Answers
For ellipses:
-First, let's use completing the square method to determine values of a(semi-major axis), b(semi-minor axis), and the coordinates of the center of the ellipse.
[tex]\mathsf{x^2+4y^2-10x-24y+45=0}[/tex][tex]\mathsf{x^2-10x+4y^2-24y=-45}[/tex][tex]\mathsf{(x^2-10x)+4(y^2-6y)=-45}[/tex][tex]\mathsf{(x^2-10x+25)+4(y^2-6y+9)=-45+25+4(9)}[/tex][tex]\mathsf{(x-5)^2+4(y-3)^2=16}[/tex][tex]\mathsf{\dfrac{(x-5)^2}{16}+\dfrac{(y-3)^2}{4}=1}[/tex][tex]\mathsf{\dfrac{(x-5)^2}{(4)^2}+\dfrac{(y-3)^2}{(2)^2}=1}[/tex]-The center of the ellipse is at C(5, 3), semi-major axis, a = 4, and semi-minor axis, b = 2.
-Since the major axis of the ellipse is horizontal, the distance between the center of the ellipse and the co-vertices of the ellipse is ±b.
[tex]\mathsf{CoV_1=(5,3+b)}[/tex][tex]\mathsf{CoV_2=(5,3-b)}[/tex]-The coordinates of the co-vertices of the ellipse are:
[tex]\mathsf{CoV_1=(5,3+2)} \longrightarrow \mathsf{CoV_1=(5,5)}[/tex][tex]\mathsf{CoV_2=(5,3-2)} \longrightarrow \mathsf{CoV_2=(5,1)}[/tex]For the parabola:
-We have the following data:
The parabola is opening to the left and axis symmetry along the major axis of the ellipse (axis of symmetry: y = 3):
[tex]\mathsf{(y-k)^2=-4a(x-h)}[/tex]The focus of the parabola is the center of the ellipses.
F = (5, 3)-The parabola is passing through the co-vertices of the ellipse:
-The parabola is passing through poînts (5, 5) and (5, 1)
-From the first data, we know that the value of k is equal to 3 because the axis of symmetry of the parabola is y = 3.
[tex]\mathsf{(y-3)^2=-4a(x-h)}[/tex]-From the second data, we know that the x-coordinate of the vertex is at h = 5 + a. (Note: the distance of the focus of the parabola and the vertex of the parabola is equal to ±a, since the parabola is opening the the left we use -a)
[tex]\mathsf{F=(5,3)}[/tex]
[tex]\mathsf{F=(h-a,k)}[/tex][tex]\mathsf{5=h-a}[/tex][tex]\mathsf{h=5+a}[/tex][tex]\mathsf{V=(h,k)}[/tex][tex]\mathsf{V=(5+a,3)}[/tex]-Substitute the coordinates of the vertex of the parabola
[tex]\mathsf{(y-3)^2=-4a[x-(5+a)]}[/tex][tex]\mathsf{(y-3)^2=-4a(x-5-a)}[/tex][tex]\mathsf{(y-3)^2=-4ax+20a+4a^2}[/tex]-From the third data, we know that if the poînts lies on the parabola, the coordinates of the poînts must satisfy the equation of the parabola.
Using the point (5, 5), x = 5, y = 5:
[tex]\mathsf{(y-3)^2=-4ax+20a+4a^2}[/tex][tex]\mathsf{(5-3)^2=-4a(5)+20a+4a^2}[/tex][tex]\mathsf{4=-20a+20a+4a^2}[/tex][tex]\mathsf{4a^2=4}[/tex][tex]\mathsf{a^2=1}[/tex][tex]\mathsf{a=1}[/tex]-Another way to solve for the value of a is using the formula for the length of the latus rectum (LR = 4a). Since the length of the latus rectum is equal to the minor axis of the ellipse, we can easily solve for the value of a.
