Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 10.
Answers
check the picture below.
Answer:
x^2/25 + y^2/81 =1
Step-by-step explanation:
solved it
Related Questions
One student can paint a wall in 10 minutes. another student can paint the same wall in 15 minutes. working together, how long will it take for them to paint the wall?
Answers
One student can paint a wall in 10 minutes
another student can paint the same wall in 15 minutes.
If they paint together the wall, the result time will be
15mn - 10mn = 5 mn
proof:
let / = minute
student 1: / / / / / / / / / /
student2: / / / / / / / / / / / / / / /
x----------------------------------------x
already done
the remain time is / / / / / = five minutes
Answer:
6 days
Step-by-step explanation:
Given that one student can paint a wall in 10 minute and another student in 15 minutes.
Since if number of persons increase, painting time decreases, this is a question of inverse proportion
Hence if they work together they can paint in one day
[tex]\frac{1}{10} +\frac{1}{15}[/tex] part of the work
i.e. work completed in 1 day when they work together
=[tex]\frac{1}{10} +\frac{1}{15} \\=\frac{9+6}{90} \\=\frac{1}{6}[/tex]
Hence in 6 days they can together complete the full work
The perimeter of a square is 96 inches. if the side length is 2x + 4, what is the value of x and the length of each side?
Answers
Melissa exercises for 20 minutes every day. She decides to increase her daily exercise time by 5 minutes each week. However, according to her doctor’s orders, she can spend no more than 45 minutes a day exercising. For how many weeks can Melissa increase her exercise time this way?
Answers
45-20 = 25 minutes.
Now we know that each week she increases her time by 5 minutes. Therefore, we have to find how many 5's can fit in the 25 minute difference.
25/5 = 5 weeks
Melissa increases 5 minutes every week for 5 weeks until she reaches her limit of 45 minutes.
I hope that helps!
Answer:
at most 5 weeks
Step-by-step explanation:
A club decides to sell T-Shirts for 15$ as a fund-raiser. It cost $20 plus $9 per T-Shirt to make them. How many T-Shirts need to be made to make a profit of at least $150?
Answers
The expression for total price of selling the T-shirts is 15T
Profit = Total cost of selling - Total cost of buying
Profit = 15T - (20+9T)
Profit = 15T - 20 - 9T
Profit = 6T - 20
To make profit ≥150
6T - 20 ≥ 150
6T ≥ 170
T ≥ 170/6
T ≥ 28.3
The minimum number of T-shirts needed is 29 T-shirts
HOW DO YOU MOVE A VARIABLE FROM ONE SIDE OF AN EQUATION TO ANOTHER? I need to know as I'm reviewing module 7 algebra and i want to know please
Answers
For example in the equation 5+a=7, subtract a from both sides to get 5=7-a.
If the initial equation was 5-a=7, add from both sides (5=a+7).
Basically, if the initial value is negative, add its value to cancel to zero.
Do the opposite if the initial value is positive.
Find the area of the circle with the given radius or diameter. Use = 3.14.
r = 6
A =
37.68 sq. units
113.04 sq. units
226.08 sq. units
Answers
Area of a circle = [tex] \pi r^{2} [/tex] = [tex]3.14 * 6 * 6 = 3.14 * 36 = 113.04 [/tex] sq. units.
Hence, the answer is B.
Answer: 113.04 sq. units
Two less than twice a number is the same as four times the number
Answers
-2+2x=4x
minus 2x both sides
-2=2x
divide by 2
-1=x
the number is -1
Final answer:
The algebraic expression representing 'two less than twice a number is the same as four times the number' is solved, resulting in the number being -1.
Explanation:
The student's question involves solving a simple algebraic equation. We are given that two less than twice a number is the same as four times the number. To represent this algebraically, let's let the unknown number be n. The phrase 'twice a number' can be written as 2n. 'Two less than' this expression would be 2n - 2. The statement implies this is equal to four times the number, which is 4n. Therefore, the equation we need to solve is 2n - 2 = 4n. To solve this equation, we need to isolate the variable n on one side of the equals sign.
