The greatest number of goodie bags he can make is 18.
The number of coloring books that would be in each bag is 4
The number of markers that would be in each bag is 5
The number of chocolate that would be in each bag is 18
What is the greatest number of goodie bags he can make?The greatest number of goodie bags he can make can be determined by calculating the highest common factor of 72, 90, 180.
The factor of a number is a number that perfectly divides another number. For example, the factors of 18 are 1, 2, 3, 6, 9, 18. The highest common factor is the highest factor of two or more numbers. The highest common factor of 4 and 8 is 4.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180.
Common factors = 1, 2, 3, 6, 9, 18
Highest common factor = 18
The number of coloring books that would be in each bag = 72 / 18 = 4
The number of markers that would be in each bag =90 / 18 = 5
The number of chocolate that would be in each bag = 180 / 18 = 18
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Solve.
please and thank you!
Answer:
Step-by-step explanation:
2(x+3)/3 + 3(x-6)/2=1-x
2x+6/3 + 3x-18/2=1-x
2(2x+6)/3 + 3(3x-18)=6-6x
4x+12+9x-54=6-6x
13x-49=6-6x
13x+6x=6+42
19x/19=48/19
x=49/19
Joanna went to the farmers market to buy some apples and oranges. She bought 8 oranges and some apples. The cost per orange was $1.79 and the cost per pound of apples was $1.49. Joanna spent a total of $23.26 on apples and oranges at the farmers market.
Let p represent the number of pounds of apples Joanna bought.
Create the equation that symbolizes this situation, and then answer the question below.
$
p + $
= $
Did Joanna buy a total of 5 pounds of apples at the farmers market?
The number of apples that were bought by Joanna is 6 pounds.
How to calculate the value?Let p = the number of pounds of apples Joanna bought.
Let o = oranges
Therefore, the equation will be:
1.49p + 8o = 23.26
1.49p + 1.79 × 8 = 23.26
1.49p + 14.32 = 23.26
1.49p = 23.26 - 14.32
1.49p = 8.94
p = 8.94/1.49
p = 6
No. Joanna didn't buy a total of 5 pounds of apples at the farmers market.
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Construct three different isosceles right triangles. Explain your method. then verify your constructions using measurement and mathematics.
A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle.
What is an Isosceles Right Triangle?A right triangle with a right angle and two sharp angles that are congruent to one another is known as an isosceles right triangle. A right triangle that is also isosceles is known as an isosceles triangle. It therefore has two sides that are identical and one right angle.
A right triangle with two equal-length legs is called an isosceles right triangle. The corresponding angles would also be congruent because the lengths of the two legs of the right triangle are equal. As a result, the two acute angles and two legs of an isosceles right triangle are congruent.
How to construct three different triangles?Constructing triangles will consist of the development of various triangles the use of a protractor, a compass and a ruler.
How constructions will use measurement and mathematics?Construction of triangles is straightforward while the measurements are given to us primarily based totally on extraordinary homes which include SSS, SAS and ASA.
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Simplify each sum or difference. State any restrictions on the variables.
-5 y / 2y-1 - y + 3 / 2y - 1
The simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
As given in the question,
Given expression is [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex]
Simplify the expression by taking the least common multiple
[tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}\\\\= \frac{-5y-y-3}{2y-1}\\ \\= \frac{-6y-3}{2y-1}\\ \\= \frac{-3(2y+1)}{2y-1}[/tex]
Restriction on the variables is given by y ≠1/2.
Therefore, the simplification of each sum or difference of given expression [tex]\frac{-5y}{2y-1} -\frac{y+3}{2y-1}[/tex] is equal to (-3)(2y+1)/ (2y-1). Restriction on the variables is given by y ≠1/2.
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What is the solution of √4 x-23 -3 = 2 ?
The solution of the given equation √(4x-23) - 3 = 2 is (x = 14.25).
What is meant by square numbers?A 'Square Number' is the result of multiplying a number or integer (not really a fraction) by itself.
