Find the area of the figure. Use 3.14 for π.
Total Area:- Area of square + area of Semicircle
Total area :- (L×B)+ (½× πr²)
Total area:- (12×12)+(½×π6²)
Total area:- 144+(½× 113)
Total area:- 144+ 56.5
Total area :- 200.5
polar & rectangular equations
Answer:
13. [tex]x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]
14. [tex]r=3\cos(\theta)-2\sin(\theta)[/tex]
Step-by-step explanation:
Question 13
Conversion from Polar equation to rectangular equation:
[tex]x=r \cos(\theta) \implies \cos(\theta)=\dfrac{x}{r}[/tex]
[tex]y=r \sin(\theta) \implies \sin(\theta)=\dfrac{y}{r}[/tex]
[tex]x^2+y^2=r^2 \implies r=\sqrt{x^2+y^2}[/tex]
Given:
[tex]r=3-2\cos(\theta)[/tex]
[tex]\textsf{Substitute }\cos(\theta)=\dfrac{x}{r}:[/tex]
[tex]\implies r=3-\dfrac{2x}{r}[/tex]
Multiply both sides by r:
[tex]\implies r^2=3r-2x[/tex]
[tex]\implies r^2+2x-3r=0[/tex]
[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }r=\sqrt{x^2+y^2}:[/tex]
[tex]\implies x^2+y^2+2x-3\sqrt{x^2+y^2}=0[/tex]
---------------------------------------------------------------------------------------------
Question 14
Conversion from Rectangular equation to polar equation:
[tex]x=r \cos(\theta)[/tex]
[tex]y=r \sin(\theta)[/tex]
[tex]x^2+y^2=r^2 \implies r^2\cos^2(\theta)+r^2\sin^2(\theta)=r^2[/tex]
Given:
[tex]x^2+y^2-3x+2y=0[/tex]
[tex]\textsf{Substitute }x^2+y^2=r^2\:\textsf{and }x=r \cos(\theta)\:\textsf{and }y=r \sin(\theta):[/tex]
[tex]\implies r^2-3r\cos(\theta)+2r\sin(\theta)=0[/tex]
Factor out common term r:
[tex]\implies r(r-3\cos(\theta)+2\sin(\theta))=0[/tex]
Divide both sides by r:
[tex]\implies r-3\cos(\theta)+2\sin(\theta)=0[/tex]
Rewrite to make r the subject:
[tex]\implies r=3\cos(\theta)-2\sin(\theta)[/tex]The base of the sailboat is 9ft and the height is 15 what is the area??
Please answer asap, 30+ points
Step-by-step explanation:
please mark me as brainlest
A straw is placed inside a rectangular box that is 3 inches by 6 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in simplest radical form.
The straw is placed diagonally in the rectangular prism, therefore, the length of the straw is √109 inches
How to find the diagonal of a rectangular prism?
Diagonal of a rectangular prism = √(l² + w² + h²)
Where,
l = lengthw = widthh = heightTherefore,
l = 6 inches
w = 3 inches
h = 8 inches
diagonal = √(6² + 3² + 8²)
diagonal = √36 + 9 + 64
diagonal = √109 inches
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Solve each system by substitution. Show all work.
y = -3x
y= x-4
since y = - 3x and y = x - 4
we have
- 3x = x - 4
4x = 4
x = 1
and then y = - 3 * 1 = - 3
(1 ; - 3)
Answer:
(1,-3)
Step-by-step explanation:
y = -3x
y= x-4
Substitute -3x for y in the second equation
-3x = x-4
Subtract x from each side
-3x-x = x-4-x
-4x = -4
Divide each side by -4
-4x/-4 = -4/-4
x=1
Now we can find y
y = x-4
y = 1-4
y= -3
(1,-3)
Which ordered pair is the solution of the system of a linear equation? (See image)
Answers:
(-4,-2)
(-4,2)
(-2,-4)
(2,4)
Check the picture below.
what is the perimeter ?
Step-by-step explanation:
the outer left side is also 50 ft.
in inner (upper) left side is also 13 ft.
the bottom line is 10+20+11 = 41 ft
this is all possible because all the angles are clearly right angles (90°).
so, the perimeter is
2×(10+20+11) + 2×50 + 2×13 = 82 + 100 + 26 = 208 ft
help me with this please
Answer:
B and C
Step-by-step explanation:
Answer:
-15/-3,-5/-1
Step-by-step explanation:
please mark me as brainlest
How many 1/ 4 cup servings are in a package of cheese that contains 6 and 1/2 cups altogether?
in essence, how many times does 1/4 go into 6 and 1/2?
