4. Stanley quilts a square rug that has an area of 400 square inches. What is the length of each side of the
rug?

A. 14 inches
B. 16 inches
C. 18 inches
D. 20 inches

The 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

Here, we have three numbers- 31, 18, and 20

To find 3 common multiples of these numbers, we first find the least common multiple or LCM of these 3 numbers.

31 is a prime number, hence it can be written as- 31 × 1

18 can be written as- 3 × 3 × 2

20 can be written as- 5 × 2 × 2

Thus, the LCM of 31, 18 and 20 will be-

3 × 3 × 5 × 2 × 2× 31 × 1

= 5580

Thus, we found the least common multiple of 31, 18 and 20.

Now, the other 2 multiples will be multiples of the LCM itself.

The other two numbers can be-

5580 × 2 = 11,160

5580 × 3 = 16,740

Thus, the 3 common multiples of 31, 18, and 20 are 5580, 11160 and 16740.

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In the shadow of the tree, Height = 4 feet

Given :

A  32-foot tree is directly between you and the sun

you are standing 105 feet away from the tree

the tree casts a 120-foot shadow

Trigonometry is one of the most important branches in mathematics that finds huge application in diverse fields. The branch called “Trigonometry” basically deals with the study of the relationship between the sides and angles of the right-angle triangle. Hence, it helps to find the missing or unknown angles or sides of a right triangle using trigonometric formulas, functions, or trigonometric identities. In trigonometry, the angles can be either measured in degrees or radians.

In this article, let us discuss the six important trigonometric functions, ratios, trigonometry tables, formulas, and identities that help to find the missing angles or sides of a right triangle.

Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle.

Solution :

Trigonometry

Length of shadow= 120-105

Length if shadow= 15 feet

height= x

X/15= 32/120

X= 15*32/120

x= 15* 16/60

x= 15*8/30

x= 15*4/15

x= 4

X = 4 feet

Height = 4 feet

In the shadow of the tree, Height = 4 feet

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Answer:

You would travel 331.80 miles

Step-by-step explanation:

79 × 4.2 = 331.8 rounded to the nearest hundredth is 331.8

after you open your keyboard click on the "?123" button then click on the "=\<" button then there u will look for the upside down V

Step-by-step explanation:

thank you !!

[tex]f^{-1}[/tex](f(6.022)) is 6.022 and [tex]f^{-1}[/tex](-10) + f(6) is -4

The general evaluation of function is

[tex]f^{-1}[/tex](f(x)) = x

Here we have to find [tex]f^{-1}[/tex](f(6.022))

Therefore [tex]f^{-1}[/tex](f(6.022)) = 6.022

Now we have to find the value of [tex]f^{-1}[/tex](-10) + f(6)

Form the table of values, we have

[tex]f^{-1}[/tex](-10) = -6 and f(6) = -10

So we have

[tex]f^{-1}[/tex](-10) + f(6) = 6 + (-10)

                     = 6 -10

                     = -4

Therefore [tex]f^{-10}[/tex] (-10)+ f(6) = -4

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The amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

A ratio is a comparison of two or more numbers that indicates their sizes and amount in relation to each other.

We have,

Patients weighing 195 pounds require 279 milligrams of medicine.

We can write this in ratio as:

= 279 / 195

Now,

We need to have both patients in proportion.

Proportion means their ratios must be equal.

Let the amount of medicine required for the second patient be M.

We have,

279 / 195 = M / 130

We will find M.

(279 x 130) / 195 = M

M = 186

Thus the amount of medicine required by a patient weighing 130 pounds is 186 milligrams of medicine.

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The x-value that is a solution of the system is x = 3.

Here we have the system of equations:

3x+y+2z= -10

x+5y+2z= -12

-2x+3y = -1

And we want to find the value of x.

Using the third equation we can write y in terms of x:

y = (-1 + 2x)/3

Now we can replace that in the other two equations:

3x + (-1 + 2x)/3 + 2z= -10

x + 5*(-1 + 2x)/3 + 2z= -12

We can simplify thes two to get:

(3 + 2/3)*x + 2z = -10 + 1/3 = -29/3

(1 + 2/3)*x + 2z = -12 +5/3 = -31/3

Now if we subtract these two equations we will get:

(3 + 2/3)*x - (1 + 2/3)*x = -29/3 + 31/3  = 2/3

2x = 2/3

x = (2/3)/2 = 1/3

x = 1/3

The x-value that is a solution of the system is x = 3.

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The answer of given expression [tex]343c^3+d^3[/tex] will be [tex](7c + d)(49c^2-7cd+d^2)[/tex]

We have given an expression [tex]343c^3+d^3[/tex] which can be written as [tex](7c)^3+(d)^3[/tex]

Using identity [tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex].   ...(1)

Put a = 7c and b = d in equation (1) , we get

  [tex](7c)^3 + (d)^3 = (7c + d) ((7c)^2 - 7cd + (d)^2)\\\\(7c)^3 + (d)^3 =(7c + d)(49c^2-7cd+d^2)[/tex]

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The two numbers which satisfy the condition that the difference between them be; 16 as required in the task content are; 17 and 1.

It follows from the task content that the two numbers whose difference amount to 16 are to be determined as required in the task content.

Given the numbers in discuss as; x and y such that;

x - y = 16

To find:

The numbers x and y.

Therefore, the possible numbers are such that; x = 17 and y = 1.

Ultimately, the two possible combination of number such that their difference is 16 are; 17 and 1.

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Answer:

Step-by-step explanation:

Bro u just subtract...:)

547.25(day 1) - 327.875(day2) = 219.375 miles as the difference(just use a calculator)

Answer:

[tex]2x[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the given number.

"Multiply the number by 4" [tex]\to 4x[/tex]

"Add 6 to the product" [tex]\to 4x + 6[/tex]

"Divide this sum by 2" [tex]\to \frac{4x + 6}2 \to 2x + 3[/tex]

"Subtract 3 from the quotient" [tex]\to 2x + 3 - 3 \to 2x[/tex]

The decimal that represents the portion of people who own dog will be 0.32.

It should be noted that decimal numbers are the numbers that are used for denoting numbers that have while numbers and fractions.

In this case, it was stated that Isaac read that 32% of people owned dogs.

Therefore, the decimal that represents the portion of people who own dog will be:

= 32 / 100

= 0.32.

The decimal that represents the portion of people who own dog will be 0.32.

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Isaac read that 32% of people owned dogs. What decimal represents the portion of people who own dog?

Answer:

Will Give Brainliest!!!! Match each step with the correct justification.

Given: QM MR

a. Given

Answer:

  12 square units

Step-by-step explanation:

You want the area of polygon FGHJ from its vertices, using some unspecified formula.

We don't know what formula you were given, but one that we like is ...

  [tex]\displaystyle A=\dfrac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]

This formula is implemented in the attached spreadsheet. The line marked Area gives half the absolute value of the sum of the numbers above.

For the given points, the formula is computed by the attached spreadsheet. We recommend this approach whenever repetitive math is involved. You will note that repeating the first two point coordinates makes the formula more straightforward.

The area of this 4×3 rectangle is 12 square units.

Answer:

[tex] \sqrt[16]{5 |2| } sdh[/tex]

usmsks

The number of different purchases you could make is 11440

The given parameters are:

Number of chocolate, n = 16

Kinds of chocolate, r = 9

The number of different purchases you could make is calculated using the following combination equation

Purchases = C(n, r)

So, we have

Purchases = C(16, 9)

Apply the combination formula

Purchases = 16!/(9! * 7!)

Evaluate the expression

Purchases = 11440

Hence, the number of different purchases you could make is 11440

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The equation of the line will be x = -6, that is, option B.

Here, we are given that a line passes through point (-6,-9) and perpendicular to y = 1/4

If two line are perpendicular to each other, the product of their slopes is equal to -1.

Here, the slope of y = 1/4 will be 0 as y is a constant value and not changing.

Let the slope of the given equation be m

them m × 0 = -1

m = -1/0

Thus, the slope is not defined, this means that the line will be parallel to x axis of the form x = k.

Now, we know that the line passes through point (-6,-9). This means that if y = -9, x will be -6. But we know that x will take only one value for all values of y.

Thus, the equation of the line will be x = -6, that is, option B.

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Your question was incomplete. Check for the full content below-

Select the correct answer.

Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6-9)?

OA. x= -9

OB. x=-6

Oc. y=9

OD. y= -4

Answer: 7/8

Step-by-step explanation:

[tex]\displaystyle\\3\frac{1}{2} :4=\\\\\frac{3*2+1}{2}:4=\\\\\frac{6+1}{2}:4=\\\\ \frac{7}{2}*\frac{1}{4} =\\\\\frac{7*1}{2*4} =\\\\\frac{7}{8}[/tex]

The width and length of the rectangle are 11 and 13 cm respectively

The perimeter of a shape is the sum of the side lengths of the shape

For all regular quadrilaterals, you add up the side lengths to determine the perimeter

The given parameters about the rectangle are

Perimeter = 37 + Width

Length = Width + 2 i.e. consecutive odd integers, and width is smaller

Rewrite the above equations as

p = 37 + w

l = w + 2

The perimeter of a rectangle is

p = 2 x (l + w)

Substitute p = 37 + w in the above equation

So, we have

2 x (l + w)= 37 + w

Substitute l = w+ 2 in the above equation

So, we have

2 x (w + 2 + w)= 37 + w

Evaluate the like terms in the above equation

So, we have

2 x (2w + 2)= 37 + w

Open the bracket in the above equation

So, we have

4w + 4= 37 + w

Evaluate the like terms in the above equation

So, we have

3w = 33

Divide both sides of the above equation by 3

So, we have

w = 11

Recall that

l = w + 2

So, we have

l = 11 + 2

Evaluate

l = 13

Hence, the width and length of the rectangle are 11 and 13 cm respectively

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The numbers in this problem are classified as follows:

A. Rational.

B. Rational.

C. Irrational.

Hence:

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Answer:

81°

Step-by-step explanation:

m∠1 + m∠2 + m∠3 = 180° because they add to form a straight angle.

Answer:

(4a3-5a-3)(2a2-7a+3)

Step-by-step explanation:

use 4a3 to multiply everything in the both brackets=

8a⁵-28a⁴+12a³. then use -5a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a³+35a²-15a. then use -3a to multiply everthing in the both brackets =

8a⁵-28a⁴+12a³-10a²+35a²-15a-6a²-21a-9.then you furthermore solve=

8a⁵-28a⁴+2a³+29a²-36a-9

Answer:

Hello,

P=(1,2)

Step-by-step explanation:

[tex]\overrightarrow{OP}=\overrightarrow{OA}+\dfrac{2}{3} *\overrightarrow{AB}\\\\=(-3,-4)+\dfrac{2}{3} *(3-(-3),5-(-4))\\\\=(-3,-4)+\dfrac{2}{3}*(6,9)\\\\=(-3,-4)+2*(2,3)\\\\=(-3,-4)+(4,6)\\\\\boxed{=(1,2)}\\[/tex]

The revenue equation of the item is r = 3.56q

The given parameters are:

Expense equation, E = 3.2q + 56000

Selling price = 3.56 per item

This means that the selling price equation is

S = Selling price per item * Number of items

So, we have

S = 3.56 * q

This gives

S = 3.56q

The total selling price of the item is the same as the revenue equation

So, we have

r = 3.56q

Note that the revenue equation is also a linear equation

Where linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

Hence, the revenue equation of the item is r = 3.56q

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Consecutive integers are those numbers that follow each other. They follow in a sequence or in order. For example, a set of natural numbers are consecutive integers.

As discussed , the numbers that follow each other in an order are called consecutive numbers or consecutive integers. These integers go from smallest to the highest, i.e. in ascending order. Some of the examples are:

From the above examples, we can see, the integers follow each other in a sequence. The difference between preceding and succeeding integers is always equal to 1.

So, given question, we can write:

For a consecutive integers, the number either increases by 1 or decreases.

First we take option 1:

12,22,32

Find out difference,

22-12=10       ,        32-22=10

The difference is '10'

Hence it is not consecutive integer.

We take option 2:

100,99,98

Find out difference,

100-99=1        ,          99-98=1

The difference is '1'

Hence it is consecutive integer.

We take option 3:

-11,-10,-9

Find out difference,

=-10-(-11)      ,       =-9-(-10)

=11-10=1       ,       =-9+10=1        

The difference is '1'

Hence it is consecutive integer.

We take option 4:

10,11,12

Find out difference,

11-10=1        ,          12-11=1

The difference is '1'

Hence it is consecutive integer.

So, 12,22,32 is not contain consecutive integer, because the difference is '10'. For a consecutive integers, the number either increases by 1 or decreases.

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The division statement 1/4 ÷ 7/16 can be seen in a real-life situation when a ratio of boys in two different classes  is being ascertained to help use the ratio of said classes to derive the distribution of textbooks

This is further explained below.

Generally, The process of combining numbers to create new numbers is referred to as division, and it is one of the four fundamental operations of mathematics.

In conclusion,  the remark on the division In real life, the ratio 1/4 to 7/16 may be observed while determining the number of male students in two distinct classrooms in order to determine how many textbooks should be assigned to each of those classes based on the number of male students in each class.

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Answer:

45.10

Step-by-step explanation:

The "quotient" is the answer or result of a division problem.  Look up "significant digits" if you want to know why I have the answer to two decimal places.

Answer:

3

Step-by-step explanation:

You are asked to find the slope of the function.
You can find the slope using the formula [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex].

For simplicity, I'll take the points (0, 0) and (1, 3) and substitute their coordinates into the formula.

[tex]m = \frac{3 - 0}{1 - 0} \to \frac31 \to 3[/tex]

Therefore, [tex]y = 3x[/tex]