Simplify the fraction 6 30​

The equation of the circular orbit and the parabolic path of the comet are

given by the center, diameter, vertex, and directrix.

Part A: The equation of the planet's orbit is; x² + y² = 50²

Part B: The equation of the comet's orbit is; \(\underline{x = -\dfrac{y^2}{280} + 60}\)

Part C: The planet's orbit and the comet's path do not intersect.

Reasons:

Part A: The center of the orbit = The origin (0, 0)

The diameter of the orbit = 100

Therefore;

\(Radius \ of \ orbit = \dfrac{100}{2} = 50\)

The radius of the planet's orbit, r = 50

The equation of a circle with center (h, k) is; (x - h)² + (y - k)² = r²

Therefore, the equation of the circle is (x - 0)² + (y - 0)² = r²

Which gives;

x² + y² = 50²

Part B: The directrix of the parabolic path is x = 70

The vertex = (60, 0)

Therefore, -p = 70

\(The \ equation \ is \ x = \dfrac{1}{4\cdot p} \cdot (y - k)^2 + h\)

Which gives;

\(The \ equation \ is \ x = \dfrac{1}{4\times (-70)} \times (y - 0)^2 + 60 = -\dfrac{y^2}{280} + 60\)

\(x = \mathbf{ -\dfrac{y^2}{280} + 60}\)

The equation of the comet's path in standard form is \(\underline{x = -\dfrac{y^2}{280} + 60}\)

Part C: At the point where the path intersect, we have;

\(x^2 = \left( -\dfrac{y^2}{280} + 60 \right)^2\)

Therefore;

\(\mathbf{\left( -\dfrac{y^2}{280} + 60 \right)^2} = 50^2 - y^2\)

Let y² = a, we get;

\(\left( -\dfrac{a}{280} + 60 \right)^2 = 50^2 -a\)

a ≈ -2015.693 and a ≈ -42784.31

y ≈ √(-2015.693) or y ≈ √-42784.31) (imaginary numbers)

The planet's orbit does not intersect the path of the comet.

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Answer:

1. 195

2. 1875

3. 23460

4. 4690

5. 574

6. 1810

7. 82278

8. 41448

(Can you please give me brainliest?)

Answer:

3 8/9

Can I get Brainliest?

Answer:

3 8/9

Step-by-step explanation:

9 goes into 35 3 times with a remainder of 8

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

rate by an elevator ascends = 29.6 feet per second

height of the  building = 1,450 feet

Time to travel from the ground floor to the roof is calculated as :

we use rate formula.

i.e

rate = distance/ time

time = distance/rate

time = 1450/ (29.6 feet/sec )

time = 1450/29.6

       = 48.98sec

as we know

60 second = 1mint

1 second = 1/60 minutes

therefore,

 time = (48.98 / 60) minutes

time = 0.8163

time = 0.812 minutes

Elevator will take 0.82 minute for travel from the ground floor to the roof. (Option B is correct).

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The perimeter of the composite figure that is given above would be = 96.6m.

To calculate the perimeter of the given shape, it has to be divided into two.

First shape is a rectangle. Therefore the perimeter of a rectangle is calculated with the formula = 2(l+w)

Where ;

length = 16m

width = 11m

perimeter = 2(16+11)

= 2×27

= 54m

The second shape:

Perimeter of triangle = l+w+h

where;

length = 18-11 = 7m

width = 16m

height = 19.5m

perimeter = 7+16+19.5 = 42.5m

Therefore, the perimeter of the shape = 54+42.5 = 96.6m

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Answer:

42 ft/s

Step-by-step explanation:

if superman travels 210 feet in 5 seconds, he will travel a fifth of 210 ft in 1 second

a fifth of 210ft is 210/5=42

hence 42ft/s is his rate.

Answer:

-1

Step-by-step explanation:

Use the slope formula to calculate

-3-6/4-(-5)

= -9/9

= -1 (Slope)

Answer:

(7±√29) /2

Step-by-step explanation:

-x²+7x=5

x²-7x+5=0

x=-(-7)/2 ±√49/4-4

 =7/2±√29 /4

 =(7±√29) /2

Answer:

----------------------

Given:

To find the arc measure (θ) in radians, we can use the formula:

Now, plug in the given values:

To solve for θ, divide both sides by 4:

Simplify the expression:

So, the arc measure (θ) is 2π/3 radians

Answer:

1 can of fruit A and 1 can of Fruit B

Step-by-step explanation:

3 + 1 : 5 + 4

= 4 : 9

Answer:

1 can of juice A + 1 can of juice B

Step-by-step explanation:

Juice A

mango : strawberry = 3 : 5

Juice B

mango : strawberry = 1 : 4

Juice C

mango : strawberry = 4 : 9

⇒ 1 can of juice A + 1 can of juice B = 3 + 1 : 5 + 4 = 4 : 9

Answer:

4x - 7

Step-by-step explanation:

The x represents Bob's age since, we don't know what it is, I put it as a variable.

2x      This represents Jeff who is 2 times Bob's age.

x - 7    Peter is younger than Bob by 7 years so we need to take away 7                    from Bob's age

2x + x - 7 + x    This would be the expression

4x - 7                Now just combine the like terms. We don't have Bob's age so the expression will stay like this.

The percentage decrease in  price of gasoline dropped from $2.10 per gallon to $1.68 per gallon is 20%

Simply dividing the decreased number by the original value and multiplying the result by 100 will yield the percentage decrease.

The formula for percentage decrease is written as

= change in price / original price * 100

the original price = 2.10

change in price = the original price - the new price

change in price = 2.10 - 1.68

change in price = 0.42

plugging known values

= 0.42 / 2.10 * 100

= 42 / 2.10

= 20%

Gasoline's price reduced from $2.10 per gallon to $1.68 per gallon by a 20% proportion.

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The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.

It follows from the task content that the volume of the cylinder which is as represented is to be determined.

Since the volume of a cylinder is;

V = 2πr²h

where r = 10 and h = 25.

V = 2π × 10² × 25.

V = 5000π.

Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.

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Answer:

4.5

Step-by-step explanation:

because 4 times 8 is 32 and .5 times 8 is 4 so 32 plus 4 is 36

To answer this question, we can proceed as follows:

1. Subtract 3.5 to both sides of the equation:

2. Multiply by 2 to both sides of the equation:

We can check this result as follows:

This result is TRUE. Then, the value for h = 7.2.

Answer:

Options (C) and (F)

Step-by-step explanation:

Polynomial function is,

f(x) = x³ - x² - 5x - 3

Possible rational roots of the given function will be = \(\frac{\pm1, \pm3}{\pm1}\)

By putting x = -1

f(-1) = (-1)³ - (-1)² -5(-1) - 3

     = -1 - 1 + 5 - 3

     = 0

Therefore, x = -1 will a root of the given function.

Now we apply synthetic division to get the other roots,

-1 |  1       -1       -5      -3

      ↓      -1         2      3

     1       -2       -3      0

Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).

Now we will find the roots of (x² -2x - 3).

x² - 2x - 3 = x² - 3x + x - 3

                = x(x - 3) + 1(x - 3)

                = (x + 1)(x - 3)

For roots of the function, f(x) = 0

(x + 1)(x - 3) = 0

x = -1, 3

Therefore, roots of the function are x = -1, 3

Options (C) and (F) are the answers.

Answer:

6 and 8

Step-by-step explanation:

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

1.55 = Toni(2)

1.56 = Morgan(1)

1.53 = Pat (3)

Step-by-step explanation:

Is it most to least because that is what i did?

Answer:

–2x2 + 13

Step-by-step explanation:

( f o g)(x) = f (g(x))

   = f (–x2 + 5)

   = 2(             ) + 3     ... setting up to insert the input formula

   = 2(–x2 + 5) + 3

   = –2x2 + 10 + 3

Answer:

k = 6 and k = -4

Step-by-step explanation:

To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.

The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).

