There are books in a library, there are 4 different kinds of books. Science books make up 3/4 of art books. Comic books are 1/4 of the total books. History books are 1/5 of the total books. History books are 80 fewer than art books. How many books are in total?

Answer: c) 27:8

Step-by-step explanation:

As volume of cube is side^3

volume of cube with side 2a is 8.a^3

volume of cube with side  3a is 27.a^3

ration of volumes is 27:8

Answer:

? = 21

Step-by-step explanation:

Parallel lines cut off proportional segments on transversals.

27/? = 18/14

18 * ? = 27 * 14

2 * ? = 3 * 14

? = 3 * 7

? = 21

Answer:

21

Step-by-step explanation:

Let the number = x

Writing the equation you have:

10x + 15 <= -17

Solve for x

Subtract 15 from both sides:

10x <= -32

Divide both sides by 10:

X <= -32/10

Simplify:

X <= -16/5 as a fraction or -3.2 as a decimal

Answer:

The correct answer is:

[tex]g(x) = x+1[/tex]

Step-by-step explanation:

Given that:

[tex]h(x) = f\circ g(x)= \sqrt[3]{x+3}[/tex]

[tex]f(x) = \sqrt[3]{x+2}[/tex]

To find:

[tex]g(x) = ?[/tex]

Solution:

Let [tex]g(x) = m[/tex]

We have

[tex]f\circ g(x)= \sqrt[3]{x+3}\\OR\\f( g(x))= \sqrt[3]{x+3}[/tex]...... (1)

Now, we have let:

[tex]g(x) = m\\\therefore f(g(x)) = f(m)[/tex]

Putting x = in f(x), we get

[tex]f(x) = \sqrt[3]{x+2}\\\Rightarrow f(m) = \sqrt[3]{m+2}[/tex]....... (2)

Comparing equation (1) and (2):

[tex]\sqrt[3]{x+3} =\sqrt[3]{m+2}[/tex]

Taking cubes both sides:

[tex]x+3=m+2\\\Rightarrow m = x+3-2\\\Rightarrow m = x+1[/tex]

[tex]\therefore g(x) = x+1[/tex]

Hence,

The correct answer is:

[tex]g(x) = x+1[/tex]

Answer:

x = 25

Step-by-step explanation:

Since it is an equilateral triangle it means that all the sides are 50. Each side is equal so, if you divide 150 by 3 you get 50. (and since perimeter is the adding of each side)

Now you want to try to figure out what the altitude is of the triangle so you divide it in half. Making the bottom side length now 25 because half of 50 is 25. You now have to use Pythagoreans theorem to figure out the altitude:

c^2 - a^2 = b^2

50^2 - 25^2 = b^2

2500 - 625 = b^2

1875 = b^2

√1875 = b

43.30127019

now you put that into the expression: x√3:

x√3 = 43.30127019

x = (43.30127019) ÷ (√3)

x = 25

Hope this helped!

Answer:

Step-by-step explanation:

Window is in the shape of rectangle

Area of the rectangular window = length * width

                                                     = 18 * 2

                                                     = 36 ft²

Answer:

36

Step-by-step explanation:

i got 100%(❁´◡`❁)

The range of the data is 10.

Box plot, which is also known as box and whisker plot, is a method of graphically representing the measures like minimum, maximum and the quartiles of the data set.

Given is a box plot.

Range of a data set is the difference between the highest and the lowest point.

The highest and lowest point of the data set is the points where the whiskers of the box plot extends to.

Here, whiskers extends from 5 to 15.

Range = Maximum - Minimum

          = 15 - 5

          = 10

Hence the range of the data set is 10.

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one pump, let's call it A, fills the reservoir by 1/60 every hour. Now, B fills it by 1/80 every hour. C empties it by 1/90 every hour. All three are on, so now we combine them into one function: t(1/60 + 1/80 - 1/90) = 1, where t = the time it takes to fill it, and 1 is just our "reservoir finally filled" marker.

isolate t onto one side and we see t = 720/13 exactly, or approximately 55.38 hours. let me know if this is the wrong answer but I'm pretty sure it is correct!

Answer:

1/time needed = 1/time of 1st pump + 1/time of 2nd pump - 1/time of 3rd pump

1/t = 1/t1 + 1/t2 - 1/t3

1/t = 1/60 + 1/80 - 1/90

1/t = 12/720 + 9/720 - 8/720

1/t = 13/720

t = 720/13 hours = 55.38 hours = 55 hours 23 minutes

Answer:25

Step-by-step explanation:

Answer:

[tex]-4(a + b = 6)[/tex]

Step-by-step explanation:

Given

[tex]a + b = 6[/tex]

[tex]4a + 2b = 19[/tex]

Required

Eliminate a

Multiply the first equation by -4

[tex]-4(a + b = 6)[/tex]

Add to the second equation

[tex]-4(a + b = 6) + (4a + 2b = 19)[/tex]

Solve brackets

[tex](-4a -4b = -24) + (4a + 2b = 19)[/tex]

Open bracket

[tex]-4a + 4a -4b + 2b = -24 + 19[/tex]

[tex]-4b + 2b = -24 + 19[/tex]

At this point, a has been eliminated;

From the list of given options, the option that answers the question is [tex]-4(a + b = 6)[/tex]

Answer:

x - 2y + 6 = 0  

Step-by-step explanation:

Going from (-2, 2) to (4, 5), we see that x (the 'run') increases by 6 and that y (the 'rise') increases by 3.  Thus, the slope of the line through these two points is m = rise / run = 3/6, or m = 1/2.

Starting with the slope-intercept formula y = mx + b, and using the x and y values from the point (-2, 2), we get

2 = (1/2)(-2) + b, or 4 = -2 + 2b, or 6 = 2b, or b = 3.  Then the slope-intercept form of the desired equation is y = (1/2)x + 3.  To obtain the standard form, we multiply all three terms of this result by 2, obtaining 2y = x + 6, or

x - 2y + 6 = 0                                                                        

Answer:

y - 7 = (1/10)(x - 5)

Step-by-step explanation:

Next time please share the possible answers.  Thank you.

Any line perpendicular to y = -10x + 1 has the slope +1/10, which is the negative reciprocal of -10.

Using the point-slope formula, we get:

y - 7 = (1/10)(x - 5)

Answer:

-15y^6z^{10}+35y^4z^6

Step-by-step explanation:

used an equation calculator

Answer:

Solution,

Hypotenuse(h)= 25

Base(b)= 20

perpendicular (p)= X

Now,

Using Pythagorean theorem:

[tex] {p}^{2} = {h}^{2} - {b}^{2} \\ {x}^{2} = {25}^{2} - {20}^{2} \\ {x}^{2} = 625 - 400 \\ {x}^{2} = 225 \\ x = \sqrt{225} \\ x = \sqrt{ {15}^{2} } \\ x = 15 [/tex]

Hope this helps...

Good luck on your assignment..

Answer:

x = 15

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² + 20² = 25² , that is

x² + 400 = 625 ( subtract 400 from both sides )

x² = 225 ( take the square root of both sides )

x = [tex]\sqrt{225}[/tex] = 15

Answer:

V = 65.548 cm³

Step-by-step explanation:

We have,

Volume of a ball is 4 cubic inches or [tex]4\ \text{inch}^3[/tex].

We know that, 1 inch = 2.54 cm

It is required to convert this volume to cubic centimetre or [tex]\text{cm}^3[/tex].

[tex]4\ \text{inch}^3=4\ \text{inch}^3\times (\dfrac{2.54\ \text{cm}}{1\ \text{inch}})^3\\\\V=65.548\ \text{cm}^3[/tex]

So, the volume of the ball is 65.548 cm³.

Answer:

{ x ≠ ±6 ∪ x ≠ ± 6}

Step-by-step explanation:

x cannot be zero even though x can be cancelled in this expression.  Furthermore, x^2 - 36 cannot be zero, and thus x ≠ ±6.

Domain is { x ≠ ±6 ∪ x ≠ ± 6}

Answer:

3000

Step-by-step explanation:

First find the 4 digit numbers that have all odd digits

Possible Odd digits  =5(1,3,5,7,9)  

So, total number of 4 digit numbers with odd digits can be calculated as  =5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the first digit as either 2,4,6,8 ( 0 would make it a 3 digit number)

The first digit can be 2,4,6,8

=4×5×5×5=500

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the third digit as either 0,2,4,6,8

Now find all the 4 digits numbers with at least 3 odd digits and the second digit as either 0,2,4,6,8

=5×5×5×5=625

Now find all the 4 digits numbers with at least 3 odd digits and the fourth digit as either 0,2,4,6,8

=5×5×5×5=625

Add them together

625+500+625+625+625=3000

Answer:

3000

Step-by-step explanation:

4*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5+5*5*5*5 = 3000

Answer:

Option a

Step-by-step explanation:

This is a nice simple problem!

Given that the function f( x ) is equivalent to 3x + 400, respectively g( x ) = 5x + 200, all we are being asked to do is find their difference. Substitute the given values as such -

h( x ) = f( x ) - g( x )

⇒ h( x ) = ( 3x + 400 ) - ( 5x + 200 ) - Distribute negative sign, taking out ( )

⇒ h( x ) = 3x + 400 - 5x + 200 - Combine like elements

⇒ h( x ) = - 2x + 200

And there you have it! Our solution should be option a ( h( x ) = - 2x + 200 )

If you would like, there is a graph of the function in the attachment below.

Answer:

It's B on edge!

Answer: C)  [tex](-\dfrac{1}{2},\dfrac{3}{2})[/tex]

Step-by-step explanation:

The given system of equations :

[tex]2(y-x) = 5+2x\ \ ...(i)\\\\ 2(y+x)=5-2y\ \ ..(ii)[/tex]

Simplify left side, we get

[tex]2y-2x=5+2x\Rightarrow\ 2y-4x=5\ \ ...(iii)\\\\ 2y+2x=5-2y\Rightarrow\ 4y+2x=5\ \ ...(iv)[/tex]

Multiplying 2 on equation (iii), we get

[tex]4y-8x=10\ \ ...(v)[/tex]

Subtracting (v) from (iv) , we get

[tex]2x-(-8x)=5-10\\\\\Rightarrow\ 2x+8x=-5\\\\\Rightarrow\ 10x=-5\\\\\Rightarrow\ x=-\dfrac{5}{10}=-\dfrac{1}{2}[/tex]

Put value of [tex]x=-\dfrac{1}{2}[/tex] in (v), we get

[tex]4y-8(-\dfrac{1}{2})=10\\\\\Rightarrow \ 4y+4=10\\\\\Rightarrow\ 4y=10-4=6\\\\\Rightarrow\ y=\dfrac{6}{4}=\dfrac{3}{2}[/tex]

hence, the solution to the system is [tex](x,y)=(-\dfrac{1}{2},\dfrac{3}{2})[/tex]

Answer:

3

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (2, - 4) , thus

y = a(x - 2)² - 4

To find a substitute (3, - 1 ) into the equation

- 1 = a(3 - 2)² - 4 ( add 4 to both sides )

3 = a

Thus

y = 3(x - 2)2 - 4 ← equation in vertex form

   = 3(x² - 4x + 4) + 4

    = 3x² - 12x + 12 + 4

     = 3x² - 12x + 16 ← equation in standard form

with coefficient of x² term = 3

Answer:

$54 for 4 months   $89 in total

Step-by-step explanation:

Lisa paid $35 at first

then she paid 0.75  per song which is 0.75 *18 = $13.5

Then just multiply 13.5 by 4 b/c of 4 months

The total amount Liza has spent after 4 months is $89.

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Given that, Lisa paid $35.00 to join an online music service, she purchases 18 songs each month at a cost of $0.75 per song,

we need to find the total amount she paid after 4 months,

So, the cost of 18 songs = 0.75 x 18 = $13.5

The cost of 18 songs in 4 months = $54

Now, the total amount she paid = $54 + $35 = $89

Hence, the total amount Liza has spent after 4 months is $89.

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Hey there! :)

Answer:

y = 0, also known as the x-axis.

Step-by-step explanation:

The equation [tex]f(x) = \frac{2}{3} ^{x}[/tex] is an exponential function.

There is an asymptote at y = 0, or the x-axis because:

[tex]\frac{2}{3} ^{x}\neq 0[/tex]

An exponential function, unless containing a vertical shift, can never cross the x-axis resulting in an asymptote at y = 0.

Answer:

a = 1 ; b = -8 ; c = -5

Step-by-step explanation:

f(p) = p² - 8p  -5

a = co-efficient of p² = 1

b = co-efficient of p = -8

c = constant = -5

Answer:

The answer is B. 30 seconds

Answer:

f, g, and h only

Step-by-step explanation:

The letters are the variables.

Answer:

quadratic

Step-by-step explanation:

Linear function is represented by the data given on the table.

" Linear equation is an algebraic expression in which highest exponent of the given variables is one. It represent a straight line."

General form of linear equation

y = ax + b

According to the data given in the table,

When x = 0 , y = -3 ,

Substitute the given values of x and y in general form of linear equation

- 3 = a × 0 + b                          

⇒ - 3 = b                                 ____(1)

When x = 1 , y = 5

  5 = a × 1 + b                        

  5 = a + b                                         ____(2)

Substitute the value of b in (2) we get,

 5 = a + ( -3)

⇒ a = 8

Substitute the value of 'a' and 'b' in general form of linear equation and check whether it is true for other values of x and y.

y = 8x  - 3

check for the x = 2

   y = 8(2) -3

⇒ y = 13

Yes , it is correct.

When x =3

   y = 8 (3) - 3

⇒ y = 21

It is correct.

Hence, we conclude that Linear function is represented by the data given on the table.

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Answer:

road side cabins

Step-by-step explanation:

Answer:

$135,629.37

Step-by-step explanation:

For computing the interest amount first we need to find out the monthly payment, present value, monthly payment and finally the interest amount which is shown below with the help of an attached spreadsheet

The value of the loan could come by

= $239,127 - $239,127 × 15%

= $203,257.95

The amount of interest saved is

= ($1,905 × 20 × 12) - ($1,399.18 × 20 × 12)

= $135,629.37