Max and Molly plan to put down all-weather carpeting on their porch. The length of the porch is 9 ft longer than twice the width, and the perimeter is 138 ft.

Answer:

Step-by-step explanation:

A translation moves a shape up, down or from side to side but it does not change its appearance in any other way.

Here also, triangle ABC and triangle A'B'C' are equal only position is changed

Answer:

6) F

7) B

Step-by-step explanation:

6)

[tex]\boxed{perimeter \: of \: rectangle = 2(length + breadth)}[/tex]

60= 2[½(n -6) +2n +5]

Expand:

60= 2(½)(n -6) +2(2n) +2(5)

60= n -6 +4n +10

Simplify:

60= 5n +4

Minus 4 on both sides:

5n= 60 -4

5n= 56

Divide both sides by 5:

n= 56 ÷5

n= 11.2

Thus, option F is correct.

7)

[tex]\boxed{area \: of \: rectangle = length \: \times breadth}[/tex]

13q +2= 9(q +6)

Expand:

13q +2= 9q +54

Bring q terms to one side, constant to the other:

13q -9q= 54 -2

Simplify:

4q= 52

Divide both sides by 4:

q= 52 ÷4

q= 13

Thus, option B is correct.

Answer: Prime

A polynomial is  prime    if its only factors over the integers are 1 and itself.

==============================================================

Explanation:

Think of the idea of factoring whole numbers like factoring 36 into 6*6 which further breaks down into (2*3)*(2*3) = 2^2*3^2. This shows that 36 is composite and not prime.

Something like 7 is prime because the only factors are 1 and itself.

This idea extends into polynomials as well.

Something like x^2+4x+4 factors to (x+2)(x+2) which shows it is not prime. On the other hand, the polynomial x^2+3x+5 is prime over the integers because we cannot factor it like the previous example. The only factors here are 1 and itself.

Factoring is handy to help determine roots of a polynomial. However, other tricks could be used such as the quadratic formula or using numerical approximation techniques.

Answer:

[tex]38[/tex] and [tex]68[/tex].

Step-by-step explanation:

Let [tex]x[/tex] be the smaller one of the two number.

[tex]x[/tex] must be a positive integer. The other number would be [tex](x + 30)[/tex].

The question states that the product of the two numbers is [tex]2584[/tex]. In other words:

[tex]x\, (x + 30) = 2584[/tex].

Rearrange this equation and solve for [tex]x[/tex]:

[tex]x^{2} + 30\, x - 2584 = 0[/tex].

The first root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) + \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= \frac{(-30) + \sqrt{900 + 10336}}{2} \\ &= \frac{(-30) + \sqrt{11236}}{2} \\ &= \frac{(-30)}{2} + \sqrt{\frac{11236}{2^{2}}} \\ &= (-15) + \sqrt{2809} \\ &= (-15) + 53 \\ &= 38 \end{aligned}[/tex].

Similarly, the second root of this quadratic equation would be:

[tex]\begin{aligned}x_{1} &= \frac{(-30) - \sqrt{30^{2} - 4 \times (-2584)}}{2} \\ &= (-15) - 53 \\ &= -68\end{aligned}[/tex].

Since the question requires that both numbers should be positive, [tex]x > 0[/tex]. Therefore, only [tex]x = 38[/tex] is valid.

Hence, the two numbers would be [tex]38[/tex] and [tex](38 + 30)[/tex], which is [tex]68[/tex].

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Answer:

  38 and 68

Step-by-step explanation:

Let x represent the average of the two numbers. Then their product is ...

  (x -15)(x +15) = 2584

  x^2 = 2584 +225 = 2809 . . . . . . use relation (x -a)(x +a) = x^2 -a^2; add a^2

  x = √2809 = 53

Then the two numbers are ...

  53 +15 = 68

and

  68 -30 = 38

The two numbers are 38 and 68.

_____

Additional comment

Solving the problem in this way is equivalent to writing the quadratic equation for the smallest (or largest) number and solving that by completing the square. The "solution" x = -53 is not relevant in this problem.

Answer:

Answer:

8.15×10^5

Step-by-step explanation:

8.15×10^5

8.15×100000

815000

Answer:

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

240÷8days=30

30×12days=360

Answer:

Step-by-step explanation:

i dont know  but work hard

Answer:

It is -80

Step-by-step explanation:

u just subtract

Answer:

0

Step-by-step explanation:

You can't divide anything by zero

0÷0=

=0

Answer:

Answer: n is 110

Step-by-step explanation:

Formular:

[tex]mean = \frac{ \sum(n_{1}, \: n _{2}, \: ...n_{n} ) }{n} \\ [/tex]

therefore:

[tex]140 = \frac{(120 + 145 + 130 + 80 + 95 + 100 + 340 + n)}{8} \\ \\ (8 \times 140) = 1010 + n \\ 1010 + n = 1120 \\ n = 1120 - 1010 \\ n = 110[/tex]

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Answer:

  A: ∠WXZ = 87°; ∠ZXY = 73°

Step-by-step explanation:

Ray XZ divides the angle WXY into parts that have a sum equal to the whole.

  (7x-4)° +(5x+8)° = 160° . . . . . whole is sum of parts

  12x = 156 . . . . . . . . . . . . . divide by °, subtract 4

  x = 13 . . . . . . . . . . . . . . divide by 12

  ∠WXZ = (7x -4)° = (7·13 -4)° = (91 -4)° = 87° . . . . . matches choice A

Answer:

5 and 7 are factors

35 is the product

Step-by-step explanation:

5 and 7 are the factors

you multiply factors to get a product

35 is a product of the factors, 5 and 7

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Unreduced: (4) + (5 • x) + (-9) + (4 • x)

Reduced: 9x – 5

Step-by-step explanation:

-4^(-5)/ 2^(-3) =

2³/(-4)^5 =

8/(-1024) =

- 1/128 (d)

Answer:

Fred is 6

Jimmy is 17

Step-by-step explanation:

Jimmy's age =2x +5

Fred's age =x

x+2x+5=23

3x=23-5

3x=18

x=6

Jimmy's age =2(6)+5=17

Fred is 6

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Answer:

  7/8 in  (you are correct)

Step-by-step explanation:

The amount of nail that goes into the framing member is ...

  1 3/4 -3/8 -1/2

  = 1 6/8 -3/8 -4/8

  = 1 -1/8 = 7/8 . . . . inches

Answer:

B. Because statistics can be applied to every field of study

Answer:

[tex] \frac{6}{7} [/tex]

Step-by-step explanation:

[tex] \frac{5}{7} - ( - \frac{1}{7} )[/tex]

[tex] \frac{5}{7} + \frac{1}{7} [/tex]

[tex] = \frac{6}{7} [/tex]

Step-by-step explanation:

[tex]8 {x}^{3} - 5 {x}^{2} + x + 2 \div {x}^{2} [/tex]

[tex]8 {x}^{3} - 5 {x}^{2} + x + \frac{2}{ {x}^{2} } [/tex]

[tex] = \frac{8 {x}^{5} - 5 {x}^{4} + {x}^{3} + 2}{ {x}^{2} } [/tex]

Answer:

X = 111°

I hope it's helps you

Answer:

Step-by-step explanation:

it apperes to me that all are rational numbers

Hope this helps

Answer:

2W + 56 = 78 , W = 10

Step-by-step explanation:

perimeter of rectangle = 2*the Length + 2*the Width

Answer:

6

Step-by-step explanation:

[tex]12 \times 1 \frac{1}{2} [/tex]

[tex]12 \times \frac{1}{2} [/tex]

[tex] = 6[/tex]

Answer:

1523797

Step-by-step explanation:

Have a good day, hope I helped

Answer:

1,523,797

Step-by-step explanation:

734,839 + 788,958

= 1,523,797