The rectangular coordinates form of r = 12 sinθ is x² + y² - 12y = 0
Given r = 12 sinθ and we are asked to convert this equation into rectangular coordinates.
The relation between polar coordinates (r,θ) and rectangular coordinates (x, y) is given by
x = r cosθ and y = r sinθ
Also, r² = (x² + y²)
r = 12 sinθ
Multiplying r both sides
r x r = 12 sinθ x r
r² = 12r sinθ
We know r sinθ = y and r² = (x² + y²)
So, x² + y² = 12y
x² + y² - 12y = 0
Hence, the rectangular coordinates form is x² + y² - 12y = 0
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2.
Triangles ABC and PQR are similar.
(a) Work out angle Q.
(b)Work out the length PQ.
Answer:
2. a)
As per the Angle sum property
∠P + ∠Q + ∠R = 180°
22° + ∠Q + 54° = 180°
∠Q = 180° - 76°
∠Q = 104°
b)
Now as per the question,
ΔABC ≅ ΔPQR
Which implies that
AB = PQ
So,
PQ = 8 cm
Step-by-step explanation:
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question 117 please !
The simplified form of the expression (3x + 8y)/(x² + 8xy + 16y²) × (x + 4y)/4
is [(3x² + 20xy + 32y²)/(4x² + 32xy + 64y²)].
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
Given, (3x + 8y)/(x² + 8xy + 16y²) × (x + 4y)/4.
= [(3x + 8y)×(x + 4y)/(x² + 8xy + 16y²)×4].
= [3x² + 8xy + 12xy + 32y²/4x² + 32xy + 64y²].
= [(3x² + 20xy + 32y²)/(4x² + 32xy + 64y²)].
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Select all the expressions that are equivalent to (12⁻₂)₈
Step-by-step explanation:
1/4096
0.000244140625
2^-12
1/(2^12)
All of the above expressions are equivalent to (12⁻₂)₈, which is a decimal representation of a number that is obtained by dividing 1 by 2 raised to the power of 12. The first and second expressions are decimal representation of the number, the third one is the representation of the number by using the base 2 logarithm, and the fourth one is the mathematical representation of the number by dividing 1 by 2 raised to the power of 12.
A quadrilateral with vertices P (1,-1), Q(3,-7), R(-9,-11) and S (-11,-5) is a parallelogram. Select the correct statement to justify the diagonals of a parallelogram bisecct each other
The distances from the midpoint M to the vertices are all the same and equivalent to 5·√2, therefore, the diagonals of the quadrilateral bisect each other.
What is a diagonal of a quadrilateral?A diagonal is a line that joins the opposite corners of the quadrilateral.
The question is without the possible options for the response.
The vertices of the quadrilateral are;
P(1, -1), Q(3, -7), R(-9, -11), and S(-11, -5)
The midpoint of the side PR = ((-9 + 1)/2, (-11 + (-1))/2) = (-4, -6)
Midpoint of the diagonal SQ = ((3 + (-11))/2, (-7 - 5)/2) = (-4, -6)
Let M represent the point of intersection of the diagonals, we get;
PM = √((1 - (-4))² + (-1 - (-6))² = 5·√2
MR = √((-9 - (-4))² + (-11 - (-6))² = 5·√2
The length of PM = The length of MR, therefore, the diagonal SQ bisects PM
Similarly, we get;
SM = √((-9 - (-4))² + (-11 - (-6))²) = 5·√2
MQ = √((3 - (-4))² + (-7 - (-6))²) = 5·√2
The length PM = MR and the lengths SM = MQ, therefore, the diagonals bisect each other.
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Answer: the product of the slopes of the diagonals PR and QS is equal to 1. Hence, the diagonals of parallelogram PQRS bisect each other.
Step-by-step explanation:
1/7 of what is 1/35 thanks!
Answer:
1/5
Step-by-step explanation:
1/7 * x = 1/35 multiply both sides by 7
x = 7/35 = 1/5
David is tracking the amount of water he drinks each day.
On Thursday, he drinks 15 cups of water.
On Friday, he drinks 12 cups of water.
What is the percent change in his water intake?
What is the original amount of water in this problem?
What is the change in David's water intake in this problem?
What is the percent change?
Is it increasing or decreasing?
The original amount of water is 15 cups.
The change in David's water intake is 3 cups.
The percent change is 20 %. This is a percent decrease.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Given that, David is tracking the amount of water he drinks each day.
On Thursday, he drinks 15 cups of water.
On Friday, he drinks 12 cups of water.
The percent change in his water intake = (12 - 15) / 15 × 100 = -20%
Where minus sign is showing a decrease in the water intake,
The original amount of water is 15 cups.
