Which of the following is the standard equation of the ellipse with vertices at (1, 0) and (11, 0) and an eccentricity of three fifths question mark
quantity x minus 6 end quantity squared over 100 plus y squared over 64 equals 1
quantity x plus 6 end quantity squared over 64 plus y squared over 100 equals 1
quantity x plus 6 end quantity squared over 16 plus y squared over 25 equals 1
quantity x minus 6 end quantity squared over 25 plus y squared over 16 equals 1
Answers
The equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
What is an ellipse?An ellipse is a locus of a point that moves in a plane such that the sum of its distances from the two points called focus adds up to a constant. It is taken from the cone by cutting it at an angle.
We have:
The vertices of the ellipse = (1, 0) and (11, 0)
Eccentricity of ellipse = 3/5
We have equations:
[tex]\rm \dfrac{\left(x-6\right)^{2}}{100}+\dfrac{y^{2}}{64}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{64}+\dfrac{y^{2}}{100}=1[/tex]
[tex]\rm \dfrac{\left(x+6\right)^{2}}{16}+\dfrac{y^{2}}{25}=1[/tex]
[tex]\rm \dfrac{\left(x-6\right)^{2}}{25}+\dfrac{y^{2}}{16}=1[/tex]
From the fourth equation:
The vertices of the ellipse:
(1, 0) and (11, 0)
The eccentricity:
c² = a² - b²
c² = 25-16
c = 3
e = c/a = 3/5
Thus, the equation fourth represents the ellipse that has vertices at (1, 0) and (11, 0), and an eccentricity of 3/5 option fourth is correct.
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Related Questions
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set
builder form using a compound inequality.
Note: To type in the sign, type <= or use the Math Quill by clicking the yellow arrow.
Answers
Answer:
Domain: Interval notation is [tex](-3, 4][/tex], set builder is [tex]\{x|-3 < x\leq4 \}[/tex]Range: Interval notation is [tex][0, 3)[/tex], set builder is [tex]\{y|0\leq y < 3\}[/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Classify each of the following variables as quantitative or qualitative. For those which are quantitative, classify them further as continuous or discrete.
a) Weight of adult females
b) Street addresses in Addis Ababa
c) Years of professional experience of employees
d) Number of courses offered to students in AAU in this semester.
Answers
Answer:
a) quantitative - continuous
b) qualitative
c) quantitative - discrete
d) quantitative - discrete
Explanation:
A qualitative variable describes an object or its property without counting or measuring. Therefore it does not include any numbers.
A quantitative variable is one which results from counting or measuring a property of an object or situation. If the variable arises from counting, it is called discrete, and if it arises from any measurement, it is called continuous.
What is the surface area of a square prism with sides that measure 8 units?
O254 units²
O 300 units²
0314 units²
0384 units²
Answers
Answer:
384 units²
Step-by-step explanation:
The area of one face is (8)(8)=64.
Multiplying this by the six faces, we get 64(6)=384
if the ratio of three angles of a triangle is 2:3:4 find the size of the largest angle
Answers
Step-by-Step Explanation:
By Angle Sum Property of a Triangle, all angles in a Triangle add up to 180°
Finding the Value of ‘x’ :-
2x + 3x + 4x = 180
5x + 4x = 180
9x = 180
x = 180/9
=> x = 20
Finding each Angle :-
2x = 2(20) = 2 * 20 = 40°
3x = 3(20) = 3 * 20 = 60°
4x = 4(20) = 4 * 20 = 80°
Hence, the Largest Angle is 80°
A 7 x 8 array is 7 rows of ____
Answers
Answer:
8
Step-by-step explanation:
It's 7 rows of 8 items
Graphing a exponential decay function
Answers
The process of Graphing a exponential decay function is shown in detail below.
There are two types of exponential equations: exponential decay and exponential growth. The fundamental shape of an exponential function and its corresponding graphs must be understood in order to fully comprehend the distinctions between exponential growth and decay. The fundamental distinction between the two is that in an exponential decay connection, the output values rise quickly as the input value rises, but in an exponential growth relationship, the output rises noticeably faster as the input value rises. Furthermore, neither of the two functions is linear, hence their rate of change is not constant. What distinguishes one equation from the other when they both have the same precise form, y = abx?
The value of the constant "b" is the fundamental factor in deciding whether the exponential function is one of growth or decay:
If function y = ab^x and b > 1then the function is an exponential growth function.If the function y = ab^x and 0<b<1 then the function is an exponential decay function. As noted before, "b" can never be exactly 1.In this way we can graph a exponential decay function
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The Gross Domestic of a country in the first quarter of 2014 was $1.3299×10×8.
