Darcy is planting trees along a new city sidewalk. She plants the same number of trees on each city block. After 5 blocks, she has planted 25 trees. After 7 blocks, she has planted 35 trees. At what rate is Darcy planting trees?​

Using translation concepts, it is found that:

a.

b.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The quadratic function has vertex at (-4,-6), hence:

y = a(x + 4)² - 6

When x = -6, y = 0, hence we use it to find a as follows:

0 = 4a - 6

a = 1.5.

Hence the function is:

y = 1.5(x + 4)² - 6.

When it is reflected over the x-axis, we have that:

y -> -y.

Hence:

y = -1.5(x + 4)² + 6.

When it is moved up 3 units, we have that y -> y + 3, hence:

y = -1.5(x + 4)² + 9.

The function is defined for all real values, assuming values from negative infinity to 9, hence:

The parent square root function is given by:

[tex]y = \sqrt{x}[/tex]

From the graph, it is found that:

Hence the rule is:

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

The translations given by the item are:

Thus:

[tex]y = -\sqrt{x + 5} + 10[/tex]

Then the function will be defined for values of -5 and greater, assuming values of 10 and less, hence:

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The rate of change is $7 per one square feet.

In order to determine the rate of change, the difference between each successive cost would be divided by the difference in each successive size.

Rate of change = change in cost /change in size

(980 - 840) / (140 - 120)

140 / 20

= $7

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Answer: the distance between the two points is √26 or about 5.1

Step-by-step explanation:

A(4,6)   B(9,7)

[tex]\boxed {L_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} }\\\\L_{AB}=\sqrt{(9-4)^2+(7-6)^2} \\\\L{ab}=\sqrt{5^2+1^2}\\\\ L_{AB}=\sqrt{25+1} \\\\L_{AB}=\sqrt{26} \\\\L_{AB}\approx5.1[/tex]

The distance between A (4, 6) and B (9, 7) is √26 or 5.1.

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Let's consider we have two points (x₁, y₁) and (x₂, y₂) the distance between these two points is given by the formula;

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

So the distance between A (4, 6) and B (9, 7) will be

[tex]d = \sqrt {\left( {4 - 9 } \right)^2 + \left( {6 - 7 } \right)^2 }[/tex]

d = √26 = 5.099

Rounded to nearest tenth ⇒ 5.1 units.

Hence "The distance between A (4, 6) and B (9, 7) is √26 or 5.1".

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Answer:

[tex] - 26 \sqrt{10} [/tex]

Step-by-step explanation:

Simplify.

[tex] \rightarrow \sqrt{40} \: \: \: \: \: \: \: \: \\ = \sqrt{4 \times 10} \: \: \: \\ = \sqrt{4} \times \sqrt{10} \\ = 2 \times \sqrt{10} \: \: \: \: \\ = 2 \sqrt{10} \: \: \: \: \: \: \: \: \: [/tex]

[tex] \rightarrow \sqrt{160} \\ = \sqrt{16 \times 10} \: \: \: \\ = \sqrt{16} \times \sqrt{10} \\ = 4 \sqrt{10} \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Let us solve the given expression now.

[tex] - \sqrt{40} - 6 \sqrt{160} \\ - 2 \sqrt{10} - 6 \times 4 \sqrt{10} \\ - 2 \sqrt{10} - 24 \sqrt{10} \\ - 26 \sqrt{10} [/tex]

Answer: 568000

Step-by-step explanation:

The area of the Triangle ABC will be 18 cm²

In the question, It is given that ∠B = 75° and ΔABC is Right angeled at ∠C = 90° and AB = 12CM.

We know that the Area of Δ is defined by : [tex](\frac{1}{2} *b*h)[/tex]

In the picture below, we have base and height BC and AC respectively.

We don't have the values for AC and BC. So to find the values of Base & Height we will use Trigonometric Ratios.

