In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police
station and the fire station. The distance between the library and the police station is 5 miles. How far apart are the police
station and the fire station?
miles

Answer:

option number 1st is the correct answer.

Answer:

the second  because it shows you the way its  

Step-by-step explanation:

Answer:

See Step-by-step

Step-by-step explanation:

b)Table:

x          x-Mean          (x-Mean)^2

1             1-7=-6             36

3            3-7=-4             16

5            5-7=-2             4

15           15-7=8             64

2            2-7=-5             25

11            11-7=4             16

12           12-7=5             25

7             7-7=0             0

c)Find the sum of the squared deviations:

(36+16+4+64+25+16+25+0)/8=23.25

d)Find the standard deviation by finding the square root of 23.25

The answer is 4.8

Answer: [tex](-4,-7)[/tex]

Step-by-step explanation:

By definition, the equation of parabola in Vertex form is:

[tex]y=a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola.

You need to remember that multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Then given the equation [tex]y = -(x + 4)^2 - 7[/tex], you know that this is:

[tex]y = -(x -(-4))^2 +(-7)[/tex]

You can observe that the value of "h" and the value of "k" of this equation are:

[tex]h=-4\\k=-7[/tex]

Therefore, the vertex is:

[tex](-4,-7)[/tex]

Answer:

slope rise 3 run 2 1/2

Step-by-step explanation:

if you start from the bottom and if you start from the top it's -3 and -2 1/2

Answer: The slope is 3 and the y-intercept is 3/2

Step-by-step explanation:

The slope of a linear function can be calculated as:

s = (y2 - y1)/(x2 - x1)

Where y2 = f(x2) and y1 = f(x1) and f(x) is the linear function.

So here we can use any two pairs of the set of data, for example, the first two.

(-1 , -3/2) and (-1/2,0)

s = (0 -(-3/2))/(-1/2 - (-1)) = (3/2)/(1/2) =(3/2)*(2/1) = 3

So the slope is equal to 3.

the y-intercept is the value of y when x = 0, in the table we can see that when x = 0. the value of y = 3/2

So the function is: y = 3*x + 3/2

and the correct option is the fourth one.

Answer:

D. x =4

Step-by-step explanation:

problem solved on picture

Answer:

5, 11,17,23,29

Step-by-step explanation:

To obtain the term in the sequence add the common difference to the previous term, that is

a(1) = 5

a(2) = 5 + 6 = 11

a(3) = 11 + 6 = 17

a(4) = 17 + 6 = 23

a(5) = 23 + 6 = 29

The first five terms of an arithmetic sequence starting with 5 and a common difference of 6 are 5, 11, 17, 23, and 29.

The first five terms of the arithmetic sequence with the first term 5 and a common difference of 6 can be found by successively adding the common difference to the previous term.

Third term (a3) = a2 + 6 = 11 + 6 = 17

Fifth term (a5) = a4 + 6 = 23 + 6 = 29

Therefore, the first five terms of the arithmetic sequence are 5, 11, 17, 23, and 29.

The angles circled in red below are same side exterior. This means that the sum of them is 180 degrees. You can make a formula like so that you will solve for x...

98 + x = 180

98 - 98 + x = 180 - 98

0 + x = 82

x = 82

Another way to solve:

The angles circled in pink below are opposite side exterior. This means that they must equal each other...

82 = x

x = 82

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:B. vertical line symmetry

Step-by-step explanation:

Answer:

D. diagonal line symmetry

Step-by-step explanation:

If f(x) = 5x^3 and g(x) = x+1, find (f•g)(x).

Note: (f•g)(x) means f(x) times g(x).

(f•g)(x) = (5x^3)(x + 1)

(f•g)(x) = 5x^4 + 5x^3

Answer: Choice C

Answer:

a = 4

Step-by-step explanation:

Assuming you require to solve for a

Given

3 = a(4 - 7)² - 33 = a(- 3)² - 33 = 9a - 33

Add 33 to both sides

9a = 36 ( divide both sides by 9 )

a = 4

Answer:

5/8 cm

Step-by-step explanation:

5/2*3/4=15/8

15/8*1/3=15/24=5/8

Answer:

V = 5/8  cm^3

Step-by-step explanation:

V = l*w*h

V = 5/2 * 3/4 * 1/3

The 3's cancel

V = 5/2 * 1/4 * 1/1

V = 5/8  cm^3

Answer:

x = 4

Step-by-step explanation:

Given

4x - 6 + 2x = 18 ← simplify left side by collecting like terms

6x - 6 = 18 ( add 6 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

The solution to the equation 4x - 6 + 2x = 18 is x = 4.

