Answer:
Step-by-step explanation:
First of all, you have a typo. But that's ok, we can work around it. The equation NOT yet in standard form for an ellipse should be:
[tex]2x^2+8y^2=16[/tex]
Putting it into standard form requires that the right side of the equation equals 1. That means that we need to divide everything by 16 to accomplish that. When we do that, we will get the standard form:
[tex]\frac{x^2}{8}+\frac{y^2}{2}=1[/tex]
The general form is either
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex] or
[tex]\frac{(x-h)^2}{b^2}+\frac{(y-k)^2}{a^2}=1[/tex]
where a is ALWAYS bigger than b. So if the bigger denominator is under the x numerator, this is an ellipse that is elongated horizontally. If the larger denominator is under the y numerator, then this is an ellipse that is elongated vertically. As you can see from our standard ellipse equation, the 8 is under the x numerator, so this is a horizontally elongated ellipse.
If [tex]a^2=8,[/tex] then [tex]a=\sqrt{8}[/tex] which is approximately 2.83 units.
If [tex]b^2=2,[/tex] then [tex]b=\sqrt{2}[/tex] which is approximately 1.41 units.
Since the ellipse is elongated horizontally, the a value starts at the center of the ellipse and goes 2.83 units to the right and left of the center; the b value starts at the center of the ellipse and goes 1.41 units both up and down from the center. But what's the center?
In the standard form above involving the h and the k in the numerators, the h and k indicate the coordinates of the center. h is like the x coordinate and k is like the y coordinate. Since our ellipse does not have [tex]c^2=8-2[/tex]a constant in a set of parenthesis for either the x or the y term, the center is at (0, 0). From the center then, we go go both right and left to (2.83, 0) and (-2.83, 0) for the vertices of the ellipse. The co-vertices would be (0, 1.41) and (0, -1.41).
The foci have the formula (h + c, k) for the focal point to the right of the center and (h - c, k) for the focal point to the left of the center. But how do we find c?
[tex]c^2=a^2-b^2[/tex]
We already know that [tex]a^2=8[/tex] and [tex]b^2=2,[/tex] so
[tex]c^2=8-2[/tex] and
[tex]c=\sqrt{6}[/tex]
That means that the foci have the coordinates [tex](\sqrt{6},0)[/tex] and [tex](-\sqrt{6},0)[/tex]
and you're done!!
Pleaseeeeee helppppppp
Answer:
The series converges to -1.5.
Step-by-step explanation:
This is a geometric series, so it converges if the number in parenthesis is between -1 and 1.
-1 < -3/5 < 1, so the series converges by the geometric series test.
Now we can plug this into the calculator (on TI-84, it's Math->0 summation) to find that the sum is -1.5. You can use 100 or another big number as a placeholder for infinity.
the value of sin^2 30° - cos^2 30° is
Answer:
-1/2
Step-by-step explanation:
Im not going to go into detail about how to compute sin30 and cos 30, but know that sine and cosine are just the ratios between the sides of a 30-60-90 triangle with a hypothenuse of 1.
With that being said:
sin^2 30 - cos^2 30
= (1/2)^2 - ((sqrt3)/2)^2
= 1/4 - 3/4
= -1/2
Answer:
-1/2
Step-by-step explanation:
A flock of birds was flying around a tree. When they landed, three birds to a branch, no branches were left and one bird had to keep flying around the tree. Then, all the birds took off, flew around the tree again and landed to sit, four to a branch. Now, no birds were left flying but one branch had no birds sitting on it. How many branches were on the tree and how many birds were in the flock?
Answer: 5 branches and 16 birds.
Step-by-step explanation:
If the number of birds is B, and the number of branches is N.
