Factor completely. (3.2² - 12x)(x2

The width of a kitchen is 4.2 metres.

Svetradugi [14.3K]

Given:

The width of a kitchen is 4.2 metres.

Kitchen cupboard widths are 60 cm.

To find:

The number of kitchen cupboard that will fit in 4.2 metres.

Solution:

Let x be the number of kitchen cupboard that will fit in 4.2 metres.

Width of 1 cupboard = 60 cm

Width of x cupboards = 60x cm

We know that, 1 m = 100 cm.

Width of a kitchen = 4.2 metres

= 4.2×100 cm

= 420 cm

Now, the width of the x cupboards is equal to width of the kitchen.

$60x=420$

$x=\dfrac{420}{60}$

$x=7$

Therefore, the number of kitchen cupboard that will fit in 4.2 metres is 7.

5 0

3 years ago

Reed uses 8 pieces of glass per square foot to make a stained glass window. How many pieces of glass will he need to make a wind

laiz [17]

To solve the problem posed in the statement we need to know the equivalence between squared foot and squared inches, and that is:
1 square foot = 144 square inches
So Reed uses 8 pieces of glass per 144 squared inches as well.
Now we can use a rule of three, simple and direct proportion to solve the question, it goes like this:
144 squared inches ------> 8 pieces glass
864 squared inches ------> x

x = (864)(8)/144
x = 48
Hence, Reed will use 48 pieces of glass to make a window that is 864 square inches.

8 0

3 years ago

Please help! Its for my big test tomorrow!

Travka [436]

Answer:

# The solution x = -5

# The solution is x = 1

# The solution is x = 6.4

# The solution is x = 4

# The solution is 1.7427

# The solution is 0.190757

Step-by-step explanation:

* Lets revise some rules of the exponents and the logarithmic equation

# Exponent rules:

1- b^m × b^n = b^(m + n) ⇒ in multiplication if they have same base

we add the power

2- b^m ÷ b^n = b^(m – n) ⇒ in division if they have same base we

subtract the power

3- (b^m)^n = b^(mn) ⇒ if we have power over power we multiply

them

4- a^m × b^m = (ab)^m ⇒ if we multiply different bases with same

power then we multiply them ad put over the answer the power

5- b^(-m) = 1/(b^m) (for all nonzero real numbers b) ⇒ If we have

negative power we reciprocal the base to get positive power

6- If a^m = a^n , then m = n ⇒ equal bases get equal powers

7- If a^m = b^m , then a = b or m = 0

# Logarithmic rules:

1- $log_{a}b=n-----a^{n}=b$

2- $loga_{1}=0---log_{a}a=1---ln(e)=1$

3- $log_{a}q+log_{a}p=log_{a}qp$

4- $log_{a}q-log_{a}p=log_{a}\frac{q}{p}$

5- $log_{a}q^{n}=nlog_{a}q$

* Now lets solve the problems

# $3^{x+1}=9^{x+3}$

- Change the base 9 to 3²

∴ $9^{x+3}=3^{2(x+3)}=3^{2x+6}$

∴ $3^{x+1}=3^{2x+6}$

- Same bases have equal powers

∴ x + 1 = 2x + 6 ⇒ subtract x and 6 from both sides

∴ 1 - 6 = 2x - x

∴ -5 = x

* The solution x = -5

# ㏒(9x - 2) = ㏒(4x + 3)

- If ㏒(a) = ㏒(b), then a = b

∴ 9x - 2 = 4x + 3 ⇒ subtract 4x from both sides and add 2 to both sides

∴ 5x = 5 ⇒ divide both sides by 5

∴ x = 1

* The solution is x = 1

# $log_{6}(5x+4)=2$

- Use the 1st rule in the logarithmic equation

∴ 6² = 5x + 4

∴ 36 = 5x + 4 ⇒ subtract 4 from both sides

∴ 32 = 5x ⇒ divide both sides by 5

∴ 6.4 = x

* The solution is x = 6.4

# $log_{2}x+log_{2}(x-3)=2$

- Use the rule 3 in the logarithmic equation

∴ $log_{2}x(x-3)=2$

- Use the 1st rule in the logarithmic equation

∴ 2² = x(x - 3) ⇒ simplify

∴ 4 = x² - 3x ⇒ subtract 4 from both sides

∴ x² - 3x - 4 = 0 ⇒ factorize it into two brackets

∴ (x - 4)(x + 1) = 0 ⇒ equate each bract by 0

∴ x - 4 = 0 ⇒ add 4 to both sides

∴ x = 4

OR

∵ x + 1 = 0 ⇒ subtract 1 from both sides

∴ x = -1

- We will reject this answer because when we substitute the value

of x in the given equation we will find $log_{2}(-1)$ and this

value is undefined, there is no logarithm for negative number

* The solution is x = 4

# $log_{4}11.2=x$

- You can use the calculator directly to find x

∴ x = 1.7427

* The solution is 1.7427

# $2e^{8x}=9.2$ ⇒ divide the both sides by 2

∴ $e^{8x}=4.6$

- Insert ln for both sides

∴ $lne^{8x}=ln(4.6)$

- Use the rule $ln(e^{n})=nln(e)$ ⇒ ln(e) = 1

∴ 8x = ln(4.6) ⇒ divide both sides by 8

∴ x = ln(4.6)/8 = 0.190757

* The solution is 0.190757

7 0

4 years ago

Read 2 more answers

A box of colored pencils contains exactly 6 red pencils. The probability of choosing a red pencil from the box is 2/7. How many

ZanzabumX [31]

Answer:

B.21

Step-by-step explanation:

Calculator

4 0

3 years ago

The expression to find the perimeter of a rectangle is 2(length + width). What is the perimeter, in units, of a rectangle of len

Allisa [31]

First you plug in the data to the formula. So it will be 2(1/3+1/2). You then want to add the fractions together but must first find the common denominator which will be 6. So it is 2(2/6+3/6). The fractions then add up to be 5/6. So all you have to do is multiply it by 2 to get 5/3 which simplifies to 1 2/3 so it is D.

4 0

3 years ago

Read 2 more answers

Factor completely. (3.2² - 12x)(x2 – 2x + 1) =​

Factor completely. (3.2² - 12x)(x2 – 2x + 1) =