We know Sin(∠) = Perpendicular/Hyoptenuse and,

Tan(∠) = Perpenciular/Base. Putting values into the respective ratios and taking ∠B = 75°, we get

=>  [tex]Sin(B) = \frac{AC}{BC} = > Sin(75) = \frac{AC}{12}[/tex]

=>  [tex]AC = 0.96 * 12 = > AC = 11.59[/tex]

Similarly, [tex]Tan(B) = \frac{AC}{BC} = > Tan(75) = \frac{11.59}{BC}[/tex]

=>  [tex]BC = \frac{11.59}{3.73} = > BC = 3.10[/tex]

Now, we have AC = 11.59cm and BC = 3.10cm putting these values in the Area of the Triangle we get :

Area = [tex]\frac{1}{2} *b*h[/tex]  => Area = [tex]\frac{1}{2}[/tex] * BC * AC

Area =  [tex]\frac{1}{2}[/tex] * 3.10 * 11.59  =>  Area = 18

Hence, we get the Area of Δ ABC = 18cm²

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Answer:

18

Step-by-step explanation:

Answer: y=-0.4x+20.2

Step-by-step explanation:

[tex]5x-2y=6\\5x-2y+2y=6+2y\\5x=6+2y\\5x-6=6+2y-6\\5x-6=2y[/tex]

Divide both parts of the equation by 2:

[tex]\displaystyle\\\frac{5x-6}{2}=y\\\\\frac{5}{2} x-3=y[/tex]

Coordinates of the intersection point of the equations:

[tex]\displaystyle\\y=\frac{5}{2}x-3 \ and\ x=8\ are:[/tex]

[tex]\displaystyle\\x=8\\Hence,\\y=\frac{5}{2} (8)-3\\\\y=\frac{5*8}{2} -3\\\\y=\frac{5*4*2}{2}-3\\\\y=5*4-3 \\\\y=20-3\\\\y=17\\Thus, (8,17)[/tex]

[tex]\displaystyle\\The\ slope\ \perp=-\frac{1}{\frac{5}{2} } \\\\The\ slope\ \perp=-\frac{2}{5}[/tex]

[tex]\displaystyle\\-\frac{2}{5} =\frac{y-17}{x-8}[/tex]

Multiply both parts of the equation by (x-8):

[tex]\displaystyle\\-\frac{2}{5}(x-8)=y-17\\\\-\frac{2}{5} x+\frac{2*8}{5} =y-17\\\\-\frac{2}{5}x+\frac{16}{5} =y-17\\\\ -0.4x+3.2=y-17\\\\ -0.4x+3.2+17=y-17+17\\\\-0.4x+20.2=y[/tex]-

Answer:

you don't

Step-by-step explanation:

this is at it's simplest form, tell your teacher that or if its online answer, talk to your tutor or teacher

Answer:

x=2

Step-by-step explanation:

[tex]4x+2x+6=18 < - Start-by-grouping-the-like-terms![/tex]
[tex]6x+6=18 < - Then-add-the-similar-elements![/tex]
[tex]6x+6-6=18-6 < - Subtract-6-from-both-sides-and-simplify.[/tex]
[tex]6x=12[/tex]
[tex]\frac{6x}{6}=\frac{12}{6} < - Divide-both-sides-by-6-to-further-simplify![/tex]
[tex]x=2[/tex]
________________________________________________________
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Answer:

Step-by-step explanation:

x^10

Answer:

52.948 m²

Step-by-step explanation:

→ State the formula for the area

length × width

→ Substitute in the numbers

8.68 × 6.1 = 52.948 m²

Answer: e=20° d=121° f=39°

Answer:

f=39°

e=20°

d=121°

Step-by-step explanation:

d=121°(vertically opposite angles are equal)

e=20°(vertically opposite angles are equal)

f=180°-(d+e)

=180-141

=39°

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

Explanation:

I'll use the substitution method.

Let's solve the second equation for x.

2y - x = -19

-x = -19-2y

x = 19+2y

Then plug that into the first equation

3x + 4y = -23

3( x ) + 4y = -23

3(19+2y)+4y = -23

3*19 + 3*2y + 4y = -23

57+6y+4y = -23

57+10y = -23

10y = -23-57

10y = -80

y = -80/10

y = -8

Use this y value to find x.

x = 19+2y

x = 19+2(-8)

x = 19-16

x = 3

---------------------------

Summary:

We found that x = 3 and y = -8

The ordered pair solution is therefore (x,y) = (3, -8)

Technically you could have stopped once reaching y = -8, since choice B is the only one that fits the description. But it helps to have practice.

Answer:

answer is B

Step-by-step explanation:

picture is upside down.

I assume you want the volume of the shape with the given cross sections. In the [tex]x,y[/tex]-plane, the base is set

[tex]\left\{(x,y) ~:~ 0\le x\le 2 \text{ and } 0 \le y \le 2-x\right\}[/tex]

Each cross section is a square plate with side length [tex]2-x[/tex] (the vertical distance between the [tex]x[/tex]-axis and the line [tex]y=2-x[/tex]) and thickness [tex]\Delta x[/tex], hence volume [tex](2-x)^2\,\Delta x[/tex].