Subtract 2n from both sides: -2 = 2n.
Divide both sides by 2 to find the value of n: n = -1.
In conclusion, the number that satisfies the condition given is -1.
The lengths of the sides of a triangle are 6, 8, 10. Can the triangle be a right triangle? Yes or no?
Answers
Redo, Answers please?
Answers
10) ?=13
14) ?=13
11+15+13 = 39
39 - 27 = 12
so
answer
? = 12
10)
18 - 11 + 13 = 20
33 - 20 = 13
so
answer
? = 13
14)
16+17+12=45
45 - 27 = 18
answer
? = 18
The area of one circle is 4 times as large as a smaller circle with a radius of 3 inches. the radius of the larger circle is
Answers
As the area of other circle is four times greater than small one
So the area of larger circle will be= 4(9π)=36π
So the radius will be
area=π r^2
36π=π(r^2)
r^2=36
√r^2=√36
r=6 inchs
ANSWER IS THAT THE RADIUSOF LARGER CIRCLE WILL BE
6 INCHES
please help on b (left of c) and c !!!
rewrite each of the following expressions so that your answer has no negative or fractional exponents
Answers
remember
[tex](ab)^c=(a^c)(b^c)[/tex]
and
[tex]x^\frac{m}{n}=\sqrt[n]{x^m}[/tex]
and
[tex](x^m)^n=x^{mn}
and
[tex]x^0=1[/tex] for all real numbers x
and
[tex]x^{-m}=\frac{1}{x^m}[/tex]
b.
[tex](x^5y^4)^\frac{1}{2}=((x^5)^\frac{1}{2})((y^4)^\frac{1}{2})[/tex]=
[tex](x^\frac{5}{2})(y^\frac{4}{2})=(\sqrt{x^5})(\sqrt{y^4})=x^2y^2\sqrt{x}[/tex]
c.
x^0=1
so
that (x^-3y)^0=1
because exponents first in pemdas
so we are left with
x^2y^-1
[tex]x^2y^{-1}=(x^2)(y^{-1})=(x^2)(\frac{1}{y^1})=\frac{x^2}{y}[/tex]
What percent of 210 is 70?
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 210&100\\ 70&x \end{array}\implies \cfrac{210}{70}=\cfrac{100}{x}\implies x=\cfrac{70\cdot 100}{210}[/tex]
so x%=x/100
'of' means multiply
so
what percent of 210 is 70 translates to
x/100 times 210=70
210x/100=70
21x/10=70
times 10 both sides
21x=700
divide both sides by 21
x=33.333333
33.33333333% of 210 is 70
A given line has the equation 10x + 2y = −2.
What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)?
Answers
Step 1
Find the slope of the given line
we have
[tex]10x+2y=-2[/tex]
Isolate the variable y
Subtract [tex]10x[/tex] both sides
[tex]2y=-10x-2[/tex]
Divide by [tex]2[/tex] both sides
[tex]y=-5x-1[/tex]
The slope of the given line is
[tex]m=-5[/tex]
Step 2
Find the equation of the line that is parallel to the given line and passes through the point [tex](0, 12)[/tex]
we know that
If two lines are parallel. then their slope are equal
In this problem we have
[tex]m=-5[/tex]
[tex](0, 12)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values
[tex]12=-5*0+b[/tex]
[tex]b=12[/tex]
the equation of the line is
[tex]y=-5x+12[/tex]
therefore
the answer is
[tex]y=-5x+12[/tex]
A volcano fills the volume between the graphs z=0 and z=1/(x^2+y^2)^10 and outside the cylinder x+y=1. find the volume.
