What is the smallest integer $k>2000$ such that both $\dfrac{17k}{66}$ and $\dfrac{13k}{105}$ are terminating decimals?.

Answers

Answer 1

The smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals is 2079.

Given

K is greater than 2000.

[tex]k> 2000\\[/tex].

Given fractions are

[tex]\dfrac{17k}{66} \ and \ \dfrac{13k}{105}[/tex].

How to find the smallest integer greater than 2000 for the fractions to be terminating decimals?

In order for the decimal equivalents to be terminating, the only factors that can remain in the denominators are 2 and 5.

Here, the given denominators are 66 and 105 respectively.

Now factors of 66 will be 2,3,11.

And the factors of 105 will be 3,5,7.

So, the value of k must be multiples of 3, 7, and 11. The LCM of these numbers will be,

[tex]3\times 7\times 11=231[/tex]

Now the value of K must be greater than 2000, so the multiple of 231 which is greater than 2000 is its [tex]9^{th}[/tex] multiple,

[tex]231\times9=2079[/tex]

Hence 2079 is the smallest integer greater than 2000 for both the fractions [tex]\frac{17k}{66} \ and \ \frac{13k}{105}[/tex] to be terminating decimals.

For more details on terminating decimals follow the link:

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Related Questions

Let f(x)=root2x. If the rate of change of f at x=c is four times its rate of change at x=1 then c=?

Answers

Answer:

[tex]c=\frac{1}{16}[/tex]

Step-by-step explanation:

[tex]f(x)=\sqrt{2x}[/tex]

[tex]f'(x)=\frac{\sqrt{2x}}{2x}[/tex]

[tex]f'(1)=\frac{\sqrt{2}}{2}[/tex]

[tex]f'(c)=\frac{\sqrt{2c}}{2c}[/tex]

[tex]f'(c)=4f'(1)[/tex]

[tex]\frac{\sqrt{2c}}{2c}=4(\frac{\sqrt{2}}{2})[/tex]

[tex]\frac{\sqrt{2c}}{2c}=2\sqrt{2}[/tex]

[tex]\sqrt{2c}=4c\sqrt{2}[/tex]

[tex]2c=32c^2[/tex]

[tex]2=32c[/tex]

[tex]\frac{1}{16}=c[/tex]

Help please
I provided screenshots of the problem below.

Answers

Answer:

This is the graph of a sine function

The y-intercept of the graph is the function value y=0

The smallest positive x-intercept of the graph is located at x=pi/2

The greatest value of y is y=2

For x between x=-pi and x=pi/2, the function value y=>0

Step-by-step explanation:

4) If foxes to deer are in a 1:3 ratio, then if there are 112 deer, how many foxes would there be?
Please help this is due tomorrow and I can’t think straight :((

Answers

112 / 3 = 37 1/3, so there should be 37 foxes if rounded to the nearest whole number.

Please help me with this

Answers

Answer:

A and F

Step-by-step explanation:

Can someone please help?

Answers

Answer:

Well a midpoint makes the cutter segment or Line in exactly in half. So the two lines cutted are equal. In this case t is the midpoint. PT and TQ are equal. So you have two expressions, make then equal to each other since they are congruent.

6x+4=8x-8

12=2x

x=6

Now PT is 6x+4

So we subsitute x for 6 since x=6

6*6+4

40

PT is 40

Two parallel lines are crossed by a
transversal.

Answers

Answer:

h = 60˚

Step-by-step explanation:

Look at where it shows the 120˚, and its verticle angle. Verticle angles are congruent, or the same meaning it's also 120˚.

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same. I'll call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles, meaning they add up to 180˚.

180˚ - 120˚, or 60˚ is your answer.

h = 60˚

The solution is, the value of h is, h = 60˚

What is an angle?

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

Look at where it shows the 120˚, and its vertical angle.

Vertical angles are congruent, or the same meaning it's also 120˚.

now, we have,

Then go to its corresponding angle, which is next to the h. Corresponding angles are also congruent, or the same.

We call this angle m to save time and hopefully confusion.

Now, h and m are supplementary angles,

meaning they add up to 180˚.

so, we have,

180˚ - 120˚,

or 60˚ is your answer.

i.e.

h = 60˚

Hence, The solution is, the value of h is, h = 60˚

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Bus route A arrives at its stop every 15 minutes. Bus route B arrives at its stop across the street every 30 minutes. If both buses are currently arriving at their stops, how many hours will pass before both buses arrive at the same time?

Answers

Answer:

2 stops, 30 min

Step-by-step explanation:

to figure this out we have to divide B's time by A's time. 30÷15 is 2.

A girl plays the same computer game lots of times.
The computer scores each game using 1 for the win, 0 for lose.
After each game, the computer calculates her overall mean score.
The graph shows the results for the first 20 games.

What percentage of the 20 games did the girl win?

Answers

Answer: 45%

From my common sense

If the graph line goes up, she wins.

If the graph line goes down, she loses.

1. Count the amounts of times which the graph line goes up.

(btw the first game she won because the graph line started at 1)

= 9

2. Calculate the winrate of her 20 games

= 9/20 * 100

= 45%

What is the name give to the angle pair 3 and 5?

Answers

Alternate Interior Angles
Alternative interior are congruent

How do I find the inverse?

Answers

g(x) as given has no inverse because there are instances of two x values giving the same value of g(x). For instance,

x = -1   ⇒   g(-1) = 4 (-1 + 3)² - 8 = 8

x = -5   ⇒   g(-5) = 4 (-5 + 3)² - 8 = 8

Only a one-to-one function can have an inverse. g(x) is not one-to-one.

However, if we restrict the domain of g(x), we can find an inverse over that domain. Let [tex]g^{-1}(x)[/tex] be the inverse of g(x). Then by definition of inverse function,

[tex]g\left(g^{-1}(x)\right) = 4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

Solve for the inverse:

[tex]4 \left(g^{-1}(x) + 3\right)^2 - 8 = x[/tex]

[tex]4 \left(g^{-1}(x) + 3\right)^2 = x + 8[/tex]

[tex]\left(g^{-1}(x) + 3\right)^2 = \dfrac{x + 8}4[/tex]

[tex]\sqrt{\left(g^{-1}(x) + 3\right)^2} = \sqrt{\dfrac{x + 8}4}[/tex]

[tex]\left| g^{-1}(x) + 3 \right| = \dfrac{\sqrt{x+8}}2[/tex]

Recall the definition of absolute value:

[tex]|x| = \begin{cases}x & \text{if }x\ge0\\-x&\text{if }x<0\end{cases}[/tex]

This means there are two possible solutions for the inverse of g(x) :

• if [tex]g^{-1}(x) + 3 \ge 0[/tex], then

[tex]g^{-1}(x) + 3 = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

• otherwise, if [tex]g^{-1}(x)+3<0[/tex], then

[tex]-\left(g^{-1}(x) + 3\right) = \dfrac{\sqrt{x+8}}2 \implies g^{-1}(x) = -3-\dfrac{\sqrt{x+8}}2[/tex]

Which we choose as the inverse depends on how we restrict the domain of g(x). For example:

Remember that the inverse must satisfy

[tex]g\left(g^{-1}(x)\right) = x[/tex]

In the first case above, [tex]g^{-1}(x) + 3 \ge 0[/tex], or [tex]g^{-1}(x) \ge -3[/tex]. This suggests that we could restrict the domain of g(x) to be [tex]x \ge -3[/tex].

Then as long as [tex]x \ge -3[/tex], the inverse is

[tex]g^{-1}(x) = -3+\dfrac{\sqrt{x+8}}2[/tex]

anybody help please again •_•​

Answers

Answer:

i am not to sure but i think its 5/13 or 5/40

What is the distance between (7, 1) and (-4, -5)?

Answers

Answer:

The distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Step-by-step explanation:

Use the distance formula [tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex] where [tex]d[/tex] is the positive distance between [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:

[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

[tex]d=\sqrt{(-5-1)^2+(-4-7)^2}[/tex]

[tex]d=\sqrt{(-6)^2+(-11)^2}[/tex]

[tex]d=\sqrt{36+121}[/tex]

[tex]d=\sqrt{157}[/tex]

Therefore, the distance between [tex](7,1)[/tex] and [tex](-4,-5)[/tex] is [tex]\sqrt{157}[/tex] units

Answer: The distance between (7,1), and (-4, -5) is 12.53.

What is the simplest form of ^4sqrt324x^6y^8

Answers

[tex]\rm{\green{Answer \: is:-}}[/tex]

[tex]3xy \sqrt[24]{ {4x}^{2} } [/tex](3xy^2 4 sqrt 4x^2)

Step-by-step explanation:

Hope it's helpful to you

Let's see

[tex]\\ \rm\Rrightarrow \sqrt[4]{324x^6y^8}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{4}{18^2x^6y^8}[/tex]

m√a^n=a^n/m

[tex]\\ \rm\Rrightarrow 18^{2/4}x^{6/4}y^{8/4}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{18}x^{3/2}y^2[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{18}\sqrt[2]{x^3}y^2[/tex]

please help ASAP! What is the area of this figure?

Answers

Answer:

The answer is 75ft. Hope this helps.

Which equation has a unite rate of 0.5

Answers

Answer:

r=0.5d

Step-by-step explanation:

Find a pair of positive integers for and b in these questions
18 + 65 = 1865
23 + 7 = 2314

Answers

Answer:

a=100

b=1

Step-by-step explanation:

18a+65b=1865

23a+7b=2314

We need to make one of the variables equal to the other

So...

The LCM for 65 and 7 is 455

So multiply 7 with 18a+65b=1865

and Multiply 65 with 23a+7b=2314

7 times 18a+65b=1865 is 126a+455b=13055

65 times 23a+7b=2314 is 1495a+455b=150410

So Subtract 126a+455b=13055 and 1495a+455b=150410

So 1369a=137355

Divide:

Which is about 100 (The actual value is 100.3323594)

Thus a=100

Substitute:

b=1

Hope this helps!

(The answer is rounded)

Multiply. −5/6⋅27
A. −67 1/2
B. −32 1/4
C.−22 1/2
D.−18 1/2

Answers

the answer is C!!!!!!!!!!!!

please help me asap

ty..

Answers

Answer:

Y = 10x + 20

Step-by-step explanation:

sorry if im wrong

Answer:

y = 2x - 4

Step-by-step explanation:

10x - 5y = 20

Subtract 10x both sides

-5y = 20 + (-10x)

Divide by -5

y = -4 + 2x

y = 2x + (-4)

if f(x) = 2x-7 and g(x)= x2-5, find g[f(5)]

Answers

Answer:

4x-12

Step-by-step explanation:

2x-5[2x-7(5)}=2x+2x-7-5

4x-12

negative integers are added to each other

The answer is 4

1. 2(5)-7, plug in 5 into f(x)
2. The answer for f(x) is 3
3. (3)^2-5, plug in the answer of g(x)
4. Get your result!

An online furniture store sells chairs and tables. Each day, the store can ship at most 55 pieces of furniture. Write an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint.

Answers

Answer:

t+c ≤ 55

Step-by-step explanation:

t+c is the total pieces of furniture and it must be at most (less than or equal to) 55 so t+c ≤ 55 is the equality that represents the possible values.

A group of friends wants to go to the amusement park. They have $180.50 to spend on parking and admission. Parking is $19.50, and tickets cost $23 per person, including tax. Write and solve an equation which can be used to determine pp, the number of people who can go to the amusement park.
equation:
answer p:

Answers

a.

The required equation is  23p + 19.50 = 180.50

Let p represent the number of people who can go to the amusement park.

Since the ticket costs $23 per person, the total amount paid for ticket is rate × number of person = $23 × p = 23p.

Since we pay $19.50 for parking, the total amount spent is T = 23p + 19.50

Since the total amount equals $180.50. T = 180.50

So, 23p + 19.50 = 180.50

The required equation is  23p + 19.50 = 180.50

b.

Solving 23p + 19.50 = 180.50, we have

23p = 180.50 - 19.50

23p = 161

p = 161/23

p = 7

So, the number of people who can go to the amusement park is 7.

Learn more about linear equations here:

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Given m=-2/3, b=-7 give the point in slope form, slope intercept form, standard form, ;general form. HELP IS NEED ASAP PLEASE!!!​

Answers

Answer:

Step-by-step explanation:

m=-2/3

b=-7

First, find the slope-intercept form.

y=mx+b

You know what the m and b values are, so simply plug them into the equation.

Slope-Intercept Form

y=-2/3x-7

From there, let's find the point-slope equation.

An easy way to find a coordinate point that the line crosses is to set one of the x or y variables equal to 0.

So let's set the x to 0.

y=-2/3x-7

y=-2/3(0)-7

y=-7

Therefore, when x is 0, y is equal to -7. We can now write our point. (0,-7)

Use the point-slope formula to write the point-slope equation.

y-y1=m(x-x1)

Point-Slope Equation

y-(-7)=-2/3(x-0)

Now, to find the standard form equation, let's find it using our slope-intercept equation. The formula to find standard form is

ax+by=c

y=-2/3x-7

Standard Form Equation

2/3x+y=-7

Pls help as I will give a 5 star rating thanks!!!!! :)

Answers

Answer:

Scale is 1/2

Step-by-step explanation:

5*1/2=5/2

12*1/2=6

Please help 10 points

Answers

The answer should be D: a - 10 = 80.
The question gives away that she had earned more last week than this week. So the result has to be greater than £80.

If we solve for a,

a - 10 = 80

Add 10 to both sides, we get a = 90

The answer is a - 10 = 80

Write a system of equations to describe the situation below, solve using elimination, and fill in
the blanks.
The manager at a community pool is looking over receipts. On a certain Monday, the pool had
16 children and 42 adults, which brought in $142. That same week on Tuesday, 24 children
and 26 adults came to the pool, which brought in $102. What are the admission prices for
children and adults?

Answers

Answer:  Child is $1 and Adult is $3, per person.

Step-by-step explanation:

We have two unknowns, so we need at least two equations.  Let C and A stand for the price of a ticket for a child and an adult, respectively.

The income for Monday and Tuesday can be calculated:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

Rearrange the second equation to isolate one of the variables.  I'll pick C:

24C + 26A = $102

C  = ($102 - 26A)/24

Now use this expression for C in the first equation

16C + 42A = $142

16(($102 - 26A)/24) + 42A = $142

16(($102 - 26A)/24) + 42A = $142

(1632 - 416A)/24 + 42A = $142

(68 - 17.3333A + 42A = $142

24.6667A = 74

A = 3  [The price of an adult pool admission is $3]

Use this value in either equation to find the price of a child's admission:

24C + 26A = $102

24C + 26*($3) = $102

24C = 102 - 78

C = $1   [The price of a child's admission to the pool is $1]

Check to see if these prices satisfy both equations:

Monday:   16C + 42A = $142

Tuesday:  24C + 26A = $102

---

Monday:   16*(1) + 42*(3)  = $142   ?   YES

Tuesday:  24*(1) + 26*(3) = $102   ?    YES

Child is $1 and Adult is $3, per person.

Solve the system by substitution
8x + y = 4
-2x - 8 =y
(answer as an ordered pair)

Answers

The answer is (2,-12)

(3-5i)^2
i know the answer I’m just confused on how to get to that point. Please and thank you!

Answers

[tex](3-5i)^2\\\\=3^2-2(3)(5i) + (5i)^2\\\\=9-30i +25i^2\\\\=9-30i +25(-1)~~~~;[i^2=-1]\\\\=9-30i-25\\\\=-16-30i[/tex]

write the equation in slo
pe intercept form -1=-2x+y

Answers

Answer:

y = -2x - 1

Step-by-step explanation:

Put y on the left and everything else on the right

need help on this one

Answers

Answer:

[tex]g(x)=\frac{1}{8} x^{3} -\frac{3}{2} x^{2} +6x-5[/tex]

Step-by-step explanation:

[tex]x=2\sqrt[3]{y-3} +4[/tex]

switch the x and y, then use order of opperations

Gravitational force acts on all object in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Answers

Because force= acceleration x mass Acceleration is constant for a body of any mass since force is exactly proportional to mass.

Answer:

[tex]\huge\color{pink}\boxed{\colorbox{black}{Answer♡}}[/tex]

The reason that a heavy body doesn't fall faster than a light body is because the greater gravitational force on the heavier body (its weight), acts on a correspondingly greater mass (inertia). The ratio of gravitational force to mass is the same for every body—hence all bodies in free fall accelerate equally.

hope helpful~

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