Possible p-values:

Possible q-values:

Therefore, all the possible values of p/q are:

\(\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}\)

To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:

\(\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}\)

\(\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}\)

\(\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}\)

\(\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}\)

Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.

Note:

If k = 6, the roots are 1 and -1/6.

If k = -4, the roots are -1 and -1/4.

Nominal and ordinal categorical variables are the two different types.

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114 is 95% of 120

100% of 120 is 120, therefore 95 percent of 120 equals 114. To learn how to solve 114 is 95 percent of what number, see the step-by-step instructions below.

114 is 95 Percent of What Number?

Formula = Number x 100

Percent = 114 x 100

95 = 120

The following shows the steps to derive this formula and find out 95% of the number is 114.

Step 1: If 95% of a number is 114, then what is 100% of that number? Set up the equation.

114

95% = Y

100%

Step 2: Solve for Y

Using cross multiplication of two fractions, we get

95Y = 114 x 100

95Y = 11400

Y = 11400

100 = 120

Answer:

(1/3)π(5-1)^3

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by the given curves about the specified line, y = 3, is

V = ∫5√(x-1) dx

V = ∫5(y-(-1)) dy

V = ∫5(y+1) dy

V = ∫5y dy + ∫5dy

V = ∫5y dy + 5

V = [y^2/2]5 + 5

V = [5^2/2] + 5

V = 5+5

V = 10

No matter how many miles are travelled, only the standard rental fee of equation $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.

An equation is a mathematical statement that proves the equality of two expressions connected by an equal sign '='. For instance, 2x – 5 = 13. Expressions include 2x-5 and 13. '=' is the character that links the two expressions. A mathematical formula that has two algebraic expressions on either side of an equal sign (=) is known as an equation. It depicts the equivalency relationship between the left and right formulas. L.H.S. = R.H.S. (left side = right side) in any formula.

The following equation is used to calculate the overall cost of renting a car:

C(x) = 0.20x + 64

where x is the amount of miles driven and C(x) is the rental car's total cost.

No matter how many miles are travelled, only the standard rental fee of $64 is paid. The total cost of the rental is determined by multiplying the miles driven by the additional $0.20 per mile price.

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Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is essentially what probability means.

The die has 10 faces, with numbers 1 through 10, but we are interested in the number of times it will land on a number less than 10. That means, there are 9 possible outcomes for each roll to be less than 10.

The expected number of times the die will land on a number less than 10 can be calculated by multiplying the probability of getting a number less than 10 on each roll by the total number of rolls.

The probability of getting a number less than 10 on each roll is 9/10, since there are 9 faces with numbers less than 10 out of the total of 10 faces.

Therefore, the expected number of times the die will land on a number less than 10 is:

E = (9/10) x 40 = 36

Therefore, Adama can expect the die to land on a number less than 10 about 36 times in 40 rolls.

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☆ 36 times.

— your in college ? im in seventh grade and got this question !

Answer:

5.6 miles

Step-by-step explanation:

\(\frac{7}{80} =\frac{x}{64}\)   Set up the proportion

\(7(64)=x(80)\)  Cross multiply

\(448=80x\)     Simplify

\(\frac{448}{80}=\frac{80x}{80}\)    Divide both sides by 80

\(5.6=x\)

The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.

Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.

What is the exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

The growth from 2009 through 2015 can be modeled using the function G(t) = 174 * 1.67^t where t is the number of years since 2009 and G(t) is measured in millions of smartphones.

The required graph of the exponential function G(t) has been attached below

Now, finding the y-intercept

G(t) = 174· 1.67^t...(i)

Substitute the value of t = 0 in the above function,

G(t) = 174* 1.67⁰

G(t) = 174(1)

G(t) = 174

The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.

Substitute the value of G(t) =500 in the exponential function(i),

500 = 174 * 1.67^t

500/174 = 1.67^t

2.8735 = 1.67^t

In(2.8735 ) = t In (1.67)

t = In (2.8735 ) / In (1.67

t = 2.05827 ≈ 2

Hence, This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.

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