Some steps are shown in converting the following conic inequality from general form to standard form. Complete the conversion and identify the shape, key feature, and which ordered pair is part of the solution set. 9x2 – 18x 4y2 16y – 11 > 0 9x2 – 18x 4y2 16y > 11 9(x2 – 2x) 4(y2 4y) > 11 9(x2 – 2x 1) 4(y2 4y 4) > 11 9 16 The conic represented in this inequality is a(n). The center is at. The ordered pair, , is a solution to the inequality.
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]
To know more about ellipse follow
https://brainly.com/question/19507943
Answer:
ellipse with a dashed line boundary
(1,-2)
(-2,0)
Step-by-step explanation:
assignment
An airplane cruises 1 kilometer in 1/12 of a minute. What is its cruising speed?
Answer:
the plain is going 12km in one minute
Step-by-step explanation:
Abbey has $25. She plans on saving $10 a week. Which inequality shows how many weeks, w, she must save to have at least $250?
Answer:
22.5 weeks
Step-by-step explanation:
5x-6=3
find the value for x
Answer:
x = 9/5 = 1 4/5
Step-by-step explanation:
5x - 6 = 3
+6 +6
(add positive 6 to the negative 6 = - 6 + 6 = 0, and to the answer = 3 = 3 + 6 = 9)
5x = 9
÷5 ÷5
x = 9/5 (improper fraction)
= 1 4/5 (mixed numeral)
Hello.
First, let's add 6 to both sides:
[tex]\tt{5x-6+6=3+6}[/tex]
[tex]\tt{5x=9}[/tex]
The next step is to divide both sides by 5:
[tex]\tt{x=\displaystyle\frac{9}{5}[/tex] (Improper fraction)
[tex]\tt{x=\displaystyle1\frac{4}{5}[/tex] (Mixed number)
I hope it helps.
Have a great day.
[tex]\boxed{imperturbability}[/tex]
a triangle has vertices d(6,1), e(2,3) and f(-1,-3). show that triangle DEF is a right angle triangle and identify the right angle triangle
We'll need the slope formula which is
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\[/tex]
We subtract the y values together, and divide that over the difference in the x values when subtracted in the same order.
Let's find the slope of line DE
[tex]D = (x_1,y_1) = (6,1) \text{ and } E = (x_2,y_2) = (2,3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{3 - 1}{2 - 6}\\\\m = \frac{2}{-4}\\\\m = -\frac{1}{2}\\\\[/tex]
The slope of line DE is -1/2.
Next, compute the slope of line EF
[tex]E = (x_1,y_1) = (2,3) \text{ and } F = (x_2,y_2) = (-1,-3)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-3 - 3}{-1 - 2}\\\\m = \frac{-6}{-3}\\\\m = 2\\\\[/tex]
The slope of line EF is 2.
Lastly, compute the slope of line FD
[tex]F = (x_1,y_1) = (-1,-3) \text{ and } D = (x_2,y_2) = (6,1)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{1 - (-3)}{6 - (-1)}\\\\m = \frac{1 + 3}{6 + 1}\\\\m = \frac{4}{7}\\\\[/tex]
The slope of line FD is 4/7.
--------------------------
To recap everything so far, we found the following:
slope of DE = -1/2slope of EF = 2slope of FD = 4/7The product of the first two slopes gets us (-1/2)*(2) = -1 showing that DE is perpendicular to EF.
Perpendicular slopes multiply to -1 as long as neither line is vertical nor horizontal.
Since DE is perpendicular to EF, this proves we have a 90 degree angle at point E.
Therefore triangle DEF is a right triangle.
Simplify the expression
a/3+3a/4
Answer:
[tex]\frac{13}{12}a\\[/tex]
Step-by-step explanation:
[tex]\frac{a}{3} + \frac{3a}{4}= \frac{13}{12}a[/tex]
Answer:
the answer is 13a/12 simplified
HELP PLEASEEEEEEEEEEEE!
Answer:
-8
Step-by-step explanation:
Answer:
-8
Step-by-step explanation:
Pull out like factors : 16 + 2x = 2 • (x + 8)
Solve::x+8 = 0
Subtract 8 from both sides of the equation::x = -8
3.2, 3 ⅔, 3.25, 3 ½ greatest to least
Answer:
3.2, 3.25, 3 1/2, 3 2/3
Step-by-step explanation:
You can put them on a number line and find out the order. Or, convert to decimals or fractions.
Omar grouped the terms and factored the gcf out of the groups of the polynomial 3x3 – 15x2 – 4x 20. his work is shown. step 1: (3x3 – 15x2) (–4x 20) step 2: 3x2(x – 5) 4(–x 5) omar noticed that he does not have a common factor. which accurately describes what omar should do next? omar should realize that his work shows that the polynomial is prime. omar should go back and regroup the terms in step 1 as (3x3 – 15x2) – (4x 20). in step 2, omar should factor only out of the first expression. omar should factor out a negative from one of the groups so the binomials will be the same.
The step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomials.
(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)
The polynomial that Omar is dealing with is:
[tex]3x^3 - 15x^2 -4x + 20[/tex]
We see that 3 times 5 = 15 and 4 times 5 = 20, so trying in that way:
[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5)[/tex]
Taking out a negative factor from second term would make the binomials same, after which we can take that common out, as shown below:
[tex]3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) + 4(-x + 5) \\3x^3 - 15x^2 -4x + 20 = 3x^2(x-5) -4(x-5) \\3x^3 - 15x^2 -4x + 20 = (x-5)(3x^2-4)[/tex]
It successfully got factored, thus not a polynomial.
Thus,the step that Omar should proceed with is given by: Option D: Omar should factor out a negative from one of the groups so the binomials will be the same.
Learn more about prime polynomials here:
https://brainly.com/question/10717989
Answer: Omar should factor out a negative from one of the groups so the binomials will be the same.
Step-by-step explanation: Answer on edge
Is the open sentence 3z = 2z + 5 true or false when z = 5?
Answer:
Your answer to your question is FALSE!!!!!!
Answer:
True
Step-by-step explanation:
Plug the value of z in: 3(5) = 2(5) + 5Simplify: 15 = 10 + 510 + 5 = 15So, the open sentence is true.I hope this helps!
You randomly draw a marble from a bag, record its color, and then replace it. You draw a red marble 9 out of 25 times. What is the experimental probability that the next marble will be red? Write your answer as a fraction, decimal, or percent.
The experimental probability that the next marble will be red is
.
Does it say how many of the marbles in the bag are red? Normally you will want to divide the amount of red marbles to the amount total marbles and you will get a percent. It's also note worthy that it states the marble going back into the bag. It would change if it was left out still.
A triangular garden has an area of 112 ft2. Its height is 2 ft more than its base. Find the measure of the base.
Answer:
14 ft.
Step-by-step explanation:
First, we will assign variables to each value. If height is h, and base is b, then
1/2bh = 112 and h=b+2.
We will use substitution in this system of equations. first, we will isolate the b in bh/2=112. To do this we will multiply both sides by 2 to isolate the variables, so bh=224. Then, to isolate just one variable, in this case, b, we will divide 224 by h, getting us b=224/h.
Then, we will substitute b for this value in h+2=b, leaving us with h+2=224/h
Then isolate the variable. h will equal either -14 or 16. Because this is a geometric shape, the value of its sides cannot be negative, so it has a height of 16.
Then, plug this into the second equation. If the height is 2 ft more than the base, then the base will be 14 ft.
Work out area of the triangle and give answer to 1.dp
Answer:
A ≈ 62.8 cm²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = [tex]\frac{1}{2}[/tex] ab sinC
where a = 10, b = 13 and C = 105° , then
A = [tex]\frac{1}{2}[/tex] × 10 × 13 × sin105° = 65 × sin105° ≈ 62.8 cm² ( to 1 dec. place )
Calculator
What is the slope of the line passing through the points (1, 2) and (5, 4)?
N
O 2
O-2
0 1
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}\implies \cfrac{2}{4}\implies \cfrac{1}{2}[/tex]
Plz help! ASAP! Will mark Brainliest
Answer:
7/8 quart
Step-by-step explanation:
I need help finding the measure of the missing angles
Answer:
x = 61°
y = 29°
Step-by-step explanation:
Since x°+29° is a right angle (90°), you would have to subtract 29 from 90 to get x.
90 - 29 = x
90 - 29 = 61
x = 61°
For y: You can infer that y°+x°=90° as well because the angles are corresponding angles. So to find y°, you would do the same thing as finding x.
90 - x = y
90 - 61 = 29
y = 29°
Hope this helps :)
What select factor was applied to the first rectangle to get the result image
Answer:
A factor of 0.2
Step-by-step explanation:
If we multiply 2.5 by 0.2, we get 0.5, the width of the smaller rectangle.
What is the slope of the line that contains (-3,5) and (-3, 6)?
Answer:
1
Step-by-step explanation:
You can find slope by the formula
y2-y1 over x2-x1
In this case, 6-5 over -3-(-3) or -3=3
This is equal to 1 over 0 which is 1
Ariel spends $330 on 3 gold rings. The rings all cost the same amount. What is the cost of each ring?
Answer:
$110
Step-by-step explanation:
divide 330 by 3
$115 i think..........................
At a recent marathon, spectators lined the street near the starting line to cheer for the runners. The crowd lined up 5 feet deep on both sides of the street for the first mile. You estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet. Using this information, how many people cheered for the runners at the start of the race? 1mile=5280 feet
Answer:
29568 people cheered for the runners at the start of the race
Step-by-step explanation:
From the question, the crowd lined up 5 feet deep on both sides of the street for the first mile.
This lined up crowd could be related to a rectangle that is 1 mile long and 5 feet wide.
First, Convert 1 mile to feet
1 mile = 5280 feet
Hence, the length of the rectangle is 5280 feet and the width is 5 feet.
Now, we will determine how many 5 feet by 5 feet square we can get from the 5280 feet by 5 feet rectangle. To do that, we will divide 5280 feet by 5 feet
5280 feet ÷ 5 feet = 1056
Hence, from the rectangle, we can get 1056 5 feet by 5 feet square.
From the question, you estimate that 14 people can comfortably fit in a square that measures 5 feet by 5 feet,
∴ 14 × 1056 people will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.
14 × 1056 = 14784 people
This is the amount of people that will comfortably fit in the crowed lined up 5 feet deep on one side of the street for the first mile.
Since the crowd lined up on both sides of the street, then
2 × 14784 people will comfortably fit in the crowed lined up 5 feet deep on both sides of the street for the first mile
2 × 14784 = 29568 people
Hence, 29568 people cheered for the runners at the start of the race.
6.
Using the incenter P, find the measure of Angle XZY
Answer: 62
Step-by-step explanation:
100 POINTS!!!
What is the square root of -2?
Answer:
± i [tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the result that [tex]\sqrt{-1}[/tex] = i
[tex]\sqrt{-2}[/tex]
= ± [tex]\sqrt{2(-1)}[/tex]
= ± [tex]\sqrt{2}[/tex] × [tex]\sqrt{-1}[/tex]
= ± [tex]\sqrt{2}[/tex] × i
= ± i [tex]\sqrt{2}[/tex]
Question 4
Solve for m.
m+ 7 = 3 + m + 4
1
m=
m = -7
no solution
infinite
solutions
infinitely many solutions
Step-by-step explanation:[tex]m+7=3+m+4[/tex]
Combine like terms
[tex]m+7=7+m[/tex]
Rearrange variables to the left side of the equation
[tex]m-m=7-7[/tex]
Apply the Inverse Property of Addition
[tex]m-m=7-7\\ 0=0[/tex]
Bases on the given conditions, the (system of) equation(s) has
[tex]infinitely\ many\ solutions[/tex]
I hope this helps you
:)
find the three consecutive even intergers such that the sum of twice the smallest number and three times the largest is 42
Answer:
6, 8, 10.
Step-by-step explanation:
Let n be any integer.
Then our first even integer will be [tex]2n[/tex]
And the consecutive integers will be [tex]2n+2[/tex] and [tex]2n+4[/tex]
We want to find the integers such that the sum of twice the smallest number (2n) and three times the largest number (2n+4) is 42. In other words:
[tex]2(2n)+3(2n+4)=42[/tex]
Solve for n. Distribute:
[tex]4n+6n+12=42[/tex]
Combine like terms:
[tex]10n+12=42[/tex]
Subtract 12 from both sides:
[tex]10n=30[/tex]
Divide both sides by 10:
[tex]n=3[/tex]
So, the value of n is 3.
This means that our first even integer is 2(3) or 6.
So, our sequence of integers is: 6, 8, 10.
And we're done!
Notes:
We use 2n because anything integer multiplied by 2 ensures that the resulting number is even. Starting out, n can be either even or odd, but by multiplying it by 2, we will get an even number.
answer? what is it?
7(3+5)+9
Answer:
65
Step-by-step explanation:
3+5=8
7x8+9
56+9
=65
Please give brainliest!
Answer:
=> 65
Step-by-step explanation:
=> 7(3+5)+9
=> 7(8)+9
=> 56+9
=> 65
The diagram shows a rectangle with its side.
a) Find an expression, in terms of x, for the perimeter of the rectangle.
b) The perimeter of the rectangle is 56 cm. Find the value of x. 1
Answer:
Ans of a = 18x
Ans of b = 3.111
Can anybody help me?
I'm on a time crunch.
x + 3= 8x -11
Question 1 options:
x=-1
x=1
x=2
x=4
Answer: x = 2
Steps: x + 3= 8x - 11
Subtract three form both sides: x + 3 - 3 = 8x - 11 - 3
Simplify: x = 8x - 14
Subtract 8x from both sides: x - 8x = 8x - 14 - 8x
Simplify: -7x = -14
Divide both sides by negative seven: -7x ÷ -7 = -14 ÷ -7
Simplify: x = 2
which sequence of transformations can be preformed on figure qrstu to show that the fugures are congruents
Answer:
Reflections, rotations, and translations produce an image that is congruent to the pre-image. Sequences of those transformations produce congruent images.
2. What is the slope of the line that passes
through the points (10, 4) and (-8, 6)?
A
9
B
с
-
-
D
18
2
Answer:
1/-9
Step-by-step explanation:
First you need to calculate rise over run with the equation [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] in this case that would be 6-4 over -8 - 10 this gets you 2/-18. This means the "rise" is 2 and the "run" is -18. This can be simplified to 1/-9.
can anyone show how to do this....6840 ÷ 7
6840 ÷ 7 = ?
6840 | 7
63 977
=54
49
=50
49
=1
⇒ 6840 ÷ 7 = 977 remainder 1