how many foci does the graph of a hyperbola have
Answers
Answer:
A graph of a hyperbola have 2 foci.
Step-by-step explanation:
Foci of a Hyperbola-
The foci of a hyperbola are two fixed points located inside each curve of a hyperbola.
The foci is a plural of the word focus i.e. two focus of a hyperbola are combinely called foci.
Hence, a graph of a hyperbola have 2 foci.
Related Questions
What polynomial identity should be used to prove that 20 = 36 − 16
Answers
Diffrence of squares is the correct answer just score pract q
Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree
Answers
the equation for this problem would be...
6/13=x/51
you then multpli the denominators on both sides and get...
6*51=13x
you then solve...
306=13x
and then you divide 13 on both sides...
x=23.54ft
the tree is 23.54ft tall
(leave a thanks and a rating if i helped) c:
The height of the tree maintaining the given ratio is 23.54 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
Don height = 6 feet
His shadow = 13 feet
The ratio of height to shadow = 6/13
Tree height = x (let's say)
Tree shadow = 51 feet
Ratio = x/51
Both ratios must be the same, therefore,
x/51=6/13
x=23.54 feet
Hence "The height of the tree maintaining the given ratio is 23.54 feet".
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PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.
Answers
so m<Q = m<P =127
answer
127
Answer:
[tex]m<P=127\°[/tex]
Step-by-step explanation:
we know that
If the trapezoid PQRS is an isosceles trapezoid
then
[tex]PS=QR[/tex] ----> congruent sides
[tex]m<P=m<Q[/tex] -----> congruent angles
In this problem we have
[tex]m<Q=127\°[/tex]
therefore
[tex]m<P=127\°[/tex]
Mr. James has cylindrical beakers that measure 4 inches in diameter and are 9 inches high. What is the volume contained within the beakers? Use 3.14 for pi. Round your answer to the nearest hundredth. 56.52 cubic inches 100.34 cubic inches 113.04 cubic inches 226.08 cubic inches
Answers
The radius is half of the diameter. Since Mr. James' beakers have a diameter of 4, their radius would be 2. 2 squared is 4.
Their height is 9 inches.
V = 3.14•4•9
V = 3.14•36
V = 113.04
The answer is C, or 113.04 cubic inches.
The answer is C, or 113.04 cubic inches.
Sue took a taxi from her home to her friends house. It cost $3.58 per mile and she gave the driver a $5 tip. If she paid $87.34, how many miles does she live from her friend?
Answers
87.34-5 = 82.34
82.34/3.58 = 23
she lives 23 miles away
Whats the perimeter of a rectangle with length 12 m and width 5m
Answers
P = 2 (17)
P = 34 m
hope it helps
Determine whether the sequence shown are arithmetic or geometric 1,8,15,22,29
Answers
8 <--- 1 + 7
15 <--- 8 + 7
22 <--- 15 + 7
29 <--- 22 + 7
is simply adding "7" to get the next value, so is an arithmetic sequence, whose common difference is 7.
if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches
Answers
The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height
Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:
Volume = 6194 in² × 6 in
Volume = 37,164 cubic inches
So, the volume of the metal tool chest is 37,164 cubic inches.
As for the lengths provided:
c = 6 inches (height)
m = 19 inches (unknown side length of the pentagon)
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a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?
Answers
P(first one being blue) = 2/10 which reduces to 1/5
not replaced
P(second one is blue) = 1/9...because u already pick a blue, meaning there is only 1 left, and there is one less marble, so there is a total of 9 marbles.
P(both events happening) = 1/5 * 1/9 = 1/45 <==
What is 5.928301 to 2 decimal places?
Answers
Final answer:
To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.
Explanation:
When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.
Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.
The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept
Answers
y = a(x - 1)^2 - 16 where a is a cosntant
at y intercept we have
-15 = a^2 - 16
a^2 = 1
so equation of the parabola is y = (x-1)^2 - 16
the equation of symmetry is x = 1 and both roots are same distance either side of the point (1,0) so the other x-intercept is 1 - 4 = (-3,0)
The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.
Answers
(l-10)*(w-20)=a-162
Substituting l for 8w and a for l*w and then 8w*w, we have
(8w-10)(w-20)=8w^2-162=8w^2-160w-10w+200=8w^2-170w+200
8w^2-170w+200=8w^2-162 , so we subtract 8w^2 from both sides as well as subtract 200 to both to get -170w=-362, so w=362/170 and
l= 8*362/170=2896/170
Find 93 • 87 using mental math.
Answers
So 3 x 7= 21
9 X 7 +63, carry the 2 = 651
Then 8 x 93
Remember that first is a zero.
8 X 3= 24
8 X 9= 72, carry the 2= 74
So that is 7440
Now
0651
+7440
8091
And that's the answer
To estimate 93 × 87 using mental math, round 87 to 90, multiply by 93 to get 8370, and subtract 3 × 93 (279) for an estimate of 8091.
