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
2 with the radical of 32
What are the domain and range of the function below? (In picture)
Answer:
Domain: [0 , ∞)
Range: (-∞ , 4]
Step-by-step explanation:
I) DOMAIN:For domain, look along the x axis.
The graph starts from x = 0 and it's ending point isn't given in the graph as it continues moving along the positive x axis.
Hence, it's ending point must be ∞
Domain of a function is:
[minimum point in x, maximum point in x]
=> [0, ∞)
"),(" is used for infinity.
"],[" for points that lie within the domain of the function.
II) RANGEFor range, look along the y axis.
The graph starts at y = 4, and continues moving downwards till infinity.
Range:
[minimum in y, maximum in y]
=> (-∞, 4]
For parenthesis, same rule as domain will be applied. 4 is naturally greater than all values in negative. Hence, maximum point will be 4 and minimum will be -∞.find the angle of rotation that maps point D onto point A
Answer:
A - 144
Step-by-step explanation:
everything else would be too far
TV that usually sells for $180.59 is on sale for 20% off. If sales tax on the TV is 9%, what is the price of the TV, including tax?
Answer:
157.47448
Step-by-step explanation:
here you go i did all the math hope this helped
Answer:
128.2189
Step-by-step explanation:
thats the price of the TV including tax
Troy is buying a car that costs $15,000. He
plans to get a 5-year loan to pay for it. He
can get a loan for $15,000 or he can pay
$3,000 from his savings and get a loan
for the rest. The savings account pays 2%
simple interest per year. The simple interest
rate for the loan is 0.5% per year.
a. How much interest over a 5-year
Answer:
300/75
Step-by-step explanation:
Cost of the Car = $15,000
a) Rate of interest received on savings(r) = 2%
Amount in savings account(p) =$3000
Time period(t) = 5 years
simple intrest.
Interest received on savings account = $300
b) Rate of interest on loan = 0.5%
IF P= 15000
intrest.
Difference between the interest = $75
c) Taking loan of the whole amount that is of $15,000 is more reasonable because though the interest is more but Troy will receive interest($300) from his savings account as well. But if he withdraws $3000 from savings and takes the loan for the rest of the amount, he would have no earnings.
what is /12x^8| /3x2 in simplest form where x>0
Answer:
2x^3
C
Step-by-step explanation:
Anita earns 40 points every time she shops at Brookshire's. She needs a total of 1,500 points to receive a free set of dishes. So far she has earned 300 points. How many more times will Anita need to shop at the grocery store to earn the points she needs to earn the dishes?
a. 1800
b. 30
c. 1200
d. 45
We know that:
1500 - 300 = required points to receive a free set of dishes1 day = 40 points.Now, let's simplify.
=> 1500 - 300 = required points to receive a free set of dishes=> 1200 = required points to receive a free set of dishes=> 1 time = 40 points=> 1 time × 30 = 40 × 30 [30 x 40 = 1200]=> 30 times = 1200 pointsConclusion:Therefore, Anita will need to visit Brookshire 30 more times to receive a free set of dishes.
Hoped this helped
[tex]BrainiacUser1357[/tex]
you went to a coffee house with 2 friends and ordered an iced coffee and dessert which came to $12.96 how much will each pay if they share in paying the total bill
Answer:
x+y=12.96, or 12.96=y=x then you can solve for x and then the other half of the total is the other amount
Which equation describes the line shown in the graph?
Answer:
D
Step-by-step explanation:
:)
Answer asap! Need help before I go to sleep.
Answer:
Step-by-step explanation:
y = (4/7)x - 1
Please help with this!
Answer:
I think this is the answer
Step-by-step explanation:
p= x+2+x+9+2x
Simplified
4xin+11in
Need help on True or False PLEASE answer!!!!
Answer:
Step-by-step explanation:
1. False
2. False
3. True
4. True
5. True
6. True
7. True
8. True
9. True
Please explain how you got to the answer. I am trying to understand the concept that went into it.
Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
A. x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
B. x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
C. x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
D.x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Answer:
D. x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Step-by-step explanation:
Evaluate 0 and 1 (xe+ex)Dx
Which of the following best describes the slope of the line below?
Answer:
Negative
Step-by-step explanation:
The slope of the line is negative because when looking at the graph, you can see that the line starts in the 2nd quadrant and ends in the 4th.
OMG HELP RN I MARK BARINLIST
Which of the following correctly describes the solutions to the inequality?
A.
There are an infinite number of solutions. The solutions are all numbers less than 2.
B.
There are an infinite number of solutions. The solutions are all numbers greater than 2.
C.
There are 7 solutions. The solutions are the numbers between 2 and 8.
D.
There are 4 solutions. The solutions are the numbers between -2 and 1.
