Answers
Answer D x=40
since x+(4x-20)=180
==>5x=200
==>x=40
Related Questions
Perform the indicated operation. then estimate to see whether the proposed results is reasonable. 11.58 + 11.9 + 9.2
32.68
22.68
33.68
31.68 Preform the indicated operation. Then estimate to see whether the proposed result is reasonable.
93.8 - 6.48
87.32
97.44
87.42
94.34
Preform the indicated operation. Then choose the best answer. 27.7 x 1.9 5.363
52.63
53.62
5.263 Choose the best estimate. 64.1 ÷ 97
641
6.41
0.641
6410 Use estimation to determine whether the result is reasonable or not. 108.93 x 32.6 Result: 355.112 Is it reasonable or not?
Answers
These problems are best done by rounding to easy numbers, then picking the closest value. Below I gave an example of how to round them and then picked the best answer.
1) 12 + 12 + 10 = 34 So 33.68 is the closest.
2) 94 - 6 = 88 So 87.42 is the closest.
3) 28 x 2 = 56 So 53.62 is the closest.
4) 60 / 100 = 0.6 So 0.641 is the closest.
5) 100 x 30 = 3000 So 355.12 is not reasonable.
MATH hw help!!!!!!!!!!!!!!!!!!!!!!!!!!!!
leon made 4 liters of lemonade for the party, but it was too strong, it was 14% lemon juice. How much 8% lemonade should he add to make a mixture that is 10% lemon juice? can someone show me how to solve this using the table or bucket method? thanks
Answers
.. (4)*(14%) + (x)*(8%) = (4 +x)*(10%) . . . . . liters and % are in each "bucket"
.. 56 +8x = 40 +10x . . . . . multiply by 100, eliminate parentheses
.. 16 = 2x . . . . . . . . . . . . . . add -40-8x, then divide by 2
.. 8 = x
8 liters of 8% lemonade should be added to make the mixture 10% lemon juice.
Charlie wants to order lunch for his friends. He'll order 5 sandwiches and a $3 kid's meal for his little brother. Charlie has $28. How much can he spend on each sandwich if they are all the same price? Choose two answers: one for the inequality that models this situation and one for the correct answer.
Answers
5x - 3 ≤ 28
Answer:
5x - 3 ≤ 28
5x ≤ 31
x ≤ 31/5 or 6.2 ($6.20)
The inequality 5x + 3 ≤ 28 represents the situation and each sandwich cost is $5.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
Let x be the cost of each sandwich.
5 sandwich costs = 5x
$3 kid's meal for his little brother.
Total cost = 5x + 3
5x + 3 = 28
5x = 25
x = $5
The inequality:
5x + 3 ≤ 28
Thus, the inequality 5x + 3 ≤ 28 represents the situation and each sandwich cost is $5.
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Elliot got some new trading cards.He has 4 packs with 20 cards each. Another pack has only 8 cards which equation show a way to find how much cards Elliot has in all?
A.c=(4×8)+20
B.c=4+20+8
C.c=(4×20)+8
Answers
PLEASE HELP!!!!!! MEDAL TO RIGHT ANSWER! Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.
A rocket is launched from atop a 76-foot cliff with an initial velocity of 135 ft/s.
A.) Substitute the values into the vertical motion formula h=-16t^2+vt+c. Let h=0
B.) Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
1.)0= -16t^2 + 135t + 76; 0.5 s
2.)0= -16t^2 + 135t + 76; 9 s,
Answers
Write an equation in slope intercept form for the line that passes through (-2,3) and is parellel to the line whose equation 3x+2y=6
Answers
On this exercise is given the equation of a line and a point, and is asked to find the equation of a line in slope-intercept form that is parallel to the given one, and that passes through the given point.
3x+2y=6 Subtract 3x in both sides
2y=-3x+6 Divide by two in both sides to isolate y
y=-3/2x+3
The slope of the given line is -3/2, which means that the slope of a line parallel to this one, have to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the slope-intercept form y=mx+b, where letter m represents the slope.
y=mx+b Substitute the values of the given point and slope
3=(-3/2)-2+b Combine like terms
3=3+b Subtract 3 in both sides
0=b
The equation in slope intercept form for the line that passes through the point (-2,3) and is parallel to the line whose equation is 3x+2y=6 is y=-3/2x or y=-3/2x+0.
