Arrange the hyperbolas in increasing order of the horizontal widths of their asymptote rectangles.
The increasing order of the horizontal widths of their asymptote rectangles is dependent on the values gotten from y = ± x.
What is a Hyperbola?
This is defined as a two-branched open curve formed by the intersection of a plane perpendicular to the bases of a double cone.
The rectangular hyperbola has two asymptotes which are defined as y = ± x in this scenario.
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A basketball team has 15 members, and 18 of them are sixth graders what percentage of the team is in sixth grade?
Answer:
120% are sixth graders
But, If you meant to say 18 basketball players and 15 6th graders, the percentage would be around 83.3%
Find the remainder of 2338when divided by 55. b) What is the inverse of 23 modulo 55 i.e. which number a has the property that 23*a has the remainder 1 when divided by 55?
a) 2338 ≡ 42 • 55 + 28 ≡ 28 (mod 55)
b) We want to find a such that
23a ≡ 1 (mod 55)
Use the Euclidean algorithm:
55 = 2 • 23 + 9
23 = 2 • 9 + 4
9 = 2 • 4 + 1
⇒ 1 = 9 - 2 • 4
⇒ 1 = 9 - 2 • (23 - 2 • 9) = 5 • 9 - 2 • 23
⇒ 1 = 5 • (55 - 2 • 23) - 2 • 23 = 5 • 55 - 12 • 23
Solve for a :
5 • 55 - 12 • 23 ≡ 1 (mod 55)
⇒ -12 • 23 ≡ 1 (mod 55)
⇒ a ≡ -12 ≡ 43 (mod 55)
Please help me answer these 2 questions with a FULL explanation so I know how to do the rest myself. Giving brainliest.
Answer to 1:
[tex]\frac{x^3}{2y^25}[/tex]
First thing you want to do is combine like terms on the bottom. Since it's multiplication, all you have to do is add the exponents. So for x you'd get x raised to the -9 power and for y you'd get 2y raised to the power of 7
Second thing is the numerator of the fraction. Since this is raising what is inside the paranthesis to a power, you must multiply this power by the powers of x and y, respectively. You should get x raised to the power of -6 and y raised to the power of -18
Here's where it gets complicated. to rationalize the problem, you must add parts from the numerator and denominator or vice versa. You cannot have any negative exponents anywhere in the fraction. So that means for x you have to add 9 to the x on the top to cancel out the -6 and rationalize the remaining x's. You should end up with x^3.
For y, you work the opposite way. Since the negatives are only on the top, you simply add 18 to the bottom y's and it remains rationalized.
If done correctly this should come out to x^3/2y^25
Answer to 2:
(x^20y^12)/256
First thing you can do on this one is to cancel out the x^0s. Anything to the power of 0 equals one so only the coefficients will remain. Multiply those together and you'll get 4.
Next you will rationalize the ys. Add the bottom 3 to the top to cancel out the denominator and you're left with y^-3. Leave it like this for now.
Now is the difficult part. You must take everything that is inside the parenthesis to the power of -4. That includes the coefficients and the exponents. 4^-4 = 1/256. This means that you now must move the coefficients to the bottom. You should currently have y^-3/(256x^5).
Now take the exponents to the power using the same rules as question 1. -3*-4 = 12 and 5*-4 = -20. You should now have y^12/(256x^-20)
Lastly, we must rationalize the denominator. To do so, move the x^-20 to the numerator and make the exponent positive. After doing this, you have the answer: (x^20y^12)/256
short answer: Write an equation in the form y=ax2+bx+c for a parabola that intersects the x-axis at -6 and 2 and passes through the point (1,-14) (2 points). Show you work.
Answer:
y = 2x^2 + 8x - 24
Step-by-step explanation:
This is a "working backwards" kind of a problem. You know the solution (the x-intercepts) and work backwards to find the equation. See image.
A builder uses parallelogram-shaped stones as decoration around a building’s windows. The stones come in many different sizes. Each stone has a base length of x inches and a height of (3x − 5) inches. Write a polynomial to describe the area of a stone. Then find the area of a stone that has a length of 6 inches.
The polynomial that describes the area of the stone is: 3x² - 5x
Area of the stone with a base length of 6 in. is: 78 sq. in.
What is the Area of a Parallelogram?Area of Parallelogram = base length × height
Given the following:
Base length = x in.Height = (3x - 5) in.Area of the parallelogram-shaped stone = x(3x - 5) = 3x² - 5x
To find the area of the stone with a base length (x) of 6 inches, substitute x = 6 into 3x² - 5x:
Area = 3(6)² - 5(6) = 78 sq. in.
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19 there is a frog and snake exhibit at
a nature center. the ratio of frogs to
snakes is 3 to 4. there are 24 snakes in
the exhibit. what is the total number of
animals in the exhibit?
a
18
c
32
b 42
d
56
Answer:
b.42
Step-by-step explanation:
the ratiois is 3 to 4 .So every 4 snakes is to 3 frogs so since there are 24 snakes devide the 24 by 4 which will give u 6 then multiply the answer by 3 which will give u 18 which represents the total number of frogs then add 18 +24 which is 42.
so then total number of frogs is 42.
Write the quadratic equation whose roots are 4 and -2 and whose leading coffecient is 2
Answer:
[tex]y=2x^2-4x-16[/tex]
Step-by-step explanation:
Factored form of a quadratic equation:
[tex]y=a(x-r_1)(x-r_2)[/tex]
where:
a is the leading coefficient[tex]r_1[/tex] and [tex]r_2[/tex] are the rootsGiven:
[tex]a = 2[/tex][tex]r_1=4[/tex][tex]r_2=-2[/tex]Substitute the given values into the formula and expand:
[tex]\implies y=2(x-4)(x-(-2))[/tex]
[tex]\implies y=2(x-4)(x+2)[/tex]
[tex]\implies y=2(x^2+2x-4x-8)[/tex]
[tex]\implies y=2x^2-4x-16[/tex]
The level of college education and wages earned are known to have a strong positive association. karen concluded that a college education causes higher earnings. is karen's conclusion valid? explain. karen's conclusion is not valid because association does not imply causation. karen's conclusion is valid because association does imply causation. karen's conclusion is not valid because causation does not imply association. karen's conclusion is valid because causation does imply association.
karen's conclusion is valid because the association does imply causation.
What is an association claim?An association claim asserts that a particular level of one variable is expected to be related to a specific level of another variable. As two variables are related, they are said to be correlated, which means that when one variable varies, the other variable tends to change as well.
An association claim must include at least two variables that are measured rather than manipulated.
While an association claim just acknowledges a connection between two variables, a causal claim goes a step further by claiming that one of the factors is responsible for altering the other.
Therefore, we can conclude that the claim which states that:
College education causes higher earnings is valid because the association does imply causation.Learn more about association claim here:
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Answer:
Association does not equal Causation, since Karen's theory does not have any evidence to prove causation, her theory is invalid.
Step-by-step explanation:
Colin's family started driving to Grandma´s house at 8:00 am. The family arrived at 11:30. How long did it take to drive to Grandma´s house? use the number line to solve the problem. (pls help)
Answer:
3 hrs 30 min
Step-by-step explanation:
A cylinder and a cone have the same radius and height. The volume of the cylinder is 150 in^3. What is the volume of the cone?
Answer:
50 cm³
Step-by-step explanation:
Given volume of cylinder is 150 in³
we know that The volume of cone 1/3rd of cylinder.
Then volume of cone is 150/3 = 50 cm³
Find the volume of the solid (pls help me :// )
=====================================================
Explanation:
The triangular face has area of base*height/2 = 4*10/2 = 40/2 = 20 square cm.
Multiply this prism base area by the depth of the prism to get 20*2 = 40 cubic cm.
It might help to place the triangular prism so the triangular face is along the ground, so you can think of that face as the floor of this triangular room. The volume of this room is equal to the floor area times the height of the room.
volume of the room = (floor area)*(height of the room)
volume of the prism = (base area)*(height of the prism)
For any prism, the base faces are always parallel and congruent to each other.
I need help! Math isn’t my best subject
Answer:
A and c
Step-by-step explanation:
multiply the 3 to both parts of equation
Answer:
it's A and C, multiply 3 with 3x and 4y
The fifth term of a geometric sequence is 781.25. Each term of the sequence is 1/5 of the value of the following term. Which recursive formula represents the situation?
