Point I is on line segment HJ. Given HI = x, IJ = 2x + 9, and
HJ = 4x, determine the numerical length of IJ.

Hi,  

a line is define by  the following equation :    y = ax+b

where  a  is the slope, and  b the value for x = 0

so you have :        a*3 +b = 3   for the first point

                              a*(-5) +b = 4  for second point  

  so you have a system :      3a+b =3

                                              -5a+b = 4

so :       3a+b -(-5a) -b = 3-4

             3a+5a +b-b = -1

             8a = -1

                a = -1/8

then a = -1/8   so , in remplacing a  by it's  value  in one equation ,   b  is :             3(-1/8) +b = 3

 -3/8 +b = 3

           b = 3 +3/8

           b =  24/8 +3/8

          b =  27/8

let's check :     3 (-1/8) + 27/8 =  -3/8 +27/8 = 24/8 = 3

first point is correct  

                         -5( -1/8) + 27/8 =  5/8 +27/8 =  32/8 = 4

second point is correct  

line  is  y = -1/8X +27/8

Answer:

1. 5/9

2. 8/6 or 1 and 2/6

3. 1 3/4

4. 7/9

Answer:

150.72 units³

Step-by-step explanation:

volume = πr²h

= 3.14×4²×3

= 150.72

Let's assume that total employees are x .

Three - fifths of x is female employees .

→ Female employees = 3x/5 .

Then male employees will be :-

→ Male employees = x - 3x/5

So male employees are 2x/5 .

→ Employees under 18 = x/4

→ Female under 18 = one - third of total female employees.

→ Female under 18 = 3x/5 (1/3)

So Female employees under 18 are x/5 .

→ Now male under 18 = x/4 - x/5

Now male above 18 are = 2x/5- x/20

Ratio of Male above 18 : Male below 18

→ 7x/20 : x/20

→ 7 : 1

So the ratio is 7 : 1 .

Answer:

7.3

Step-by-step explanation:

Tenth is the first digit after decimal sign

Given number is:

Since the next digit after the tenth digit is 9>5, we add 1 to tenth digit and drop the rest digits on the right of digit 2

So we get:

Answer:

(D) [tex]3 \pm i\sqrt{3}[/tex]

Step-by-step explanation:

We can solve this using the quadratic formula, where a is 1, b is -6, and c is 12.

[tex]\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\frac{-(-6)\pm\sqrt{6^2-4\cdot1\cdot12}}{2\cdot1}\\\\\frac{6\pm\sqrt{36-48}}{2}\\\\\frac{6\pm\sqrt{-12}}{2}\\\\\frac{6\pm i\sqrt{12}}{2}\\\\3\pm i\sqrt{3}\\\\[/tex]

Hope this helped!

Answer:

-13.5v-21.6

Step-by-step explanation:

Distribute Rule: a(b+c) = ab+ac

2.7(-5v-8)

= 2.7*(-5v) + 2.7(-8)

= -13.5v-21.6

Step-by-step explanation:

The answer to your question is (D) 16. This is the answer because if count by 16's it goes 16, 24, 36, etc. since 24 is a multiple its could also be x

Answer:

12, Increase

Step-by-step explanation:

12 is by far the lowest in the set, and removing the number would raise the mean.

Answer:

[tex]y = \$335931.5 + \$110668.5x[/tex]

Step-by-step explanation:

Given

[tex]Salary\ in\ 2000 = \$446,600[/tex] (Median)

[tex]Salary\ in\ 2008 = \$1,331,948[/tex] (Median)

Required

Determine a Linear Equation

The above question illustrates an Arithmetic Progression (AP)

The nth term of an AP is

[tex]T_n = a + (n - 1) d[/tex]

In this case;

[tex]a = Salary\ in\ 2000 = \$446,600[/tex]

[tex]n = 2008 - 2000 + 1 = 9[/tex]

[tex]T_n = Salary\ in\ 2008 = \$1,331,948[/tex]

Substitute these in the given formula

[tex]\$1,331,948 = \$446,600 + (9 - 1) d[/tex]

[tex]\$1,331,948 = \$446,600 + 8d[/tex]

Collect Like Terms

[tex]\$1,331,948 - \$446,600 = 8d[/tex]

[tex]\$885348 = 8d[/tex]

Divide both sides by 8

[tex]d = \$110668.5[/tex]

The linear equation is generated as follows;

[tex]T_n = a + (n - 1) d[/tex]

In this case;

[tex]a = Salary\ in\ 2000 = \$446,600[/tex]