Determine whether the statement is always, sometimes, or never true. Complete the explanation. In parallelogram MNPQ, the diagonals MP and NQ meet at R with MR = 7 cm and RP = 5 cm. ; diagonals of a parallelogram each other.
Answers
In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, the statement is always true.
Explanation:The statement is always true. In a parallelogram, the diagonals bisect each other, meaning that they divide each other into two equal parts. Therefore, if MR = 7 cm and RP = 5 cm, then NR = 7 cm and RQ = 5 cm. The diagonals MP and NQ meet at point R, so we have MR = NR and RP = RQ, confirming that the statement is always true.
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What is the rate and unit rate of 16 dollars for 9 books?
Answers
The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all entry tickets during the off-peak season. The Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets to the water park during the off-peak season. 78 = one-half x + (x − 6) What is the regular price of a child's ticket?
Answers
0.5(a + 2c) = 78
0.5(a + a -6)=78
0.5(2a-6)=78
a-3=78
a=81
c=a-6
c=81-6
c=75
Mr. sam's swimming pool is in the shape of a parallelogram, as shown. what is the area of his swimming pool? 189 ft² 234 ft² 279 ft² 585 ft² parallelogram a b c d with side a d parallel to side b c and side a b is parallel to side d
c. point e is on side a
b. a e is 5 feet. dc is 26 feet. a dotted segment d e runs from point d to the opposite side a b and is perpendicular to side a
b. d e is 9 feet.
Answers
Answer: 234
Answer:234
Can someone help me with 2-5?
Answers
Let's say there are 1000 people at the game
0.27*1000 = 270 of them are students
0.06*1000 = 60 are students who didn't buy a program
60/270 = 0.222 = 22.2% of the students will not buy a program
So the answer is roughly 22% when rounded to one decimal place
===========================================================
Problem 3
Like with problem 2, we'll assume 1000 people at the game
0.73*1000 = 730 adults
0.42*1000 = 420 adults buy a program
approximately 420/730 = 0.5753 = 57.53% of the adults bought a program which rounds to 58%
Answer: 58%
===========================================================
Problem 4
The answer here is simply 63% since this is the percent form of 0.63
The value 0.63 is the total for the "Yes" column
You already found this value by adding up the values in the "yes" column from the original table: 0.42+0.21 = 0.63
===========================================================
Problem 5
x = total number of students and adults combined
look in the "students" row and "no" column. The value of 0.06 is found there.
0.06*x = 35
0.06*x/0.06 = 35/0.06
x = 583.333
which rounds to 583
So there are 583 people.
The more surface area an ice cube has, the more quickly it melts to cool a beverage. mark states that the ideal ice cube would be a prism that is a perfect cube of dimensions 2 by 2 by 2. denise thinks that the prism should be more flat, with dimensions of 1 by 2 by 4. which rectangular prism gives the greatest surface area, making for a better ice cube?
Answers
Answer: D
Step-by-step explanation:
Denise Rectangular prism gives the greatest surface area, making for a better ice cube.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
The surface area of a rectangular prism can be calculated by adding up the areas of all six faces.
The surface area of a prism with dimensions l, w, and h is given by:
A = 2lw + 2lh + 2wh
For Mark's prism (2 by 2 by 2), the surface area is:
A = 2(2 × 2) + 2(2 × 2) + 2(2 × 2)= 24
For Denise's prism (1 by 2 by 4), the surface area is:
A = 2 (1 × 2) + 2 (1 × 4)+ 2 (2 × 4)= 28
So both prisms have the different surface area of 24 square units and 28 square units.
Hence, Denise rectangular prism gives the greatest surface area, making for a better ice cube
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A) what is the value such that 50% or more of the students studied longer than that value?
a. 2 hours
b. 9 hours
c. 15 hours
d. 18 hours
e. 29 hours
Answers
someone help a sister out
Answers
x= -2 for the bottom
If f(x)=2x-4 and g(x)=x^2 , what is f(g(x)) ?
