We have been an equation in polar coordinates [tex]r=10\text{sin}(\theta)[/tex]. We are asked to write our equation in rectangular coordinates.
We know that the equation [tex]r=2b\text{sin}(\theta)[/tex] is equation of a circle with a radius [tex]|b|[/tex] and center at [tex](0,b)[/tex].
Let us find the value of b.
[tex]2b\text{sin}(\theta)=10\text{sin}(\theta)[/tex]
[tex]\frac{2b\text{sin}(\theta)}{2\text{sin}(\theta)}=\frac{10\text{sin}(\theta)}{2\text{sin}(\theta)}[/tex]
[tex]b=5[/tex]
We know that equation of a circle in rectangular coordinates is [tex](x-h)^2+(y-k)^2=r^2[/tex]
Since [tex]b=5[/tex], so radius is 5 and center is at point (0,5).
[tex](x-0)^2+(y-5)^2=5^2[/tex]
[tex]x^2+(y-5)^2=25[/tex]
Therefore, our required equation would be [tex]x^2+(y-5)^2=25[/tex].
Answer:
x^2+y^2=10y
Step-by-step explanation:
d on edg
Which of the following shows that polynomials are closed under addition when two polynomials 4x + 6 and 2x2 − 8x − 4 are added? 2x2 − 4x + 2; will be a polynomial 2x2 − 4x + 2; may or may not be a polynomial 2x2 − 12x − 10; will be a polynomial 2x2 − 12x − 10; may or may not be a polynomial
Answer:
The answer is a
Step-by-step explanation
2x2 - 4x + 2 will be a polynomial
(4x + 6) + (2x² - 8x - 4)
= 4x + 6 + 2x² - 8x - 4
= 2x² + (4x - 8x) + (6 - 4)
= 2x² - 4x + 2
And it is polynomial (it has more than 1 term)
Answer:
A. [tex]2x^{2} - 4x + 2[/tex] ; will be a polynomial
Step-by-step explanation:
(4x + 6) + (2x² - 8x - 4)
= 4x + 6 + 2x² - 8x - 4
= 2x² + (4x - 8x) + (6 - 4)
= 2x² - 4x + 2
Polynomial (it has more than 1 term)
Hope that help!
Find the volume of the sphere whose radius is 0.8 cm
Answer:
2.14 cm^3
Step-by-step explanation:
V = 4/3 pi r^3
V = 4/3 pi 0.512
V = 2.14
Using this formula, you just plug in your current values into a calculator and out comes the answer!
[tex]\frac{4}{3}[/tex]πr³
[tex]\frac{4}{3}[/tex]π(0.512)
^ (do 0.8³, which equals 0.512)
ANSWER: 2.14
If u could answer this u would be magical
Answer:
12r^2 +r -7
Step-by-step explanation:
9r^2 +4r -7 +3r^2 -3r
Combine like terms
9r^2 +3r^2 +4r -3r -7
12r^2 +r -7
In a right triangle, 0 is an acute angle and cos0= 6/11. Evaluate the other five trigonometric functions of 0.
Answer:
sin O = √85/11, csc O = 11/√85
cos O = 6/11, sec O = 11/6
tan O = √85/6, cot = 6/√85.
Step-by-step explanation:
cos = adjacent / hypotenuse = 6/11, so the opposite side to angle O
= √(11^2 - 6^2)
= √85.
csc O = 1/sin O
sec O = 1/cos O
cot O = 1/tan O.
Write two numbers that multiply to the value on top and add to the value on bottom.
how many different outcomes are possible from rolling a six sided cube four times
Answer:
1296 different outcomes
Step-by-step explanation:
Each cube has 6 possible values (from 1 to 6), and for each additional cube rolled, we have 6 more possible values, and the final number of different outcomes is the product of all the number of possible values for each cube.
So, if we roll the cube four times, the total number of different outcomes is:
6 * 6 * 6 * 6 = 1296
We have 1296 different outcomes from rolling the six sided cube four times.
Solve the quadratic equation for x.
