Answer: The students can be divided into 7 groups.
Each group will have 3 boys and 8 girls.
Step-by-step explanation:
There are 21 boys and 56 girls.
To divide them so that each group has the same number of both boys and girls.
We find GCD(21,56).
21 = 3 x 7
56 = 2 x 2 x 2 x 7
GCD (21,56) = 7
So, the students can be divided into 7 groups.
Number of girls in each group = [tex]\dfrac{56}{7}=8[/tex]
Number of boys in each group = [tex]\dfrac{21}{7}=3[/tex]
So, each group will have 3 boys and 8 girls.
The value of
y
is directly proportional to the value of
x
.
x
.
if
y
=
42
y
=
42
when
x
=
84
,
x
=
84
,
what is the value of
y
y
when
x
=
35
x
=
35
Answer:
y = 17.5
Step-by-step explanation:
Given that y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 42 when x = 84, then
42 = 84k ( divide both sides by 84 )
0.5 = k
y = 0.5x ← equation of proportion
When x = 35, then
y = 0.5 × 35 = 17.5
A small cab carries 4 people. How many small cabs will I need to transport 44 people?
Verify 1) x³+y³=(x+y)(x²-xy+y²)
2) x³-y³=(x-y)(x²+xy+y²)
using some non-zero positive integers and check by actual multiplication. can you call these as identities?
x³ + y³ = (x + y)(x² - xy + y²)
x³ - y³ = (x - y)(x² + xy + y²).
Proof for 1st Identity :
★ x³ + y³ = x (x² - xy + y²) + y(x² - xy + y²)
⟶ x³ + y³ = x³ - x²y + xy² + x²y - xy² + y³
⟶ x³ + y³ = x³ + y³
Proof for 2nd identity :
★ x³ - y³ = x(x² + xy + y²) - y(x² + xy + y²)
⟶ x³ - y³ = x³ + x²y + xy² - x²y - xy² - y³
⟶ x³ - y³ = x³ - y³
For example,Let us assume that,
x = 1
y = 2
So,
✯ x³ + y³ = 1³ + 2³
⟹ (x + y)(x² - xy + y²) = 1 + 8
⟹ (1 + 2)(1² - (1)(2) + 2²) = 9
⟹ 3 * (1 - 2 + 4) = 9
⟹ 3 * 3 = 9
⟹ 9 = 9
✯ x³ - y³ = 1³ - 2³
⟹ (1 - 2) * (1² + (1)(2) + 2²) = 1 - 8
⟹ ( - 1) * (1 + 2 + 4) = - 7
⟹ ( - 1) * (7) = - 7
⟹ - 7 = - 7
Thus , they can be called as identities/formulae as they are very useful in finding the value of a certain equation or an expression easily.
I hope it will help you.
Regards.
What is the solution to 3x-10x+5=5x+17
Answer:
x = -1
Step-by-step explanation:
3x - 10x + 5 = 5x + 17 (collect like terms)
-7x + 5 = 5x + 17 (subtract 5x on both sides)
-12x + 5 = 17 ( subtract 5 on each side)
-12x = 12 ( divide by -12 on each side)
x = -1
Answer:
x = - 1
Step-by-step explanation:
[tex]3x - 10x + 5 = 5x + 17[/tex]
Add the like terms.
[tex] - 7x + 5 = 5x + 17[/tex]
Add 7x to both sides.
[tex]5 = 12x + 17[/tex]
Subtract 17 from both sides.
[tex] - 12 = 12x[/tex]
[tex] - \frac{12}{12} = x[/tex]
[tex] - 1 = x[/tex]
As an estimation we are told 5 miles is 8 km.
Convert 44 km to miles.
Answer:
44 km converte to miles is 27.3403.
Answer:
27,5 miles
Step-by-step explanation:
sooo, you need to see how many Miles Is 1km..
5:8= 0,625
So when we know 0,625 mile = 1km then
44x0,625 = 27,5
And the result is 27,5 miles
What is the average rate of change in height over the entire 5 seconds?
Answer:“To get the average rate of change between 2 points...” To get the average rate of change between 2 points, plug in their coordinate values into the equation (y2-y1)/(x2-x1). The values come from the points (x1,y1) and (x2,y2).
Step-by-step explanation:
Question in picture please answer
Answer:
-16
Step-by-step explanation:
-2=2+V/4
-V/4=2+2
-V/4=4
-V=4x4
-V=16
V=-16
Find ABC, Please help!
Answer:
50°
Step-by-step explanation:
Angle A = AngleB (Corresponding angles)
x=2x-50
x=50°
Hope it helps
Answer:
∠ ABC = 50°
Step-by-step explanation:
2x - 50 and x are corresponding angles and congruent, thus
2x - 50 = x ( subtract x from both sides )
x - 50 = 0 ( add 50 to both sides )
x = 50
Thus
∠ ABC = x = 50°
- 2/3 × 3/5 + 5/2 - 3/5 × 1/6
Answer:
2
Step-by-step explanation:
(-2/3 x 3/5) + 5/2 - (3/5 x 1/6)
-2/3 x 3/5 = -6/15 = -2/5 (simplified)
3/5 x 1/6 = 3/30 = 1/10 (simplified)
Changed equation: -2/5 + 5/2 - 1/10
-2/5 x 2 = -4/10
5/2 x 5 = 25/10
Changed equation: -4/10 + 25/10 - 1/10
Answer: 20/10 = 2 (simplified answer)
Two less than seven times a number c is written as
That's your answer .
HW DUE IN A FEW MINS PLZ HELP ASAPPPPP
Step-by-step explanation:
sorry for too many pictures and I'm sorry for messing up other question numbers but that's that
hope u get it in time
Please please help meee
Answer:
<X= 111 , <Y= 69, <Z 111
Step-by-step explanation:
X and Z are corresponding
solve for Y
180-111= 69
A bag contains 12 blue blue marbles and 8 red marbles what is the ratio of the blue marbles to red marbles
Answer:
12:8 or 12 to 8 or u could do it in fraction form
Step-by-step explanation:
Answer:
12:8 or 12 to 8
Explanation:
The ratio of blue marbles to red marbles is 12 to 8
How do I turn a equation to factored form
Answer:
what equation is it?? bc it's important to know witch one
How do you know if an equation has one solution, no solutions, or infinitely many solutions?
Answer:
Summary. If the equation ends with a false statement (ex: 0=3) then you know that there's no solution. If the equation ends with a true statement (ex: 2=2) then you know that there's infinitely many solutions or all real numbers.
Step-by-step explanation:
To determine whether an equation has one solution, no solutions, or infinitely many solutions, we need to examine the relationship between the variables and the consistency of the equation.
Here are the general guidelines:
1. One Solution: An equation has one solution if the variables can be assigned specific values that satisfy the equation, resulting in a unique solution. When solving the equation, you will find a specific value or set of values for the variables that make the equation true. The solution is often a numerical value or a specific point in a coordinate system.
2. No Solutions: An equation has no solutions if there is no value or combination of values for the variables that satisfy the equation. When solving the equation, you will arrive at a contradiction or an inconsistency. For example, if you encounter a statement like 2 = 5 during the solution process, it indicates that the equation has no solutions.
3. Infinitely Many Solutions: An equation has infinitely many solutions if any value assigned to the variables will satisfy the equation. This typically occurs when the equation is an identity or when there are variables on both sides of the equation that cancel out during the solution process, resulting in the equation always being true. In such cases, any value can be substituted for the variables, and the equation will remain true.
Determining the nature of the solutions often involves algebraic manipulation, simplification, and analysis of the equation to determine if it is consistent, inconsistent, or an identity.
Learn more about equation here
https://brainly.com/question/12385602
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Heeeeeeeeelp pls I need help
Answer:
I am pretty sure that is is 64
Step-by-step explanation:
but i used a calculator soooo
A fishing boat with two people on it runs out of gas while out in a bay. The people set off an emergency flare from a height of 2 meters above the water. The flare has an initial vertical velocity og 30 meters per second. How long does it take the flare to reach its maximum height? What is that height?
Answer:
Step-by-step explanation:
time taken to reach the max height is expressed according to the projectile equation;
tmax = u/g
Given u = 30m/s
g is the acceleration due to gravity = 9.81
t = 30/9.81
t = 3.0secs
hence it will take the flare 3.06secs to reach its maximum height.
Max height = u²/2g
Max height = 30²/2(9.81)
Max height = 900/19.62
Max height = 45.87m
If the people set off an emergency flare from a height of 2 meters above the water, the total height will be 45.87 + 2 = 47.87m
Carl is planning out his route for an upcoming race. He uses negative numbers to represent points before the finish line and positive numbers to represent points past the finish line. On Carl's map, the last water station is at − 27 1 4 −27 4 1 minus, 27, start fraction, 1, divided by, 4, end fraction meters, and his family is watching him at 9 1 2 9 2 1 9, start fraction, 1, divided by, 2, end fraction meters. What does 0 00 meters represent?
Answer:
0 represents the start point
Step-by-step explanation:
Given
[tex]Before\ Finish\ Line = -27\frac{1}{4}[/tex]
[tex]After\ Finish\ Line = 9\frac{1}{2}[/tex]
Required
What does 0 represents
In a race; there's always a starting point, irrespective of the current position of the racer.
This position is always at the 0 point.
Hence:
The 0 meters represents the start point
Answer:
The finish line
#2: Tell whether the function below is linear or exponential.
y = 4 • 2^x
Answers
O Linear
O Exponential
Answer:
Exponential
Step-by-step explanation:
For this question you need to understand what is a linear function and what is an exponential function.
Linear function is a function where any variable x,y,z has the power of maximum 1 for example
x+y=1
7x+2y=10
1000x+9999y=40000
The numbers look too big but its the same category as linear function because all the variable in the equation are to the power of 1
Whereas, An exponential function is a mathematical function of the following form: [tex]y=a^x[/tex] where x is a variable, and a is a constant called the base of the function. Most commonly exponential functions are involved with mathematical symbol [tex]e[/tex].
So in your question [tex]y=4.2^x[/tex] where x the variable has become the power/degree the fucntion is an exponential function.
Carl drives to the beach at 50 mph. When he returns home he is able to travel at 55
mph. Assuming the trip home takes him a half hour less, find the distance to the beach.
Answer:
the distance to the beach is 27.5 miles (multiple choice is under rated)
HELP PLEASEEEE!!
Choose the equation with the correct grouping symbols.
A. 45 + 45 ÷ (3 ÷ 3) = 20
B. 45 + [45 ÷ (3 ÷ 3)] = 20
C. [45 + (45 ÷ 3)] ÷ 3 = 20
D. 45 + (45 + 3 ÷ 3) = 20
Answer:
C
Step-by-step explanation:
(45+(15))/3=20
In a certain Algebra 2 class of 28 students, 9 of them play basketball and 17 of them
play baseball. There are 6 students who play neither sport. What is the probability
that a student chosen randomly from the class plays both basketball and baseball?
Answer: Probability of a student playing both basketball and baseball is 4/28 or 14.3%
Step-by-step explanation:
1) Students playing atleast one sport = 28 - 6 = 22
2) N(Basketball ∩ Baseball) = N(Basketball) + N(Baseball) - N (Basketball U Baseball)
N(Basketball ∩ Baseball) = 9 + 17 - 22 = 4
3) Number of students playing both basketball and baseball = 4
Total number of students = 28
Probability of a student playing both basketball and baseball is 4/28
4/28= 0.1428571429 x 100%= 14.3%
Answer:4/28
Step-by-step explanation:4/28
6(x-2=4(x+3) what does x equal
Hey mate here is your answer.
➛ 6(x-2) = 4(x+3)
➛ 6x-12 = 4x + 12
➛ 6x - 4x = 12 + 12
➛ 2x = 24
➛ x = [tex] \frac{24}{2} [/tex]
⛬ x = 12
ANSWER!!!!! PLEASE!!!!!! QUCKLY NOWWW!!!!
A candy manufacturing plant manufactures 18,000 pieces of candy in an 12 hour shift. The candy produced varies directly with the hours worked. How many pieces of candy can be manufactured in a 4 hour shift?
Answer:
6000 pieces of candy will be made in a 4 hour shift
Step-by-step explanation:
the ratio is 18000/12 if you find the unit it would be 1,500 pieces per 1 hour. multiply that by 4 and you would get 6000.
please help thank you!!!
Answer:
s = 11.7 ft
Step-by-step explanation:
The bedroom is square, and the area A is equal to 137 ft^2.
Since the area formula for a square is A = s^2, s = √A.
Here, s = √137 ft, or s = 11.7 ft (to the nearest tenth of a ft)
Which statement describes the behavior of the graph of the function shown at the vertical asymptotes?
As x approaches -7 from the left, y approaches ∞.
As x approaches -7 from the right, y approaches -∞.
As x approaches 7 from the left, y approaches –∞.
As x approaches 7 from the right, y approaches –∞.
Answer:
its D
Step-by-step explanation:
if you look at the graph I shared, the end behaviors are
As x approaches -7 from the left, y approaches -∞.
As x approaches -7 from the right, y approaches ∞.
As x approaches 7 from the left, y approaches ∞.
As x approaches 7 from the right, y approaches –∞.
The only one that maches this description is D
Answer:d
Step-by-step explanation:
just d
Shannon's little brother is 7 weeks old. She is exactly
3 years and 3 days older than he is. How old is Shannon in days?
Assume that a year is 365 days.
Answer:
1147 days
Step-by-step explanation:
3x365= 1095
7x7=49
1095+49+3=1147
Using elimination method.
1:x+y=16
x-y=0
Answer:
x = 8 and y = 8
Step-by-step explanation:
Giving equations:
x + y = 16
x - y = 0
Unknown:
Find the values of x and y= ?
Solution:
x + y = 16 ---- (i)
x - y = 0 ------(ii)
Add i and ii:
2x = 16
x = 8
Subtract i and ii;
2y = 16
y = 8
Add my snaq k1nglean if anyone wants to ttrade you gotta be 16+
1. Five times a number minus 4 is 6.