Which of the following are square roots of the number below ? check all that apply 81

a. 18
b.-(81)^1/2
c.9
d.81^1/2

Answers

Answer 1

Answer: The answers are:
b.-(81)^1/2
c.9
d.81^1/2

√a = -a^1/2 ⇒ √81 = -81^1/2
√a = a^1/2 ⇒ √81 = 81^1/2

√81 = √9²
√a² = a ⇒ √9² = 9
√a² = -a ⇒ √9² = -9

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Which of the following is equivalent to 6x 2 + x - 12 ?A. (2x + 3)(3x - 4)
B. (2x - 3)(3x - 4)
C. (2x + 3)(3x + 4)
D. (6x + 3)(x - 12)
E. (x + 3)(2x - 12)
Please show me step by step how to solve this problem
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Answers

$6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\n\n=(2x-3)(3x+4)\n\nother\ method:\n\n6x^2+x-12\na=6;\ b=1;\ c=-12\n\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(289)=17$

$x_1=(-1-17)/(2\cdot6)=(-18)/(12)=-(3)/(2);\ x_2=(-1+17)/(2\cdot6)=(16)/(12)=(4)/(3)\n\n6x^2+x-12=6(x+(3)/(2))(x-(4)/(3))=2\cdot3(x+(3)/(2))(x-(4)/(3))\n\n=2(x+(3)/(2))\cdot3(x-(4)/(3))=(2x+3)(3x-4)$

Sin78 ×cos42+cos78×sin42 evaluate without the use of a calculator

Answers

sin a * cos b + cos a * sin b=sin (a+b)

sin 78 * cos 42 + cos 78* sin 42=sin (78+42)=sin 120=sin(180-120)=
sin 60=√3 / 2

Answer: sin 78 * cos 42 + cos 78* sin 42=√3 / 2

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm, the exact length of the other leg is _______ cm. A. √ 3
B. 1
C. 3
D. 4

Answers

Answer:

The length of the other leg is 1 cm.

Step-by-step explanation:

By using the pythagorean theorem

Hypotenuse² = Perpendicular² + Base²

As given

If the hypotenuse of a right triangle is 2 cm and one leg is √ 3 cm.

Let us assume that the unknown length be x.

Thus

2² = Perpendicular² + Base²

$4^(2)= (√(3))^(2) + x^(2)$

$(√(3))^(2) = 3$

4 = 3 + x²

x² = 4 -3

$x = √(1)$

x = 1 cm

Therefore the length of the other leg is 1 cm.

The exact length of the other leg is B. 1 cm.

The diagram shows a dilation of segment AB. Whichstatements are true about the dilation? Select all that
apply
The dilation is an enlargement
The dilation is a reduction
Point O is the center of dilation.
The scale factor is 3.
The scale factor is 9.

Answers

Answer: 1, 3, 4

Step-by-step explanation:

I took the test on Edge. No brainliest needed. =)

Answer:

1,3,4

Step-by-step explanation:

Which represents the solution(s) of the system of equations, y = –x2 + 6x + 16 and y = –4x + 37? Determine the solution set algebraically.a.(3, 25)
b.(–3, 49)
c.(3, 25) and (7, 9)
d.(–3, 49) and (–7, 65)

Answers

Answer: c.(3, 25) and (7, 9)

y = –x^2 + 6x + 16 and y = –4x + 37

Plug in -4x+37 for y in first equation . It becomes

$-x^2 + 6x + 16= -4x+37$

Combine like terms. add 4x and subtract 37 on both sides

$-x^2 + 10x - 21=0$

Divide the whole equation by -1 to remove negative sign from -x^2

$x^2 - 10x + 21=0$

Now factor the left hand side

(x-7)(x-3) = 0

x-7 =0 and x-3=0

x= 7 and x=3

Now we find out y using y = –4x + 37

when x= 7 , then y=-4(7) +37 = 9

when x= 3, then y=-4(3) + 37 = 25

We write solution set as (x,y)

(7,9) and (3,25) is our solution set

TO determine the solution set of the equations given above, we can use substitution method. We do as follows:

y = –x2 + 6x + 16 and y = –4x + 37

–x2 + 6x + 16 = –4x + 37
-x^2 +10x -21 = 0
x = 7 and 3
y = 9 and 25

Therefore, option C is the correct answer.

Which of these items is the better buy? A. An 8-pack of glue sticks for $3.99 or 1 glue stick for $0.54? B. A 12-pack of tape for $2.50 or 1 roll of tape for $0.19 c. A 100-pack of pencils for $4.88 or 1 pencil for $0.05 d. A 50-pack of paper clips for $0.89 or a 25-pack of paper clips for $0.45

Answers

Answer: A is the 8-pack, B is the single roll, C is the 100 pack, D is the 50 pack.

Step-by-step explanation:

For each of these, multiply the smaller number by a number that has a product of the bigger number, example D. multiply 25 by 2 to get 50, then compare the totals.

Answer:

the first one is an 8 pack of glue sticks

the second one is 1 tape roll for .19

the third one is 100 pack of pencils for 4.88

the fourth one is a 25 pack of paper clips

Step-by-step explanation:

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