Answer:
B
Step-by-step explanation:
The dot on 2 is an open spot, so 2 isn't part of the solution. the arrow points towards +∞ so, yeah. b
i need help plz
thanks
128x^2-162
How do you factor this
If any doubt leave a comment
Solve using substitution. (Explanation too please)
y = 7x + 2
y = 10x − 1
Expressions equivalent to 8 to the negative 2 power times 3 to the negative 2 power
Answer:
0.0007361111111111111+0.001;
0.0027361111111111111-0.001;
1.0017361111111111111-1;
Step-by-step explanation:
you calculate 8^(-2)*3^(-2) that gives you 0.0017361111111111111 and then you add 1 anywhere you want and then say -1 where you put that +1 and that's all
Write an equation in slope-intercept form for the line with slope 6 and y-intercept -3
Answer:
y = 6x - 3
Step-by-step explanation:
What’s the difference for this equation!!!
Answer:
2x^2 + 11x – 1
Step-by-step explanation:
In Ms. Rivera’s desk, there are 14 yellow markers. There are 8 more pink markers than yellow markers, and 6 more blue than pink. How many markers does Mrs. Rivera have in her desk?
Answer:
64
Step-by-step explanation:
since ms. rivera has 8 more pink markers than yellow markers you would add 8 and get 22, so she has 22 pink markers and 14 yellow. for the blue markers it says she has 6 more blue markets than pink so you would add 6 to the 22 pink markers and get 28.
So ms. rivera has 14 yellow, 22 pink, 28 blue
add them all together and you get 64.
The total number of markers Mrs. Rivera have in her desk is 64.
Given that, Ms. Rivera’s desk, there are 14 yellow markers.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the total number of markers be x.
There are 8 more pink markers than yellow markers
So, number of pink markers = 14+8
= 22
There are 6 more blue markers than pink markers
So, number of blue markers = 22+6
= 28
Here, x= Number of yellow markers + Number of pink markers + Number of blue markers
= 14+22+28
= 64
Therefore, the total number of markers Mrs. Rivera have in her desk is 64.
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A scuba diver descends farther down into the ocean from an initial depth of 12.8 feet below sea level. The scuba diver descends at a constant rate for 312 minutes and reaches a depth no more than 49.2 feet below sea level.
What is the maximum rate, r, that the scuba diver may descend?
r≥10.4
r≤10.4
r≥13 7/9
r≤13 7/9
Answer:
[tex]r \geqslant 10.4[/tex]
The maximum rate at which the diver will descend will be 7 feet per hour.
What is the rate of change?The rate of change is the change of a quantity over 1 unit of another quantity.
Most of the time the rate of change is the change with respect to time.
For example the speed 3meter/second.
As per the given,
Initial depth of scuba diver = 12.8 feet
Let's say the rate of a scuba diver is "r".
Initial depth + depth cover with constant rate ≤ final depth
12.8 + (312/60)r ≤ 49.2
r ≤ 7
Thus, the maximum rate at which a diver can descend is 7 feet per hour.
Hence"The maximum rate at which the diver will descend will be 7 feet per hour".
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The Hayes family and the Rodrigues family use their sprinklers last summer. The water output rate for the Hayes family sprinkler was 15 L per hour. The water Output rate for the Rodriguez family speakers is 30 L per hour.Families used their sprinklers for a combined total of 75 hour result in a total water of output of 1725 L how long was a sprinkler used?
Answer:
Hayes family: 35 hoursRodrigues family: 40 hoursStep-by-step explanation:
Let x and y represent the usage hours by the Hayes and Rodrigues families, respectively. The problem statement gives us relations that can be used to write equations for volume of use and for total hours.
15x +30y = 1725 . . . . . total liters of use
x + y = 75 . . . . . . . . . total hours of use
The second equation lets us write an expression for y:
y = 75 -x
This can be substituted into the first equation to give ...
15x +30(75 -x) = 1725
-15x + 2250 = 1725 . . . . . . simplify
-15x = -525 . . . . . . . . . . . subtract 2250
x = 35 . . . . . . . . . . . . . . divide by -15
y = 75 -35 = 40
The Hayes family used their sprinklers for 35 hours; the Rodrigues family used theirs for 40 hours.
Joe wants to build a doll house for his daughter. He wants the doll house to look just like his house. His house is 29 feet wide and 32 feet tall at the highest point of the roof. If the dollhouse will be 2.5 feet wide, how many feet will its highest point be? (Round your answer to one decimal place.)
Answer:
3.5 feet
Step-by-step explanation:
The highest point of the dollhouse will be 2.76 feet.
What is proportion?A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio.
Given that,
The width of house = 29 feet.
And the height of the house = 32 feet.
Also, the width of dollhouse = 2.5 feet
Let the height of the doll is x feet.
To find the value of x,
Use proportion property,
29 / 32 = 2.5 / x
x = (32 × 2.5) / 29
x = 80 / 29
x = 2.758
the height of the doll is 2.76 feet.
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please help me out on this one
Answer:
6/6 or 1
Step-by-step explanation:
bow tie method
7/8 = ?/48
A. 1
B. 42
C. 6
D. 13
7/8= B. 42/48
#HOPE THIS HELP
Michael is saving money to buy a bike. So far, he
has saved $25 which is four-fifths of the total cost
of the bike. How much does the bike cost?
Let X = total cost of game
(4/5) X = $25
Multiply both sides of equation by 5/3
(5/3)(3/5) X = (5/3) $25
X = $35
Can anyone help with this?
what do i do for the 2 boxes circled in purple? help!