First we have the equation:
B = 3*N + 1
(3 birds per branch + 1 that was flying around)
for the second equation we have:
B = 4*(N - 1)
(4 birds per branch, but one branch had no birds on it, so there are N -1 branches used)
now we can write:
3*N + 1 = 4*(N - 1)
3*N + 1 = 4*N - 4
4 + 1 = 4*N - 3*N
5 = N
So we had 5 branches, now we can replace it in one of the equations and find the number of birds.
B = 3*N + 1 = 3*5 + 1 = 16
Answer:
deposition
Step-by-step explanation:
Please help me now plz
Answer:
B
Step-by-step explanation:
The equation of the circle is (x + 1)² + (y + 3)² = 6². When we plug in (-6, -6) we get (-6 + 1)² + (-6 + 3)² = 6², which is a true statement so that means that the point is on the circle.
What is the solution to the equation Negative (5 minus (a + 1)) = 9 minus (5 minus (2a minus 3))?
[tex]\text{Solve:}\\\\-(5-(a+1))=9-(5-(2a-3))\\\\-(5-a-1))=9-(5-2a+3))\\\\-(4-a)=9-(8-2a)\\\\-4+a=9-8+2a\\\\-4+a=1+2a\\\\\text{Subtract a from both sides}\\\\-4=1+a\\\\\text{Subtract 1 from both sides}\\\\\boxed{-5=a}[/tex]
Answer:
The answer is A: a=-5
Step-by-step explanation:
took the test
On a coordinate plane, triangle L M N has points (2, 1), (1, 1), (1, 3). Triangle L prime M prime N prime has points (negative 4, negative 4), (negative 3, negative 4), (negative 3, negative 2). Which sequence of transformations produces TriangleL'M'N' from TriangleLMN? a translation 5 units down and 2 units to the right followed by a reflection across the y-axis a reflection across the y-axis followed by a translation 5 units down and 2 units right a translation 5 units down and 2 units to the left followed by a reflection across the y-axis no sequence of transformations
Answer:
(A)a translation 5 units down and 2 units to the right followed by a reflection across the y-axis
Step-by-step explanation:
If a point is reflected across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite.
Triangle LMN has points (2, 1), (1, 1), (1, 3).
Triangle L'M'N' has points (-4,-4), (-3,-4), (-3,-2).
From the given options:
Option A: A translation 5 units down and 2 units to the right followed by a reflection across the y-axis
Given the points: (2, 1), (1, 1), (1, 3) of Triangle LMN
A translation 5 units down(x,y-5): (2,-4), (1,-4), (1,-2)2 units to the right(x+2, y-5): (4, -4), (3, -4), (3, -2)Reflection across the y-axis: (-4,-4), (-3,-4), (-3,-2)Therefore, the sequence of transformation in Option A produces Triangle L'M'N'.
Answer:Which sequence of transformations produces
TriangleL'M'N' from TriangleLMN?
a reflection across the y-axis followed by a translation 5 units down and 2 units right
a translation 5 units down and 2 units to the left followed by a reflection across the y-axis
no sequence of transformations
the answer is ''A'' a translation 5 units down and 2 units to the right followed by a reflection across the y-axis.
Step-by-step explanation:
i took the quiz today.
Consider the statement: “In a triangle, the measure of an
exterior angle is always greater than the measure of the
adjacent interior angle."
Which of the following would serve as a counterexample?
Answer:
See the example given in the picture attached.
Step-by-step explanation:
No options are given, so I made my own example. In the picture attached, we can see that the measure of the exterior angle A is less than the measure of the adjacent interior angle B.
12
11
10
NA
9
3
8
4
7
5
6
H(4 1/2, -3 1/4) x (3 3/4, -1 3/4) what the midpoint of hx
Answer:
(3 7/8, 2 3/4)
Step-by-step explanation:
To find the midpoint, the formula is (x1-x2)/2 and (y1-y2)/2. So, in this case, our x1 is 4 1/2 and our x2 is -3 1/4. Subtract x2 from x1 and you will get 7 3/4. Then, divide by 2 to get 3 7/8. This is our x-coordinate.
Our y1 is 3 3/4 and our y2 is -1 3/4. Subtract y2 from y1 to get 5 1/2. Then divide by two to get 2 3/4. This is our y-coordinate.
Now we have our x and y coordinates.
(3 7/8, 2 3/4)
workers are loading boxes onto a truck . So far, they have loaded 48 boxes onto the truck. According to their inventory, they still need to load 96% of boxes on the truck. What is the total number of boxes the workers are loading on the truck? Explain.
Answer:
1,200
Steps down below
Step-by-step explanation:
Steps
1: 48=4% loaded on truck and they have 96% left to load
2: so set up a proportion and it should look like this
3: 48 over x = 4 over 100
4: 48/x=4/100
6: do cross multiplication 100×48= 4,800÷ 4 = 1,200 total on truck
Answer: 1,200 total on truck
Hope this helps.
i have no idea how to do word problems and they’re a little harder
Answer: Answer choice 1, 3, 5
Step-by-step explanation:
This is more of analyzing a graph rather than a word problem.
We are told that 4 pm is at 16 hrs after midnight. You can see that the graph increases up to 4 pm. We can say 1 is correct.
After 6 pm at 18 hrs, we can see that the graph decreases. We can say 3 is correct.
Looking at the slope of the graph, 12 to 16 has a steeper slope than 8 to 12. We can say the temperature increases faster at 12 to 16 than 8 to 12.
find the center and radius of the circle: (x+9)^2+(y-6)^2=25
Answer:
The center is (-9,6) and the radius is 5
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2+(y-k)^2=r^2
where (h,k) is the center and r is the radius
(x - -9)^2+(y-6)^2=5^2
The center is (-9,6) and the radius is 5
Circle equation: (x - h)^2 + (y - k)^2 = r^2
(h, k) is the center.
r is the radius.
(h, k) in the given equation is (-9, 6). This is the center.
We need to take the square root of 25 since the formula has r^2.
√25 = 5
So, the radius is 5.
Best of Luck!
an article bought for $125 was sold for $175 the profit as a percentage of the cost price was
Answer:
40%
Step-by-step explanation:
Step 1: 175-125-50
Step 2: 50/125=0.4=40%
Answer:
40% profit
Step by step explanation:
There is a profit of $50.
If you were to find the percentage, you would divide 50 by 125. This would give you 0.4
Bety compró 16 pares de calcetas, entre blancas y negras, y pagó $339. Los pares de calcetas blancas cuestan $24 y las negras $19. Plantea el sistema de ecuaciones y resuelve por el método que creas conveniente. Después toma foto y súbela en donde se indica.
Answer:
Sistema de ecuaciones:
x+y= 16
24x+19y=339
Respuesta:
x=7, y=9
Step-by-step explanation:
Con la información del enunciado puedes plantear las siguientes ecuaciones:
x= cantidad de calcetas blancas
y= cantidad de calcetas negras
x+y= 16 (1)
24x+19y=339 (2)
Para resolver las ecuaciones, debes iniciar despejando x en 1:
y=16-x (3)
Después, debes reemplazar (3) en (2) y despejar x para encontrar su valor:
24x+19(16-x)=339
24x+304-19x=339
5x=339-304
x=35/5
x=7
Luego, puedes reemplazar el valor de x en (3) para encontrar y:
y=16-x
y=16-7
y=9
De acuerdo a esto, x= 7, y=9.
when sunayana purcased a video-game she paid Rs 162.50 as VAT at the rate of 13%. find its cost without levying VAT. Rs 1250 is answer please how to take out this answer
Answer: 1250
Step-by-step explanation:
Let x be the cost before vat
13/100x = 162.50
x = 162.50 x 100/13
x = 162.50 / 2.13
x = 1250
Work out an estimate for the value of
48.7 × 61.2/11.3
Answer:
[tex]263.755[/tex]
Step-by-step explanation:
[tex]48.7 \times 61.2 \div 11.3 \\ 2,980.44 \div 11.3 \\ = 263.755752 [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The right answer is 263.755
Look at the attached picture
Hope it will help you
Good luck on your assignment..
Which of these four sets of side lengths will form a right triangle?
Set 1
StartRoot 2 EndRoot cm, 9 cm, StartRoot 7 EndRoot cm
Set 2
2 in., StartRoot 5 EndRoot in., 9 in.
Set 3
StartRoot 6 EndRoot mm, 2 mm, 10 mm
Set 4
StartRoot 2 EndRoot ft, StartRoot 7 EndRoot ft, 3 ft
Set 1
Set 2
Set 3
Set 4
Answer:
on e d g e n u i t y 2020, the answer is Set B
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
On the coordinate plane shown, each grid unit represents 10 feet. Polygon QRST has vertices Q(20, 30), R(−10, 30), S(−10, −20), and T(20, −20), and represents the floor plan of a room. Find the perimeter and area of the room.
The coordinate plane is missing, so i have attached it.
Answer:
Perimeter of room = 140 ft
Area of room = 1200 sq.ft
Step-by-step explanation:
From the cordinate plane attached, we can see the polygon QRST which represents the floor plan of the roo.
Thus;
The length of the sides of the room are;
ST = RQ = 30
QT = RS = 40
Perimeter of a rectangle is the sum of all sides of the rectangle.
Thus, perimeter of the room = (30 × 2) + (40 × 2) = 140 ft
Now, area of a rectangle is the product of two perpendicular sides.
Thus area of room = 40 x 30 = 1200 sq.ft
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation.
Answer:
The answer is C
AFGH is a right triangle.
Answer:
A. TRUE
Step-by-step explanation:
7²+√51²= 10²
49+51=100
Answer is TRUE
If f(x) = {3x+53x−5if −5
Answer:
-385
Step-by-step explanation:
If -5 = x, then f(x) = -15-365-5 which is -385.
please help image attached i have everything before question 11 it’s due this morning
Answer:
11. 7x+28
Step-by-step explanation:
Answer:
Step-by-step explanation:
10) 4x+12
11) 7x+28
12)2x+16
13)9x+54
14)3x+33
15) 5x+35
16) 6x+24
17)8x+72
18) 4x+20
3. A telephone pole is supported by two wires on opposite sides. At the top of the pole, the wires
form an angle of 55º. On the ground, the ends of the wires are 11.0 m apart. One wire makes a
(4) 41° angle with the ground.
a) How long is each wire? (round to the nearest tenth)
b) How tall is the pole? (round to the nearest tenth)
I understand A, but please help with B ASAP!!!!
Answer: a) length of the wires are 8.1m and 13.4m
b) length of pole is 8.8m
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo. Triangle ABC is formed. Since the sum of the angles in a triangle is 180°, it means that angle B would be
180 - (41 + 55) = 84°
a) AC and BC are the lengths of each wire.
CD is the height of the pole
To determine AC, we would apply sine rule which is expressed as
a/SinA = b/SinB = c/SinC
Therefore,
11/Sin55 = BC/Sin 41 = AC/Sin84
1) 11//Sin 55 = BC/Sin 41
Cross multiplying, it becomes
11Sin41 = BCSin55
11 × 0.6561 = BC × 0.8192
BC = 7.2171/0.8192 = 8.8m
2) 11/Sin55 = BC/Sin 41 = AC/Sin84
1) 11//Sin 55 = AC/Sin 84
Cross multiplying, it becomes
11Sin84 = ACSin55
11 × 0.9945 = AC × 0.8192
AC = 10.9395/0.8192
AC = 13.4m
b) triangles ACD and BCD are right angle triangles. To determine CD, we would apply the sine trigonometric ratio.