3x2+12x=0
x =
or x =
Answer:
x=0, x=-4
Step-by-step explanation:
Answer:
x=0, x=4
Step-by-step explanation: yes
Which graph shows the information in the table?
Minutes in Hours
Number of Minutes Number of Hours
30 0.5
60 1
90 1.5
120 2
Answer:
The last graph
Step-by-step explanation:
In the first and third one the labels are switched. And the minutes should be on the x axis while the hours should be on the y axis.
The second one is incorrect because it literally says that 0 minutes= 0.5 hour
Answer:
A (the first graph on edge)
Step-by-step explanation:
Looking at the graph, we can see that the graph that has the line pass through (30, .5) is going to be the correct one.
Miriam took a survey, asking each family in her neighborhood how many pets they have. She made a graph showing the results: [asy] size(5.5cm); draw((0,30)--(0,0)--(41,0)); for(int i=1; i<7; i+=1) {draw((0.6,5*i)--(-0.6,5*i)); draw((0.6,5*i)--(41,5*i),black+0.5+dashed); }; path a=(3,0)--(3,30)--(9,30)--(9,0)--cycle; path b=(9,0)--(9,15)--(15,15)--(15,0)--cycle; path c=(15,0)--(15,15)--(21,15)--(21,0)--cycle; path d=(21,0)--(21,30)--(27,30)--(27,0)--cycle; path e=(27,0)--(27,5)--(33,5)--(33,0)--cycle; path f=(33,0)--(33,5)--(39,5)--(39,0)--cycle; fill(a,gray); fill(b,gray); fill(c,gray); fill(d,gray); fill(e,gray); fill(f,gray); draw(a); draw(b); draw(c); draw(d); draw(e); draw(f); label(rotate(-45)*scale(0.8)*"0 pets",(5,-1),SE); label(rotate(-45)*scale(0.8)*"1 pet",(11,-1),SE); label(rotate(-45)*scale(0.8)*"2 pets",(17,-1),SE); label(rotate(-45)*scale(0.8)*"3 pets",(23,-1),SE); label(rotate(-45)*scale(0.8)*"4 pets",(29,-1),SE); label(rotate(-45)*scale(0.8)*"5 pets",(35,-1),SE); label(scale(0.8)*"1",(-0.6,5),W); label(scale(0.8)*"2",(-0.6,10),W); label(scale(0.8)*"3",(-0.6,15),W); label(scale(0.8)*"4",(-0.6,20),W); label(scale(0.8)*"5",(-0.6,25),W); label(scale(0.8)*"6",(-0.6,30),W); label(scale(0.8)*rotate(90)*"Number of families",(-3.5,15),W); [/asy] What is the average number of pets per family?
Answer:
1.8
Step-by-step explanation:
The graph of the problem is plotted using Asymptote and attached.
From the graph:
6 Families had 0 Pets3 Families had 1 Pets3 Families had 2 Pets6 Families had 3 Pets1 Family had 4 Pets1 Family had 5 PetsThere are a total of 20 families.
Average Number of Pets
[tex]=\dfrac{6*0+3*1+3*2+6*3+1*4+1*5}{20} \\\\=\dfrac{36}{20}\\\\=1.8[/tex]
The average number of pets per family is 1.8.
Answer:
1.8
Step-by-step explanation:
The bar chart tells us that:
6 families each have 0 pets,
3 families each have 1 pet,
3 families each have 2 pets,
6 families each have 3 pets,
1 family has 4 pets, and
1 family has 5 pets.
The total number of pets in all these families is (6 ∙ 0) + (3 ∙ 1) + (3 ∙ 2) + (6 ∙t 3) + (1 ∙ 4) + (1 ∙ 5) = 36. The number of families is 6 + 3 + 3 + 6 + 1 + 1 = 20. Therefore, the average number of pets per family is 38/20 = 1.8.
Candita uses 1 of an ounce of green paint each time she draws a green line on her painting. She draws a total of 7 green
lines. Which expression represents the amount of green paint that Candita used drawing green lines on the painting? Check
all that apply.
1+1+1+1+1+1+1
0 1 2 + 1 2 + 1 2 + 2 / 2
This results in the total amount of 7/8 ounce of green paint used.
The amount of green paint that Candita used for drawing seven green lines on her painting can be represented by the expression 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8. Each 1/8 ounce of green paint is used for one green line, and she draws a total of 7 green lines. So, we simply add up seven times the fraction 1/8.
The sum can be calculated as:
1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8Which equals:
7/8 ounce of green paintThis is the total amount of paint she used to draw all the green lines.
Determine the inverse of a function. please help!
What is the equation that represents the line?
Answer: -7-4
Step-by-step explanation:
Special Segments, Please help!
x= 1, 3, 7
Answer:
x=3
Step-by-step explanation:
Secant-Secant Formula:
(whole secant) x (external part) = (whole secant) x (external part)
9*4 = 12*x
36 = 12x
Divide each side by 12
36/12 = 12x/12
3 =x
Lilly constructed a box in the shape of a rectangular prism. The amount of space inside of the box is 180 cubic inches. What is the height of Lilly’s box?
Answer:
B
Step-by-step explanation:
3 in.
5(2x + 4) = 50 (Given)
10x + 20 = 50 (Distributive Property)
10x = 30 (?)
x = 3 (Division Property)
Fill in the missing reason for the argument shown.
Answer:
The answer is: D.) subtraction property
Step-by-step explanation:
The missing reason in the algebraic equation is the Subtraction Property of Equality, which involves subtracting the same number from both sides of an equation to maintain equality.
The missing reason for the argument shown is the Subtraction Property of Equality.
When we go from the step 10x + 20 = 50 to 10x = 30, we are subtracting 20 from both sides of the equation. This property states that if you subtract the same number from both sides of an equation, the two sides remain equal.
Therefore, the complete series of steps with their corresponding properties is:
5(2x + 4) = 50 (Given)
10x + 20 = 50 (Distributive Property)
10x = 30 (Subtraction Property of Equality)
x = 3 (Division Property)
Which descriptions can describe more than one triangle? Select two options. side lengths of 6 ft, 8 ft, and 10 ft angle measurements of 35°, 35°, and 110° angle measurements of 30°, 409, and 50° angle measurements of 40°, 60°, and 80° Oside lengths of 4 cm, 6 cm, and 9 cm
The descriptions that can define more than one triangle is
a) angle measurements of 35°, 35°, and 110°
b) angle measurements of 40°, 60°, and 80°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now the measurements of the triangle are
a)
angle measurements of 35°, 35°, and 110°
A triangle must have length sides that fulfil the Triangle Inequality Theorem and interior angles that add up to 180 degrees.
When two triangles are comparable, their corresponding sides have a proportionate ratio and their corresponding angles have a congruent relationship.
So , several triangles with the same internal angles are possible
b)
angle measurements of 40°, 60°, and 80°
Now , several triangles with the same internal angles are possible
Hence , the triangle is solved
To learn more about triangles click :
https://brainly.com/question/16739377
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The descriptions that can describe more than one triangle are:
Angle measurements of 35°, 35°, and 110°
Side lengths of 6 ft, 8 ft, and 10 ft
The descriptions that can describe more than one triangle are:
Angle measurements of 35°, 35°, and 110°: This set of angles can form more than one triangle because the sum of angles in a triangle is always 180°. So, even though two angles are equal (35° each), their combination with a larger angle (110°) allows for multiple triangle constructions.
Side lengths of 6 ft, 8 ft, and 10 ft: This set of side lengths satisfies the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Thus, there are multiple triangles possible with these side lengths.
Question
Which descriptions can describe more than one triangle? Select two options.
side lengths of 6 ft, 8 ft, and 10 ft
angle measurements of 35, 35, and 110°
angle measurements of 30°, 40, and 50°
angle measurements of 40°, 60°, and 80°
side lengths of 4 cm, 6 cm, and 9 cm
Select the points that are solutions to the system of inequalities. Select all that apply
Answer:
(-10, 10) and (0,10).
Step-by-step explanation:
For a point to be a solution to the system of inequalities, you will need to see which of the points falls into the shaded area.
When we test out each of the points, we can see that only:
(-10, 10) and (0,10) fall into the blue-shaded area.
Answer:
-10,10 and 0,10
Step-by-step explanation:
alvs verified 100% correct
PLEASE HELP! CORRECT ANSWERS ONLY! 20 POINTS
In two or more complete sentences discuss the advantages and disadvantages of investing in a 529 plan versus investing in a money market account.
Answer:
1.) In 529 plan, Your account earns interest and you can contribute as much as you want. But Your investment options are limited and the money must be used for college
2.) While in money market account, the account pays higher interest than traditional savings accounts, but limited to writing no more than three checks a month. Some banks limit your cash withdrawals.
Step-by-step explanation:
Money market deposit accounts are better choices than 529 plan for money you might need to tap at a moment’s notice to cover an emergency or an unexpectedly large expense. They pay higher interest than ordinary savings accounts and give you immediate access to your money
While in 529 savings plan, If you don’t use the money invested for college tuition, you will be penalized 10 percent when you withdraw the money to use it for something else. In addition, both your state and the federal government will tax the earnings on your account in your current tax bracket.
The models all represent a real-world problem. How would you match the models to a problem? Find a problem with the same variables and the same relationship between the quantities. Find a problem that has the same numbers. Find a problem that has the same variables. Find a problem that has the same x-values.
Answer A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
hope this helps!
Help me please “Match each expression to its simplified form” picture listed
Answer:
See explanation
Step-by-step explanation:
To find the percentage of a number, multiply the number by the decimal form of the percentage.
To find the decimal point of a percentage, remove the percent sign, then move the decimal point two spaces to the left. For example, 25% becomes 0.25.
Now, let's move on to solving the problems.
1. 0.22 * 198 = 43.56 (option #4)
2. 0.07 * 980 = 68.6 (option #2)
3. 0.15 * 75 = 11.25 (option #3)
4. 0.45 * 62 = 27.9 (option #1)
The data plots represent the hours students study each week in two different classrooms.
The mean number of hours a student in Mr. Hart’s class studies is hours.
The mean number of hours a student in Ms. Perry’s class studies is hours.
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s class.
Poop
Answer:
The data plots represent the hours students study each week in two different classrooms
The mean number of hours a student in Mr. Hart’s class studies is (4.6) hours.
Answer: 4.6
The mean number of hours a student in Ms. Perry’s class studies is (2.8) hours.
Answer: 2.8
A typical student in Mr. Hart’s class studies a typical student in Ms. Perry’s (more than) class.
Answer: More than
Hope this helps
Final answer:
This inquiry involves comparing mean study times and understanding statistical concepts like the 30th percentile and hypothesis testing. The analysis includes determining if study habits have changed and interpreting the implications of percentile ranks among students.
Explanation:
The student's question pertains to statistics, specifically the comparison of mean study times between two classrooms and understanding of percentiles and hypothesis testing in the context of education research. When comparing the mean study times of students in Mr. Hart’s class to those in Ms. Perry’s class, it’s important to gather the numerical data representing the average weekly study hours for each class – which seems missing in the provided details. To understand the 30th percentile, in the context provided, it refers to the number of hours below which 30 percent of the students fall. Thus, thirty percent of students in the high school study seven or fewer hours per week, implying that the majority study more. To conduct a hypothesis test about whether study times have changed, one would set a null hypothesis stating that there has been no change in study time (with the mean study time equal to 2.5 hours), and an alternative hypothesis suggesting that the mean study time has increased. A statistical test (such as a t-test) would then be conducted to assess these hypotheses.
When planning a collaborative exercise for measuring student work habits, it is advisable to incorporate data collection and statistical analysis practices to allow students to understand real-world application of statistical concepts. The example given where students are asked to record their hourly activities over the course of a week is an excellent practice in self-monitoring and time management.
Angle FEG is similar to triangle IHJ. Find the value of X.
Answer:
[tex]x = 14.8[/tex]
Step-by-step explanation:
As these triangles are similar, every side and angle corresponds and this is key to calculating this equation.
First, look at the side that is labeled [tex]x + 8[/tex] and find the corresponding side on the other triangle. Write this out as a fraction as shown below. Now find two corresponding sides that are both marked (the base lines) and write them out as a fraction as well (note that which ever triangle you are solving for, it's numbers will go on the top of the fraction)
[tex]\frac{x + 8}{36} = \frac{38}{60}[/tex]
We want to get the [tex]x[/tex] by its self and at the moment it is divided by 36. To remove the 36, we need to multiply both sides of the equation by 36
36 x [tex]\frac{x + 8}{36} = \frac{38}{60}[/tex] x 36
This cancels out both the 36s on the left leaving us with
[tex]x + 8 = \frac{38}{60}[/tex] x 36
all that needs to happen now is to remove the +8 so we are just left with [tex]x[/tex]. to do this, just subtract 8 from both sides and we are left with
[tex]x = \frac{38}{60}[/tex] x 36 - 8
calculate 38 ÷ 60 x 36 - 8 = 14.8
∴ [tex]x = 14.8[/tex]
I hope this was helpful and not too long :-)
How many solutions exist for the given equation?
1/2(x + 12) = 4x – 1
1.zero
2.one
3. two
4. infinitely many
Answer:
one
Step-by-step explanation: you cant simplify the equation so that both sides can be divided to get the same equation, if you graph it theres not a parabola so the only thing left is one.
Answer:
One solution
Step-by-step explanation:
To solve this problem, isolate x.
1/2(x + 12) = 4x - 1
Dividing 1/2 from both sides, we get x + 12 = 8x - 2
Subtracting 12 from both sides, we get x = 8x - 14
Subtracting 8x from both sides, we get -7x = -14
Dividing -7 from both sides, we get x = 2
Since this problem is able to be solved with only one answer, there is one solution: x = 2.
Simplify. Express your answer as a single term using exponents. 6689x 6689
Answer:
(6689)^2
Step-by-step explanation:
6689x 6689
There are 2 terms multiplied together and they are identical
a*a = a^2
6689x 6689 = (6689)^2
then p=3.
Use the equation k = 3n to find the value of k when n = 3.
Answer:
k = 9
Step-by-step explanation:
n = 3, so substitute 3 for n in the equation
k = 3(3)
k = 9
Which of the following pair of right triangles cannot be proven to be congruent? Select all that apply.
What is the value of a if the point (a, 2) is also on the line?
Answer:
i think -7
Step-by-step explanation:
but im not sure
The Fahrenheit measure of temperature is a function of the Celsius measure. The Fahrenheit measure is 32 more than StartFraction 9 Over 5 EndFraction times the Celsius measure. Which equation best fits the situation? Use g to represent the function. a. x (g) + 32 = StartFraction 9 Over 5 EndFraction (x) b. x (g) = StartFraction 9 Over 5 EndFraction (x) + 32 c. g (x) + 32 = StartFraction 9 Over 5 EndFraction (x) d. g (x) = StartFraction 9 Over 5 EndFraction (x) + 32
Answer:
D. [tex]g(x) = \frac{9}{5}\cdot x + 32[/tex]
Step-by-step explanation:
The mathematical transcription of the statement is:
[tex]g(x) = \frac{9}{5}\cdot x + 32[/tex]
Which corresponds with option D.
I need help! Please answer below on card A
Answer:
x = 8
DBC = 32
Step-by-step explanation:
The sum of the two smaller angles is the larger angle
23+4x = 55
Subtract 23 from each side
23+4x-23 =55-23
4x = 32
Divide each side by 4
4x/4 = 32/4
x = 8
Then we want to find DBC = 4x = 4*8 = 32
The function ƒ(x) = x is transformed to g(x) = 2x. What type of transformation has occurred?
Question 6 options:
A)
Reflection
B)
Vertical translation
C)
Rotation
D)
Can't be determined
Answer:
Scaling
Step-by-step explanation:
Scaling was the type of transformation used on f(x), such that:
[tex]g (x) = 2 \cdot f(x)[/tex]