circle is centered at (-4,-7)The circle passes through the point (-5,-9) . What is its radius?

The height of the projectile after 4 seconds is 421.28 ft.

The projectile is in the air for 8.015 seconds.

The horizontal distance traveled by the projectile is 881.77 ft.

The maximum height of the projectile is 464.1 ft.

To solve this problem, we can use the kinematic equations of motion for a projectile.

Let's assume that the initial height of the projectile is zero.

What is the height of the projectile after 4 seconds:

We can use the equation:

\(y = yo + vot + 1/2at^2\)

where

y = height of the projectile

yo = initial height (zero in this case)

vo = initial vertical velocity = 220 sin(60°) = 190.53 ft/sec

a = acceleration due to gravity \(= -32.2 ft/sec^2\) ( negative since it acts downwards)

t = time = 4 sec

Plugging in the values, we get:

\(y = 0 + (190.53)(4) + 1/2(-32.2)(4)^2 = 421.28 ft\)

Therefore, the height of the projectile after 4 seconds is 421.28 ft.

Long is the projectile in the air:

The time of flight of a projectile can be calculated using the equation:

t = 2vo sinθ / g

where θ is the launch angle and g is the acceleration due to gravity.

Plugging in the values, we get:

t = 2(220 sin(60°)) / 32.2 = 8.015 sec

Therefore, the projectile is in the air for 8.015 seconds.

Horizontal distance traveled by the projectile:

The horizontal distance traveled by the projectile can be calculated using the equation:

\(x = xo + vot + 1/2at^2\)

where

x = horizontal distance traveled

xo = initial horizontal position (zero in this case)

vo = initial horizontal velocity = 220 cos(60°) = 110 ft/sec

a = acceleration due to gravity (zero in the horizontal direction)

t = time = 8.015 sec

Plugging in the values, we get:

\(x = 0 + (110)(8.015) + 1/2(0)(8.015)^2 = 881.77 ft\)

Therefore, the horizontal distance traveled by the projectile is 881.77 ft.

Maximum height of the projectile:

The maximum height of a projectile can be calculated using the equation:

\(ymax = yo + (vo^2 sin^2 \theta ) / 2g\)

Plugging in the values, we get:\(ymax = 0 + (190.53^2 sin^2(60\degree )) / (2)(32.2) = 464.1 ft\)

Therefore, the maximum height of the projectile is 464.1 ft.

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Answer:

-4

-3

-32

-2

Step-by-step explanation:

Let's do the Y's first

In order to find Y's first, we'll have to plug the X's into the equation 7X-4

We have 2 X's, 0 and -4

Plugging those in

7(0)-4 = -4

7(-4)-4 = -32

For the X's, we have to plug in the Y's then actually solve for X

-25 and -18 are our Y's

-25 = 7X-4

Adding 4 is -21 =7X

Dividing by 7 = -3

-18 = 7X-4

Adding 4 is -14=7X

Dividing by 7 = -2

Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine

The number of different strings that can be made from the letters in ORONO using some or all of the letters is 63

Suppose there are n items.

Suppose we have

\(i_1, i_2, ..., i_k\)

sized groups of identical items.

Then the permutations of their arrangements is given as

\(\dfrac{n!}{i_1! \times i_2! \times ... \times i_k!}\)

We're given the word ORONO.

3 ways: O, R, or N

Subcase: Consists O:

5 ways: OR, RO, ON, NO, OO

Subcase: Doesn't consist O:

2 way: RN, NR

Total permutation under this case = 5+2 = 7

Subcase: Consists 3 'O':

1 way: OOO

Subcase: Consists 2 'O':

6 ways: OOR, ROO, ORO, OON, NOO, ONO

Subcase:  Consists 1 'O':

6 ways: ORN, ONR, RNO, RON, NOR, NRO (or that there are 3 distinct letters to be arranged, which can be done in 3! = 6 ways)

Subcase: Doesn't consist O:

0 ways as only R and N cannot form three letter string.

Total permutation under this case = 1+6+6= 13

Subcase: Consists 3 'O':

So, we've got {O,O,O,R,N}

3 'O's are mandatory, so fourth letter is either R or N:

O, O, O, R can arrange themselves in : \(4!/3! = 4 \: \rm ways\) (as total 4 words but 3 are identical)

Similarly, O, O, O, N can arrange themselves in 4 ways,

So when 4 letter string from ORONO consists of 3 'O's, then total 4+4=8 distinct strings can be made.

Subcase: Consists 2 'O':

So, we've got {O,O,R,N}

The total permuations of these 4 letters, of which 2 are identital is:

\(\dfrac{4!}{2!} = 12\)

Subcase:  Consists 1 'O':

0 ways: Single 'O' and one-one R and N cannot form four letter string.

Subcase: Doesn't consist O:

0 ways as only R and N cannot form four letter string.

Total permutation under this case = 8+12 = 20

All 5 letters of ORONO would be used.

There are 3 identical objects, so total number of their permutation is:

5!/3! = 20

Thus, from all these cases, we conclude that:

Total permutations of string letters using some or all letters of ORONO is:

3+7+13+20+20 = 63

Thus,  the number of different strings that can be made from the letters in ORONO using some or all of the letters is 63

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello, please consider the following.

m and n are the two numbers.

m + n = 24, right?

n = 2 m

We replace n in the first equation, it comes

m + 2m =24

3m = 24 = 3*8

So, m = 8 and n = 16

Thank you

The first number is 8 and second number is 16.

Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

Given that the sum of two numbers is twenty-four

The second number is equal to twice the first number

Let x and y are the two numbers.

According to the question,

m + n = 24,

n = 2m

Substitute the value of n in the first equation,

m + 2m =24

3m = 24

m = 24/3

m = 8

Substitute the value of m in the n = 2m

So, n = 2(8)

n = 16

Hence, the first number is 8 and second number is 16.

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Answer:

40

Step-by-step explanation:

let x = # of Qs on the test

0.85x = 34

x = 34/0.85 = 40

Answer:

Step-by-step explanation:

To simplify the expression, we can combine the square roots and simplify the exponents.

Starting with the expression:

3√(16x^7) * 3√(12x^9)

Let's simplify each term separately:

Simplifying 3√(16x^7):

The index of the radical is 3, so we need to group the terms in sets of three. For the variable x, we have x^7, which can be grouped as x^6 * x.

Now, let's simplify the number inside the radical:

16 = 2^4, and we can rewrite it as (2^3) * 2 = 8 * 2.

So, 3√(16x^7) becomes:

3√(8 * 2 * x^6 * x) = 2 * x^2 * 3√(2x)

Simplifying 3√(12x^9):

Again, the index of the radical is 3, and we group the terms in sets of three. For the variable x, we have x^9, which can be grouped as x^6 * x^3.

Now, let's simplify the number inside the radical:

12 = 2^2 * 3.

So, 3√(12x^9) becomes:

3√(2^2 * 3 * x^6 * x^3) = 2 * x^2 * 3√(3x^3)

Now we can multiply the simplified terms together:

(2 * x^2 * 3√(2x)) * (2 * x^2 * 3√(3x^3))

Multiplying the coefficients: 2 * 2 * 3 = 12.

Multiplying the variables: x^2 * x^2 = x^4.

Now, let's combine the square roots:

3√(2x) * 3√(3x^3) = 3√(2x * 3x^3) = 3√(6x^4).

Therefore, the simplified expression is:

12x^4 * 3√(6x^4)

Step-by-step explanation:

The limit of (sin(x)) / x as x approaches 0 is a well-known limit in calculus, known as the limit definition of the derivative of the sine function.

lim (x -> 0) (sin(x)) / x = 1

This limit can be proven using L'Hopital's rule or by considering the Taylor series expansion of the sine function about x = 0:

sin(x) = x - (x^3) / 6 + (x^5) / 120 + ...

As x approaches 0, the higher order terms in the Taylor series become arbitrarily small, and the expression (sin(x)) / x approaches 1. This shows that the limit of (sin(x)) / x as x approaches 0 is equal to 1.

Answer:

5/21  or  24% probability

Step-by-step explanation:

There is 5 points on line DF and 21 points on line AK

Therefor it is 5/21  or .239095=approx. 24%

Ciana should purchase the skirt at the store across town because the total economic cost will be lowest.

Ciana makes $30 per hour at her work, and her purchase decision includes the opportunity cost of lost wages:

Total economic cost:

Local store = $114 + [1/4 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $144

Across town = $86 + [1/2 hours x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $131

Neighboring city = $60 + [1 hour x 2 (round trip) x $30] + (1/2 hours x $30 spent shopping) = $135

Ciana should buy a skirt at the store across town. Because it has the lowest total economic cost ($131).

Opportunity cost is the lost benefit or additional cost of choosing one activity or investment over another. Economic costs include both accounting costs and opportunity costs.  

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Answer:

x ≈ 2.5

Step-by-step explanation:

Use tan∅ to solve this problem:

tan23° = x/6

x(tan23°) = x

x = 2.54685

Answer:

51.256km/hr

Step-by-step explanation:

average speed is equal to the distance over time

Time = 5hr

distance = 256.28 km

speed = 256.28/5

speed =51.256km/hr

Answer:

the answer is 7/6 cups

Step-by-step explanation:

You add 1/2 + 2/3 and then you make sure the denominators are the same. It will turn into 3/6 + 4/6 and when you add that you get 7/6 cups.

Answer:

it is answer C: 7/6

Step-by-step explanation:

1/2 = 0.50 ( division )

2/3 = 0.66 ( division )

0.50 + 0.66 = 1.16 ( addition )

answer c is 7/6 .... 7 divided by 6 is 1.16.