Sin # = opposite side/adjacent side
Considering triangle ACD,
Sin 41 = CD/13.4
CD = 13.4Sin41 = 13.35 × 0.6561
CD = 8.8m
3/7 of 8th graders play sports. is 3/5 of the 8th graders that play sports are boys, what fraction of the 8th graders are boys
Answer:
[tex]\dfrac{9}{35}[/tex] is the fraction of 8th graders who are boys.
Step-by-step explanation:
Let total number of 8th graders = [tex]x[/tex]
Given that, [tex]\frac{3}{7}[/tex] of 8th graders play sports
[tex]\Rightarrow[/tex] 8th graders who play sports = [tex]\frac{3}{7} \times x[/tex]
Also, Given that, [tex]\frac{3}{5}[/tex] of 8th graders that play sports are boys
Number of 8th graders that play sports, and are boys = [tex]\frac{3}{5} \times \text{Number of 8th graders who play sports}[/tex]
[tex]\Rightarrow \dfrac{3}{5} \times \dfrac{3}{7} \times x\\\Rightarrow \dfrac{9}{35} \times x[/tex]
Hence, the answer is:
[tex]\dfrac{9}{35}[/tex] is the fraction of 8th graders who are boys.
In 1626, the Dutch bought Manhattan Island, now part of New York City, for $24.75 worth of merchandise. Suppose that, instead, $24.75 had been invested in an account that paid 3.75% interest each year. Find the balance in 2020
Answer:
The balance in 2020 is $47,810,662.65576
Step-by-step explanation:
In order to find the balance in 2020, first we would have to calculate the number of year as follows:
number of years, t=2020-1626
number of years, t=394
Therefore, to calculate the balance in 2020, we would have to use the following formula:
f(t)= 24(1.0375)∧394
f(t)=24*1,992,110.94399
f(t)=$47,810,662.65576
The balance in 2020 is $47,810,662.65576
In this figure,
AB | CD
mZ4 = 30° what is mZ8?
Hey there! :)
Answer:
m∠8 = 30°.
Step-by-step explanation:
Since AB || CD, m∠4 = m∠8 because they are corresponding angles. Therefore:
If m∠4 = 30°, m∠8 = 30°.
Answer:
30 = <8
Step-by-step explanation:
<4 and <8 are corresponding angles and corresponding angles are equal when the lines are parallel
<4 = <8
30 = <8
3 intersecting lines are shown. A line contains points E, D, A, and B. Another line intersects the line at point A and contains points F, A, C. A line connects points D and F.
Given Line segment E D is-congruent-to Line segment D B , which statements about the figure are true? Check all that apply.
Line segment E B is bisected by Line segment D F .
A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
Line segment E B is a segment bisector.
FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Answer:
The one with arrows are the answers
->Line segment E B is bisected by Line segment D F .
->A is the midpoint of Line segment F C .
Line segment F C bisects Line segment D B.
->Line segment E B is a segment bisector.
->FA = One-halfFC.
Line segment D A is congruent to Line segment A B .
Step-by-step explanation:
I did it on edge and got it right
Answer:
1. Line segment E B is bisected by Line segment D F .
2. A is the midpoint of Line segment F C .
4.Line segment E B is a segment bisector.
5. FA = One-halfFC.
Find the length of arc QS
Answer:
QS ≈ 4.71 units
Step-by-step explanation:
The arc QS is calculated as
QS = circumference of circle × fraction of circle
= 2πr × [tex]\frac{90}{360}[/tex] ( r is the radius )
= 2π × 3 × [tex]\frac{1}{4}[/tex]
= 6π × 0.25 ≈ 4.71 units ( to the nearest hundredth )
find the area of the shape below
Answer:
108!
Step-by-step explanation:
The area of a trapezoid is
1/2 x h x (b1 + b2)
plug it in!
24 x 1/2 x 9
12 x 9
108
1 72 miles in 24 hour
Unit rate please!!!!!
Answer:
7.1
Step-by-step explanation: