the points (4, -6) and (9, -6) represent the location of two towns on coordinate grid, where one unit is equal to one mile. what is the distance, in miles, between the two towns? Is it 5 miles the difference, can anyone explain please!

Answer:

[tex]\large\boxed{d=3\sqrt5}[/tex]

Step-by-step explanation:

[tex]\text{the formula of a distance between two points}\ A(x_1,\ y_1)\ \text{and}\ B(x_2,\ y_2):\\\\|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\=========================\\\\\text{We have}\ (4,\ 9)\ \text{and}\ (-2,\ 6).\ \text{Substitute:}\\\\d=\sqrt{(-2-4)^2+(6-9)^2}=\sqrt{(-6)^2+(-3)^2}=\sqrt{36+9}=\sqrt{45}\\\\\sqrt{45}=\sqrt{9\cdot5}=\sqrt9\cdot\sqrt5=3\sqrt5[/tex]

The distance between the points (4, 9) and (-2, 6) is approximately 6.71 units.

Identify the coordinates:

Let (x₁, y₁) = (4, 9) and (x₂, y₂) = (-2, 6).

Apply the distance formula:

The distance formula is given by:

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

Substitute the coordinates into the formula:

d= [tex]\sqrt{((-2)-4)^{2} +(6-9)^{2} }[/tex]²​

Simplify the terms inside the square root:

d=[tex]\sqrt{(-6)^{2} +(-3)^{2} }[/tex]

d=[tex]\sqrt{36+9}[/tex]

d=[tex]\sqrt{45}[/tex]

Simplifying further, we get:

d≈6.71

For this case we have to define trigonometric relations of rectangular triangles that:

Then, according to the figure we have:

[tex]Sin (G) = \frac {15} {17}\\Cos (G) = \frac {8} {17}[/tex]

Answer:

[tex]Sin (G) = \frac {15} {17}[/tex]

Option D

For this case we must multiply the following expression:

[tex](3x-5) (- x + 4)[/tex]

We must apply distributive property, which by definition establishes that:[tex](a + b) (c + d) = ac + ad + bc + bd[/tex]

[tex](3x-5) (- x + 4) = (3x) (- x) + (3x) (4) + (- 5) (- x) + (- 5) (4) = - 3x ^ 2 + 12x + 5x-20 = -3x ^ 2 + 17x-20[/tex]

Answer:

[tex]-3x ^ 2 + 17x-20[/tex]

Answer:

[tex]\large\boxed{\text{Table 1:}\ y=4x+1}\\\boxed{\text{Table 2:}\ y=\dfrac{1}{2}x-1}[/tex]

Step-by-step explanation:

Tables show linear functions.

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept → (0, b)

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

===================================================

Table 1:

(0, 1) → b = 1, (1, 5)

[tex]m=\dfrac{5-1}{1-0}=\dfrac{4}{1}=4\\\\y=4x+1[/tex]

Table 2:

(4, 1), (6, 2)

[tex]m=\dfrac{2-1}{6-4}=\dfrac{1}{2}\\\\y=\dfrac{1}{2}x+b[/tex]

Put the coordinateso f the point (4, 1) to the equation of a line:

[tex]1=\dfrac{1}{2}(4)+b[/tex]

[tex]1=2+b[/tex]         subtract 2 from both sides

[tex]-1=b\to b=-1[/tex]

[tex]y=\dfrac{1}{2}x-1[/tex]

Answer: 90[tex]\pi \\[/tex]

Step-by-step explanation:

Final answer:

The volume of a right circular cylinder with a radius of 3 inches and a height of 10 inches is calculated using the formula V = πr²h, which gives 282.74 cubic inches.

Explanation:

To calculate the volume of a right circular cylinder, you can use the formula V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder. In this instance, the radius (r) is 3 inches, and the height (h) is 10 inches.

Using these values, you can plug them into the formula:

V = π × (3 in)² × 10 in

V = 3.14159 × 9 in² × 10 in

V = 3.14159 × 90 in³

V = 282.74 in³

Therefore, the volume of the cylinder is 282.74 cubic inches.

Answer:

the desired equation is y = (-1/5)x - 5.

Step-by-step explanation:

Parallel lines have the same slope.  Here that slope is -1/5.

Let's use the slope-intercept form of the equation of a straight line:

y = mx + b

We know this new line passes through (-10, -3).  Substitute -3 for y in y = mx + b, as well as -10 for x and -1/5 for m:

-3 = (-1/5)(-10) + b and solve for b:

-3 = 2 + b.  Then b = -5, and the desired equation is y = (-1/5)x - 5.

Answer:

Part a) The equation of the line is

[tex]y-32=1.8(x-0)[/tex] or [tex]y=1.8x+32[/tex]

Part b) The slope of the line is [tex]m=1.8\frac{\°F}{\°C}[/tex]

Part c) The y-intercept is 32 (For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32)

Step-by-step explanation:

Let

x ----> degrees Celsius

y ----> degrees Fahrenheit

we have the points

[tex](0,32),(100,212)[/tex]

Part a) Find the equation of the line

Find the slope m

[tex]m=(212-32)/(100-0)[/tex]

[tex]m=180/100[/tex]

[tex]m=1.8\frac{\°F}{\°C}[/tex]

The equation of the line into slope point form is equal to

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1.8\frac{\°F}{\°C}[/tex]

Point [tex](0,32)[/tex]

substitute

[tex]y-32=1.8(x-0)[/tex] ----> equation of the line into slope point form

[tex]y=1.8x+32[/tex] ---> equation of the line into slope intercept form

Part b) What is the slope of the line?

The slope of the line is [tex]m=1.8\frac{\°F}{\°C}[/tex]

That means

The rate of change of the temperature is 1.8 degrees Fahrenheit by each degree Celsius

Part c) What is the y-intercept of the line?

we have

[tex]y=1.8x+32[/tex] ---> equation of the line into slope intercept form

The y-intercept is 32

The y-intercept is the value of y when the value of x is equal to zero

That means

For a degrees Celsius equal to zero, the degrees Fahrenheit is equal to 32

Answer: Option B.

Step-by-step explanation:

You need to use the formula for calculate the volume of a cylinder:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You know that the paint can has a radius of 9.5 centimeters and a height of 28 centimeters:

[tex]r=9.5cm\\h=28cm[/tex]

Then, you need to substitute these values into  [tex]V=\pi r^2h[/tex] to get the final result (In this case you can use [tex]\pi=3.14[/tex])

 [tex]V=(3.14) (9.5cm)^2(28cm)[/tex]

[tex]V=7934.78cm^3[/tex]

Answer:

the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂

so, the parallelogram is rhombus.

Step-by-step explanation:

A parallelogram is  a rhombus if diagonals intersect each other at right angle and the diagonals intersect at mid point.

We are given vertices:

A(-3,2)

B(-2,6)

C(2,7)

D(1,3)

The diagonals of the parallelogram will be:

AC and BD.

Slope of AC = y₂ - y₁ / x₂- x₁ where A = (-3,2)  and C = (2,7)

Putting values:

Slope of AC = 7-2/2-(-3) = 5/5  

Slope of AC = 1

Slope of BD = y₂ - y₁ / x₂- x₁ where B = (-2,6) and D = (1,3)

Putting values:

Slope of BD = 3-(6) / 1-(-2) = -3/3

Slope of BD = -1

AS, Slope of AC = - 1/ Slope of BD

So, the diagonals intersect and right angle.

Now finding the mid point Z₁ of AC and Z₂ of BD:

Midpoint of AC = Z₁ = A+C/2

Putting values:

=(-3,2) + (2,7) / 2

= (-1,9)/2

= (-1/2, 9/2)

Mid point of BD = Z₂ = B+D / 2

Putting values:

=(-2,6) + (1,3) / 2

= (-1,9)/2

= (-1/2, 9/2)

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂ i.e.

Z₁ = Z₂, the diagonals intersect at the same midpoint.