[tex]\mathsf{LR=4a}[/tex][tex]\mathsf{4=4a}[/tex][tex]\mathsf{a=1}[/tex]-Substitute the value of a in the equation:
[tex]\mathsf{(y-3)^2=-4a[x-(5+a)]}[/tex][tex]\mathsf{(y-3)^2-4(1)[x-(5+1)]}[/tex][tex]\mathsf{(y-3)^2=-4(x-6)}[/tex][tex]{\boxed {\red{{\mathsf{(y-3)^2=-4(x-6)}}}}}[/tex](ノ‥)ノ
Related Questions
Line segment A' B' is the result after line segment AB goes through a single transformation. In which transformation would the measure of line segment A'B' be different than the measure of line segment AB?
Answers
[tex]\color{indigo}\rule{1pt}{1000000pt}[/tex]
Two consecutive positive integers have a product of 156. Find the integers.
The integers are ___
Answers
So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!
So let us assume the unknown positive integers as a and (a + 1).
★ Product of both integers :-
a (a + 1) = 156 [Equation formed]★ Solving the equation :-
[tex]: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}[/tex]
Therefore,
First positive integer is 12★ Second positive integer :-
2nd positive integer = a + 1 2nd positive integer = 12 + 1 2nd positive integer = 13dont mind my answers thanks for helping me out have a good day
Answers
Answer:
ACD and DCB are supplementary and others are correctly chosen ...
Find the solution(s) to 2x2 - 5x – 3 = 0. Check all that apply.
A. x = }
B. x= -1
0 C. x= -3
D. x= 2
E. x = 3
Answers
Answer:
E. x = 3
Step-by-step explanation:
The equation can be factored by considering the factors of the product of the first and last coefficients. Those factors must have a sum equal to the middle coefficient.
(2)(-3) = -6 = (-6)(1) = (-3)(2) = ... other factors with positive sums
The sums of the factor pairs shown are -5 and -1. We're interested in the factor pair {-6, 1}. Replacing the middle term coefficient with the sum of these, we can write the equation in a way that lets us factor pairs of terms.
2x² -6x +x -3 = 0 . . . . . . . . replace -5x with -6x+1x
2x(x -3) +1(x -3) = 0 . . . . . . factor pairs of terms
(2x +1)(x -3) = 0 . . . . . . . . . complete the factoring
Solutions are the values of x that make these factors zero:
2x +1 = 0 ⇒ x = -1/2
x -3 = 0 ⇒ x = 3
_____
Additional comment
A number of methods are used to find the factors of a quadratic with a leading coefficient other than 1. When the coefficients are small integers, this is one of the more straightforward methods: actually listing and examining the pairs of factors of "ac." If "ac" has a large number of divisors, other methods may be more practical.
Answer:
x = 3 AND x = -1/2
Step-by-step explanation:
its right
What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?
Answers
Answer:
f(x) = -(x + 8)(x -14)
= -(x2 - 112 - 6x)
= -x2 + 6x + 112 --- (1)
We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.
The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation
a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is
x = -b/2a
= -(6)/[2(-1)]
= 3
Substituting the value of x = 3 in equation (1) we get,
Now y = -(3)2 + 6(3) + 112
= -9 + 18 + 112 = 121
So the vertex point coordinates are (3, 121) and the y value is 121.
The graph below verifies the vertex point.
vertex of the graph
What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
Summary:
The y-value of the vertex of the function f(x) = -(x +
Answer:
Step-by-step explanation:
D or 121 got it right on edgenuty
Evaluate the expression:
Will mark brainlyest!!
Answers
Answer:
6
Step-by-step explanation:
pemdas=parenthesis, exponents, multiplication, division, addition, subtraction. with this, we multiply 2 x the absolute value of -3, which is just 3. therefore, 6. now we see we need to subtract the absolute value of 6 from the absolute value of 8, which gives us 2. and 2+4 is 6.
Answer: 6
Step-by-step explanation:
8-2 x 3+4
2x3=6
8-6+4
2+4
=6
hope this helps
Solve 196x2 + 25 = 0 by using square roots.
Answers
LOCKS SOON WILL GIVE BRAINLEST! 50 POINTS!!! For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
Answers
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
What is the law of cosines and sines?The law of cosines can be used to determine the measures of the triangle if the angles are known. The law is given by:
a² = b² + c² - 2bc*cosA
a,b,c are the sides and A, B, C are the angles.