Answers
What is the first step in solving 12 (9+5) - 6 (3)?
Answers
Help! Halfway there. Two square pyramids have the same volume. For the first pyramid, the side length of the base is 16 in and the height is 28. On the 2nd pyramid the height is 112. What is the side length of the base of the 2nd pyramid?,
Answers
h = height
s = slant height
a = side length
e = lateral edge length
r = a/2
V = volume
L = lateral surface area
B = base surface area
A = total surface area
Pyramid 1.
h = 28 m
s = 29.1204 m
a = 16 m
e = 30.1993 m
r = 8 m
V = 2389.33 m³
L = 931.854 m2
B = 256 m²
A = 1187.85 m²
Pyramid 2
h = 112 m
s = 112.071 m
a = 7.99999 m
e = 112.143 m
r = 3.999995 m
V = 2389.33 m³
L = 1793.14 m²
B = 63.9999 m²
A = 1857.14 m²
A segment can have more than one bisector.
True
False
Answers
A line passes through the point (–7, 5) and has a slope of 1/2. Which is another point that the line passes through?
(–13, 9)
(–9, 13)
(9, 13)
(13, 9)
Answers
_____
The change in x for the offered points is -6, -2, 16, 20, so the slope of 1/2 will make the change in y be -3, -1, 8, 10. When added to 5, these values are 2, 4, 13, 15. Only 13 matches the second coordinate of the given answer, so only (9, 13) will be a point on the line.
Answer:
Option C is correct.
Another point is, (9, 13)
Step-by-step explanation:
Point slope form states the equation of a straight line in the form [tex]y-y_1=m(x-x_1)[/tex]; ......[1]
where
m is the slope of the line and
[tex](x_1, y_1)[/tex] are the coordinates of a given point on the line.
As per the given condition we have;
[tex](x_1, y_1)[/tex] = (-7, 5)
Slope(m) = 1/2
then; substitute these in [1] we have;
[tex]y -5 = \frac{1}{2}(x-(-7))[/tex]
or
[tex]y -5 = \frac{1}{2}(x+7)[/tex]
Using distributive property; [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]
[tex]y-5= \frac{1}{2}x+\frac{7}{2}[/tex]
Add 5 on both sides we get;
[tex]y=\frac{1}{2}x+\frac{7}{2} + 5[/tex]
Simplify:
[tex]y= \frac{1}{2}x+\frac{17}{2}[/tex]
Only option which satisfy the above line equation is (9, 13).
Check:
put x = 9 and y = 13
[tex]13= \frac{1}{2}(9)+\frac{17}{2}[/tex]
[tex]13=\frac{9}{2}+\frac{17}{2} =\frac{26}{2} = 13[/tex] True.
Therefore, the another point that the line passes through is, (9, 13)
f(5)= 3.14r^{2}
pls help
Answers
.. F(r) = πr^2
and you want to evaluate it for r=5, you put 5 in place of every instance of r, then do the arithmetic.
.. F(5) = π*5^2
.. F(5) = 3.14*25 = 78.5
Alisha has a $15,000 car loan with a 6 percent interest rate that is compounded annually. How much will she have paid at the end of the five-year loan term?
total amount = P (1 + i)t
$19,500.25
$15,900.50
$20,073.50
Answers
r = 6 / 1,200 = .005
Principal = 15,000
n = number of payments = 5 yrs * 12 months = 60
TOTAL Loan Cost = (.005 * 15,000 * 60) / 1 -(1.005^-60)
TOTAL Loan Cost = 4,500 / (1 - 0.7413721962)
TOTAL Loan Cost = 4,500 / 0.2586278038
TOTAL Loan Cost = 17,399.52
Although it is NOT one of the choices, I think my answer of 17,399.52 is correct. Using a monthly loan payment calculator, I get 289.99 for the monthly payment. 290*60 months = 17,400 so that seems correct.