As,

the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and

Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂

so, the parallelogram is rhombus.

- I think if it was standard notation then it would be 3.05 * 10 = 30.5 - 3 = 27.5.

The volume of a cylinder with a given diameter and height using the formula V = πr²h is equal to 8471π km³.

The volume of the cylinder can be calculated using the formula for the volume of a cylinder: V = πr²h.

Given a diameter of 22 km (which means a radius of 11 km) and a height of 7 km, substitute these values into the formula to find the volume.

Substitute the values into the formula:

V = π × (11 km)²×7 km

Calculate the volume:

V = 8471π km³

Therefore, the volume is 8471π km³.

Answer:

B

Step-by-step explanation:

221-60=161 which means that you can be 161 max to ride with your friend in the same car.

i just saw this too and someone else said b so yeth

Answer:

C = 7pi = 21.98 inches

Step-by-step explanation:

The circumference of a circle is given by

C = pi * d

 where d is the diameter

C = pi * 7

If we use 3.14 as an approximation for pi

C = 3.14 * 7

C =21.98 in

Answer:

Let's solve your equation step-by-step.

x2+4x+5=0

Step 1: Use quadratic formula with a=1, b=4, c=5.

x=

−b±√b2−4ac

2a

x=

−(4)±√(4)2−4(1)(5)

2(1)

x=

−4±√−4

2

Answer:

No real solutions.

Answer:

x=-2+-i

Step-by-step explanation:

Solve the equation for x by finding a, b, c of the quadratic then applying the quadratic formula.

Answer:

together they can plant 175 seeds in 10 minutes

Answer with Step-by-step explanation:

Cara plants 5 seeds in 2 minutes.

⇒ Cara plants 5×5 seeds in 2×5 minutes

⇒ In 10 minutes Cara plant 25 seeds.

Wade plants 3 times as many seeds in half the time as Cara.

⇒ Wade plants 3×5 seeds in 2/2 minutes

i.e. Wade plants 15 seeds in 1 minute.

In 1×10 minutes Wade plants 15×10 seeds

i.e. In 10 minutes Wade plants 150 seeds.

150+25=175

Hence, they can together plant 175 seeds in 10 minutes.

Answer:

The answer is G. (-2,3)

Step-by-step explanation:

The point where they meet is (-2,3), therefore that is the solution. Hope that helps! :)

Answer: $139.60  

Step-by-step explanation:

$40 for coming

$29.60 for parts

56 times 1.25 for labor  = 70

70 + 29.6 + 40  =  139.6

The total cost (c) of the repair is given by the sum of the costs for parts, labor, and the service call that is [tex]\$139.60[/tex]

First, we calculate the labor cost. The plumber charged $56 per hour and worked for 1 1/4 hours. To find the total labor cost, we multiply the hourly rate by the time worked:

Labor cost = [tex]hourly \ rate \times \ time \ worked[/tex]

Labor cost =[tex]\$56 \times 1 1/4 hours[/tex]

Labor cost =[tex]\$56 \times (1 + 1/4) hours[/tex]

Labor cost = [tex]\$56 \times (5/4) hours[/tex]

Labor cost = [tex]\$56 \times 1.25 hours[/tex]

Labor cost = $70

Next, we add the cost for parts and the service call to the labor cost to find the total cost:

Total cost (c) = cost for parts + labor cost + service call cost

Total cost (c) = $29.60 + $70 + $40

Total cost (c) = $139.60

Answer:

4.25

Step-by-step explanation:

To find the scale factor divide the image coordinates by the original coordinates, that is

scale factor = [tex]\frac{-12.75}{-3}[/tex] = [tex]\frac{29.75}{7}[/tex] = 4.25

The answer would be 4.25

Answer:

3 < x < 8

-2 < x < 4

12 < x ≤ 17

Step-by-step explanation:

x is less than 8 and greater than 3

i.e 3 < x < 8

x is less than 4 and greater than -2

i.e -2 < x < 4

x is greater than 12 and less than or equal to 17

i.e 12 < x ≤ 17

the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:

