The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.

Answer: Maximum of 5 days

Step-by-step explanation: To find that conclusion, you subtract the "610" from "1,800" getting "1,190". But to find the amount of days you would need to divide "1,190" by "238" to get your 5 days.

An equation is formed of two equal expressions. The maximum number of days Wayne can stay at a resort within his budget is 5.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Wayne's budget for the vacation is $1,800. Therefore, the total amount spent by Wayne during the vacation should be equal to his budget.

Also, it is given that the airfare for the vacation is $610. also, the cost of staying in a hotel for a day is $238. Therefore, the expression for x days staying can be written as,

Total cost = $610 + $238(x days)

Since the total cost or expenses should be equal to the budget, therefore, we can write,

Total cost = budget

610 + 238x = 1800

238x = 1800 - 610

238x = 1190

x = 1190 / 238

x = 5

Hence, the maximum number of days Wayne can stay at a resort within his budget is 5.

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Step-by-step explanation:

Hey, there!!

It's so simple, you just use the formula as given and put the values in it.

Radius of a circle (r) = 13 cm.

pi= 3.14

Now,

Circumference = 2× pi × r

= (2× 3.14 × 13) cm

= 81.64 cm

Therefore, the answer is 82 cm.

Hope it helps..

Answer:

The answer = 82 cm.

Step-by-step explanation:

By using the formula,

C=2×3.14×13

C= 81.64

then,

The nearest hundredth = 82 cm.

Answer:

Option C

Step-by-step explanation:

There should be no difference ($0). This is  true about a balanced budget. Therefore, the correct option is option C among all the given options.

When your expenses are equivalent or lower than to your income, you have a balanced budget. In other words, your ability to live within your means will be shown by a balanced budget.

Any period during that a budget is not in deficit is sometimes referred to as a balanced budget. In other words, your budget is balanced if it is at a profit and has income left over. There should be no difference ($0). This is  true about a balanced budget.

Therefore, the correct option is option C among all the given options.

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Answer:

A) [tex]y=-5x-4[/tex]

B) [tex]y=-5x+4[/tex]

C) [tex]y=\frac{x-4}{5}[/tex]

Step-by-step explanation:

So we have the equation:

[tex]y=5x+4[/tex]

Let's write this in function notation. Thus:

[tex]y=f(x)=5x+4[/tex]

A)

To flip a function over the x-axis, multiply the function by -1. Thus:

[tex]f(x)=5x+4\\-(f(x))=-(5x+4)[/tex]

Simplify:

[tex]-f(x)=-5x-4[/tex]

B) To flip a function over the y-axis, change the variable x to -x. Thus:

[tex]f(x)=5x+4\\f(-x)=5(-x)+4[/tex]

Simplify:

[tex]f(-x)=-5x+4[/tex]

C) A reflection over the line y=x is synonymous with finding the inverse of the function.

To find the inverse, switch x and f(x) and solve for f(x):

[tex]f(x)=5x+4[/tex]

Switch:

[tex]x=5f^{-1}(x)+4[/tex]

Subtract 4 from both sides:

[tex]x-4=5f^{-1}(x)[/tex]

Divide both sides by 5:

[tex]f^{-1}(x)=\frac{x-4}{5}[/tex]

And we're done :)

Answer:

the value of M angle 3 is 70° and M angle 1 is (90-70)=20° and angle 3 - angle 1 is 70° - 20° is 50°

Answer:

The correct option is;

b. Simpsons Rule

Step-by-step explanation:

The midpoint rule involves the estimation of the area under the curve with the aid of rectangular shaped approximations

The trapezoidal rule, involved the approximation of the curve by linear approximations by using piece by piece linear functions

In the Simpson's rule the curve is approximated using piece by piece quadratic functions. The intervals are partitioned into even numbered smaller intervals having the same width and we approximate the resulting integrals of the intervals.

Answer:

a.  [tex]P(Both) = \frac{1}{60}[/tex]

b.   [tex]P(None) = \frac{3}{4}[/tex]

c.  [tex]P(At least 1) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

A fair 6-sided die

A fair 10-sided die

Both have an ace side

For the 6-sided die;

Probability of landing on Ace: P(A)

[tex]P(A) = \frac{1}{6}[/tex]

Probability of not landing on Ace: P(A')

[tex]P(A') = \frac{5}{6}[/tex]

For the 10-sided die;

Probability of landing on Ace: P(B)

[tex]P(B) = \frac{1}{10}[/tex]

Probability of not landing on Ace: P(B')

[tex]P(B') = \frac{9}{10}[/tex]

Solving (a): Both landing on Ace

This is calculated as thus;

[tex]P(Both) = P(A) * P(B)[/tex]

[tex]P(Both) = \frac{1}{6} * \frac{1}{10}[/tex]

[tex]P(Both) = \frac{1}{60}[/tex]

