The given inequality shows an ellipse with a center at (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be [tex]b=\sqrt{\dfrac{26}{4} }[/tex]
What is an ellipse?The equation of an ellipse is written in the form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
The center is (h,k) and the larger of a and b is the major radius and the smaller is the minor radius.
Now the given inequality is
[tex]9x^2+18x+4y^2+16y-11 > 0[/tex]
[tex]9x^2+18x+4y^2+16y > 11[/tex]
[tex]9(x^2-2x)+4(y^2+4y) > 11[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 11+9+16[/tex]
[tex]9(x^2-2x+1)+4(y^2+4y+4) > 26[/tex]
On further solving
[tex]9(x-1)^2+4(y+2)^2 > 26[/tex]
[tex]\dfrac{(x-1)^2}{\dfrac{26}{9} } + \dfrac{(y+2)^2}{\dfrac{26}{4} } > 1[/tex]
Thus by comparing the equation with the standard form
[tex]\dfrac{(x-h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]
Thus we can see that the center (h,k) is (1,-2)
The major axis will be [tex]a=\sqrt{\dfrac{26}{9} }[/tex]
The minor axis will be[tex]a=\sqrt{\dfrac{26}{4} }[/tex]
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Answer:
ellipse with a dashed line boundary
(1,-2)
(-2,0)
Step-by-step explanation:
assignment
anu borrows 12,500 as 12% per annum for 3 years at simple interest find the simple interest she has to pay at the end of 3 years
Answer:
The interest is 4,500
Step-by-step explanation:
We use the simple interest formula,
I = Prt
where
I = interest
P = principal amount = 12,500
r = interest rate = 12% = 0.12
t = time = 3 years
I = Prt
I = 12,500 × 0.12 × 3
I = 4,500
2^4. 2^5-(2^2)^2
Simplify the expression
Answer:
Today: Monday, 12 October 2020
Hour: 17.31 WIB (in Indonesian)
_________________________
2⁴ × 2⁵ - (2²)²
= 2⁹ - 2⁴
= 512 - 16
= 496
(100 points, Need help with this ASAP) I bought a used grain silo. I am going to use it as a groom's room at our venue. I am going to paint the inside of it to brighten it up a little. I need to decide how many cans of paint to buy. The silo is 15' across and 10' tall to the top of the cylindrical part. The top of the silo looks like a funnel. It is also 15' across. It is 4' tall. The ceiling is the funnel top. A can of paint covers approximately 400 sq ft. How many cans of paint will I need to buy?
Answer:
2 cans of paint
Step-by-step explanation:
Surface area of an open cylinder = [tex]2\pi rh[/tex]
(where r is the radius and h is the height)
⇒ SA = 2 × [tex]\pi[/tex] × (15 ÷ 2) × 10 = 150[tex]\pi[/tex] ft²
Surface area of an open cone = [tex]\pi r\sqrt{h^2+r^2}[/tex]
(where r is the radius and h is the height)
⇒ SA = [tex]\pi[/tex] × (15 ÷ 2) × √(4² + 7.5²) = 63.75[tex]\pi[/tex] ft²
Total surface area = 150[tex]\pi[/tex] + 63.75[tex]\pi[/tex] = 213.75[tex]\pi[/tex] = 671.52 ft² (nearest hundredth)
If one can of paint covers approx. 400 ft² then 2 cans of paint needed to cover 671.52 ft²
If x = 9 when y = 36 and x is directly
proportional to y, what is x when y= 6?
Answer:
1.5
Step-by-step explanation:
9 times 4 = 36
1.5 times 4 = 6
If x = 9 when y = 36 and x is directly proportional to y, then x will be 1.5, when y = 6.
What is directly proportional?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
We know that
36 / 9 = 6 /x
Cross multiply;
36 · x = 9 · 6
Simplify;
36x = 54
Divide each side by 36;
36x ÷ 36 = 54 ÷ 36
Simplify;
x = 1.5
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Write the prime factorization of 126.
Answer is attached
Which grade you in btw?
PLEASE HELP ME FRIENDS
Answer:
x=10
Step-by-step explanation:
Since the two given expressions are alternate interior angles ( as a result of the parallel line, which are indicated by the arrows on the two lines going through the middle line, the transversal) you can set them equal to each other.
5x-10 = 3x+10
add 10 on both sides
5x = 3x + 20
subtract 3x on both sides
2x=20
divide by 2 on both sides
x=10
Answer:
10=x
40 degrees for both
Step-by-step explanation:
3x+10=5x-10
3x+20=5x
20=2x
10=x
3(10)+10=40
5(10)-10=40
Help me please help
Answer:
165°
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..
..
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.............
How to determine if a series converges or diverges.
{56, 63, 70, 77,..., 126} the best set builder notation
Answer:
7
Step-by-step explanation:
63-56 = 7
After an increase of 25%, there were 800 students in Hockessin Middle School. How many students were at the middle school before the increase?? ( please answer!! )
Please help i need to complete this by tomorrow
Answer:
ED: 6.5 cm BE = 14.4 cm
Step-by-step explanation:
Add 20 and 5 to get side AC.
25/20 gives us the scale factor to go from 25 triangle ABE to triangle ACD.
Multiply 26 by the SF to get AD.
Subtract length of AD by AE to get ED. You should get 6.5 cm (don't forget units!!!!)
To go from triangle ACD to triangle ABE, we can do 20/25 to get the scale factor.
Using that number, multiply it with 18 to get BE.
The answer should be 14.4 cm.
This is possible because the two triangles ACD and ABE are similar via the angle angle angle similarity theorem depicted in my screenshot.
Answer:
ED = 6.5 cm , BE = 14.4 cm
Step-by-step explanation:
Δ ABE and Δ ACD are similar ( by the AA postulate ) then the ratios of corresponding sides are in proportion, that is
(a)
[tex]\frac{AD}{AE}[/tex] = [tex]\frac{AC}{AB}[/tex] ( substitute values )
[tex]\frac{AD}{26}[/tex] = [tex]\frac{25}{20}[/tex] ( cross- multiply )
20 AD = 650 ( divide both sides by 20 )
AD = 32.5
Then
ED = AD - AE = 32.5 - 26 = 6.5 cm
(b)
[tex]\frac{BE}{CD}[/tex] = [tex]\frac{AB}{AC}[/tex] ( substitute values )
[tex]\frac{BE}{18}[/tex] = [tex]\frac{20}{25}[/tex] ( cross- multiply )
25 BE = 360 ( divide both sides by 25 )
BE = 14.4 cm
First, rewrite 3/4 and 7/9 so that they have a common denominator.
Answer:
3/36 and 7/36
Step-by-step explanation:
The new fractions with common denominator are 27/36 and 28/36
What are fractions?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, rewrite 3/4 and 7/9 so that they have a common denominator.
To make their denominator common, multiply, the first fraction by 9 and second denominator by 4,
Then,
3×9/4×9 = 27/36
7×4/9×4 = 28/36
Hence, the new fractions with common denominator are 27/36 and 28/36
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When a number n is decreased by 12 and then the result is multiplied by 3, the product is equal to 21 . Write an equation and solve it to find the value of n .
The equation is , The value is .
Answer:
Step-by-step explanation:
19-12=7x3=21
If you place these marbles in a bag close your eyes and choose a marble what is the probability that it will be blue?
Answer:
6/14
Step-by-step explanation:
There are 14 marbles in total.
Out of the 14 marbles, 6 are blue.
which type of transformation maps triangle GFH onto triangle G'F'H'
translation
reflection
rotation
dilation
Answer:
ROTATION IS THE CORRECT ANSWER!
Step-by-step explanation:
Cuz
Answer:
rotation is correct! :))
Step-by-step explanation:
bc when i clicked rotation, the answer was valid and correct.
6. Leveled Practice Resting heart rate is a measure of how
fast the heart beats when a person is not performing
physical activity. The graph shows the number
of heartbeats over time for a given person.
a. Use two sets of coordinates to write an equation
to describe the relationship.
280 -
II
m is
-2
y=
Х
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
m = (280 - 140)/ (4 - 2) = 70
The equation of the line from the graph.
y = 70x
The heart's resting heart rate is 70 beats per minute.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
The following coordinates are from the given graph.
(1, 70), (2, 140), (3, 210), and (4, 280)
Now,
m = (280 - 140)/ (4 - 2) = 140/2 = 70
The equation from the graph can be written as,
y = mx + c
(1, 70) = (x, y)
70 = 70 x 1 + c
c = 70 - 70
c = 0
So,
The equation of the line from the graph.
y = 70x
1 minute = 70 heartbeats.
The heart's resting heart rate is 70 beats per minute.
Thus,
m = (280 - 140)/ (4 - 2) = 140/2 = 70
The equation of the line from the graph.
y = 70x
The heart's resting heart rate is 70 beats per minute.
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Need help
I will give brainliest
Answer:
4c=12
Step-by-step explanation:
In the chart, it shows 12 and 4 c. Since they equal the same thing, the equation is 4c=12.
i do not what the answer for this Luca is mountain climbing with Tommy and has just climbed a 16-meter vertical rock face. Tommy is standing at the bottom of the cliff, looking up at Luca. If Tommy is 20 meters away from Luca, how far away from the cliff is Tommy standing?
Answer:
Plug in a = x, b = 16, c = 20
Step-by-step explanation:
A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 PM
Answer:
Approximately [tex]58.2\; \text{nautical miles}[/tex] (assuming that the bearing is [tex]{\rm S$29^{\circ}$W}[/tex].)
Step-by-step explanation:
Let [tex]v[/tex] denote the speed of the ship, and let [tex]t[/tex] denote the duration of the trip. The magnitude of the displacement of this ship would be [tex]v\, t[/tex].
Refer to the diagram attached. The direction [tex]{\rm S$29^{\circ}$W}[/tex] means [tex]29^{\circ}[/tex] west of south. Thus, start with the south direction and turn towards west (clockwise) by [tex]29^{\circ}[/tex] to find the direction of the displacement of the ship.
The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of [tex]v\, t[/tex]. The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly [tex]29^{\circ}[/tex].
Since the hypotenuse is of length [tex]v\, t[/tex], the dashed line segment opposite to the [tex]\theta = 29^{\circ}[/tex] vertex would have a length of:
[tex]\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}[/tex].
Substitute in [tex]\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}[/tex] and [tex]t = 6\; \text{hour}[/tex]:
[tex]\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}[/tex].
Adam and 3 riends go on holiday together for a week .The costs of the holiday will be shared equally between 4 friends .These are the cost: £1460 for 4 return plane tickets £720 for the accomidation £180 for the car hire for a week . How does adam have to pay for his share of the cost
Answer:
Adam's share is £590
Step-by-step explanation:
Given
Return Ticket = £1460
Accommodation = £720
Car Hire = £180
Required
Determine Adam's share
First, we need to determine the total cost.
Total = Return Ticket + Accommodation + Car Hire
Total = £1460 + £720 + £180
Total = £2360
Next, is to determine the average.
[tex]Average = Total/4[/tex]
[tex]Average = 2360/4[/tex]
[tex]Average = 590[/tex]
Hence;
Adam's share is £590
What is the relationship between corresponding sequences 2 1 4 2 6 3 8 4 10 5 (GIVING BRAINLIEST)
Answer: to find the answer you need to
Step-by-step explanation:
Create a table with headings n and an where n denotes the set of consecutive positive integers, and an represents the term corresponding to the positive integers. You may pick only the first five terms of the sequence. For example, tabulate the series 5, 10, 15, 20, 25, . . .
Solve the first common difference of a. Consider the solution as a tree diagram. There are two conditions for this step. This process applies only to sequences whose nature are either linear or quadratic.Condition 1: If the first common difference is a constant, use the linear equation ax + b = 0 in finding the general term of the sequence.
And yeah
Pls help me
AND
PLS FOLLOW THE RULES
TROLL FOR POINTS= REPORT
FIRST AND CORRECT ANSWER= BRAINLIEST
( NO LINKS ) at all
Answer:
20 miles :)
Step-by-step explanation:
Pythagorean theorem formula: 16^2 + 12^2 = c^2
256 + 144 = c^2
400
[tex]\sqrt{400}[/tex] = 20
C = 20
Have an amazing day!!
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Evaluate y = 3x, when x = -4.
A
y = -12
y = 1/81
y = -81
Answer:
y = -12
Step-by-step explanation:
Plug the value of x (-4) into the original equation and solve:
y = 3(-4)
y = -12
How many millimetres are there in 7.4 centimetres?
Answer:
74
Step-by-step explanaction
Formula=multiply the length value by 10
A remote-control airplane is descending at a rate of 24.91 meters per second. What will be its change in height after 3 1/2 seconds? Round your answer to the nearest meter.
Answer:-87
Step-by-step explanation
-24.91 times 3 1/2 equals -87
The change in height after 3 and 1/2 seconds will be 87 meter.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that remote-control airplane is descending at a rate of 24.91 meters per second.
We need to multiply the rate and height will be;
-24.91 x 7/2 = -87 m
Hence, the change in height after 3 and 1/2 seconds will be 87 meter.
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Two angles are complementary angles, if ∠A measures 38 ° , What is the measurement of the other angle?
Answer:
52°
Step-by-step explanation:
complementary angles sum to 90° , then the measure of the other angle is
90° - 38° = 52°
Bashir and his friend are renting I 2 bedroom, 2 bathroom property together. The monthly rent is
4
$1,150.00 and monthly utilities will average $485.00. Bashir will pay 4/5 of the rent since his bedroom is
larger, but they will split the cost of utilities equally. Determine what amount Bashir will pay each
month for rent and utilities
$242.50
$920.00
$817.50
$1,162.50
Answer:
d. $1162.50
Step-by-step explanation:
485 ÷ 2 = 242.50
1150 = 5/5 (100%)
÷ 5
230 = 1/5 (20%)
× 4
920 = 4/5
920 + 242.5 = $1162.50
What is an equation of the line that passes through the points (0, -5) and
(-5,-1)?
Answer:
we find first slope
m=(-5+1)/(0+5)
m=-4/5
y-y1=m(x-x1)
y+ 5=(-4/5)(x-0)
5y+25=-4x
so equation is. 4x+5y+25=0
Answer:
y=[tex]-\frac{4}{5}[/tex]x-5
Step-by-step explanation:
The coordinates (0,-5) tells us the y intercept of the line, which is -5.
To find the equation of the line, we have to use the equation [tex]m=\frac{y2-y1}{x2-x1}[/tex] to find the slope of the line. Plug in the values of the other coordinates (-5,-1) into the equation, which would then leave you with :
m=[tex]\frac{(-1)-(-5)}{(-5)-0}[/tex]
we then solve for m(the slope) and we get:
m=[tex]-\frac{4}{5}[/tex]
so the equation of the line is y=[tex]-\frac{4}{5}[/tex]x-5
Can someone help me please
Answer:
theres four lines of symmetry goes up, side, and both diagonal ways
Step-by-step explanation:
Which of the following best describes the slope of the line below?
A. Zero
B. Undefined
C. Positive
D. Negative
Answer:
Undefined
Step-by-step explanation:
It is undefined because the x value equals multiple y values so the slope is undefined :)
Have a great day!!
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Answer: Choice B
Undefined
Reason:
Vertical lines always have undefined slopes.
This is because slope = rise/run, but run = 0 for vertical lines. The "run" describes how much the line moves to the right, but such a thing doesn't happen since it's stuck on one x value only.
So we could have something like slope = rise/run = 1/0 = undefined. Dividing over zero is not allowed.