Is it possible to arrange 152 books on a shelf so that the first shelf has 7 fewer books than the second shelf and 11 more than the third shelf?

Answer:

2y - 12x = 3

Step-by-step explanation:

gradient of line PQ= (7-8)/ 4+2

-1/6

gradient of perpendicular bisector of line PQ=

-1 ÷ -1/6

-1× -6

6

coordinates of the midpoint of line PQ

(-2+4)/2, (8+7)/2

(1, 15/2)

the perpendicular bisector passes through the midpoint of line PQ

Equation of the perpendicular bisector

y - 15/2 = 6(x - 1)

multiply through by 2

2y - 15 = 12(x - 1)

2y - 15 = 12x - 12

2y - 12x = 3

Answer:

LCM = 2^4 x 5^1 x 7^1 = 560

Step-by-step explanation:

we know that $1290 is to be divided on a 7:8 ratio, so we'll start off by dividing 1290 by (7+8) and give each person accordingly

[tex]1290~~ at~~ 7:8\implies 7\cdot \cfrac{1290}{7+8}~~ :~~8\cdot \cfrac{1290}{7+8} \\\\\\ 7\cdot 86~~:~~8\cdot 86\implies 602~~ :~~688[/tex]

Answer:

x=6,y=4

Step-by-step explanation:

10x-9(x-2)=24

10x-9x+18=24

x=24-18

x=6

sub x

y=6-2

y=4

Answer:

x=6 y=4

Step-by-step explanation:

Substitute x-2 in for y: 10x-9(x-2)=24

Distribute: 10x-9x+18=24

Subtract 10x-9x=1x

Subtract 18 from both sides

x=6

Substitute 6 for x

y=6-2

y=4

x=6 y=4

Answer:

This doens't realy make sense dude

Answer:100 Estudiantes dieron su discurso

Step-by-step explanation:

120÷6=20

20x5=100

100 Students

How?

120÷6=20

You can do this,

or you can do

120×1/6=20

_____________________________________________

20×5=100

Therefore,

100 students gave their speeches.

Answer:

it will be an 91 or 88

Step-by-step explanation:

[tex]\dfrac 27 >b +\dfrac 57\\\\\implies 2 > 7b +5~~~;[ \text{Multiplying both sides by 7}]\\\\\implies 2-5>7b\\\\\implies -3>7b\\\\\implies -\dfrac 37 >b\\\\\implies b<-\dfrac 37\\\\\\\text{Interval,}~ \left(-\infty, -\dfrac 37 \right)[/tex]

Answer:

The bisector of a given angle

Step-by-step explanation:

Because, the given picture shows an acute angle and the markings on it are of which you can see when a bisector is being searched for.

Answer:

Adelina

Step-by-step explanation:

Answer:

$12.96

Step-by-step explanation:

Before Tax Price: $12.00

Sale Tax: 8.00% or $0.96

After Tax Price: $12.96

Answer:

Hope it will help you a lot.

Answer:

1470 inches cubed

Step-by-step explanation:

Vol=length × width × height

But ALSO,

length × width = Area,

So we find another Volume equation,

Vol = BaseArea × height

This is the information you are given in the question.

Vol = 210 × 7

Vol = 1470 inches cubed

Answer:

DC

Step-by-step explanation:

If we rotate a segment around a point 360 degrees, we have rotated it around to its original point. Similarly, if we rotate it 180 degrees, we have rotated it to the side opposite of where it once was relative to the point.

What we can do is see how much 144 degrees is of 360 and use that to determine how far around we rotate AE around F.

144/360

divide by 12 because that is a common factor of both the numerator and denominator

12 / 30

divide by 2 because that is a common factor

6/15

divide by 3 because that is a common factor

2/5

Therefore, 144/360 = 2/5. This means that we rotate segment AE 2/5 of the way around point F. We have 5 sides in the polygon ABCDE, and each represents 1/5 of the way around. Going counterclockwise, ED represents 1/5, DC represents 2/5, and so on. We are looking for 2/5, so DC is our answer

Answer:

−6n≥−12

Step-by-step explanation:

The correct inequality to show the given statement is,

⇒ - 6n ≥ - 12

Where, 'n' is any number.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The statement is,

''The product of - 6 and a number is no less than - 12.''

Now, Let a number = n

So, We can formulate the correct inequality is,

⇒ - 6n ≥ - 12

Learn more about the inequality visit:

https://brainly.com/question/25944814

#SPJ2

Answer:

Option a is the best method with compass and straight edge.

Step-by-step explanation:

Answer:

64m^2 - 112m + 49

Step-by-step explanation:

You just do the math lol.

Answer:

64m^2 + 112m + 49

Step-by-step explanation:

I got it right in Grandpoint.

Answer:

-13x. (I think)

Step-by-step explanation:

The question is an illustration of a system of linear equations.

Let the number of miles be x.

Getting trained and licensed

So, the equation is:

[tex]y=450 + 2x[/tex]

Delivery

So, the equation is:

[tex]y = 350 + 6x[/tex]

Hence, the system of linear equations is:

[tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]

To solve the equation, we equate both, as follows:

[tex]450 + 2x = 350 + 6x[/tex]

Collect like terms

[tex]6x - 2x = 450 - 350[/tex]

[tex]4x = 100[/tex]

Divide both sides by 4

[tex]x = 25[/tex]

Substitute 25 for x in [tex]y=450 + 2x[/tex]

[tex]y = 450 + 2 \times 25[/tex]

[tex]y = 450 + 50[/tex]

[tex]y = 500[/tex]

Hence, the solution to the equation is (25,500)

Read more about linear equations at:

https://brainly.com/question/14323743

Answer:

it looks like y int is about 2550

Step-by-step explanation:

Answer:

the answer is infinite

Step-by-step explanation:

would u like me to explain?

Answer:

Oslo

Step-by-step explanation:

The farther the number from zero at the right hand side, the colder.

So its Oslo

I hope this helps!

Answer:

440 miles

Step-by-step explanation:

First, you need to calculate the number of miles per hour. To do this, take the total number of miles traveled and divide it by the number of hours it took. 360/9=40. This means Kaitlyn drove at 40 miles per hour. Then, we need to multiply 40 by 11 to figure out the number of miles she drove in 11 hours because her speed stayed the same. 40*11=440. This means Kaitlyn will have driven 440 miles in 11 hours.

Hope this helps! :)

Answer:

1/8

Step-by-step explanation:

I took the test this is it

Problem 1

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

Explanation:

The vertices are (-12,0) and (12,0). Both of which are on the same horizontal line. Because of this, we have a hyperbola that opens leftward and rightward. Such hyperbolas are of the form

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]

where (h,k) is the center and the a,b terms help set up the asymptotes.

The midpoint of the vertices (-12,0) and (12,0) is the point (0,0). This is the center. So we know that h = 0 and k = 0.

For left/right opening hyperbolas, the asymptotes can be described as the equations:

y = (b/a)x

y = (-b/a)x

Or we can condense them into [tex]y = \pm \frac{b}{a}x[/tex]. Compare this to the given equation [tex]y = \pm\frac{5}{12}x[/tex] to see that b = 5 and a = 12.

Therefore, we get the following:

[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1\\\\\frac{(x-0)^2}{12^2}-\frac{(y-0)^2}{5^2}=1\\\\\frac{x^2}{144}-\frac{y^2}{25}=1[/tex]

That points us to choice D.

You chose the correct answer.

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

Problem 2

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

Explanation:

Divide both sides by 3600 so we can turn that "3600" into "1". Then our goal is to get that "1" to its own side like so:

[tex]25x^2-144y^2 + 3600 = 0\\\\\frac{25x^2-144y^2 + 3600}{3600} = \frac{0}{3600}\\\\\frac{25x^2}{3600}-\frac{144y^2}{3600} + \frac{3600}{3600} = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} + 1 = 0\\\\\frac{x^2}{144}-\frac{y^2}{25} = -1\\\\-\frac{x^2}{144}+\frac{y^2}{25} = 1\\\\-\frac{x^2}{12^2}+\frac{y^2}{5^2} = 1\\\\[/tex]

We see that a = 12 and b = 5 like earlier, so we end up with the same asymptotes as before. The only difference is that this hyperbola opens upward/downward rather than left/right.

You made the correct choice in picking answer A. Both of your answers are correct. Nice work.

Answer:

45

Step-by-step explanation:

just typing this so I'll have 20

Answer:

Width = 38.57cm

Step-by-step explanation:

Perimeter = 270cm

Let x be the width, so

Length = 2 1/2 x = 5x/2

Perimeter of Rectangle = 2(length + width)

270cm = 2(5x/2 + x)

270 = 5x + 2x

7x = 270

x = 38.571 cm

Therefore, the width is 38.57cm (rounded to 2nd decimal place)

Answer:

width = 38.6 cm (approx.)

Step-by-step explanation:

let the width be x cm, so that the length is 2.5x cm.

Perimeter = 2 (length + width)

2 (length + width) = 270 cm

or, 2 (2½x cm + x cm) = 270 cm

or, 3½x cm = 270/2 = 135 cm

or, x = 270/7 cm = 38.6 cm (approx.)

Answer:

5/8

Step-by-step explanation:

The answer is 5/8 because 4*5 equals 20 and 4*8 equals 32. Therefore, you have to do the same thing you do to the numerator to the denominator. In addition, you I divided 20 by 4 which is 5 and 32 divided by 4 is 8. So, it is 5/8.

Answer:

y > - x - 4

Step-by-step explanation:

1) Find the equation of the line

2) The equation of the line is y = - x - 4

3) Identify where the graph is shaded

4) It is shaded above and to the right of the line

5) This means that it is more positive/ greater than the unshaded areas

6) Switch the = sign to > to signify the inequality

7) All done!

Step-by-step explanation:

the delimiter line is going through the points (-4, 0) and (0, -4).

the line function

y = mx + b

m is the slope of the line, b is the y-intercept (the y value when x = 0).

the slope is the ratio of "y coordinate change / x coordinate change" when going from one point to another.

so, for the 2 found points :

x changes by +4 (from -4 to 0)

y changes by -4 (from 0 to -4).

the slope m is then

-4/+4 = -1

and the y-intercept is -4 (as explained).

so, the line is

y = -x - 4

and the graphic says that all values greater than our equal to the line values are valid, so

y >= -x - 4