- Option C: [tex]\(\frac{1}{2}k\)[/tex]

- Option D: [tex]\(k + 2\)[/tex]

The correct option is (C) and (D).

the calculation step by step to find expressions equivalent to [tex]\(k - \frac{k}{2}\):[/tex]

1. Given Expression:

 [tex]\[ k - \frac{k}{2} \][/tex]

2. Step 1: Find a Common Denominator:

  To combine the fractions, we need a common denominator. The common denominator for \(2\) and \(1\) is \(2\). So, let's rewrite the expression:

[tex]\[ k - \frac{k}{2} = \frac{2k}{2} - \frac{k}{2} \][/tex]

3. Step 2: Subtract the Fractions:

  Subtract the numerators while keeping the common denominator:

[tex]\[ \frac{2k - k}{2} = \frac{k}{2} \][/tex]

4. Step 3: Simplify:

  Divide the numerator by (2):

[tex]\[ \frac{k}{2} = \frac{1}{2}k \][/tex]

Therefore, the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:

- Option C: [tex]\(\frac{1}{2}k\)[/tex]

- Option D: [tex]\(k + 2\)[/tex]

Answer:c

Step-by-step explanation:

Answer: D because they are all corresponding numbers.

Answer:20 students chose option 1

Step-by-step explanation:

20 students chose option 1

answer

Answer:

20

Step-by-step explanation:

In the sentence of = multiply. So you multiply 5/8 x 32

5/8 x 32/1  next you simply  

5/1 x 4/1   =20/1 = 20

Answer:

The equation to calculate what divided by 72 equals 12 is as follows:

X/72 = 12

Where X is the answer. When we solve the equation by multiplying each side by 72, you get get:

X = 864

Therefore, the answer to what divided by 72 equals 12 is 864.

I hope it helps!!

To find the value of x in the equation x/12 = 12/72, simplify 12/72 to get 1/6. Then, multiply both sides by 12 to solve for x, resulting in x = 2.

To solve the equation x divided by 12 = 12 divided by 72, we need to perform some algebraic manipulation to isolate x. First, rewrite the equation as a fraction:

Next, simplify the fraction on the right-hand side:

Now the equation looks like this:

To solve for x, multiply both sides of the equation by 12:

So, the value of x is 2.

Answer:

D. 597

Step-by-step explanation:

This question is on  finding the inverse of a 3×3  matrix

The general formula of finding a 3×3 matrix is given by;

[tex]A=\left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&i\end{array}\right] = a.D\left[\begin{array}{ccc}e&f&\\h&i&\\&&\end{array}\right] -b.D\left[\begin{array}{ccc}d&f&\\g&i&\\&&\end{array}\right] + c.D\left[\begin{array}{ccc}d&e&\\g&h&\\&&\end{array}\right][/tex]

where D is determinant

Given ;

[tex]k=\left[\begin{array}{ccc}14&-13&0\\3&8&-1\\-10&-2&5\end{array}\right] then ;\\\\\\\\ =14 D \left[\begin{array}{ccc}8&-1&\\-2&5&\\&&\end{array}\right]  -13D\left[\begin{array}{ccc}3&-1&\\-10&5&\\&&\end{array}\right] + 0.D\left[\begin{array}{ccc}3&8&\\-10&-2&\\&&\end{array}\right][/tex]

= 14 [ 40-2] - -13[ 15-10] + 0

=14 [38] - [-65]+0

=532+65

=597

Answer:

[tex]\large\boxed{x\leq-27}[/tex]

Step-by-step explanation:

[tex]\dfrac{x}{-9}\geq3\qquad\text{change the signs}\\\\\dfrac{x}{9}\leq-3\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}\leq(-3)(9)\\\\x\leq-27[/tex]

Answer:

Obtuse triangle

Step-by-step explanation:

The longest side of the triangle is 26 in, so that will be the hypotenuse.

By an extension of the Pythagorean theorem:

Where a and b are the legs, and c is the hypotenuse.