Answer choices are in the image attached.
The recursive formula of the geometric sequence is [tex]a_{n} = 5a_{n-1}[/tex] and a1 = 1.25
How to determine the recursive formula?The given parameters are:
Fifth term = 781.25
Term = 1/5 * following term
The second parameter above means that:
[tex]a_n = \frac{1}{5} * a_{n+ 1}[/tex]
Multiply both sides by 5
[tex]a_{n+1} = 5a_n[/tex]
Remove 1 from the terms
[tex]a_{n} = 5a_{n-1}[/tex]
Using the formula [tex]a_n = \frac{1}{5} * a_{n+ 1}[/tex], we have the first term to be:
[tex]a_1 = \frac 15 * a_2[/tex]
[tex]a_2 = \frac 15 * a_3[/tex]
[tex]a_3 = \frac 15 * a_4[/tex]
[tex]a_4 = \frac 15 * a_5 = \frac 15 * 781.25 = 156.25[/tex]
So, we have:
[tex]a_3 = \frac 15 * 156.25 = 31.25[/tex]
[tex]a_2 = \frac 15 * 31.25 = 6.25[/tex]
[tex]a_1 = \frac 15 * 6.25 = 1.25[/tex]
Hence, the recursive formula is [tex]a_{n} = 5a_{n-1}[/tex] and a1 = 1.25
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Answer:
A
Step-by-step explanation:
what is 300 in scintifiyc notation?
300 written in scientific notation is 3 × 102.
hope this was helpful.
Step-by-step explanation:
Need help finding the area of the shaded region
Check the picture below, the assumption being that the 6ft line is perpendicular to the 18ft line and thus making a right-triangle.
now, if we just get the whole area of the containing parallelogram and then get the area of the triangle and subtract it from that of the parallelogram's, what's leftover is the area we didn't subtract, the shadead area.
[tex]\stackrel{ \textit{\LARGE Areas}}{\stackrel{parallelogram}{(18)(10)}~~ - ~~\stackrel{triangle}{\cfrac{1}{2}(18)(6)}}\implies 180~~ - ~~54\implies 126[/tex]
You have a standard deck of 52 cards. Find the probability of drawing one card, then drawing another without replacement.
A) You draw an even-numbered card and then a face card.
B) Both cards you drew are "4" or higher (if aces are considered low cards and face cards are nonnumerical)
C) You drew a black face card and then a black "5".
Assuming that the all the cards have the same probability of being drawn we get:
A) P = 0.07B) P = 0.21C) P = 0.001How to find the probabilities?
We have a deck of 52 cards.
A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.
On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:
p = 16/52
Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:
q = 12/51
The joint probability is the product of these two:
P = (16/52)*(12/51) = 0.07
b) Both cards are 4 or larger.
There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:
p = 24/52
For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:
q = 23/51
The joint probability is:
P = (24/52)*(23/51) = 0.21
C) There are 6 black face cards, so the probability first is:
p = 6/52
Then there are 2 black cards with the number 5, so the probability is:
q = 2/51
The joint probability is:
P = (6/52)*(2/51) = 0.001
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What expression is equivalent to 7/12
Answer:
14/24 is one expression equivalent to 7/12.
Answer:
14/24,21/36,28/48,35/60,42/72,49/84,56/96 are equivalent to 7/12...
Find the domain and range of f^-1 given f(x)=1/4-9x 
Find the area of the regular polygon
Answer:
a = 337.214 m2
Step-by-step explanation:
hope this helps
Find the equation of the line.
Use exact numbers.
y
y
8-
7
6+
-9-8-7-6-5-4-32
2 3 4 5 6 7 8 9
-27
-3
-4
-5
-6
-8
Answer:
Could you possible line the numbers up a little bit, it'd be better to understand that way.
[SOLVED] The following data values are amperage outputs from electrical testing.
60, 60, 61, 62, 63, 63, 65, 65, 70, 72, 73, 98
Use the drop-down menus to identify the key values.
What is the median? ✔ 64
What is Q1, the median of the lower half of the data? ✔ 61.5
What is Q3, the median of the upper half of the data? ✔ 71
What is the interquartile range, or Q3 – Q1? ✔ 9.5
The median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
We have data:
60, 60, 61, 62, 63, 63, 65, 65, 70, 72, 73, 98
The median = (63+65)/2 = 64
Q1 = (61+62)/2 = 61.5
Q2 = (70+72)/2= 71
Q3 - Q1 = 71 - 61.5 = 9.5
Thus, the median of the data is 64, the value of Q1 is 61.5, the value of Q2 is 71, and the value of Q3-Q1 is 9.5
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Answer:
Use the drop-down menus to identify the key values.
What is the median? ✔ 64
What is Q1, the median of the lower half of the data? ✔ 61.5
What is Q3, the median of the upper half of the data ✔ 71
What is the interquartile range, or Q3 – Q1? ✔ 9.5
Step-by-step explanation:
edge 2023
Deremine the general solution of sin 2x - 4cos2x
Answer:
[tex]x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex], where k is any integer
Step-by-step explanation:
Let's start by getting all the trig functions on one side and all the constants on the other. We can do this by dividing both sides by [tex]\cos{2x}[/tex]:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=4[/tex]
This ratio looks familiar! It just so happens that the tangent function is defined as the ratio of sine to cosine. In our case:
[tex]\dfrac{\sin{2x}}{\cos{2x}}=\tan{2x}[/tex]
Substituting this back into our equation, we have [tex]\tan{2x}=4[/tex]. We can unwrap the 2x by applying the inverse tangent function to both sides, giving us [tex]2x=\tan^{-1}{4[/tex]. Note, this specific solution only accounts for values of 2x between 0 and 2π radians. To make it general, we can add the term πk to the end of the right side, where k is any integer. We use π as a coefficient because the tangent function has a period of π radians, and it repeats its values every period.
Finally, we divide both sides of the equation by 2 to isolate x, giving us
[tex]2x=\tan^{-1}{4}+\pi k\\x=\frac{1}{2}\left(\tan^{-1}{4}+\pi k\right)[/tex]
There are 90 people going on this feild trip. The budget allows for $542.94 total for tickets to the Buccaneers game. There is a service fee of $45.82. How much does each ticket cost?
Find the volume of the cylinder (3.14 for pi)
Answer:
The volume of the cylinder is equal to 70.65 cm³.
General Formulas and Concepts:
Geometry
Volume Formula [Cylinder]: V = πr²h
r is radiush is heightStep-by-step explanation:
Step 1: Define
Identify given variables from diagram.
r = 3 cm
h = 2.5 cm
Step 2: Find Volume
[Volume Formula - Cylinder] Substitute in variables:∴ we found the volume of the cylinder to be 70.65 cm³.
---
Topic: Geometry
How do exponents fit into the order of operations
Answer:
Exponents are done before addition, subtraction, multiplicaton, and division
Step-by-step explanation:
PEMDAS=
Parenthases
Exponents
Multiply
Divide
Add
Subtract
please help me with this please.......asap
Answer:
B and D because I know that I think
Please Help me ( i give brainly) Given the graphs of the three functions below...At what x value are all functions equal to each other?
x = 0
x = 10
x = 7
x = 4
Answer:
7
Step-by-step explanation:
Because it is asking what X value are all the functions equal to just find a point that lies on X that they all come to.
In this case it's 7
Answer:
x = 7
Step-by-step explanation:
The functions are equal to each other where the lines of the functions intersect each other.
The intersection point is (7, 3).
The x-value at this point is 7.
Hence, x = 7.
The equation is the formula that relates the circumference of a circle to the radius. this gives us the ability to calculate pi if we physically measure a circle's circumference and radius. solve the equation for to get the formula you would use to perform this activity.
Answer:
π = C/(2r)
Step-by-step explanation:
The equation that relates the circumference of a circle to the radius is ...
C = 2πr
__
We can divide both sides of the equation by 2r to get an expression for π.
[tex]C=2\pi r\\\\\dfrac{C}{2r}=\dfrac{2\pi r}{2r}\\\\\boxed{\pi=\dfrac{C}{2r}}[/tex]
if r=5 and h=3cm what is the volume of the cone (assume pi =3.14
Answer:
should be 78.5
Step-by-step explanation:
the formula for volume of a cone is V = pi^2 x H/3
so if you plug in the values you get V= 3.14 x5^2 x3/3 making the awsnser 78.5
