Solve the inequality.
x + 5 < 6
x<

Answer:

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Step-by-step explanation:

[tex](15 {x}^{3} + 22 {x}^{2} - 15x + 2)[/tex]

Apply Rational Root Theorem, our possible roots will be

plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).

I

I tried root -2 and it work so

If we apply synthetic dividon, we would be left with

[tex]15 {x}^{2} - 8x + 1[/tex]

We can factor this regularly.

Apply AC method that a number

AC will multiply to 15 but add to -8.

The answer are -5 and -3 so we write this as

[tex]15 {x}^{2} - 5x - 3x + 1[/tex]

Factor by grouping

[tex](15x {}^{2} - 5x) - (3x + 1)[/tex]

[tex]5x(3x - 1) - 1(3x - 1)[/tex]

So our factor are

[tex](5x - 1)(3x - 1)(x + 2)[/tex]

Draw an equilateral triangle with side lengths 5 inches each. Each interior angle is 60 degrees (this is true of any equilateral triangle).

Now draw an equilateral triangle of 10 inches each. The angles will be the same as before. We can see that the triangles are not congruent. Congruent triangles must have the same side lengths, but clearly the second one is larger than the first.

This is an example of why knowing solely the congruency of the angles is not enough to prove the triangles congruent or not. We would need to know something about the sides (whether they are congruent or not) to be able to determine overall triangle congruency.

Answer:

Because even though the angles may be the same, the lengths can be different. In an isosceles triangles, this may be the case.

Step-by-step explanation:

Answer:

The population of town A = 18,000

The population of town B = 15,000

The population of town C = 20,000

Step-by-step explanation:

Given;

A:B = 6:5

B:C = 3:4

total population = 53,000

A + B + C = 53,000

[tex]\frac{A}{B} = \frac{6}{5} \\\\A = \frac{6B}{5} \\\\\Also;\\\\\frac{B}{C} = \frac{3}{4} \\\\C = \frac{4B}{3} \\\\then;\\\\\frac{6B}{5} +B+ \frac{4B}{3} = 53,000\\\\multiply \ through \ by \ "15"\\\\18B + 15B + 20B = 795,000\\\\53B = 795,000\\\\B = \frac{795,000}{53} \\\\B = 15,000[/tex]

Now solve for A and C;

[tex]A = \frac{6 \times 15,000}{5} = 18,000\\\\C = \frac{4 \times 15,000}{3} = 20,000[/tex]

Answer:

a = 78.5 cm²

Step-by-step explanation:

a = πr²

a = 3.14 * 5²

a = 3.14 * 25

a = 78.5 cm²

Answer:

Step-by-step explanation:

If p = t + v and t is 5/2 and p is 0, then

0 = 5/2 + v and

v = -5/2

Answer:

1/3

Step-by-step explanation:

3÷6/1 is the same thing as 3÷6

and when reducing to the lowest term gives 1÷3 or 1/3

first ,length(l)=14 feet,

bredth(b)=6feet.

now, perimeter = 2(l+b)

=2(14+6)

= 2×20

= 40 feeet

Hope this helps you....

Answer:

3/8

Step-by-step explanation:

Let us represent the total fabric as an integer = 1

Ellen divides a piece of fabric into 8 equal sections by drawing chalk lines.

= 1/8, hence each section = 1/8

Then she cuts off 5 of the sections to make into placemats.

This is written as: 5 sections × 1/8 = 5/8

The fraction of the fabric that is left is calculated as:

1 - 5/8

Lowest Common Denominator = 8

Hence: 8 - 5/8 = 3/8

The fraction of the fabric that is left is 3/8

Answer:

radius = [tex]\sqrt{26}[/tex] units

Step-by-step explanation:

The radius r is the distance from the centre to a point on the circle.

Using the distance formula to calculate r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (1, - 3)

r = [tex]\sqrt{(1-2)^2+(-3-2)^2}[/tex]

  = [tex]\sqrt{(-1)^2+(-5)^2}[/tex]

   = [tex]\sqrt{1+25}[/tex]

    = [tex]\sqrt{26}[/tex]

Answer:

Use SOHCAHTOA

Step-by-step explanation:

If you don't know what this is, it means Sin=opposite/hypotenuse, cos=adjacent/hypotenuse, tan=opposite/adjacent. There is more than 1 way to solve this, but here's how I did it.

Starting with part A, we are trying to find the hypotenuse of the triangle. We have an angle and the side opposite of that angle, so we can use the sin function.

Sin(54) = 12.2 / hypotenuse

Sin(54) * hypotenuse = 12.2

Hypotenuse = 12.2 / sin(54) = 15.1

Now for Part B

Finding the last angle

180-90-54=36

So now, we have this angle and the side adjacent to it. We are trying to find the opposite side, so let's use the tan function

Tan(36) = opp / 12.2

opp = tan(36) * 12.2 = 8.9

You can double check these answers using pythagorean theorem. Hope this helps

Given:

The equation is:

[tex]30n-C+200=0[/tex]

To find:

The slope intercept form of the given equation.

Solution:

We have,

[tex]30n-C+200=0[/tex]

We need to write the given equation in the form of [tex]C=mn+b[/tex].

Adding C on both sides, we get

[tex]30n-C+200+C=0+C[/tex]

[tex]30n+200=C[/tex]

Interchanging the sides, we get

[tex]C=30n+200[/tex]

This equation is in the form of [tex]C=mn+b[/tex], where m is 30 and b is 200.

Therefore, the slope intercept form of the given equation is [tex]30n-C+200=0[/tex].

Answer:

13328 N

Step-by-step explanation:

9.8 m/s^2 • 1360 = X

13328 N = X

Step-by-step explanation:

the asymptotes of f(x) :

(4x-π) = π/2

4x = 3π/2 => x = 3π/8

(4x-π) = 3π/2

4x=5π/2 => x = 5π/8

the answer is

D. X= 3pi/8, x=5pi/8

Answer:

10 ^3 * 10 ^2

1/ 10 ^5

10*10*10*10*10

Step-by-step explanation:

10 ^4^1 = 10 ^(4*1) = 10 ^4

10 ^3 * 10 ^2 = 10 ^(3+2) = 10 ^5

1/ 10 ^5 = 10 ^5

10 ^3^2 = 10 ^(3*2) = 10 ^6

10*10*10*10*10 =10 ^5

Answer:

in picture

Step-by-step explanation:

Brainliest please~

Answer:

c =2

Step-by-step explanation:

4.5c/4.5=9/4.5

c =2

The angles represented by (2x - 60) and (60 - 2x) cannot be supplementary because their sum add up to zero instead of 180°.

Answer:

I've attached the Answer

Answer:

56Pi

Step-by-step explanation:

Area of small circle:

Pi*r^2

25Pi

Area of large circle:

Pi*r^2

81Pi

Area of the 2D doughnut :

Large -small circle = 81Pi-25Pi

Answer:

x     -1      1    3

y      -2    -4   2

Step-by-step explanation:

y=x^2-x-4

when x=-1

y=(-1)^2-(-1)-4

y=1+1-4

y=-2

when x=1

y=(1)^2-(1)-4

y=1-1-4

y=-4

when x=3

y=(3)2-(3)-4

y=9-3-4

y=9-7

y=2

Answer:

False

Step-by-step explanation:

Answer:

24 rolls

Step-by-step explanation:

12 rolls           x rolls

------------  = ------------------

4 dollars           8 dollars

Using cross products

12*8 = 4x

96 = 4x

Divide by 4

96/4 = 4x/4

24 =x

24 rolls

Answer:

32x^2+4x

3x-7, g(x)=2x^(2)-3x+1, h(x)=4x+1, k(x)

Answer:

a line and a plan are considered parallel if they have no points in common if two parallel planes are cut by a third plane then the lines of intersection are parallel

Answer:

1. 194

2. 189

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

1. 194 people increased.

2. Edith has 189 stamps more than Parick.

Step-by-step explanation:

1. 991 - 797 = 194

2. 826 - 637 = 189

Answer:

A) x + 5y = 20

B) x + 3y = 14

Multiplying A) by -1

A) -x -5y = -20 then adding B)

B) x + 3y = 14

-2y = -6

y = 3

x = 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

9). Dimensions of the logo = 4 inch by 6 inch

   ∵ 12 inches = 1 feet

    ∴ 1 inch = [tex]\frac{1}{12}[/tex] feet

   Therefore, dimensions of the logo (in feet) will be,

   [tex]\frac{4}{12}[/tex] feet by [tex]\frac{6}{12}[/tex] feet  Or [tex]\frac{1}{3}[/tex] feet by [tex]\frac{1}{2}[/tex] feet

   Dimensions of the logo which are 6 times larger than the original one.

    Dimensions of the advertisement = [tex]\frac{6}{3}[/tex] feet by [tex]\frac{6}{2}[/tex] feet

                                                            = 2 feet by 3 feet

    Area of the advertisement = 2 × 3

                                                = 6 feet²

10). By the property of similar polygons,

     "Corresponding sides of two similar polygons are proportional"

     If the dimensions of two similar polygons are 'x' and 'kx'

     Ratio of the perimeter of two polygons = [tex]\frac{\text{Perimeter of the image polygon}}{\text{Perimeter of the original polygon}}[/tex] = k

     Ratio of area of two similar polygons = [tex]\frac{\text{Area of the image polygon}}{\text{Area of the original polygon}}[/tex] = k²

     Ratio of volumes of two similar polygons = [tex]\frac{\text{Volume of the image polygon}}{\text{Volume of the original polygon}}[/tex] = k³

Answer:

c or b

tep-by-step explanation:

Answer:

9 over 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

x^2 + 12 - 45 = 0

solving by middle term break method

x^2 + (15 - 3) - 45 = 0

x^2 + 15x - 3x - 45 = 0

x(x + 15) - 3(x + 15) = 0

(x + 15)(x - 3) = 0

either x + 15 = 0            OR, x - 3 = 0

x + 15 = 0

x = 0 -15

x = -12

x - 3 = 0

x = 0 + 3

x = 3

therefore x = -12,3

i have done solution for the given question in two different methods.

the solution done in note copy is by using quadratic formula.

Answer:

Conservation

Step-by-step explanation:

Conservation is the principle that an object maintains the same size and shape even if it is repositioned or divided in certain ways.