The equation of an ellipse with a center at origin, a height of 12 units, and a width of 19 units is x^2/(9.5^2) + y^2/(6^2) = 1.
Explanation:The student is asking for an equation of an ellipse. An ellipse has a standard form equation given by x^2/a^2 + y^2/b^2 = 1, where 'a' is the semi-major axis and 'b' is the semi-minor axis. The semi-major axis and the semi-minor axis are half of the major axis (width) and minor axis (height) respectively. Here, the width or major diameter of the ellipse is given as 19 units and the height or minor diameter as 12 units.
Thus, the semi-major axis is 19/2 = 9.5 and the semi-minor axis is 12/2 = 6. As the ellipse's center is at the origin, the equation of the ellipse is given by: x^2/(9.5^2) + y^2/(6^2) = 1.
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The equation of the ellipse in standard form with a center at the origin, a height of 12 units, and a width of 19 units is x²/(19/2)² + y²/(6)² = 1.
Explanation:The equation of an ellipse in standard form with the center at the origin is given by x²/a² + y²/b² = 1, where a is the semimajor axis (half the width) and b is the semiminor axis (half the height).
Given a width of 19 units and a height of 12 units, the semimajor axis will be half of the width and the semiminor axis will be half of the height. So, the equation of the ellipse will be x²/(19/2)² + y²/(12/2)² = 1.
Simplifying, x²/(19/2)² + y²/(6)² = 1. This is the equation of the ellipse in standard form with a height of 12 units and a width of 19 units.
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In a lottery daily game, a player picks four numbers from 0 to 9 (without repetition). How many different choices does the player have
a) If order matters?
b) If order does not matter?
Answer:
a) If order matters, choices the player have = 5040
b) If order does not matter, choices the player have = 210
Step-by-step explanation:
n = 10, r = 4
When the order matters, its permutation.
permutation without repetition = P(n, r) = [tex]\frac{n!}{(n - r)!}[/tex]
= [tex]\frac{10!}{(10 - 4)!}[/tex]
= [tex]\frac{10!}{6!}[/tex]
= 5040
When the order doesn't matter, its combination.
combination without repetition= C(n, r) = [tex]\frac{n!}{r!(n - r)!}[/tex]
= [tex]\frac{10!}{4!(10 - 4)!}[/tex]
= [tex]\frac{10!}{4! × 6!}[/tex]
= 210
If order matters, there are 5,040 different choices. If order does not matter, there are 210 different choices.
Explanation:a) If order matters, the player has 10 choices for the first number, 9 choices for the second number (since it cannot be the same as the first), 8 choices for the third number, and 7 choices for the fourth number. Therefore, the total number of different choices is 10 * 9 * 8 * 7 = 5,040.
b) If order does not matter, the player is selecting a combination rather than a permutation. The number of combinations of four numbers chosen from a set of ten is given by the formula nCr = n! / (r!(n-r)!). In this case, n = 10 and r = 4, so the number of different choices is 10! / (4!(10-4)!) = 210.
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What would the mode be with this data set??
5,5,5,5,5
ANSWER=5
EXPLANATION
The Mode is known as the number that occurs most often in a set of data, so the data being 5,5,5,5,5 only has fives in it so the answer must be 5.
Hello There!
The mode is the number that occurs the most in a set of numbers. In this case, there is only 5 numbers but they are all the same so the mode of the data set shown would be 5.
The price of a ring was increased by 8% to £486. What was the price before the increase?
Step-by-step explanation:
price before increased be x
After it is increased by 8% it becomes1.08x
equal to 486
so 1 .08x=486
x=£450
The price of the ring before the increase was £450.
What is the Selling Price?
This refers to the value given to a product when sold to consumers from the retailers or wholesalers.
