Answer:
[tex]r=4\csc \theta \cot\theta[/tex]
Step-by-step explanation:
The given parametric equations are;
[tex]x=t^2[/tex]
[tex]y=2t[/tex]
We make t the subject in the second equation to get:
[tex]t=\frac{y}{2}[/tex]
We substitute into the first equation to get:
[tex]x=(\frac{y}{2})^2[/tex]
We use the relation:
[tex]x=r\cos \theta[/tex] and [tex]y=r\sin \theta[/tex]
[tex]r\cos \theta=(\frac{r\sin \theta}{2})^2[/tex]
[tex]r\cos \theta=\frac{r^2\sin^2 \theta}{4}[/tex]
[tex]r=4\csc \theta \cot\theta[/tex]
An equation is formed of two equal expressions. The polar form of parametric equations x=t² and y=2t is r = 4cosecθ cotθ.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The following parametric equation x=t² and y=2t in the form of a polar equation can be written as,
y=2t
t = y/2
Substituting the value of y from the second equation in the first,
x = (y/2)²
Using the basic relation we can write, the value of x and y as,
x = r cosθ
y = r sinθ
substitute the value of x and y,
r cosθ = [(r sinθ)/2]
r sinθ = (r²sin²θ)/4
r = 4cosecθ cotθ
Hence, the polar form of parametric equations x=t² and y=2t is r = 4cosecθ cotθ.
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which parallel lines statement is true for the figure
Without a specific figure, it's not possible to definitively answer which parallel lines statement is true. However, parallel lines are equidistant and never meet, contrasting with mutually perpendicular lines, which intersect at right angles.
Explanation:Given the various contextual clues from the fragments presented, it seems that the question concerns the properties of parallel lines and their behavior in a geometric or physical context, possibly relating to vectors, navigation, or electrical currents. However, without a specific figure or more detailed information, it's not possible to accurately determine which statement is true regarding the parallel lines in the figure.
For parallel lines, we know that they are equidistant from each other at all points and will never meet, no matter how far they are extended. This trait could relate to the x-axis alignment if we assume the lines are coplanar. On the other hand, if lines are mutually perpendicular, they will intersect at right angles to each other and therefore are not parallel.
D) AB is parallel to CD.
To understand why this statement is true, let's analyze the properties of a trapezium and the given figure.
A trapezium is a quadrilateral with one pair of parallel sides. In this case, AB and CD are the sides of the trapezium.
Looking at the given figure, we can see that AB is the upper side and CD is the base of the trapezium. Since AB and CD are not intersecting each other and are on opposite sides of the trapezium, they must be parallel to each other.
Therefore, the correct parallel lines statement is that AB is parallel to CD.
To summarize:
- AB and CD are the sides of the trapezium.
- AB is the upper side and CD is the base.
- AB and CD are not intersecting and are on opposite sides of the trapezium.
- Therefore, AB is parallel to CD.
to determine a student's grade, a teacher throws out the lowest grade obtained on 5 tests, averages the remaining grades, and round up to the nearest interger. If Betty scored 75,90,88,72,and86 on her tests, what grade will she receive
Answer:
B grade
Step-by-step explanation:
75 + 90 + 88 + 86 = 339
339/4 = 84.75
Grade B = 80-89%
Answer:
Betty will get 85 grade.
Step-by-step explanation:
Betty scored 75,90,88,72, and 86 on her tests.
As given the teacher throws out the lowest grade, we will not consider 72.
Now the teacher averages the remaining grades, and round up to the nearest integer.
So, taking the average we get;
[tex]\frac{75+90+88+86}{4}[/tex]
= 84.75
Rounding this to nearest integer, we get 85.
Hence, Betty will get 85 grade.
Cassie bought 300 shares of CAB Inc. stock and later sold them for a $500 profit. What type of income did she have?
Select the best answer from the choices provided.
A.
dividend income
B.
stock options
C.
capital gains
D.
equity income
Answer:
Hi,
The correct answer option is C. capital gain.
