If the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
What is a hyperbola?A hyperbola is a particular kind of smooth curve that lies in a plane and is classified by its geometric characteristics or by equations for which it is the solution set.
A hyperbola is made up of two mirror images of one another that resemble two infinite bows.
These two sections are known as connected components or branches.
The hyperbola's equation is expressed as (y−k)2b2−(x−h)2a2=1.
The transverse axis is defined by b, the conjugate axis by a, and the center is defined by (h,k).
The section of a line that a hyperbola's vertices form.
The inverse of the hyperbola is a Limaçon with an inner loop if the circle's center is in one of the foci.
Therefore, if the circle's center is in one of the foci, the inverse of the hyperbola is a Limaçon with an inner loop.
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Radicals help please
The simplified form of radical √18 . 3√5 = 9√10
What is radical?In mathematics, a radical expression is defined as any expression containing a radical (√) symbol. Many times it is used to determine the square root of a number. However, it can also be used to describe a cube root, a fourth root, or higher. When the radical symbol is used to denote any root other than a square root, there will be a superscript number in the 'V'-shaped part of the symbol.
For example, ³√(8) means to find the cube root of 8. If there is no superscript number, the radical expression is calling for the square root.
The term underneath the radical symbol is called the radicand.
Given radical
√18 . 3√5
⇒ √(9 × 2) . 3√5
⇒ 3√2 . 3√5
⇒ 9(√2.5)
⇒ 9√10
⇒ 28.46
Hence, The radical √18 . 3√5 can be simplified to 9√10 having value = 28.46
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Mia brought n shirts that were originally priced at $26.99 each shirt was on sale for $5.99 off the original price that she bought them which expression can be used to find the total sale price of n shirts
The total sale price of n shirts can be found using the following expression:
total sale price = n * (26.99 - 5.99)
This expression first calculates the sale price of a single shirt by subtracting the discount from the original price, and then multiplies that value by the number of shirts to get the total sale price.
For example, if Mia bought 3 shirts, the total sale price would be 3 * (26.99 - 5.99) = 3 * 21 = 63.
(NEED HELP ASAP!!)
What are the coordinates of the focus of the parabola?
A: (8, 6)
B: (-8, 6)
C: (-8, 2)
D: (8, 2)
Answer:
C: (-8, 2)
Step-by-step explanation:
Given parabola:
[tex]y=-\dfrac{1}{8}x^2-2x-4[/tex]
For the quadratic equation in the form y = ax² + bx + c, the x-value of the vertex is -b/2a.
Therefore, the x-value of the vertex of the given parabola is:
[tex]\implies x=-\dfrac{b}{2a}=-\dfrac{-2}{2\left(-\frac{1}{8}\right)}=-8[/tex]
To find the y-value of the vertex, input x = -8 into the given equation:
[tex]\implies y=-\dfrac{1}{8}(-8)^2-2(-8)-4=4[/tex]
Therefore, the vertex (h, k) of the parabola is (-8, 4).
The focus of the parabola is (h, k+p) where:
(h, k) is the vertex[tex]p=\dfrac{1}{4a}[/tex]Therefore:
[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]
What is the quotient of the following rational expression?
(x ^ 3 + 3x ^ 2 - 4x + 5)/(x ^ 2 - 2)
An expression is defined as a set of numbers, variables, and mathematical operations. The quotient of the following rational expression is (x+3), while the remainder is (-2x+11)/(x²-2).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be solved as,
[tex]\dfrac{x^3+3x^2-4x+5}{x^2-2}\\\\\\= x + \dfrac{3x^2-2x+5}{x^2-2}\\\\\\= x + 3+\dfrac{-2x+11}{x^2-2}[/tex]
Hence, the quotient of the following rational expression is (x+3), while the remainder is (-2x+11)/(x²-2).
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P is the centroid of ΔXYZ. If XU = 48, what is PU?
The value of the PU in the given triangle is 19.
What is centroid?The center of the thing is represented by its centroid. The centroid of a triangle is the location where the triangle's three medians intersect. It can alternatively be described as the location where the three medians come together. A line connecting a side's midpoint and the triangle's opposite vertex is called the median.
Given,
'p' is the centroid of triangle XYZ and XU is 57.