Hence,
Given that the price before the increase is X
If increased by 8%,
It becomes 1.08x=486
Collect like terms
x= £450
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Solve for x
|4x - 3| = 20
Answer: [tex]x=\frac{23}{4}[/tex] and [tex]x=-\frac{17}{4}[/tex]
Step-by-step explanation:
Given the equation [tex]|4x - 3| = 20[/tex], you can set up two cases:
Case 1: [tex]4x-3>0[/tex]
[tex]4x-3=20[/tex]
Solve for the variable "x", therefore you get:
[tex]4x=20+3\\\\x=\frac{23}{4}[/tex]
Case 2: [tex]4x-3<0[/tex]
[tex]-4x+3=20[/tex]
Solve for the variable "x". Then, you get:
[tex]-4x=20-3\\\\x=\frac{17}{-4}\\\\x=-\frac{17}{4}[/tex]
Therefore, the solution is:
[tex]x=\frac{23}{4}[/tex] and [tex]x=-\frac{17}{4}[/tex]
56. Mikayla is filling a glass sphere with water.
If the diameter of the sphere is 12 inches,
what is the minimum amount of water she
needs to completely fill the sphere?
The minimum amount of water she needs to completely fill the sphere is; 904.32 inches³
How to find the Volume of a Sphere?
The formula for Volume of a Sphere is given as;
V = ⁴/₃πr³
We are given;
Diameter; d = 12 inches
Thus;
Radius; r = 12/2 = 6
To get the minimum amount of water she needs to completely fill the sphere, we just plug in the relevant values into the volume equation to get;
V = ⁴/₃π(6)³
V = 904.32 inches³
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Solve for r.
12 - - = 2r +1
r=
Answer:
r=5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
Fiona’s school has three hallways that make up three sides of a triangular building design. In the morning, Fiona walks 90 yards through the first hallway to get to the next. In the afternoon, she walks 60 yards through a second hallway to exit the building. What are the possible lengths of the third hallway that she did not walk through? between 30 yards and 60 yards between 30 yards and 90 yards between 30 yards and 120 yards between 30 yards and 150 yards
Answer:
"between 30 yards and 150 yards"
Step-by-step explanation:
Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:
Possible length of 3rd side would be between "x - y" and "x + y"
Here, given x = 90 and y = 60, so the possible length of 3rd side would be:
90 - 60 = 30,
90 + 60 = 150
Hence, in between 30 and 150
Answer:
its D between 30 and 150 just took test on ed got a 100
Step-by-step explanation:
Anik is married and earns $29,560 per year. What is his
weekly federal withholding?
$44.89
$90.34
$82.88
$45.17
$41.44
90.34 because you divide 29,560 and 12 and then the answer to that by 12 and then divide by 4 and then divide by 7 and round
PLEASE HELP RIGHT AWAY
Answer:
95
Step-by-step explanation:
Week Number of Beetles
0 16
1 16 + (16/4) = 20
2 20 + (20/4 ) = 20 + 5 = 25
3 25 + (25/4 ) = 25 + 6.25 ≈ 31
4 31 + (31/4) = 31 + 7.75 ≈ 31+8 ≈ 39
5 39 + (39/4) = 39 + 9.75 ≈ 39 + 10 ≈ 49
6 49 + (49/4) = 49+ 12.25 ≈ 49+12 ≈ 61
7 61 + (61/4) = 61 + 15.25 ≈ 61 + 15 ≈ 76
8 76 + (76/4) = 76 + 19 = 95
Hence there will be approximately 95 beetles by 8th week
The independent variable in the relationship is the and should be placed on the . The dependent variable in the relationship is the and should be placed on the .
The independent variable is manipulated or controlled by the experimenter and is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable and is usually placed on the vertical axis of a graph.
Explanation:In a scientific study, the independent variable is the variable that is manipulated or controlled by the experimenter, and it is usually placed on the horizontal axis of a graph. The dependent variable is the variable that is measured to see the effect of the independent variable, and it is usually placed on the vertical axis of a graph.
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I'm not sure understanding this at ALLLLL
Answer:
17. Scale Factor is 3:1
18. Scale Factor is 1:3
Step-by-step explanation:
Scale Factor: In two similar shapes, the ratio of their corresponding sides is called scale factor.
17. Give the scale factor of Figure A to Figure B
Figure A has sides:
Hypotenuse = 15
Perpendicular = 12
Base = 9
Figure B has sides:
Hypotenuse = 5
Perpendicular = 4
Base = 3
So, if we divide all sides of figure A by 3 we get Figure B
So, Figure A : Figure B
3:1
18. Give the scale factor of Figure B to Figure A
Figure B has sides:
Hypotenuse = 5
Perpendicular = 4
Base = 3
Figure A has sides:
Hypotenuse = 15
Perpendicular = 12
Base = 9
If we multiply 3 with the sides of Figure B we can get the sides of Figure A.
So scale factor is 3.
So, Figure B : Figure A
1:3
Answer:
17) 3 : 1
18: 1 : 3
Step-by-step explanation:
Figure A and Figure B are similar triangle.
Scale Factor of A : B
= 9 : 3
= 3 : 1
Scale Factor of B : A
= 3 : 9
= 1 : 3
What is the scale factor of this dilation?
A) 1/2
B) 1/3
C) 2
D) 3
Answer:
2
Step-by-step explanation:
From X to the black dot it is 2 and from the black dot to Y it is 3
From X' to the black dot it is 4 and from the black dot to Y' it is 6
The lengths are getting twice as bigger
Answer:
2
Step-by-step explanation:
U can use this formula
Image 1/image 2
Jay went to an amusement park. The park charges an entrance fee of $10.50 and $4.50 for every ride. Jay spent $46.50 on entrance fees and rides. Which fuction can be used to find the number of rides he went on?
10.50+4.50x=46.50
This is the fuction to use to solve the problem.
The function that can be used to find the number of rides he went on is
46.50 = 4.5x + 10.50
What is linear equation?A linear equation is a mathematical expression involving variables raised to the first power only.
It takes the form ax+b=0, where
a and b are constants, and x is the variable.
Represent the number of rides he went on by x
the total amount on rides will be
4.5x
The entrance fee = $10.50
Total amount = 45x + 10.50
Therefore, the equation that represents the number of rides he went on is
46.50 = 45x + 10.50.
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Last year Golden State Warriors won 80% of the first 15 matches. Then they won the rest of the three matches. What percent of all matches did they win?
Answer:
83.33%
Step-by-step explanation:
We first need to evaluate 80% of the first 15 matches in order to determine the number of watches out of 15 which they won.
80 % of 15 = 80/100 * 15 = 12
12 matches out of the first 15 were won.
Since the team won the rest of the 3 remaining matches, the total number of matches won becomes;
12 + 3 = 15
The team thus won 15 matches out of a total of 15 + 3 =18 matches .
The percent of all matches won is ;
15/18 * 100 = 83.33%
Tasty Treats Baking Company asked a random sample of 100 students in the senior class at Ridgemont High School the question, “Do you prefer chocolate or butterscotch Tasty Treats?” Everyone surveyed had to pick one of the two answers, and 42%, percent said they preferred chocolate.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
A) About 42%, percent of all students at Ridgemont High prefer chocolate.
B)About 42%, percent of all students in the senior class at Ridgemont High prefer chocolate.
C)42%, percent of this sample preferred chocolate, but we cannot conclude anything about the population.
Answer:B!!
Step-by-step explanation:
Answer a is incorrect because only the seniors were questioned and answer c is incorrect because nothing was mentioned in the question about only testing males.
Your answer is B
.......Help Please......
Answer:
(7,5) is the vertex
Step-by-step explanation:
Maria solved the equation 34=+19
34
=
x
+
19
. Although her final answer was correct, she could have found it in a simpler way. Which sentence best explains why?
