Find the factorization of the polynomial below.

81x^2 - 18x + 1

A. (9x + 1)^2

B. (18x + 1)^2

C. (18x - 1)^2

D. (9x - 1)^2

[tex]2x {}^{2} - x - 4[/tex]

[tex]x = \frac{ - ( - 1) + \sqrt{1 - 4(2)( - 4)} }{2(2)} = \frac{1 + \sqrt{33} }{4} [/tex]

[tex]x = \frac{1 - \sqrt{33} }{4} [/tex]

[tex](x - \frac{1 + \sqrt{33} }{4} )(x - \frac{1 - \sqrt{33} }{4} )[/tex]

[tex](4x - 1 - \sqrt{33} )(4x - 1 + \sqrt{33} )[/tex]

Answer:

D

Step-by-step explanation:

[tex]4\sqrt{x2[/tex] means [tex](x^{2})^{\frac{1}{4} }[/tex] so then according to indices rule, the powers will be multiplied. Do the same thing for y and z as well, and you will get the answer

Answer:

Step-by-step explanation:

Answer:

Question 42

area of a triangle = 1/2 × base × height

Given:

Substituting given values into the formula:

⇒ 14 = 1/2 × x × (x + 3)

⇒ 28 = (x + 3)x

⇒ 28 = x² + 3x

⇒ x² + 3x - 28 = 0

⇒ (x - 4)(x + 7) = 0

⇒ x = 4, x = -7

As length is positive, x = 4 only.

⇒ height = 4 + 3 = 7 in

⇒ base = 4 in

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Question 43

volume of a cuboid = length x width x height

Given:

Substituting given values into the formula:

⇒ 72 = 6 × (2x - 5) × x

⇒ 12 = (2x - 5)x

⇒ 12 = 2x² - 5x

⇒ 2x² - 5x - 12 = 0

⇒ (x - 4)(2x + 3) = 0

⇒ x = 4, x = -1.5

As length is positive, x = 4 only.

⇒ height = 4 in

⇒ width = 2(4) - 5 = 3 in

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Question 44

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substituting given values into the formula:

⇒ (x - 7)² + x² = 13²

⇒ x² - 14x + 49 + x² = 169

⇒ 2x² - 14x - 120 = 0

⇒ x² - 7x - 60 = 0

⇒ (x - 12)(x + 5) = 0

⇒ x = 12, x = -5

As length is positive, x = 12 only.

⇒ one leg = 12 m

⇒ other leg = 12 - 7 = 5 m

Using it's concept, it is found that the domain for the expressions is, respectively, given by:

[tex]x \neq 0, x \neq 0, (-\infty, \infty), (-\infty, \infty), x \neq 2[/tex]

It is the set that contains all possible input values.

In a fraction, the denominator cannot be zero, hence:

The third expression can be simplified, as:

(x + 5)/(x + 5) = 1.

The same is true for the fourth, as:

x²/x = 1.

Neither has any restriction, hence their domain is all real numbers, represented by [tex](-\infty, \infty)[/tex].

More can be learned about the domain of a function at https://brainly.com/question/25897115

Answer:

Step-by-step explanation:

c

Answer:

Mode

Step-by-step explanation:

As you can see, the mode on the first data set is 10, the mode on the other is 30.

Answer:

C. Area is the total distance around the outside of a shape.

Step-by-step explanation:

Answer:

Area is the total distance around the outside of a shape, Would be correct.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the answer is C

( -6 , 1 )

y = -1/2x - 2

if x = -6

y = -1/2(-6) - 2

y = 3 - 2

y = 1

Answer:

Angle A=87°

Step-by-step explanation:

(5x-3)°+(4x+21)°=180°

9x°+18°=180°

9x°+18°-18°=180°-18°

9x°=162°

9x°/9°=162°/9°

x=18°

Angle A=(5x18-3)°

(90-3)°

Angle A=87°

Answer:

x= -28

Step-by-step explanation:

1. First you have to add 14 to both sides to get the x by itself. That's always the first thing you have to do. Get x by itself.

2. After that, you should have -x= 28. You can't leave it like that because it is still not simplified. It's basically saying 28 is the opposite of x. What's the opposite of positive? Negative.

3. Therefore, your final answer should be -28

Answer:

x = -28

Step-by-step explanation:

Hey! First, lets establish our equation :)

-14 -x = 14

Now, we are going to get our x alone on a single side, to do this, we are going to add 14 to both sides to be able to cut out -14 on the left side!

-14 -x = 14

+14      +14

     -x = 28

The last thing we have to do is divide both sides by -1 to get x by itself without it being negative!

-x = 28

÷-1  ÷-1

x = -28

So, x, is equal to -28 (negative 28!) :)

Hope this Helps! :)

Have any questions? Ask below in the comments and I will try my best to answer.

-SGO

The opposite sides PQ and RS of the parallelogram PQRS are congruent

The value of the length QS is 6 cm

The given parameters are:

PQ = 4x - 1

RS = 3x + 7

Opposite sides are congruent.

So, we have:

4x - 1 = 3x + 7

Collect like terms

4x - 3x = 1 + 7

Evaluate the expressions

x = 8

The perimeter is calculated using:

Perimeter = 2(QS + RS)

This gives

2(QS + RS) = 74

Divide by 2

QS + RS = 37

Substiute RS = 3x + 7

QS + 3x + 7 = 37

Substitute 8 for x

QS + 3*8 + 7 = 37

This gives

QS + 31 = 37

Subtract 31 from both sides

QS = 6

Hence, the value of the length QS is 6 cm

Read more about parallelograms at:

https://brainly.com/question/2844650

Answer:

6cm or b

Step-by-step explanation:

Line BF is one of the three angle bisectors that meet at point F (incenter), hence, line BF as it relates to ABC is called the: interior angle bisector.

An interior angle bisector can be described as the line segment that divides an interior angle into two halves.

When the three interior angle bisector of a triangle meet at a point, the point is referred to a the incenter.

The diagram guven shows the incenter where the three interior angle bisectors meet.

Therefore, line BF as it relates to ABc is called the: interior angle bisector.

Learn more about the interior angle bisector on:

https://brainly.com/question/4421815

Answer:

(2,10)

Step-by-step explanation:

Whenever you want to find the point that is closest, it will always be perpendicular to the line

This is because the perpendicular line is the shortest distance to a point (it will make 90 degrees with the line)

So

In order to find the slope of the perpendicular line, you take the slop and you do the negative reciprocal of it.

In this case:

the slope is 5

So:

the negative reciprocal is -1/5

Now we know the slope of the line that will be made by point P to intersect with y=5x

Then, you use the equation:

y=mx+b

and plug in the numbers that you know which is the y coordinate, x coordinate, and slope to find the y-intercept:

0 = -1/5(52) + b

b = 52/5

Finally, set the equations equal to each other to find the point that the perpendicular line intersects y=5x

5x = -1/5x + 52/5

x = 2

then to find the y coordinate you plug the x back into the equation:

y = 5(2)

y = 10

So the answer is (2,10)

Answer:

$69.60

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

G-14

O-14

O-14

so 14•3=42

Answer:

140% - 7/5 - 1.4

4% - 1/25 - 0.04

56% - 2.8/5 - 0.56

95% - 19/20 - 0.95

Lets let Teddy be x.

Sister 1: x+3

Sister 2: x-7

If we subtract the younger sister (sister 2) from the older sister (sister 1), we get:

x+3 - (x-7) = x+3 - x + 7 = 10

The older sister was 10 years old when the younger sister was born.

Answer:

a = 600

Step-by-step explanation:

Algebraically:

[tex]a*5 = 3000\\a = \frac{3000}{5}\\ a = 600[/tex]

Answer:

140 inches cubed

Step-by-step explanation:

Use the formula V = length * width * height to find the volumes of each block, then add them together to get the combined volume. So, (5 * 4 * 5) + (4 * 5 * 2) = 140 inches cubed, which is the combined volume.

Hopefully this helps- let me know if you have any questions!

Answer:

50°

Step-by-step explanation:

because angles on straight line add up to 180°,

180-130=50 :)

Answer:

5.5 and 6

Step-by-step explanation:

i got it wrong and it told me this was the correct answer

Answer:

5.5 and 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Change all the units to be the same. 1yd= 3 feet so 2yd x 3ft =6ft

new Dimensions 4x8 and 3x8

2.  View images

Answer:

0.65 is a number greater than 0.6 but less than 0.7

Answer:

a) J':(-7,7) K':(-5,2) L':(-2,3)

b) The x coordinates remained the same, the y coordinates swapped from negative to positive.

Step-by-step explanation:

Aside: I'm using J', K', and L' to denote the new locations of J,K,L after the reflection.

When an object is reflected over the x-axis, it means it's positive points will flip to negative y space, and negative points will flip to positive y space.

That said, J, for instance, will have the same X-coordinate, but its Y-coordinate will flip from negative to positive. Doing this with every vertex mirrors the triangle over the X-axis.

Therefore, J:(-7,-7) will become J':(-7,7), and likewise with K and L becoming K':(-5,2) and L':(-2,3).

Answer:

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

10z + 4 + 8z + 2 = 168

first we find z

z = 9

5×9 +2 is 47

ANSWER IS 47

Answer:

x=23

Step-by-step explanation:

An inscribed angle is half of the intercepted arc.