The change in David's water intake is (15-12) = 13 cups.
Hence, the answers are;
The original amount of water is 15 cups.
The change in David's water intake is 3 cups.
The percent change is 20 %. This is a percent decrease.
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I need the answer...
find the solution to the differential equation dydt=y2(4 t), y=8 when t=1.
The solution to the differential equation is ln |y| = 4t - 4.
The given differential equation can be written as ∆y/∆t = y2(4t). This is a first-order separable differential equation, which can be solved using the separation of variables method. To do this, we first isolate the dy/dt term on one side of the equation. We can then separate the two variables (t and y) by moving all terms with t to one side and all terms with y to the other side. This gives us ∆y/y2 = 4∆t. We can then integrate both sides to find the solution.
Integrating both sides with respect to y gives us the following:
ln |y| = 4t + C,
where C is an integration constant. We can use the boundary condition to solve for C. The boundary condition states that y=8 when t=1, so substituting this into the equation above gives us ln |8| = 4 + C. Solving for C gives us C=-4.
Therefore, the solution to the differential equation is ln |y| = 4t - 4. Rearranging this equation gives us y = e4t-4, which is the solution to the differential equation.
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Let a1 =,a2= and b=. For what value (s) of h is b in the plane spanned by a1 and a2?
When h=-17 is b in the plane spanned by a1 and a2.
For the plane spanned by a1 and a2, y is a linear combination of a1 and a2 if it is in the plane,
y = a a1 + b a2
where a and b are constants,
[4,1,h] = a[1,4,-2] + b[-2,-3,7]
[4,1,h] = [a - 2b,4a -3b,-2a+ 7b]
by the rules of vector addition and multiplication.
Vectors are equal if their components are equal:
4 = a - 2b
1 = 4a - 3b
h = -2a + 7b
solve for a and b from the first two equations so that we can find h,
b = -3
h = -17
We see that -2[1,4,-2] - 3[-2,-3,7] = [4,1,-17].
so ,the value of h=-17 is b in the plane spanned by a1 and a2.
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Connor bought a scarf that costs 13 dollars and a watch that costs 13 dollars. At the counter, he received a discount. If he only paid 18 dollars total, how many dollars was the discount?
$10.66 is dollars was the discount .
How does discount work?
Discount is a term that describes a sum or a percentage subtracted from a product's usual selling price. Make sure you need all of the items you plan to buy before waiting until after the holiday when you can frequently find them at a significant discount.
Discount is a term that refers to a reduction in the cost of a commodity or service.
Discount:
(13 x 18)/100 = $2.34
13 - 2.34 = $10.66
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What are the coordinates for point C?
Responses
(2, 8)
(2, -8)
(-2, 8)
(-2, -8)
Answer: option c.
Step-by-step explanation:
The system of equations models the prices per share, y, for two stocks over time, x. Which represents the viable solutions to the system?
−y ≤ 3x + 4
−3x + 3y ≤ −9
A. All real number values of x and y
B. (5, 15)
C. All real number values, with y ≥ 0
D. (15, 5)
The option that describes the viable solution for the system is all real number values, with y ≥ 0 which is denoted as option C.
What is Inequality?This is referred to as a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
all real number values, with x >=0 and y>=0
The following system of inequalities is given below:
-y ≤ 3x + 4
-3x - 3y ≤ 9 which can be rewritten as:
-3y ≤ 9 + 3x
-3y/3 ≤ 9/3 + 3x/3
-y ≤ 3 + x
The system of inequalities is therefore:
-y ≤ 3 + x
-y ≤ 3x + 4
Since x and y are both positive or 0, the system is true and we can conclude that the correct choice is option C which is all real number values, with y ≥ 0
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What values of x satisfy the following equations?
(a) P(-x ≤ T22 ≤ x)=0.98
(b) P(T13x)=0.85
(c) P(T26
(d) P(T₂≥x)=0.025
For (a), x must be the 98th percentile of T22. For (b), x must be the 85th percentile value of T13. For (c), x must be the 26th percentile of T26. For (d), x must be the 97.5th percentile of T2.
For (a), the value of x must be the 98th percentile of T22, which is the value of x such that 98% of the data points of T22 are less than or equal to x. For (b), the value of x must be the 85th percentile of T13, which is the value of x such that 85% of the data points of T13 are less than or equal to x. For (c), the value of x must be the 26th percentile of T26, which is the value of x such that 26% of the data points of T26 are less than or equal to x. For (d), the value of x must be the 97.5th percentile of T2, which is the value of x such that 97.5% of the data points of T2 are less than or equal to x. In order to find these values of x, one must first calculate the percentiles of the given variables. This can be done by sorting the data points in ascending order and then calculating the percentile of each data point. After the corresponding percentile of each data point has been calculated, the desired values of x can be determined by finding the data point whose percentile matches the desired value.