[tex]\stackrel{mixed}{6\frac{1}{2}}\implies \cfrac{6\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{13}{2}\div \cfrac{1}{4}\implies \cfrac{13}{2}\cdot \cfrac{4}{1}\implies \cfrac{13}{1}\cdot \implies \cfrac{4}{2}\cdot 13\cdot 2\implies 26[/tex]
Please help this is using the digits 0 to 9
Answer:
1% of 100 = 1
Step-by-step explanation:
simple and easy :D hope this helps
Benito made a small pitcher of fruit punch. He mixed together lemonade and cherry juice. Use the picture to find the amount of juice Benito made. A 9 liters В 100 milliliters C 900 milliliters D2 liters 900 milliliters
The amount of juice by Benito is an illustration of volumes
The amount of juice made is 900 milliliters
How to determine the amount of juice made?The question is incomplete, as the figure and the dimensions are not given.
So, I will give a general solution
Assume the following parameters
Shape of the punch = CylinderRadius = 4Height = 18The amount of juice would be:
V = πr^2h
This gives
V = 3.14 * 4^2 * 18
Evaluate
V = 904.32
Approximate
V = 900
Hence, the amount of juice made is 900 milliliters
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Which one should I choose
Answer:
b) Quad ABCD must be a rectangle and could be a rhombus
Step-by-step explanation:
:)
At a height of 316 meters, the Bell Tower is the tallest building in Morgansville. Hank is creating a scale model of this building using
the scale 100 meters: 1 meter.
To the nearest tenth of a meter, what will be the height of the scale model?
Answer:
Scale: 100 meters per 1 meter
Actual: 316 per unknown meters(our scale)
So order our units:-
Scale 1 x_______ _______ = _______, solve for x;
Meters 100 3161/100 = x/316
*316 *316
3.16 = x, 3.16 rounded = 3.20 is the scale.
Please I need help
Will give brainlest answer !!!!!!
Answer:
See below ↓
Step-by-step explanation:
We need to check the different time intervals to find the max. height
t = 0 or 1 [both give same result]f(1) = -16(1) + 16(1) + 12 = 12 feet2. t = 2
f(2) = -16(2)² + 16(2) + 12 = -20 feet⇒ Clearly as she is diving, her maximum height will be her initial height which is 12 feet
⇒ To achieve this, it takes her 0 seconds [initial height = no time needed]
Taking f(x) = 0 [surface of water → just touching/hit the water]
0 = -16x² + 16x + 124x² - 4x - 3 = 04x² - 6x + 2x - 3 = 02x(2x - 3) + 1(2x - 3) = 0(2x + 1)(2x - 3) = 0x is positivex = 3/2 = 1.5 seconds⇒ After 1 second, she is 12 feet above the water
⇒ The diving board is 12 feet above the water
The area of a circular fountain is 121pi square feet. What is the diameter of the fountain?
Answer:
22 feet
Step-by-step explanation:
Area of circle = pi(r²)
the square root of 121 is 11, so r = 11
d = 2r
d = 22
Divide and simplify if possible sqrt 250x^16/sqrt 2x.
Answer:
125x^15
Step-by-step explanation:
Hope this helps! :)
8,14,20, Find the 49th term.
Answer:
2,8,14,20...… the 49th term is 294.
Step-by-step explanation:
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!
Answer:
294
Step-by-step explanation:
formula
an=a1 +(n-1)d
n= unknown term
d= difference between each term
8=a1
14=a2
20=a3
a49=8+(49-1)×(6)
a49= 8+ 48 ×(6)
a49= 8+ 288
a49= 294
Sharon is preparing for a trip to kuwait. she calculates that she will need $1,166 to be converted to kuwaiti dinar. if the exchange rate of us dollars to kuwaiti dinar is 1:0.2879, how many dinar does sharon have? round your answer to two decimal places. a. 335.69 dinar b. 405.00 dinar c. 3,356.91 dinar d. 4,050.02 dinar
Answer:
335.69
Step-by-step explanation:
If the exchange rate of USD to Kuwaiti Dinar is 0.2879, multiply the amount of USD by the exchange rate to get the answer.