GPD=$
Answers
The GDP of the country for 2014 is $5.3196 × 10⁸.
What is multiplication?Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given the Gross Domestic of a country in the first quarter of 2014 was $1.3299×10⁸. Therefore, the GDP of the country for that year will be,
GDP = 4 × (Gross Domestic for a single quarter)
= 4 × ($1.3299×10⁸)
= $5.3196 × 10⁸
Hence, the GDP of the country for 2014 is $5.3196 × 10⁸.
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Any help will do! Thank you!
Answers
Let's take this problem step-by-step:
First let's set up the equation for the cost for one week of renting the car
agency charges $230 per week[tex]charge = 230[/tex]
agency charges $0.25 per mile (lets set the number of miles as 'x')[tex]charge = 230 + 0.25x[/tex]
The total cost was 415, therefore:
[tex]415 =230 + 0.25x\\185 = 0.25x\\x = 740[/tex]
Therefore, you traveled 740 miles
Answer: 740 miles
Hope that helps!
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ABC is an isosceles triangle, with AB = AC. find X
Answers
Answer:
67.13°
Step-by-step explanation:
First separate triangles then you use Pythagoras theorem to get the third side and then apply the sine rule
Factorise and evaluate
50 × 11 + 50 × 9
Answers
Answer:
1000
Step-by-step explanation:
50 × 11 + 50 × 9 ← factor out 50 from each term
= 50(11 + 9)
= 50(20)
= 1000
Evaluate: y(x+x)+3, where x=1 and y=3 A. 3 B. 10 C. 9 D. 5
Answers
Answer:
C. 9
Step-by-step explanation:
y(x+x) +3
{x= 1 , y= 3}
Putting values..
3 (1+1) +3
= 3 (2) +3
= 6 + 3
= 9
So, the option C. 9 is the correct answer.
Write an algorithm to find Area of square?
Answers
Step-by-step explanation:
AREA OF SQUARE:
A square is simply a rectangle with equal sides. As a result, the length and breadth of a square are equal. As a result, the area of a square is the product of two square sides, or in simpler terms, squares of the side.
Area = Side^{2}Area=Side
2
We use the following formula to compute the area of a rectangle after being given the length and width of the rectangle as input.
ALGORITHM:
Step 1 : Start
Step 2: Input Side
Step 3: Area = Side \times× Side
Step 4: Print area
Step 5: Stop
How many full cases and additional items are needed to fulfill the order 80 6
Answers
The number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The question is incomplete.
The complete question is:
80 units needed 6 units per case. What are the number of cases and the number of additional units?
Total number of units = 80 units
6 units per case
Number of case = 80/6 = 13.33 ≈ 13
Total units if the number of cases = 13
= 13×6
= 78
Additional units = 80 - 78 = 2 units
Thus, the number of cases is 13 and the additional units are 2 if the 80 units needed 6 units per case.
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From Khan Academy Pre Algebra
Please Evaluate This Question:
Answers
answer is this in decimal form if this is what ur looking for 4.21900462…
hope it helps....
Answer:
17.8
Step-by-step explanation:
Suppose a jar contains 12 red marbles and 12 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red
Answers
The probability that both are red marbles is 0.2391
How to determine the probability?The given parameters are:
Red =12
Blue = 12
Total = 24
The probability of selecting the first red marble :
P(Red) = 12/24
Now, there are 11 red marbles and 23 marbles in all
The probability of selecting the second red marble :
P(Red) = 11/23
The required probability is:
P = 12/24 * 11/23
Evaluate
P = 0.2391
Hence, the probability that both are red marbles is 0.2391
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Steve is ordering burgers and individual pizzas for $1000. He plans to buy not more than 80 items. The costs of each burger and each pizza are $7 and $4. Select the inequality that describes this situation. Use the given numbers and the following variables. x = the number of burgers. y = the number of pizzas.
Answers
[tex]x+y\leq 80[/tex]
[tex]7x+4y=1000[/tex]
The number of burgers = [tex]x[/tex]
the number of pizzas = [tex]y[/tex]
the cost of each burger = $[tex]7[/tex]
the cost of each pizza = $[tex]4[/tex]
not more than 80 items: [tex]x+y\leq 80[/tex]
total price =[tex]7x+4y=1000[/tex]
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Which of these could be the graph of F(x) = log₂ x?
A
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
The graph of the function is shown in the attached image.
