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2 years ago

Factorize 81xsquared+180x+100

Mathematics

1 answer:

bekas [8.4K]2 years ago

5 0

Answer:

81x²+180x+100
9x²+180x+10²
using (a+b)²=a²+b²+2ab
9x²+2(9x)(10)+10²
(9x+2)²=(9x+2)(9x+2)

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Three consecutive even numbers have a sum between 84 and 96.

ELEN [110]

Answer:

a. 84 < n + (n + 2) + (n + 4) < 96

b. 26 < n < 30

Step-by-step explanation:

Let n = 1st number

n+2 2nd even number

n+4 = 3rd even number

The sum of these 3 numbers is

n+n+2+n+4

It must be between 84 and 96 (it does not include this 84 and 96)

84< n+n+2+n+4 < 96

Now we need to solve this

Combine like terms

84 < 3n +6< 96

Subtract 6 from all sides

84 -6 < 3n+6-6 < 96 -6

78 < 3n < 90

Divide all sides by 3

78/3 < 3n/3 < 90/3

26 < n< 30

5 0

3 years ago

Kat owns 15% more figurines than she did last year. She purchased F figurines this year. Which of the following expressions coul

Stella [2.4K]

Answer: F / 0.15 = 100F / 15 = 20F / 3 ≈ 6.67F.

Explanation:

1) The three expresssions, F / 0.15; 15 F / 100; 3F / 20; are equivalent.

2) The number of figurines Kat owned last year may be expressed in terms of the number the of figurines purchased, F, this year, and the 15%, following this procedure:

Call n the amount of figurines owned last year.

F is the number of figurines purchased: F = 15%n = 0,15n

Hence, you just need to clear F from the expression F = 0.15n

Divide both sides by 0.15:

F / 0.15 = n or n = F / 0.15 (reflexive property)

To prove the equialavence of the other expresssions you just have to use the properties of multiplication or division:

(F / 0.15) × (100 / 100) = 100F / 15

100F / 15 = (100/5)F / (15/5) = 20F / 3 ≈ 6.67F

4 0

3 years ago

Read 2 more answers

FACTOR and list your 4 steps: 5x^2y - 30xy^2

Dahasolnce [82]

Answer:

5x • (x + 3y) • (x - 2y)

Step-by-step explanation:

6 0

2 years ago

Find the altitude of an isosceles triangle with a vertex angle of 70° and a base of 246

Neporo4naja [7]

The base angles are both equal to (180-70) / 2 = 55 degrees

and 1/2 base = 123

so we have tan 55 = a / 123 where a = altitude
a = 123 * tan55 = 175.66

7 0

3 years ago

The width of a rectangle is 3 less than its length find the width of the rectangle if its perimeter is 26ft

Marta_Voda [28]

The width of rectangle is 5 feet.

Let us assume the length of rectangle to be x. So, the width of rectangle will be (x - 3).

Now, as per the known fact, perimeter, length and width of rectangle are related by the formula -

Perimeter = 2 × (length + width)

Keep the values in formula to find the value of width

26 = 2 × (x + x - 3)

Performing addition of variables inside the bracket

26 = 2 × (2x - 3)

Shifting 2 to other side of equation to find the value of x

2x - 3 = $\frac{26}{2}$

Performing division to find the value of x

2x - 3 = 13

Shifting 3 to other side of equation to find the value of x

2x = 13 + 3

Performing addition to find the value of x

2x = 16

Shifting 2 as denominator to other side of equation to find the value of x

x = $\frac{16}{2}$

Performing division to find the value of x

x = 8

So, length of rectangle is 8 feet

Width of rectangle = x - 3

Width of rectangle = 8 - 3

Width of rectangle = 5 feet

Hence, the width of rectangle is 5 feet.

Learn more about calculation involving rectangle -

brainly.com/question/24571594

#SPJ4

7 0

1 year ago