how do i do part (iii). the answer is 2 but i got the answer based on guessing. how do i do this w/o guessing? thank you.
Answers
Answer:
(i) 2² · 3 · 7
(ii) 3024
(iii) k = 16
(iv) 12 cm
Step-by-step explanation:
Part (i)The first few prime numbers are: 2, 3, 5, 7, 11, 13, 17, ...
To find which prime numbers multiply together to make 84, start by dividing 84 by the first prime number, 2:
⇒ 84 ÷ 2 = 42
As 42 is not a prime number, we need to divide again:
⇒ 42 ÷ 2 = 21
As 21 is not a prime number, we need to divide again.
21 is not divisible by 2, so let's try dividing by the next prime number, 3:
⇒ 21 ÷ 3 = 7
As 7 is a prime number, we can stop.
Therefore, 84 is the product of:
⇒ 84 = 2 · 2 · 3 · 7
As 2 appears two times, we can write this using exponents:
⇒ 84 = 2² · 3 · 7
Part (ii)Lowest Common Multiple (LCM): The lowest multiple shared by two or more numbers.
Prime Factors Method of finding LCM
Step 1
Find the prime factorization of each number.
From part (i): 84 = 2² · 3 · 7
Given in part (ii): 432 = 2⁴ · 3³
Step 2
Write each number as a product of primes, matching primes vertically where possible:
[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf LCM & = & 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3 &\cdot & 7\end{array}[/tex]
Step 3
Bring down the primes in each column then multiply the factors to get the LCM:
⇒ LCM = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 7
⇒ LCM = 2⁴ · 3³ · 7
⇒ LCM = 3024
Part (iii)From part (ii) we know that the prime factorization of 432 is:
432 = 2⁴ · 3³
A perfect cube is a number multiplied by itself three times.
One of the factors of 432 is a perfect cube → 3³.
Therefore,
[tex]\begin{aligned}432 & = 2^4 \cdot 3^3\\\\\implies \dfrac{432}{2^4} & = 3^3\\\\\dfrac{432}{16} & = 3^3\end{aligned}[/tex]
So we need to divide 432 by 2⁴ to get the perfect cube 3³.
Therefore,
⇒ k = 2⁴
⇒ k = 2 · 2 · 2 · 2
⇒ k = 16
Part (iv)To find the largest possible length of the side of the square, we need to find the greatest common factor of 432 and 84.
Prime Factors Method of finding GCF
Step 1
Find the prime factorization of each number.
From part (i): 84 = 2² · 3 · 7
Given in part (ii): 432 = 2⁴ · 3³
Step 2
Write each number as a product of primes, matching primes vertically where possible:
[tex]\begin{array}{ r c c c c c c c ccccccccc}84&=& 2 & \cdot & 2 & \cdot & & & & & 3& \cdot & & & && 7\\\\432 &=& 2 & \cdot & 2 &\cdot & 2& \cdot & 2& \cdot & 3& \cdot & 3& \cdot & 3\\\\\cline{1-17} \\\sf GCF & = & 2 & \cdot & 2 & \cdot & & & & & 3& & & & && \end{array}[/tex]
Step 3
Bring down the primes in the columns where both numbers have the factor, then multiply the factors to get the GCF:
⇒ GCF = 2 · 2 · 3
⇒ GCF = 12
Therefore, the largest possible length of the side of the square is 12 cm.
Related Questions
Givien h(x) = -x- 5, find h(-6)
Answers
Answer:
h(-6) = 1
Step-by-step explanation:
Hello!
Substitute -6 for x in the equation.
Evaluateh(x) = -x - 5h(-6) = -(-6) - 5h(-6) = 6 - 5h(-6) = 1h(-6) is 1.
Question 10
Divide £64 in the ratio 3:5
Answers
Answer:
24:40
Step-by-step explanation:
3:5
This means there are 8 divisions altogether - 8 parts to be split (3+5=8)
64 / 8 = 8
8x3 = 24
8x5 = 40
£24:£40
Hope this makes sense!
Find the linear function represented by the graph.
The slope of the line is
.
The y-intercept of the line is at
.
What linear function is represented by the graph?
Answers
Step-by-step explanation:
photo please ......................
Answer:
Step-by-step explanation:
need to see the graph
Pigeonhole suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. is the following statement true or false:
Answers
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior: FALSE
What is a sophomore?A sophomore in the United States is a student in their second year at an educational institution, usually a secondary school or a college or university, but also other types of post-secondary educational institutions. A sophomore in high school is equivalent to a tenth-grade or Class-10 student.In sports, a sophomore is a professional athlete in their second season.As in the description, it is given that a sophomore in high school is equivalent to a tenth-grade or Class-10 student.
So, the above-given statement becomes false as it says that every student is a sophomore but the class has juniors and seniors.
Therefore, the statement "suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior" is FALSE.
Know more about sophomore here:
https://brainly.com/question/23382435
#SPJ4
The complete question is given below:
Suppose that every student in a discrete mathematics class of 25 students is a sophomore, a junior, or a senior. Is the following statement true or false:
"The course must have at least five sophomores, or at least 20 juniors, or at least 10 seniors."
Which exponential function bests models the graph below?
A.
B.
C.
D.
D.
Answers
Choose the angle name JWT
Answers
The placement of the J and T doesn’t matter as long as the W is in the middle
=. What does the expression (x+3)(9) represent? Why?
Answers
I hope this helps!! :)
Help I need some help due tomorrow
Answers
Answer:
Angle 1: 141 degrees
Angle 2: 39 degrees
Angle 3: 141 degrees
Step-by-step explanation:
Angle 2 and Angle 4 are equal since they are vertical angles. This means that Angle 2 is equal to 39 degrees.
Angle 1 and Angle 4 add up to 180 degrees. We call these supplementary angles. This means that Angle 1 is equal to 180-39=141 degrees.
Angle 1 and Angle 3 are vertical angles, so Angle 3 is also equal to 141 degrees.
Find all the integer solutions of each system of inequalities {y>=0 {72-y>=4
Answers
The integer solutions of each of the system of inequalities are 0, 1, 2, 3, .....65, 66, 67, 68. There are total 69 integer values that y can take.
In the question, we are given the inequalities:-
y ≥ 0 and 72 - y ≥ 4
We have to find the integer solutions of each of the system of inequalities.
From 72 - y ≥ 4, we can write,
72-4 ≥ y
68 ≥ y
Hence, from 68 ≥ y and y ≥ 0, we can write,
68 ≥ y ≥ 0
Hence, y can take 69 integer values from 0 to 68, both included.
To learn more about system of inequalities, here:-
https://brainly.com/question/19526736
#SPJ4
(c) Solve the equation 7x³ +28x² = 0
Answers
Answer:
x = - 4 , x = 0
Step-by-step explanation:
7x³ + 28x² = 0 ← factor out 7x² from each term on the left side
7x²(x + 4) = 0
equate each factor to zero and solve for x
7x² = 0 ⇒ x² = 0 ⇒ x = 0
x + 4 = 0 ⇒ x = - 4
. Use Structure is the product the same
when multiplying 22 x (-5) and multiplying
(-5) x 22? Explain.
Answers
Answer:
Yes.
Step-by-step explanation:
Let's say a=22 and b=-5
According to the Commutative Property of Multiplication, a*b=b*a. Hence, 22*(-5)=(-5)*22.
22*(-5)=
-(22*5)=-110
(-5)*22=
-(5*22)=-110
-110=-110 √
Find the sum of (8.6 x 106) and (3.7 x 105). Write the final answer in scientific notation.
8.97 x 105
8.97 x 106
1.23 x 1010
12.3 x 1011
Answers
Answer:
8.97 x [tex]10^{6}[/tex]
Step-by-step explanation:
To add in scientific notation, the exponents need to be the same for the bases of 10. You can either make them both to the exponent of 6 or 5. It does not matter. I made them both to the power of 5
(8.6 x [tex]10^{6}[/tex]) + (3.7 x [tex]10^{5}[/tex])
(86 x [tex]10^{5}[/tex]) + (3.7x[tex]10^{5}[/tex])
(86 x 3.7) x [tex]10^{5}[/tex]
89.7 x[tex]10^{5}[/tex] Rewrite in scientific notation
8.97 x [tex]10^{6}[/tex]
Find the rate of change for each set of ordered pairs. What is
the average rate of change of all three sets?
(1, 15), (2, 12)
(-1,14), (3, 10)
(3,11), (5, 15)
Write your answer to the average rate of change as a fraction,
a/b.
Answers
Answer:
Find the rate of change for each set of ordered pairs. What is
the average rate of change of all three sets?
(1, 15), (2, 12)
(-1,14), (3, 10)
(3,11), (5, 15)
Write your answer to the average rate of change as a fraction,
a/b.
Step-by-step explanation:
A carton has a length of 2 2/3 feet, width of 1 1/8 feet, and height of 1 1/5 feet. What is the volume of the carton? (5 points)
Group of answer choices
5 2/5 cubic feet
7 1/5 cubic feet
4 1/5 cubic feet
3 3/5 cubic feet
Answers
Answer:
3 3/5
Step-by-step explanation:
Bombonica s-a gândit la un număr, i-a adăugat 74, rezultatul obţinut l-a mărit de 10 ori, iar din
noul rezultat a luat de 7 ori câte 86 şi a obţinut 318, număr care reprezenta numărul zilelor de când
fusese răpit împăratul. La ce număr s-a gândit?
Answers
[tex]x + 74 \cdot 10 - (7 \cdot 86) = 318[/tex]
[tex]x+74\cdot \:10-7\cdot \:86=318[/tex]
[tex]x+740-7\cdot \:86=318[/tex]
[tex]x+740-602=318[/tex]
[tex]x+138=318[/tex]
[tex]x = 318 - 138 = 80[/tex]
Imparatul s-a gandit la numarul 80.
find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continuesm8, 0, 8, 0,
Answers
The formula for the general term and of the sequence is ±8.
What do we mean by sequence?A sequence in mathematics is an enumerated collection of objects in which repetitions are permitted and order is important. It, like a set, has members (also called elements, or terms). The length of the sequence is defined as the number of elements (which could be infinite). Unlike a set, the same elements can appear multiple times in a sequence at different positions, and the order does matter. Formally, a sequence can be defined as a function from natural numbers (the sequence's positions) to the elements at each position. The concept of a sequence can be expanded to include an indexed family, which is defined as a function from an index set that may or may not is numbered to another set of elements.To find the formula for the given sequence:
Given sequence: 8, 0, 8, 0, So, the formula cen be ±8.+8 to get the terms of odd numbers and -8 to get the terms of even numbers.Therefore, the formula for the general term and of the sequence is ±8.
Know about more sequences here:
https://brainly.com/question/6561461
#SPJ4
(x+2, y+3)
help please
Answers
Answer:
is that the equation ? is that all they gave you
im going to answer but do you mean
(x +2y+3)
Step-by-step explanation:
HELP! (3x4)+ 52 MARKING BRAINLY!
Answers
Answer:
64
Step-by-step explanation:
[tex]3 \times 4\\= 12\\= 12 + 52\\= 64[/tex]
Answer:
64
Step-by-step explanation:
first 3 x 4 = 12
12+52=64
A startup sports public relations company is looking to grow. They currently represent 2 clients and plan on representing 3 additional clients each year. The following graph can be used to help determine the number of clients, y, the company will have after x years.
ased on the context, what is the range of the function?
[0, ∞)
[2, ∞)
[−7, 7]
ℝ
Answers
Based on the context, the range of this function is given by: C. [−7, 7]
What is a range?A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.
How to identify the range of this graph?The vertical extent of a graph represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of function f(x) shown, we can infer and logically deduce the following:
Range = [−7, 7]
Read more on range here: brainly.com/question/17295757
#SPJ1
Which shows ray C A?
Answers
i don’t understand this i already tried but got 1.25 bad i’m pretty sure it’s wrong
Answers
Answer:
Smallest integer=14
Step-by-step explanation:
(x+x+2+x+4+x+6)/4=17
(4x+12)/4=17
4x+12=68
4x=68-12
4x=56
x=56/4
x=14
numbers are: 14, 16, 18, 20
If real gdp in a particular year is $80 billion and nominal gdp is $240 billion, the gdp price index for that year is 100. 300. 240. 200.
Answers
Answer:
If real GDP in a particular year is $80 billion and nominal GDP is $240 billion, the GDP price index for that year is: 300.
Step-by-step explanation:
-(16 - 5x) simplified
Answers
Answer:
5x-16
Step-by-step explanation:
-(16 - 5x)
Use distributive property to open parenthesis.
-(16 - 5x)=
=(-1*16)+(-1*-5x)=
=(-16)+(5x)=
=5x-16
Finding x.
5x-16=0
5x=16
x=3.2
Hope this helps!
Please mark as brainliest if correct!
please hurry I really need help!
13. The table shows the times of runners completing a
marathon. To qualify for the next marathon, a
runner's time must be less than 3 hours. Which
runners qualify?
Cho
Kevin
Runner
Ojas
Sydney
Time (h)
3-1/
3.2
8
30
13
360
3-
Answers
Answer:
Step-by-step explanation:
the answer is 30
Which number is greater,
23
×
10
3
or
11
×
10
4
? How do you know? Show your work and explain your steps.
Answers
Answer:
Answer: 11x10^4 is greater. Step-by-step explanation: 23x10^3 = 23x10x10x10 = 23000. 11x10^4 = 11x10x10x10x10 = 110000. 110000 is greater than 23000.
Step-by-step explanation:
cos
Select the domain and range of the graph in set-builder and interval notation.
Answers
The domain of the function:{x|x<-1 and x>1} or (-∞,-1] ∪[1,∞) and the range of the function {y|y∈R} or (-∞,∞) .
A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.
In the given graph we can see that the values of x are all real values greater than 1 and all real values less than 1
Therefore the domain of the function is set-builder notation is given by:
{x|x<-1 and x>1}
The domain of the function in interval notation is given by:
(-∞,-1] ∪[1,∞)
Therefore the range of the function is set-builder notation is given by:
{y|y∈R}
The range of the function in interval notation is given by:
(-∞,∞)
To learn more about domain and range:
https://brainly.com/question/28135761
#SPJ9
How do I simplify this?
Answers
1- 3/4 = 0.25 which is equivalent to 1/4
the problem now looks like 7/4 / 1/4
you cancel out both 4
this problem simplified looks like 7/1
which is equivalent to 7 if you divide
If f (x) = 3x - 1 and g (x) = x² + 1, find the following.
a) g(-4) + f(-2) =
b) f(1) - g(0) =
Will give brainliest and 5 star rating. Thank you. :)
Answers
The value of the functions are:
a. g(-4) + f(-2) = 24
b.. f(1) - g(0) = 1
What is a function?A function can be defined as an expression showing the relationship between two variables.
Given the functions;
f (x) = 3x - 1 g (x) = x² + 1g(-4); substitute the value of x as - 4 in g(x)
g(-4) = (-4)² + 1
g(-4) = 16 + 1
g(-4) = 17
f(-2); substitute the value of x as - 2 in f(x)
f(-2) = 3(-2) - 1
f(-2 = -7
a. g(-4) + f(-2) = 17 -(-7)
g(-4) + f(-2) = = 24
f(1) = 3(1) - 1
f(1) = 2
g(0) = (0)² + 1
g(0) = 1
b. f(1) - g(0) = 2 - 1
f(1) - g(0) = 1
Thus, the value of g(-4) + f(-2) and f(1) - g(0) are 24 and 1 respectively.
Learn more about functions here:
https://brainly.com/question/17043948
#SPJ1
Will give brainliest.
Answers
Answer:
Option 3
Step-by-step explanation:
First tke lcm i.e. 6 then multiply the dinominator to make six.
Multiply tje above no. With the same digit the sub. The numerators
Answer:
c) 7/6
Step-by-step explanation:
The difference will be,
→ (5/3) - (1/2)
→ (10/6) - (3/6)
→ (10 - 3)/6
→ 7/6
So, the answer is 7/6.
8 256m to km shortcut method and 25 000 mm to hm and 864 dm to dam and