I do not think that formula you posted is correct. (Compare it to the one I posted.)
Answer:
20,073.50
Step-by-step explanation:
i used the formula
Factor. 25m^100 - 121n^16
Answers
a^2 - b^2 = (a + b)(a - b)
In your question all 4 factors must be perfect squares in order to use this property.
25 = 5*5
m^100 = m^50 * m^50
121 = 11 * 11
n^16 = n^8 * n*8
All four parts are perfect squares as required.
a = 5m^50
b = 11n^8
a^2 - b^2 = (5m^50 - 11n^8)(5m^50 + 11n^8)
Helppp!!! Will fan and Medal!!!
suppose n is an integer. select all statements below that are true:
n^2 + n is always an even integer
n^2 + n is always an even integer when n is even
n^2 + n is always an even integer when n is odd
n^2 + n is never an even integer when n is odd
n^2 + n is never an even integer
n^2 + n is sometimes an even integer
Answers
When n = 0 then 0^2 + 0 = 0. n = 1 we have 1^2 + 1 = 2. And when n = 2 we have 2^2 + 2 = 6. When n= 3 we have 3^2 + 3 = 12. When n = 4 we have 4^2 + 4 = 20. When n = 5 we have 5^2 + 5 = 30. When n = 6 = 6^2 + 6 = 42. And finally when n = 7 we have 7^2 + 7 = 56. So at n = 1, 2, ...7, ... Our values are = 2, 6, 12, 20, 30, 42, and 56. It is obvious that n is always an even number. Hence n^2 + n is always an even integer for all positive integers.
When n = -1 we have (-1)^2 - 1 = 0 when n = -2 we have (-2)^2 -2 = 2. When n = -3 we have (-3)^2 - 3 = 6. When n = -4 we have (-4)^2 - 4 = 16 - 4 =12. When n =-5 we have (-5)^2 -5 = 20. When n = -6 we have (-6)^2 - 6 = 30. When n = (-7)^2 - 7 = 42. Hence n^2 + n is always even for all integers
Which equation is true for the value b = 2? 2b + 24 = 30 3b − 2 = 4 b + 4 = 8 2b − 3 = 0
Answers
Hope this helps.
Answer:
3(b – 2) = 24
Step-by-step explanation:
Solve this problem, and identify the percent, amount, and base.
What percent of 60 is 45?
Answers
hope this helps
- Ashley
Answer:
45 is 75% of 60
Step-by-step explanation:
If we want to know what percentage of 60 is 45, our 100% will be 60.
to find out what percentage is 45 we apply a simple rule of three
[tex]60 \longrightarrow 100\\ 45\longrightarrow x\\ x=\frac{45(100)}{60}= 75[/tex]
@ganeshie8
Which of the following would appear in the Credits column of a bank statement for a checking account?
A. An online bill payment
B. Interest earned
C. Bank fees
D. An ATM withdrawal
Answers
Answer:
Interest earned
Step-by-step explanation:
(APEX)
PLEASE PLEASE PLEASE PLEASE HELP ME!
suppose ruth ann has 3 routes she can travel between the school to the library and 5 routes from the library to her home. how many routes are there from ruth anns school to her home with a stop at the library.
a. 9
b. 60
c. 15
d. 25
Answers
There are 3 routes between school and the library.
There are 5 routes from the library to her home.
Therefore, there are 3 x 5 = 15 total routes
Which of the following polynomials corresponds to the product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3?
Answers
The product of the multivariate polynomials 4x - 3y + 5 and x + 2y - -3 is 4x^2 + 5x + 5xy - 16y^2 + 19y - 27.
