An ellipse centered at the origin has a vertical major axis of 12 units and an eccentricity of 0.5.
What is the equation of the ellipse?
The equation of the ellipse formed is x²/11.7² + y²/12² = 1
Equation of an ellipseThe formula for calculating the equation of an ellipse is expressed as;
x²/a² + y²/b² = 1
where
a and b are the minor an major axis respectively;
Given the following
b = 12
e = 0.5
Determine the value of a
e² = √b²-a²/b
0.5² = √12²-a²/12
12 * 0.25 = √144-a²
9 = 144 - a²
a² = 136
a = 11.7
Substitute into the fomula
x²/11.7² + y²/12² = 1
Hence the equation of the ellipse formed is x²/11.7² + y²/12² = 1
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Eight less than four times a number is twelve. What is the number?
5
1
-3
-5
please help, thank u!
Answer:
False
Step-by-step explanation:
Angles 1 and 2 are not adjacent because they do not share any common line segments with each other.
Answer:
False
Step-by-step explanation:
The definition of adjacent angles is two angles that share a common side and a common vertex. Also, they don't overlap
So in this case ∠1 and ∠2 share the common vertex A but do not share the common side, so these angles are not adjacent.
In this diagram, an example of adjacent angles would be ∠1 and ∠3.
Here's a visual example to understand what I meant
If you roll two fair six-sided dice, what is the probability that the sum is 9 or higher?
Pls answer!!!
Answer:
4/11
Step-by-step explanation:
The chance of getting the sum of any number(2 thought 12) is 1/11
so
9 = 1/11
10 = 1/11
11 = 1/11
12 = 1/11
so, 4/11
What is 564-53.2
Explain how you worked it out
Then what is 700.3-89.3
Explain how you worked it out
If a 3 ft tall cardboard box casts a 6 ft long
shadow, then how tall is a tent that casts a
18 ft shadow?
Answer:
9 ft tall.
Step-by-step explanation:
The box that is 3 feet tall casts a 6 foot shadow, which is double the height. If we use inverse operations because we start with the shadow we will get 9 feet because 18 divided by 2 is nine.
Tripp decided to go on vacation to the beach. After driving 60% of the way, he decided to stop for lunch. If he stopped for lunch after 240 miles of driving, how many total miles will he have to drive?
Answer:
40=10% im rightthe total is 400
Step-by-step explanation:
Please Help me answer all 4 questions with a full explanation so I can solve the rest on my own.
[tex]\\ \rm\Rrightarrow (2x^2)^3.2yx^0=8x^6.2y=16x^6y[/tex]
[tex]\\ \rm\Rrightarrow (2x^4y^3)^3.2x^4y^4=8x^{12}y^6.2x^4y^4=16x^{16}y^{10}[/tex]
[tex]\\ \rm\Rrightarrow (m^3n^0(2m^3n^2)^4)^2=(m^316m^{12}n^8)^2=(16m^{15}n^8)^2=256m^{30}n^{16}[/tex]
[tex]\\ \rm\Rrightarrow (2xy^3)^2.2x^2y^0=4x^2y^6.2x^2=8x^4y^6[/tex]
ASAP ASAP ASAP PLS ANSWER
area triangle:
(1.7m×2m)×2
= 1.7m²
-> 2 triangles so: 1.7m²×2= 3.4m²
area rectangles(walls):
2m×3m
= 6m²
-> 2 walls so: 6m²×2=12m²
area bottom rectangle:
3m×2m=6m²
-> total area:
6m²+12m²+3.4m²= 21.4m²
There are 4 consecutive even integers that sum to 68. What are the integers?
Hi there,
Let x be the first number.Then the next three even numbers are x+2, x+4, and x+6.The sum of these numbers is 68So,
x + (x + 2) + (x + 4) + (x + 6) = 68Simplify and solve for x.
4x + 12 = 684x = 68 - 12x = 56/4x = 14In the context of this problem, the equation x=14 means that the first number is 14. The next three even numbers are 16, 18, and 20.