For instance, 3 multiplied by 3 equals 3 squared, or 3 x 3 = 32. So, in essence, a square number is really the exponential form of multiplying a number or integer by itself. Also, if we multiply the number on its own again, we get the integer's cube, a x a x a = a³.Now, as per the given equation;
√(4x-23) - 3 = 2
This could also be written as;
√(4x-23) = 2 + 3
√(4x-23) = 5
Now, squaring on the both side;
(4x-23) = 25
Open the brackets;
4x - 32 = 25
4x = 25 + 32
4x = 57
x = 14.25
Therefore, the solution of the given equation √(4x-23) - 3 = 2 is calculated as (x = 14.25).
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what is 1492949 x 14232416344123432?
Answer:
2.12482717E22
Step-by-step explanation:
Evaluate each expression for x=0 . (x-4)+12
After evaluating the expression for x=0, the equation (x-4)+12 = 8
⇒ ((0)-4)+12
⇒ -4 + 12
⇒ 8
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Solve the inequality 4-2x>7-3x
Hello,
[tex]4 - 2x > 7 -3x[/tex]
[tex]3x - 2x > 7 - 4[/tex]
[tex]x > 3[/tex]
S = ] 3 ; +∞ [
Find the tenth term of each arithmetic sequence. 15,23,31, ...........
The 10th term of an Arithmetic Progression (AP) is (a₁₀ = 87.)
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between the two mathematical orders is a constant value (AP). Arithmetic Sequence is another name for it.
We'd come across a few important words in AP that were denoted as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP also can be described in aspects of common differences.
The following is the formula for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows: Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the given sequence is; 15,23,31, ...........
Consider the first term is'a₁' = 15
Consider 'a₂' = 23 is the second term.
Consider the third term is 'a₃' = 31
Calculate the common difference;
d = a₂ - a₁
Put the values in the above obtained equation;
d = 23 - 15 = 8
Now, to estimate the value of the 10th term using the formula of nth term.
an = a + (n − 1) × d , n = total number of terms = 10.
Put all the values;
a₁₀ = 15 + (10 - 1) × 8
a₁₀ = 15 + 9 × 8
a₁₀ = 15 + 72
a₁₀ = 87
Therefore, the value of the 10th term is calculated as a₁₀ = 87.
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Write an equation of a line that is perpendicular to y = 6x + 3 that passes through (−6, 4).
Answer:
y = - [tex]\frac{1}{6}[/tex] x + 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x + 3 ← is in slope- intercept form
with slope m = 6
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then
y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (- 6, 4 ) into the partial equation
4 = 1 + c ⇒ c = 4 - 1 = 3
y = - [tex]\frac{1}{6}[/tex] x + 3 ← equation of perpendicular line
Solve each system by substitution. Check your answers.
t = 2r + 3 , 5r - 4t = 6
By substitution, the solution of the system of equations, t = 2r + 3 and 5r - 4t = 6, is (r , t) = (-6 , -9).
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in r and t,
t = 2r + 3 (equation 1)
5r - 4t = 6 (equation 2)
Since the first equation is already expressed in variable t in terms of r, substitute the value of t to the second equation.
5r - 4t = 6 (equation 2)
5r -4(2r + 3) =6
5r - 8r - 12 = 6
Combining all terms containing the variable r on one side and the constants on the other side of the equality, and solving for r.
5r - 8r - 12 = 6
5r - 8r = 6 + 12
-3r = 18
r = -6
Substitute the value of r in the first equation and solve for t.
t = 2r + 3 (equation 1)
t = 2(-6) + 3
t = -12 + 3
t = -9
Hence, the solution of the given system of equations is (r , t) = (-6 , -9).
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12 and 5/6x -14x + 1/6
Answer:
-x
Step-by-step explanation:
12 5/6=77/6
77/6x-14x+1/6x
77/6x+1/6x-14x
78/6x-14x
78/6x-84/6x
-6/6x
-x
Answer:
-9750
Step-by-step explanation:
Joan drives 333.5 miles before she has to buy gas. Her car gets 29 miles per gallon.
How many gallons of gas did the car start out with?
Answer:
11.5 gallons
Step-by-step explanation:
Let the amount of gas be x gallons.
The product of gallons and MPG gives us the number of miles, show this as equation and solve for x:
miles/gallons * gallons = miles29x = 333.5x = 333.5/29x = 11.5solve the inequality
Answer:
the inequality solution is -19
Helpp, practice problems.
