What is the greatest common factor of 42 and 84

Answer:

h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

Step-by-step explanation:

Given in the question a piece of cardboard having dimensions 32 by 40

Suppose we cut square of length x

When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths

Formula for the volume of box

v = height * length  * width

v = x  (32-2x)  (40-2x)

v = 4x³ - 144x² + 1280x

Find derivative and equal it to 0

dv/dx = 4(3)x² - (2)144x + 1280

      0 = 12x² - 288x + 1280

x1 = 18.110

x2 =5.88

Select x and plug value of x to find dimension

(32-2x) > 0

2x < 32

 x < 16

so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm

h = 6 cm  

l = (32-2(6)) =  20 cm

w = (40-2(6)) = 28 cm

Answer:

4x - 12

Step-by-step explanation:

Expand 8 - 4(-x + 5) as follows:

              8 + 4x - 20

               4x - 12    (First answer is the correct one)

8-4(-x+5)

Multiply the bracket by -4 first .

8+4x-20

--=positive

-+= negative

4x-12

8-20=-12 because 12 is bigger than 8

Answer:A

Answer:

two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Answer:

If two figures have the same size and shape, then they are congruent. The term congruent is often used to describe figures like this. In this tutorial, take a look at the term congruent!

Step-by-step explanation:

Answer:

y int (0, -2) x int (5, 0) slope 2/5

Step-by-step explanation:

2(0)-5y=10

-5y=10

y=-2

2x-5(0)=10

2x=10

x=5

2x-5y=10

-5y=-2x+10

y=2/5 x -2

Final answer:

The width of the parking lot is 11 meters and the length is 33 meters.

Explanation:

To find the width of the rectangular parking lot, let's assume that the width is 'x'. According to the given information, the length of the parking lot is three times the width, so the length is 3x.

The formula for the perimeter of a rectangle is P = 2(length + width). In this case, the length is 3x and the width is x. Plugging in these values, we get:
P = 2(3x + x) = 2(4x) = 8x

We know that the length of the parking lot is 88 meters, so we can set up an equation:
88 = 8x
To solve for x, divide both sides of the equation by 8: x = 11.

Therefore, the width of the parking lot is 11 meters and the length is 3 times the width, which is 33 meters.

Answer:

there wouldbe 9 of height i think

Step-by-step explanation:

[tex]v=\frac{\pi r^2h}{3} \\\text{solving for h}\\3v=\pi r^2h\\\\\boxed{\frac{3v}{\pi r^2}} = h[/tex]

Answer:

9.8

Step-by-step explanation:

[tex]51.94 /5.3=9.8[/tex]

Answer: 9.8

How I Found The Answer: All You Had To Do Was Divide 51.94 by 5.3. Which Equals 9.8

Answer:

8 projects

Step-by-step explanation:

28 : 3,5 = 8

Final answer:

Mia can complete 8 full projects with 28 yards of ribbon by dividing the total yards by the yards needed per project, after converting 3 1/2 yards to an improper fraction (7/2).

Explanation:

The subject of this question is Mathematics, and the question would typically fall under a middle school grade level. To solve the problem about the number of projects Mia can complete, we need to use division. Mia has a total of 28 yards of ribbon and needs 3 1/2 yards of ribbon for each project. By converting the mixed number to an improper fraction, we get 7/2 yards per project; then we can divide the total yards by the yards needed per project.

To calculate how many full projects Mia can complete:

Mia can complete 8 full projects with the ribbon she has.

Answer:

The equation of the line is y = -2x + 7

Step-by-step explanation:

* Lets study how to make an equation of the line from two point

- If the line passes through points (x1 , y1) and (x2 , y2)

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope is m = (y2 - y1)/(x2 - x1)

- The y-intercept means the line intersect the y-axis at point (0 ,c)

* Now lets solve the problem

∵ The line passes through points (-3 , 13) and (4 , -1)

- Let (-3 , 13) is (x1 , y1) and (4 , -1) is (x2 , y2)

∵ m = (y2 - y1)/(x2 - x1)

∴ m = (-1 - 13)/(4 - -3)

∴ m = (-14)/7 = -2

- Lets write the form of the equation

∵ y = mx + c ⇒ substitute the value of m

∴ y = -2x + c

- To find the value of c use one of the two points to substitute the

  values of x and y in the equation

∵ The line passes through (4 , -1)

∴ -1 = -2(4) + c

∴ -1 = -8 + c ⇒ add 8 to both sides

∴ -1 + 8 = -8 + 8 + c

∴ 7 = c

∴ y = -2x + 7

* The equation of the line is y = -2x + 7

median: 3

lower quartile: approximately 2.25

higher quartile: approximately 4.75

minimum: 0

maximum: 6

hope that helps

Answer:

d only balance sheet accounts.

Step-by-step explanation:

Only permanent accounts are on the balance sheet which includes

assets, liabilities and equity acct.

A trial balance contains all accounts in the general ledger with their account balances, which are used to prepare financial statements such as the balance sheet and income statement.So,option a is correct.

A trial balance is an accounting report that lists all the accounts in the general ledger of an entity along with their respective account balances. It is prepared to check the arithmetical accuracy of the accounting records - to ensure that debits equal credits. Therefore, the correct answer to the question is:

a) All accounts contained in the general ledger with account balances.

The trial balance includes both income statement accounts, such as revenue and expenses, and balance sheet accounts, which include assets, liabilities, and equity accounts. It is commonly used as a step in the process of preparing the financial statements, which include the balance sheet, income statement, and statement of retained earnings. These components provide a more comprehensive view of an entity's financial health at a certain point in time or over a specified period.

Answer:

the answer is A and C

Step-by-step explanation:

Answer:

Every line on the net has a measurement of 16.

Step-by-step explanation:

Every edge dimension of the cube has a measurement of 16, so the corresponding edges of the net (all edges) will have a measurement of 16. Put the number 16 next to each line on the net.

For this case we have that the distance between two points is:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) :( 3 \sqrt {2}, 4 \sqrt {3})\\(x_ {2}, y_ {2}) :( 3 \sqrt {2}, - \sqrt {3})[/tex]

Substituting:

[tex]d = \sqrt {(3 \ sqrt {2} -3 \sqrt {2}) ^ 2 + (- \sqrt {3} -4 \sqrt {3}) ^ 2}\\d = \sqrt {(0) ^ 2 + (- 5 \sqrt {3}) ^ 2}\\d = \sqrt {0+ (25 * 3)}\\d = \sqrt {75}\\d = 5 \sqrt {3}\\d = 8.66[/tex]

Answer:

[tex]d = 8.66[/tex]

Answer:

The student spent 60 minutes studying and got a 90 on the test

Step-by-step explanation:

The x coordinate is 60, which means they spent 60 minutes studying

The y coordinate is 90 which means they got a score of 90 on the test

The student spent 60 minutes studying and got a 90 on the test

Answer:

I would cost $4.75

Step-by-step explanation:

9.50 / 2

4.75

Hope it´s helpfull :)

Answer:

6 cans cost $4.75

Step-by-step explanation:

To solve this divide $9.50 by 12. This will give you $0.7916... per one can.With that same number multiply it by 6 and you get $4.75.

No 5/8 is bigger because half of 8 is 4 and 5 is greater than 4

In comparing 1/2 gallon and 5/8 gallon, using equivalent fractions shows that 5/8 gallon is larger than 1/2 gallon.

In the comparison of 1/2 gallon and 5/8 gallon, it's important to remember that fractions provide a way of representing parts of a whole. With fractions, the numerator represents the part while the denominator represents the total parts. So here, the fraction 5/8 represents 5 parts of a total 8 parts, where 1 gallon is considered the 'whole' or 'total' amount.

To determine if 1/2 is greater or less than 5/8, we want to make the denominators the same for comparison. Multiply the numerator and the denominator of the first fraction (1/2) by four to get it to the same denominator as the second one. This results in 4/8 for the first fraction.

Now, comparing 4/8 and 5/8, we find that 5/8 is greater than 4/8. Therefore, 5/8 gallon is indeed more than 1/2 gallon.

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The answer for this problem is 40167.

To round this up to the nearest 10, if the ones is above 5, round it up.

To the nearest 10

40170

Answer:

40,170

Explanation:

 25,222

+14,945

 40,167

Then to round, we look at the ones column. Since there is a 7, which is greater than or equal to five, we round up to 70 from 67.

So our final answer is 40,170

Hope this was helpful, let me know of you need any further explanation!

Answer:

The number of pounds collected by Steve is [tex]39-j[/tex]

Step-by-step explanation:

Let

j----> the number of pounds collected by Joy

s ---> the number of pounds collected by Steve

we know that

[tex]j+s=39[/tex]

Solve for s

That means-----> Isolate the variable s

Subtract j both sides

[tex]s=39-j[/tex]

Substitute all values for x and y into their placement

y<1-6x

(1)<1-6(-1)

1<7

The coordinate pair is (-1,1)

Answer:

A.

Step-by-step explanation:

To make a decimal into a percent you just move the decimal 2 times to the right.

0.24 = 24%

The percentage of females polled supported Wilson is about 44%

Given:

Total frequency of females polls = 0.54

Frequency of polls got by Wilson = 0.24

We have to find the percentage of female polls supported Wilson.

[Percentage Polls) × (Total frequency of females polls)] / 100 = Frequency of polls got by Wilson

⇒ Percentage polls = (0.24 × 100) / 0.54

⇒ Percentage polls = 44.44%

Therefore, the percentage of females polled supported Wilson is about 44%.

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Answer:

8 Batches

Step-by-step explanation:

Simple. Since it takes 2/3 of a cup for one batch, we divide 5 1/3 by 2/3, wich equals 8.

She make total number of 8 batches.

Amount of sugar required per batch =  [tex]\frac{2}{3} [/tex] cup

Since, Elena used [tex]5\frac{1}{3} [/tex]  cups of sugar to make multiple batches of cookies.

To find number of batches she make, divide total amount of sugar by amount of sugar per batch.

Number of batches she make,

                             [tex]=5\frac{1}{3}\div\frac{2}{3}\\ \\ =\frac{16}{3}*\frac{3}{2}=8 [/tex]

Hence, She make total number of 8 batches.

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Answer:90+33 = 123

123-180=77

So 77

Step-by-step explanation:

Answer:

The answer is 77

Answer:

Step-by-step explanation:

Only (c) makes sense.  The game draws people, which in turn means more cars and heavier traffic in the surrounding area.

Answer:

C) The traffic is heavier around the stadium when a game is being played. Games being played cause more traffic.

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

The expression (a + b)(x + y) is not equivalent to (a + x)(b + y). When the terms are distributed, (a + x)(b + y) yields a different result compared to the original expression.

The expression (a + b)(x + y) is equivalent to a(x + y) + b(x + y) and (b + a)( y + x) because the order of addition in each element doesn't change the overall result. However, the expression (a + x)(b + y) is not equivalent to the original expression.

To understand why, let's distribute the terms in each equivalent expression:

(a + b)(x + y) = ax + ay + bx + by

(b + a)( y + x) = ay + ax + by + bx = ax + ay + bx + by

a(x + y) + b(x + y) = ax + ay + bx + by

As you can see, all these three expressions give the same result when distributed. But, if we now distribute the terms in (a + x)(b + y):

(a + x)(b + y) = ab + ay + bx + xy

It's clear that it does not yield the same result. Thus, option A) (a + x)(b + y) is not equivalent to the original expression (a + b)(x + y).

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Answer:

C. 17 - 12 = d + 12 - 12

Step-by-step explanation:

You need to get d by itself and in order to do that you need to subtract 12

Answer:

A coordinate pair that works as a solution is (1,3)

Answer:

A coordinate pair that works as a solution is (1,3)

Step-by-step explanation:

The answer is:

a) Her reasoning is incorrect, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.

b) We have that:

[tex]\sqrt{200}=14.14[/tex]

and rounding to the nearest tenth, we have that:

[tex]\sqrt{200}=14.1[/tex]

To solve the problem, we need to remember the following property of square roots:

[tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex]

We are given the expression:

[tex]\sqrt{200}[/tex]

We can rewrite it by the following way:

[tex]\sqrt{100*2}[/tex]

Now, applying the square root property we have:

[tex]\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}=14.14[/tex]

Therefore,

a) Her reasoning was wrong, she applied a wrong operation, the way to simplify the expression was using the square root property. If we want to extract a number of a square root, we must square that number first in order not to modify the expression.

b) We have that:

[tex]\sqrt{200}=14.14[/tex]

and rounding to the nearest tenth, we have that:

[tex]\sqrt{200}=14.1[/tex]

Have a nice day!

Answer:

B

Step-by-step explanation:

45+27=72

A- 15 times 9 equals 135

B- 8 times 9= 72

C 45 times 18 equals 810,

D- 14 times 12 equals 68

Luke does a work of 308Nm

If we have a constant force [tex]\vec{F}[/tex] that acts on a body in the same direction as the displacement [tex]\vec{s}[/tex], then the work [tex]W[/tex] is defined as the product of the force magnitude [tex]F[/tex] and the displacement magnitude [tex]s[/tex]. In other words:

[tex]W=Fs[/tex], which is valid for a constant force in direction of straight-line displacement.

In this problem:

[tex]F=22N \\ \\ s=14m[/tex]

Therefore:

[tex]W=22\times 14 \\ \\ \boxed{W=308Nm}[/tex]