As [tex]\Delta x\to0[/tex] and the number of cross sections grows to infinity, the total volume of the plates converges to volume of the solid [tex]S[/tex], given by the definite integral

[tex]\displaystyle \int_0^2 (2-x)^2 \, dx = \int_0^2 x^2 \, dx = \frac{2^3-0^3}3 = \boxed{\frac83}[/tex]

(where we make the substitution [tex]2-x\mapsto x[/tex])

The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are

So, the direction angles are

Given a vector r = xi + yj + zk where

The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are

So, their direction angles are

As an example, let r = 3i + 4j + 5k

So, r = √(x² + y² + z²)

= √(3² + 4² + 5²)

= √(9 + 16 + 25)

= √50

= 5√2

The direction cosines of the vector r with direction angles α, β, γ to the x, y and z axis are

So, the direction angles are

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The volume of the parallelepiped is 299³ units.

So,

The volume of parallelopiped can be calculated using the steps below.

Now, the volume of parallelopiped is increasing:

[tex]v=\left|\begin{array}{lll}-5 & -5 & 1 \\-1 & 6 & 1 \\6 & 3 & 7\end{array}\right|[/tex]

The matrix's determinant is:

⇒ -5(42 - 3) +5(-7 -6) +1(-3 - 36)

⇒ -5(39) +5(-13) +1(-39)

⇒ -195 -65 -39

⇒ |-299| = 299

Therefore, the volume of the parallelepiped is 299³ units.

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The volume of the cone with radius 3 and height of the cone 6 is 56.52.

Any shape's volume in geometry is the area it takes up in a three-dimensional space. As a result, the space occupied by a cone in three dimensions is known as its volume.

The formula for the radius of a cone is given as:

r = √( 3 × V / π × h)

Where h is the height of the cone, V is the volume of the cone.

Now, squaring the above equation.

(r)² = [  √( 3 × V / π × h) ]²

r² = [ √ (3 × V) / √ ( π × h ) ]²

3V = π × r² × h

V = π × r² × h / 3

We have,

r = 3, h = 6, and π = 3.14

V = ( 3.14 × (3)² × 6 / 3 )

V = 3.14 × 3 × 6

V = 56.52

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Answer:

8

Step-by-step explanation:

Answer:

none is

Step-by-step explanation:

Answer:

x = 36

Step-by-step explanation:

Answer:

7:13

Step-by-step explanation:

5:43

1 hour from 5:43 will be 6:43

17 mins from 6:43 will be 7:00

13 mins from 7:00 will be 7:13

Answer:

{3 1/4} / {2 1/6} =

1.5  

Step-by-step explanation:

Answer:

Exact Form:

3/2

Decimal Form:

1.5

Mixed Number Form:

1 1/2

Answer:

9

Step-by-step explanation:

Answer:

Step-by-step explanation:

12312ejljaslkjkfdsjkdsfafsd

Answer:

<1 = 168

<2 = 12

Step-by-step explanation:

First, you need to solve for x

8x + x -9 = 180

9x -9 = 180

9x = 189

x = 21

Now, substitute in 21 for x for both angles

8(21) = 168

(21) - 9 = 12

The area of the rectangle will be 24sq, units.

To determine the area of various polygons, there exist specialized formulae. The general formula for rectangles is as follows:

A = width x length

Given, the coordinates of the rectangle are W(0,1), X(3,4), Y(-1, 8), Z(-4,5)

So the length of rectangle will be = distance between W and X will be -

⇒[tex]\sqrt{(3 - 0)^{2} + (4-1^{2}) }[/tex]

⇒[tex]\sqrt{18}[/tex]

The breadth of rectangle will be = distance between X and Y

⇒ [tex]\sqrt{(3 + 1)^{2} + (8-4)^{2} }[/tex]

⇒ [tex]\sqrt{32}[/tex]

Now, area of rectangle = length × breadth

⇒ [tex]\sqrt{18}[/tex] × [tex]\sqrt{32}[/tex]

⇒ 24 sq. units

So, the area of the rectangle will be - 24 sq. units

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Step-by-step explanation:

first add all the n together

3n and 4n

add those together too

7n

now add 2+4

6 now

7n\-7n =6/-7n = -1n