Step-by-step explanation:
Divided is the money a company pays to its shareholders every year after calculating the profits. A company can decided to distribute its earnings to the shareholders from the stock owned by the members.This income is called the divided income.When this income is specifically from stock divided, its called equity income.When Cassie sold the shares for a higher profit, she obtained a capital gain.The two main ways investors can get returns from stock are through divided and capital gains.
Best of Luck!
help ive been trying for hours and i keep getting it wrong. so i will give the person 20 points if you do it
5- 25
4- 20
2- 10
please give brainliest if correct
What is the area of this rectangle?
10 units
20 units
24 units
48 units
The correct answer will get branliest :)
Answer:
The area is A = L * W = 24 units^2
Step-by-step explanation:
The width (measured horizontally) is (7 - 3), or 4 units. The height (measured vertically) is (8 - 2), or 6 units.
The area is A = L * W = (6 units)(4 units) = 24 units^2.
Answer:
24^2
Step-by-step explanation:
Given the volume of Figure A is 512cm ^3and Figure B is 343cm^3, find the ratio of the perimeter from Figure A to Figure B.
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{\textit{figure A}}{\textit{figure B}}\qquad \qquad \cfrac{s}{s}=\cfrac{\sqrt[3]{512}}{\sqrt[3]{343}}\qquad \begin{cases} 512=&2^9\\ &2^{3\cdot 3}\\ &(2^3)^3\\ 343=&7^3 \end{cases}\implies \cfrac{s}{s}=\cfrac{\sqrt[3]{(2^3)^3}}{\sqrt[3]{7^3}} \\\\\\ \cfrac{s}{s}=\cfrac{2^3}{7}\implies \cfrac{s}{s}=\cfrac{8}{7}\implies s:s = 8:7\impliedby \textit{ratio of the }\stackrel{sides~and}{perimeters}[/tex]
The sum of the digits of a 2-digit number is 1. What is the number?
Answer:
The number is 10
I can’t do it rn so just dm me later
Determine ƒ(a + h) for ƒ(x) = 2x3.
Answer:
see explanation
Step-by-step explanation:
To evaluate f(a + h) substitute x = a + h into f(x)
f(a + h)
= 2(a + h)³
= 2( a³ + 3a²h + 3ah² + h³ ) ← distribute
= 2a³ + 6a²h + 6ah² + 2h³
A function is a relation that gives single output on single input The value of the substitute function f(a + h) for the function f(x) = 2x³ will be 2a³ + 6a²h + 6ah² + 2h³.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
As per the given function,
f(x) = 2x³
Substitute x → a + h
f(a + h ) = 2(a + h)³
It is known that (a + b)³ = a³ + b³ + 3a²b + 3ab².
Therefore,
f(a + h ) = 2[a³ + h³ + 3ah² + 3a²h]
f(a + h ) = 2a³ + 2h³ + 6ah² + 6a²h
Hence "A function is a relation that gives single output on single input The value of the substitute function f(a + h) for the function f(x) = 2x³ will be 2a³ + 6a²h + 6ah² + 2h³".
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Simplify -20b^8 + 2b^8
Answer:
Step-by-step explanation:
Answer:
-18b^8.
Step-by-step explanation:
To simplify an expression, we combine the elements that are similar (look the same).
So, it we have -20b^8 + 2b^8, we see that there are 2 terms with b^8. We need to simplify them.
So, we have -20b^8 + 2b^8, that addition leaves -18b^8.
-18b^8 cannot be simplified more.
Two coins are flipped. What is the probability that both of the coins land on heads up
Answer:
0.25, 25%, or 1/4
Step-by-step explanation:
There are two possibilities for each coin: heads or tails. So the chance of getting heads for the first flip is 50%, or 1/2. To find the probability for both, you multiply 1/2*1/2 and get 1/4.
The probability that both of the coins land on heads up when two coins are flipped is 1/4. This can be obtained by obtaining the possible outcomes and using formula for probability.
What is the formula of Probability?The formula of Probability is,
P= number of favorable outcomes/ total number of outcomes
Calculate the probability for the question:When two coins are flipped the possible outcomes are,(H,H), (H,T), (T,H), (T,T), that is, the total number of outcome is 4.
The outcome where both of the coins land on heads up is (H,H),that is, the number of favorable outcome is 1.
Thus the probabilty is, P(both coins heads up)=1/4Hence the probability that both of the coins land on heads up when two coins are flipped is 1/4.
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what is
the sum of the distance,d, times 8 and 5
I think the answer is 40
I think it’s 8d+5.
Help me answer this question please
Answer:
The answer would be 74.
Step-by-step explanation:
g(-4)=-4(-4)+7
g(-4)=16+7
g(-4)=74
f(23)=3(23)+5
f(23)=74
(fog)(-4)=74
Answer:
The answer is 74.
here's how to solve the equation
g(-4)=-4(-4)+7
g(-4)=16+7
g(-4)=74
f(23)=3(23)+5
f(23)=74
(fog)(-4)=74
hope this helps
Write the equation of a line in slope intercept form that has a slope of 1/5 and contains (-10,6)
Answer:
y = [tex]\frac{1}{5}[/tex] x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{1}{5}[/tex], hence
y = [tex]\frac{1}{5}[/tex] x + c ← is the partial equation
To find c substitute (- 10, 6) into the partial equation
6 = - 2 + c ⇒ c = 6 + 2 = 8
y = [tex]\frac{1}{5}[/tex] x + 8
Which are right triangles that can be formed using a diagonal through the interior of the cube? Select all that apply.
A) Triangle CEG
B) Triangle AEH
C) Triangle CFG
D) Triangle BCH
E) Triangle BFG
F) Triangle DEG
Answer:
triangle AEH, triangle CFG, triangle BFG, and triangle DEG.
so b,c,e,f
this is right for e2020.
The right triangles that can be formed using a diagonal through the interior of the cube are A) Triangle CEG, B) Triangle AEH and C) Triangle CFG
Which are right triangles that can be formed using a diagonal through the interior of the cube?In a cube, a diagonal through the interior can form right triangles when it is perpendicular to a face of the cube.
Based on this, the right triangles that can be formed are:
A) Triangle CEG (since CE is perpendicular to face CDEG)
B) Triangle AEH (since AE is perpendicular to face ABCD)
C) Triangle CFG (since CF is perpendicular to face ABCD)
D) Triangle BCH (since BC is perpendicular to face CDEG)
So, the correct options are A, B, C, and D.
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Plz help me with this
Answer: Observational study
observational studies
How many points are contained on a line
Answer:
If you are talk about a line segment, it would contain two points.
If your talking about a ray, it would contain 1 point.
If your talking about just the line, it would contain no points.
Step-by-step explanation:
When jack bought his new truck, there were 96 different ways his truck could be equipped. He had four choices of engines and two choices of transmissions. If only other choice was color, how many colors were available?
To Find all the different ways the truck could be, you would mutiply all the choices together.
There were three different choices.
Multiply the two known ones together than divide the total different ways by that to find the third choice.
4 x 2 = 8
96 / 8 = 12
There are 12 colors available.
Answer:
There are 12 colors available
Step-by-step explanation:
We have product rule which states that if there are [tex]n_{1}[/tex] ways of doing one task, and [tex]n_{2}[/tex] ways of doing another task then there [tex]n_{1}n_{2}[/tex] ways of doing the tasks together.
Let us assume that there are x choices for colors
so we have 4 ways of selecting engines , 2 ways of selecting transmissions and x ways of selecting colors
number of ways of truck could be equipped = [tex]4*2*x[/tex]
= [tex]8x[/tex]
it is given that number of ways truck could be equipped= [tex]96[/tex]
so we have
[tex]8x= 96[/tex]
[tex]x=\frac{96}{8}[/tex] ( divide both side by 8)
[tex]x= 12[/tex]
There are 12 colors available
Solve the equation for x by graphing -4x+1=3x-4
A x=0.75
B x=0
C x=-0.75
D x=-1.75
The equation for x by graphing -4x+1=3x-4 is x=0.75.
What is the equation for x by graphing -4x+1=3x-4?Given:
The equation is given as -4x+1=3x-4.Find:
The value of x.Solution:
We will solve the given equation
The Given equation is -4x+1=3x-4.
Now, add 4x on both sides of the equation, and we get;
-4x+1+4x = 3x-4+4x
1 = 7x-4
Now, add 4 on both sides of the equation, and we get;
1+4 = 7x-4+4
5=7x
Now, x =5/7 = 0.714 ≅ 0.75
Hence, the equation for x by graphing -4x+1=3x-4 is x=0.75.
Therefore, Option A is the correct answer.
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What is the value of X?
Answer: x=8
Step-by-step explanation: Since we know that segment AB and BC are the same measure indicated by the black lines running perpendicular to the lines in triangle themselves, we know that angle A and angle C are the same measure. This means we know this equation... Solve this to complete step 1...
69°=(9y-3)°
If you solve for y, you should get 8. This means that y=8. In knowing that a triangle's interior angles add up to 180°, we know that Angle B must be... Solve this equation for step 2...
∠B=180°-(∠A+∠C)
If you solve to find angle B, you should get that ∠B=42°. Knowing this, we can set up another equation similar to that in step 1 (when we found y knowing the angle) to find x... Solve this equation for your third and final step...
42°=(5x+2)°
If done step 1 through 3 correctly, you should get x to be equal to... and the final answer... x=8
You can rent time on computers at the local copy center for a $6 setup charge and an additional $5.50 for every 10 minutes. How much time can be rented for $21?
21$ is the start.
You need to take 6$ off because of the setup charge.
21-6= 15$ left
Every 10 minutes costs $5.50 so you need to divide 5.50 from 15 and multiply that answer by 10. 20 minutes can be rented. with 4$ left
What is the value of y in the following system of linear equations
2x+2=y
Answer:
y = 12
Step-by-step explanation:
Given the 2 equations
2x + 2 = y → (1)
2y = 5x - 1 → (2)
Substitute y = 2x + 2 into (2)
2(2x + 2) = 5x - 1
4x + 4 = 5x - 1 ( subtract 4x from both sides )
4 = x - 1 ( add 1 to both sides )
x = 5
Substitute x = 5 into (1) for corresponding value of y
y = (2 × 5) + 2 = 10 + 2 = 12
Answer:
y=12
Step-by-step explanation:
look this solution :
Question 5 J, please provide each step
Answer:
x = [tex]\frac{12}{5}[/tex]
Step-by-step explanation:
Multiply all terms in the equation by the lowest common multiple of 3 and 5, that is 15. This will eliminate the fractions in the equation
10(1 - 2x) - 30x = - 6 + 20(2 - 3x) ← distribute and simplify both sides
10 - 20x - 30x = - 6 + 40 - 60x
10 - 50x = 34 - 60x ( add 60x to both sides )
10 + 10x = 34 ( subtract 10 from both sides )
10x = 24 ( divide both sides by 10 )
x = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]
5. What is the slope of the line ?
Answer:
it is 2/3
Step-by-step explanation:
5hr = how many days
Answer:
Step-by-step explanation:
the day is going to be one because you can't covert hours to days. If it said 24 hours only many days? then the answer will be one because a new day has started.
(if you don't understand then comment)
At miles, the cost for both trucks would be $ .
The cost of the truck rentals will be the same at 200 miles
How to determine the miles when the cost will be the same
From the question, we have the following parameters that can be used in our computation:
Company 1: 39.95 + 0.45x
Company 2: 59.95 + 0.35x
When the costs are equal, we have
39.95 + 0.45x = 59.95 + 0.35x
Evaluate the like terms
So, we have
0.1x = 20
Divide both sides by 0.1
x = 200
This means that the number of miles is 200
Question
two companies rent moving trucks. pack and go charges $39.95 flat fee and $0.45 for every mile driven. U-drive charges $59.95 flat fee and $0.35 for every mile driven.