Answers
For this case, we use
the cylindrical coordinates:
x² + y² = r²
dV = r dz dr dθ
The limits are:
z = 0 to z = 1/(r²)^10 = 1/r^20
r = 1 to ∞
θ = 0 to 2π
Integrating over the limits:
V = ∫ [0 to 2π] ∫ [1 to ∞] ∫ [0 to 1/r^20] r dz dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] rz | [z = 0 to 1/r^20] dr dθ
V = ∫ [0 to 2π] ∫ [1 to ∞] 1/r^19 dr dθ
V = ∫ [0 to 2π] −1/(18r^18) |[1 to ∞] dθ
V = ∫ [0 to 2π] 1/18 dθ
V = θ/18 |[0 to 2π]
V = π/9
The volume of the volcano is an illustration of definite integral
The volume of the volcano is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
The graphs are given as:
[tex]\mathbf{z = 0}[/tex] and [tex]\mathbf{z = \frac{1}{(x^2 + y^2)^{10}}}[/tex]
The cylinder is:
[tex]\mathbf{x + y =1}[/tex]
For cylindrical coordinates, we have:
[tex]\mathbf{r^2 =x^2 + y^2}[/tex]
So, we have:
[tex]\mathbf{z = \frac{1}{(r^2)^{10}}}[/tex]
[tex]\mathbf{z = \frac{1}{r^{20}}}[/tex]
Where:
[tex]\mathbf{r = 1 \to \infty}[/tex]
[tex]\mathbf{\theta = 0 \to 2\pi}[/tex]
So, the integral is:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{20}}} \, r\ dr } \, d\theta }[/tex]
Cancel out r
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {\frac{1}{r^{19}}} \, dr } \, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{V = \int\limits^{2\pi}_0 {\int\limits^{\infty}_1 {r^{-19}} \, dr } \, d\theta }[/tex]
Integrate
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}r^{-18}}} |\limits^{\infty}_1 \, d\theta }[/tex]
Expand
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(\infty^{-18} -1^{-18}) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}(0 -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{-\frac{1}{18}( -1) }} , d\theta }[/tex]
[tex]\mathbf{V = \int\limits^{2\pi}_0 {{\frac{1}{18} }} , d\theta }[/tex]
Integrate
[tex]\mathbf{V = \frac{1}{18}(\theta)|\limits^{2\pi}_0}[/tex]
Expand
[tex]\mathbf{V = \frac{1}{18}(2\pi - 0)}[/tex]
[tex]\mathbf{V = \frac{1}{18}(2\pi )}[/tex]
Cancel out 2
[tex]\mathbf{V = \frac{1}{9}\pi}[/tex]
Hence, the volume is: [tex]\mathbf{\frac{1}{9}\pi}[/tex]
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The circle given by x^2+y^2-4x-10=0 can be written in standard form like this: (x-h)^2+y^2=14. What is the value of h in this equation??
Answers
Answer: H=2
Step-by-step explanation:
we just need to complete the square for the x terms
gropu x terms
x^2-4x
take 1/2 of linear coefient and square it
-4/2=-2, (-2)^2=4
x^2-4x+4
factor
(x-2)^2
h=2
The value of h is 2.
Completing the square for the x terms by grouping x terms
x^2-4x
Taking 1/2 of linear coefficient and squaring it.
-4/2=-2, (-2)^2=4
x^2-4x+4
Factorizing the equation.
(x-2)^2
h=2.
What is an equation?An equation is a mathematical statement this is made of two expressions related with the aid of an identical sign. As instance, 3x – 5 = 16 is an equation. To fix this equation, we get the value of the variable x as x = 7.
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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -(x-4)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answers
g(x) is f(x) reflected about the about the x-axis and shifted to the right by 4 units.
Since -x^2-5 = 0 implies x = +-sqrt(5)i, there are no x-intercepts
Transformations:
Reflect f(x) in the x-axis,
then vertically shift the result down by 5 units,
to get g(x).