Explanation:The product of two multivariate polynomials can be found by multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms. In this case, we have:
(4x - 3y + 5)(x + 2y - -3) = 4x(x + 2y - -3) - 3y(x + 2y - -3) + 5(x + 2y - -3)
Using the distributive property, we can simplify this to:
4x^2 + 8xy - 12x - 3xy - 6y^2 + 9y + 5x + 10y - -15
Combining like terms:
4x^2 + 5x + 5xy - 16y^2 + 19y - 27
PLEASE HELP
8.08, part 2
11. Find an equation in standard form for the hyperbola with vertices at (0, ±6) and foci at (0, ±9).
A) y squared over 45 minus x squared over 36 = 1
B) y squared over 81 minus x squared over 36 = 1
C) y squared over 36 minus x squared over 81 = 1
D) y squared over 36 minus x squared over 45 = 1
12. Find an equation in standard form for the hyperbola with vertices at (0, ±4) and asymptotes at y = ± 1 divided by 4. x.
A) y squared over 16 minus x squared over 64 = 1
B) y squared over 16 minus x squared over 256 = 1
C) y squared over 256 minus x squared over 16 = 1
D) y squared over 64 minus x squared over 4 = 1
13. Eliminate the parameter.
x = t - 3, y = t2 + 5
A) y = x2 + 6x + 14
B) y = x2 - 14
C) y = x2 - 6x - 14
D) y = x2 + 14
14. Find the rectangular coordinates of the point with the polar coordinates.
ordered pair 3 comma 2 pi divided by 3
A) ordered pair negative 3 divided by 2 comma 3 square root 3 divided by 2
B) ordered pair 3 square root 3 divided by 2 comma negative 3 divided by 2
C) ordered pair negative 3 divided by 2 comma 3 divided by 2
D) ordered pair 3 divided by 2 comma negative 3 divided by 2
15. Find all polar coordinates of point P where P = negative pi divided by 6 .
A) (1, negative pi divided by 6 + (2n + 1)π) or (-1, negative pi divided by 6 + 2nπ)
B) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + 2nπ)
C) (1, negative pi divided by 6 + 2nπ) or (1, pi divided by 6 + (2n + 1)π)
D) (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
16. Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°.
A) (4 square root 2 , 135°), (-4 square root 2 , 315°)
B) (4 square root 2 , 45°), (-4 square root 2 , 225°)
C) (4 square root 2 , 315°), (-4 square root 2 , 135°)
D) (4 square root 2 , 225°), (-4 square root 2 , 45°)
17. The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph.
a circular graph with an inner loop on the left
[-5, 5] by [-5, 5] (5 points)
A) r = 3 + 2 cos θ
B) r = 2 + 3 cos θ
C) r = 2 + 2 cos θ
D) r = 4 + cos θ
18. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = -2 + 3 cos θ
A) No symmetry
B) y-axis only
C) x-axis only
D) Origin only
19. A railroad tunnel is shaped like a semiellipse, as shown below.
A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis.
The height of the tunnel at the center is 54 ft, and the vertical clearance must be 18 ft at a point 8 ft from the center. Find an equation for the ellipse.
20. Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.
r = 2 cos 3θ
Answers
Since all the vertices and the foci lie along the y axis, therefore, we would need the following equation for vertical hyperbola:
[tex] \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1 [/tex]
Since (h,k) = (0,0)
Therefore, the above equation becomes,
[tex] \frac{(y)^2}{a^2} - \frac{(x)^2}{b^2} = 1 [/tex]
Now the distance between the vertices is:
2a = 12
=> a = 6
And the distance between the foci is:
2c = 18
=> c = 9
Since,
[tex]c^2 = a^2 + b^2[/tex]
