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Sati [7]
3 years ago
15

Prove by factorization √16×81=√16×√81

Mathematics
1 answer:
Oksanka [162]3 years ago
4 0

Answer:

√16×81 = 4×9 or √1296 = 36

√16×√81 = 4×9 = 36

Step-by-step explanation:

√81×16

We simplify 81 and 16 by prime factorisation (expressing a number as a product of its prime factors).

√81 = √3×3×3×3 = √9×9 = √9² = 9

√16 = √2×2×2×2 = √4×4 = √4² = 4

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WILL GIVE BRAINLIEST!!
VMariaS [17]

Answer:

A(-1,4)\to A''(-1,-1)

B(0,2)\to B''(1,0)

C(1,2)\to C''(1,1)

D(-2,4)\to D''(-1,2)

Step-by-step explanation:

The given trapezoid has vertices at A(−1,4), B(0,2), C(1,2) and D(2,4).

The transformation rule for 90° counterclockwise rotation is

(x,y)\to(-y,x)

This implies that:

A(-1,4)\to A'(-4,-1)

B(0,2)\to B'(-2,0)

C(1,2)\to C'(-2,1)

D(2,4)\to D'(-4,2)

This is followed by a translation 3 units to the right.

This also has the rule: (x,y)\to (x+3,y)

A'(-4,-1)\to A''(-1,-1)

B'(-2,0)\to B''(1,0)

C'(-2,1)\to C''(1,1)

D'(-4,2)\to D''(-1,2)

Therefore:

A(-1,4)\to A''(-1,-1)

B(0,2)\to B''(1,0)

C(1,2)\to C''(1,1)

D(-2,4)\to D''(-1,2)

3 0
3 years ago
Urgent!! Will mark brainliest!!
anastassius [24]

Answer:

1) tanФ = 0.8392 ⇒ 2nd answer

2) cosФ = 20/29 ⇒ 3rd answer

3) cosФ = -√2/2 , cotФ = -1 ⇒ first answer

Step-by-step explanation:

* At first check the quadrant of the angle

∵ 180° < Ф < 270°

∴ Ф lies on the third quadrant

* Remember in the 3rd quadrant tanФ and cotФ only positive

∵ sinФ ≅ -0.7660

∵ tan²Ф = sec²Ф - 1

∵ secФ = 1/sinФ

∵ secФ = 1/-0.7660

∴ sec²Ф = (1/-0.7660)²

* Substitute this value in the equation

∴ tan²Ф = (1/-0.7660)² - 1 = 0.70428594 ⇒ take √ for both sides

∴ tanФ ≅ ± 0.8392

∵ Ф lies on the 3rd quadrant

∴ tanФ = 0.8392

* At first check the quadrant of the angle

∵ 0° < Ф < 90°

∴ Ф lies on the first quadrant

* Remember in the 1st quadrant all are positive

∵ sinФ = 21/29

∵ sin²Ф + cos²Ф = 1

∴ (21/29)² + cos²Ф = 1 ⇒ subtract (21/29)² from both sides

∴ cos²Ф = 1 - (21/29)² = 400/841 ⇒ take √ in both sides

∴ cosФ = ± 20/29

* Because Ф lies in the 1st quadrant

∴ cosФ = 20/29

* Remember that when the point is at the terminal side of angle Ф

∴ Its x-coordinate is cosФ

∴ Its y-coordinate is sinФ

* The point is (-√2/2 , √2/2)

∵ x-coordinate is negative ad y-coordinate is positive

∴ the point is on the 2nd quadrant

∴ 90° < Ф < 180°

∴ The values of sinФ and cscФ only positive

* From previous we know that:

∴ cosФ = -√2/2

∴ sinФ = √2/2

∵ cotФ = cosФ/sinФ

∴ cotФ = -√2/2 ÷ √2/2 = -√2/2 × 2/√2 = -√2/√2 = -1

* cosФ = -√2/2 , cotФ = -1

3 0
3 years ago
Which graph represents the piecewise-defined function? y={−45x−3   if  x&lt;03x−10   if  x≥2
Nikitich [7]

Step-by-step explanation:

y=\left \Bigg\{ {\big{-45x-3 \qquad x < 0} \atop \big{3x - 10 \qquad x \geq2 }} \right.

\begin {array}{c|c}{ x&y}}\\ -\infty&-\infty\\-2&-93\\-1&-48\\ 0 &-3^*\\1&nothing\\2&-4\\3&-1\\4&2\\ \infty&\infty\\\end{array}

* open dot

You did not provide the graphs to choose from so use the table above to determine which graph fits those coordinates.

Make sure that:

  • (0, -3) has an open dot
  • nothing is plotted between x = 0 and x = 2
  • (2, -4) has a closed dot
3 0
3 years ago
What is the slope of this line?<br><br> A: - 1/3<br><br> B: - 2/3<br><br> C: 2/3<br><br> D: 1/3
bezimeni [28]

Answer:

The answer is C. 2/3

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please help me anyone help ?!!!!!!
Andre45 [30]
Its c the line meets right a -3
6 0
3 years ago
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