:
Given data
Princiapal= $5000
Rate=2.3%
Time= 15years
The function that will model this situation is given as
A=P(1+rt)
The above function is a simple interest function
Substitute our data we can find the amount A
A=5000(1+0.023*15)
A= 5000(1+0.345)
A=5000(1.345)
A=5000*1.345
A=$6725
Hence the value of the investment after 15 years is $6725
Calculate the area of a parallelogram with a 4 inch side, a 10 inch side, and 3 inches tall
Answer:
30
Step-by-step explanation:
Assuming your parallelogram looks like the one in the attached image.
The area of a parallelogram is base x height, [tex]A=bh[/tex].
The base is 10; the height is 3, so A = 10 x 3 = 30.
Answer:
30
Step-by-step explanation:
Which statement about triangles is NOT true?
The sum of the measures of the interior angles of any triangle is equal to 180°.
The sum of the measures of the interior angles of any triangle is equal to 360°
All triangles have at least 2 acute angles.
An isosceles triangle has two equivalent angles.
BEST ANSWER GETS BRAINLIEST
Answer:
I believe the second is wrong
Kahn starts a savings account with$14. He will put in an equal amount each week. After 7 weeks, he will have $56.
Rate of change per week_____
Initial value_____?
Help please
Answer:
The rate of change per week is $6.
Step-by-step explanation:
56 - 14 = 42
42/7 = $6
6 dollars were added each week.
The price of gas went up by 0.5% last month.
Suppose gas currently costs $2.44 a gallon.
If the price of gas continues to increase at this rate, what will it cost on year from now?
If price of gas went up by 0.5% last month. Suppose gas currently costs $2.44 a gallon. If the price of gas continues to increase at this rate then 2.5864 cost on year from now
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
0.5% convert to decimal
0.5/100=0.005
We need to calculate what is 0.5 percentage of 2.44.
0.005×2.44=0.0122
The cost increases after one year i.e is twelve months.
0.0122×12=0.1464
Now add 0.1464 with 0.0122
2.44+0.1464
Two point five eight six four.
=2.5864
Hence 2.5864 is the price of gas after one year.
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write the slope-intercept form of the equation of the line trough the given point with the given slope.
trough : (1, -4), slope= -8
A.y=8x+4
B.y=-8x+4
C.y=4x+8
D.y=3x+8
Given:
Point = (1,-4), Slope - 8
Point = (1,5), Slope =1
To find:
The slope-intercept forms of the given lines.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
The point slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
where, m is the slope of the line.
We have, Point = (1,-4), Slope - 8. So, the equation of the line is:
[tex]y-(-4)=-8(x-1)[/tex]
[tex]y+4=-8x+8[/tex]
[tex]y=-8x+8-4[/tex]
[tex]y=-8x+4[/tex]
Therefore, the correct option is B.
We have, Point = (1,5), Slope =1. So, the equation of the line is:
[tex]y-5=1(x-1)[/tex]
[tex]y-5=x-1[/tex]
[tex]y=x-1+5[/tex]
[tex]y=x+4[/tex]
Therefore, the correct option is D.
Please help, I am extremely bad at graphing.
HELPPP QUICK PLS I WOULD GIVE YOU THE BRAINIEST PLSSS HELPP MEEE BEFORE I HAVE A BREAKDOWN PLS What is the midpoint of a line segment with endpoints at (-4,15) and (22, 3)?
Answer:
(5.5, 12.5) OR (11/2, 25/2)
I would put in the decimal value as the answer, but of you like then you can add the fraction as an answer.
Step-by-step explanation:
We are given the endpoints (-4, 15) and (22, 3) to find the midpoint. In order to find the midpoint, we will use its formula.
Midpoint formula :- (x1 + x2 / 2, y1 + y2 / 2)
(x1 + x2 / 2, y1 + y2 / 2)
(-4 + 15 / 2, 22 + 3 / 2)
(11 / 2, 25 / 2) ---> (5.5, 12.5) Midpoint
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(50 POINTS) Math Inverse Functions please help
Answer:
See below.
Step-by-step explanation:
a. See pic below.
b. Yes because it passes the vertical line test. Any vertical line moving horizontally across the graph intersects only one point on the graph at a time.
c.
Domain: all real numbers
Range: all real numbers greater than or equal to 4
d.
Domain: all real numbers greater than or equal to 4
Range: all real numbers
e.
See pic below.
f. No because it does not pass the vertical line test.
I need a good answer and an explanation, please
Answer:
2,10
Step-by-step explanation:
we can see where the line touches the x-axis but right at the line making the points have a 0 as the y, (2,0) and (10,0) the others have don´t have 0 in the y place. To make it short there are 2 points touching the x-axis, not above or below but on the line.
Triangle ABC is a right triangle. The lengths of the legs are 60 centimeters and 80 centimeters. What is the length, in centimeters, of the hypotenuse?
Answer:
100 cm
Step-by-step explanation:
Given:
a = 60
b = 80
a² + b² = c²
60² + 80² = c²
3600 + 6400 = c²
c² = 10000
[tex]\sqrt{c^2} =\sqrt{10000}[/tex]
c = 100
Answer
100 cm
Step-by-step explanation:
<3
Points just solve 2 + 3 <3
Answer:
5
Step-by-step explanation:
Thank you <3 :)
help fast and thank you please no files
Answer:
8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
2x+2.5y = 34
x+y = 15
0.5y = 4
y=8
What is the solution to this system of equations?
Answer:
(2, 6).
Step-by-step explanation:
The solution is the ordered pair where the 2 lines intersect.
Answer:
(2, 6)
Step-by-step explanation:
Take a look at the graph.
The problem has rather helpfully graphed out the two equations presented to us, and the point in which both lines intersect is (2, 6), making this pair your solution.
If you'd like to check, plug in the corresponding variables.
x = 2
y = 6
First equation:
y = x + 4
6 = 2 + 4
6 = 6
The equation is true.
Second equation:
y = -0.5x + 7
6 = (-0.5 x 2) + 7
6 = -1 + 7
6 = 6
This equation is true as well.
Please inform me of any mistakes.
Find the volume of a right circular cone that has a height of 19.4 cm and a base with a diameter of 9.9 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer:
V = 497.8 cm^3
Step-by-step explanation:
Thats Righttt
The volume of the cone is 1592.6 cm³
What is volume?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The right circular cone's vertex is immediately above the base's centre. The line connecting the vertex with the centre point of the base is perpendicular to the cone's radius. A cone, on the other hand, can have its vertex anywhere.
Given that, a right circular cone with the height of 19.4 cm and a base with a diameter of 9.9 cm. we need to find the volume,
Volume of cone = 1/3 × π × radius² × height
= 1/3 × 3.14 × (9.9/2)² × 19.4
= 1592.6 cm³
Hence, the volume of the cone is 1592.6 cm³
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If you take my son’s age and multiply it by one and a half times his age you get 24. How old is my son?
Answer:
3/2x=24
X=48/3
X=16
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please please help asap and show the work! no links
hello
the angles make up co-interior so the two would add up to 180º.
so we can set up a basic equation:
3x-10+5x-30=180
add like terms:
8x-40=180
add 40 to both sides:
8x=220
divide by 8
x=27.5º
hope this helps and have a good day :)
Find the surface area of the cone in terms of pie
Answer:
SA = 80π
Step-by-step explanation:
SA = πr² + πr·slant height
A can of tuna fish has a height 1inch and the diameter of 3inches how many square inches of paper are needed for the label? How many square inches of metal are needed to make the can including the top and bottom. Round your answer to the nearest whole number use 3.14 for it
Answer:
9.4
Explanation:
Solve for perimeter to find how long the label is
2(3.14)(1.5)
What is the directrix of the parabola with the following equation?
(y - 1)2 = -4(x - 1)
Answer:
x = 2
Step-by-step explanation:
If side 1 is 13, side 2 is 12, and side 3 is 18, can a triangle be made?
Answer:
no
Step-by-step explanation: