MATH HELP!!! 100PTS!!!
Write the parametric equations
x=5sinθ,y=3cosθ,0≤θ≤π
in the given Cartesian form.
(y^2)/9=
with x≥0.
Answer:
[tex]\dfrac{y^2}{9}=1-\dfrac{x^2}{25}[/tex]
Step-by-step explanation:
When converting parametric equations that involve trig functions to Cartesian equations, use trig identities to eliminate the parameter.
Given parametric equations:
[tex]x=5 \sin \theta, \quad y=3 \cos \theta, \quad 0\leq \theta\leq \pi[/tex]
Square the equation for x:
[tex]\implies x^2=(5 \sin \theta)^2=25 \sin^2 \theta[/tex]
Use the identity [tex]\sin^2 x+\cos^2x =1[/tex] to write [tex]x^2[/tex] in terms of cos:
[tex]\implies x^2=25(1-\cos^2 \theta)[/tex]
Isolate [tex]\cos^2 \theta[/tex] :
[tex]\implies \dfrac{x^2}{25}=1-\cos^2 \theta[/tex]
[tex]\implies \cos^2 \theta=1- \dfrac{x^2}{25}[/tex]
Square the equation for y:
[tex]\implies y^2=(3 \cos \theta)^2=9 \cos ^2 \theta[/tex]
Replace [tex]\cos^2 \theta[/tex] with the found equation involving [tex]x^2[/tex] :
[tex]\implies y^2=9\left(1-\dfrac{x^2}{25}\right)[/tex]
Divide both sides by 9:
[tex]\implies \dfrac{y^2}{9}=1-\dfrac{x^2}{25}, \quad \textsf{with }x\geq 0[/tex]
(1 out of 5 parts) please help >3
Answer:
option D
Step-by-step explanation:
Convert the mixed fraction to improper fraction.As denominators are different, find the LCM of denominators.Find equivalent fractions using the LCMNow subtract and then convert improper fraction to mixed fraction.[tex]\sf 5\dfrac{3}{6}=\dfrac{33}{6}\\\\2\dfrac{1}{3}=\dfrac{7}{3}[/tex]
LCM of 6 , 3 = 6
[tex]\sf \dfrac{33}{6}-\dfrac{7}{3}=\dfrac{33}{6}-\dfrac{7*2}{3*2}\\[/tex]
[tex]\sf =\dfrac{33}{6}-\dfrac{14}{6}\\\\=\dfrac{33-14}{6}\\\\= \dfrac{19*3}{6*3=\dfrac{57}{18}}\\\\=3\dfrac{3}{18}[/tex]
What are the new coordinates? Marking brainliest whoever gets it!
Answer:
a = (9,8)
b=(10,6)
c=(4,3)
Step-by-step explanation:
basically, you just take the original coordinates and add the translation to it.
so a was -1,6 so just at 10 to -1 as they are x coordinates nad add 2 to 6 because they are Y coordinates and you just do it for all of the points.
trying to see what my answer would be
Answer:
B. [tex]2^{-14}*5^{10}[/tex].
Step-by-step explanation:
Use the power of a power property.
[tex](2^{-7}*5^{5} )^{2}[/tex]
Multiply all the exponents in the parenthesis by 2.
[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]
The answer is B. [tex]2^{-14}*5^{10}[/tex].
Hope this helps!
(5x²+36x+40)/(x+6)
Your answer should give the quotient and the remainder.
The quotient of the polynomial exists 5x+6 + (4 / x+6).
What is meant by quotient and remainder?The number of periods we have subtracted exists named the quotient (of the division of by ) The number that exists leftover after subtracting as usually as possible exists named the remainder (of the division of by ).
Given: (5x²+36x+40)/(x+6)
(5x²+36x+40)/(x+6) = 5x + (6x+40 / x+6)
Dividing the above equation
(6x+40) / (x+6) = 6+(4 / x+6)
Therefore, (5x²+36x+40)/(x+6) = 5x+6 + (4 / x+6)
The quotient of the polynomial exists 5x+6 + (4 / x+6).
