If the asymptotes of a hyperbola are the x- and y-axes, it is known as a rectangular hyperbola?
Final answer:
A rectangular hyperbola is defined by the angle between its asymptotes being 90°, with its Equation represented as x'y' = a².
Explanation:
Rectangular Hyperbola: When the angle between the asymptotes of a hyperbola is 90°, it is called a rectangular hyperbola. In this case, b = a and the eccentricity is √2. The Equation to a rectangular hyperbola is x'y' = a².
find the product of 80x^4/y^3 ×xy/5x^2
A rectangular prism has a length of 212 meters, a width of 4 meters, and a height of 214 meters.
What is the volume of the prism?
Enter your answer in the box as a simplified mixed number or a decimal.
m³
The volume of the rectangular prism is 22 1/2 m³
What is the volume of the rectangular prism?A rectangular prism is a three-dimensional object. It is made up of six faces, twelve sides and six vertices.
Volume = length x width x height
2 1/2 x 4 x 2 1/4
5/2 x 4 x 9/4 = 720 / 32 = 22 1/2 m³
Here is the complete question: A rectangular prism has a length of 21/2 meters, a width of 4 meters, and a height of 21/4 meters.
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what is the average of -10.25 and 125.75
Choose the correct simplification of the expression (−2x + 4y)(3x − 7y). −6x2 − 2xy − 28y2 6x2 + 26xy − 28y2 −6x2 + 26xy + 28y2 −6x2 + 26xy − 28y2
Answer:
[tex] - 6 {x}^{2} + 26xy - 28 {y}^{2} [/tex]
Step-by-step explanation:
The given expresion is:
(−2x + 4y)(3x − 7y)
We expand using the distributive property: (a+b)(c+d)=a(c+d)+b(c+d)
We apply this property to get:
[tex]( - 2x + 4y)(3x - 7y) = - 2x \times(3x - 7y) + 4y(3x - 7y)[/tex]
We expand further to obtain:
[tex] - 6 {x}^{2} + 14xy + 12xy - 28 {y}^{2} [/tex]
[tex] - 6 {x}^{2} + 26xy - 28{y}^{2} [/tex]
Answer:
[tex](-2x+ 4y)(3x - 7y)=-6x^2+26xy-28y^2[/tex]
Step-by-step explanation:
We multiply each term in the parentheses, by those of the other parenthesis:
[tex](-2x+ 4y)(3x - 7y)=(-2x)(3x)+(-2x)(-7y)+(4y)(3x)+(4y)(-7y)\\=-6x^2+14xy+12xy-28y^2[/tex]
Now, we simplify.
We have two terms that contain xy:
[tex]=-6x^2+26xy-28y^2[/tex]
Wich will be the correct simplification of the expressionn [tex](-2x+ 4y)(3x - 7y)[/tex]
Write the time another way 23 minutes after 4
Sierra sawed 10 1/2 inches off the end of a board. the remaining board was 37 1/2 inches long. how long was the boared that sierra started with? please explain answer
Which number completes the inequality? -5.13< ?< -4.8
Find the area of the circle with the given radius or diameter. Use pi = 3.14. r = 2
Complete the square to write y = 3x2 + 12x + 7 in vertex form, y = a(x - h)2 + k. y = 3(x2 + 4x) + 7 y = 3(x2 + 4x +4) + 7 -
Answer:
A. 12
B. 3
C. -2
D. -5
Step-by-step explanation:
Verified on edge, just finished it
The Vertex form is y= 3(x+ 2)² -5 and a= 3, h= -2, k= -12.
What is Vertex Form?The vertex form of a quadratic function is f(x) = a(x – h)² + k, where a, h, and k are constants.
Vertex form, one of the usual forms for quadratic functions, emphasises the coordinates of the vertex of the function's graph.
Given:
y = 3x² + 12x + 7
Now writing the equation in vertex form
y = 3x² + 12x + 7
y = 3x(x + 4) + 7
Adding and subtracting 12 on both side
y= 3(x²+ 4x) + 7 -12 + 12
y= 3(x² + 4x + 4) + 7- 12
y= 3(x+ 2)² -5
Now, Comparing it with y = a(x - h)² + k we get
a= 3
h= -2
and, k= -12
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a rectangular park is 4 miles long and 2 miles wide. how long is pedestrian route that runs diagonally across the park
If an object is dropped from a height of 55 feet, the function d=-16t^2+55 gives the height of the object after t seconds. Graph this function. Approximately how long does it take the object to reach the ground (d=0)
Simplify: (–5) • (7) – (6) • (–2)
The correct answer is -23.
