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3 years ago

The rectangle below has an area of 30k3 + 6k2.

Mathematics

1 answer:

Anit [1.1K]3 years ago

8 0

9514 1404 393

Answer:

length: (5k +1)
width: 6k^2

Step-by-step explanation:

The GCF of the two terms is the second term: 6k^2. When that is factored out, you have ...

area = (6k^2)(5k +1)

According to the problem statement, this is interpreted as ...

width: 6k^2

length: 5k+1

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Which could be the first step in simplifying this expression? Check all that apply. (x cubed x Superscript negative 6 Baseline)

PtichkaEL [24]

Answer:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

Step-by-step explanation:

$(x^{3} x^{-6} )^{2}$ is the expression given to be solved.

First of all let us have a look at 3 formulas:

$1.\ p^a \times p^b = p^{(a+b)}\\2.\ (p^a \times q^b)^c = (p^{a})^c \times (q^{b})^c\\3.\ (p^a)^b = p^{a\times b}$

Both the formula can be applied to the expression( $(x^{3} x^{-6} )^{2}$ ) during the first step while solving it.

Applying formula (1):

$(x^{3} x^{-6} )^{2}$

Comparing the terms of $(x^{3} x^{-6} )$ with $p^a \times p^b$

$p=x, a =3, b=-6$

$\Rightarrow x^{3+(-6)}\\\Rightarrow x^{3-6}\\\Rightarrow x^{-3}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $(x^{-3} )^{2}$

Applying formula (2):

Comparing the terms of $(x^{3} x^{-6} )^{2}$ with $(p^a \times q^b)^c$

$p=q=x, a =3, b=-6, c=2$

$\Rightarrow (x^{3})^2\times (x^{-6})^2\\\text{Applying Formula (3)}\\x^6 x^{-12}$

So, $(x^{3} x^{-6} )^{2}$ is reduced to $x^6 x^{-12}$ .

So, the answers can be:

$(x^{-3} )^{2}$

$x^6 x^{-12}$

8 0

3 years ago

Use of law of sines or law of cosines to find the length of side AB PLEASE SHOW WORK!!

NemiM [27]

Answer = 462.738°
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3 years ago

Convert 12 cups to quarts

Trava [24]

Answer: 3 quarts

using the information 1 cup = 0.25 quarts, we can use dimensional analysis or a conversion factor to find the number of quarts in 12 cups.

start by expressing x as your unknown value being the number of quarts

there are 3 quarts in 12 cups

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Umber 8. What is the value of the expression - -g-(-5) =-9 - 5 5

pantera1 [17]

First, we want to subtract the numbers within the parenthesis. However, to do this we must put each number over a common denominator. We can do his by multiplying

by the appropriate for of

(

−

)

⇒

(

[

]

−

)

⇒

(

−

)

⇒

(

)

Next, we can multiply the two fractions to complete the evaluation of the expression:

(

)

⇒

Now, we can factor the numerator and denominator so we can cancel common terms. This will give the simplest form of the fraction:

⇒

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3 years ago

A. Find PR in the diagram b. Find the perimeter of quadrilateral PQRS

Elan Coil [88]

Answer:

Step-by-step explanation:

The quadrilateral has 4 sides and only two of them are equal.

A) to find PR, we will consider the triangle, PRQ.

Using cosine rule

a^2 = b^2 + c^2 - 2abcos A

We are looking for PR

PR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70

PR^2 = 64 + 49 - 112 × 0.3420

PR^2 = 113 - 38.304 = 74.696

PR = √74.696 = 8.64

B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,

We will use the sine rule because only one side,PR is known

For sine rule,

a/sinA = b/sinB

SP/ sin 35 = 8.64/sin110

Cross multiplying

SPsin110 = 8.64sin35

SP = 8.64sin35/sin110

SP = (8.64 × 0.5736)/0.9397

SP = 5.27

SR = SP = 5.27

The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm

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3 years ago