Reflection across y=3

Simplify using the vertical method. (3k + 4)(3k^2 – 5k – 3)

liubo4ka [24]

Answer:

$9k^{3} -3k^{2}-29k-12$

Step-by-step explanation:

Step 1: Expand by distributing sum groups.

$3k(3k^{2} -5k-3)+4(3k^{2} -5k-3)$

Step 2: Expand by distributing terms.

$9k^{3} -15k^{2} -9k+4(3k^{2} -5k-3)$

Step 3: Expand by distributing terms.

$9k^{3}-15k^{2} -9k+12k^{2} -20k-12$

Step 4: Collect like terms.

$9k^{3}+(-15k^{2} +12k^{2} )+(-9k-20k)-12$

Step 5: Simplify.

$9k^{3} -3k^{2}-29k-12$

3 0

3 years ago

2. The width of a rectangle is 5 units less than the length. If the area is 150 square units, then find the dimensions of the re

xz_007 [3.2K]

Answer:

The length = x = 15 units

The width = x-5 = 10 units

Step-by-step explanation:

Let 'x' be the length of a rectangle

As the width of a rectangle is 5 units less than the length.

so

width of rectangle will be = w = x - 5 units

Area = 150 square units

Using the formula

Area = length × width

$150=\left(x\right)\left(x-5\right)$

$150=x^2-5x$

$x^2-5x=150$

Subtract 50 from both sides

$x^2-5x-150=150-150$

$x^2-5x-150=0$

$\left(x+10\right)\left(x-15\right)=0$

if

$ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)$

$x+10=0\quad \mathrm{or}\quad \:x-15=0$

$x=-10,\:x=15$

As length can not be negative. so

x = 15 units

Hence,

The length = x = 15 units

The width = x-5 = 15-5 = 10 units

5 0

2 years ago

Shanti is taking a cube-shaped gift to a friend's birthday party. She wants to wrap it but she doesn't have very much paper, so

Marrrta [24]

Answer:

It will take Shanti 150 square inches of paper to wrap the gifts

Step-by-step explanation:

Shanti wraps the gift she is taking to a friend's birthday party. She doesn't have very much paper, so she does not overlap any of the edges. The side lengths of the cube are all 5in.

How much paper did it take to cover the gift?

Solution

To solve this, you will find the surface area of a cube

Surface area of a cube = 6a^2

Where,

a=side length of the cube

a= 5 in

a^2=a × a

=5 × 5

=25 in^2

a^2=25 in^2

Surface area of a cube = 6a^2

=6 × 25 in^2

=150 in^2

It will take Shanti 150 square inches of paper to wrap the gifts

7 0

3 years ago

Read 2 more answers

A school bus has seating for 75 students. There are 13 buses at a school. What is the maximum number of students

stepan [7]

Answer:

75 students and 13 buses are just 75 x 13

975 students

Step-by-step explanation:

75 x 13 = 975

7 0

3 years ago

Read 2 more answers

A tree is currently 8 feet tall and grows 3 feet per year . Model this scenario with an arithmetic sequence in explicit form.

raketka [301]

Don't think this is technically math

6 0

3 years ago

Reflection across y=3​

Reflection across y=3