Does a hyperbola have an inverse?

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.

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

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.

The parabola narrows as the quadratic coefficient increases. The parabola's width increases as the quadratic coefficient decreases.

The graphs' width and whether or not they slant upward or downward depend on the quadratic term's coefficient, a for the parent function.

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The simplified form of radical √18 . 3√5 = 9√10

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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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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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.

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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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

(Hope this helped! If you have any questions about this please comment) :D

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

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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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 sin θ = - 3/5 and the terminal side of θ lies in quadrant III, then cos θ is  -4/5

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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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°

Answer:40

Step-by-step explanation:

325 students - 5 going in cars.

320 students left / 8 busses = 40 students per bus

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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The value of the PU in the given triangle is 19.

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:

The value of expression -x³+3x²+5x+1 is -1235 when x is 12

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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Answer:

9.7

Step-by-step explanation:

[tex]cos(59)=5/x\\\\x*cos(59)=5\\\\x=5/cos(59)\\\\[/tex]

x ≈ 9.7

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

Answer:

$270

Step-by-step explanation:

20% of 225 is 45. So, 225+45=270

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

x = 6 does not satisfy the given 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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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).

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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Answer:

3111.5.

Step-by-step explanation:

3112 - 0.5 = 3111.5.

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

Answer:

the volume of triangular prism in cubic meters is 5*12+3*13=99

5×12×3×13=2340

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.

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:

Therefore:

[tex]\implies \textsf{Focus}=\left(-8,4+\dfrac{1}{4\left(-\frac{1}{8}\right)}\right)=\left(-8,2)[/tex]

The interquartile range (IQR) of the data in the dot plot is 3.5.

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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