Which are the foci of the hyperbola represented by 5y2 – 4x2 – 80 = 0?
(–6, 0) and (6, 0)
(0, –6) and (0, 6)
(0, –5) and (0, 5)
(–5, 0) and (5, 0)
The foci of the hyperbola represented by (0, –6) and (0, 6). Then the correct option is B.
What is a hyperbola?The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.
The equation of the parabola is given below.
5y² – 4x² – 80 = 0
Then the equation can be written as
y² / 4 – x² / 5 – 4 = 0
y² / 16 – x² / 20 = 1
Then the value of eccentricity will be
a² = 16 and b² = 20
Then we have
e = √[1 + (b² / a²)]
e = √[1 + (20 / 16)]
e = 1.5
Then the focus of the parabola will be
⇒ (0, ±ae)
⇒ (0, ± 4 x 1.5)
⇒ (0, ±6)
⇒ (0, –6) and (0, 6)
Then the correct option is B.
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Tim has 9 pencils in his book bag. Jaime has 3 more pencils than Tim. Which of the following equations would describe n, the number of pencils that Jaime has in her book bag?
Mr.Baker is making a box using all of a 48-inch strip of oak. the box will be 14 inches wide. how long will the box be?
The length of the box made by Mr. Baker is 10-inch
Mr. Baker has strip of 48- inch long oak, by this strip he is making the rectangle box of width 14-inch.
The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.
As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.
The width of the box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
⇒ length of the box = (48 - 2*14)/2
⇒ length of the box = 10 inches
Thus the Mr. Baker made the box which is 10 inches long.
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What is the solution to the following equation?
3( x - 4 ) - 5 = x - 3
A. x = 8
B. x = 3
C. x = 12
D. x = 7
Answer:
x = 7
Step-by-step explanation:
3(x - 4) - 5 = x - 3
3x - 12 - 5 = x - 3
2x = -3 + 12 + 5
2x = 14
x = 7
I need help, I need to find the volume of this
Answer:
396 Km³to the nearest hundred400 Km³Step-by-step explanation:
volume of a cuboid = Length × Width × Height Cubic units
6 × 11 × 6 =
66 * 6 =
396 Km³
to the nearest hundred
400 Km³
Perform the operation and
simplify.
x² + 10x + 24
3x² + 3x
÷ (x + 6)
244x3+1474x2+63x/
x+6
Megan bought 3 tickets to the ballet for $57.50. How much would it cost for her to buy 15 tickets?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction
Prepare the journal entry to record each of the following four separate insurances of stock a. corporation issue 4000 share of 5$ par value common stock for 35000 cash
The preparation of the journal entry to record the accounting transaction can be seen in the table below.
How do you prepare a journal entry to record an account?Initially, when preparing a journal, you have to read the transaction carefully and comprehend it. Discover which accounts need to be credited and debited before entering a journal entry.
From the given information:
The common stock par value = no of shares × par value of shares
The common stock par value = 4000 shares × $5/ share
The common stock par value = $20000
However, the amount paid in capital excess of the par value for the common stock is:
= $35000 - $20000
= $15000
Therefore, the Journal entry can be computed as follows:
Date Account Title Post Ref Debit ($) Credit ($)
Cash 35,000
Paid-in capital in excess of par
value, common stock 20,000
(To record the insurance of common stock)
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where are mc donalds
Answer:
all over the world
Step-by-step explanation:
use g00g!e maps
Answer:
Not in Russia
Step-by-step explanation:
McDonald's left Russia following the violations of human rights
In 2010, the number of clown costumes sold at a single costume shop was 11. By 2015, that number had grown to 23. Assuming a constant increase in clown costume sales, calculate the average rate of change (the slope) from 2010 to 2015.
The average rate of change = 109%
What is the meaning of Rate of Change ?Rate of Change is the measure of the increase or decrease in the value with respect to the initial value.
It is given that
No of clown sold in 2010 = 11
No of clown sold in 2015 = 23
The average rate of change = ((23-11)/11 ) *100 %
The average rate of change = 109%
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Solve for B -9/3+ B equals -1
Answer:
-2
Step-by-step explanation:
-9/3=-3
-3+b=-1
b=-1+3
b=-2
Use the graph to Write an equation of the line(3,165)(1,55)
Answer:
y=55x
Step-by-step explanation:
(y1-y2)/(x1-x2)=(165-55)/(3-1)=55
55 is the slope
To find y-intercept:
y=55x+b
substitute 1 for x and 55 for y
55=55(1)+b
b=0
So y= 55x
the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x. To write the equation of the line that passes through the points (3, 165) and (1, 55), you can use the point-slope form of a linear equation, which is: y - y₁ = m(x - x₁)
where (x₁, y₁) is one of the points on the line, m is the slope of the line.
First, calculate the slope (m) using the given points (3, 165) and (1, 55):
m = (y₂ - y₁) / (x₂ - x₁) = (55 - 165) / (1 - 3) = (-110) / (-2) = 55
Now that you have the slope (m = 55) and one of the points (let's use (3, 165)), you can plug them into the point-slope form:
y - 165 = 55(x - 3)
Now, you can simplify and rewrite this equation in slope-intercept form (y = mx + b):
y - 165 = 55x - 165
To isolate y, add 165 to both sides:
y = 55x
So, the equation of the line passing through the points (3, 165) and (1, 55) is y = 55x.
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Separable differential equation
y’ln^2y+ysqrtx=0 y(0)=e
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
How to solve separable differential equation
In this question we must separate each variable on each side of the equivalence, integrate each side of the expression and find an explicit expression (y = f(x)) if possible.
[tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex]
[tex](\ln y)^{2}\,dy = -y \cdot \sqrt{x}\, dx[/tex]
[tex]-\frac{(\ln y)^{2}}{y}\, dy = \sqrt{x} \,dx[/tex]
[tex]-\int {\frac{(\ln y)^{2}}{y} } \, dy = \int {\sqrt{x}} \, dx[/tex]
If u = ㏑ y and du = dy/y, then:
[tex]-\int {u^{2}\,du } = \int {x^{\frac{1}{2} }} \, dx[/tex]
[tex]-\frac{1}{3}\cdot u^{3} = \frac{2\cdot x^{\frac{3}{2} }}{3} + C[/tex]
[tex]u^{3} = -2\cdot x^{\frac{3}{2} } + C[/tex]
[tex](\ln y)^{3} = - 2\cdot x^{\frac{3}{2} } + C[/tex]
[tex]C = (\ln e)^{3}[/tex]
[tex]C = 1[/tex]
And finally we get the explicit expression:
[tex]\ln y = \sqrt [3]{-2\cdot x^{\frac{3}{2} }+ 1}[/tex]
[tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex]
By applying the theory of separable ordinary differential equations we conclude that the solution of the differential equation [tex]\frac{dy}{dx} \cdot (\ln y)^{2} + y\cdot \sqrt{x} = 0[/tex] with y(0) = e is [tex]y = e^{\sqrt [3]{-2\cdot x^{\frac{3}{2} }+1}}[/tex].
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Question 4: 11 pts
Elena wants to earn at least $180 a week to help her parents with bills. She determines that
she can charge $15 an hour to babysit and can earn $10 an hour bagging groceries. She can
only work 13 hours per week. Write and graph a system of linear inequalities that shows the
number of hours she can work so she can help her parents. Use x for the number of hours
babysitting and y for the number of hours bagging groceries.
our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph can be seen at the end.
How to get the system of inequalities?Here we have the variables:
x = number of hours babysitting.y = number of hours bagging groceries.We know that she can only work 13 hours per week, then we have:
x + y ≤ 13.
And she wants to earn at least $180 per week, then:
x*$15 + y*$10 ≥ $180.
So our system of inequalities is:
x + y ≤ 13.
x*$15 + y*$10 ≥ $180.
The graph of the system can be seen below. The solution set is defined by the zone where the two shaded regions intersect (where we also should add the restrictions x >0, y > 0).
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.Let S =(5, 10, 15, 20, 25, 30} be the sample space of an experiment and let T = {5,10}, V = {5, 20, 30} and W = {10, 15, 25} be the events of the experimen.
I meed the true answer. tnx!
A set is a mathematical model for a collection of items. The set of W' is {5, 20, 30}.
What is a set?A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.
The complete question is given below.
Q13.
T ∪ V = Data points that are in T or V or both.
T ∪ V = {5, 10, 20, 30}
Q14.
T ∩ W = Data points that are in T and W both.
T ∩ W = {10}
Q15.
W' = Data points that are not in W.
W' = {5, 20, 30}
Hence, the set of W' is {5, 20, 30}.
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Choose the letter of the equation for
the graph.
The graphed trigonometric function is the one in option a.
Which is the equation of the graph?The key parts that we can see on the graph are:
The midline is y = 1.From this we know that the correct option is either a or b.
at x = 0, f(x) = 0.Now we can evaluate options a and b in x = 0 and see which one is equal to zero.
for a:
y = sin(0 - pi/2) + 1 = sin(-pi/2) + 1 = -1 + 1 = 0
for b:
y = cos(0 + pi/2) + 1 = 0 + 1 = 1
Then we can see that option a is the correct option.
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Please solve this for me
Answer:
f(x) = square root of x
g(x) = 4x - 1
Step-by-step explanation:
Which point on the number line represents the product (Negative 4) (negative 2) (negative 1)?
A number line going from negative 10 to positive 10. Point A is negative 8, point B is negative 7, point C is 7, point D is 8.
The point on the number line represents the product (- 4), (- 2), and (- 1) will be the negative 8. Then the correct option is A.
What is multiplication?It is also known as the product. If the object n is given to m times, then we just simply multiply them.
The point on the number line represents the product (- 4), (- 2), and (- 1) will be
Then the product will be
-4 x -2 x -1 = -8
Then the correct option is A.
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find the least common denominator 3/2x+4 and -11/3x+6
Answer: 6x+12
Step-by-step explanation: Both denominators can be multiplied to create 6x + 12.
2x + 4
2x(3) + 4(3)
6x+12
3x + 6
3x(2) + 6(2)
6x+12
I hope this helps!
what figure was rotated
Answer: Rectangles
Step-by-step explanation:
Whenever rectangles are rotated about an axis, a cylinder is formed.
6. 0, 16, 32, 48, 64, ______, ______, ______
what is the next 3 numbers.
Answer:
Step-by-step explanation:
Remark. Since 6 has a decimal after it, I take it that is the question number.
y = 16x is the basic formula. x starts at 0. Then you add 16 to each number to get the next number in the sequence. Or you could do it the way I propose it.
x 0 1 2 3 4 5 6 7
y 0 16 32 48 64 80 96 112
How would you know the answer (important)
Answer:
okay so I can't see the last option on ur sheet but when u graph this equation the point that lies on the curve is (2,-3) so that is the vertex but if I move up this curved line it passes through the Y axis at (0,-1), the Last answer that I can't see it wouldn't happen to be (-1,6) would it
Alejandro kicks a football. The graph below shows the height of the football hh in meters after tt seconds. What is the football’s greatest height?
Answer:
The answer will be 30.625 m
Use the drawing tool(s) to form the correct answer on the provided graph.
Consider the function given below.
Plot this piecewise function on the provided graph.
Drawing Tools
Select
Point
Open Point
Line Segment
Ray
●
O
y = -2;
-10
--5;
Click on a tool to begin drawing.
-8
7;
-6
-8 <
-2 < <5
≤ 9
5 < 1
10
8-
6-
4-
2
< -2
Delete
Undo
8
Reset
10
The attached graph represents the piecewise function.
How to plot the graph?The complete question is in the image
The function is given as:
[tex]f(x) = \left[\begin{array}{cc}3&x \le -3\\2x + 1&-3 < x < 4 \\-2&x \ge 4\end{array}\right[/tex]
Next, we plot the functions by their domain
See attachment for the piecewise function.
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On a trip to Florida, Santina drove 203 miles and Carole drove 189 miles. How many more miles did Santina drive than Carole?
A restaurant uses 80 pounds of potatoes per week. The restaurant owner buys the potatoes in 10-pound bags from a local farmer. How many bags will the owner need to buy this week?
Answer:
1. santina drove 14 more miles than carole
2. the owner will need to buy 8 bags this week
Step-by-step explanation:
1. 203-189= 14
2. if they use 80 pounds a week and can only buy 10 pounds in one bag, they'll need 8 bags to equal 80 pounds since each bag is 10 pounds
1. 14
2. 8
3. 48
4. 318
5. 23
6. 4
7. a) 10 b) 60 c) 8 d) 107
8. $1,532
9. 1
10. $15.50
11. .95
Step-by-step explanation:
Please answer all three questions Pleaseeeeee tysmm <3
Answer: 2 3/4 > 2.68 is correct (only)
Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68
The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.
Sqrt(63) = 7.93, and 7.93 > 8.11 is false.
Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2
Convert the number in scientific notation to standard notation.
[tex]1.8 * 10^6[/tex]
if f(x)=x+10 find f(7)
Answer:
17
Step-by-step explanation:
→ Substitute 7 f(x) into the function
7 + 10
→ Solve
17
Answer:
f(7) = 17
Step-by-step explanation:
To find f(7), substitute x = 7 in the function. Thus, you will receive:
[tex]\displaystyle{f(7)=7+10}\\\\\displaystyle{f(7)=17}[/tex]
Henceforth, the value of f(7) is 17.
Learn More:
https://brainly.com/question/27923727An elephant went 119 km moving 42 km/h how many hours did the journey take?
2 1/6
2 1/2
2 5/6
Answer:
1 HR ---> 42 km
? .----> 119 km
119 * 1/42
2.833
Answer:
[tex]\boxed {2 \frac{5}{6}}[/tex]
Step-by-step explanation:
Formula used :
[tex]\boxed {Time = \frac{Distance}{Speed}}[/tex]
Solving :
Time = 119/42
Time = 17/6
Time = 2 5/6 hours
Which of the following values are in the domain of the function graphed
below? Check all that apply.
Answer:
A. -2B. -1D. 0E. 4Step-by-step explanation:
The domain includes all x values, and here, it is [-2, 4].