Solving (b): None landing on Ace

This is calculated as thus;

[tex]P(None) = P(A') * P(B')[/tex]

[tex]P(None) = \frac{5}{6} * \frac{9}{10}[/tex]

[tex]P(None) = \frac{1}{6} * \frac{9}{2}[/tex]

[tex]P(None) = \frac{1}{2} * \frac{3}{2}[/tex]

[tex]P(None) = \frac{3}{4}[/tex]

Solving (c): At least one landing on Ace

This is calculated as thus;

[tex]P(At least 1) = 1 - P(None)[/tex]

[tex]P(At least 1) = 1 - \frac{3}{4}[/tex]

[tex]P(At least 1) = \frac{4 - 3}{4}[/tex]

[tex]P(At least 1) = \frac{1}{4}[/tex]

The required probabilities are,

(a):[tex]P(A)=\frac{1}{60}[/tex]

(b):[tex]P(B)=\frac{3}{4}[/tex]

(c):[tex]P(C)=\frac{59}{60}[/tex]

Given that the die having the 6 sides.

The formula for finding the expected probability is,

[tex]P(A)=\frac{m}{n}[/tex]

Where m= Number of expected observation

n= Number of total observation

Part(a):

P(Both landed on ace) is,

[tex]P(A)=\frac{1}{6} \times\frac{1}{10} \\=\frac{1}{60}[/tex]

Part(b):

P(Neither landed on ace) is,

[tex]P(B)=[1-\frac{1}{6} ][1-\frac{1}{10} ]\\=\frac{3}{4}[/tex]

Part(c):

P(At least one not land on ace) = 1 - P(Both landed on ace)

[tex]1-\frac{1}{60} =\frac{59}{60}[/tex]

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Answer:

Q (3.4)

Step-by-step explanation:

Midpoint for point (x1,y1) and (x2,y2) is given by

(x1+x2)/2, (y1+y2)/2.

__________________________________________________________

Given

one endpoint ( R(1, -1)

midpoint is M(2,1.5)

we have to find coordinates of endpoint Q

let Q(x,y)

Thus, for x coordinate of  midpoint

2 = (1+x)/2

=> 2*2 = 1+x

=> 4 = 1+x

=> x = 4-1 = 3

x coordinate of midpoint m is 3

________________________

for y coordinate of  midpoint

1.5 = (-1+y)/2

=> 2*1.5 = -1+y

=> 3 = -1+ y

=> y = 3 + 1 = 4

y coordinate of midpoint m is 4

Thus,  the coordinates of endpoint Q (3.4)

Answer:

D. 6 feet.

Step-by-step explanation:

The third longest side of ABCD is 12 feet long and the third longest side of EFGH is 18 feet long.

As they are similar the corresponding sides are in the same ratio so

12/18 =  x/9 where x is the 4th side of ABCD.

2/3 = x/9

3x = 18

x = 6 feet.

Answer:

⅓y

Step-by-step explanation:

[tex] \frac{1}{3} \times y \\ = \frac{1}{3} y[/tex]

Answer:

Step-by-step explanation:

4x12-5x6-14=0, the highest power of the variable in this equation is 12 so to make it a quadratic equation we should replace x12 by y2. Hence to rewrite the given equation as quadratic just substitute x6=y.

Answer:

35000

Step-by-step explanation:

Answer:

x >3

Step-by-step explanation:

2(2x - 3) > 6

Divide each side by 2

2/2(2x - 3) > 6/2

2x-3 > 3

Add 3 to each side

2x-3+3 > 3+3

2x>6

Divide by 2

2x/2 > 6/2

x >3

Answer:

x > 3

Step-by-step explanation:

First, you're going to divide both sides by two

2( 2x - 3) / 2 and 6/2

After that, you will simplify that into....

2x - 3 > 3

Then you want to add three to both sides like so

2x - 3 + 3 > 3 + 3

Once you're done with that, go ahead and simplify the problem

2x > 6

Then, divide by two on each side

2x/2 > 6/2

Lastly, simplify your answer and that's the solution

x > 3

I hope this helped! :)

Answer:

Hey!

Your answer is 15,360!

Step-by-step explanation:

4% of 16,000 is 640

SO...

To find out the last year's amount of voters we have to minus 640 from 16,000...

16,000 - 640 = 15,360

HOPE THIS HELPED!!

Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

[tex]y=(x-1)^{2} -4[/tex]                                  [switch x with y, and y with x]                        

[tex]x=(y-1)^2-4[/tex]                                  [add both sides by 4]

[tex]x+4=(y-1)^2[/tex]                                  [square root both sides]

[tex]\sqrt{x+4} =y-1[/tex]                                    [add both sides by 1]

[tex]\sqrt{x+4} +1=y[/tex]

[tex]f^-^1(x)=1+\sqrt{x+4}[/tex]

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.

Answer:

ADD 4

Step-by-step explanation:

you want to get 2x by itself so you want to do opposite of -4 so you would do +4 and they cancel out, and what you do to one side you do to the other so

2x = 12 +4

2x = 16

and then you would divide the 2 on both sides so

x = 8 ... just in case you later need to know what x is :)

Answer:

Its either 1.98 percentage or 51.

Step-by-step explanation:

Divison?

Answer:2%

Step-by-step explanation: 38.76-0.76=38

38(1+r)=38.76

__________

38

1+r=1.02

R=0.02 (2%)

Answer:

8

Step-by-step explanation:

Answer:

Hey there!

2x+3y=18

2(3)+3(4)=18

6+12=18

18=18, so this is a valid ordered pair.

Let me know if this helps :)

Answer:

For F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

a. [tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. [tex]r = \sqrt{\frac{GMm}{F}}[/tex]

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

a. [tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. [tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Step-by-step explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

The first thing to do is cross multiply, so that the equation gives

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides of the equation by [tex]Gm[/tex], we then get

[tex]\frac{Fr^{2} }{Gm} = \frac{GMm}{Gm}[/tex]

Then, [tex]\frac{Fr^{2} }{Gm} = M[/tex]

Hence,

[tex]M = \frac{Fr^{2} }{Gm}[/tex]

b. r =

F=GMm/r^2

[tex]F = \frac{GMm}{r^{2} }[/tex]

Likewise, we will first cross multiply, we then get

[tex]Fr^{2} = GMm[/tex]

Now, divide both sides by [tex]F[/tex], so that the equation becomes

[tex]\frac{Fr^{2} }{F} = \frac{GMm}{F} \\[/tex]

∴ [tex]r^{2} = \frac{GMm}{F} \\[/tex]

Then,

[tex]r = \sqrt{\frac{GMm}{F}}[/tex]

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

The first thing to do is cross multiply, so that the equation becomes

[tex]Mp^{2} = kxa^{3} \\[/tex]

Now, divide both sides by M, we then get

[tex]\frac{Mp^{2} }{M} = \frac{kxa^{3} }{M}[/tex]

∴ [tex]p^{2} = \frac{kxa^{3} }{M}[/tex]

Then,

[tex]p = \sqrt{\frac{kxa^{3} }{M}}[/tex]

b. a =

M=kxa^3/p^2

[tex]M = \frac{kxa^{3} }{p^{2} }[/tex]

Also, we will first cross multiply to get

[tex]Mp^{2} = kxa^{3} \\[/tex]

Then, divide both sides of the equation by [tex]kx[/tex] to get

[tex]\frac{Mp^{2} }{kx}= \frac{kxa^{3} }{kx}\\[/tex]

[tex]\frac{Mp^{2} }{kx}= a^{3}[/tex]

∴ [tex]a^{3} = \frac{Mp^{2} }{kx}[/tex]

Then,

[tex]a = \sqrt[3]{\frac{Mp^{2} }{kx}}[/tex]

Step-by-step explanation:

[tex] \frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8} [/tex]

Answer:

see attachement

Step-by-step explanation:

Solve for x:

8 x + 26 - 3/x + 6/x^2 = 0

Hint: | Write the left hand side as a single fraction.

Bring 8 x + 26 - 3/x + 6/x^2 together using the common denominator x^2:

(8 x^3 + 26 x^2 - 3 x + 6)/x^2 = 0

Hint: | Multiply both sides by a polynomial to clear fractions.

Multiply both sides by x^2:

8 x^3 + 26 x^2 - 3 x + 6 = 0

Hint: | Look for a simple substitution that eliminates the quadratic term of 8 x^3 + 26 x^2 - 3 x + 6.

Eliminate the quadratic term by substituting y = x + 13/12:

6 - 3 (y - 13/12) + 26 (y - 13/12)^2 + 8 (y - 13/12)^3 = 0

Hint: | Write the cubic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

8 y^3 - (187 y)/6 + 799/27 = 0

Hint: | Write the cubic equation in standard form.

Divide both sides by 8:

y^3 - (187 y)/48 + 799/216 = 0

Hint: | Perform the substitution y = z + λ/z.

Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:

799/216 - 187/48 (z + λ/z) + (z + λ/z)^3 = 0

Hint: | Transform the rational equation into a polynomial equation.

Multiply both sides by z^3 and collect in terms of z:

z^6 + z^4 (3 λ - 187/48) + (799 z^3)/216 + z^2 (3 λ^2 - (187 λ)/48) + λ^3 = 0

Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.

Substitute λ = 187/144 and then u = z^3, yielding a quadratic equation in the variable u:

u^2 + (799 u)/216 + 6539203/2985984 = 0

Hint: | Solve for u.

