Our library has 3,489 non-fiction books, 8,617 fiction books and 1,240 reference books. If there are 564 students and each student borrows 6 books, how many books will be left in the library?

Step-by-step explanation:

The arc drawn must be in the interior side of the angle to be bisected because while constructing the angular bisector, we make an arc cutting both the rays of the angle, so in order to cut the angle in to two equal part, we should make arcs in the interior part of the angle subtended so that it bisects the angle in two equal parts.        

Answer:

The fourth one

Step-by-step explanation:

coplanar means the points on the plane and only B,E,D,C  is on the plane

Hence, B,E,D,C is your answer

Answer: Option A.

Step-by-step explanation:

We have the functions f(x) and g(x), that are inverses between them.

This means that if:

f(x) = y

then:

g(y) = x.

now, remember that:

When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).

So before we whe had:

f(x) = y.

and now in that same place, we have:

g(y) = x.

So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )

So A is true.

B) This depends on the function:

if we have f(x) = x  + 1.5

then f(0) = 1.5

now we want that:

g(1.5) = 0, then we can write:

g(x) = x - 1.5

Now f(x) and g(x) are inverses, and we would have that:

f(x) = g(x) + 3.

So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.

C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.

Answer:

x = 7

Step-by-step explanation:

Start by solving for [tex](y+x)^2[/tex] which is a common expression for both equations. Then in the first equation:

[tex]3\,x5\,(y+x)^2=16\\3x-16=5\,(y+x)^2\\(y+x)^2=\frac{3\,x-16}{5}[/tex]

and in the second equation:

[tex]4\,x+2\,(y+x)^2=30\\2\,(y+x)^2=30-4\,x\\(y+x)^2=15-2\,x[/tex]

Now we make the two [tex](y+x)^2[/tex] expressions equal so we get:

[tex]\frac{3\,x-16}{5} =15-2\,x\\3\,x-16=75-10\,x\\13\,x=75+16\\13\,x=91\\x=7[/tex]

Answer:

3 is a coefficient. (Option B)

Step-by-step explanation:

A coefficient in a term is the number placed before the variable. The coefficient multiplies the variable.

In the given expression, 3 would be the coefficient in [tex]3b^2[/tex].

A, C, and D are answers to an expression depending on the expression's operation.

In this case, option B would be the correct answer.

Hope this helps.

Answer:

[tex]\huge \boxed{\mathrm{B. \ coefficient}}[/tex]

Step-by-step explanation:

[tex]3b^2[/tex]

[tex]b^2[/tex] is being multiplied by 3.

A coefficient is a number used to multiply a variable.

Answer:

Its about plants

Step-by-step explanation:

Answer:

331.52 oz

Step-by-step explanation:

Google :D

Answer:

a

Step-by-step explanation:

Answer:

Hey there!

These lines only intersect at one point, so there is only one solution.

Let me know if this helps :)

Answer:

one solution

Step-by-step explanation:

The solutions are where the graphs intersect

There lines cross at one point (0,3), so there is one solution

Answer:

8 and 3

Step-by-step explanation:

8+3=11

8*3=24

Answer:

27a³

Step-by-step explanation:

9⁴xa⁷b⁴ / 3⁵xa⁴b⁴

(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴

3⁸xa⁷b⁴ / 3⁵xa⁴b⁴

3³a³

27a³

Answer:

Janine's answer is incorrect.

Step-by-step explanation:

Rigid transformations are methods by which the image of a given figure or object can be produced either by rotation, translation, dilation or reflection.

Since Janine used translation method for the transformation, the dimension of the shape is preserved but not its initial position. To translate AABC to AA'B'C', each point should shift three units left and five units down.

Therefore, the appropriate translation rule is:

(x, y) ⇒ (x + 3, y + 5)

Answer:

90

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The domain is the input values, that is the x- values

The range is the output, that is the y- values.

Thus using values from table

domain : {- 2, 0, 2 }, range : { - 1, 0, 1 }

Answer:

Net Cash-flow = Cash Inflows - Cash Outflows

The net amount of cash that a company has is the difference between the cash coming in(revenue) and the cash going out (expenses).

Spreadsheet 1

= Cash Inflows - Cashflows

= 2,350 - 2,335

= $15

Spreadsheet 2

= Cash Inflows - Cashflows

= 2,270 - 2,260

= $10

Spreadsheet 3

= Cash Inflows - Cashflows

= 2,380 - 2,380

= $0

Spreadsheet 4

= Cash Inflows - Cashflows

=  2,150 - 2,055

= $95

Spreadsheet 4 has the greatest net cash flow at $95.

Answer:The answer is A

Answer:

36

Step-by-step explanation:

Function is:

After 4 1/2 hours, h = 4 1/2 = 4.5

Answer:

36

Step-by-step explanation:

4×4.5=18

18×2=36

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Answer:

1st evening = 7 + 20 = 27 calls

2nd evening = 3 (20 ) = 60 call

3rd evening = 20 calls

Step-by-step explanation:

total calls for the last three evenings = 107 phone calls

2nd evening = 3x as many calls as the 3rd evening

1st evening = 7 more calls than the 3rd evening.

find:

how many calls did she receive each evening?

let T (total) = 107

let x = 3rd evening.

let 2nd = 3x

let 1st = (7 + x)

T = 1st + 2nd + 3rd

107 = (7 + x) + 3x + x

107 - 7 = 5x

100 = 5x

x = 100 / 5

x = 20

therefore,

1st evening = 7 + 20 = 27 calls

2nd evening = 3 (20 ) = 60 call

3rd evening = 20 calls

Answer:

1st  = 27 calls

2nd  = 60 call

3rd = 20 calls

Step-by-step explanation:

total calls = 107 phone calls

2nd  = 3x

1st = 7 + 3x

T (total) = 107

T = 1st + 2nd + 3rd

107 = (7 + x) + 3x + x

107 - 7 = 5x

100 = 5x

x = 100 / 5

x = 20

so,

1st = 7 + 20 = 27 calls

2nd  = 3 (20 ) = 60 call

3rd  = 20 calls

Answer:

Option (A) and (E)

Step-by-step explanation:

Characteristics of the quadratic function representing the path of a whale as it surfaces for air is,

y = -4x²

1). Since domain of the given function will be all real number x until ocean hits the shore on both the sides of the path.

2). Range of the function will be the value of y from the bottom of the ocean to the surface.

3). Whale will touch the surface of the ocean at one point only.

4). Function 'f' will increase initially upto the surface of the ocean and then it will decrease.

5). Point where the hale touches the surface will be maximum.

Therefore, Options (A) and (E) will be the correct options.

Answer:

The answer is A and E hope this helps

Step-by-step explanation:

Answer:

(a) = 71 cm

(b) = 89 cm

Step-by-step explanation:

(a.)

perimeter of a rectangular field = 324 m

length (l) = 91 m

width (w) = ?

Now,

Perimeter Of Rectangle

= P = 2(l + w)

= 2(91 + w) = 324m

= 182 + 2w = 324m

= 2w = 324 - 182m

= 2w = 142m

= w = 142/2

= w = 71

(b.)

area of rectangular painting = 5696 cm²

width (w) = 64 cm

length (l) = ?

Now,

Area Of Rectangle

A = l × w

= l × 64 = 5696

= l = 5696/64

= l = 89 cm

FOR (a)

= P = 2(l + w)

= P = 2(91 + 71) = 324 cm

FOR (b)

= l × w

A = 89 × 64 = 5696

Answer:  -7x should be written as -15x+8x or 8x-15x

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

Explanation:

Multiply the first coefficient 6 and the last term -20 to get -120

We need to find factors of -120 that add to the middle coefficient -7

Through trial and error you should find that

-15 + 8 = -7

-15 * 8 = -120

Therefore, we break the -7x into -15x+8x

----------------------------

Extra info: if you want to fully factor by grouping, then follow these steps

6x^2 - 7x - 20

6x^2 - 15x + 8x - 20 ... break up -7x

(6x^2 - 15x) + (8x - 20) .... group into pairs

3x(2x - 5) + 4(2x - 5) .... factor each group

(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5

So 6x^2-7x-20 fully factors to (3x+4)(2x-5)

We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.

Step-by-step explanation:

It is given that, Jan is painting a square canvas. The length of one side of the canvas is 4 feet.

We need to write an equation to show how to find the area of the canvas.

For a square, all its sides are equal. Let the side is x. The area of a square is given by :

[tex]\text{Area}=\text{side}^2\\\\A=x^2\\\\A=4^2\\\\A=16[/tex]

So, the equation that shows the area of the canvas is [tex]A=x^2[/tex].

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

Explanation:

If we're on a number line, then R could be at either R = 5 or R = -5. This is so the distance from A to R is 5 units. Distance is never negative. You count out the spaces to get the distance, or use subtraction and absolute value.

Saying "distance from A to R is 5" can be written as AR = 5. Meaning segment AR is 5 units long.

Now if AT = 7, then T could be at 7 or -7 on the number line. The reasoning as similar as to why R could be at -5 or 5.

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

Explanation:

The distance from B to A, or vice versa, is 3 units. You can count out the spaces between the points, or you could subtract the x coordinate values then use absolute value

|B - A| = |-2-1| = |-3| = 3

or

|A - B| = |1-(-2)| = |1+2| = |3| = 3

Whichever method you prefer, the distance between the two points is 3 units.

----------

The area of the rectangle is 12 square units, and we know one dimension of the rectangle is 3 units. The other dimension must be 12/3 = 4 units.

Point C is directly below point B. Specifically C is 4 units below B.

Start at B(-2,2) and move down 4 units to get to C(-2,-2). Then move to the right 3 units to get to D(1,-2)

Or you could start at A(1,2) and move 4 units down to get to D(1,-2) and then move 3 units to the left to get to C(-2,-2)

Answer:

Answer choice = B - C(−2, −4), D(1, −4)

Answer:

Third option, last one

Step-by-step explanation:

Let's solve for x first.

|2x| - 12 = -2

|2x| = 10

2x = 10 or -2x = 10

x = 5 or x = -5

The number line that represents this is the last one.

Answer:

-3/2 and 1

Step-by-step explanation:

Given the  arithmetic sequence  (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2

From the  sequence given;

T1 = y+2, T2 = y+3 and T3 = 2y²+1

d = y+3-(y+2) = 2y²+1- (y+3)

open the parenthesis

y+3-y-2 = 2y²+1- y-3

1 = 2y²+1- y-3

1 = 2y²- y-2

2y²- y-2-1 = 0

2y²- y-3 =0

Factorize the resulting expression

2y²- y-3 =0

2y²- 2y+3y-3 =0

2y(y-1)+3(y-1) = 0

(2y+3)(y-1) = 0

2y+3 = 0 and y-1 = 0

2y = -3 and y =1

y = -3/2 and 1

Hence the possible values of y are -3/2 and 1

Answer and Step-by-step explanation:

The calculation of midpoints, relative frequencies and cumulative frequencies are shown below:-

For Midpoint = [tex]\frac{Lower\ limit\ +\ Upper\ limit}{2}[/tex]

For Relative frequency = [tex]\frac{Frequency}{Total\ number\ of\ frequency}[/tex]

Class         Frequency     Midpoints    Relative       Cumulative

                                                             frequency     frequency

16​-26              17                     21                0.047          0.047

27​-37              45                    32               0.123           0.17

38​-48              66                   43                0.181            0.351

49​-59              67                    54               0.184           0.535

60​-70              82                    65              0.225            0.76

71​-81                 66                   76               0.181            0.941

82​-92              22                   87                0.060          1.001

Total                365

Therefore for computing the cumulative frequency we simply added relative frequency with previous cumulative frequency for class 27-37 and in the same manner of every class.

The rate at which something occurs over a particular period of time or in a given sample:

"An increase in the frequency of accidents due to increased overtime"

Use the frequency distribution shown below to construct an expanded frequency distribution.

The formula to calculate the midpoint and relative frequency are given below.

[tex]\rm Midpoint = \dfrac{Lower \ limit + Upper \ limit }{2}[/tex]

[tex]\rm Relative \ frequency = \dfrac{Frequency}{total \ frequency}[/tex]

The frequency distribution to construct an expanded frequency distribution is given below.

Class  Frequency   Midpoints  Relative frequency  Cumulative frequency      

16​-26              17                     21                0.047          0.047

27​-37              45                    32               0.123           0.17

38​-48              66                   43                0.181            0.351

49​-59              67                    54               0.184           0.535

60​-70              82                    65              0.225            0.76

71​-81                 66                   76               0.181            0.941

82​-92              22                   87                0.060          1.001

Total                365

To know more about Frequency click the link given below.

https://brainly.com/question/17740069

Answer:

A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)

Hope this helps!

Answer: Mass of lamina = 4

Step-by-step explanation: A lamina is a plate in 2 dimensions, described by the plane it covers and its density function, [tex]\rho(x,y)[/tex].

To determine mass of the lamina:

mass (M) = [tex]\int {\int\limits_D \rho(x,y) \, dA[/tex]

where D is region bounded by the axis.

For the question:

M = [tex]\int\limits^2_0 {\int\limits^2_0 xy \, dy \,dx[/tex]

Calculating the double integral:

M = [tex]\int\limits^2_0 { x\frac{y^{2}}{2} \,dx[/tex]

M = [tex]\int\limits^2_0 { x(\frac{2^{2}}{2}-0)} \,dx[/tex]

M = [tex]\int\limits^2_0 { 2x} \,dx[/tex]

M = [tex]\frac{2.2^{2}}{2} - 0[/tex]

M = 4

The mass of lamina is 4 units.