Plug in: 3.5² + 25² ₙ 26²

Powers: 12.25 + 625 ₙ 676

Add: 637.25 < 676.

That means that this triangle is obtuse.

Answer:

Obtuse

Step-by-step explanation:

Using law of cosine, we can find the angle between the shorter sides:

c² = a² + b² − 2ab cos C

26² = 25² + 3.5² − 2(25)(3.5) cos C

cos C ≈ -0.221

C ≈ 102.8°

102.8° is greater than 90°, so the triangle is obtuse.

Answer:

B(2,1,1)

Step-by-step explanation:

Given:

-3x-3y+2z=-7  

z=1  

-2x-3y+z=-6

Let -3x-3y+2z=-7   be equation i,  z=1  be equation ii and -2x-3y+z=-6  be equation iii

Solving the system of simultaneous equation by substituting value of z from equation ii to i , we get:

-3x-3y+2=-7

-3x-3y=-7-2

-3x-3y=-9                      -------iv

Solving the system of simultaneous equation by substituting value of z from equation ii to iii, we get:

-2x-3y+1=-6

-2x-3y=-6-1

-2x-3y=-7

re-arranging the above equation, we get

3y=-2x+7

substituting value of 3y from above in equation iv, we get

-3x-(-2x+7)=-9

-3x+2x-7=-9

-x=-9+7

-x=-2

x=2

Now putting x=1 from above in equation v, we get

3y=-2(2) +7

3y=-4+7

3y=3

y=3/3

y=1

Hence the solution of system of given equations is (2,1,1) !

The answer is:

The correct option is B.(2, 1, 1)

We can solve the system of equations by using the reduction method. The reduction method consists of reducing the variables in order to be able to calculate the other variables to finally calculate all the variables.

We are given the equations:

I.

[tex]-3x-3y+2z=-7[/tex]

II.

[tex]z=1[/tex]

II.

[tex]-2x-3y+z=-6[/tex]

Since the second equation is already solved, let's work with the first and third one, so, calculating we have:

[tex]\left \{ {{-3x-3y+2z=-7} \atop {-2x-3y+z=-6}} \right.[/tex]

Now, multiplying the first equation by -1 in order to reduce the variable "y", we have:

[tex]\left \{ {{3x+3y-2z=7} \atop {-2x-3y+z=-6}} \right\\\\x-z=1[/tex]

Then, substituting "z" into the obtained equation:

[tex]x-1=1\\x=1+1=2[/tex]

Now, substituting "x" and "z" into the first equation, we have:

[tex]-3x-3y+2z=-7[/tex]

[tex]-3*(2)-3y+2*(1)=-7[/tex]

[tex]-6-3y+2=-7[/tex]

[tex]-3y-4=-7[/tex]

[tex]-3y=-7+4[/tex]

[tex]-3y=-3[/tex]

[tex]y=\frac{-3}{-3}=1[/tex]

Hence, we have that the solutions are:

[tex]x=2\\y=1\\z=1[/tex]

So, the correct option is B.(2, 1, 1)

Have a nice day!

Answer:

14 and 18

Step-by-step explanation:

Small number : a

Larger number : a + 4

( a + 4 )^2 - a^2 = 128

a^2 + 8 a + 16    = 128

             8 a        = 128 - 16

                a         = 112 / 8

                a          = 14

And a + 4 = 18

Answer:

Option C is correct.

Step-by-step explanation:

Number of students of Deerlake middle school that voted = 442

Percentage of student that voted = 76%

Let x be the total number of student.

According to the Question,

[tex]\frac{76}{100}\times x=442[/tex]

[tex]x=442\times\frac{100}{76}[/tex]

[tex]x=582[/tex]

Therefore, Option C is correct.

Answer:

Step-by-step explanation:

B

Answer: Option A: A vertical line that the line of the graph aproaches but never intecepts it.

Step-by-step explanation:

An asymptote is a graph line that aproaches infinitely to something (in this case a vertical line), but it does not touch it (so never intercepts the graph).

This means that the graph aproaches but never intercepts the line, so the correct answer is A.