Tyler is packing lunches for a local youth program. He has 36 sandwiches, 72 apples, and 108 granola bars. What is the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars? How many of each item will the lunch contain?
Answer:
The greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.
Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars
Step-by-step explanation:
The greatest common divisor (GCD) of two or more numbers is the largest number by which these numbers can be divided, that is, it is the largest number that divides them all exactly.
In other words, the greatest common divisor of two numbers a and b is the largest number that divides a and divides b.
To find the greatest common divisor of two or more numbers, you start by breaking those numbers down into prime factors. In this case:
36=2²*3²
72 = 2³*3²
108 = 2²*3
The greatest common divisor is obtained by choosing only the prime factors common to the numbers, raised to the smallest exponent. That is, you choose only the common factors and those that are repeated must be raised to the minimum exponent.
The 2 appears as a prime factor in the three decompositions, whose minimum exponent is 2.
3 also appears as a common factor, whose minimum exponent is 1.
By doing the multiplication to get the greatest common divisor, you get:
2²*3=12
So the greatest number of lunches he can pack so that each lunch has an equal number of sandwiches, apples, and granola bars is 12.
To calculate how many lunches each item will contain, you simply divide the amount you have of each item by the most lunches Tyler can pack, 12.
Sandwiches: 36÷12= 3
Apples: 72÷12= 6
Granola bars: 108÷12= 9
Each lunch will contain 3 sandwiches, 6 apples and 9 granola bars
What is the slope of the line containing the points (-8, 1) and (4,7)?
Which choices are in the solution set of the equation below? Check all that
apply.
10x = 30
A. 3.5
B. 1.5
C. 1
D1/3
E. 5
F. 3
Rewrite the expression in the form z n z n z, start superscript, n, end superscript. Z − 1 3 z − 5 6 = z − 6 5 z − 3 1 =start fraction, z, start superscript, start superscript, minus, start fraction, 1, divided by, 3, end fraction, end superscript, end superscript, divided by, z, start superscript, start superscript, minus, start fraction, 5, divided by, 6, end fraction, end superscript, end superscript, end fraction, equals () Stuck
Answer:
[tex]2z^4[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{z^{-1}}{3} \div\frac{z^{-5}}{6}[/tex], we are to write it in the form of [tex]nz^n[/tex]. To do that we will simplify the given indicinal expression as shown;
[tex]\dfrac{z^{-1}}{3} \div\dfrac{z^{-5}}{6}\\= \dfrac{z^{-1}}{3} \times\dfrac{6}{z^{-5}}\\= \dfrac{6z^{-1}}{3z^{-5}}\\ = \dfrac{2z^{-1}}{z^{-5}}\\[/tex]
According to indices [tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex], the resulting equation will become;
[tex]= \dfrac{2z^{-1}}{z^{-5}}\\= 2z^{-1-(-5)}\\= 2z^{-1+5}\\= 2z^{4}[/tex]
Hence expression in the form [tex]nz^n \ is \ 2z^4[/tex].
Answer:
9z
Step-by-step explanation:
Khan Academy
If (72)p = 76, what is the value of p?
2
3
4
8
Answer:
it would be +2
Step-by-step explanation:
the equation would be (72)+2= 76
Answer: Positive 2
Step-by-step explanation:
my brain is just cool like that
What’s the value of x
7x -1 + 9x + 5 = 180
16x = 180 - 5 + 1
16x = 176
x = 176/16
x = 11
Step-by-step explanation:
(7x-1)+(9x+5)=180 ( since its a straight line )
16x+4=180
x= 11
How do I add Rational Numbers I never really understand how my online school teaches it.
Answer:
1. To add or subtract rational expressions with unlike denominators, first find the LCM of the denominator. ...
2. Write each expression using the LCD. ...
3. Add or subtract the numerators.
4. Simplify as needed.
Is X =5 a solution to the equation X -3x+10=5?− 3 x + 10 = 5 ?
Answer:
No; x=1.6
Step-by-step explanation:
The John Jay Theater Dept has tickets at $6 for adults, $4 for teachers, and $2 for students. A total of 280 tickets were sold for one showing with a total revenue of $1010. If the number of adult tickets sold was twice the number of teacher tickets, how many of each type of ticket were sold for the showing?
Answer:
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Step-by-step explanation:
Cost of tickets
Adults = $6
Teachers = $4
Students = $2
Total tickets sold = 280
Total revenue = $1010
Let
x = number of adults tickets
y = number of teachers tickets
z = number of students tickets
x + y + z = 280
6x + 4y + 2z = 1010
If the number of adult tickets sold was twice the number of teacher tickets
x = 2y
Substitute x=2y into the equations
x + y + z = 280
6x + 4y + 2z = 1010
2y + y + z = 280
6(2y) + 4y + 2z = 1010
3y + z = 280
12y + 4y + 2z = 1010
3y + z = 280 (1)
16y + 2z = 1010 (2)
Multiply (1) by 2
6y + 2z = 560 (3)
16y + 2z = 1010
Subtract (3) from (2)
16y - 6y = 1010 - 560
10y = 450
Divide both sides by 10
y = 450/10
= 45
y = 45
Substitute y=45 into (1)
3y + z = 280
3(45) + z = 280
135 + z = 280
z = 280 - 135
= 145
z = 145
Substitute the values of y and z into
x + y + z = 280
x + 45 + 145 = 280
x + 190 = 280
x = 280 - 190
= 90
x = 90
Therefore,
number of adults tickets sold = x = 90
number of teachers tickets = y = 45
number of students tickets = z = 145
Maria cut 3/4 yard of ribbon into pieces that are 1/8 yard long. How many pieces of ribbon did Maria cut? PLEASE HELP MEEEEE!!!
Answer:
6 pieces
Step-by-step explanation:
Solve the absolute value equation. Check
for extraneous solutions.
a. |2x + 5 |= 11
Answer:
3
Step-by-step explanation:
|2x + 5| = 11
2x + 5 = 11
2x = 11 - 5
2x = 6
x = 3
I need help pls!!!
It is really important for my high school assignment!
Answer
Step-by-step explanatio
clause A
pls help me answer this question if correct I'll make brainylist!!!
Answer:
C. 11 3/4
Step-by-step explanation:
3 + 3 + 2 + 2 = 10
1/4 + 3/4 + 1/4 = 1 1/4
1/2 -> 2/4
2/4 + 1 1/4 = 1 3/4
10 + 1 3/4 = 11 3/4
Find x to the nearest hundredth place.
Answer:
C. 24.27 cm
Step-by-step explanation:
sin 65° = opposite ÷ hypotenuse
sin 65° = 22/x
multiply both sides of the equation by x
(sin 65°)x = 22
divide both sides of the equation by sin 65°
x = 22 ÷ sin 65°
punch in 65 sin into your calculator
x = 22 ÷ 0.90631
x = 24.27 cm
A stack of 20 coins contains only nickels and
quarters and has a total value of $4. How many of each
coin are in the stack?
Answer:
16 quarters and 4 nickels
4×25=1.00 × 4 = 4.00 4×4=16-quarters
20-16=4-nickels
Step-by-step explanation:
Hope this helps!
s= {(0,5), (-9,3) , (-8 , -8), (3, -9)
whats the domain
Answer:
0,-9,-8,3
Step-by-step explanation:
Domain
0
-9
-8
3
which represents the graph plzz help
Answer:
y=2-1x
Step-by-step explanation:
the would be the answer because the way your line is going
4x3-5x2-17x-8 divided by x+1
Answer:
4x2 - 9x - 8
Step-by-step explanation:
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50.
Complete question:
Benjamin decides to treat himself to breakfast at his favorite restaurant. He orders chocolate milk that costs \$3.25$3.25dollar sign, 3, point, 25. Then, he wants to buy as many pancakes as he can, but he wants his bill to be at most \$30$30dollar sign, 30 before tax. The restaurant only sells pancakes in stacks of 444 pancakes for \$5.50$5.50dollar sign, 5, point, 50. Let SSS represent the number of stacks of pancakes that Benjamin buys. 1) Which inequality describes this scenario?
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Cost of chocolate milk = $3.25
Cost of pancakes = $5.50 (stack of 4)
Number of stacks of pancakes purchased = S
Maximum amount spent ≤ $30
Cost of chocolate + (Cost of pancake stack * number of stacks) ≤ $30
3.25 + 5.50S ≤ 30
5.50S ≤ 30 - 3.25
5.50S ≤ 26.75
S ≤ 26.75 / 5.50
S ≤ 4.86
Hence maximum number of pancake stacks he can purchase without exceeding budget = 4
Hence total number of pancakes = number of stacks * number in a stack
= 4 * 4
= 16
Answer:
Chose option have answer 3.25+5.50S [tex]\leq[/tex] 30
16 pancakes
Step-by-step explanation: If you find answer from Khan please use this answer
An artist has completed
1
4
of a painting in 2 weeks. At what rate is she working?
Answer:
1 painting /8 weeks
Step-by-step explanation:
Answer:
1 full painting every 8 weeks
Step-by-step explanation:
she completed 1/4 every 2 week which is 0.25
if 0.25x4 =1
so if you multiply 2x4 weeks= 8
Solve the system of equations –4x – 4y = -8 and 3x + 7y = –18 by combining
the equations.
Answer:6 im not to sure
Step-by-step explanation:
all integers between -14 and 10
Answer:
-13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Step-by-step explanation:
what 2 integers is the square root of 70 between?
What is the equation of the line y=4x-6
Answer:
B
Step-by-step explanation:
what is 825 divided by 15?
13 + x - 5 + 4x + 2y
Coefficients:
Constants:
Like terms:
Help
Answer:
coefficients: 1, 4
like terms 13, -5 and 1x, 4x
constant: 13, 5
!!!!! HELP PLS will mark brainliest
Anyways, the question isn't clear. Can you get a better screenshot?
Answer:
Domain, -1<x<=6
Range, -3<=y<=5
Step-by-step explanation:
Just trust me
1. Find the value of the polynomial 5 - 3x + 7 at:
(i) x=1
Find the distance between the following two points: *
(3,6) and (9,2)
Answer:
Step-by-step explanation:
(3 , 6 ) ;( 9 , 2)
Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]= \sqrt{(9-3)^{2}+(2-6)^{2}}\\\\=\sqrt{6^{2}+(-4)^{2}}\\\\=\sqrt{36+16}\\\\=\sqrt{52}\\\\=\sqrt{2*2*13}\\\\=2\sqrt{13}[/tex]
[tex] \frac{b - 4}{6 } = \frac{b}{2} [/tex]
Can somene explain how to do this please.
Use cross-multiplication
[tex]\frac{b - 4}{6} = \frac{b}{2}\\2(b- 4) = 6b\\2b - 8 = 6b\\2b - 6b = 8\\-4b = 8\\b = -2[/tex]