The law of sines are used to determine the measures of the triangle if the angles are known. The law is given by:
a/sinA = b/sinB = c/sinC
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
Find out more on cosines and sines at: https://brainly.com/question/25830682
montreal canadiens memorabilia is on sale for 40% off due to their disappointing season how much would a jersey that cost $80 be after sales and tax
what is 40$ of 80?
Answers
40*100 = 0.4
0.4*80 = 32
Answer:
nothing much just got home
f(3) if f(x) = 2x + 5 =
Answers
Answer:
11
Step-by-step explanation: Uh- if X=3 then it would be 2(3) +5. 2x3 is 6, and 6+5 is 11.
Answer:
11
Step-by-step explanation:
2(3) + 5
simplify
6 + 5 = 11
hope this helps
The price of an item has been reduced by 55%. The original price was $51
Answers
Answer:$22.95
Step-by-step explanation: The original price is 51%
Discount is 55% of $51= 55/100×51=$28.05
Deduct the discount from the original price. $51-$28.05=$22.95
A company makes concrete bricks that are shaped like rectangular prisms. Each brick is 5inches long, 4inches wide, and 2inches tall. How much concrete will they need to make 1600 bricks?
Answers
Answer:
The answer would be 64,000.
Step-by-step explanation:
To find the area of one concrete block you will multiple length x width x height. Using the measurements provided, one block will equal 40. You will then multiple this by 1,600 to equal 64,000.
It took an airplane 3 hours to go 1725 miles.
How many miles per hour
Answers
Answer:
575 mph
Step-by-step explanation:
The plane is traveling at 575 mph.
1725/3
575
A taco shop sells tacos and fountain drinks.
Nash bought two tacos and three fountain drinks
for $13. Everly bought four tacos and two
fountain drinks for $14. Write and solve a
system of equations to determine the cost of a
taco and a fountain drink.
Answers
The cost of one taco is $2, while the cost of one fountain drink is $3.
What are the system of equations that represent the question?
2t + 3f = $13 equation 1
4t + 2f = $14 equation 2
Where:
t = number of tacos bought f = number of drinks boughtHow many drinks were bought?Multiply equation 1 by 2:
4t + 6f = 26 equation 3
Subreact equation 2 from equation 3
4f = 12
Divide both sides by 4
f = 12 / 4
f = $3
How many tacos were bought?
Subsistute for f in equation 1
2(t) + (3 x 3) = $13
2t + 9 = 13
2t = 13 - 9
2t = 4
t = 4/2
t = $2
To learn more about simultaneous equations, please check: https://brainly.com/question/25875552
*URGENT*
If you were at the Market Square and you wanted to get to the Doctor’s Office, according to the map, how would you get there? (Write your answer according to units.)
Answers
Answer: (2,-5) X:2. Y:-5
Move accross 2 units to the right and then 5 units down from 2
The table shows the average bill totals for given numbers of diners at Simone’s restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?
Persons Bill Amount
1 ------------$40
2 $80
7 -------------$280
9 $360
11 $440
A.(12, 460
B.(20, 800)
C.(24, 1,020
D.(27, 1,080)
E.(28, 1,110)
HELPP
Answers
Answer:
(B) and (D)
Step-by-step explanation:
it's B and D because they are the only two points with constant rate
show how to rewrite 1/5 with the denominator of 10
Answers
Answer:
2/10
Step-by-step explanation:
Since the denominator is 10, we must find what the numerator is so that the fraction can be equal to 1/5. Since 10 is twice of 5, we multiply 2 by 2 as well. With that, we get a final answer of 2/10.
What is the equation of a line that passes through the hypotenuse of the right triangle in the graph?
A. 1/5x
B. y=5x
C. y=-5x
D. y=2/5x
Answers
Answer:
y = 5x
Step-by-step explanation:
Hey there!