=> [tex]b^2 = 45[/tex]
Hence, the equation becomes,
[tex]\frac{(y)^2}{36} - \frac{(x)^2}{45} = 1[/tex] (Option D:y squared over 36 minus x squared over 45 = 1)
12. Ans: (B)
The hyperbola's standard form is(as it is a vertical):
[tex] \frac{y^2}{16} - \frac{x^2}{b^2} = 1 [/tex] -- (X)
=> [tex]y^2 = ( \frac{16}{b^2})*(b^2 + x^2) [/tex]
=> y = ± [tex]( \frac{4}{b} ).x[/tex] --- (A)
Since asymptotes at y = ± [tex]( \frac{1}{4} ).x[/tex]. --- (B)
Compare (A) and (B), you would get,
[tex] \frac{4}{b} = \frac{1}{4}[/tex]
=> b=16
The equation (X) would become:
[tex] \frac{y^2}{16} - \frac{x^2}{256} = 1 [/tex] (Option-B)
13. Ans: (A) [tex]y = x^{2} + 6x + 14[/tex]
Equations given:
x = t - 3 --- (equation-1)
y = [tex]t^{2}[/tex] + 5 --- (equation-2)
From equation-1,
t = x + 3
Put the value of t in (equation-2),
[tex]y = (x+3)^{2} + 5[/tex]
[tex]y = x^2 + 9 + 6x + 5[/tex]
[tex]y = x^2 + 6x + 14[/tex]
Hence, the correct option is (A)
14. Ans: (A)
The polar coordinates given: [tex](3, \frac{2 \pi }{3} )[/tex] = (r, θ)
Since,
x = r*cosθ,
y = r*sinθ
Plug-in the values of r, and θ in the above equations:
x = (3) * cos(120°); since [tex]\frac{2 \pi }{3}[/tex] = 120°
=> x = [tex]- \frac{3}{2} [/tex]
y = (3) * sin(120°);
=> y = [tex] \frac{3 \sqrt{3} }{2} [/tex]
Ans: (x,y) = [tex](- \frac{3}{2} ,\frac{3 \sqrt{3} }{2})[/tex] (Option A)
15. Ans: (D)
The general forms of finding all the polar coordinates are:
1) When r >= 0(meaning positive): (r, θ + 2n [tex] \pi [/tex]) where, n = integer
2) When r < 0(meaning negative): (-r, θ + (2n+1) [tex] \pi [/tex]) where, n = integer
Since r is not mentioned in the question, but in options every r slot has the value r=1, therefore, I would take r = +1, -1(plus minus 1)
θ(given) = [tex] \frac{- \pi }{6} [/tex]
When r = +1(r>0):
(1, [tex] \frac{- \pi }{6} [/tex] + 2n[tex] \pi [/tex])
When r = -1(r<0):
(-1, [tex] \frac{- \pi }{6} [/tex] + (2n+1)[tex] \pi [/tex])
Therefore, the correct option is (D): (1, negative pi divided by 6 + 2nπ) or (-1, negative pi divided by 6 + (2n + 1)π)
16. Ans: (B)
In polar coordinates,
[tex]r = \sqrt{x^{2} + y^{2}} [/tex]
Since x = 4, y=4; therefore,
[tex]r = \sqrt{16 + 16} = 4 \sqrt{2} [/tex]
To find the angle,
tanθ = y/x = 4/4 = 1
=> θ = 45° (when [tex]r =4 \sqrt{2} [/tex])
If r = -[tex]r =4 \sqrt{2} [/tex], then,
θ = 45° + 180° = 225°
Therefore, the correct option is (B) (4 square root 2 , 45°), (-4 square root 2 , 225°)
17. Ans: (B)
(Question-17 missing Image is attached below) The general form of the limacon curve is:
r = b + a cosθ
If b < a, the curve would have inner loop. As you can see in the image attached(labeled Question-17), the limacon curve graph has the inner loop. Therefore, the correct option is (B) r = 2 + 3 cosθ, since b = 2, and a = 3; and the condition b < a (2 < 3) is met.
18. Ans: (C)
Let's find out!
1. If we replace θ with -θ, we would get:
r = -2 + 3*cos(-θ )
Since, cos(-θ) = +cosθ, therefore,
r = -2 + 3*cos(θ)
Same as the original, therefore, graph is symmetric to x-axis.
2. If we replace r with -r, we would get:
-r = -2 + 3*cos(θ )
r = 2 - 3*cos(θ)
NOT same as original, therefore, graph is NOT symmetric to its origin.
3. If we replace θ with -θ and r with -r, we would get:
-r = -2 + 3*cos(-θ )
Since, cos(-θ) = +cosθ, therefore,
r = 2 - 3*cos(3θ)
NOT same as original, therefore, graph is NOT symmetric to y-axis.
