Using a system of equations, it is found that since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.
For the system, we consider that:
x is the number of books on the first shelf.y is the number of books on the second shelf.z is the number of books on the third shelf.In total, there are 152 books, hence:
[tex]x + y + z = 152[/tex]
The first shelf has 7 fewer books than the second shelf, hence:
[tex]x = y - 7[/tex]
Also, it has 11 more books than the third shelf, hence:
[tex]x = z + 11[/tex]
Then:
[tex]y - 7 = z + 11[/tex]
[tex]z = y - 18[/tex]
Then, replacing in the first equation:
[tex]x + y + z = 152[/tex]
[tex]y - 7 + y + y - 18 = 152[/tex]
[tex]3y = 177[/tex]
[tex]y = \frac{177}{3}[/tex]
[tex]y = 59[/tex]
The number of books in each shelf has to be countable, that is, cannot be decimal.
Then, since the solution of the system does not involve decimal numbers, it is possible to arrange the books in this way.To learn more about system of equations, you can take a look at https://brainly.com/question/14183076
PLEASE HELP WILL MARK BRAINIEST!!!!!
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.
Find the square (8m-7)^2
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.
Hello plz help with these two.
Problem 1
Answer: Choice D--------------
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
Answer: Choice A--------------
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.
Which term has the definition "A relationship in which two variables change at the same rate
what is the slope of (8,3) (-5,3)
Answer:
-13x. (I think)
Step-by-step explanation:
The perimeter of the shape is
feet.
Answer:
This doens't realy make sense dude
If I have a 93.3 in my class and I took a test, got 75% on it (the test is worth 20 points) what would my grade be? I need help ASAP!!!!
Answer:
it will be an 91 or 88
Step-by-step explanation:
2/7>b+5/7 solve the inequality
[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]
Can someone help with this math problem?
Answer:
Hope it will help you a lot.
Which fractions are equivalent to the fraction below. 20/32
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.
Josh and Adelina are staff members for a political candidate. They are considering hiring callers who will call voters and ask for donations. (picture below)
a) only adelina's
b) only josh's
c) both statements are correct
d) neither statements are correct
Answer:
Adelina
Step-by-step explanation:
A rectangle has a perimeter of 270cm and its length is 2½cm times its width find its width
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.)
rotate segment AE about point F 144 degrees
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
It was in -5 degrees Celsius Copenhagen and -10 degrees Celsius in Oslo. Which city was
colder?
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!
Enter the correct answer in the box. Write your answer in the form y = mx + b, using the appropriate inequality symbol in place of the equal sign. HELP MEEE ASAPPPP ILL GIVE BRAINLIEST!!!!!!
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
Which inequality represents this statement?
The product of −6 and a number is no less than −12.
−6n≤−12
−6n>−12
−6n≥−12
−6n<−12
Answer:
−6n≥−12
Step-by-step explanation:
The correct inequality to show the given statement is,
⇒ - 6n ≥ - 12
Where, 'n' is any number.
What is Inequality?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
Pls answer this question
Yesterday, 5/6 of the 120 students in a contest gave their speeches. How many students gave their speeches.
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.
2. Find the equation of the perpendicular bisector of line PQ where the co-ordinates of P and Q are P (-2, 8) and Q (4,7)
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
A book store is hosting a special night in which familles can enjoy a story and craft time. Tickets to the event must be bought ahead of time and are $1.50 for children and $2.50 for adults. So far, 45 children's tickets have been sold, which is 60% of the total tickets sold. How many tickets have been sold so far? Show or explain how you got your answer.steps please
Answer:
45
Step-by-step explanation:
just typing this so I'll have 20
16,40 and 56 LCM
Solve this problem
Answer:
LCM = 2^4 x 5^1 x 7^1 = 560
Step-by-step explanation:
I hope this helps you !!A sum of $1290 is to be divided between two people in the ratio of 7 to 8. How much does each person receive?
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]
9. Sofija buys a bracelet for $14.50 plus 8% tax.
Momoka buys a necklace for $12 plus 8% tax.
Enter the sum, in dollars, that Sofija and
Momoka paid, including tax.
Answer:
$12.96
Step-by-step explanation:
Before Tax Price: $12.00
Sale Tax: 8.00% or $0.96
After Tax Price: $12.96
Getting trained and licensed as a truck driver involves a one-time cost of $450. Gas and insurance end up costing about $2 per mile. For the first delivery, you will get paid $350 plus $6 per mile that you drive. Write 2 equations and solve this system.
The question is an illustration of a system of linear equations.
The system of linear equations is: [tex]y=450 + 2x[/tex] and [tex]y = 350 + 6x[/tex]The solution to the equation is (25,500)Let the number of miles be x.
Getting trained and licensed
One time cost: $450Gas and Insurance: $2 per mileSo, the equation is:
[tex]y=450 + 2x[/tex]
Delivery
First delivery: $350Rate: $6 per mileSo, 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
QUESTION 22 PLEASE HELP ME!!!!
Answer:
the answer is infinite
Step-by-step explanation:
would u like me to explain?
A desk drawer is shaped like a rectangular prism. The height of the drawer is 7 inches. The bottom of the drawer has an area of 210 square inches.
What is the volume of the desk drawer?
Enter your answer in the box.
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
Kaitlyn drove 360 miles in 9 hours. If she continues driving at the same speed, how far will she have driven in 11 hours?
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! :)
10x-9y=24
y= x-2
find x and y
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
Help me plzzzzzzz! I need this today!
Answer:
it looks like y int is about 2550
Step-by-step explanation:
Evaluate the expression when x = 8 and y = 1.
x2y
Answer:
1/8
Step-by-step explanation:
I took the test this is it
PLEASE HELP WILL MARK BRAINIEST!!!!!!!
Answer:
Option a is the best method with compass and straight edge.
Step-by-step explanation: