Determine the equation of a sine function that would have a range of {y|6<=y<=9} and a period of 60 degrees

Answer:

Ajay has 10 rupees and Ragu has 20 rupees.

Step-by-step explanation:

Let's say Ajay has a rupees, and Ragu has r rupees.

Ragu lends 5 rupees to Ajay.

r - 5 = a + 5

r = a + 10

Ajay lends 5 rupees to Ragu.

5(a - 5) = r + 5

5a - 25 = r + 5

r + 5 = 5a - 25

r = 5a - 30

5a - 30 = a + 10

4a = 40

a = 10 rupees

r = 5 * 10 - 30

r = 50 - 30

r = 20 rupees

Hope this helps!

Answer:

Ajay has 15 Rupees while Ragu has 45 Rupees

Step-by-step explanation:

I believe by " one five", you mean fifteen

Let the original amount that Ajay has be "a"

Let the original amount that Ragu has be "r"

If Ragu lends Ajay 15 rupees, Ragu will now have, (r - 15) while Ajay will have (a + 15)

Since both of them will have equal amount, r - 15 = a + 15

r = a + 30.............(1)

If Ajay lends Ragu 5 rupees, Ajay will have a - 5 while Ragu will have r + 5.

Since Ragu will now have 5 times the amount Ajay has, r + 5 = 5(a - 5)

r + 5 = 5a - 25

r = 5a - 30.............(2)

Equating equations (1) and (2):

a + 30 = 5a - 30

4a = 60

a = 15

Substitute a = 15 into equation (2)

r = 5(15) - 30

r = 75 - 30

r = 45

Ajay has 15 Rupees while Ragu has 45 Rupees

Answer:

25

Step-by-step explanation:

let his age be x, then

5 years ago his age was x - 5 and in 5 years will be x + 5 , thus

(x - 5)(x + 5) = 600 ← expand factors using FOIL

x² - 25 = 600 ( add 25 to both sides )

x² = 625 ( take the square root of both sides )

x = [tex]\sqrt{625}[/tex] = 25

Answer:

[tex]\boxed{Age \ of \ man = 25 \ years}[/tex]

Step-by-step explanation:

Let the age be x

Then, the given condition is:

(x-5)(x+5) = 600     [ x-5 for age 5 years ago and x+5 for age 5 years after ]

Using Formula [tex](a+b)(a-b) = a^2-b^2[/tex]

[tex]x^2-25 = 600[/tex]

Adding 25 to both sides

[tex]x^2 = 600+25[/tex]

[tex]x^2 = 625[/tex]

Taking sqrt on both sides

[tex]x = 25[/tex] years

Answer:

3,896 have signed up from other countries

Step-by-step explanation:

In this problem we are required to calculate the number of signups from other countries.

well, since we know the total sign ups to be 3,922

And also we know that 26 out of the total signed up from the USA

This means that the sign ups from other countries will be

3,922-26=3,896

Answer:

The height of the cylinder is 4 x units.

The area of the cylinder’s base is One-fourthπx2 square units

Step-by-step explanation:

Formula for volume of the cylinder:

V = r² π h

Volume of the cylinder=

πx^3

Diameter=x

Radius (r)=diameter/2

=x/2

V = r² π h

πx^3=(x/2)^2πh

πx^3=(x^2/4)πh

Divide both sides by π

x^3=(x^2/4)h

Make h the subject of the formula

h=x^3÷x^2/4

=x^3×4 / x^2

=4x^3 / x^2

=4*x*x*x / x*x

h=4x

Area of the base:

B = r² π

Recall, r=x/2

B=(x/2)^2 * π

=(x^2/4)π

=πx^2/4

=1/4(πx^2)

The area of the cylinder’s base is One-fourthπx2 square units.

Answer:

B & E

Step-by-step explanation:

Edge 2020

Answer:

Jackson's distance from the finish line after x minutes will be given as;

since from the statements we know that x represents the number of minutes he had run, for us to be able to calculate his  distance from the finish line we simply solve the problem mathematically as follows;

x=80-8y

Step-by-step explanation:

from the initial representation we have x+8y=80,

from the preliminary statement we know x to be the number of minutes from the start of the race to the current point Jackson.

so we assume that y in the equation represents the number of distance covered by the x minutes in miles.

that is how we end up with ;

x=80-8y.

Answer:

1

Step-by-step explanation:

If y=x, than the only way

y=rx can be possible is if r=1

Hope this helps!

