Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes.
y = ± square root of x^2 - 5
A. Asymptotes: y = ± x
B. Asymptotes: y = ± 5/3 x
C. Asymptotes: y = ± 5/3 x
D. Asymptotes: y = ± x
Answer:
3rd graph is the correct graph
Step-by-step explanation:
Given is the equation of hyperbola as
[tex]y = ± \sqrt{x^2-5}[/tex]
Square both sides and rearrange to get
[tex]y^2=x^2-5 \\x^2-y^2 =5[/tex]
Vertices are [tex](\sqrt{5} ,0) \\(-\sqrt{5} ,0)[/tex]
Asymptotes would have the same equation as hyperbola except constant term as 0
[tex]x^2-y^2 =0[/tex]
are the asymptotes
Or [tex]y = ± x[/tex] option d is right.
Mr. and Mrs. Lorenzo want to buy a home valued at $213,500. If they have 18% of this amount saved for a down payment, how much have they saved? a. $384.30 b. $3,843.00 c. $38,043.00 d. $38,430.00
Answer:
D
Step-by-step explanation:
The volume v of a rectangular prism is determined using the formula where l is the length w is the width and h is the height of the prism l. Carltren solves for w and writes the equivalent equation w=V/lh. Using this formula what is the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches
Answer:
width of the rectangular prism is 4.5 inches.
Step-by-step explanation:
Carltren solves for w and writes the equivalent equation as [tex]w=\frac{V}{lh}[/tex]
Now, we have to find the width of a rectangular prism that has a volume of 138.24 cubic inches a height of 9.6 inches and a length of 3.2 inches.
Thus, we have
V = 138.24 cubic inches
l = 3.2 inches
h = 9.6 inches.
Substituting these values in the above formula to find w
[tex]w=\frac{138.24}{3.2\cdot9.6}[/tex]
On simplifying, we get
[tex]w=4.5[/tex]
Thus, width of the rectangular prism is 4.5 inches.
HELLO! who can help me?
Name one segment that is tangent to Circle Q
A) Line BC
B) Line DE
C) Line GH
D) Line QE
Answer:
GH
Step-by-step explanation:
Using the transformation T: (x, y) (x + 2, y + 1), find the distance named.
Find the distance CC'
Answer:
The distance CC' is [tex]\sqrt5units[/tex]
Step-by-step explanation:
Given the transformation T: (x, y) (x + 2, y + 1)
we have to find the distance CC'
Let coordinate of C are (a,b).
Now, by using transformation T the coordinates of C' are (a+2,a+1)
By using distance formula,
[tex]CC'=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\= \sqrt{(a+2-a)^2+(b+1-b)^2}\\\\=\sqrt{4+1}=\sqrt5 units[/tex]
Hence, the distance CC' is [tex]\sqrt5units[/tex]
find a value of the constant k such that the limit exists:
lim (x^2+4x+k)/(x+2) as x goes to -2 ...?
What is the standard form equation of the line shown below?
Graph of a line going through negative 1, 1 and 1, 4
−3x + 2y = 5
3x − 2y = −5
y − 4 = three halves(x − 1)
y = three halvesx + five halves
Final answer:
The standard form equation of the line through the points (-1, 1) and (1, 4) is 3x - 2y = -5.
Explanation:
The standard form equation of a line can be represented as Ax + By = C, where A, B, and C are constants. To find the equation of the line through the points (-1, 1) and (1, 4), we can use the point-slope form.
First, find the slope using the formula m = (y2 - y1)/(x2 - x1). In this case, m = (4 - 1)/(1 - (-1)) = 3/2.
Next, choose one of the given points, let's say (-1, 1), and substitute the values into the point-slope formula. y - y1 = m(x - x1). We have y - 1 = (3/2)(x - (-1)).
Simplify the equation by distributing the slope and rearranging the terms. y - 1 = (3/2)x + 3/2.
Finally, convert the equation to standard form by moving all terms to one side and multiplying by a common denominator. 3x - 2y = -5.
Given the problem below, which set of equations translates the information using variables a, b, and c?
Old MacDonald grew some apples, bananas, and coconuts. He decided to package his fruit and price it as follows:
1 apple, 5 bananas, 1 coconut for $14
3 apples, 3 bananas, 3 coconuts for $18
1 apple, 2 bananas, 3 coconuts for $14
A.a + 5b + c = 14
3a + 3b - 3c = 18
a + 2b + 3c = 14
B.a + 5b + c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14
C.2a + 5b + c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14
D.a + 5b + 3c = 14
3a + 3b + 3c = 18
a + 2b + 3c = 14 ...?
The correct set of equations based on the information given about the pricing of apples, bananas, and coconuts by Old MacDonald is: a + 5b + c = 14, 3a + 3b + 3c = 18, and a + 2b + 3c = 14.
Explanation:The student is asking which set of equations corresponds to the problem given, involving prices for apples, bananas, and coconuts. In the context of this problem, variables a, b, and c represent the price of an apple, a banana, and a coconut, respectively. By analyzing the problem's given information, we can deduce the following equations:
a + 5b + c = 143a + 3b + 3c = 18a + 2b + 3c = 14These equations reflect the costs of different combinations of fruit based on the prices provided by Old MacDonald. To solve for the variables a, b, and c, we could use a system of linear equations.
Wich immigrants would not likely face prejudice
A triangle with a base of 4 units and a height of 14 units?
If 8 = x + y and y > 0, then x is ___ 8.
Choose the relationship symbol that makes the statement true.
A. <
B. =
C. >
Answer: The correct option is,
A. <
Step-by-step explanation:
Given,
[tex]8=x+y-----(1)[/tex]
Also,
[tex]y > 0[/tex]
Adding x on both sides ( additive property of inequality )
[tex]x+y>x+0[/tex]
[tex]x+y>x[/tex]
From equation (1),
[tex]8>x[/tex]
Hence, x is less than 8,
We use < sign for less than,
⇒ x is '<' 8
Option A is correct.
If two polygons have the same area, they must have the same number of sides.
True
False
Answer:
Its False c:
Step-by-step explanation:
need help which of the following appear in the diagram
The length of TR is 17 units. What are the lengths of SV and QT?
SV=___ units
QT=___ units
Answer:
SV= 41 units
QT: 21 units
Step-by-step explanation:
hope it helps:)
Given TR = 17 units, TRS = 9x - 4, VRS = 3x + 2, and QRV = 4x + 1, with x ≈ 1.583. SV ≈ 6.749 units and QT ≈ 7.332 units.
To find the lengths of SV and QT, we'll first set up equations based on the given relationships between the lengths of the segments.
Given:
- Length of TR = 17 units
- Length of TRS = 9x - 4
- Length of VRS = 3x + 2
- Length of QRV = 4x + 1
We need to find the lengths of SV and QT.
1. Length of TRS + Length of VRS = Length of TR (by the segment addition postulate)
9x - 4 + 3x + 2 = 17
12x - 2 = 17
12x = 17 + 2
12x = 19
x = 19 / 12
x ≈ 1.583
Now that we have found the value of x, we can find the lengths of SV and QT.
2. Length of SV = Length of VRS = 3x + 2
Length of SV = 3(1.583) + 2
≈ 4.749 + 2
≈ 6.749 units
3. Length of QT = Length of QRV = 4x + 1
Length of QT = 4(1.583) + 1
≈ 6.332 + 1
≈ 7.332 units
So, the lengths are:
- SV ≈ 6.749 units
- QT ≈ 7.332 units
How does 0.42 divide by 0.35 equal 1.2?
what is the sum of this infinite geometric series? 2+ 2/5+2/25+2/125+..... ...?
Final answer:
The sum of the infinite geometric series 2 + 2/5 + 2/25 + 2/125 + ... is 2.5, determined by using the formula for the sum of a convergent geometric series, which in this case is S = 2 / (1 - 1/5).
Explanation:
The question you've asked relates to the sum of an infinite geometric series. The series given is 2 + 2/5 + 2/25 + 2/125 + ..., which is a series where each term after the first is found by multiplying the previous term by 1/5. To find the sum of this infinite geometric series, we can use the formula for the sum of a convergent geometric series, which is S = a / (1 - r), where 'S' is the sum of the series, 'a' is the first term, and 'r' is the common ratio (the factor we multiply by to get each term in the series).
In this case, the first term 'a' is 2, and the common ratio 'r' is 1/5. So our formula becomes S = 2 / (1 - 1/5), which simplifies to S = 2 / (4/5) or S = 2 * (5/4), which gives us S = 2.5. Therefore, the sum of the infinite geometric series is 2.5.
a honda element with a dealer invoice price is $19,700 was retail price at $23,000. How much is the approximate percent markup based on selling price?
Reggie has 195 trading cards. Each week, he purchases 16 more trading cards.
How many trading cards will he have after 12 weeks?
Fill in the blank. If two chords of a given circle are congruent then they must ___________.
A. be diameters
B. be parallel
C. be perpendicular
D. be equidistant from the center of the circle
How many radians is 270°??
Convert the follow statement into a conditional statement. All squares are rectangles
If an object is a square, then it is a rectangle
If an object is a rectangle, then it is a square.
An object is a square so it is a rectangle.
An object is a rectangle so it is a square.
120% of what number is 36?
Answer:
The answer is 30.
Step-by-step explanation:
A person on a moving sidewalk travels 21 feet in 7 seconds.the moving sidewalk has a length of 180 feet how long wil it take to move from one end of the sidewalk to the other
Which ordered pair is a solution of the equation 2x − y = 9 (-4,1)
(-2,5)
(5,1)
(6,-3)
solve by substitution
x=-3y-2
-4x-5y=8
What is the decimal representation of 2/10 ?
a.20b. 2.0c. .2d. 2.10
how do you do prime factorization on a negative number?
ex:
-48, 108
The weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs. What is the range of actual weights of the object?
Answer:
[tex]144.9\leq x\leq 145.5[/tex]
Step-by-step explanation:
Let x represent actual weight of object.
We have been that the weight of an object on a particular scale is 145.2 lbs. The measured weight may vary from the actual weight by at most 0.3 lbs.
[tex]|\text{Actual}-\text{Ideal}|\leq \text{Tolerance}[/tex].
Upon substituting our given values, we will get:
[tex]|x-145.2|\leq 0.3[/tex]
Applying absolute value rule [tex]|u|\leq a=-a\leq u\leq a[/tex], we will get:
[tex]-0.3\leq x-145.2\leq 0.3[/tex]
Add 145.2 on each side:
[tex]-0.3+145.2\leq x-145.2+145.2\leq 0.3+145.2[/tex]
[tex]144.9\leq x\leq 145.5[/tex]
Therefore, our required range will be [tex]144.9\leq x\leq 145.5[/tex].
If f(n) = n^ 2 - n, then f(-4) is _____.
-20
20
12
-12
f(-4) = 20 when evaluated in the given function f(n) = n^2 - n. This result was obtained through substitution in the function followed by simplification.
Explanation:In this problem, you are given a function f(n) = n^2 - n. To find the value of f(-4), you simply need to substitute -4 in place of n in the function and compute.
So,
f(-4) = (-4)^2 - (-4)
= 16 - (-4)
= 16 + 4 = 20
Learn more about Function Evaluation here:https://brainly.com/question/35863537
#SPJ1
Sheila is ordering pizzas for a party. each plain pizza costs $9.00, and each topping costs $1.50. the delivery charge is $3.00. write a function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings. how much will 5 pizzas cost?
Answer: [tex]c=12x+3[/tex], where c is the total cost of x pizzas.
The cost of 5 pizzas = $63
Step-by-step explanation:
Given : Cost of each pizza = $9.00
Cost of each topping = $1.50
⇒ Cost of 2 toppings = 2 x $1.50 = $3.00
Then, the cost of each pizza having 2 toppings = $9.00+ $3.00= $12.00
Let x be the number of pizzas .
Then , the cost of x pizzas = 12x
Since , Delivery charge = $3.00
Then, the total cost of ordering x pizzas( in dollars) = Cost of x pizzas+ Delivery charge = 12x+3
Function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings : [tex]c=12x+3[/tex] , where c is the total cost.
Put x= 5
[tex]c=12(5)+3=60+3=63[/tex]
Hence, the cost of 5 pizzas = $63