To make some additional money, Vanessa began to
walk her sister's dog in order to help the dog lose
weight. Each week, the dog lost 0.2 pounds of weight
from walking with Vanessa. If the dog's starting weight
was 40 pounds, find the number of weeks that it will
take for the dog to weigh 38 pounds.


write an equation and isolate the variable.

Answer:

Slope of the parrelel line: -2/3x

Slope of the perpendicular line: 3/2x

Step-by-step explanation:

Lets first put this into slope intercept form:

y = mx + b

9y = -6x - 1

y = -2/3x = 1/9

So our slope is -2/3x

If we have a line parrelel to this, it means it has the exact same slope, but a different b value.

So the slope of this parellel line would also be -2/3x

Next we need to find the slope of the perpendicular line.

This is the exact opposite of our slope.

To find this, lets first understand our slope.

Our slope is the change in y over the change in x:

Δy/Δx

A perpendicular line is going to be the flipped, and negative of this.

You can think of a perpendicular line being:

-Δx/Δy

Since our slope is -2/3x

Our perpendicular line would be 3/2x

So our answer for the second question is 3/2x

Useful things to remember:

Hope this helps!

Answer:

B and C

Step-by-step explanation:

I hope you find this helpful

Answer:

7375

24

Step-by-step explanation:

c=5500+125(15)

c=7375

8500=5500+125n

Step-by-step explanation:

Answer:

Step-by-step explanation:

It will take 48 minutes to make 140 airplanes. 35 × 4 = 140 airplanes. So take 12 × 4 = 48 minutes.

Answer:

it's D. 265F

Step-by-step explanation:

subtract 136 by -129 and you get 265

Answer:

x = 11

Step-by-step explanation:

∠ EAB = ∠ AED = 4x ( alternate angles )

∠ AEB and ∠  GEB are adjacent angles on a straight line and sum to 180° , so

∠ AEB + 125° = 180° ( subtract 125° from both sides )

∠ AEB = 55°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ EBC is an exterior angle of the triangle , then

∠ EBC = ∠ AEB + ∠EAB , that is

9x = 55 + 4x ( subtract 4x from both sides )

5x = 55 ( divide both sides by 5 )

x = 11

Answer: The filled out chart is shown below.

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

Explanation:

For each row, we divide the number of locations over the population count. Treat the population values in millions. Something like 35.2 million means 35,200,000 which is the same as writing 35.2*10^6 when using scientific notation. I prefer to stick to scientific notation.

In the first row, they computed 1460/(35.2*10^6) = 0.0000415 = 4.15*10^(-5); the last entry of 4.15 for this row represents having 4.15 stores for 100,000 people. In other words, we chop off the 10^(-5) portion in 4.15*10^(-5). This is because the 10^(-5) portion represents "1 out of 100,000".

The other remaining rows are handled the same way. I'll show the steps for the second row

Like the previous row, each value is approximate.

Check out the table below. The stuff in gray represents the new entries that were previously blank.

A is the scale or vertical stretch

H is what makes it move right or left.

K is what makes it move up or down.

a = 1

h = -2

k = -7

y = (1) (x-(-2))² + (-7)

y= (x + 2)² -7

(Also, you will learn b in the equation. The equation would be a(b(x-h))² + k. B would be about horizontal compression.)

Step-by-step explanation:

3(10000) + 1700 - 20

30000 + 1700 - 20

31680

Answer:

d

Step-by-step explanation:

do 6 times 6

Answer:

Michaels' proof is wrong. His second point says that ∠AKG ≈ ∠AKL with the Vertical Angles Theorem as his justification, which is incorrect. Angles AKG and AKL are not vertically opposing angles, but they form a linear pair, so in this case, Daniels's proof is correct. 

Step-by-step explanation:

Please correct me if I'm wrong :)

Answer:

The second table with all values of x = -5 does not represent a function. what the function and input value of x will return one and only one value for y. and this table when you input a value for x of -5 you get three different values therefore this table does not represent a function

Answer:

Step-by-step explanation:

The table

x y

-5 1

-5 -2

-5 -5

does not represent a function, because for the same input (-5) there are 3 different outputs.

Compare this to the table

 x y

-5 1

-3 -2

-1 -5

in which all the inputs (x values) are unique (one of a kind) and each input has exactly one output (y value) connected to it.

(first base + second base)x height ÷ 2

Step-by-step explanation:

[tex]\displaystyle \rm -2z+3-z=-4z+2 \\\\ -3z+3=-4z+2 \\\\ 4z-3z=-3+2 \\\\ \underline{z=-1 \ \ \ \ } \\\\[/tex]

[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]

Given to solve: -2z+3-z = -4z+2

⇛ -3z + 3 = -4z + 2

⇛ -3z + 4z = 2 - 3

⇛ z = -1

Required value of z is -1. The steps we followed are: We shifted z to a single side and other numbers to other side. Then we equated to get the result.

Answer:

it takes me 14 minutes to go to class

Answer:

x = 7

Step-by-step explanation:

The sum of exterior angles in a polygon is 360°.

( 11x - 5 )° + ( 4x + 29 )° + ( 6x + 13 )° + ( 9x - 15 )° + 67° + 61° = 360°

30x + 22 + 128 = 360

30x = 210

x = 7

Answer:

1)y=2x+7

2) unsure what the question is due to blur

3)y=3/4x-2

4)y=-2x

Answer:

Step-by-step explanation:

1) (1,9) ; slope = 2

Point slope form:

y - y₁ = m(x - x₁)

y - 9 = 2(x - 1)

Slope intercept form:

y - 9 = 2x - 2

    y = 2x - 2 + 9

 y = 2x + 7

3) (-4 , -5)  ; slope = 3/5

Point slope form:

y - y₁ = m(x - x₁)

[tex]y - [-5] = \dfrac{3}{4}(x - [-4])\\\\\\y + 5 = \dfrac{3}{4}(x + 4)[/tex]

Slope intercept form:

[tex]y + 5 = \dfrac{3}{4}x + 4*\dfrac{3}{4}\\\\y + 5 =\dfrac{3}{4}x + 3\\\\y = \dfrac{3}{4}x +3 -5 \\\\\\y = \dfrac{3}{4}x - 2[/tex]

Answer:

x = 7

Step-by-step explanation:

If u // v, then

19x - 3 = 130   {Corresponding angles are congruent}

19x = 130 + 3

19x = 133

x = 133/19

x = 7

(-9,6) and (-3,2) help pls

Answer : -12.8

Answer:

The maximum value of g(x) is 3 greater than the maximum value of f(x).

Step-by-step explanation:

The function modeled by the equation, f(x) = - (x - 3)² + 9, represents a quadratic function in vertex form.  

The vertex form is given by: f(x) = a(x - h)² + k, where:

⇒ The value of a is the vertical compression or stretch factor, which essentially determines the width of a parabola. The value of a also determines where the graph of a parabola opens:

⇒ (h, k) = Vertex of the parabola.

Given these definitions, we can assume the following information regarding  the quadratic function,  f(x) = - (x - 3)² + 9:

The vertex form of an absolute value function is given by: g(x) = a|x - h| + k, where:  

⇒ The value of a determines the following:

⇒ (h, k) = Vertex of the absolute value function.

⇒ x = h represents the axis of symmetry.

The axis of symmetry is the imaginary point on the graph that intersects through the h-coordinate of the vertex, thereby dividing the graph into two symmetrical parts.

Observing the given table of values, especially how the y-values increasingly peak towards g(x) = 12, then decreases back down starting at g(x) = 8.  It is important to take notice of the y-values, as it represents the resulting output provided by the given input (x-value).  

The increasing, followed by the decreasing y-values imply that the graph must be facing downward. Since we specified that the maximum point provided by g(x) = 12, then it means that it is the vertex occurs at point, (1, 12).

Therefore, the maximum value of g(x) is 3 greater than the maximum value of f(x).  

Answer:

1014

Step-by-step explanation:

Remember this formula to find certain terms in arithmetic sequences:

[tex]t_{n} =t_{1} +(n-1)d[/tex]

n = term number

[tex]t_{1}[/tex] = term #1

d = common difference

Sequence = 24, 34, 44, 54...

We are looking for term #100

So we do

[tex]t_{100} = 24 + (100-1)10\\t_{100} = 24 + 1000 - 10\\t_{100} = 24 + 990\\t_{100} = 1014[/tex]

Step-by-step explanation:

hrer do it this way

it is correct

Reproduce the proof. When n = 1, we have

n³ + 2n = 1³ + 2 = 3

which is clearly divisible by 3.

Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have

(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2

= n³ + 2n + 3 (n² + n + 1)

The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.

So the claim that 3 divides n³ + 2n is true for all natural numbers n.

Answer:

265

Step-by-step explanation:

you only need to do is simplify the expression.

Answer:

The leading coefficient of the function shown is negative and the function shown has a maximum vertex point.

Step-by-step explanation:

The leading coefficient is the term with the highest degree in a polynomial.

For example in 4x² + 3x + 1 the leading coefficient would be 4x² as 4x² is the term with the highest degree.

The leading coefficient tells us whether the equation, when graphed, will rise or fall.

If the leading coefficient is negative then the equation will fall when graphed, in contrast if the leading coefficient is positive the equation will rise when graphed.

Looking at the graph, it appears that the equation is falling, meaning that the leading coefficient must be negative.

If the equation falls then it has a maximum point, if it rises then it has a minimum point.

Because the equation shown falls it will have a maximum point.