Checking we see that 14+16+18+20=68.
What are consecutive integers?Consecutive integers are integers that follow each other in order.If anyone can help me with this then thank you. :)
Answer:
steps below
Step-by-step explanation:
(a) first green: 8/23 AND 2nd green: 7/22
AND: multiplication.. 8/23 x 7/22 = 28/253 ≈ 0.11 (11%)
(b) 15/23 x 8/22
find the solution for x when x^3 = 27/8
Answer:
3/2
Step-by-step explanation:
[tex] {x}^{3} = \frac{27}{8} [/tex]
[tex] x = \sqrt[3]{ \frac{27}{8} } = \frac{3}{2} [/tex]
The area of a rectangle is x² + 2x -15. If its length is x + 2 units, what is its width?
Length of the rectangle is 8 units
Step-by-step explanation:
Step 1: Find the length, let width be x.Area of the rectangle = 48 units
Length = x + 2
⇒ Area = Length × Breadth
48 = x (x + 2)
48 = x² + 2x
x² + 2x - 48 = 0
x² + 8x - 6x + 48 = 0 (Product Sum rule to factorise)
x(x + 8) - 6(x + 8) = 0
(x - 6)(x + 8) = 0
⇒ x = 6, -8 (negative value is neglected)
∴ x = 6
x + 2 = 8
Pls help me if u can
This is a statistics problem involving Group Frequency Distribution Table. See the attached and the details below.
What is a Group Frequency Distribution Table?By dividing observations into intervals and tabulating the frequencies for each interval, data can be organized. A grouped frequency table is the end product.
The intervals in this distribution are referred to as classes.
What is the Estimated Mean of the Grouped Frequencies?This is obtained by dividing the sum of the product of all mid points and their frequencies by the total number of observations.
That is Estimated Mean = (f * x)/n ------See the attached sheet.
⇒ 503/50
= 10.06
What is the Estimated Median of the Grouped Frequencies?The median of the 50 observations = 28
This is arrived at by dividing the sum of 25th and the 26th number by 2.
That is (28 + 28)/28=28
This median falls in to the third class - 25-29. Hence, the median group is 25-29.
The estimated median value is computed as follows:
Estimated Median = L + (((n/2)-B)/G) x w
Where :
L is the lower class boundary of the group containing the mediann is the total number of valuesB is the cumulative frequency of the groups before the median groupG is the frequency of the median groupw is the group widthInserting the values we have :
L = 25
n = 50
B = 0 + 1 = 1
G = 2
w = 5
Estimated Median = 25 + (((50/2)-1)/2 ) * 5
= 25 + (24/2) * 5
= 85
How do you calculate the Estimated Mode?By observation, the modal group is 30-34. This is because it has the highest frequency of 4.
Hence, the Estimated Mode (EM) is arrived at using the formula:
EM = L + (fₙ-fₙ₋₁)/(fₙ-fₙ₋₁) + (fₙ-fₙ₊₁) x w
where:
L is the lower class boundary of the modal groupfn-1 is the frequency of the group before the modal groupfn is the frequency of the modal groupfn+1 is the frequency of the group after the modal groupw is the group widthNote that
L = 30
fn-1 = 2
fn = 4
fn+1 = 3
w = 5
Hence,
EM = 30 + (4-2)/((4-2) + (4-3)) x 5
= 30 + (2/(2+1)) x 5
= 30 + (2/3) x 5
EM = 33.33
In summary,
Estimated Mean: 10.06Estimated Median: 85Estimated Mode: 33.33Learn more about Group Frequency Distribution at:
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A local business has an area reserved behind the store for a parking lot that is 78 meters long by 19 meters wide. The stalls of the lot are at 90° angles to a required aisle that bisects the lot. The aisle is 8 meters by 78 meters. An area reserved for a parking lot is 78 meters long by 19 meters wide. 2 stalls and an aisle are in the reserved area. The aisle is 78 meters long and 8 meters wide. Use the layout of the parking lot to answer the questions. What is the total area available for cars to park? m2. If the parking spaces are compact, they have an area of 12.5 m2. How many compact parking spaces will fit in the lot? . If the parking spaces are not compact, they will be 3 meters by 5.5 meters. How many noncompact parking spaces will fit in the lot?
The total area available for cars to park is 858 square meters, the number of compact parking space is 68 and the number of non-compact parking space is 52
The total area available
The dimension of the parking lot is:
78 meters by 19 meters
The dimension of the aisle is:
8 meters by 78 meters
The total area available is the difference between the area of the parking lot and the area of the aisle.
So, we have:
Available Area = 78 * 19 - 8 * 78
Available Area = 858
Hence, the total area available for cars to park is 858 square meters
The number of parking space
The total area available for cars to park is 858 square meters, and the area of each parking spot is 12.5 square meters
So, the number of parking lot is:
n = 858/12.5
n = 68.64
Remove the decimal
n = 68
Hence, the number of parking space is 68
The number of parking space for non-compact parking space
The total area available for cars to park is 858 square meters, and the dimension of each parking spot is 5.5 meter by 3 meters
So, the number of parking lot is:
n = 858/(5.5 * 3)
n = 52
Hence, the number of parking space is 52
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Answer:
The above answer is correct!
To put it a bit more simply:
First box: C. 858
Second box: C. 68
Third box: B. 52
Step-by-step explanation:
Hope this helps!
Your friend says that the quotient 3/8 divided by 1/8 is 1/3 what is the correct quotient? What mistake did you friend likely make?
Answer:
its 1/8
Step-by-step explanation:
he said 1/3 it does not match the other 2 numbers hope its right ;-; also helpfull
What is the solution of the equation 6+q=25 1/2
Answer:
q = 19 1/2.Step-by-step explanation:
Unknown value is q.
Solve for the unknown value:
6 + q = 25 1/2q = 25 1/2 - 625 1/2 - 6= 19 1/2.q = 19 1/2.Answer is q = 19 1/2.Answer:
[tex]q=19\frac{1}{2}[/tex]
Step-by-step explanation:
Step 1: Subtract 6 from both sides
[tex]6 + q = 25\frac{1}{2}[/tex]
[tex]6 -6 + q = 25\frac{1}{2}-6[/tex]
[tex]q = (25-6)\frac{1}{2}[/tex]
[tex]q=19\frac{1}{2}[/tex]
Answer: [tex]q=19\frac{1}{2}[/tex]
Hope this helps! Let me know if you have any questions
If 45%of a number, n, is 225, what is 74% of n?
Answer:
if 45% of a number ,n, is 225, then 74% of a number ,n,is 370
Graph the system of inequalities. Then use your graph to identify the point that represents a solution to the system.
y < 6
y ≥ –3x – 1
A. (0, 6)
B. (6, 0)
C. (-6, 5)
D. (-6, -2)
Answer:
Your answer is B
Step-by-step explanation:
6.14 Checkpoint: Systems of Linear Inequalities
I took the test.
Three quarters the product of two numbers x and y
The Three quarters the product of two numbers x and y is 3/4 *x* y
What is algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
In elementary algebra, those symbols represent quantities without fixed values, known as variables.
As, quarters represent 1/4
So, three quarters= 3/4
Let the two number be x and y.
Then , 3 quarters of x and y product be,
=3/4*x*y
= 0.75*x*y
Hence, the expression of given statement is 3/4*x*y.
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what is the equation of line a [2 points]
Answer:
The two-point form of a line is used for finding the equation of a line given two points (x1,y1) ( x 1 , y 1 ) and (x2,y2) ( x 2 , y 2 ) on it. The two point-form of a line is:y−y1=y2−y1x2−x1(x−x1) y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) OR y−y2=y2−y1x2−x1(x−x2) y − y 2 = y 2 − y 1 x 2 − x 1 ( x − x 2 ) .
Solve for xx. Enter the solutions from least to greatest.
