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Kipish [7]
3 years ago
7

Factorise the following using the Difference of Two Squares or Perfect Squares rule: a) (2x-2)^2 - (x+4)^2 b) (3x+4) (3x-4)

Mathematics
1 answer:
emmainna [20.7K]3 years ago
7 0

Answer:

Step-by-step explanation:

Hello, please consider the following.

a)

(2x-2)^2 - (x+4)^2 \\\\=(2x-2-(x+4))(2x-2+x+4)\\\\=(2x-2-x-4)(3x+2)\\\\=\boxed{(x-6)(3x+2)}

b)

(3x+4) (3x-4)\\\\=(3x)^2-4^2\\\\=\boxed{9x^2-16}

Thank you.

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Five widgets and three gadgets cost $109. 90.
erma4kov [3.2K]

Answer:

one gadget costs $15.80

Step-by-step explanation:

Let w = cost of one widget

Let g = cost of one gadget

Given:

  • Five widgets and three gadgets cost $109. 90

⇒ 5w + 3g = 109.9

Given:

  • One widget and four gadgets cost $75. 70

⇒ w + 4g = 75.7

Rewrite  w + 4g = 75.7  to make w the subject:

⇒ w = 75.7 - 4g

Substitute into  5w + 3g = 109.9  and solve for g:

⇒ 5(75.7 - 4g) + 3g = 109.9

⇒ 378.5 - 20g + 3g = 109.9

⇒ 378.5 - 109.9 = 20g - 3g

⇒ 268.6 = 17g

⇒ g = 15.8

Therefore, one gadget costs $15.80

To find the cost of one widget, substitute the found value for g into
w = 75.7 - 4g and solve for w:

⇒ w = 75.7 - 4(15.8)

⇒ w = 75.7 - 63.2

⇒ w = 12.5

Therefore, one widget costs $12.50

5 0
2 years ago
Find the area of the trapezoid.<br> Answer options: 8sqrt2, 4sqrt3, 12.0, 16sqrt2
Elis [28]

Answer:

=  8sqrt2

Step-by-step explanation:

Area of a trapezium is given by the formula;

1/2(a+b)h ;

Where a and b are the parallel sides and h is the perpendicular height.

a = 3 cm, b= 5 cm

To get; h, we use the Pythagoras theorem;

h² = 3² - 1²

   h² = 8

h = √8

  = √4√2

 = 2√2

Thus;

Area = 1/2(3 +5) 2√2

         = 1/2 ×8 × 2√2

       <u>  = 8√2 cm² or  8sqrt2 cm²</u>

8 0
3 years ago
Simplify the scalar multiplication on the matrix.
Romashka-Z-Leto [24]

Answer:

third option

Step-by-step explanation:

Given

3 \left[\begin{array}{ccc}-2&5\\1&0\\\end{array}\right]

Multiply each element in the matrix by 3

= \left[\begin{array}{ccc}3(-2)&3(5)\\3(1)&3(0)\\\end{array}\right]

= \left[\begin{array}{ccc}-6&15\\3&0\\\end{array}\right]  

7 0
3 years ago
Use this expression to name each item. 7m3 + 6r2 – 3r - 8
Vitek1552 [10]

Answer:

In the given expression 7m^3 + 6r^2 - 3r - 8

Variables = m, r

Coefficients = 7, 6 and -3

constant= -8

Step-by-step explanation:

We are given the expression 7m^3 + 6r^2 - 3r - 8

We need to give variable, coefficients and constant.

Variable: The value of variable may change. It can be represented by x, y or any other letter

Coefficients: A numerical or constant quality that is placed with the variable. For example in 4x, 4 is coefficient

Constant: It is fixed value. It cannot be changed.

So, in the given expression 7m^3 + 6r^2 - 3r - 8

Variables = m, r

Coefficients = 7, 6 and -3

constant= -8

4 0
3 years ago
Is 216 more than 30% of 720​
Natali [406]

Answer:

No, it is equal

Step-by-step explanation:

30% of 720 is 216.

5 0
3 years ago
Read 2 more answers
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