To solve the equation 4x - 6 + 2x = 18, we need to combine like terms and isolate the variable x.

First, let's combine the like terms on the left side of the equation:

4x + 2x - 6 = 18

This simplifies to:

6x - 6 = 18

Next, we can isolate the variable x by adding 6 to both sides of the equation:

6x - 6 + 6 = 18 + 6

This simplifies to:

6x = 24

To solve for x, we can divide both sides of the equation by 6:

(6x)/6 = 24/6

This simplifies to:

x = 4

Therefore, the solution to the equation 4x - 6 + 2x = 18 is x = 4.

To learn more about the Equation of line click:

https://brainly.com/question/21511618

#SPJ6

Answer:

5.29

Step-by-step explanation:

Answer:

5.29

Step-by-step explanation:

Answer:

2W+3  I am really sorry if that's wrong, I don't think it is though GOODLUCK

Step-by-step explanation:

Answer:

The correct answer is option A.   2w + 3

w = 5 inches

Step-by-step explanation:

It is given that, the length of a rectangle is 3 inches more than twice its width, and its area is 65 square inches.

To find the correct option

If 'w' is the width of rectangle, then length = 3 inches more than the twice the width

length   = 2w + 3

The correct answer is option A.   2w + 3

To find the width

We have area = 65 square inches

Length * Width = 65

(2w + 3) * W = 65

2w² + 3w - 65 = 0

Solving we get ,

w = 5 and -6.5

Therefore w = 5 inches

Final answer:

To complete the square for the equation x² - 9x + _____ = 6, the constant term should be (81/4). This is obtained by dividing the coefficient of x by 2 and then squaring it.

Explanation:

The constant term required to complete the square for the equation x² - 9x + _____ = 6 can be found using a specific algebraic method. To complete the square, the coefficient of the x term should be divided by 2 and then squared. Therefore, for the equation provided, we take (-9/2) and square it, which results in (81/4). The complete equation after adding the constant term will be x² - 9x + 81/4 = 6 which, after completing the square, can be written as (x - 9/2)² = 6 + 81/4.

Hello There!

145 is 23.39% of 620

HOW TO SOLVE

Equation: Y = P% * X

We need to solve our equation for "P"

P% = Y/X

P% = 145/620

p = 0.2339

Convert decimal to percent:

Percent = 0.2339 * 100 = 23.39%

Answer:

7

Step-by-step explanation:

27 + 27 = 54

54 + 3

57

Smaller number is: 7

1. The monomials are:

[tex]15 {x}^{4} {y}^{6} = 3 \times 5 {x}^{4} {y}^{6} [/tex]

and

[tex]6 {x}^{5} {y} = 2 \times 3 {x}^{5} y[/tex]

The highest common factor is the product of the least powers of the common factors.

The HCF is

[tex]3 {x}^{4} y[/tex]

2. The monomials are:

[tex]12 {x}^{3} = {2}^{2} \times 3 {x}^{3}[/tex]

[tex]4 = {2}^{2} [/tex]

The HCF is

[tex]{2}^{2} = 4[/tex]

Answer:

Final result :

 x + 2

 —————

 x - 1

Step-by-step explanation:

Step-1 : Multiply the coefficient of the first term by the constant   7 • 3 = 21  

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   -10 .

     -21    +    -1    =    -22  

     -7    +    -3    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -3  

                    7x2 - 7x - 3x - 3

Step-4 : Add up the first 2 terms, pulling out like factors :

                   7x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (7x-3)  •  (x-1)

            Which is the desired factorization

Please mark brainliest and have a great day!

Answer:

Here's what I get.

Step-by-step explanation:

[tex]\dfrac{ 7x^{2} + 11x - 6}{ 7x^{2} - 10x + 3}[/tex]

One way is to factor the numerator and the denominator

[tex]\dfrac{ 7x^{2} + 11x - 6}{ 7x^{2} - 10x + 3} = \dfrac{(7x - 3)(x + 2)}{ (7x - 3)(x - 1)} = \dfrac{x+2}{x-1}\\\\\text{Except when } x = \dfrac{3}{7}[/tex]

Answer:

The value of x is 55 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- It has 4 equal sides

- Every two opposite sides are parallel

- Every two opposite angles are equal

- Every two adjacent angles are supplementary (their sum is 180°)