To learn more about quotient polynomial refer to:
https://brainly.com/question/17082527
#SPJ9
Which equation can be used to solve for xxx in the following diagram?
Answer: A. 2x + 30 = 90
Step-by-step explanation:
You want to choose answer A because you know that together the section of 2x and the section of 30 equal 90 degrees (we know this because the other side shows the right angle which equals 90 degrees).
The equation 2x + 30 = 90 will be used to determine x so option (A) will be correct.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given an angle with two participants, one is 2x and another one is 30°.
Now if we look right-hand side angle it is a right-angle i.e. 90°.
Since the complete angle above a straight line is 180°
So,
2x + 30 + 90° = 180°
2x + 30 = 90
Hence "The equation 2x + 30 = 90 will be used to determine x".
For more about the angle,
brainly.com/question/13954458
#SPJ6
Solve this for me anyone?
Answer:
52 degrees
Step-by-step explanation:
Really easy, i learned it this summer
1. 180-128=52
2. 3=52 cus alternate interior angles
Mr. smith leaves 3 hours before mrs smith. if he averages 55mph and she 65mph how many hours will it take mrs smith to catch up
It will take 16hr 30min for Mrs. Smith to catch up.
To find how many hours will it take Mrs smith to catch up:Let,
t + 3 = Time of Mr. Smith
t = Time of Mrs. Smith
v1 = 55 mph the speed of Mr. Smith
v2 = 65 mph the speed of Mrs. Smith
Formula: Distance = speed × time
v1 ( t + 3) = v2t
55 ( t + 3 ) = 65t
65t = 55t + 165
65t - 55t = 165
10t = 165
t = 16.5 hr
t = 16 hr 0.5 × 60 min
t = 16 hr 30 min
Therefore, it will take 16hr 30min for Mrs. Smith to catch up.
Know more about distance here:
https://brainly.com/question/17273444
#SPJ4
Is B equal to C in this geometry problem? I just need to know, that and then I can solve the rest.
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene.
In the diagram shown:
AB = AC = AD
In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
Which statement is true about the given function?
f(x) >0 over the interval (-3).
f(x) >0 over the interval (-∞∞).
f(x) <0 over the interval (-3).
Of(x) <0 over the interval (-x).
Intro
20
10
-10
-20
Done. I need an answer ASAP
Answer: Choice C
Reason:
The curve is below the x axis on the interval [tex]-\infty < \text{x} < 3[/tex] which shortens down to the interval notation [tex](-\infty, 3)[/tex], so this is when f(x) < 0.
Can anyone help please?
Answer:
A'(-3, 12)B'(9, 6)C'(-6, -6)Step-by-step explanation:
Dilation about the origin multiplies each coordinate value by the dilation factor.
For dilation factor k, the new coordinates are ...
(x, y) ⇒ (kx, ky)
Your dilation factor is 3, so the transformation is ...
(x, y) ⇒ (3x, 3y)
A(-1, 4) ⇒ A'(-3, 12)
B(3, 2) ⇒ B'(9, 6)
C(-2, -2) ⇒ C'(-6, -6)
What ia an equation of the line that is parallel to y=3x-8 and passes through the point (4,-5)?
Answer:
y = 3x - 17
========================
Given liney = 3x - 8Parallel lines have equal slopes, so its equation is in the form of:
y = 3x + bSince it passes through the points (4 , - 5), find the value of the y-intercept b by substituting x- and y- coordinates into this equation:
- 5 = 3*4 + b- 5 = 12 + bb = -5 - 12b = - 17The equation of the parallel line is:
y = 3x - 17PLEASE HELP!! This graph shows the bird population of a large lake. Note that the
number of birds at the lake in the month of December is zero. What
does this extreme drop between November and December MOST
likely represent?
Select one:
O a. The beginning of duck hunting season.
O b. A reflection of the migratory nature of the birds at the lake.
O c. An inaccurate collection of data, and so, invalid results.
Od. A reflection of the hibernation patterns of the birds at the
lake.
The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.
In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.
Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.
Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.
Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.
Learn more about graphs at
https://brainly.com/question/14323743
#SPJ1
Answer: A reflection of the migratory nature of the birds at the lake.
The sequence of transformations that can be performed on quadrilateral ABCD to show that it is congruent to quadrilateral GHIJ is a v
Answer this please !
Answer:
6
Step-by-step explanation:
[tex]\frac{y}{2} =x^{2} -7[/tex]
[tex]\frac{a}{2} =2^{2} -7[/tex]
[tex]\frac{a}{2} =-3[/tex]
[tex]a=-6[/tex]
[tex]\frac{b}{2} =1^{2} -7[/tex]
[tex]\frac{b}{2} =-6[/tex]
[tex]b=-12[/tex]
From the calculations above, we learn that line l and the curve intersect at (2, -6) and (1, -12). Next, we will set up a system of linear equations to solve for the slope and the y-intercept of line l.
[tex]-6=2m+b[/tex]
[tex]-12=m+b[/tex]
[tex]-24=2m+2b[/tex]
[tex]18=-b[/tex]
[tex]b=-18[/tex]
[tex]-12=m-18[/tex]
[tex]m=6[/tex]
Therefore, the slope of line l is 6.
Answer:
slope = 6
Step-by-step explanation:
substitute the given points into the equation of the curve to find a and b
(2, a )
[tex]\frac{a}{2}[/tex] = 2² - 7 = 4 - 7 = - 3 ( multiply both sides by 2 to clear the fraction )
a = - 6
then point (2, a ) = (2, - 6 )
(1, b )
[tex]\frac{b}{2}[/tex] = 1² - 7 = 1 - 7 = - 6 ( multiply both sides by 2 )
b = - 12
then point (1, b ) = (1, - 12 )
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 6 ) and (x₂, y₂ ) = (1, - 12 )
m = [tex]\frac{-12-(-6)}{1-2}[/tex] = [tex]\frac{-12+6}{-1}[/tex] = [tex]\frac{-6}{-1}[/tex] = 6
What equation is parallel to 3y = 6x-10 and passes through A(4,5)?
Answer:
57?
Step-by-step explanation:
PLEAZE HELP IM STUCK PLS
Answer:
[tex]T_{23}=-153[/tex]
Step-by-step explanation:
[tex]T_{23}=a+(n-1)d\\[/tex]
[tex]=a+(23-1)d=a+22d[/tex]
Now [tex]a=-21[/tex] and
[tex]d=-27-(-21)\\=-6[/tex]
So [tex]T_{23}==21+((22)6\times-1)[/tex]
[tex]=-153[/tex]
There are a total number of 38 possible equally likely outcomes on a roulette wheel. Out of the 38 outcomes, there are 18 odd-numbered outcomes. What's the probability of rolling an odd number
The probability of rolling an odd number is 9/19.
According to the statement
Total number of possible outcomes = 38
Odd numbered of outcomes = 18
Now we find the probability
Probability = possible outcomes / total outcomes
Probability = 18/38
Probability = 9/19
So, The probability of rolling an odd number is 9/19.
Learn more about PROBABILITY here https://brainly.com/question/24756209
#SPJ4
LMNP is rotated 90 degrees clockwise about the origin. What are the coordinates of M’?
A. M’ (-4,3)
B. M’ (4,-3)
C. M’ (3,-4)
D. M’ (-3,-4)
The coordinates of M' is M'(-3,-4).
According to the statement
LMNP is rotated 90 degrees clockwise about the origin.
and we have to find the coordinates of M'.
so,
when it is rotated then it take four steps to reach at the end.
So, due to its moving procedure it takes four steps to reach at end.
and due to the four step procedure it's coordinates are changes four time and that's why at the end the coordinates we have to find are become a -3 and -4. So, the coordinate we get are -3 and -4
Due to this procedure the coordinate of m' become M'(-3,-4)
So, The coordinates of M' is M'(-3,-4).
Learn more about Coordinates here https://brainly.com/question/4289712
#SPJ1
Answer: B. M'(4, -3) Just took the test
Step-by-step explanation:
Determine the measure of
Answer:
M: 74.579° = 74°34'43" = 1.30164
O: 49.421° = 49°25'17" = 0.86256 rad
Which bag has more fruit? Use the ratios to justify your answer.
The bag that has more fruits is the second bag, because the ratio is greater.
Which bag has more fruits?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
Number of fruits in the first bag : (3/8) x 60 = 22.50
Number of fruits in the second bag :(7/17) x 60 = 24.71
Here is the complete question:
Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.
To learn more about ratios, please check: https://brainly.com/question/25927869
#SPJ1
Use properties to rewrite the given equation. Which equations have the same solution as the equation
x + + x = – x plus StartFraction 2 Over 3 EndFraction plus x equals StartFraction one-half EndFraction minus StartFraction 1 Over 5 EndFraction x.x
The equation computed shows that the correct options are A, B, and D.
How to illustrate the information?1) The equation we want to rewrite is;
³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x
(³/₅ + 1)x + ²/₃ = ¹/₂ – ¹/₅x
⁸/₅x + ²/₃ = ¹/₂ – ¹/₅x
This corresponds with the solution in Option A
2) ³/₅x + ²/₃ + x = ¹/₂ – ¹/₅x
Let us use multiplication property of equality which states that if we multiply both sides of an equation by the same quantity, then both sides remain equal.
Let's get rid of the denominators by multiplying each term by the LCM of the denominators. LCM of 2,3,5 is 30. Thus;
30(³/₅x) + 30(²/₃) + 30x = 30(¹/₂) - 30(¹/₅x)
Simplifying gives;
18x + 20 + 30x = 15 - 6x
This solution corresponds with that in option B
3) We will make use of additive property of equality which states that when we add the same number to both sides of an equation, then both sides remain equal.
Let's add 6x to both sides of 18x + 20 + 30x = 15 - 6x;
18x + 20 + 30x + 6x = 15 - 6x + 6x
⇒ 24x + 30 + 20 = 15
Using subtractive property of equality, let us subtract 20 from both sides to get;
24x + 30 + 20 - 20 = 15 - 20
This corresponds with the solution in Option D.
Complete question:
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all that apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
Learn more about equations on:
https://brainly.com/question/11358415
#SPJ1
A research center poll showed that 85% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? The probability that someone does not believe that it is morally wrong to not report all income on tax returns is (Type an integer or a decimal.)
The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
For given question,
A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.
so, the probability that someone have this belief is P = 0.85
We know that in probability,
p = 1 - q
where;
p is probability of success
q is probability of failure.
Thus the probability that someone does not have this belief would be,
= 1 - P
= 1 - 0.85
= 0.15
Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15
Learn more about the probability here:
https://brainly.com/question/3679442
#SPJ4
Which are the solutions of x² = 19x + 12
Answer:
[tex]\{x=\frac{19-\sqrt{409} }{2}\ , \ x=\frac{19+\sqrt{409} }{2}\}[/tex]
Step-by-step explanation:
x² = 19x + 12
⇔ x² - 19x - 12 = 0
Calculating the discriminant :
b² - 4ac = (-19)² - 4×1×(-12) = 409
The discriminant is positive ,then the equation has two solutions.
[tex]x=\frac{19-\sqrt{409} }{2} \ \ or\ \ x=\frac{19+\sqrt{409} }{2}[/tex]
7-2x≥15
solve for inequality
graph the solution
shade the possible solutions
1 -12 13 -4 -42 4
The solution set of the inequality is x ≤ - 4. The graph of inequality is shown below and the points x = - 4, x = - 12, x = - 42 are part of the solution set.
How to solve an inequality
In this question we must use algebraic axioms and theorems to solve an inequality and graph the solution set with the help of a graphing tool. Now we proceed to present the procedure to solve for x:
7 - 2 · x ≥ 15
7 - 15 ≥ 2 · x
2 · x ≤ - 8
x ≤ - 4
Now we present the graph of the inequality. The points x = - 4, x = - 12, x = - 42 are part of the solution set.
To learn more on inequalities: https://brainly.com/question/20383699
#SPJ1
The dot plots below show the scores for a group of students who took two rounds of a quiz:
Two dot plots are shown one below the other. The title for the dot plot on the top is Round 1 and the title for the bottom plot is Round 2. Below the line for each dot plot is written Score. There are markings from 5 to 9 on the line at intervals of one. There are 2 dots above the mark 5, 3 dots above the mark 6, 4 dots above the mark 7, and 1 dot above the mark 8. For the bottom dot plot there are 6 dots above the mark 6, 2 dots above the mark 8, and 2 dots above the mark 9.
Which of the following inferences can be made using the dot plot?
A. The range of each round is the same.
B. There is no overlap between the data.
C. Round 1 scores were higher than round 2 scores.
D. Round 2 scores were lower than round 1 scores.
The inference that can be made from the dot plot is the range of each round is the same.
What is the inference that can be made?A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.
Range is the difference between the largest number and smallest number.
Range of round 1 = 8 - 5 = 3
Range of round 2 = 9 - 6 = 3
To learn more about dot plots, please check: brainly.com/question/22746300
#SPJ1
how do I find x on the attached right triangle
?
The value of x from the given triangle is 32√3/3
SOH CAH TOA identityIn order to determine the value of x, first we need to determine the hypotenuse side of the smaller triangle.
sin 60 = 8√2/H
H = 8√2/sin60
H = 8√2 * 2/√3
H = 16√2/√3
H = 16√6/3
For the value of x, we will use the expression
sin45 = (16√6/3)/x
1/√2 = 16√6/3x
3x = 16√12
3x = 32√3
x = 32√3/3
Hence the value of x from the given triangle is 32√3/3
Learn more on SOH CAH TOA here: https://brainly.com/question/20734777
#SPJ1
A and B are independent events. P(S) = 0.40 and P(B) = 0.30. What is P(A and B)
The value of the probability P(A and B) is 0.12
How to determine the probability?The given parameters are
P(A) = 0.40
P(B) = 0.30
Given that the events are independent events;, we have:
P(A and B) = P(A) * P(B)
So, we have:
P(A and B) = 0.40 * 0.30
Evaluate
P(A and B) = 0.12
Hence, the value of the probability P(A and B) is 0.12
Read more about probability at
https://brainly.com/question/11234923
#SPJ1
im stuck on this one
The value of X is 2/3 and -3/2.
According to the statement
we have given equation is 6x^2+5x-6 =0
and we have to find x by the factorization.
Factorization defines the the operation of resolving a quantity into factors.
So, by factorization method the equation is written as
6x^2+5x-6 =0
After forming factors the equation becomes
6x^2+9x-4x-6 =0
3x(2x+3) -2(2x+3) =0
By taking common
(3x-2) (2x+3) = 0
Now equate values equal to 0. and after that the output will get in the form of value of X.
Here the value of x is 2/3 and -3/2
So, the value of X is 2/3 and -3/2.
Learn more about Factorization here https://brainly.com/question/25829061
#SPJ1
A method of sampling that enables researchers to specify for each case in the population the probability of its inclusion in the sample is referred to as ______ sampling.
Simple Random sampling
Meaning:
Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected.
For example, if you randomly select 1000 people from a town with a population of 100,000 residents, each person has a 1000/100000 = 0.01 probability. That's a simple calculation requiring no additional knowledge about the population's composition. Hence, simple random sampling.
Advantage:
Simple random sample advantages include ease of use and accuracy of representation. No easier method exists to extract a research sample from a larger population than simple random sampling.
Learn more about Sampling on:
https://brainly.com/question/9910540
#SPJ4