Express 112 as a product of prime numbers in index form?

Answers

Answer 1
                                   112
                                    /  \
                                  2   56
                                       /  \
                                     2   28
                                          /  \
                                         2  14
                                              /  \
                                             2  7

So, the answer is 2 x 2 x 2 x 7 or 2^3 x 7
Answer 2

Final answer:

To express 112 as a product of prime numbers in index form, we perform prime factorization to get 2⁴ x 7.

Explanation:

To express 112 as a product of prime numbers in index form, we start by performing prime factorization, which is breaking down a composite number into the prime numbers that, when multiplied together, give the original number.

Let's find the prime factors of 112:

112 is divisible by 2 (the smallest prime number).112 ÷ 2 = 5656 is also divisible by 2, so 56 ÷ 2 = 28Continuing this process, 28 ÷ 2 = 14, and then 14 ÷ 2 = 7The number 7 is a prime number and cannot be divided further.

So, we can express 112 as a product of prime factors as 2⁴ × 7¹ or simply 2⁴ × 7, since any number to the power of 1 is the number itself.


Related Questions

Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bedroom that measures 12 feet by 14 feet. He multiplies 12 x 14 = 168 to get an exact answer of how much border he needs. He concludes that he does not have enough border for the whole job.

1. Tell how you can critique Jason’s reasoning.

2. Critique Jason’s reasoning

3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense

Answers

Let's summarize the facts:

the tape is 75 feet long

the bedroom is 12 feet by 14 feet. 

1. Tell how you can critique Jason’s reasoning.

If you want to Critique Jason's reasoning, you could a) ask yourself the same questions that Jason did and see if you would come with the same answers and used the same analysis or b) analyse Jason's answer to see if he did a mistake or missed an important detail and made a thought mistake


2. Critique Jason’s reasoning

 I will use the option b from above:  

Jason first multiplied 12 x 14 = 168. This multiplication is correct, but what did he get? He needed to get the perimeter of the bedroom  because it was only the wallpaper border, not the wallpaper itself - so getting the perimeter was needed, but this we get by the formula ( 2* *(length+width), not length* width - as Jason did.
So Jason made a mistake here! his actual answer should be 2*(12+14)=2*26=52, so the tape of 75 feet would have been enough!

3. Jason uses an overestimate to decide how many rolls of wallpaper he needs for another’s room. Explain why his reasoning to use an overestimate does or does not make sense

Using an overestimate is often a good idea- in case some of the tape gets damaged, he will have some left. However, since his calculations are wrong by a lot (he multiplies rather than adds and multiplies by 2), his overestimate will be a lot higher than would be practical - he would be left with a lot of leftovers and spend too much money. So his reasoning does not make sense

Students in a science class are divided into 6 equal groups with at least 4 students in each group for a project. write and solve an inequality that represents the number of students in the class

Answers

There are a total of 6 groups.

And each group contains at least 4 students.

So the minimum number of students is:

minimum = 6 * 4 = 24 students

 

Let us say that x represents the number of students, hence:

x ≥ 24

Final answer:

To represent the number of students in the class, we can write the inequality 24 ≤ x.

Explanation:

To represent the number of students in the class, let's assume that the total number of students in the class is represented by the variable 'x'. Since the students are divided into 6 equal groups and each group has at least 4 students, we can write the inequality:
6 * 4 ≤ x

Simplifying the inequality:
24 ≤ x

This inequality represents that the total number of students in the class should be greater than or equal to 24.

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Wat is $60 for 8h unit rate

Answers

the unit rate is $7.50
The unit rate is 7.5/hr

Find the hypotenuse of the right triangle if the perpendicular leg is 12 and base is 5

Answers

pythagoras rule

hypotenuse power two  = 12 power 2   + 5 powered 2 
                                        = 144 + 25= 169

so hypotenus = radical 169 = 13

How many ways can i distribute 3 slices of pizza to 3 people of fairness doesn't matter?

Answers

You could cut the slice up into 3 more pieces or however many slices of that slice of pizza and distribute it among 3 people unfairly.

Translate and solve: the quotient of a number x and -8 is 25

Please help,
Thank you :)

Answers

Well if you were to put the problem into words, it'd be:
x/-8 = -25

Thus, to solve for x, multiply both sides by -8:
x/-8(-8) = -25(-8)
x = 200

Which linear inequality is represented by the graph?y ≤ x − 1y ≥ x − 1y < 3x − 1y > 3x − 1

Answers

First, work out the equation of the graph.
Equation of a straight line graph is given in the form [tex]y = mx+c[/tex] where [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the y-intercept.

The graph given shows the line intercept y-axis at (0, -1)

To work out the slope, choose any two coordinates then find their vertical and horizontal distance. Say we choose (0, -1) and (3, 0)
The vertical distance is 1 and the horizontal distance is 3, so the slope is
[tex]m = \frac{-1-0}{0-3}= \frac{-1}{-3}= \frac{1}{3} [/tex] 

Then form the equation for the line
[tex]y=mx+c[/tex]
[tex]y= \frac{1}{3}x-1 [/tex]→ Multiply each term by 3
[tex]3y = x - 3[/tex]

Now the inequality part, the shaded region is above the line, so the values intended are 'greater than' and the line is a bold line, so the inequality is 'greater than or equal to' and the symbol is ≥

The inequality is then
3y ≥ x - 3

Note: None of the options show this answer. Maybe check if the original options have been copied correctly. 

Solution: As the line shown in the graph passes through (3,0) and (0,-1).

So, equation of line passing through (3,0) and (0,-1) is given by two point formula i.e equation of line passing through (p,q) and (a,b) is given by

→[tex]\frac{y-q}{x-p}=\frac{q-b}{p-a}[/tex]

→[tex]\frac{y-0}{x-3}=\frac{0+1}{3-0}[/tex]

So ,the equation of line is ,→3 y = x-3

  → x- 3 y -3= 0 or y=x/3 -1

take point (0,0) and putting in the above equation, we see that ,L.H.S>R.H.S

Similarly if you take other points , like (1,0).(0,1) we see that ,L.H.S>R.H.S.

it means the above equation can be written as , y≥x/3 -1.

None of the option is correct.


Which expression is equivalent to 3x(1.05)?

A: 3x + 3x + 3x
B: 1.05x + 1.05x + 1.05x
C: x + 3.15
D: 1.05x + 3

Answers

3x(1.05) 

answer
B: 1.05x + 1.05x + 1.05x

A science museum charges an admission fee of $10 per adult and $6 per child. If the museum had 2,000 visitors on a particular day and the total collection was $18,800, how many adults and children visited the museum?

Answers

a = adult
c = child

10a + 6c = 18,800
a + c = 2,000

In the second equation, subtract c from both sides.

a = 2000 - c

Put this into the first equation.

10(2000 - c) + 6c = 18800

Multiply everything in the parenthesis by 10.

20,000 - 10c + 6c = 18,800

Combine like terms.

20,000 - 4c = 18,800

Subtract 20,000 from both sides.

-4c = -1,200

Divide -4 on both sides.

c = 300

Put this into the second equation.

a + 300  = 2,000

Subtract 300 from both sides.

a = 1,700

Hope this helps!

The sum of two numbers is 44 . the larger number is 12 more than the smaller number. what are the numbers?

Answers

Let x be the number 

x+(12+x)=44
2x+12=44
2x=32
x=32/2
x=16 

The two numbers are 16, 28 

Hope I helped :) 

The equation 4(2x + 3y) =4(3y +2x) is an example of which property? Question 4 options:

A. Distributive Property

B. Identity Property of Addition

C. Associative Property of Addition

D. Commutative Property of Addition

Answers

Final answer:

The equation 4(2x + 3y) = 4(3y + 2x) is representing the Commutative Property of Addition, which means the order in which you add numbers does not change the sum.

Explanation:

The equation in your question, 4(2x + 3y) = 4(3y +2x), is an example of the Commutative Property of Addition. This property means that the order in which you add numbers does not change the sum. In this case, (2x + 3y) and (3y + 2x) are the same because of the Commutative Property of Addition, the order of 2x and 3y doesn't impact the result. The multiplication by 4 on both sides does not change this property being applied.

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the probability distribution table shows the proportion of people living in the five different regions of a city there are now 4200 residents in the city.

How many live in the south region?

Photo attached

Answers

Since there are a total of 4,200 residents and the question is asking for the amount in the south region, take the distribution number from the chart, 0.16, and multiply it by 4,200.
4200 ×.16 = 672

672 residents

Answer: Number of residents live in south region= 672 residents.


Step-by-step explanation:

Given:- Total residents in the city =4200

let A be the event of residents live in south region the,

Probability of residents live in south region P(A) = 0.16

So, Number of residents live in south region=Product of probability of residents live in south region and total residents in the city =0.16×4200=672 residents.

The length of a rectangle is twice the width. the perimeter is 32 cm more than the width. find the dimensions of the rectangle.

Answers

Width: x
Length: 2x
Perimeter=2x+2x+x+x=6x
32 cm more than width means x+32
6x=x+32
5x=32
x=6.4
Dimension is 6.4×12.8 (width×length)

The dimensions of the rectangle are 6.4 and 12.8 respectively.

What is the perimeter of the rectangle?

The formula for calculating the perimeter of a rectangle is given by :

P = 2 ( L + w )

The length of a rectangle is twice the width. And the perimeter is 32 cm more than the width.

L = 2w

Now substituting into the formula , we have

Width: x

Length: 2x

Perimeter P = 2 ( L + w ) = 2(3x) = 6x

Since 32 cm more than width means x+32

6x = x + 32

5x = 32

x = 6.4

Hence, Dimension is 6.4 × 12.8.

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I can’t seem to figure out how I would graph this? Someone help please

Answers

Label the number line, put a filled in circle on 2 and make it go left. Then put a clear circular on 2 and make it go right.
check the picture below.

An employee works 21 days per month if they worked an average of 7.5 hours per day how many hours do they work per month

Answers

7.5 times 21 = 157.5 hours. 

You can verify that by dividing 157.5 by 21 to see how many hours she worked in a day. 

157.5 divided by 21 is 7.1 hours

My answer is correct!

The length of a rectangle is 1 ft more than double the width, and the area of the rectangle is 45 ft2 . find the dimensions of the rectangle.

Answers

A = L * W
A = 45
L = 2W + 1

45 = W(2W + 1)
45 = 2W^2 + W
2W^2 + W - 45 = 0
(2W - 9)(W + 5) = 0

W + 5 = 0
W = -5...not this one because it is negative

2W - 9 = 0
2W = 9
W = 9/2
W = 4.5 <=== the width is 4.5 ft

L = 2W + 1
L = 2(4.5) + 1
L = 9 + 1
L = 10 <=== the length is 10 ft

The width of the rectangle is 4.269ft and the length is  8.538 ft.

What are the area and perimeter of a rectangle?

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, The length of a rectangle is 1 ft more than double the width.

Assuming the width to be x ft, therefore length would be (2x + 1) ft.

We know area of a rectangle(A) = length×width.

∴ x×(2x + 1) = 45.

2x² + 2x = 45.

2x² + 2x - 45 = 0.

[tex]x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:2\left(-45\right)}}{2\cdot \:2}[/tex].

[tex]x_1=\frac{-2+2\sqrt{91}}{2\cdot \:2},\:x_2=\frac{-2-2\sqrt{91}}{2\cdot \:2}[/tex].

[tex]x=\frac{-1+\sqrt{91}}{2},\:x=-\frac{1+\sqrt{91}}{2}[/tex].

[tex]\left(\m\quad x=4.26969\dots ,\:x=-5.26969\dots \right)[/tex].

∴ x = 4.269ft is the admissible value as length can not be negative.

∴ length is 8.538 ft.

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The coordinate of the midpoint of segment AB is (-3, 2). Find the coordinate of A if the coordinate of B is (0, 2).

A =

(-6,2)
(-3/2,2)
(3,2)

Answers

The answer is (-6,2). I hope this helped you!

Given that AE is a tangent of the circle with the center at B, BC = 3.5, and AE = 24, which is the length of EC?
7
13
25
49

Answers

We are actually given here a right triangle where EC is the hypotenuse. The length of one side is AE = 24, and the other side AC is simply twice BC, so AC = 7:

EC^2 = AE^2 + AC^2

EC^2 = 24^2 + 7^2

EC = 25

the sum of three integers is 92. the second number is three times the first number. the third number is ten less than twice the first number. find the integers

Answers

1st number = x

 2nd number = 3x

3rd number = 2x-10

x +3x + 2x-10 =92

6x - 10 = 92

6x =102

x = 102/6

x = 17

1st number = 17

2nd number = 17*3 = 51

 3rd number = 17 *2 = 34-10 = 24

17 + 51 + 24 = 92

 3 numbers are 17, 51 and 24

The box plots show male and females grades in mathematics class: Which of the following best describes the information about the interquartile ranges?

Answers

I think the answer is "The interquartile range for females should be higher because the overall mean is higher".

Answer:

D

Step-by-step explanation:

"the male interquartile is not accurate because the first quartile is missing"

Find the quotient. y 9 ÷ y 3 y3 y6 y9 y27

Answers

y^9 ÷ y^3 = y^(9-3) = y^6

answer
y^6

Answer:

The quotient is [tex]y^6[/tex]

Step-by-step explanation:

Given expression is,

[tex]y^9\div y^3[/tex]

[tex]=\frac{y^9}{y^3}[/tex]

By using quotient of powers property of exponent,

[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]

[tex]=y^{9-3}[/tex]

[tex]=y^6[/tex]

Hence, the quotient is [tex]y^6[/tex]

Second option is correct.

Dona found that she had 7 almonds left over after filling a number of bags with 25 almonds each. She let b represent the number of bags and wrote an expression to represent the total number of almonds. She found that mr022-1.jpg and then substituted to find the total number of almonds.

Answers

b is the number of bags: 20 bags
7 almonds are left
25 bags in each bag

25almonds x 20 bags= 500 almonds

500 almonds + 7 left = 507 total almonds

25b +7 would be the correct expression

The total number of almonds can be represented by the equation:

x = 25b + 7

How to solve Algebra Word problems?

We can use the information given in the question to set up an equation to represent the total number of almonds.

Let b represent the number of bags, and

let x represent the total number of almonds.

According to the problem, each bag contains 25 almonds, and there are 7 almonds left over. Therefore, the total number of almonds can be represented by the equation:

x = 25b + 7

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tom can wash 44 plates in 3 minutes. how many seconds will it take him to wash 12 wash? show your work.

Answers

49.090 seconds. Cross multiply 44/180 x 12/x.    X= 49.090

If each password must contain at least one upper-case letter, one lower case letter and one number, how many passwords are there? unanswered

Answers

There are 26 letters in the alphabet and 10 numbers (0-9)
So it will be 26x26x10=6,760

divide three fourths ÷ two fifths

Answers

Your answer would be on eof the three
15/8
1.875
1 7/8
Hope this helps...
3/4 divided by 2/5 =    1 and 7/8

3/4 ÷ 2/5 = 
3 x 5=  15             7
-------    ---   =   1  ----
4 x 2=   8              8

Hope this helps!

lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily. How much interest has Lloyd earned?
5,189.00
8,024.70
3,090.64
8,094.50

Answers

the answer to this question is"D"

Answer:

Option C is the answer: $3,090.64

Step-by-step explanation:

Lloyd opened a savings account 13 years ago with a deposit of $5,003.86 the account has an interest rate of 3.7% compounded daily.

Means p = 5003.86

r = 3.7% or 0.037

t = 13

n = 365 (assuming there are 365 days in a year)

[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]

[tex]A=5003.86(1+\frac{0.037}{365} )^{4745}[/tex]

=> [tex]A=5003.86(1.00010136)^{4745}[/tex]

A = $8094.09

Interest earned = [tex]8094.09-5003.86=3090.26[/tex] dollars

This is closest to option C, hence, option C is the answer.

You are playing a game. you lose 4.8 points,lose another 7.6 points, and then win 2.5 points. what is the overall change in your score

Answers

You lose (4.8 +7.6) = 12.4 points and win 2.5 points; then, 12.4 - 2.5 = 9.9 pints;
Finally, you lose 9.9 points.

The Overall Change in score is 9.9 points.

What is overall change?

Overall Change is the difference of initial average and final average.

Given that you are playing a game and lose 4.8 points and again loose 7.6 points and finally win 2.5 points.

According to question we have

4.8 + 7.6 = 12.4

Then 12.4 - 2.5 = 9.9 points

Hence, Overall Change in the score is 9.9 points.

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Find the axis of symmetry for this parabola : y= 2(x-7)(x+9)

Answers

y = 2(x-7)(x+9)
y = 2x - 14x (x +9)
y = 2x^2 +18x -14x^2 + 126x
y = -12x^2 +144x
axis of symmetry = -b / 2a
= -144 / 2*-12
= 6
axis of symmetry x = 6





John received change worth $13. He received 10 more dimes than nickels and 22 more quarters than dimes. How many coins of each did he receive?

Answers

Final answer:

John received 10 nickels, 20 dimes, and 42 quarters.

Explanation:

Let's solve this problem step by step:

Let's assume the number of nickels = x

Number of dimes = x + 10 (10 more dimes than nickels)

Number of quarters = x + 10 + 22 (22 more quarters than dimes)

Given that the total value of change is $13, we can form the equation:

0.05x + 0.10(x + 10) + 0.25(x + 10 + 22) = 13

Simplifying the equation, we get:

0.05x + 0.10x + 1 + 0.25x + 7.75 = 13

Combining like terms, we get:

0.40x + 8.75 = 13

Subtracting 8.75 from both sides:

0.40x = 4.25

Dividing by 0.40:

x = 10.625

Since we can't have a fractional number of nickels, we round down to the nearest whole number.

Therefore, John received 10 nickels, 10 + 10 = 20 dimes, and 10 + 10 + 22 = 42 quarters.

∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 . What is the value of x? Enter your answer in the box.

Answers

5x+10=7x-12.... 24=12x.......2=x


Vertical angles are congruent, so E=F

5x+10=7x-12
10=2x-12
22=2x
11=x
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