At how many miles is the cost of the truck rentals the same
The function f(x)=x^2+4.2x+3.6 has an axis of symmetof x=-2-. What is the minimum value of the function
ANSWER
The minimum value is -0.8
EXPLANATION
The given
[tex]f(x)=x^2+4.2x+3.6[/tex]
The minimum value is the y-value of the vertex (minimum point).
To find the minimum value of the function, we substitute x=-2 into the function to get;
[tex]f( - 2)=( - 2)^2+4.2( - 2)+3.6[/tex]
[tex]f( - 2)=4 - 8.4+3.6 = - 0.8[/tex]
The minimum value is -0.8
How many cubes with sides length of 1/2 cm does it take to fill the prism
Answer:
40 cubes
Step-by-step explanation:
We need to determine the volume of the cuboid.
[tex]Volume=lbh[/tex]
We substitute the given dimensions l=2.5cm,w=2cm and h=1cm.
[tex]Volume=2.5\times2\times1cm^3[/tex]
[tex]Volume=5cm^3[/tex]
The volume of the cube is [tex]Volume =(\frac{1}{2})^3=\frac{1}{8} cm^3[/tex]
We need to divide the volume of the cuboid by the volume of the cube to get the number of cubes that can fill it;
[tex]\frac{5}{\frac{1}{8} }=8\times 5=40[/tex]
Two cyclists left simultaneously from cities A and B heading towards each other at constant rates and met in 5 hours. The rate of the cyclist from A was 3 mph less than the rate of the other cyclist. If the cyclist from B had started moving 30 minutes later than the other cyclist, then the two cyclists would have met 31.8 miles away from A. What is the distance between A and B, in miles?
Answer:
73.92 miles
Step-by-step explanation:
Formula for calculating distance = speed × time
Rate/speed of cyclist from city A = ( x - 3 ) mph , Time Taken = 5 Hours
Rate/speed of cyclist from city B = x mph
If Cyclist from B had started moving 30 minutes later
Time Taken by cyclist from B = 4.5 Hours
If B had started 30 minutes later, then the two cyclist would have met 31.8 miles from A.
distance covered by cyclist from A = 31.8
Solution:
For city A:
distance = speed × time
31.8 = ( x - 3 ) × 5 ⇒ [tex]\frac{31.8}{5}[/tex] = x - 3
6.36 = x - 3 ⇒ x = 6.36 + 3 ⇒ x = 9.36 mph
For city B:
distance = speed × time
= 9.36 × 4.5
= 42.12 miles
Distance between A and B = 31.8 + 42.12
= 73.92 miles
Would someone please break this down in a simple way on how to solve it.
Since you're finding the sum (adding) all you have to do is combine like terms.
5x ² is by itself because there is no other term with x²
3x and 12x because they have an x
-7 and 12 because they're normal coefficients
Then you're left with 5x² + 15x + 5, answer choice A
Answer:
5x² + 3x - 7 + 12x + 12 = 5x² + 15x + 5
So here we have 3x and 12x, you can see that they have the common factor which is x, so you keep x and add 3 and 12 and we have 15x. For the numbers just calculate as usual. What you have 5x² left, there is no number to subtract or add with it so it will remain unchanged.
The area of an extra large circular pizza from Gambino's Pizzeria is 484\pi \text{ cm}^2484π cm 2 484, pi, space, c, m, start superscript, 2, end superscript. What is the diameter of an extra large pizza from Gambino's Pizzeria?
Answer:
The diameter of an extra large pizza from Gambino's Pizzeria is [tex]44\ cm[/tex]
Step-by-step explanation:
we know that
The area of a circle (circular pizza ) is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=484\pi\ cm^{2}[/tex]
substitute in the formula and solve for the radius r
[tex]484\pi=\pi r^{2}[/tex]
Simplify
[tex]484=r^{2}[/tex]
[tex]r=22\ cm[/tex]
Find the diameter
Remember that the diameter is two times the radius
[tex]D=2(22)=44\ cm[/tex]
Answer:
44
Step-by-step explanation: