Answer: 9 on the x axis and 18 on the y axis
Answer:
[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:\:\mathrm{semi-major\:axis}\:b=6,\:\:\mathrm{semi-minor\:axis}\:a=3[/tex]
Step-by-step explanation:
[tex]\left(2x-3\right)^2+\left(y+3\right)^2=36\\\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1\:\mathrm{is\:the\:ellipse\:standard\:equation}\\\mathrm{with\:center}\:\left(h,\:k\right)\:\mathrm{and\:}a,\:b\mathrm{\:are\:the\:semi-major\:and\:semi-minor\:axes}\\\mathrm{Rewrite}\:\left(2x-3\right)^2+\left(y+3\right)^2=36\:\mathrm{in\:the\:form\:of\:the\:standard\:ellipse\:equation}\\\left(2x-3\right)^2+\left(y+3\right)^2=36\\\mathrm{Rewrite\:as}\\\left(2x-3\right)^2+\left(y+3\right)^2-36=0[/tex]
[tex]\mathrm{Simplify}\:\left(2x-3\right)^2+\left(y+3\right)^2-36:\quad 4x^2-12x+y^2+6y-18\\4x^2-12x+y^2+6y-18=0\\\mathrm{Add\:}18\mathrm{\:to\:both\:sides}\\4x^2-12x+y^2+6y=18\\Factor\:out\:coefficient\:of\:square\:terms\\4\left(x^2-3x\right)+\left(y^2+6y\right)=18\\\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}4\\\left(x^2-3x\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}\\\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}1[/tex]
[tex]\frac{1}{1}\left(x^2-3x\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}\\\mathrm{Convert}\:x\:\mathrm{to\:square\:form}\\\frac{1}{1}\left(x^2-3x+\frac{9}{4}\right)+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)\\\mathrm{Convert\:to\:square\:form}\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y^2+6y\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)\\\mathrm{Convert}\:y\:\mathrm{to\:square\:form}[/tex]
[tex]\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y^2+6y+9\right)=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\mathrm{Convert\:to\:square\:form}\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y+3\right)^2=\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\mathrm{Refine\:}\frac{9}{2}+\frac{1}{1}\left(\frac{9}{4}\right)+\frac{1}{4}\left(9\right)\\\frac{1}{1}\left(x-\frac{3}{2}\right)^2+\frac{1}{4}\left(y+3\right)^2=9[/tex]
[tex]\mathrm{Divide\:by}\:9\\\frac{\left(x-\frac{3}{2}\right)^2}{9}+\frac{\left(y+3\right)^2}{36}=1\\\mathrm{Rewrite\:in\:standard\:form}\\\frac{\left(x-\frac{3}{2}\right)^2}{3^2}+\frac{\left(y-\left(-3\right)\right)^2}{6^2}=1\\\mathrm{Therefore\:ellipse\:properties\:are:}\\\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:a=3,\:b=6\\b>a\:\mathrm{therefore}\:b\:\mathrm{is\:semi-major\:axis\:and}\:a\:\mathrm{is\:semi-minor\:axis}[/tex]
[tex]\mathrm{Ellipse\:with\:center}\:\left(h,\:k\right)=\left(\frac{3}{2},\:-3\right),\:\:\mathrm{semi-major\:axis}\:b=6,\:\:\mathrm{semi-minor\:axis}\:a=3[/tex]
What is a
1/3 + a = 5/4
Which is equivalent to log Subscript 2 Baseline n = 4?
log n = StartFraction log 2 Over 4 EndFraction
n = StartFraction log 2 Over log 4 EndFraction
n = log 4 times log 2
log n = 4 log 2
Answer: log n = 4log2
Step-by-step explanation:
The 4th option is correct. The expression [tex]\log n=4(\log 2)[/tex] is equivalent to the given expression.
Important information:
The given expression is [tex]\log_2 n=4[/tex].We need to find the equivalent equation.
Logarithms:Using the property of logarithm, the given expression can be written as:
[tex]\dfrac{\log n}{\log 2}=4[/tex] [tex]\left[\because \log_ab=\dfrac{\log b}{\log a}\right][/tex]
[tex]\log n=4(\log 2)[/tex]
Thus, the 4th option is correct.
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Can you please help
#6 GRADE
Answer:
the interger would be 15 because you earn 15 so therfore it would be 15.
Step-by-step explanation:
Candice won the lottery for 30000 dollars.However 20% of her money has to go to the state for taxes.How much money will she receive after paying taxes?
Answer:
She will receive $24,000 after paying taxes
Step-by-step explanation:
This question can be solved using a rule of three.
20% of her money has to go to the state for taxes. So she will receive 100-20 = 80%. $30000 is 100% = 1. How much is 80% = 0.8?
$30000 - 1
$x - 0.8
x = 30000*0.8
x = 24000
She will receive $24,000 after paying taxes
All of the following are radii except
Answer:
all of the following are radi except ij or ji the other two are right
Step-by-step explanation:
Two numbers have a sum of 25 and a difference of 5. Find two numbers.
Answer:
the answer is 15 and 10
Step-by-step explanation:
Pleaseeeeee helpppppppp i will mark brainlest
Answer:
B
Step-by-step explanation:
Answer:
B=40°
Step-by-step explanation:
Sum of angles in a triangle =180°
90°+50°+x°=180°
140°+×°=180°
Collect like terms
x°=180°-140°
x°=40°
The spinner is divided into 8 equal sections. A spinner divided into 8 equal sections labeled brown, green, red, purple, brown, green, yellow, blue. What is the probability of spinning blue or green? StartFraction 1 over 8 EndFraction StartFraction 3 over 8 EndFraction One-half StartFraction 5 over 8 EndFraction
Answer:
for bule its 1/8 and green its 2/8
Step-by-step explanation:
The probability of spinning blue or green is equal to 1/4.
What is probability?The probability of an even tells the chances of occurrence of that event.
Given,
The spinner is divided into 8 equal sections:
brown, green, red, purple, brown, green, yellow, blue
Probability of all the colors is equal.
Therefore, probability of any color = 1/8
Probability of green = 1/8
Probability of blue = 1/8
The probability of spinning blue or green = Probability of green +
Probability of blue
= 1/8 + 1/8
= 2/8
= 1/4
Hence, probability of spinning blue or green is equal to 1/4.
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You have been tracking how much you spend on gas every month for several months and found that on average you spend about $60 per month. If you had to guess, what would you expect the IQR (Interquartile Range) of your gas spending to be? Would $1, $5 or $100 be most logical? Give statistical reasoning to back up your answer.
Answer: $5
Step-by-step explanation: The interquartile range (IQR) refers to the difference between the upper(75%) quartile and lower(25%) quartile of a distribution. Hence, ensuring that the middle 50% is being captured. With the average given as $60, having a interquartile range capturing the middle 50% as $1 seems so small from a statistical stand point. Similarly, an interquartile range of $100 capturing the middle 50% is also too large and nearly impossible if the average price is $60. However, a price of $5 sit well in between considering the average price of $60
Work out 5/7 of 100
Give your answer correct to the nearest whole number.
Answer:
71
Step-by-step explanation:
100÷7≈14.1
14.1×5=70.5
70.5 rounded to the nearest whole number is 71
Which statements are true ?
Answer:
The true statements
Step-by-step explanation:
lol
Determine if line AB is tangent to the circle.
Answer:
Is a tangent
Step-by-step explanation:
~ By definition, a tangent to circle is a straight line, presently perpendicular to a radius if one. In this case tangent AB should be perpendicular to the radius. If we were to call the center O, we would say AB should be perpendicular to OA. ~
1. Now let us say at the moment that AB is a tangent. If that is so, it should be that m∠A = 90 degrees ( ° ), provided AB is ⊥ to OA by definition.
2. Now the triangle ABO is a right triangle, and with that is should be that Pythagorean Theorem is applied. This can help us prove if AB is a tangent or not. If Pythagorean Theorem is not applicable it would mean ABO is not a right angle triangle, that AB is not ⊥ to OA, and thus can't be a tangent.
3. Let us say x ⇒ side OA, and that side BO = 9 + 8 + 17:
AB^2 + OA^2 = BO^2,
15^2 + x^2 = 17^2,
x = 8
4. Now there are two radii present, OA is only one of them. As radii are ≅, OA = other radii, 8 = 8
5. This proves that Pythagorean Theorem is applicable, that ABO is a right triangle, that m∠A = 90°, and that by definition AB is a tangent
* I have already answered this question before *
como calcular el área de un cono?
Answer:
La fórmula para el área total de superficie de un cono recto es T. S. A. = π rl + π r 2 . Ejemplo 2: Encuentre el área lateral de superficie de un cono recto si el radio es de 6 pulgadas y la altura de inclinación es de 10 pulgadas.
Answer:
La fórmula para el área total de superficie de un cono recto es TSA = π rl + π r
2. Ejemplo
2: encuentre el área lateral de superficie de un cono recto si el radio es de 6 pulgadas y la altura de inclinación es de 10 pulgadas.
Step-by-step explanation:
I WILL GIVE BRAINLIEST!!!! - YEAR 9 MATHS!!
ABCD is a square with sides of length 9cm. How many points (inside or outside the square) are equidistant from B and from C, and are exactly 6cm from A?
Answer: one point only.
Step-by-step explanation:
Since the length of the sides of the square is 9 cm, taking a point outside the square which is equidistant from point B and C will never give exact 6 cm from A.
The only way to achieve this is by taking a equidistant point inside.
You can achieve exactly 6 cm from point A from point between B and C
But can only achieve a single point if it has to be equidistant from point B and C.
Batman, who is having a slow year for crime, has resorted to saving cats from very tall buildings. Our fearless 6 foot tall hero is 40 feet from the the Petsmart building the cat was trying to break in to, in order to get his paws on the pumpkin spice cat nip. Batman sights the top of the building at a 30° angle, how high is the building?
please answer in square root form
Brian has 5 marbles, Sarah has 9 marbles, Jimi has 4 marbles, and Juan has 6 marbles. They want to redistribute the marbles so that each person has the same number of marbles. If the marbles are redistributed, then how many should each person get?
Answer:
6
Each Person should get 6 marbles
Step-by-step explanation:
edg2020
What is the answer to this question? Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 3a to the third power and 4a to the third power.
Answer:
Step-by-step explanation:
Since the length of both legs of the right angle triangle are given, we would determine the hypotenuse, h by applying Pythagoras theorem which is expressed as
Hypotenuse² = one leg² + other leg²
Therefore,
h² = (3a)³ + (4a)³
h² = 27a³ + 64a³
h² = 91a³
Taking square root of both sides,
h = √91a³
The formula for determining the perimeter of a triangle is expressed as
Perimeter = a + b + c
a, b and c are the side length of the triangle. Therefore, the expression for the perimeter of the right angle triangle is
√91a³ + (3a)³ + (4a)³
= √91a³ + 91a³
Please help me in this question.Easy question.
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You can use Pythagoras theorem as it is a right angle
a^2 + b^2 = c^2
where 'c' is the hypotenuse
Rearrange this to find a side length
c^2 - a^2 = b^2
where 'b' is the missing length
10^2 - 8^2 = b^2
100 - 64 = b^2
b^2 = 36
Square root this to get the answer
b = 6cm
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how many times smaller is the surface area of a cube if the side length is multiplied 1/2
Answer:
1/4, or 4 times smaller
Step-by-step explanation:
Since the surface area of a cube is just the combination of the area of all of the square sides, and the formula for those is s^2, if the side length was decreased by 1/2 then the surface area would decrease by (1/2)^2=1/4. Hope this helps!
Answer correct for brainliest!
Answer:
Output value
Step-by-step explanation:
Simplify by combining like terms: 9x - 14y + 9 + 13y
Answer:
9x-y+9
Step-by-step explanation:
so what you do first is combine -14y and 13 y and you get -y
whats the answer to 4(6p+9y)
Answer: The answer is 60p.
Step-by-step explanation:
1) You first simplify what is in parenthesis.
(6p+9p) = (15p)
2) Next, you multiply (15p) by 4.
4(15p) = 60p
3) You simplified the expression of
4(6p+9p) to 60p.
Will mark as brainliest if correct
Answer:
-2/3
Step-by-step explanation:
The only way the answer could be one is if the exponent is 0
So 3x-2=0:
3x = -2
x = -2/3
Hope this helps!
Use the spinner to find the theoretical probability of the event. Type your answer in box below in simplified fraction form.
a. Spinning red ___________
b. Spinning a 1 __________
c. Spinning an odd number ___________
d.Spinning a 9 _____________
Answer:
A.) 1/3
B.) 1/6
C.) 1/2
D.) 0
Step-by-step explanation:
Total number of faces on spinner = 6
Probability = (required outcome / Total possible outcomes)
A)
P(spinning Red):
n(Red) / n(total)
n(red) = 2, n(total) = 6
P(spinning red) = 2/6 = 1/3
B.)Spinning a 1 :
n(1) = 1
Therefore, P(spinning 1) = 1/6
C.) spinning an odd number :
Odd numbers = 1,3,5
P(spinning an odd number) = 3/6 = 1/2
D.) spinning a 9:
9 isn't a number on the wheel
P(spinning a 9) = 0/6 = 0
4. The area of the rectangle shown is 200 square units. Find the value of x.
1 point
Your answer
Answer: x = 40
Step-by-step explanation:
Here is the complete question:
The area of the rectangle shown is 200 square units. Find the value of x. Width: 8 Length: 1/2x+5
The area of a rectangle is length multiplied by the width.
Area = Length × Width
Area = 200
Width = 8
Length = 200/8 = 25
Since length is 25 and it has bee denoted as 1/2x + 5. This will be:
1/2x + 5 = 25
1/2x = 25 - 5
1/2x = 20
x = 20 × 2
x = 40
Check:
= 1/2x + 5
= (1/2 × 40) + 5
= 20 + 5
= 25
If the pattern below follows the rules starting with 10 every consecutive line has a number one less than previous line how many marbles must be in the seventh mine
A.7
B.4
C.6
D. Need more information
Answer:4
Step-by-step explanation:
Just count lol n I did it rn
Answer:
4
Step-by-step explanation:
trust me
pls answer i will make u BRAINLIST >_< HELP ME PLS
Answer:
see below
Step-by-step explanation:
1/2 + 4/6
Get a common denominator of 6
1/2 * 3/3 = 3/6
3/6 + 4/6 = 7/6
We change back to a mixed number
1 1/6
Answer:
7/6 or 1 1/6
Step-by-step explanation:
In this case, you're adding 1/2 plus 4/6.
One strategy you can use to solve this problem is by getting the common denominator.
1/2 is equal to 3/6.
Then you could add 3/6 to 4/6 and you'll get 7/6.
Now depending on the teacher they might want you to have an improper fraction or mixed number.
You can get this mixed number by dividing 7/6 which equals 1 1/6.
Hope this helped :)
A prism with a square base has a volume of 96 ft3. The height of the unit is 6 feet. A prism has a length of l, width of 2, and height of 6 feet. Given what you know about the figure, complete these sentences. The area of the square base is feet2. The length of the prism is feet. The width of the prism is feet.
Answer:
The area of the square base is 16 feet the length of the prism is 4 feet, and the width of the prism is 4 feet.
Step-by-step explanation:
The length of the prism is L = 4 feet
What is the volume of a prism?A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.
The volume of a prism is the product of its base area and height
Volume of Prism = B x h
where B = base area of prism
h = height of prism
Given data ,
A square base has a volume of 96 ft3 and a height of 6 feet. Since the volume of a prism is given by the product of the area of the base and the height, we can find the area of the square base as follows:
Volume = area of base x height
96 = area of base x 6
Area of base = 16 ft²
Now, we are given a prism with length of l, width of 2, and height of 6 feet. Since the base is a square, we can set l equal to the width and solve for it using the area of the base we found earlier:
Area of base = l²
16 = l²
l = 4 feet
Hence , the length of the prism is 4 feet and the width is 2 feet
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Someone please help me
Answer: The slope is 6
Step-by-step explanation: pic
I hope this helps
Answer:
The slope is:
[tex]m = 2[/tex]
Step-by-step explanation:
-Use the equation to find the slope:
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
-Use both points [tex](-1,-5)[/tex] and [tex](2,1)[/tex] for the slope formula:
[tex]m = \frac{1-(-5)}{2-(-1)}[/tex]
-Then , you solve the formula:
[tex]m = \frac{1+5}{2+1}[/tex]
[tex]m = \frac{6}{3}[/tex]
[tex]m = 2[/tex]
So, the slope is [tex]2[/tex] .
Which statement is correct regarding the measurements of the parallelogram?
sly
4
(-2,3)
(7,3)
2
1
-3 7-6 -5 -3 -2 -14
2 3 4
5/87
8
X
-2
(-5, 4)
(4,4)
5
-6
O The base is 7 and the height is 7, so the area is 7(7) = 49 square units.
O The base is 7 and the height is 3, so the area is 7(3) - 21 square units.
O The base is 9 and the height is 6, so the area is 9(6) = 54 square units.
© The base is 9 and the height is 7 so the area is 907-63 square units
Answer:
© The base is 9 and the height is 7 so the area is 907-63 square units
Answer:
The answer is D
Step-by-step explanation:
The base is 9 and the height is 7, so the area is 9(7) = 63 square units