By comparing the intercepts of the linear equation with the ones in the graph, we conclude that the given graph corresponds with the linear equation.
How to know if the graph represents the given equation?
Here we have the linear equation:
1.5*s + 3.5*c = 21
And we have a graph, which we want to see if it is the graph of the linear equation.
To check this, we just need to look at the intercepts, the variable "c" is on the vertical axis and the variable "s" is on the horizontal axis.
The "s" intercept is what we get when we take c = 0, replacing that we will get:
1.5*s + 3.5*0 = 21
1.5*s = 21
s = 21/1.5 = 14
This means that the line should pass through the point (14, 0), and we can see that this happens.
The other intercept is what we get when we take s = 0.
1.5*0 + 3.5*c = 21
c = 21/3.5 = 6
The other intercept is at (0, 6), which we also can see on the graph.
With that is enough to conclude that the given graph represents the given linear equation.
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7. Nina has 2/3 cup of shampoo left in the shampoo bottle. She uses 1/8 cup of shampoo to wash her hair. If nina washes her hair every day, how many days can she wait before opening a new bottle of shampoo?
Answer:
5 days
Step-by-step explanation:
Make 1/8 and 2/3 have the same denominator
the Least common multiple is 24
1/8 becomes 3/24 and 2/3 becomes 16/24
she can use it 5 more times with a remainder of 1/24 of a cup of shampoo remaining
Approximate:
A. √370
B. √71
Which equation does NOT represent a direct variation?
a. y=x
b. 2 x-y=5
c. 2 x-y=0
d. 2 x-5 y=0
The graph of 2x - y = 5 does not represent a direct variation.
Direct variation is variation in which the quotient of the two variables is constant. A constant ratio of two quantities means that one quantity varies directly with the other or that the two quantities vary directly. In symbols, the direct variation formula is y=k*x or k=y/x.
k is known as the constant of variation or the constant of proportionality.
This means that as x increases, y increases, and as x decreases, y decreases, and their ratio is always the same.
The graph of the direct variation equation is a straight line through the origin.
The graph of 2x-y =5 does not pass through the origin, so it does not represent a direct variation. (consult the images attached below).
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The continental U.S is about 200 miles wider than Australia.
What number should replace the question mark on the U.S map?
Cole is taking a 170-mile trip by car. If he drives for 2 hours with an average speed of 60 miles per hour, how many miles will he still need to drive to complete his trip?
A: 50
B: 110
C: 120
D: 340
Cola need 50 miles to drive to complete his trip.
Option A is true.
What is Distance?
The total movement of an object without any regard to direction is called distance.
Given that;
Cole is taking a 170-mile trip by car.
He drive for 2 hours with an average speed of 60 miles per hour.
Now, Distance cover in 2 hours with speed 60 miles per hour is calculated as;
Since, Distance = Speed x time
Hence, Distance = 60 x 2 = 120 miles.
So, Remaining speed to complete his trip = 170 - 120 = 50 miles.
Hence, Cola need 50 miles to drive to complete his trip.
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Read the problem. Identify what you need to know. Then organize the data to solve the problem.
Find the probability that a point chosen at random lies in the shaded region.
A. 0.22
B. 0.25
C. 0.28
D. 0.32
The probability that a point is chosen at random will lie in the shaded area will be 0.32.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Here favorable outcomes will be the shaded portion and the total outcome will be the total circular portion.
Favorable Outcome = Area of shaded portion = 1/2 x 18 x 18/2
= 81 inch sq.
Total Outcome = Total area = 81 π inch sq.
Probability, P(E) = 81/ 81 π = 1/32
Hence, the probability that a point chosen at random will lie in the shaded area is 0.32.
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A school allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £48 each and are on offer for
1/6
off.
A train ticket for the day will cost £15 each.
If 2 teachers and the maximum number of students attend, how many students go on the trip
Answer: 38 pounds
Step-by-step explanation: School allots £1500 to spend on a trip to the theatre.
Theatre tickets have a regular cost of £35 each and are on offer for 1/5 off
therefore 4/5*35 = 28 for the tickets
:
A train ticket for the day will cost £15 each.
therefore total cost for each: 28 + 15 = 43 pounds each
:
If 2 teachers and the maximum number of students attend, how much money will the school have left over?