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two of the interior angles of a triangle are 45.5 degrees and 14.6 degrees. what is the third interior angle of the triangle?
The third interior angle of the triangle is 119.9 degrees
Triangle is a closed polygon consist of three sides, three angle or three segment.
Triangle has three angle which if we sum all of those three angle it will be 180 degrees.
Triangle can be divided into several type :
1. Equilateral triangle which all of the angle is equal ( 180 degrees / 3 = 60 degrees each )
2. Isosceles triangle which have two equal angle, and the third angle is different
3. Scalene triangle which all of the angle is different
From the question, we have data :
1. First Angle is 45.5 degrees
2. Second Angle is 14.6 degrees
For the Third angle, we just simply subtract 180 degrees with the first and second angle. So it will be :
Third Angle = 180 degrees - ( 45.5 degrees + 14.6 degrees )
= 180 degrees - 60.1 degrees
= 119.9 degrees
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what two types of feet are prominent in these lines
In poetry, the two main types of feet are iambic and trochaic.
Iambic foot: An iambic foot consists of two syllables, with the first syllable being unstressed and the second syllable being stressed. This creates a rhythmic pattern of "da-DUM" that gives iambic meter its characteristic "rising" sound. Iambic meter is one of the most common types of meter in English poetry, and is often associated with a natural, conversational rhythm.
Trochaic foot: A trochaic foot consists of two syllables, with the first syllable being stressed and the second syllable being unstressed. This creates a rhythmic pattern of "DA-dum" that gives trochaic meter its characteristic "falling" sound. Trochaic meter is less common than iambic meter in English poetry, but is still used in a variety of forms and styles. It can create a sense of tension or urgency, and is often used in poetry that is meant to be dramatic or suspenseful.
It's important to note that these two types of feet are just two of many possible metrical patterns that can be found in poetry. However, they are two of the most basic and widely recognized, and a good starting point for understanding the rhythms and structures of poetic meter.
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given the function f(x)=−x2−6x 13, determine the direction in which a parabola sketching this function would open.
The parabola f(x) = -x² - 6x - 13 is open downward.
Write the equation in vertex form f(x) = a(x-h)² + k
So, f(x) = -x² - 6x - 13
= -(x² + 6x + 13)
= -(x² + 6x + 9 + 4)
= -((x + 3)² + 4)
= -(x + 3)² - 4
Here, a = -1, h = -3 and k = -4
If a > 0, the parabola is open upward and if a < 0, the parabola is open downward.
In f(x) = -(x + 3)² - 4, a= -1 < 0. Therefore, the parabola is open downward.
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can some tell me what's the distributive property of 68 ÷ 4 pls I need it tomorrow
What’s the measurements
What is the slope of the line passing through the points (-3, 4) and (2, -1)?
Answer:
m = -1
Step-by-step explanation:
Slope = rise/run = (y2 - y1) / (x2 - x1)
Points (-3, 4) (2, -1)
We see the y decrease by 5 and x increase by 5, so the slope is
m = -5/5 = -1
A bagel factory produced 647 bags of bagels. There were 14 bagels in each bag. How many bagels did the factory produce?
Answer:
9058 Bagels
Step-by-step explanation:
14x657 I hope this helped!
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Answer:
what is this? ahdhdjxkdjjshsysusiiaiajsjjdyxc
A sunflower's height was measured at 42 inches. The second time the flower was measured its height was 70 inches. What was the percent change in the height of the sunflower between the two measurements? Increase or decrease? amount of change original amount = percent= Substitute and solve:
Answer:
67%
Step-by-step explanation:
Percent change is the change divided by the original value. The change for the flower is (70" - 42") = 28"
The original value was 42".
Percent change is (28"/42")*(100%) = 67%
certain standardized math exams have a mean of 100 and a standarad deviation of 60. of a sample of 36 students who take this exam, what percent could you expect to score above 110
Using the Normal Z-distribution and the values from the Z-table, We can calculate that 12.5% can be expected to score between 70 and 90 according to the value of the mean and standard deviation provided.
A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it.
mean =100
standard deviation =60
70≤ x ≤ 90
70 - 100 ≤ x - 100 ≤ 90 -100
-0.5 ≤ Z ≤ -0.167
P = 0.125(From Z-Table)
Required percentage = 12.5%
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The correct question is:
certain standardized math exams have a mean of 100 and a standard deviation of 60. of a sample of 36 students who take this exam, what percent could you expect to score between 70 and 90?