Z varies directly as x^3 and inversely as y^3. If z=167 when x = 3 and y=10, find z if X=4 and y=6
Answers
Answer is 1832.7
step by step
z=kx^3 / y^3
167=27k/1000
k=16700/27
k=6185.2, then
z=6185.2×4^3/6^3
z=6185.2×64/216
z=1832.7
find the perimeter: (use 3.14 for pi):
Answers
Answer:
10.676 mm
Step-by-step explanation:
The perimeter of a circle (circumference) formula is 2*(3.14)*r. Therefore since r is 1.7, 2*3.14*1.7 = 10.676 mm.
Hope this helps!!! Please mark me as brainliest!!!
Solve the problem.
The length of a rectangular room is 9 feet longer than twice the width. If the room's perimeter is
198 feet, what are the room's dimensions?
Answers
Answer:
width is 30, and the length 69.
Step-by-step explanation:
In order to do this, we need to do ALGOOBRAA
lets say x is equal to the width of the room
then, that means the length is (9+2x) Sooooo,
198=2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you dont know what that is, then go search it up :/
so,
198=2x+18+4x
198=6x+18
180=6x
30=x
BAM
Now, we know that the width is 30, bro.
That means the length is 60+9, Which is 69.
Therefore, the width is 30, and the length 69.
Sry if im wrong btw.
The width of rectangle is 30, and the length is 69.
What is Rectangle?
A rectangle is a quadrilateral. The opposite sides of a rectangle are equal and parallel to each other. The interior angle of a rectangle at each vertex is 90°. The sum of all interior angles is 360°. The diagonals bisect each other.
Here, lets say x is equal to the width of the room
then, that means the length is (9+2x) So,
198 = 2x+2(9+2x)
Using the distributive property, we know that
2(9+2x)=18+4x
If you don't know what that is, then go search it up :/
so,
198 = 2x+18+4x
198=6x+18
180=6x
30=x
Now, we know that the width is 30,
That means the length is 60+9, Which is 69.
Thus, the width of rectangle is 30, and the length is 69.
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use the point-slope formula to write an equation of the line that passes through (6,- 3) and (3,1).
Write the answer in slope-intercept form (if possible).
Answers
The slope of the line is
[tex]\frac{-3-1}{6-3}=\frac{-4}{3}[/tex]
Substituting into point-slope form using the point (3,1),
[tex]\boxed{y-1=-\frac{4}{3}(x-3)}\\\\y-1=-\frac{4}{3}x+4\\\\\boxed{y=-\frac{4}{3}x+5}[/tex]
Answer: The equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex] +5.
Step-by-step explanation:
Point-slope formula : (y - y1) = m(x - x1)
y = y coordinate of second point
y1 = y coordinate of first point
m = slope
x = x coordinate of second point
x1 = x coordinate of first point
slope (m) = [tex]\frac{1-(-3)}{3-6}[/tex]
m = [tex]\frac{4}{-3}[/tex] or [tex]\frac{-4}{3}[/tex]
now put values in point-slope formula : (y - 1) = [tex]\frac{-4}{3}[/tex](x - 3)
y - 1 = [tex]\frac{-4x}{3\\}[/tex] + 4
y = [tex]\frac{-4x}{3}[/tex] +5
So the equation of the line that passes through (6,- 3) and (3,1) is y = [tex]\frac{-4x}{3}[/tex]+5.
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Using side lengths only, could the triangles be similar?
Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.
No, StartFraction 0.5 Over 1 EndFraction not-equals StartFraction 1 Over 1.5 EndFraction not-equals StartFraction 1.5 Over 2 EndFraction.
Yes, StartFraction 0.5 Over 1 EndFraction = StartFraction 0.5 Over 1 EndFraction.
Yes, One-half = StartFraction 0.5 Over 1 EndFraction.
Yes, StartFraction 1.5 Over 1 EndFraction = StartFraction 2 Over 1.5 EndFraction.
Answers
The triangles are not similar as the ratios are different.
How to depict the triangle?ΔXYZ
XY = 1.5, XZ = 1, ZY = 2
Δ QSR
QR =1, RS = 1.5, SQ = 0.5
Ratios:
XY/SQ = 1.5/0.5
XZ/QR = 1/1
ZY/RS = 2/1.5
The answer is no because ratios are different
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Find x and Y pls help
Answers
Answer:
Step-by-step explanation:
Comment
The angle supplementary to x and 3x are equal.
Supplementary angles = 180
Solution
x + 3x = 180
4x = 180 Divide by 4
4x/4 = 180/4
x = 45
The angle supplementary to x is 3x
3x = 3*45
3x = 135
This angle is vertically opposite y. Vertically opposite angles are equal. So y = 135
Answer
x = 45
y = 135
What is 1+1? 10 point if u get it right.