She could've subtracted 19 from both sides of the equation in the second step to find the value of [tex]x[/tex] immediately, rather then add 19 to both sides.
[tex]34=x+19 \\ \\ 34-19=x+19-19 \\ \\ x=15[/tex]
Answer:
19 should have been subtracted from, not added to, both sides of the equation.
Step-by-step explanation:
The mean absolute deviation is a measure of . This value represents the average distance each value is from the .
Previous
Answer:
I am not sure i am sorry if i was smart i would know but ya sorry
Step-by-step explanation:
::::::::::::::
Graph f(x)=x2 +2x-3 label x and y intercept and vertex with their coordinates and draw axis of symmetry
Answer:
f(x) = x² + 2x - 3 ..….equation1
The graph of function will be a parabola
Standard form of parabola:
y=ax²+bx+c
x-coordinate of the vertex can be found using
x = [tex]\frac{−b}{2a}[/tex]
from equation 1 find values for a, b, and c.
a = 1, b = 2, c = -3 ⇒ x=−2/2(1) ⇒ x = -1
substitute the value of x into equation 1 for y-coordinate
f(-1) = (-1)² + 2(-1) – 3 ⇒ −4
vertex =(-1,−4)
Axis of symmetry = x = -1,
Axis of symmetry is vertical and passes through the vertex with equation
x = -1
For x-intercept, put y = 0
x² + 2x - 3=0 ⇒ x² + 3x -x - 3=0 ⇒ x( x + 3 ) -1 ( x + 3 ) ⇒ ( x − 1 )( x + 3 ) = 0
equate each factor to zero and solve for x
x − 1 = 0 ⇒ x = 1, x + 3 = 0 ⇒ x = -3
x-intercept = { 1, -3 }
For y-intercepts put x = 0
y = (0)² + 2(x) - 3
y = -3
y-intercept = ( 0 , -3 )
The points for the vertex, x-intercepts, and y-intercept and axis of symmetry are plotted on the graph.
Please help I am confused
A. 10% of n is q; n = 10q
B. 25% of x is 320; x = 1280
C. 15% of y is q; y = 6.666....7q
Answer:
a = 90
b = 7.81
c = 60
use the formula a=p(1+r/n)nt to find the compound interest account . zakk deposited $5600.0in an account which compounded 1.9%quarterly and left there for ten years. what was the amount in the account at the end of ten years,?
Answer:
[tex]A=\$6,768.75[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=10\ years\\ P=\$5,600\\ r=0.019\\n=4[/tex]
substitute in the formula above
[tex]A=\$5,600(1+\frac{0.019}{4})^{4*10}[/tex]
[tex]A=\$5,600(1.00475)^{40}=\$6,768.75[/tex]
Solve 2.02W = -3.636
Answer: W=-1.8
Step-by-step explanation:
Divide both sides by 2.02 and you are left with W=-1.8.
Hope this helps!
Answer:
W = -1.8
Step-by-step explanation:
Step 1: Divide 2.02 on both sides.
W = -1.8
Simplify (x + y + 3)(x + y - 4)
Answer:
x²+2xy-x+y²-y-12
Step-by-step explanation:
(x+y+3)(x+y-4)
= x(x+y-4)+y(x+y-4)+3(x+y-4)
= x²+xy-4x+xy+y²-4y+3x+3y-12
= x²+2xy-x+y²-y-12
The answer is:
The simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Why?To solve the problem, we need to remember how to use the distributive property and how to add like terms.
The distributive property can be defined as follow:
[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]
The like terms are the terms that share the same variable and the same exponent, for example:
[tex]3x+x+ x^{2}=x^{2} +4x[/tex]
We were able to add the first and the second term because they share the same variable and the same exponent.