To simplify the given expression, we need to perform the indicated operations and follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Given expression: (–5) • (7) – (6) • (–2)
Step 1: Perform the multiplications inside the parentheses.
(–5) • (7) = –35
(6) • (–2) = –12
Step 2: Perform the subtraction operation.
–35 – (–12) = –35 + 12 = –23
Therefore, the simplified expression is:
[tex](-5) \cdot (7) - (6) \cdot (-2) = -35 + (-12) = -23[/tex]
In a shipment of 400 parts, 14 are found to be defective. How many defective parts should be expected in a shipment of 1,000? Really need this I'm giving you maximum points
37.5 x 10(-6) in scientific notation?
convert 39/5 to a mixed number written in lowest terms
In the standard (x,y) coordinate plane below, the points ( 0,2), (8,2), (3,6), and (11,6) are the vertices of a parallelogram. What is the area, in square units, of the parallelogram
The area of the parallelogram is 32 square units.
What is a parallelogram?Parallelogram is a quadrilateral that has two pairs of parallel sides.
In a parallelogram, opposite sides and angles are equal.
The adjacent angles add up to 180 degrees.
We have,
First, we can plot the points on the coordinate plane to get a better visual understanding of the parallelogram:
| (3,6) (11,6)
| *-----------*
| / /
| / /
| / /
| / /
| *-----------*
| (0,2) (8,2)
|
Now,
We can see that the base of the parallelogram is the line segment connecting (0,2) and (8,2), which has a length of 8 units.
To find the height of the parallelogram, we can observe that the line segment connecting (0,2) and (3,6) is perpendicular to the base, and has a length of 4 units.
Therefore,
The height of the parallelogram is 4 units.
Now,
The area of a parallelogram is given by the formula:
Area = base x height
Plugging in the values we found, we get:
Area = 8 x 4
Area = 32
Therefore,
The area of the parallelogram is 32 square units.
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Andy has 9 math books and 6 reading books if you wants to distribute them evenly among some bookshelves so that each has the same combination of books with none left over what is the greatest number of bookshelves Andy can use
10x - 4 = 2 ( ? ) is it a) 5x - 4 b) 5x - 2 c) 10x - 4 d ) 10x - 8
Jessica grows two types of tomato plants in her garden. For each type, she records the heights, in inches, of five plants.
What can she infer about the heights of the plants?
Type 1: {42, 56, 44, 60, 48}
Type 2: {62, 59, 68, 55, 66}
Type 1 plants and Type 2 plants do not have similar height distributions.
Type 1 and Type 2 plants have similar height distributions.
Type 1 plants and Type 2 plants have identical height distributions.
Type 1 and Type 2 plants have somewhat similar height distributions.
The inference that can be made is that D. Type 1 and Type 2 plants have somewhat similar height distributions.
What is Inference?This refers to a statement or assertion that is made about something, which may or may not be true.
Hence, we can see that based on the height of the plants, there is a similarity in the heights of Type 1 and Type 2 plants, hence it can be inferred that Type 1 and Type 2 plants have somewhat similar height distributions.
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The product of 7 and a number, increased by 3, is equal to twice the number, subtracted from 39.
Find the number
During each minute of a comedy show, Carlin laughs 555 times. Carlin watches 333 comedy shows every day, and each show is 404040 minutes long. How many times does Carlin laugh every day due to the comedy shows?
Answer: 600
Step-by-step explanation:
Given : The number of times Carlin laughs in each minute = 5
The number of comedy show Carlin watched = 3
The length of each comedy show = 40 minutes
Total minute she watched Comedy show will be :-
[tex]40\times3=120\text{ minutes}[/tex]
Then , the total number of times Carlin will be :-
[tex]120\times5=600[/tex]
Hence,Carlin laughs 600 times every day due to the comedy shows.
PLEASE HELP!!!!!
Give the piecewise function shown below select all of the statements that are true
A. f(4)=7
B. f(1)=0
C. f(-1)=2
D. f(-2)=0
GIVEN circle P with arc AE = 53 , arc BA =68 and arc CB =72
match the following angles with their corresponding measurements
All the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
The theory that is mainly used to find out the angles of the above diagram is that;
the sum of the internal angles of a triangle is 180°.
when the angles of arcs have been given(e.g: BA) that means from the centre of the circle to point B has been rotated by 53° to point A.
Next from point A to point E, the angle rotated is 68°
the addition of these 2 angles give the angle rotated from point B to point E,
that is angle no.7
m∠7 = 53° + 68° = 121°
consider ΔPBE,
PB and PE are radii therefore isosceles triangles
In isosceles triangles the angles opposite equal sides are equal
if the angle is x°, then there are 2 angles with values x each
x° +x° + 121° = 180°
2x° = 59°
x = 29.5°
therefore m∠3 = 29.5°
next connect PC and consider ΔPCB,
according to given information, C∠PB = 72°
as PC and PB are radii ΔPCB is an isosceles triangle, then the angles (y°) opposite radii are equal
2y° + 72° = 180°
y° = 54°
then consider ΔPCD, again an isosceles triangle
as a straight line has an angle of 180°
B∠PC + C∠PD = 180°
72° + C∠PD = 180°
C∠PD = 108°
as ΔPCD is an isosceles triangle, P∠CD and P∠DC are equal (take this angle as z°)
2z° + 108° = 180°
z° = 36°
B∠CD is a sum of y and z angles
therefore m∠8 = y + z
m∠8 = 54° + 36° = 90°
there is also a tangent line that cuts point D of the circle. this tangent cuts D and is perpendicular to the PD radius
this indicates that lines PD and HD are perpendicular to each other
hence, forms a right angle where it cuts each other.
therefore H∠DP / m∠4 = 90°
C∠DH /m∠5 is the difference between P∠DH and P∠DC
m∠5 = 90° - 36° = 54°
m∠1 and m∠6 together make a straight line therefore the sum of these 2 angles is 180°
by looking at the options of answers given the 2 angle values given that add up to 180° are 116.5° and 63.5°.
m∠1 is the acute angle therefore m∠1 = 63.5°
m∠6 is the obtuse angle therefore m∠6 = 116.5°
consider ΔDFB
D∠FB is 180° - m∠1 = 180° - °63.5 = 116.5°
D∠FB + F∠DB(w°) + D∠BF (m∠3)= 180°
116.5 + w° + 29.5° = 180°
w° = 34°
m∠2 = m∠4 + w°
= 90° + 34°
= 124°
finally all the answers are
m∠1= 63.5°
m∠2 = 124°
m∠3 = 29.5°
m∠4 = 90°
m∠5 = 54°
m∠6 = 116.5°
m∠7 = 121°
m∠8 = 90°
Sean divides 8 cups of granola into 1/4-cup servings. How many servings of granola does he have?
you deposit 2800 in a savings account that earns 1% annual intrest compounded semiannually.Write a function that represents the balance after t years
The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex]
What is Compound Interest?Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Here, P = $2800
I = 1 % compounded semiannually = 0.5 % = 0.005
Time = t years
n = 2t semi-years
We know that,
[tex]A = P(1+i)^n[/tex]
[tex]A = 2800 ( 1 + 0.005 )^{2t}[/tex]
[tex]A = 2800 X 1.005^{2t}[/tex]
Thus, The function which represent the given situation for Amount by compound interest is [tex]A = 2800 X 1.005^{2t}[/tex].
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Two runners are to race one lap on a circular track, the radius to the inside circle is 50m.the radius on the outside lane is 51m. How much of a head start should the runner on the outside get?
Tmuch of a head start should the runner on the outside get would be = 2πm.
How to calculate the length of head start for the runner outside?
To calculate the length of head start for the runner outside against the inside runner, the following steps should be taken as follows:
The formula for circumferential of circle = 2πr
Circumference of inner circle;
= 2× π×50
= 100π
Circumference of outer circle;
= 2×π×51
= 102π
The length of head start for the runner outside = 102π-100π = 2πm
An arrangement of marbles has 12 marbles in the first row and 10 rows in all. In each successive row one marble is added.
What is the explicit rule for this situation, and how many marbles will be in the 10th row?
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of marbles in the 10th row
An = 11 + 11n, An = 12 + n, An = 11 + n, An = 12 + 10n, 19, 20, 21,
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
The explicit rule for this situation is An = 12 + n, where "n" represents the row number.
To find the number of marbles in the 10th row, you can plug in n = 10 into the explicit rule:
A10 = 12 + 10
A10 = 22
So, there will be 22 marbles in the 10th row.
Matching the answers:
Explicit rule: An = 12 + n
Number of marbles in the 10th row: 22
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what do you call an object with one fixed endpoint that extends to infinity
56. exercise. for natural numbers a and b, give a suitable definition for "least common multiple of a and b", denoted lcm(a, b). construct and compute some examples.