To find 93 × 87 using mental math, we can employ a strategy that simplifies the multiplication process. One way is to round one of the numbers to the nearest multiple of ten, perform the multiplication, and then adjust the result accordingly. Here, we can round 87 up to 90 and multiply 93 by 90. This is easier because 90 is a multiple of 10.
93 × 90 = (93 × 9) × 10 = 837 × 10 = 8370
Since we rounded 87 to 90, we overestimated by 3 per unit of 93. Hence, we need to subtract 3 times 93 from 8370.
3 × 93 = 279
Thus, 8370 - 279 = 8091.
the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle
Answers
If you don't know, the Pythagorean Theorem states that for any right triangle the sum of the squares of both of the legs is equals to the hypotenuse.
[tex]a^2 + b^2 = c^2[/tex]
Where the variables a and b are the legs and c is the hypotenuse.
The variables a and b are interchangeable but not c.
Plug in the values that we know.
[tex]5^2 + b^2 = 8^2[/tex]
[tex]25 + b^2 = 64[/tex]
[tex]b^2 = 39[/tex]
[tex]b = \sqrt{39}[/tex]
So, the other leg is equal to the square root of 39 units.
The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units
What is Pythagoras theorem?The square of the hypotenuse is equal to the sum of the square of the other two sides.
Mathematically;
l^2 = a^2 + b^2
Given
l = 8 units
a = 5 units
Substitute
8^2 = 5^2 + b^2
64 - 25 = b^2
b^2 = 6.2units
Hence the length in units of the other leg of the triangle is 6.2 units
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Select the additive inverse of 51
Answers
What can we add to 51 to make it equal to 0. Set up an equation.
Let x = the additive inverse of 51
x + 51 = 0
Solve for x.
x + 51 = 0
x = -51 <-- Subtract 51 from both sides
So, -51 is the additive inverse of 51.
Which of the following types of functions cannot have "all real numbers" as either its domain or its range? Exponential function Quadratic function Linear function Inverse Variation function
Answers
For the exponential function:The domain of exponential functions is all real numbers. And the range are all real numbers greater than zero.
For the quadratic function: The domain is all real numbers, and the range is all real numbers f(x) such that f(x) ≤ 4.
For the linear function: Domain and range all real numbers.
For the inverse variation function (hyperbola): two asymptotes are excluded from the domain of all real numbers and one excluded from the range.
So, according to these, the exponential function, the quadratic function and the inverse variation function cannot have "all real numbers" as either its domain or its range. Only the linear has.
The growth of a new strain of bacteria is represented by 7=79.31(1.48)^x,where x represents the number of days and y represents the number of bacteria. which is the best prediction for the number of bacteria on day 6
A.833
B.117
C.704
D.647
Answers
Y (6)=79.31×(1.48)^(6)
Y (6)=833
Answer:
A. 833
Step-by-step explanation:
Given:
The growth of a new strain of bacteria is represented by [tex]y = 79.31(1.48)^x[/tex], where "x" represents the number of days and "y" represents the number of bacteria.
We need to find the number of bacteria on day 6.
So, here x = 6, we need to plug in x = 6 in the given function and find the answer.
[tex]y = 79.31(1.48)^6[tex]
Simplify the above expression, we get
y = 833.49
The bacteria cannot be in decimal form, let's round off the answer to nearest whole number.
y = 833
Therefore, answer is A. 833
(06.06) Which of the following demonstrates the Commutative Property of Multiplication? 3(4a − 2) = 12a − 6 3(4a − 2) = (4a − 2) ⋅ 3 12a − 6 = (4a − 2) ⋅ 3 (3 ⋅ 4a) − 2 = 3(4a − 2)
Answers
3(4a - 2) = (4a - 2) * 3 <==
so its the second option:-
3(4a - 2) = (4a - 2).3
What is
5.63×
10
−6
in decimal form?
a. 0.00000563
b. 0.000000563
c.5,630,000
d. 56,300,000
Answers
The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.
Answers
A = 75
L = W + 10
75 = W(W + 10)
75 = W^2 + 10W
W^2 + 10W - 75 = 0
(W + 15)(W - 5) = 0
W + 15 = 0
W = -15...not this one because it is negative
W - 5 = 0
W = 5 <=== width is 5 ft
L = W + 10
L = 5 + 10
L = 15 <=== length is 15 ft
First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.
Explanation:This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:
x*(x + 10) = 75
You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.
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Please help! Given b = 4 and h = 1, what is the equation of the graph if the parent function is y = sqrt x?
A. y = sqrt (4x - 4)
B. y = sqrt (4x + 4)
C. y = - sqrt (4x - 4)
D. y = - sqrt (4x + 4)
Answers
To solve this problem, we make use of the formula:
y = a sqrt (b (x – h)) + k ---> 1
Since we are given the parent function:
y = sqrt (x) ---> 2
Then this automatically means that:
a = 1 and k = 0
So going back to equation 1 at a = 1 and k = 0:
y = 1 sqrt (b (x – h))
Since it is given that, b = 4 and h = 1, therefore:
y = sqrt (4 (x – 1))
y = sqrt (4 x – 4)
Answer:
A. y = sqrt (4 x – 4)
This prism has a volume of 112 cm3. What would the volume of the prism be if each dimension was doubled?
(Scale factor is 2)
224 cm3
896 cm3
448 cm3
336 cm3
Answers
If each dimension was doubled, the volume of the prism would be: B. 896 cm³.
What is a scale factor?In Geometry and Mathematics, a scale factor simply refers to the ratio of two corresponding side lengths in two similar geometric figures such as pentagons, which can be used to either horizontally or vertically enlarge (increase) or reduce (decrease or compress) a function that represents their size.
In Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:
Scale factor of volume = (Scale factor of dimensions)³
Scale factor of volume = (2)³
Scale factor of volume = 8
Therefore, the new volume is given by;
New volume of prism = 112 × 8
New volume of prism = 896 cm³.
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A basketball is thrown with an initial upward velocity of 25 feet per second from a height of 8 feet above the ground. The equation h=−16 t 2 +25t+8 h=−16t2+25t+8 models the height in feet t seconds after it is thrown. After the ball passes its maximum height, it comes down and then goes into the hoop at a height of 10 feet above the ground. About how long after it was thrown does it go into the hoop?
Answers
-16t^2 + 25t - 2 = 0
t = 1.48 seconds
find the value of x if f(x) equals 7 f(x) equals 4x minus 1
Answers
Neptune has 8 known moons. This is 2 more than 1/3 of the number of known moons on Saturn. How many moons is Saturn known to have?
Answers
Through setting up and solving the equation 1/3 * x + 2 = 8, where x represents the number of Saturn's moons, it was determined that Saturn is known to have 18 moons.
Explanation:The student's question pertains to a comparison of the moons of Neptune and Saturn, using mathematical operations to deduce the number of known moons of Saturn. First, we're told that Neptune has 8 known moons, which is said to be 2 more than 1/3 of the number of known moons on Saturn. We are seeking to solve for the number of moons that Saturn has.
To find out, we set up an equation where 1/3 of the number of moons of Saturn plus 2 equals the number of Neptune's moons: 1/3 * x + 2 = 8, where x represents the number of Saturn's moons. Solving for x, we subtract 2 from both sides to get 1/3 * x = 6. We then multiply both sides by 3 to isolate x and find that x = 18.
Therefore, Saturn is known to have 18 moons according to the given information.
Which of the following sets is not finite?
Answers
The point (-2, 6) is on the line given by which of the equations below?
A.
y = 4x
B.
y = 2x
C.
y = 3x
D.
y = -3x
Answers
for (-2, 6) = (x, y) which also means that x = -2 and y = 6
A/ y = 4x => 6 = 4.(-2) <=> 6 = (-8) Absurd
B/ y = 2.x => 6 = 2.(-2) <=> 6 = (-4) Absurd
C/ y = 3x => 6 = 3.(-2) <=> 6 = (-6) Absurd
D/ y = -3x => 6 = (-3).(-2) <=> 6 = 6 Right Answer
Use the horizontal line test to identify the relation whose inverse is not a function.
Answers
The graph 3 whose inverse is not a function.
What is an inverse of a function?The inverse function agrees with the resultant, operates and reaches back to the original function. If you consider functions, f and g are inverse, f(g(x)) = g(f(x)) = x.
Horizontal Line Test :-
Let f be a function. If any horizontal line intersects the graph of f more than once, then f does not have an inverse. If no horizontal line intersects the graph of f more than once, then f does have an inverse.
So, according to the definition, the only graph which follows the rule of horizontal lines test is the graph 3.
Hence, the graph 3 whose inverse is not a function.
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By using the horizontal line test, a relation whose inverse is not a function is: D. relation D.
In Mathematics and Euclidean Geometry, the horizontal line test states that if the graph of a function (f) is intersected by any horizontal line more than once, then, the function (f) does not have an inverse.
Conversely, if the graph of a function (f) isn't intersected by any horizontal line more than once, then, the function (f) has an inverse.
By critically observing the graph of the given relation shown in the image attached below, we can logically deduce that it does not have an inverse because it didn't pass the horizontal line test.
Geometry Question Please Help!!!!
Answers
We have the vertex is (-3,-2) so we have [tex]h=-3[/tex] and [tex]k=-2[/tex]
Substituting -3 and -2 into the [tex]f(x)[/tex]
[tex]f(x)=a(x--3)^{2}+(-2) [/tex]
[tex]f(x)=a(x+3)^{2}-2 [/tex]
Hence, the correct answer is option D
Find the value of x for which abcd must be a parallelogram 5x-1 2x+5
Answers
5 x - 1 = 2 x + 5
5 x - 1 + 1 = 2 x + 5 + 1
5 x - 2 x = 2 x - 2 x + 6
3 x = 6
x = 6 : 3
Answer:
x = 2