* Now lets solve the problem

- A square divided into two rectangles

- Each rectangle contains a shaded rhombus

- The shaded rhombus has two adjacent angles their measures are

 (2x + 20)° and 50°

∵ Every two adjacent angles in the rhombus are supplementary

∵ The sum of the supplementary angles = 180°

∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°

- lets put the equation and solve it to find x

∴ (2x + 20)° + 50° = 180° ⇒ add the like terms

∴ 2x + 70° = 180° ⇒ subtract 70° from both sides

∴ 2x = 110° ⇒ divide both sides by 2

∴ x = 55°

* The value of x is 55

Answer:

r=3

Step-by-step explanation:

24π=2π(r^2+r)

Divide each side by 2 pi

24π/2π =2π/2π(r^2+r)

12 = r^2 +r

Subtract 12 from each side

12-12 = r^2 +r -12

0 =  r^2 +r -12

Factor

What number multiply to -12 and add to 1

4*-3 = -12

4-3 = 1

0= (r+4) (r-3)

Using the zero product property

r+4 =0          r-3 =0

r+4-4 =0-4   r-3+3=0+3

r = -4           r = -3

Assuming r is the radius, r must be positive

r =3

bearing in mind that the average rate of change = slope, and for that we can simply use two points off the table.

[tex]\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} -2&12\\ 0&3\\ 3&-10.5\\ 7&-28.5\\ \cline{1-2} \end{array}\qquad \qquad \begin{array}{llll} (\stackrel{x_1}{-2}~,~\stackrel{y_1}{12})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-10.5}) \\\\\\ slope \implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-10.5-12}{3-(-2)} \\\\\\ \cfrac{-10.5-12}{3+2}\implies \cfrac{-22.5}{5}\implies -\cfrac{4.5}{1}\implies -4.5 \end{array}[/tex]

The rate of change of y with respect to x for the given function with coordinates expressed in the table is; dy/dx = -9/2

The rate of change of y with respect to x for a given linear function is simply the slope expressed as;

dy/dx = (y2 - y1)/(x2 - x1)

Let us take the first 2 coordinates which are;

(-2, 12) and (0, 3)

Thus;

dy/dx = (3 - 12)/(0 - (-2))

dy/dx = -9/2

Or dy/dx = -4.5

Read more at; https://brainly.com/question/19378449

Answer:

x = 2

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ nlog x

• log x + log y ⇔ log(xy)

• log x = log y ⇒ x = y

Given

3 ln2 + ln8 = 2ln(4x)

ln2³ + ln8 = ln(4x)²

ln8 + ln8 = ln16x²

ln(8 × 8) = ln16x²

ln64 = ln16x², hence

16x² = 64 ( divide both sides by 16 )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

Answer: x=2 so B on edg

Answer:

12 adults:10 children

Step-by-step explanation:

i don't know how i got it i just know it because i had this exact same question before and i guessed and this was the correct answer :|

Answer:

12 Adults 10 Children

is correct

Answer:

c) y + 5 = 2x

Step-by-step explanation:

Insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.

Answer:

B

Step-by-step explanation:

B because the line doesn't go through any of the data points.

Answer:

216

Step-by-step explanation:

The area dilation ratio is the square of the length dilation ratio

The area of the original  rectangle is 6*4=24

the length dilation ratio is 1:3

the area dilation ratio would be 1:3² which is 1:9

The resulted area=24*9

=216

Answer:

$878.25

Step-by-step explanation:

Continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of compoundings.

Here, P = 560, r = 0.09, and t = 5.

A = 560e^(0.09×5)

A = 878.25

Final answer:

To calculate the future value of an investment compounded continuously, use the formula A = Pert. In this case, the investment will be worth approximately $877.29 in 5 years.

Explanation:

To calculate the future value of an investment compounded continuously, we can use the formula A = Pert, where A is the future value, P is the initial principal, r is the annual interest rate, and t is the time in years. In this case, P = $560, r = 0.09, and t = 5. Plugging these values into the formula, we get:

A = 560e^(0.09⋅5)

A ≈ 560e^0.45

A ≈ 560 ⋅ 1.5662

A ≈ $877.29

Therefore, the investment will be worth approximately $877.29 in 5 years.

Answer:

1/6.

Step-by-step explanation:

Total number of tokens in the bag = 4 + 14 + 6 = 24.

There are 4 red tokens so the probability of picking a red

=  4/24

= 1/6.