A can factory requires 2 sheets of metal to make 36 cans and 10 sheets of metal to make 180 cans. The proportionality constant between the number of cans made and the number of sheets of metal used is
a-36
b-18
c-288
d-5
Answers
Calculate the upper and lower limit for a 95% confidence interval about this mean. a family needs a new car, but isn't sure they can fit the payment into their budget. a sample of 36 months of grocery bills yields a mean of $94 with a standard deviation of $10. if the upper limit of a 95% confidence level is below $100, the family can afford to buy the car. standard error = (standard deviation)/(square root of sample size) upper limit (dollars and cents) lower limit (dollars and cents)
Answers
To find the upper and lower limits of a 95% confidence interval for the given data, calculate the standard error, use the multiplier of 2, and apply the formula Sample mean ± Multiplier * Standard error.
To calculate the upper and lower limit for a 95% confidence interval, we use the formula: Confidence interval = Sample mean ± Multiplier * Standard error. For this case, the sample mean is $94 and the standard deviation is $10. The standard error is calculated as $10 / √36 = $10 / 6 ≈ $1.67.
With a 95% confidence level, the multiplier is approximately 2. Therefore, the upper limit would be $94 + 2($1.67) = $94 + $3.34 ≈ $97.34, and the lower limit would be $94 - $3.34≈ $90.66.
Simplify 5 − (−1).
a. 6
b. −6
c. 4
d. −4
Answers
Subtracting a negative number is the same as adding a positive.
So instead of
5 - (-1)
We could write
5 + 1
5 + 1 = 6
The answer is 6.
Hope this helps! :)
Answer: it is a
Step-by-step explanation: :) :v :B
A ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t^2
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answers
You get : [tex]-16t^2-4t+70[/tex] which can be further simplified to [tex]8t^2+2t-35[/tex] if you divide all of the numbers by -2.
Here you can use the quadratic formula again!
You get the numbers to be : 1.97 and -2.22
I had made a mistake to think that negative numbers can be included but in these questions, you can't have negative numbers as your answer. So the correct answer is 1.97!
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. 1.97 is the time taken by the ball to hit the ground.
What is Distance?Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.
Given that a ball is thrown from a height of 70 feet with an initial downward velocity of 4/fts. The ball's height h (in feet) after t seconds is given by the following.
h=70-4t-16t²
Now we can take h=0
h=-16t²+70-4t
-16t²+70-4t
Divide by 2
-8t²-2t+35
Now apply quadratic formula
a=-8, b=-2, c=35
t=-b±√b²-4ac/2a
t=2±√-2²-4(-8)(35)/2(-8)
t=2±√4+1120/-16
we get t= 1.97 and t= -2.22
You get the numbers to be : 1.97 and -2.22
We do not consider negative values. So the correct answer is 1.97
Hence 1.97 is the time taken by the ball to hit the ground.
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HELP if f(x)=-14x-2, then f^-1(x)=?
Answers
[tex]f(x) = -14x - 2 [/tex]
[tex]y = -14x - 2 [/tex]
[tex]x = -14y - 2 [/tex]
[tex]x+2 = -14y [/tex]
[tex]-14y = x+2 [/tex]
[tex]y = -\frac{x+2}{14} [/tex]
[tex]f^{-1}(x) = -\frac{x+2}{14} [/tex]
Find the missing length.
Answers
a^2+b^2=c^2
12^2+9^2=c^2
144+81= c^2
225=c^2
15=c
Final answer: c=15
Determine the number of possible triangles, abc, that can be formed given c = 85°, a = 10, and c = 13. 0 1 2
Answers
m∠C = 85°, a= 10, c = 13
From the Law of Sines,
sin(A)/a = sin(C)/c
sin(A) = (a/c)*sin(C)
= (10/13)*sin(85°)
= 0.7663
m∠A = sin⁻¹ 0.7663 = 50°, or 130°
When m∠A = 50°, obtain
m∠B = 180° - (m∠A + m∠C) = 180 - (50+85) = 45°
Again from the Law of Sines, obtain
b = (sinB/sinC)*c = 9.2
When m∠A = 130°, obtain
m∠B = 180° - (130 + 85) = -35° (not possible)
Therefore this triangle does not exist.
Answer:
There is only one possible triangle, with
A=50°, B=45°, C=85°, a=10, b=9.2, c=13.
Final answer:
Correcting for the apparent typo in the question, assuming 'c' refers to an angle and a side length respectively, there can only be one possible triangle formed given the angle and two sides. This is based on geometric principles where a unique triangle can be determined from an angle opposite and its respective side length.
Explanation:
The question presents a probable typo since it mentions two different values for 'c'. Assuming 'c = 85°' refers to an angle, and 'c = 13' refers to the length of a side opposite this angle, the proper interpretation involves finding possible triangles given an angle and two sides. However, the principles of geometry dictate that with one angle and two sides specified, especially in this non-ambiguous manner where one side length and the angle opposite are known, one can determine a unique triangle, assuming the given information leads to a viable geometric figure.
By using the Law of Sines, one might attempt to find the other angles or sides, but since we only have one angle and one side length, we directly know there's no ambiguity - geometrically speaking, there's only one way to construct such a triangle, thus, only one possible triangle can be formed given the corrected assumptions.
A square garden plot has an area of 75 ft^2. Find the length of each side in simplest radical form. Calculate the length of each side to the nearest tenth of a foot..
Answers
The area of a square is calculated by the formula:
A = l²
As A = 75 ft², we have:
75 = l²
l = √75
Now, note that: 75 = 3 . 25 = 3 . 5²
So:
l = √(3 . 5²) = √3 . √(5²)
l = 5√3 ft
Now, we can assume √3 = 1.73
l ≈ 5 * 1.732
l ≈ 8,7 ft (Note that I have already put it in the nearest tenth)
OK :)
Which value is in the domain of f(x)?
A.) –7
B.) –6
C.) 4
D.) 5
Answers
f(x) = -2x + 3 0<x <= 4
hope that helps
Answer:
C) 4
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]
The function is defined on two intervals.
The first interval is
[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].
[tex]-7[/tex] does not belong to any of these intervals.
[tex]-6[/tex] does not also belong to any of these intervals.
[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].
Hence 4 is in the domain of f(x).
[tex]5[/tex] does not also belong to any of the intervals.
Therefore the correct answer is C.
What is the circumference of this circle, in millimeters? use 22/7 for pi
r = 49
Answers
Answer: circumference = 308mm
Step-by-step explanation: the formula for the circumference of a circle is given by
C=2πr
Given that r=49mm
Pi=22/4
C=2*22/7*49
C=44*7=308mm
In geometry, the circumference of a circle is the distance around it. That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge of a disk, circumference is a special case of perimeter.
Constantine picks two letters at random from the word constantinople with replacement. what is the probability that both letters picked are consonants?
Answers
P(picking a consonant) = 9/14
P(2 letters are consonants with replacement) = 9/14 * 9/14 = 81/196
When 332 college students are randomly selected and surveyed, it is found that 113 own a car. find a 99% confidence interval for the true proportion of all college students who own a car?
Answers
n = 332, sample size
p = 113/332 = 0.3404, sample proportion
99% confidence interval
The confidence interval for the population is calculated from
[tex]p \pm z^{*} \sqrt{ \frac{p(1-p)}{n} } [/tex]
where z* = 2.58 for the 99% confidence level (from tables)..
[tex]2.58 \sqrt{ \frac{0.3404(1-0.3404)}{332} } =0.0671[/tex]
Therefore the 99% confidence interval is
(0.3404 - 0.0671, 0.3404 + 0.0671) = (0.2733, 0.4075)
Answer:
The 99% confidence interval is (0.273, 0.408) or (27%, 41%).
That is, between 27% and 41% of the students own cars.
Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x^5 + 9x^4 + 5x^3 + 3
Answers
In this case because the highest order term is -3x^5, as x approaches -oo, y approaches +oo. And as x approaches +oo, y approaches -oo.
I need to know the solution
Answers
For the second one, get x by itself as a whole number. Multiply each side by 8. You get x=16. The answer is x=16. Hope this helps! ;)
and
c. x=16
you can also get an app that is called script calculator that helps with that