Answer:both a and b are correct

Step-by-step explanation:

Answer:

w=7.25

Step-by-step explanation:

w + 1.5 = 8.75

1.5 - 8.75 = w

Answer:

D. The zeros are 3 and -10, because y = (x - 3)(x + 10).

Step-by-step explanation:

\(y=x^2+7x-30\)

\(0=x^2+7x-30\)

\(0=(x+10)(x-3)\)

Therefore, D is correct by the Zero Product Property

Step-by-step explanation:

First, find the slope of the line using the slope formula where (1, -3) = (x1, y1) and (3, 7) = (x2, y2).

\(m = \frac{y2 - y1}{x2 - x1} \)

\(m = \frac{7 - ( - 3)}{3 - 1} \)

\(m = \frac{10}{2} = 5\)

Use point-slope form to find the equation.

\(y - y1 = m(x - x1)\)

\(y - ( - 3) = 5(x - 1)\)

\(y + 3 = 5x - 5\)

Subtract 3 on both sides

\(y = 5x - 8\)

To put the equation in function notation, simply change the y to f(x) and you'll get

f(x) = 5x - 8

Answer:

y=5x-8

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(7-(-3))/(3-1)

m=(7+3)/2

m=10/2

m=5

y-y1=m(x-x1)

y-(-3)=5(x-1)

y+3=5(x-1)

y=5x-5-3

y=5x-8

Please mark me as Brainliest if you're satisfied with the answer.

Answer:

32/5

Step-by-step explanation:

Convert the mixed number 6 2/5 into an improper fraction by multiplying the denominator by the whole number and then add the numerator.

Ex: 6 2/5 = 5 x 6 +3  

Answer:

x=5

Step-by-step explanation:

.

Answer:

y=4x+2

Step-by-step explanation:

Use the equation for slope-intercept form (y-y1=m(x-x1). Plug in your variables. y-2=4(x-0). Simplify. y-2=4x. Add two to both sides to get y by itself. y=4x+2.

It took Emily 33.4 minutes to make dinner.

A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.

To solve the problem, we have to convert the mixed number  \(9 \frac{1}{10}\)   to a decimal number:

⇒ \(9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}\)

⇒ \(\frac{91}{10}\)  =  9.1

This means that Emily finished making dinner 9.1 minutes sooner than the cake.

To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:

⇒ 42.5 - 9.1 = 33.4 minutes

Therefore, it took Emily 33.4 minutes to make dinner.

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Answer:

The rate of change in the submarine's elevation is 26.0 feet per second.

Step-by-step explanation:

She begins 151 feet below sea level

Thus, her initial point is y₁ = 151 feet below sea level

i.e. at t₁=0 seconds, y₁ = 151 feet below sea level

After descending for the 3 seconds, she is 229 feet below sea level.

Thus, her second point is y₂ = 229 feet below sea level after 3 seconds

i.e. at t₂=3 seconds, y₂ = 229 feet below sea level

The rate of change is basically the slope. Thus, the rate of change can be obtained by taking the slope.

slope = rate of change = (y₂ - y₁)/(t₂ - t₁)

                                      = (229 - 151) / (3 - 0)

                                       = 78/3

                                       = 26.0

Therefore, the rate of change in the submarine's elevation is 26.0 feet per second.

Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

Q = 52.5

Step-by-step explanation:

given P is directly proportional to Q then the equation relating them is

P = kQ ← k is the constant of proportion

to find k use the condition Q = 30 when P = 40 , then

40 = 30k ( divide both sides by 30 )

\(\frac{40}{30}\) = \(\frac{4}{3}\) = k

P = \(\frac{4}{3}\) Q ← equation of proportion

when P = 70 , then

70 = \(\frac{4}{3}\) Q ( multiply both sides by 3 to clear the fraction )

210 = 4Q ( divide both sides by 4 )

52.5 = Q

Answer:

C = 31.4 inches

Step-by-step explanation:

To find the circumference of a circle, the formula is d(pi), or 2r(pi)

We are given the radius, so let's just plug in the number:

2(5)(pi)

So our circumference would be 10pi

We have to get an approximation here, so we would do 10(3.14)

That would be 31.4 inches

I hope this helps, let me know if you have any questions.

Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

To write the height of Debbie as a fraction of the height of Leo in its simplest form is this: 17/18.

Writing one figure as a fraction of another can be done by representing the figures as numerators and denominators. In this case, what we will have is 85/90. That is the height of Debbie divided by the height of Leo.

To express this fraction in its simplest form will mean dividing the figures until they can no longer be divided. Using 5 as a common factor for dividing, we can conclude that the simplest form of the answer is 17/18.

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The algebraic expression for Desmond's height is x + 5.

If we let "x" represent Niki's height in inches, then Desmond's height can be represented by "x + 5", since Desmond is 5 inches taller than Niki.

So the algebraic expression for Desmond's height is x + 5.

Algebraic expressions is consist of variables, numbers, and mathematical operations (such as addition, subtraction, multiplication, and division).

They can contain one or more variables and can be evaluated for different values of the variables.

For example, the expression 3x + 5y - 2z is an algebraic expression that contains three variables (x, y, and z) and three coefficients (3, 5, and -2) that are multiplied by those variables. Algebraic expressions are commonly used in algebra to represent mathematical relationships and solve problems.

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