Answers
Answer:
11
Step-by-step explanation:
duh add 1 and 1 merge it together to get 11
that's a hard question imma go with 2 though
Step-by-step explanation:
for this problem let's let x=1 and y also =1 so x+y=2 hope this helps
pls help!!!
What is the range of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
Answers
Answer:
All real numbers greater than or equal to 2.
Step-by-step explanation:
To find the range, we look at the y values. Since all the y values never dip under 2 and also keep increasing to infinity, the range is [tex]y\geq 2[/tex].
Answer:
all real numbers greater than or equal to 2
Step-by-step explanation:
Edge
Find the value of JN in the figure.
Answers
Answer:
JN = 32
Step-by-step explanation:
Δ JMN and Δ JKL are similar ( AA postulate )
then the ratios of corresponding sides are in proportion, that is
[tex]\frac{JM}{JK}[/tex] = [tex]\frac{JN}{JL}[/tex] ( substitute values )
[tex]\frac{24}{33}[/tex] = [tex]\frac{JN}{JN+12}[/tex]
[tex]\frac{8}{11}[/tex] = [tex]\frac{JN}{JN+12}[/tex] ( cross- multiply )
11 JN = 8(JN + 12)
11 JN = 8 JN + 96 ( subtract 8 JN from both sides )
3 JN = 96 ( divide both sides by 3 )
JN = 32
Many doctors rely on the use of intravenous medication administration in order to achieve an immediate response of a particular drug's effects. The concentration, C, in mg/L, of a particular medication after being injected into a patient can be given by the function G(t) = (- 8t ^ 2 + 56t)/(t ^ 2 + 3t + 2) where the time, t, is hours after injection. Part A: What is the domain of the function C(t) based on the context of the problem? Show all necessary calculations. Part B: Graph the function to determine the greatest concentration of the medication that a patient will have in their body.
Answers
Graphs are used to show the relationship between variables, where the variables are represented by a pair of axes.
The domain of the function is t ≥ 0
The greatest concentration of the medication is 5mg/L
Given that:
C(t) = [tex]\frac{-8t^2 + 56t}{t^2 +3t + 2}[/tex]
(a): The domain of the function
Because the medication concentration C(t) is a function of time (t), the domain is the possible values t can take.
t, cannot take negative values (i.e. it is not possible to have a negative time).
The least possible value of t is 0
So, the domain of the function based on the context is: t ≥ 0
(b) The greatest concentration of the medication
From the graph (see attachment), the maximum y-value is 5.
Hence, the greatest concentration of the medication is 5 mg/L
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Complete the statements below with the process used to achieve steps 1-4.
Select the correct answer from each drop-down menu.
Consider the equation below.
-2(5x+8)=14+6x
The equation was solved using the following steps.
Answers
The statements can be completed by using the following :
1) -2 is multiplied with (5x+8)
2) transposing of numeral values and variable values
3) The numerical values are taken one side and added to each other
4) 30 is divided by -16
5) The numerator and denominator are cancelled to the lowest possible value
x= -15/8
Given: -2(5x+8)=14+6x
and steps for solving them have also been given
In the first step, -2 is multiplied with (5x+8) and we get
-10x -16 = 14 +6x
In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14
In step 3,
The numerical values are taken one side and added to each other and we get -16x=30
In step 4, 30 is divided by -16
In step 5, they are cancelled to the lowest possible value and we get
x= -15/8
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A. 10%
B.15%
C.28%
D.25%
Answers
Answer: 10%
Step-by-step explanation:
She had a total of $16,800. Subtracting the $5700 standard deduction and the $3650 exemption, we get:
[tex]16800-5700-3650=7450[/tex]
Which falls within the 10% tax bracket.
Two fire trucks on the ground on either side of a burning building or 1.3 miles apart. they each measure the angle of elevation to the fire which are 58° and 52°. How far is each truck from the fire? Please help ASAP thank you so much!
Answers
The distance of the first truck from the fire is 0.578 mile and the distance of the second truck from fire is 0.722 mile.
Distance of each truck from the fireUsing sine rule, we find the length of AB and BC as shown in the image.
a/sin A = b/sin B = c/sin C
Angle C = 180 - (58 + 52) = 70⁰
1.3/(sin 70) = b/(sin 52)
b = (1.3sin 52) / (sin 70)
b = 1.09 mile
c = (1.3sin 58) / (sin 70)
c = 1.1732 miles
Bisect angle C, and use sine rule again to find the lengths of bisected line AB.
1.09/(sin 90) = x/[sin (90 - 58)]
1.09/(sin 90) = x/(sin 32)
x = (1.09 sin 32)/(sin 90)
x = 0.578 mile
Truck B's position from the fire = 1.3 miles - 0.578 mile = 0.722 mile
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