:
let s = no. of students
43(s+2) =< 1500
43s + 86 =< 1500
43s =< 1500 - 86
43s =< 1414
s =< 1414/43
s =< 32.88, 32 students max
:
find how much left over. plus 2 teachers = 34 people
1500 - 43(34) =
1500 - 1462 = 38 pounds left over
PLEASE HELP! i just need someone to check my answer
3y=84 y=?
does it equal 28?
Answer:
yes, because 3 X 28 is 84
Step-by-step explanation:
4y+20x-12=0 solve for y, would appreciate some help, in struggling a bit
Answer:
y = 3 - 5x
Step-by-step explanation:
Answer:
Step-by-step explanation:
4y+20x−12=0
4y−12=−20x
4y=−20x+12
4y=12−20x
4/4y = 12−20x / 4
y= 12−20x / 4
y=3−5x
question is in the picture
Answer:
18 tables: $143
t tables: $35 + $6t
Step-by-step explanation:
35 + 6t
35 + 6(18) = 35 + 108 = 143
Evaluate each expression for the given values of the variables.
4(2m - n) - 3(2m - n) ; m=-15 and n=-18
The result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12
Given,
The algebraic expression = 4(2m - n) - 3(2m - n)
Expand the terms
4(2m - n) - 3(2m - n)= 8m-4n-6m+3n
Combine the like terms
8m-4n-6m+3n = 2m-n
We know,
m= -15
n= -18
Substitute the values in the expression
2m-n= 2(-15)-(-18)
=-30+18
= -12
Hence, the result of the expression 4(2m - n) - 3(2m - n) for the variables m= -15 and n= -18 is -12
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From least to greatest
-17,-4, 7
Answer:
+ 10
Step-by-step explanation:
what is the solution for
-x + 3/7 = 2x - 25/7
?
In linear equation, 4/3 is the solution for equation .
What is linear equation?
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.-x + 3/7 = 2x - 25/7
On solving
- 7x + 3/7 = 14x - 25/7
- 7x + 3 = 14x - 25
14x + 7x = 25 + 3
21x = 28
x = 28/21 = 4/3
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A sequence is defined by a₁ = 4, an = a(n-1) + 4. What is the 6th term of the
sequence?
Hence , the 6th term of the sequence is 24
Arithmetic Progression (AP) could be a sequence of numbers so as, during which the distinction between any 2 consecutive numbers could be a constant worth. it's conjointly known as Arithmetic Sequence. as an example, the series of natural numbers: one, 2, 3, 4, 5, 6,… is associate degree patterned advance, that includes a common distinction between 2 serial terms (say one and 2) adequate to one (2 -1).
It is given that first term is 4 and nth term is a(n) = a(n-1) + 4 ......(1)
Putting n = 6 in equation (2) , we get sixth term
a(6) = 4(6-1) +4
a(6) = 4(5) + 4
a(6) = 20 + 4
a(6) = 24
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Identify the volume of the composite figure. Round to the nearest tenth.
Answer:
860.7 m³ (nearest tenth).
Step-by-step explanation:
The given composite figure appears to be a rectangular prism with a cylinder omitted.
Volume of a rectangular prism
[tex]V=w\:h\:l[/tex]
where:
w = widthh = heightl = lengthVolume of a cylinder
[tex]V=\pi r^2 h[/tex]
where:
r = radiush = heightTherefore, the formula for the volume of the composite figure is:
[tex]\large\boxed{V=whl- \pi r^2h}[/tex]
From inspection of the given diagram:
w = 10 ml = 10 mh = 12 mr = 3 mSubstitute these values into the formula to find the volume of the composite figure:
[tex]\begin{aligned}\implies V&=whl - \pi r^2h\\& = 10 \cdot 12 \cdot 10- \pi \cdot 3^2 \cdot 12\\& = 120 \cdot 10- \pi \cdot 9 \cdot 12\\& = 1200- 108 \pi\\& = 1200 - 339.292006...\\& = 860.7\; \sf m^3\;(nearest\:tenth)\end{aligned}[/tex]
Therefore, the volume of the composite figure is 860.7 m³ (nearest tenth).