$1,166 x 0.2879 = 335.6914
335.6914 rounded to the nearest hundredth (two decimal places) is 335.69
So, it is A, 335.69 dinar.
335.69 dinar Sharon will get in exchange for $1,166 option (a) 335.69 is correct.
What is the ratio?It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.
We have a total amount that will need to convert = $1,166
Exchange rate of us dollars to kuwaiti dinar = 1 : 0.2879
It means $1 converted into 0.2879 dinar
The amount $1,166 in kuwaiti dinar = 1166×0.2879
= 335.69 dinar
Thus, 335.69 dinar Sharon will get in exchange for $1,166 option (a) 335.69 is correct.
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Three playing cards in a row. Can you name them with these clues? There is a two to the right of a king. A diamond will be found to the left of a spade. An ace is to the left of a heart. A heart is to the left of a spade. Now, identify all three cards.
Answer:
Ace of Diamonds, King of Hearts, Two of Spades ( hope this helps)
Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth
Which algebraic expressions are binomials? Check all that apply.
xyStartRoot 8 EndRoot
x2y – 3x
6y2 – y
y2 + StartRoot y EndRoot
4xy – two-fifths
x2 + StartFraction 3 Over x EndFraction
The algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5
What are polynomials?Polynomials are algebraic expressions having only addition, subtraction, multiplication and exponentiation (non-negative) of variables involved in it.
What are terms in polynomials?Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.
Example:
[tex]x^3 + 3x +5[/tex]
is a polynomial consisting 3 terms as
[tex]x^3[/tex], 3x and 5
If there is one term, the polynomial will be called monomial.If there are two terms, the polynomial will be called binomialIf there are three terms, the polynomial will be called trinomialChecking all the options:
Option 1: [tex]xy\sqrt{8}[/tex]It has only one term, so its not a binomial.
Option 2: [tex]x^2y - 3x[/tex]It has two terms, and there is only integer powers of variables and variables are in multiplication in forming terms, so its a polynomial. And because of two terms and being polynomial, it is binomial.
Option 3: [tex]y^2 + \sqrt{y}[/tex]Because of square root over variable 'y', the variable 'y' got non-integer power 1/2 as square root is also written as exponentiation by 1/2.
Thus, its not a polynomial.
Option 4: [tex]4xy - 2/5\\[/tex]Its a polynomial as there are constants only and variables with multiplication. And because of two terms and being polynomial, it is binomial.
Option 5: [tex]x^2 + \dfrac{3}{x}[/tex]we can write the second term as:
[tex]\dfrac{3}{x} = 3x^{-1}[/tex]
Thus, the variable x has negative power. Thus, its not a polynomial. Or simply, since the variable is in division in simplified form, therefore, its not a polynomial.
Thus, the algebraic expressions out of the given options that are binomials is given by: Option B: x^2y - 3x and Option D: 4xy - 2/5
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A cone has a base radius of 4.3 cm and perpendicular height of 8.4 cm.
It has the same volume as a sphere. Find the radius of the sphere.
Answer:
R=3.38627
Step-by-step explanation:
WILL GIVE BRAINLIST IF SHOWS MUST BE CORRECT
The number of goals scored by players on a soccer team is represented by the box plot below.
The measure of variability that best describes how the values in this data set vary is
A. Median
B. mean absolute deviation
C. interquartile range
D. mean
E. mode
because
A. there is an odd number of values in the data set
B. there is an outlier in the data set
C. the data distribution is symmetric
.
The measure of variability that describes the values in the box plot is: C. interquartile range, because: C. the data distribution is symmetric.
What is a Symmetric Data Distribution in a Box Plot?A symmetric data distribution is depicted on a box plot when the median is in the middle of the rectangular box, and the whiskers are of almost the same length at both sides of the box. Such data distribution is said to be normally distributed.
A normally distributed data distribution is symmetric.
Interquartile range is a measure of variability in a box plot, which is the range of the rectangular box.
Therefore, the measure of variability that describes the values in the box plot is: C. interquartile range, because: C. the data distribution is symmetric.
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: the mass of an average classroom meter stick is roughly 0. 2 kg.
the mass of the moon is approximately 7*1022 kg.
question 1: how many meter sticks does it take to equal the mass of the moon? explain or show your reasoning
Using proportions, it is found that it takes [tex]3.5 \times 10^{23}[/tex] meter sticks to equal the mass of the moon.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, one meter stick has a mass of 0.2 kg. How many meter sticks are needed for a mass of [tex]7 \times 10^{22} \text{kg}[/tex]? The rule of three is given by:
One meter stick - 0.2 kg
x meter sticks - [tex]7 \times 10^{22} \text{kg}[/tex]
Applying cross multiplication:
[tex]0.2x = 7 \times 10^{22}[/tex]
[tex]x = \frac{7 \times 10^{22}}{0.2}[/tex]
[tex]x = 35 \times 10^{22}[/tex]
[tex]x = 3.5 \times 10^{23}[/tex]
It takes [tex]3.5 \times 10^{23}[/tex] meter sticks to equal the mass of the moon.
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Which student solved the equation 107 d = 1,733.4 correctly?
Gianna's work: 107 d = 1,733.4. 1,733.4 times 107 = 185,473.8.
Teddy's work: 107 d = 1,733.4. 1,733.4 minus 107 = 1,626.4.
Sid's work: 107 d = 1,733.4. 1,733.4 + 107 = 1,880.4.
Sammi's work: 107 d = 1,733.4. 1,733.4 divided by 107 = 16.2.
Answer:
Sammis work is correct
Step-by-step explanation:
when handling equations such as 107d= 1,733.4
you see that d is being multiplied to 107 to equal the total,
so to find the answer to d you would divide 107 by the total to get your value of d
Answer:the last one
Step-by-step explanation:
If the coefficient of determination is 0. 12 and ssy = 225, then what is the sum of squares regression for an analysis of regression?
The coefficient of determination is the ratio of the sum of squares regression and the ssy
The sum of squares regression is 27
How to determine the sum of squares?The given parameters are:
Coefficient of determination, R^2 = 0.12
SSy = 225
The coefficient of determination is calculated as:
R^2 = SSR/SSY
So, we have:
0.12 = SSR/225
Make SSR the subject
SSR = 0.12 * 225
Evaluate the product
SSR = 27
Hece, the sum of squares regression is 27
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The sum of squares regression is 27
What is the coefficient of determination?The coefficient of determination or R squared method is the proportion of the variance in the dependent variable that is predicted from the independent variable.
The coefficient of determination is calculated by using the following formula;
[tex]\rm R^2 = \dfrac{SSR}{SSY}\\\\ 0.12= \dfrac{SSR}{225}\\\\ SSR = 225 \times 0.12 \\\\ SSR = 27[/tex]
Hence, the sum of squares regression is 27.
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#SPJ3
6:4 is equivalent to ___:24.
What number do you think should go on the blank?
Answer:
36:24
Step-by-step explanation:
The second number was :24, and you started out with 6:4.
To get the 24, you would have to multiply the 4 by 6 to get the 24.
So, multiply the first number 6, as well by 6.
6 x 6 = 36
36:24
:)
Answer: 36
Step-by-step explanation: 6:4 = __:24
1. 4 goes into 24, 6 times because 4x6=24 so you have to multiply 6 to 6 and 6x6=36.
Plssss help me with this!!!! It’s really hard
Answer:
2x < 10 would show that even 'if' x would make 2 larger, it still wouldn't match up to 10. But in this case, 2 would turn into 10. 10 = 10.
What strategy would be the best to solve this problem?
To get into shape, Miles ran for 1 minute on Monday, 3 minutes on Tuesday, 6 minutes on Wednesday, and 10 minutes on Thursday. If he continues, how many minutes will Miles run on Sunday?
A. guess, check and revise
B. work backwards
C. use a formula
D. look for patterns
Answer:
D. look for patternsStep-by-step explanation:
Number the weekdays, and relevant time, then look for the pattern
Monday = 1, time = 1 minTuesday = 2, time = 3 minWednesday = 3, time = 6 minThursday = 4, time = 10 minFriday = 5, time = xSaturday = 6, time = ySunday = 7, time = zWe get the series:
1, 3, 6, 10, x, y, zIf you notice, the difference between the terms is:
2, 3, 4, ...It indicates the following terms are:
x = 10 + 5 = 15y = 15 + 6 = 21z = 21 + 7 = 28Since z represents the seventh term, the running time on Sunday is 28 minutes.
As we see looking for patterns helped to solve the question.
Correct choice is D
Answer:
D
Step-by-step explanation:
Because its D