Now, we are given the expression:
[tex](x+y+3)(x+y-4)[/tex]
So, simplifying we have:
[tex](x + y + 3)(x + y - 4)=(x*x)+(x*y)-(4*x)+(y*x)+(y*y)-(4*y)+(3*x)+(3*y)-(3*4)\\\\(x + y + 3)(x + y - 4)=x^{2} +xy-4x+xy+y^{2}-4y+3x+3y-12\\\\(x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Hence, we have that the simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Have a nice day!
please answer me x and my step correct please
Answer:x=4√6
Step-by-step explanation:
In ∆DCB, cos30°=BC/DB
√3/2*16=BC
BC=8√3
Applying PYTHAGORAS THEOREM in ∆BAC,
(8√3)^2=2x^2
x=4√6
Answer:
[tex]x=4\sqrt6}[/tex]
Step-by-step explanation:
Look at the picture.
ΔACD it's a triangle 30° - 60° - 90°. The sides are in ratio 1 : √3 : 2.
Therefore
CD : CB : DB = 1 : √3 : 2.
If BC = 16, then CD = 16 : 2 = 8 and CB = 8√3
ΔABC it's a triangle 45° - 45° - 90°. The sides are in ratio 1 : 1 : √2.
Therefore
AC : AB : CB = 1 : 1 : √2
If CB = 8√3, then AB = x = (8√3)/(√2)
[tex]x=\dfrac{8\sqrt3}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}=\dfrac{8\sqrt6}{2}=4\sqrt6[/tex]
Factorisation of ax^2 + bx + c
Answer:
-5(t+3)(t-6)
Step-by-step explanation:
-5²+15+90
= -5(t²-3t-18)
= -5(t+3)(t-6)
How many complex roots does the equation below have?
x 6 + x 3 + 1 = 0
The number of complex roots is
Answer:
The number of complex roots is 6.
Step-by-step explanation:
Descartes's rule of signs tells you that the number of positive real roots is 0. The number of negative real roots will be at most 2. The minimum value of the left side will be between x=0 and x=-1, but will never be negative. Thus all six roots are complex.
_____
The magnitude of x^3 will exceed the magnitude of x^6 only for values of x between -1 and 1. Since the magnitude of either of these terms will not be more than 1 in that range, the left-side expression must be positive everywhere.
Answer:
6
Step-by-step explanation:
triangleABC is a right triangle. if AC=15 and BC=17, what is AB
Answer:
The answer in the procedure
Step-by-step explanation:
I will analyze two cases
see the attached figure to better understand the problem
case a) applying the Pythagoras Theorem
I assume that the hypotenuse is BC
[tex]AB^{2}=BC^{2}-AC^{2}[/tex]
substitute the given values
[tex]AB^{2}=17^{2}-15^{2}[/tex]
[tex]AB^{2}=64[/tex]
[tex]AB=8\ units[/tex]
case b) applying the Pythagoras Theorem
I assume that the hypotenuse is AB
[tex]AB^{2}=BC^{2}+AC^{2}[/tex]
substitute the given values
[tex]AB^{2}=17^{2}+15^{2}[/tex]
[tex]AB^{2}=514[/tex]
[tex]AB=\sqrt{514}=22.67\ units[/tex]
solve for x X - 47 = 192
Answer: x = 239
Step-by-step explanation:
You need to get rid of everything else except the x = #
So, to do that you need to take the -47 and add 47 on each side.
That would get you x = 239
Answer:
239
Step-by-step explanation:
X - 47 = 192
X = 192 + 47
X = 239
the diameter of a circle is 4 feet. what is the circumference
Answer:
C=12.57 ft
Step-by-step explanation:
Answer: 12.56 feet.
Step-by-step explanation:
the volume of a cylinder is found by?
Answer:
Step-by-step explanation:
Base x width x height
For this case we have by definition that the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where we have to:
A: It is the radius of the cylinder
h: It is the height of the cylinder
To find the volume of a cylinder we must have the radius and the height. In an equivalent way we can have the diameter, the radius is obtained by dividing the diameter by 2.
Answer:
[tex]V = \pi * r ^ 2 * h[/tex]