To start with the hypotenuse of a triangle is the longest side of it
and to get an equation of a line you would use
y = mx + b
where m is the slope
and b is the y-intercept
to get the slope you would do rise over run
rise/run
take 2 points and see how much it rises and runs to the next point
you would then get 5
then we figure out the y-intercept where the line intercepts the y-axis
in this case 0
In conclusion the answer is y = 5x + 0
we can also remove the 0 because it is unnecessary
y = 5x
A rectangle has vertices at coordinates 0,0 3,0 0,6 what is the area of the rectangle
Answers
Answer:
18
Step-by-step explanation:
The figure is made up of a semi circle and triangle find the area of the figure use 3.14
Help pleaseee points=13
Answers
Answer:
63.25
Step-by-step:
39.25 + 24 = 63.25 ft squared
Answer:
Step-by-step explanation:Does anyone know what this would be?
Find the surface area of the right triangular prism (above) using its net (below).
Answers
Answer:
The Answer is 96 units squared
Step-by-step explanation:
First, you find the area of all the sides:
Triangle 1: 6
Triangle 2: 6
Rectangle 1: 21
Rectangle 2: 28
Rectangle 3: 35
Then you add all of the numbers together.
6+6+21+28+35 = 96 units squared
I hope this helps :)
Find the missing measurement for x.
Answers
Answer:
EASYYY 90°
Step-by-step explanation:
30 + 60 = 90
180-90=90
also
thats a right angle which is always 90°
ALSO
the angle opposite another angle is always the same measurement.
4/9÷1/2 as a fraction (simplest form)
Answers
Answer:
8/9
Step-by-step explanation:
4/9 ÷ 1/2 = dividing by 1/2 is the same as multiplying by its reciprocal 2/1
4/9 × 2/1 = (4×2)/(9×1) multiply numerators (top numbers) and multiply denominators (bottom numbers)
What are the solutions of 12 - x2 =0?
O x=2/3 and x = -2/3
O x= 3, and x = -373
O x= 4,3 and x = -4/3
O x=6 and x = -6
Answers
I’ll give you brainliest for the first person with an answer
Answers
Answer:
1296mm^2
Step-by-step explanation:
Surface Area of the Rectangular Prism to the left on top of the box:
Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving 162mm^2
Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving 162mm^2
So, the total surface area of the rectangular prism to the left on top, is 324mm^2
Surface Area of the Triangular Prism:
Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get 108mm^2.
Area of the rectangle: lw, so 15mm * 9mm = 135mm^2
So, the total surface area of the triangular prism is 243mm^2
Surface Area of the Rectangular Prism at the bottom:
Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, 378mm^2
Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, 162mm^2
Area of the rectangle at the very bottom = lw, 21mm * 9mm = 189mm^2
So, the total surface area of the rectangular prism at the bottom is 729mm^2
Add all the total surface areas of each shape to get the total surface area of the figure:
324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2
The surface area of the figure above is 1296mm^2
Help for the brainiest answer quickly please
Answers
Answer:
C
Step-by-step explanation:
What’s The Answer Of This? Please HELP FAST
Answers
Answer:
those are corrisponding angles which means they equal each other making <H and <G both 57 degrees
Find, from first principle the derivative of 1/x^2+1 with respect to x.
Answers
Answer:
d/dx = -2/x^3
Step-by-step explanation:
1/x^2 + 1
We can solve for the derivative using the power rule
d/dx = -2/x^3 + 0
d/dx = -2/x^3
Find the perimeter of the parallelogram.
Will mark brainlyest!!
Answers
Answer:
58cm
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
16 +16=32
13+13=26
32+26=58
Hope it Helps
MAn article is
bought and sold at a profit of one fourth of selling
price. Find the profit percent.
Answers
Answer:
25% profit
Step-by-step explanation:
Statement
An article is bought and sold at a profit of one fourth of selling price.
⇒ Buying price = x
⇒ Selling price = Buying price (1 + 1/4) = 5x/4
Profit %
Selling price - Buying price / Buying price(5x/4 - x) / x(x/4) / x⇒ 1/4⇒ 0.25⇒ 25% profit