Find the positive solution to the quadratic equation:

u = (17 (9 sqrt(157) - 188))/1728

Hint: | Perform back substitution on u = (17 (9 sqrt(157) - 188))/1728.

Substitute back for u = z^3:

z^3 = (17 (9 sqrt(157) - 188))/1728

Hint: | Take the cube root of both sides.

Taking cube roots gives 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) times the third roots of unity:

z = 1/12 17^(1/3) (-(188 - 9 sqrt(157)))^(1/3) or z = -1/12 (-1)^(2/3) 17^(1/3) (188 - 9 sqrt(157))^(1/3) or z = -1/12 17^(1/3) (188 - 9 sqrt(157))^(1/3)

Hint: | Perform back substitution with y = z + 187/(144 z).

Substitute each value of z into y = z + 187/(144 z):

y = 1/12 (-17 (188 - 9 sqrt(157)))^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 11/12 17^(2/3) ((-1)/(188 - 9 sqrt(157)))^(1/3) - 1/12 (-1)^(2/3) (17 (188 - 9 sqrt(157)))^(1/3) or y = -(11 17^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) - 1/12 (17 (188 - 9 sqrt(157)))^(1/3)

Hint: | Simplify each solution.

Bring each solution to a common denominator and simplify:

y = 1/12 (153 sqrt(157) - 3196)^(1/3) - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) or y = 1/12 17^(1/3) (11 ((-17)/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) or y = -1/12 17^(1/3) (1/(188 - 9 sqrt(157)))^(1/3) ((188 - 9 sqrt(157))^(2/3) + 11 17^(1/3))

Hint: | Perform back substitution on the three roots.

Substitute back for x = y - 13/12:

Answer: x = -13/12 - (11 (-17)^(2/3))/(12 (188 - 9 sqrt(157))^(1/3)) + 1/12 (153 sqrt(157) - 3196)^(1/3) or x = 1/12 17^(1/3) (11 (-17/(188 - 9 sqrt(157)))^(1/3) - (-1)^(2/3) (188 - 9 sqrt(157))^(1/3)) - 13/12 or x = -1/12 (17/(188 - 9 sqrt(157)))^(1/3) (11 17^(1/3) + (188 - 9 sqrt(157))^(2/3)) - 13/12

Answer:

The correct answer is, "8x + 2x^2 + 21 / (x + 5)(x - 3)"

Step-by-step explanation:

This is 100% correct! :)

Answer:

Natural numbers < Whole Numbers < Rational numbers < Integers

Step-by-step explanation:

Natural numbers are the numbers that are called counting numbers.They are numbers you can count. But Zero is not among them. Basically, Natural numbers are numbers you can count with the exception of Zero.

Whole numbers are a bit more than natural numbers. Unlike Natural numbers, whole numbers contain Zero. As a result, we can say they're counting numbers Zero inclusive.

Rational numbers are numbers that are written as ratio. They can be written as a fraction, but then, both the denominator and the numerator would have to be whole numbers.

Integers are whole numbers including negative numbers. Remember, whole numbers are an extension of natural numbers? Well then, Integers are an extension of Whole numbers.

Answer:

Quadrant 1:

(6,4) and (3,2)

Quadrant 2:

(-3,4)

Quadrant 3:

(-2,-8) and (-1,-12)

Quadrant 4:

(6,-5)

HOPE THIS HELPS!!!!!! :)

<3333333333

Answer:

i need the number line first lol

Step-by-step explanation:

mark brainliest

Answer: if your on apeand your options were

79,72,63,83 the answer is 72

14

(a + b)² = a² + 2ab + b²

x² + _x + 49

a = x

b = 7

2ab = 2×x×7 = 14x => 2b = 14

Answer:

[tex]\Huge \boxed{\mathrm{14}}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

Square of a sum formula:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

x² + ___ x + 49

The value of a is x.

The value of b is 7, since 7² = 49.

[tex]x^2 +2(x)(7)+7^2[/tex]

[tex]x^2 +14x+49[/tex]

The missing coefficient is 14.

[tex]\rule[225]{225}{2}[/tex]

Answer:

Coterminal angles are angles with the same terminal side.

When we have an angle A, the coterminal angles can be written as:

A + k*(360°)

where k can be any integer number. (Notice that when we have k = 0, means that A is coterminal with itself)

Then the set of all the coterminal angles to -225° is:

{-225° + k*360°I k ∈ Z}

where Z is the set of integer numbers.

Answer:

C=0,10E+5

Step-by-step explanation:

La respuesta es que la expresión que indica el costo mensual "C" en función de la energía "E" consumida es:

C=0,10E+5

Esto teniendo en cuenta que se indica que hay una tarifa fija de $5 por mes y que a esto se debe sumar el resultado de multiplicar la energía consumida por el valor del kilowatt-hora.