1) √3 √7 = √21
2) √5 √245 = √5 √5 * 49 = √5 * 7√5 = 7 √5 * 5 = 7 √25 = 7 * 5 = 35
3) √77 ÷ √11 = as is. can't be simplified.
4) (√59)² = 59 ; the square root was cancelled by squared.
5) 3√6 x 8√7 = 3 * 8 √6 * 7 = 24 √42
6) 5√3 x 6 √3 = 5 * 6 √3 * 3 = 30 √9 = 30 * 3 = 90
7) 40√30 ÷ 5√3 = (40 / 5) * (√30 /√3) = 8 * ((√3 *10) / √3) = 8 √10
8) (6√5)² = 6² * √5² = 36 * 5 = 180
Answer:
125
Step-by-step explanation:
Given
f(x) = 5x²
g(x) = 2x + 3
Now
g(-4) = 2 * (- 4) + 3
= - 8 + 3
= - 5
Also
f(g(-4)) = f( -5)
= 5 * ( -5)²
= 5 * 25
= 125
Answer:
the answer is 3
Step-by-step explanation:
(-5x-3)(-5x+3)=(5x)^2 - (3)^2
A difference of squares is the difference of two squared terms.
We have
a^2 - b^2
We can factorize the difference of squared terms like this:
a^2-b^2 = (a+b)(a-b)
We have (-5x-3)(-5x+3)
Lets prove it:
(-5x-3)(-5x+3) = (-5x*-5x)+(-5x*3)+(-3*-5x)+(-3*3)
(-5x-3)(-5x+3) = 25x^2+(-15x)+(15x)+(-9)
(-5x-3)(-5x+3) = 25x^2-15x+15x-9
(-5x-3)(-5x+3) = 25x^2-9
(-5x-3)(-5x+3) = (5x)^2 - (3)^2
Option B: The area of the trapezoid is 157.5 m²
Explanation:
We need to determine the area of the trapezoid.
The area of the trapezoid can be determined by the formula,

where h is the height, a and b are the base of the trapezoid.
From the figure, it is obvious that
,
and 
Substituting these values in the formula, we have,

Simplifying the terms, we have,

Multiplying the terms in the numerator, we have,

Dividing, we get,

Thus, the area of the trapezoid is 157.5 m²
Hence, Option B is the correct answer.
Answer:
No.
Step-by-step explanation:
For polygon PQRST to be considered a scaled copy of polygon ABCDE, it means every segments of polygon ABCDE were increased proportionally by a scale factor.
The segments in polygon PQRST were not gotten using the same scale factor, hence, it is not a scaled copy of the original polygon, ABCDE.
Segment CD = 2 units, it corresponds to segment RS = 4 units. Scale factor = RS/CD = 4/2 = 2
Segment BC = 1 unit, it corresponds to segment QR = 1 unit. Scale factor = QR/BC = 1/1 = 1 units.
Varying scale factor shows polygon PQRST is not a scaled copy of polygon ABCDE.