Since p is the centroid the 'U', 'V', and 'W' are the mid pint of side'YZ', 'XZ', and 'XY'
from the centroid Theorem, we can write;
XP = 2/3 * XU
plug the values 'XU' in the above equation:
XP = 2/3 *57
XP = 2*19
XP = 38
from figure:
XP + PU = XU
PU = XU - XP
Plug 'XU' and 'XP'
PU = 57 -38
PU = 19
therefore, the PU of the given triangle is 19 units.
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Complete question:
Anne-Marie bought a new couch at Buykea for $225. She used a 20% off coupon in her purchase. What was the original price of the couch?
Answer:
$270
Step-by-step explanation:
20% of 225 is 45. So, 225+45=270
How do you find the horizontal asymptote of a limit?
The way to find the horizontal asymptote of the limit is evaluate the limit of the function as it approaches infinity, and again as it approaches negative infinity.
The term asymptote in math is defined as a line that the graph of a function approaches as either x or y go to positive or negative infinity.
Here we have to find the horizontal asymptote of a limit.
The process of finding the horizontal asymptote is the line y = 0 is called the asymptote of the graph, and it also represents the value that f(x) will never quite reach.
Here we can also say that f ( x ) = 1 x is asymptotic to the line y = 0.
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Please help me !!
this the last question !!
Answer:
2 ≥ p
Step-by-step explanation:
-14 ≤ -7p
Divided both sides by -7. Because divided by a negative number, the < will turn to >
So, the equation is
2 ≥ p
Because there is an equal, the circle will be close and to the left of 2.
Answer:
2 ≥ p
Step-by-step explanation:
Have a great day :) <3
n% of 400 = 150
please HELLPPP
Answer:
150 of 400 can be written as:
150400To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
150400 × 100100= (150 × 100400) × 1100 = 37.5100Therefore, the answer is 37.5%
If you are using a calculator, simply enter 150÷400×100 which will give you 37.5 as the answer.
Please help quick! This is past due! Thanks
Answer:
15.92 rotations
Step-by-step explanation:
We need to find the circumference, then divide the distance of the driveway by the circumference.
C = (pi)(d)
C = (3.14)(16)
C = 50.24
400/50.24 = 7.971783 one way to the mailbox. Since it asks for the "journey to the mailbox", let's double it, giving us 15.9235669
HELP ASAP
|x+12|, if x>-11
Answer:
it should be x+12
Step-by-step explanation:
if x is bigger than -11, then the answer will always be positive
We have given a function; [tex]|x+12|, if x > -11[/tex] if x is bigger than -11, then the answer will always be positive.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
We have given a function;
[tex]|x+12|, if x > -11[/tex]
The modulus of any number always gives the positive term.
if x is bigger than -11, then the answer will always be positive.
Let x = 2
then we get
[tex]|x+12| = |2+12| \\\\= 14[/tex]
So, we can see that the answer is positive.
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A bunch of ballons contains many different colors. red 17 purple 11 orange 3 green 1 yellow 2 What is the probability that a randomly selected balloon will be red? Write your answer as a fraction or whole number.
Answer: 1/2
Step-by-step explanation:
Number of red balloons = 17
Number of purple balloons = 11
Number of orange balloons = 3
Number of green balloons = 1
Number of yellow balloons = 2
Total number of balloons = 34
The probability that a randomly selected balloon will be red will be:
= Number of red balloons/Total number of balloons
= 17/34
= 1/2
Each dot in the following dot plot represents the number of goals Luis scored in one lacrosse
season.
H
43
44
+
+
45
46
Number of goals
47
1
48
Find the interquartile range (IQR) of the data in the dot plot.
I goals
The interquartile range (IQR) of the data in the dot plot is 3.5.
What is IQR?The interquartile range is a measure of where the “middle fifty” is in a data set. Where a range is a measure of where the beginning and end are in a set, an interquartile range is a measure of where the bulk of the values lie. That’s why it’s preferred over many other measures of spread when reporting things like school performance or SAT scores.
In descriptive statistics, the interquartile range is a measure of statistical dispersion, which is the spread of the data. The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data.
The upper and lower median values are shown below which would be the mean of the 2 middle values shown in the brackets below:
43, (44, 44,) 44, | 45, | 45, (47, 48,) 48
Upper median (Q3) = (47+48) ÷ 2 = 47.5
Lower median (Q1) = (44+44) ÷ 2 = 44
=>Step 4: Subtract the lower median from the upper median to get the IQR.
IQR = Upper median (Q3) - Lower median (Q1)
IQR = 47.5 - 44
IQR = 3.5
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3112 was rounded to the nearest one.
What is the lower bound?
Answer:
3111.5.
Step-by-step explanation:
3112 - 0.5 = 3111.5.
HELPP :( please show working?
Answer:
4 3/11
Step-by-step explanation:
Find the function of the first two points
slope = delta y/delta x
slope = y1-y2/x1-x2
slope = (11-(-1))/(-10-1)
slope = 12/-11
Find the y intercept
y=(-12/11)x+b
-1 = (-12/11)*-1+b
-1 = 12/11+b
-23/11=b
y=(-12/11)x-23/11
Plug in x to find y
y=(-12/11)2-23/11
y= 4 3/11
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true. (2 points)
x = 6 does not satisfy the given equation.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that an equation, 5(x – 3) = x + 13
Checking if x = 6 satisfy the equation or not,
5(x – 3) ? x + 13
5(6-3) ? 6+13
5×3 ? 19
15 ≠ 19
Hence, x = 6 does not satisfy the equation.
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Find the largest prime number that divides the quantity 0! + (1!) x 1 + (2!) x 2 + (3!) x 3 + ... + (50!) x 50
The largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.
We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.
0! = 1
1! = 1
2! = 2
3! = 6
...
50! = 30414093201713378043612608166064768844377641568960512000000000000
Now we can write the expression as
(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)
We can notice that the number is very large, and it's impractical to factorize it using traditional methods.
We can use the property that if n is not divisible by a prime number p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.
The next step would be to check if the remaining number is divisible by any prime numbers.
Since it's impractical to check for all the prime numbers, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)
Which is approximately 5.5e+22.
Therefore, the largest prime number that divides the quantity is the largest prime number less than 5.5e+22.
It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.
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If this policyholder causes a huge, serious accident with both bodily injuries and property damage, what is the highest amount their liability coverage will provide?
A. ) $544. 58
B. ) $300,000
C. ) $400,000
D. ) Unlimited amounts, depending on the number of people injured
C). The highest amount their liability coverage will provide is $400,000
This is because most standard liability policies will provide up to $300,000 for bodily injury and $100,000 for property damage, but the policyholder may be able to purchase additional coverage for higher limits if they need it. The exact amount of coverage will depend on the policy the policyholder purchased.
Liability insurance is a component of the general insurance system of risk financing that protects the purchaser from the risks of liabilities imposed by lawsuits and similar claims, as well as the insured if the purchaser is sued for claims covered by the insurance policy.
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When x 12" to the "-x^3+3x^2+5x+1"
The value of expression -x³+3x²+5x+1 is -1235 when x is 12
What is Expression?An expression is combination of variables, numbers and operators.
Given polynomial is -x³+3x²+5x+1
We need to find the value of the polynomial when x is 12.
To find this we just need replace x with 12
-(12)³+3(12)²+5(12)+1
Minus twelve cube plus three times of twelve square plus five times of twelve plus one
-1728+3(144)+5(12)+1
-1728+432+60+1
-1728+493
-1235
Hence, the value of expression -x³+3x²+5x+1 is -1235 when x is 12
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20 workers can paint a building in 21 days. If work has to be finished in 15 days, find the number of extra workers required.
Step-by-step explanation:
20 workers finish work in 21 days.
the necessary work effort is 20×21 = 420 workdays.
the same effort is needed even if the overall time is shorter.
x workers in 15 days.
x × 15 = 420
x = 420/15 = 28 workers.
so, 28-20 = 8 additional workers are needed to finish the work in 15 days.
sum of interior angles find measure angle BCA
Answer:
d) 76
Step-by-step explanation:
there are 180 degrees inside a triangle
so, 40+(3x+10)+(2x+20) = 180
combine 'like terms' to get:
5x + 70 = 180
subtract 70 from each side to get:
5x = 110
divide each side by 5:
x = 22
m∠BCA = 3(22)+10
= 66+10
= 76°
On Monday, 325 students went on a trip to the zoo. All 8 buses were filled and 5 students had to travel in cars. How many students were in each bus ?
Answer:40
Step-by-step explanation:
325 students - 5 going in cars.
320 students left / 8 busses = 40 students per bus
Uppose you have a bag of marbles and of the marbles are . If you choose one without looking, the probability you choose marble is
. How can you write this probability as a decimal? Write this probability as a decimal. Use a word or phrase to describe this probability.
How do you change the fraction to a decimal?
A. Multiply the numerator and denominator by .
B. Divide the denominator by the numerator.
C Divide the numerator by the denominator..
D. Multiply the numerator by the denominator.
6. If sin θ = - 3/5and the terminal side of θ lies in quadrant III, find cosθ .
When sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is -4/5
What is terminal side of an angel?The terminal side of an angle refers to the line that intersects the initial line to make an angle
In the problem the terminal side is said to be in the third quadrant and the in the third quadrant sin θ = - 3/5
sin θ = opposite / hypotenuse
using Pythagoras the adjacent is 4, in third quadrant we have -4
cos θ = - adjacent / hypotenuse = -4/5.
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ILL BRAINLIEST YOU PLEASE HELP ME
Answer:
9.7
Step-by-step explanation:
[tex]cos(59)=5/x\\\\x*cos(59)=5\\\\x=5/cos(59)\\\\[/tex]
x ≈ 9.7
1. Pia drew a circle with a circumference of C and a diameter of 14 in. Pia knows that C = ad, and she wrote
the following equation to represent the value of n.
14
С
(a) There is an error in Pia's equation. Write an equation to correctly represent the value of 1. Show
=
your work
(b) Write an equation and find the circumference of the circle.
The circumference of the circle is 43.98 in.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.
Given:
Pia drew a circle with a circumference of C and a diameter of 14 in
We have to find the circumference of the circle.
Since,
Circumference = 2*π*r
Here
Diameter of circle = 14 in.
⇒ Radius of circle = 7 in.
⇒ Circumference = 2*π*7 = 43.98 in.
Hence, the circumference of the circle is 43.98 in.
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Nora needs at least $115 for a new cell phone. She has already saved $45. She earns $7 an hour at her job. Write and solve an inequality to find how many hours she will need to work to buy the phone.
Answer:
Nora needs to work 10 hours to get 70 dollars to be able to have 115 to buy the new phone.
Step-by-step explanation:
45+7x = 115
45+7(10)
45+70
115
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How do you know if a graph is wider or narrower than the parent function?
The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.
Define the condition for wider graph of the parent function?The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.
The parabola ends point up when the quadratic coefficient is positive.The parabola's ends point down when the quadratic coefficient is negative.The parabola narrows as the quadratic coefficient increases.The parabola's width increases as the quadratic coefficient decreases.The axis of symmetry is moved away from the y-axis by the linear-term coefficient b. The quadratic coefficient's sign and the linear coefficient's sign both affect the shift's direction.The y-intercept is impacted by the constant term c. The intercept point just on y-axis increases higher the higher the number is.To know more about the parent function, here
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You are currently working two jobs so that you can earn enough money to go to the beach for Spring Break Pollo Tropical
(x) and Jason's Deli (4). Pollo Tropical pays $8/hour and requires that you work at least 10 hours/week. Jason's Deli pays
$8.75/hour but does not allow students to work more than 20 hours per week. Due to commitments, at school, you can't
work more than 28 hours/week. Write the objective function and a system of inequalities to model this situation.
Answer:
First, let's define two variables:
x = number of hours that you work at the Pollo Tropical per week
y = number of hours that you work at Jason's Deli per week
Now, you want to get enough money to go to Spring Break, we do not know how much money we need for this, so let's suppose that you need M.
With the given information, we know that the weekly earnings are:
x*$8 + y*$8.75
We can define this as the objetive function, the one that says how much money you get as a function of x and y:
M(x, y) = x*$8 + y*$8.75
Now, we know that:
"Pollo Tropical requires that you work at least 10 hours per week"
Then:
x ≥ 10
"Jason's Deli does not allow students to work more than 20 hours per week."
y ≤ 20
"you can't work more than 28 hours/week."
x + y ≤ 28
Then we have:
M(x, y) = x*$8 + y*$8.75
And the system of inequalities is:
x ≥ 10
y ≤ 20
x + y ≤ 28
What is the volume of the triangular prism in cubic meters?
What is the surface area of the triangular prism in square meters?
Answer:
the volume of triangular prism in cubic meters is 5*12+3*13=99
5×12×3×13=2340