[tex]d = \$110668.5[/tex]

[tex]T_n = y[/tex]

[tex]n = x[/tex]

Substitute these in the given formula

[tex]y = \$446,600 + (x - 1) * \$110668.5[/tex]

Open bracket

[tex]y = \$446,600 + \$110668.5x - \$110668.5[/tex]

Collect Like Terms

[tex]y = \$446,600 - \$110668.5 + \$110668.5x[/tex]

[tex]y = \$335931.5 + \$110668.5x[/tex]

Hence, the linear equation is

[tex]y = \$335931.5 + \$110668.5x[/tex]

Answer:

4 (c - 6)

Step-by-step explanation:

Simplify the following:

6 c - 2 c - 16 - 8

Hint: | Group like terms in 6 c - 2 c - 16 - 8.

Grouping like terms, 6 c - 2 c - 16 - 8 = (6 c - 2 c) + (-8 - 16):

(6 c - 2 c) + (-8 - 16)

Hint: | Combine like terms in 6 c - 2 c.

6 c - 2 c = 4 c:

4 c + (-8 - 16)

Hint: | Evaluate -8 - 16.

-8 - 16 = -24:

4 c + -24

Hint: | Factor out the greatest common divisor of the coefficients of 4 c - 24.

Factor 4 out of 4 c - 24:

Answer: 4 (c - 6)

Answer:

Hey there!

The equation is x+2x+5+6x-17+3x+2, or 12x-10

12x-10=50

12x=60

x=5

Let me know if this helps :)

Answer:

x=-2

Step-by-step explanation:

Vertical lines are of the form x=

The x coordinate is -2

x=-2

Answer:

11

Step-by-step explanation:

You're done! Therefore, the answer is 11.

Answer:

11

Step-by-step explanation:

I know this has already been answered but I need points, lol. i would add the step by step explanation but someone has already done so, so i dont feel the need to.

gothychan

Answer:

Hey there!

I see you have to right idea, the first step is to write the equation: 6x-15+2x-2+4x-7=180. We can simplify this to 12x-24=180

Solving for x, we get that x=17.

Let me know if this helps :)

The value of x is 17.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180, regardless of whether it is acute, obtuse, or right.

Given:

<S = (6x – 15)°, <T = (2x − 2)°, and <U = (4x – 7).

Now, Using Angle Sum Property

<S+ <T + <U= 180

6x - 15 + 2x -2 + 4x - 7= 180

12x - 24= 180

12x = 204

x= 204/12

x= 17

Hence, the value of x is 17.

Learn more about angle sum Property here:

https://brainly.com/question/4316040

#SPJ5

Answer:

Step-by-step explanation:

Boys : Girls = 7 : 8

Let the number of boy = 7x

The number of girls = 8x

Number of boys after 20% increase = 120% of 7x

                                                            = 1.2 * 7x

                                                             = 8.4 x

Number of girls after 10% increase = 110% of 8x

                                                           = 1.1 * 8x

                                                           = 8.8x                    

After increase in number of boys & girls = 8.4x : 8.8x

                      = 84 : 88    { reduce to simplest form by giving by 4th table}

                     = 21 :  22

Answer:

The solution set of the quadratic function [tex]x^{2}+6\cdot x +10[/tex] is [tex]\{-3+i,-3-i\}[/tex] .

Step-by-step explanation:

Let be a second-order polynomial (quadratic function) is standard form and equalized to zero:

[tex]a\cdot x^{2}+b\cdot x + c = 0[/tex]

Its roots can be determined by the Quadratic Formula in terms of its polynomial coefficients, which states that:

[tex]x_{1,2} = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]

Given that [tex]a = 1[/tex], [tex]b = 6[/tex] and [tex]c = 10[/tex], the roots of the polynomial are, respectively:

[tex]x_{1,2} = \frac{-6\pm \sqrt{6^{2}-4\cdot (1)\cdot (10)}}{2\cdot (1)}[/tex]

[tex]x_{1,2} = -3\pm i[/tex]

[tex]x_{1} = -3+i[/tex]

[tex]x_{2} = -3 -i[/tex]

The solution set of the quadratic function [tex]x^{2}+6\cdot x +10[/tex] is [tex]\{-3+i,-3-i\}[/tex] .

Answer:

440m

Step-by-step explanation:

First you would square root the value 12100 to get one of the length of the square.

[tex]\sqrt{121000}[/tex]=110m

A square has four sides so,

110*4=440m

Answer:

440m

Step-by-step explanation:

Formula of a square's field : a square

So, area is 12,100. Then, let's take this value into the square root.

Now, we found the one edge of this square which is 110m

For finding perimeter, a square has a 4 edge. So, we multiple 110 x 4 = 440m.

Answer: Hi!

To make an expression that represents ten and a number being divided (hence, quotient) we will use the variable x for the unknown number:

10 ÷ x

You would use this expression to represent the quotient of 10 and a number.

Hope this helps!

The quotient of 10 and a number​ is equal to [tex]\frac{10}{n}[/tex].

In Mathematics, quotient simply means division i.e the division of a particular number by another number.

In this exercise, you will simply divide the value of 10 by n.

Therefore, translating the word sentence into an algebraic expression, we have;

Quotient of 10 and a number is:

[tex]Quotient = \frac{10}{n}[/tex]

Read more: https://brainly.com/question/22970937

Answer:

complete graph

Step-by-step explanation:

In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges

hope it helps :)

please mark it the brainliest!

Answer:

it would be a complete graph

Step-by-step explanation:

Answer:

71°

142°

Step-by-step explanation:

[tex] \because QS \: is \: the \: bisector \: of \: \angle \: PQR\\

\therefore m\angle RQS =m\angle PQS\\

\because m\angle RQS = 71\degree...(given) \\

\huge \red{ \boxed{\therefore m\angle PQS = 71\degree}} \\ \because \: m\angle \: PQR = m\angle PQS + m\angle RQS \\ \because \: m\angle \: PQR = 71\degree + 71\degree \\ \huge \purple{ \boxed{\therefore \: m\angle \: PQR = 142\degree}}[/tex]

Answer:

6

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

∠ c  = 90° ( angle in a semicircle ), thus

d = 180° - (16 + 90)° = 180° - 106° = 74° ( angles in a Δ )

If one angle is 16° then the measure of angle d is 76°.

An angle is the figure formed by two rays called the sides of the angle, sharing a common point called the vertex of the angle.

We know that each angle of a rectangle and square is equal to 90°. When we observe the given figure then we can see that angles are formed in a rectangle and a,b,c,d,14 and 16 all are in rectangle, so in this way, 14°+d=90°.

d=90-14

d=76°

Hence if one angle is 16° then the measure of angle d is 76°.

Learn more about angles at https://brainly.com/question/25716982

#SPJ2

Answer:

8m

Step-by-step explanation:

x = hypotenuse since they want the point of observation to the top of the tree

cos 60 = 4/x

x = 4 / cos 60

x = 8m

Answer:

The answer is

Step-by-step explanation:

The area of the flower bed is larger than 10 square feet.

Hope this helps....

Have a nice day!!!!

Answer:

The difference between an expression and an equation is that an expression has no equal sign whereas an equation does.

Step-by-step explanation:

Answer:

a) 16.82 mg

b) 24 days

Step-by-step explanation:

Formula for exponential growth is given as:

[tex]A=A_0b^{\frac{t}{c}}[/tex]

Where A is the final population

[tex]A_0[/tex] is the initial population

b is the growth factor

c is the time taken for the growth 'b'

t is the amount of time

Here, We are given the following:

[tex]A_0[/tex] = 5 mg

b = 2 (Given because it doubles)

c = 4 days

a) A = ?

Using the formula:

[tex]A=5 \times 2^{\frac{7}{4}}\\\Rightarrow A=5 \times 2^{1.75} \\\Rightarrow A = \bold{16.82\ mg}[/tex]

b) Given

A = 320 mg

t = ?

Using the above formula again:

[tex]320 = 5 \times 2^{\frac{t}{4}}\\\Rightarrow \dfrac{320} 5= 2^{\frac{t}{4}}\\\Rightarrow 2^{\frac{t}{4}} = 64\\\Rightarrow 2^{\frac{t}{4}} = 2^6\\\Rightarrow \dfrac{t}{4} = 6\\\Rightarrow t = 6 \times 4\\\Rightarrow \bold{t = 24\ days}[/tex]

So, the answers are:

a) 16.82 mg

b) 24 days

Answer:

its correct

Step-by-step explanation:

check

Answer:

2.8125

Step-by-step explanation:

Answer:

Product 1, because the function is exponential.

Step-by-step explanation:

If you take set the equation to 9 years. You will see that product one would be 2^9 = 512 and Product 2 would be 9^2 + 12 = 93. Product one will continue to grow exponentially while Product two will not grow as much in comparison.

Answer:

Product 2, because the function is exponential

Step-by-step explanation:

i got it right on my quiz