Have a good day! :)

Answer:

1

Step-by-step explanation:

y = rx

Use any set of x and y-coordinates in the equation and solve for r.

For example, use (5.8, 5.8).

5.8 = r(5.8)

Divide both sides by 5.8:

r = 1

Answer: r = 1

Answer: It is option 2 or B

Step-by-step explanation: Simple and easy, the test said it was right too.

Answer:

slope of the line containing the given points (6,-1) AND (5,-7) is 6

point- slope form of the equation is

(y+1)= 6(x-6)  ( because, i'm choosing the point (6,-1)

Step-by-step explanation:

slope = (-7 + 1) / (5 - 6 ) = -6/-1 = 6

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

(y+1 ) = 6 ( x-6)

Answer:

55 games

Step-by-step explanation:

What we have to figure out is the total amount of games they played the whole year. We know they won 20% of their games, which equates to 11 games won in total. In order to find the total amount of games we will need to set up the equation [tex]g = 11/20[/tex]%. We solve this accordingly: [tex]g = (11/20) *100[/tex]; [tex]g = (.55)*100[/tex]; [tex]g = 55[/tex].

Answer:

x = 1/3 and x = 1.

Step-by-step explanation:

3x^2 - 4x + 1 = 0

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

The solutions are when either 3x - 1 = 0 or x - 1 = 0.

3x - 1 = 0

3x = 1

x = 1/3

x - 1 = 0

x = 1

So, x = 1/3 and x = 1.

Hope this helps!

Answer:

c) 100

Step-by-step explanation:

This is the best choice because the number is not too low or too high. He will get an accurate probability.

Answer:

2/21.

Step-by-step explanation:

[tex]\frac{2}{7}[/tex] ÷ 3 = (2 / 7) * (1 / 3) = (2 * 1) / (7 * 3) = 2 / 21 = 0.0952380952.

Hope this helps!

Write 3 as 3/1

Now you have 2/7 / 3/1.

When you divide by a fraction change the divide to multiply and flip the second fraction over

Now you have 2/7 x 1/3 now multiply top by top and bottom by bottom to get

2/21

Answer:

[tex]\large \boxed{\sf \ \ \ -1, \ -5, \ -\dfrac{1}{4} \ \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:

[tex]P(x) = 4x^4 + 13x^3-49x^2-73x-15[/tex]

First of all, what is the rational zeroes theorem?

If P(x) is a polynomial with integer coefficients

and if (p and q being integer)

[tex]\dfrac{p}{q}[/tex]

is a zero of P(x), meaning

[tex]P(\dfrac{p}{q})=0[/tex]

then p is a factor of the constant term of P(x) and

q is a factor of the leading coefficient of P(x).

How to apply it here?

The constant term of P(x) is -15

The leading coefficient of P(x) is 4

so p is a factor of -15

q is a factor of 4

15 = 1 * 5 * 3

4 = 2 * 2 * 1

q can be 1, 2, 4

-p can be 1, 3, 5, 15

so it gives the following potential solutions

-1, -3, -5, -15

[tex]\dfrac{-1}{2}, \dfrac{-3}{2}, \dfrac{-5}{2}, \dfrac{-15}{2}[/tex]

[tex]\dfrac{-1}{4}, \dfrac{-3}{4}, \dfrac{-5}{4}, \dfrac{-15}{4}[/tex]

Let's compute P(x) for x in this list of potential solutions

x P(x)

-1 0

-3 -264

-5 0

-15 148680

-0.5 7.875

-1.5 -39.375

-2.5 -185.625

-7.5 4948.125

-0.25 0

-0.75 7.96875

-1.25 -15.9375

-3.75 -324.84375

It gives -1, -5 and -0.25

Conclusion

The possible rational zeroes of P(x) are

-1

-5

[tex]\dfrac{-1}{4}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

This is the graph I inputted into desmos.

Step-by-step explanation:

Next time, using a graphing calculator will work! However, making a table for the x and y outputs will also make it easier to graph points.

For example: see attached image of table.