Round to two decimal places.
(x + 8)^2 - 7 = 0
Find the value for k for which y= 2x+k is a tangent to the curve y=2x^2-3 and determine the point of intersection
Answers:
k = -3.5
Intersection point is (0.5, -2.5)
================================================
Explanation:
Apply the derivative to y=2x^2-3 and you should get dy/dx = 4x
The derivative helps determine the slope of the tangent at any point on the curve.
The slope of the tangent line y = 2x+k is 2.
We want the slope of the tangent to be 2, so we'll replace the dy/dx with 2 and solve for x.
dy/dx = 4x
2 = 4x
x = 2/4
x = 0.5
Plug this into the curve's original equation.
y = 2x^2 - 3
y = 2(0.5)^2 - 3
y = -2.5
Therefore, the tangent line y = 2x+k and the curve y = 2x^2-3 intersect at the point (0.5, -2.5). This is the point of tangency.
We'll use the coordinates of this point to determine k.
y = 2x+k
-2.5 = 2(0.5) + k
-2.5 = 1 + k
k = -2.5-1
k = -3.5
Visual verification is shown below. I used GeoGebra to make the graph, but you could use any other tool you prefer (such as Desmos).
Sam receives a shipment of 36 football helmets. Of the 36 football helmets in the shipment, four of them were scratched and need to be returned. If another shipment of 108 helmets arrive, then how many are likely to be scratched
The number of football helmets which are likely to be scratched from the 108 helmets is; 12.
What is the number of helmets likely to be scratched?It follows from the task content that of the initial shipment of 108 football helmets; four of them were scratched.
On this note, the number of helmets likely to be scratched from the new shipment of 108 helmets can be evaluated by ratios as;
x = (108 × 4)/36 = 12 scratched helmets.
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A scientist studies a sample that weighs 1 ounce, which is about 28 grams. About how many grams would be in a 48-ounce sample?
Answer: 1344g
Step-by-step explanation:
if 1 ounce = 28 grams and we have 48 ounces,
multiply 48 by 28 to find the amount of grams
48×28 = 1344g
What is the domain of the function y= 1/x +4?
+?
Answer:
x i think its the awnser
Step-by-step explanation:
Set the denominator in 1x−4 1 x - 4 equal to 0 to find where the expression is undefined. Add 4 to both sides of the equation. The domain is all values of x that make the expression defined.
Please help!! 50 points!!
Use the exponential equation below to answer Part A, Part B, and Part C.
35^x = 8
Part A: Explain the steps to solve the equation.
Part B: Rewrite the exponential equation in logarithmic form using the definition of logarithms.
Part C: Use the equation from Part B to solve for x. Round to the nearest hundredth
Answer:
a) below
b) log_35 (8) = x
c) x = 0.58487
Step-by-step explanation:
a) 35^x=8
apply the exponent rule
xln(35) = ln(8) → x = ln(8)/ln(35) → x = 3ln(2)/ln(35)
x = 0.58487
c) log_35 (8) = x
x = log_35 (8)
base form (Rewrite 8 in power)
x = log_35 (2^3)
log rule: log_a(x^b) = b*log_a(x)
log_35 (2^3) = 3log_35(2)
x = 3log_35(2)
x = 0.58487
Enter the y coordinate of the solution to this system of equations.
6x + y = 8
x − 2y = 10
Answer
Please see attached photo below for detailed analysis
Explanation
hope this helps.please rate and mark brainliest!!!HELP ME WITH THIS PLEASE HUURRYY
Answer:
the answer would be A, 78.52
Step-by-step explanation:
A package of 8 notebooks costs $10.80. This equation can be used to determine the cost, n, in dollars, of each notebook in the package.
8n = 10.80
What is the cost, in dollars, of each notebook in the package?
Enter your answer in the box.
Answer:
$1.35
Step-by-step explanation:
8n = 10.80
Divide both sides by 8 to get n alone.
n = 10.80/8 = $1.35