.What is the probability an individual student likes between 5.5 and 8.5 songs from Eminem?
It is not possible to determine the probability that an individual student likes between 5.5 and 8.5 songs from Eminem without any additional information. Probability is a measure of the likelihood of an event occurring, and it requires data or information about the event in question. In this case, without knowing the number of songs from Eminem the student has heard, the student's taste in music, or any other relevant information, it is impossible to determine the probability that the student likes between 5.5 and 8.5 songs from Eminem.
Simplify
5x5²
Leaving your answer in index form
Answer: 5^3
Step-by-step explanation: since we know that 5^2=5x5 (which equals to 5x5x5), our answer is 5^3
Melania is trying to estimate √30. she uses this table of values. What should she do next to find √30 to the nearest hundredth?
A pail hold 220. 5 ounce (oz) of water when full. The bucket loe 0. 2 oz of water per econd. In how many econd will the bucket be 30% full? Round your anwer to the nearet econd
The bucket will be 30% full at 772 seconds
What is velocity?It is a physical quantity that indicates the displacement of a mobile per unit of time, it is expressed in units of distance per time, for example (miles/h, km/h).
The formula and procedure we will use to solve this problem is:
v= x/t
Where:
x = volumet = timev = velocityInformation about the problem:
Total = 220.5 ozv = 0.2 oz/svolume = total *30%Calculating how many ounces the bucket will be when it has 30% full:
Volume = 220.5 * 30%
Volume = 66.15oz
The bucket will lose:
x = 220.5oz - 66.15oz
x = 154.35 oz
The time that the bucket will have 66.15 oz (30%) is:
t = x/v
t = 154.35 oz / 0.2 oz/s
t = 771.75 s = 772 s
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Correctly written question:
A pail holds 220.5 ounces (oz.) of water when full. The bucket loses 0.2oz of water per second. In how many seconds will the bucket be 30% full? Round your answer to the nearest second.
If a translation maps H onto J, which of the following statements is true?
G
H
Ol=K
O
GH = 2 GJ
GK
HI 2 JK
K
If a translation maps H onto J, the option from the following statements which is true is: ∠I ≅ ∠K (Option 1)
What is a translation in math?A translation is a sort of transformation that involves sliding each point in a figure the same distance in the same direction. The four fundamental translations or transformations in geometry are:
Translation. Reflection.Rotation.Resizing or dilation.With regard to the above answer, note that, because both triangles have the same vertex, angle HGI is equivalent to angle JGK. Angle H is parallel to angle J.
As a result, by converting angle I to angle K, their measurements will be equivalent. As a result, the angle I is congruent with angle K.
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Full Question:
If a translation maps H onto J, which of the following statements is true?
1. ∠I ≅ ∠K
2. GH = 2GJ
3. ∠G ≅ ∠K
4. HI = 2JK
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary).
16,48,144,...
Find the 6th term.
the 6th term of the geometric sequence will be 3888.
What is geometric sequence?
A geometric progression or geometric sequence is the order in which each word is different from the next by a common ratio. The next term in the series is produced by adding a constant (that is not zero) to the term that came before it. A, ar, ar2, ar3, ar4, etc. are used as substitutes.
Mathematicians use the term "Geometric Progression" (GP) to describe a type of sequence in which each word is formed by multiplying the previous term by a predetermined number, or "common ratio". An integer geometric series gets that follows a pattern is another name for this development.
The terms are given, 16,48,144
a = 16
r = 48/16 =3
The 6th term will be= a(r)[tex])^{5}[/tex]
= 16(3)[tex])^{5}[/tex]
= 16* 243
=3888
Hence, the 6th term of the geometric sequence will be 3888.
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eric walks around a man-made circular lake (pictured above) two times. how far (in miles) has he walked?
The amount of total distance walked (in miles) has walked by Eric in a man made circular lake is 62.8 miles.
A circle's circumference is the length of its perimeter. The circumference of a circle can be calculated using length units such as centimeters, meters, or kilometers by opening a circle and measuring the boundary in the same way that we would measure a straight line.
Let's now discover the components of circumference. The three most crucial components of a circle are those three.
Center: The circle's center is a point that is set apart from the other points on the circumference by a predetermined amount.Diameter: The diameter is the distance across the circle that must pass through the center; it is a line that must meet the circumference at both ends.Radius: The radius of a circle is the distance a circle's center is from any point along its perimeter.Circumference = D*π
Total distance walked two times = 2.C
=2* D* π
=2x10x3.14
=62.8 miles
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