Answer:

3x+7=10x+17

Step-by-step explanation:

1.9

10x

27x

Answers:

Equation is  3x+7 + 10x+17 = 180 (there are infinitely many other ways to write the equation)

x = 12

Angles are 43 and 137

==========================================================

Explanation:

The horizontal lines are parallel, so the same side interior angles marked are supplementary. The angles add to 180

(3x+7) + (10x+17) = 180 is the equation, or one variation of such

13x+24 = 180

13x = 180-24

13x = 156

x = 156/13

x = 12 is the value of x

Use this x value to find the measure of each angle

3x+7 = 3*12+7 = 43

10x+17 = 10*12+17 = 137

The two angles are 43 and 137 degrees

Note how 43 and 137 add to 180.

Answer: 4

Step-by-step explanation:

Answer:

4 buckets

Step-by-step explanation:

number of buckets needed = 96 / 30

= 3.2

Since 3.2 is not a whole number (buckets cannot be split into small portions), and each bucket can only hold 30 golf balls, 4 buckets are needed to hold all golf balls.

Or else, if there is only 3 buckets, only 30x3 = 90 balls can be held, meaning there are 6 left.

Answer: 9.9

Step-by-step explanation:

SINE RULE:

7/sin(31) = q / sin(47)

Therefore q = 7 / sin(31) * sin(47)

which equals: 9.9 to the nearest tenth.

Answer:

q = 9.9

Step-by-step explanation:

We can use the rule of sines

sin R             sin Q

------------- = ------------

PQ                 PR

sin 31            sin 47

------------- = ------------

 7                q

Using cross products

q sin 31 = 7 sin 47

Divide by sin 31

q = 7 sin 47 / sin 31

q =9.939995043

To the nearest tenth

q = 9.9

Answer:

Step-by-step explanation:

Angles at a point add up to 360°

To find x add up all the angles and equate them to 360°

That's

168 + 123 + x = 360

291 + x = 360

x = 360 - 291

x = 69°

Hope this helps you

Answer:

x = 69

Step-by-step explanation:

The sum of a circle is 360 degrees

x+ 168+123 = 360

Combine like terms

x +291 = 360

Subtract 291 from each side

x+291-291 = 360-291

x =69

Answer:

[tex] s = 5.8 [/tex]

Step-by-step Explanation:

Given:

∆RST,

m < T = 17°

t = RS = 5

m < S = 20°

s = RT = ?

Apply the Law of Sines to find s

[tex] \frac{s}{sin(S)} = \frac{t}{sin(T)} [/tex]

[tex] \frac{s}{sin(20)} = \frac{5}{sin(17)} [/tex]

Multiply both sides by sin(20) to make s the subject of formula.

[tex] \frac{s}{sin(20)}*sin(20) = \frac{5}{sin(17)}*sin(20) [/tex]

[tex] s = \frac{5*sin(20)}{sin(17)} [/tex]

[tex] s = 5.8 [/tex] (to nearest tenth)

Answer:

[tex]\large \boxed{X = 4}[/tex]

Step-by-step explanation:

5/2.5 = X/2

To solve a proportion, use the following equation:

(numerator * opposite denominator) =  (numerator * opposite denominator)

Substitute in given numbers

(5 * 2) = (X * 2.5)

Multiply to simplify

10 = 2.5X

Divide both sides of this equation by 2.5

[tex]\large \boxed{X = 4}[/tex]

Hope this helps :)

Step-by-step explanation:

The probability that either Jack or Jill will be selected on the first draw is 2/30.

The probability that the other person will be selected on the second draw is 1/29.

The probability of both events is (2/30) (1/29), which simplifies to 1/435.

Answer:

60 cents or $0.60

Step-by-step explanation:

9.00/15 = 0.6

Answer:

$.60

Step-by-step explanation:

This is just 9 divided by 15 which is $.60

Answer:

A

Step-by-step explanation:

[tex] \frac{ {6}^{3}. {2}^{6} }{ {2}^{3 } } = \frac{ {2}^{3}. {3}^{3}. {2}^{6} } { {2}^{3} } = {2}^{6} . {3}^{3} [/tex]

Answer:

[tex]\huge\boxed{\sqrt[4]{16a^{-12}}=2a^{-3}=\dfrac{2}{a^3}}[/tex]

Step-by-step explanation:

[tex]16=2^4\\\\a^{-12}=a^{(-3)(4)}=\left(a^{-3}\right)^4\qquad\text{used}\ (a^n)^m=a^{nm}\\\\\sqrt[4]{16a^{-12}}=\bigg(16a^{-12}\bigg)^\frac{1}{4}\qquad\text{used}\ a^\frac{1}{n}=\sqrt[n]{a}\\\\=\bigg(2^4(a^{-3})^4\bigg)^\frac{1}{4}\qquad\text{use}\ (ab)^n=a^nb^n\\\\=\bigg(2^4\bigg)^\frac{1}{4}\bigg[(a^{-3})^4\bigg]^\frac{1}{4}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{(4)(\frac{1}{4})}(a^{-3})^{(4)(\frac{1}{4})}=2^1(a^{-3})^1=2a^{-3}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]=2\left(\dfrac{1}{a^3}\right)=\dfrac{2}{a^3}[/tex]

Step-by-step explanation:

[tex]4(x-7)=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3(x+2)+2.11\\\\Distribute\\\\4x+28=0.3x+0.6+2.11\\\\Combine\\like\\terms\\\\4x+28=0.3x+2.71\\\\Subtract\\\\3.7x+28=2.71\\\\Subtract\\\\3.7x=-25.29\\\\Divide\\\\x=\tex{ about }6.83513514[/tex]

Hope it helps <3

Answer:

x = 83/10=8^3/10=8.3

Step-by-step explanation:

4(x − 7) = 0.3(x + 2) + 2.11

Use the distributive property to multiply 4 by x−7.

4x−28=0.3(x+2)+2.11

Use the distributive property to multiply 0.3 by x+2.

4x−28=0.3x+0.6+2.11

Add 0.6 and 2.11 to get 2.71.

4x−28=0.3x+2.71

Subtract 0.3x from both sides.

4x−28−0.3x=2.71

Combine 4x and −0.3x to get 3.7x.

3.7x−28=2.71

Add 28 to both sides.

3.7x=2.71+28

Add 2.71 and 28 to get 30.71.

3.7x=30.71

Divide both sides by 3.7.

x= 3071/370

Expand  3.7/30.71≈8.3 by multiplying both numerator and the denominator by 100.

x = 83/10

Answer:175

Step-by-step explanation:

1. Turn 28% into a decima: 0.28

2. Multiply 1250 by 0.28 to get the amount of ninth grade students:350

3. Half the amount of ninth grade students:175

Answer:

The answer is 175

Step-by-step explanation:

Because I read the problem carefully and identified that the explanation is way too long so I am gonna make this short and easy for you. I am correct, just Trust me :)

Answer:

The number of possible outfits Dustin can wear is 73 outfits

Step-by-step explanation:

The information given are;

The number of hats Dustin has = 5

The number of shirts Dustin has = 5

The number of pants Dustin has = 5

The number of shoes Dustin has = 5

The colors of Dustin's clothing are blue, green, gray, silver, and gold

Given that the shoes go with at least two other clothing of the same color, we have;

The number of ways the color of the shoes can be selected = 5 ways

The number of ways of selecting the same color for 2 of the remaining 3 clothing = 3 ways

The number of ways of selecting the color of the fourth clothing = 5 ways

The total number of ways = 5 × 3 × 5 = 75 ways

The number of ways in which all silver can be selected = 1 way

The number of ways in which all gold can be selected = 1 way

Since Dustin refuses to wear all silver and all gold, the total number  of ways the outfits can be selected = 75 - 1 - 1 = 73 ways = 73 is the number of possible outfits

Therefore, the number of possible outfits Dustin can wear = 73 outfits.

Answer:

On a coordinate plane, a parabola opens down

has a vertex at (negative 0.5, 6.75)

The vertex is the maximum value. The axis of symmetry is x = negative one-half.

The domain is all real numbers

Step-by-step explanation:

Answer:

The vertex is the maximum value.

The axis of symmetry is x = negative one-half.

The domain is all real numbers.  

Step-by-step explanation:

The answer above is correct.

Answer:

$186.89

Step-by-step explanation:

Let's start by finding the area of the floor.

Area of a trapezium can be found with the formula:

A=(a+b)/2*h

Let's plug our values in.

A=(10+16)/2*7.6

Simplify.

A=26/2*7.6

A=13*7.6

A=98.8

The area of the floor is 98.8 square meters.

Find how many litres of paint are needed.

98.8/1.9=52

He needs 52 liters of paint.

52/5=10.4

He needs 11 5 liter cans of paint.

Each one costs %16.99.

16.99*11=186.89

It would cost $186.89 to buy all the paint he needs.

Answer:

140 degrees.

Step-by-step explanation:

As MQ  = NR and MNOP is a trapezoid MNRQ is an isosceles trapezoid.

So m<MNR = m < NMQ.