Ans: The graph is symmetric to: x-axis only!
19. (Image is attached below) As the question suggests that it is a horizontal ellipse, therefore, the equation for the horizontal ellipse is:
[tex] \frac{x^{2}}{a^{2}} + \frac{y_{2}}{b_{2}} = 1 [/tex] -- (A)
Since, x = 8f,
y = 18ft,
b = 54ft,
[tex]a^{2}[/tex] = ?
Plug-in the values in equation (A),
(A)=> [tex] \frac{64}{a^{2}} + \frac{324}{2916} = 1 [/tex]
=> [tex]a^{2}[/tex] = 72
Therefore, the equation becomes,
Ans: [tex] \frac{x^{2}}{72} + \frac{y_{2}}{2916} = 1 [/tex]
20. Ans: x-axis only
Let's find out!
1. If we replace θ with -θ, we would get:
r = 2*cos(-3θ )
Since, cos(-θ) = +cosθ, therefore,
r = +2*cos(3θ) = Same as original
Therefore, graph is symmetric to x-axis.
2. If we replace r with -r, we would get:
-r = 2*cos(3θ )
r = -2*cos(3θ) = Not same
3. If we replace θ with -θ and r with -r, we would get:
-r = 2*cos(-3θ )
Since, cos(-θ) = +cosθ, therefore,
r = -2*cos(3θ) = Not Same
Ans: The graph is symmetric to: x-axis only!
Final answer:
To find the equations of the axes, asymptotes, and conjugate hyperbola of a given hyperbola in general form, algebraic manipulation including finding the hyperbola's center, complementing squares for x and y, and determining the asymptote slopes is necessary.
Explanation:
When encountering the equation of a hyperbola in the general form ax² + 2hxy + by² + 2gx + 2fy + c = 0, finding the axes, asymptotes, and equation of the conjugate hyperbola requires a series of steps and some algebraic manipulation. Here's an outline how you would typically approach it:
First, find the center of the hyperbola by solving the system of equations derived from the partial derivatives with respect to x and y set to zero.
Transform the equation by completing the square for both x and y terms to determine the values of the semi-major and semi-minor axes.
To find the slopes of the asymptotes, you'd use the equation derived from the general form by setting the constant term such that only the x and y squared terms remain.
Lastly, the conjugate hyperbola can be determined by changing the signs associated with the squared terms.
As an example, an original hyperbola's equation might look like 8x² + 10xy - 3y² - 2x - 4y - 2 = 0. After required algebraic manipulations, which include centering the hyperbola and finding the orientation of the axes, the equations to the asymptotes are derived by setting the constant term to create the equation 8x² + 10xy - 3y² = 0 and solving for y in terms of x. Meanwhile, the conjugate hyperbola is found by negating the sign of the y squared term in the transformed equation of the original hyperbola.
a painter needs to cover a triangular region 60 meters by 68 meters by 71 meters. a can of can cover 70 square meters.. how many cans will be needed??,
Answers
perimeter = 60 + 68 +71 = 199
SEMI-Perimeter = 199/2 = 99.5
Area = sq root (99.5 * (99.5-60) * (99.5-68) * (99.5-71)
Area = sq root (99.5 * 39.5 * 31.5 * 28.5)
Area = sq root ( 3,528,381.94 )
Area = 1,878.4 square meters
1,878.4 / 70 sq mtr per can means you will need
26.83 cans OR 27 cans
To cover the triangular region, the painter will need approximately 29 cans of paint.
Explanation:To find the number of cans needed to cover the triangular region, we first need to calculate the total area of the region. We can do this by using the formula for the area of a triangle: A = (1/2) * base * height. Assuming the 60 meters side is the base, we can use the formula to find the area: A = (1/2) * 60 * 68. The area of the triangular region is 2040 square meters. Since each can covers 70 square meters, we can divide the total area by the area covered by each can: 2040 / 70 = 29.14.
Therefore, the painter will need approximately 29 cans of paint to cover the triangular region.
Learn more about Calculating the number of paint cans needed for a triangular region here:https://brainly.com/question/16550947
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