The length of a rectangle is three times its width. The perimeter of the rectangle is at most 112 cm.

Which inequality models the relationship between the width and the perimeter of the rectangle?



2w+2⋅(3w)≥112
2w+2⋅(3w)<112
2w+2⋅(3w)>112
2w+2⋅(3w)≤112

Answer:

24(2+3)=24.2+24.3=48+72

Step-by-step explanation:

Given form of number is 48+72.

we have to apply the distributive property to express the above number.

The distributive property is

a(b+c)=ab+ac

Multiply the common term with the term inside the parentheses

So to express 48+72 we have to take the highest factor outside

Let us take 24 outside, we get

24(2+3)=24.2+24.3=48+72

Hence applied

The required expression is [tex]24(2+3)[/tex] by using the distributive property.

Given:

The given expression is [tex]48+72[/tex].

To find:

The equivalent expression by using the distributive property.

Explanation:

According to the distributive property:

[tex]a(b+c)=ab+ac[/tex]

We have,

[tex]48+72[/tex]

It can be rewritten as:

[tex]48+72=24\times 2+24\times 3[/tex]

Using the distributive property, we get

[tex]48+72=24(2+3)[/tex]

Therefore, the required expression is [tex]24(2+3)[/tex].

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lcm 16 & 10 = 80

lcm j^8 & j^9 = j^9

lcm k^8 & k^4 = k^8

lcm m^5 & m^6 = m^6

answer is: 80j^9k^8m^6

Answer:

  28

Step-by-step explanation:

Let n represent the number.

Twice the sum of the number and 2 is ...

  2(n +2)

Three times the difference of the number and 8 is ...

  3(n -8)

The problem statement tells us these quantities are equal, so ...

  2(n +2) = 3(n -8) . . . . the given quantities are equal

  2n +4 = 3n -24 . . . . . use the distributive property to eliminate parentheses

  2n +28 = 3n . . . . . . . add 24

  28 = n . . . . . . . . . . . . subtract 2n

The number is 28.

_____

Check

The sum of the number and 2 is 30; twice that is 60.

The difference of the number and 8 is 20; three times that is 60--the same number.

Answer:

80%

Step-by-step explanation:

Let us suppose x percent of Bill's salary is equal to Jacks's salary.

Thus, we can write

x% of 87.50 = 70

Mathematically, we can write this as

[tex]0.0x\times87.50=70[/tex]

Solve the equation for x

[tex]0.0x=\frac{70}{87.50}\\\\x=\frac{70}{87.50}\times100\\\\x=80[/tex]

Therefore, Jack's salary is 80% of Bill's salary

Answer: So, the required inequality that can be used to represent this situation is [tex]2x+3\leq 31[/tex]

Step-by-step explanation:

Let the age of Catie's brother be 'x'.

Let the age of Catie be 'x+3'.

According to question, the sum of their ages is no more than 31.

So, it becomes,

[tex]x+x+3\leq 31\\\\2x+3\leq 31[/tex]

So, the required inequality that can be used to represent this situation is

[tex]2x+3\leq 31[/tex]

Answer:-  2. ∠JKM≅∠LKM

5. MK≅MK

6. AAS congruence postulate.

7. Corresponding parts of congruent triangles are congruent.

8. Definition of equidistant.

Therefore the complete proof will be

Proof :- 1. KM is the line bisector of ∠JKL.  [Given]

2. ∠JKM≅∠LKM             [Definition of bisector]

3. ∠KXM and ∠KYM are right angles [Given]

4. ∠KXM ≅ ∠KYM [All right angles are congruent]

5. MK≅MK  [reflexive property of congruence]

6. ΔKXM ≅ ΔKYM  [AAS congruence postulate]

7. MX≅MY [Corresponding parts of congruent triangles are congruent]

8. Point  M is equidistant from the sides of ∠JKL [Definition of equidistant]

Hence proved.

The required equation of the line is y = 3x which passes through the origin with the slope 3.

The slope of the line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

We have to determine the equation of the line that passes through the origin with slope 3.

Let's assume slope-intercept form:

So required line in the slope-intercept form is:

y = mx + b

where m is the slope and b is the y-intercept.

In this case, the slope of line m = 3, and the line passes through the origin

So, therefore equation will be:

y = 3x + 0 or

y = 3x

Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.

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Answer:

The answer is [tex]9[/tex]

Step-by-step explanation:

we have

[tex](243)^{\frac{2}{5}}[/tex]

we know that

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

so

[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]

Remember that

[tex]243=3^{5}[/tex]

Substitute

[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]

Answer:

4.

Step-by-step explanation:

[tex]18x^{2} -32 = 2(9x^{2} -16)[/tex]

we apply difference of squares

2(3x-4)(3x+4)

So, the missing term is 4.

The missing term in the factorization 18x² − 32 = 2(3x + ?)(3x − 4) is 4.

Factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form. Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.

For an integer, Factorization is decomposition of that integer in terms of smaller integers; when multiplied with each other give back that considered number. Those composing integers are called factors of that considered integers.

WE have given an expression as;

18x² − 32 = 2(3x + ?)(3x − 4)

Now we apply difference of squares;

2(9x² - 16)

2(3x + 4)(3x - 4)

OR

2(3x-4)(3x+4)

Therefore, the missing term is 4.

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1. less than  ( I gave x a number and did both equations )

2. the equation = 400 which is greater than 35

divide 714 by 12

714 / 12 = 59.5 spools per week

Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.

So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].

Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.

Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].

ANSWER: [tex](-3,-1)[/tex]

Answer:

(-3, -1)

Step-by-step explanation:

The x-intercepts of the graphed function are -2, -1, 1, and 2

The x-intercept is the point where the graph crosses the x-axis

This means that the point on the x-axis where y = 0

From the graph, we have:

x = -2, -1, 1, and 2 when y = 0

Hence, the x-intercepts of the graphed function are -2, -1, 1, and 2

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Answer:

29 4/25 square inches (not given in the options)

Step-by-step explanation:

A square is a plain 4 sided shape with equal sides. As such, all sides of a square are equal. If the length o a side of a square is s, the area of the square will be s² while the perimeter will be 4s.

Area of square = (5 2/5 inches)²

= (27/5 inches)²

= 729/25 square inches

= 29 4/25 square inches